Solution Manual For Foundations of Financial Management, 18th Edition by Stanley, Geoffrey Hirt, Bar by ACADEMIAMILL

Solutions Manual for Foundations of Financial Management, 18th Edition by Stanley Block, Geoffrey Hirt, Bartley Danielsen Chapter 1 The Goals and Functions of Financial Management Discussion Questions 1-1

What effect did the recession of 2007-2009 have on government regulation? It was greatly increased.

1-2

What advantages does a sole proprietorship offer? What is a major drawback of this type of organization? A sole proprietorship offers the advantage of simplicity of decision making and low organizational and operating costs. A major drawback is that there is unlimited liability to the owner.

1-3

What form of partnership allows some of the investors to limit their liability? Explain briefly. A limited partnership allows some of the partners to limit their liability. Under this arrangement, one or more partners are designated general partners and have unlimited liability for the debts of the firm; other partners are designated limited partners and are liable only for their initial contribution. The limited partners are normally prohibited from being active in the management of the firm.

1-4

In a corporation, what group has the ultimate responsibility for protecting and managing the stockholders’ interests? The board of directors.

1-5

What document is necessary to form a corporation? The articles of incorporation.

1-6

What issue does agency theory examine? Why is it important in a public corporation rather than in a private corporation?

Agency theory examines the relationship between the owners of the firm and the managers of the firm. In privately owned firms, management and the owners are usually the same people. Management operates the firm to satisfy its own goals, needs, financial requirements and the like. As a company moves from private to public ownership, management now represents all owners. This places management in the agency position of making decisions in the best interest of all shareholders. 1-7

What are institutional investors important in today’s business world? Because institutional investors such as pension funds and mutual funds own a large percentage of major U.S. companies, they are having more to say about the way publicly owned companies are managed. As a group, they have the ability to vote large blocks of shares for the election of a board of directors, which is supposed to run the company in an efficient, competitive manner. The threat of being able to replace poor performing boards of directors makes institutional investors quite influential. Since these institutions, like pension funds and mutual funds, represent individual workers and investors, they have a responsibility to see that the firm is managed in an efficient and ethical way.

1-8

Why is profit maximization, by itself, an inappropriate goal? What is meant by the goal of maximization of shareholder wealth? The problem with a profit maximization goal is that it fails to take account of risk, the timing of the benefits is not considered, and profit measurement is a very inexact process. The goal of shareholders’ wealth maximization implies that the firm will attempt to achieve the highest possible total valuation in the marketplace. It is the one overriding objective of the firm and should influence every decision.

1-9

When does insider trading occur? What government agency is responsible for protecting against the unethical practice of insider trading? Insider trading occurs when anyone with non-public information buys or sells securities to take advantage of that private information. The Securities and Exchange Commission is responsible for protecting markets against insider trading. In the past, people have gone to jail for trading on non-public information. This has included company officers, investment bankers, printers who have information before it is published, and even truck drivers who deliver business magazines and read positive or negative articles about a company before the magazine is on the newsstands and then place trades or have friends place trades based on that information. The SEC has prosecuted anyone who profits from inside information.

1-10

In terms of the life of the securities offered, what is the difference between money and capital markets? Money markets refer to those markets dealing with short-term securities that have a life of one year or less. Capital markets refer to securities with a life of more than one year.

1-11

What is the difference between a primary and a secondary market?

A primary market refers to the use of the financial markets to raise new funds for the corporation. After the securities are sold to the public (institutions and individuals), they trade in the secondary market between investors. It is in the secondary market that prices are continually changing as investors buy and sell securities based on the expectations of corporate prospects. 1-12

Assume you are looking at many companies with equal risk. Which ones will have the highest stock prices? Given companies with equal risk, those companies with expectations of high return will have higher common stock prices relative to those companies with expectations of poor returns.

1-13

How is the time value of money concept related to the valuation of stocks? The value of an investment that is expected to earn money in the future can be calculated using time-value of money principles. Corporations are expected to pay dividends to their shareholders. The current value of these future dividends is the present value. The present value of a stock’s future dividends should be the same as the stock’s current price.

Chapter 2 Review of Accounting Discussion Questions 2-1.

Discuss some financial variables that affect the price-earnings ratio.

The price-earnings ratio will be influenced by the earnings and sales growth of the firm, the risk or volatility in performance, the debt-equity structure of the firm, the dividend payment policy, the quality of management, and a number of other factors. The ratio tends to be future-oriented, and the more positive the outlook, the higher it will be.

2-2.

What is the difference between book value per share of common stock and market value per share? Why does this disparity occur?

Book value per share is arrived at by taking the cost of the assets and subtracting out liabilities and preferred stock and dividing by the number of common shares

outstanding. It is based on the historical cost of the assets. Market value per share is based on the current assessed value of the firm in the marketplace and may bear little relationship to original cost. Besides the disparity between book and market value caused by the historical cost approach, other contributing factors are the growth prospects for the firm, the quality of management, and the industry outlook. To the extent these are quite negative or positive; market value may differ widely from book value.

2-3.

Explain how depreciation generates actual cash flows for the company.

The only way depreciation generates cash flows for the company is by serving as a tax shield against reported income. This non-cash deduction may provide cash flow equal to the tax rate times the depreciation charged. This much in taxes will be saved, while no cash payments occur.

2-4.

What is the difference between accumulated depreciation and depreciation expense? How are they related?

Accumulated depreciation is the sum of all past and present depreciation charges, while depreciation expense is the current year’s charge. They are related in that the sum of all prior depreciation expense should be equal to accumulated depreciation (subject to some differential related to asset write-offs).

2-5.

How is the income statement related to the balance sheet?

The earnings (less dividends) reported in the income statement is transferred to the ownership section of the balance sheet as retained earnings. Thus, what we earn in the income statement becomes part of the ownership interest in the balance sheet.

2-6.

Comment on why inflation may restrict the usefulness of the balance sheet as normally presented.

The balance sheet is based on historical costs. When prices are rising rapidly, historical cost data may lose much of their meaning—particularly for plant and equipment and

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inventory.

2-7.

Explain why the statement of cash flows provides useful information that goes beyond income statement and balance sheet data.

The income statement and balance sheet are based on the accrual method of accounting, which attempts to match revenues and expenses in the period in which they occur. However, accrual accounting does not attempt to properly assess the cash flow position of the firm. The statement of cash flows fulfills this need.

2-8.

What are the three primary sections of the statement of cash flows? In what section would the payment of a cash dividend be shown?

The sections of the statement of cash flows are:

Cash flows from operating activities Cash flows from investing activities Cash flows from financing activities

The payment of cash dividends falls into the financing activities category.

2-9.

What is free cash flow? Why is it important to leveraged buyouts?

Free cash flow is equal to cash flow from operating activities:

Minus:

Capital expenditures required to maintain the productive capacity of the firm.

Minus:

Dividends (required to maintain the payout on common stock and to cover any preferred stock obligation).

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The analyst or banker normally looks at free cash flow to determine whether there are sufficient excess funds to pay back the loan associated with the leveraged buyout. 2-10.

Why is interest expense said to cost the firm substantially less than the actual expense, while dividends cost it 100 percent of the outlay?

Interest expense is a tax-deductible item to the corporation, while dividend payments are not. The net cost to the corporation of interest expense is the amount paid multiplied by the difference of one minus the applicable tax rate.

For example, $100 of interest expense costs the company $65 after taxes when the corporate tax rate is 35 percent—for example, $100 × (1 – 0.35) = $65.

Problems 1.

2-1.

Income Statement (LO1) Frantic Fast Foods had earnings after taxes of $410,000 in the year 20X1 with 301,000 shares outstanding. On January 1, 20X2, the firm issued 30,000 new shares. Because of the proceeds from these new shares and other operating improvements, earnings after taxes increased by 25 percent. a.

Compute earnings per share for the year 20X1.

Compute earnings per share for the year 20X2.

Solution:

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Frantic Fast Foods a. Year 20X1

= $410,000 / 301,000 = $1.36 b. Year 20X2 Earnings after taxes = $410,000 × 1.25 = $512,500 Shares outstanding = 301,000 + 30,000 = 331,000

Earnings per share = $512,500 / 331,000 = $1.55

2-2.

Income statement (LO1) Sosa Diet Supplements had earnings after taxes of $800,000 in the year 20X1 with 200,000 shares of stock outstanding. On January 1, 20X2, the firm issued 50,000 new shares. Because of the proceeds from these new shares and other operating improvements, earnings after taxes increased by 30 percent. a.

Compute earnings per share for the year 20X1.

Compute earnings per share for the year 20X2.

Solution: Sosa Diet Supplements a. Year 20X1

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Earnings per share = Earnings after taxes Shares outstanding = $800,000 = $4.00 200,000 b. Year 20X2

Earnings after taxes  $800,000  1.30  $1,040,000 Shares outstanding  200,000  50,000  250,000 Earning per share  $1,040,000  $4.16 250,000

2-3.

Gross profit (LO1) Swank Clothiers had sales of $375,000 and cost of goods sold of $246,000. What is the gross profit margin (ratio of gross profit to sales)?

If the average firm in the clothing industry had a gross profit of 30 percent, how is the firm doing?

Solution: Swank Clothiers a. Sales............................................................ $375,000 Cost of goods sold ........................ 246,000 Gross Profit ........................$129,000

b. With a gross profit of 34 percent, the firm is outperforming the industry average of 30 percent.

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2-4.

Operating profit (LO1) A-Rod Fishing Supplies had sales of $2,500,000 and cost of goods sold of $1,710,000. Selling and administrative expenses represented 10 percent of sales. Depreciation was 6 percent of the total assets of $4,680,000. What was the firm’s operating profit?

Solution:

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A-Rod Fishing Supplies Sales ........................$2,500,000 Cost of goods sold ........................1,710,000 Gross Profit ........................790,000 Selling and administrative expense* ............. 250,000 Depreciation expense** ........................280,800 Operating profit ........................$ 259,200 * 10% × $2,500,000 = $250,000 ** 6% × $4,680,000 = $280,800 5.

Income statement (LO1) Arrange the following income statement items so they are in the proper order of an income statement: Taxes

Earnings per share

Shares outstanding

Earnings before taxes

Interest expense

Cost of goods sold

Depreciation expense

Earnings after taxes

Preferred stock dividends

Earnings available to common

Operating profit Sales

stockholders Selling and administrative expense

Gross profit

2-5.

Solution: Sales – Cost of goods sold Gross profit – Selling and administrative expense

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– Depreciation expense Operating profit – Interest expense Earnings before taxes – Taxes Earnings after taxes – Preferred stock dividends

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Earnings available to common stockholders Shares outstanding Earnings per share

Income statement (LO1) Given the following information, prepare an income statement for the Dental Drilling Company.

Selling and administrative expense ............................................... $ 112,000

2-6.

Depreciation expense ....................................................................

73,000

Sales ...............................................................................................

489,000

Interest expense ............................................................................

45,000

Cost of goods sold ..........................................................................

156,000

Taxes ..............................................................................................

47,000

Solution: Dental Drilling Company Income Statement Sales ........................$ 489,000 Cost of goods sold ........................$ 156,000 Gross profit ........................$ 333,000 Selling and administrative expense ............... $ 112,000 Depreciation expense ........................$ 73,000 Operating profit ........................$ 148,000 Interest expense ........................$ 45,000 Earnings before taxes ........................$ 103,000 Taxes ........................$ 47,000 Earnings after taxes ........................ $ 56,000

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Income statement (LO1) Given the following information, prepare in good form an income statement for Jonas Brothers Cough Drops.

Selling and administrative expense ............................................... $ 328,000 Depreciation expense ....................................................................

195,000

Sales ............................................................................................... 1,660,000

2-7.

Interest expense ............................................................................

129,000

Cost of goods sold ..........................................................................

560,000

Taxes ..............................................................................................

171,000

Solution: Jonas Brothers Cough Drops Income Statement Sales ........................$1,660,000 Cost of goods sold ........................560,000 Gross profit ........................1,100,000 Selling and administrative expense ............... 328,000 Depreciation expense ........................195,000 Operating profit ........................ 577,000 Interest expense ........................ 129,000 Earnings before taxes ........................ 448,000 Taxes ........................ 171,000 Earnings after taxes $.......................277,000

Determination of profitability (LO1) Prepare in good form an income statement for Franklin Kite Co. Inc. Take your calculations all the way to computing earnings per share.

Sales ...............................................................................................

$900,000

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2-8.

Shares outstanding ........................................................................

50,000

Cost of goods sold ..........................................................................

400,000

Interest expense ............................................................................

40,000

Selling and administrative expense ...............................................

60,000

Depreciation expense ....................................................................

20,000

Preferred stock dividends ..............................................................

80,000

Taxes ..............................................................................................

50,000

Solution: Franklin Kite Company Income Statement Sales ........................$900,000 Cost of goods sold ........................400,000 Gross profit ........................500,000 Selling and administrative expense ............... 60,000 Depreciation expense ........................20,000 Operating profit ........................$420,000 Interest expense ........................40,000 Earnings before taxes ........................$380,000 Taxes ........................50,000 Earnings after taxes ........................$330,000 Preferred stock dividends ........................80,000 Earnings available to common stockholders . 250,000 Shares outstanding ........................50,000 Earnings per share ........................$5.00

Determination of profitability (LO1) Prepare an income statement for Virginia Slim Wear. Take your calculations all the way to computing earnings per share.

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Sales ............................................................................................... $1,360,000

2-9.

Shares outstanding ........................................................................

104,000

Cost of goods sold ..........................................................................

700,000

Interest expense ............................................................................

34,000

Selling and administrative expense ...............................................

49,000

Depreciation expense ....................................................................

23,000

Preferred stock dividends ..............................................................

86,000

Taxes ..............................................................................................

100,000

Solution:

Virginia Slim Wear Income Statement Sales ........................$1,360,000 Cost of goods sold ........................ 700,000 Gross profit ........................660,000 Selling and administrative expense ............... 49,000 Depreciation expense ........................ 23,000 Operating profit ........................588,000 Interest expense ........................ 34,000 Earnings before taxes ........................554,000 Taxes ........................ 100,000 Earnings after taxes ........................454,000 Preferred stock dividends ........................86,000 Earnings available to common stockholders .$ 368,000 Shares outstanding ........................104,000 Earnings per share ........................$ 3.54 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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10.

Income statement (LO1) Precision Systems had sales of $820,000, cost of goods of $510,000, selling and administrative expense of $60,000, and operating profit of $103,000. What was the value of depreciation expense? Set this problem up as a partial income statement and determine depreciation expense as the plug figure.

2-10. Solution: Precision Systems Sales ........................$820,000 Cost of goods sold ........................510,000 Gross profit ........................310,000 Selling and administrative expense ............... 60,000 Depreciation (plug figure) ........................ 147,000 Operating profit ........................$103,000

11.

Depreciation and earnings (LO1) Stein Books Inc. sold 1,900 finance textbooks for $250 each to High Tuition University in 20X1. These books cost $210 to produce. Stein Books spent $12,200 (selling expense) to convince the university to buy its books. Depreciation expense for the year was $15,200. In addition, Stein Books borrowed $104,000 on January 1, 20X1, on which the company paid 12 percent interest. Both the interest and principal of the loan were paid on December 31, 20X1. The publishing firm’s tax rate is 30 percent. Did Stein Books make a profit in 20X1? Please verify with an income statement presented in good form.

2-11. Solution: Stein Books Inc. Income Statement For the Year Ending December 31, 20X1

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Sales (1,900 books at $250 each) ................................. $475,000 Cost of goods sold (1,900 books at $210 each) ........... 399,000 Gross profit ....................................... 76,000 Selling expense ....................................... 12,200 Depreciation expense ...................................... 15,200 Operating profit…… ....................................... $ 48,600 Interest expense ($104,000 × 12%).............................. 12,480 Earnings before taxes ....................................... 36,120 Taxes @ 30% ....................................... 10,836 Earnings after taxes ....................................... $ 25,284

12.

Determination of profitability (LO1) Lemon Auto Wholesalers had sales of $1,000,000 last year and cost of goods sold represented 78 percent of sales. Selling and administrative expenses were 12 percent of sales. Depreciation expense was $11,000 and interest expense for the year was $8,000. The firm’s tax rate is 30 percent. a.

Compute earnings after taxes.

Assume the firm hires Ms. Carr, an efficiency expert, as a consultant. She suggests that by increasing selling and administrative expenses to 14 percent of sales, sales can be increased to $1,050,900. The extra sales effort will also reduce cost of goods sold to 74 percent of sales. (There will be a larger markup in prices as a result of more aggressive selling.) Depreciation expense will remain at $11,000. However, more automobiles will have to be carried in inventory to satisfy customers, and interest expense will go up to $15,800. The firm’s tax rate will remain at 30 percent. Compute revised earnings after taxes based on Ms. Carr’s suggestions for Lemon Auto Wholesalers. Will her ideas increase or decrease profitability?

2-12. Solution: Lemon Auto Wholesalers Income Statement a. Sales ................. $1,000,000 Cost of goods sold (78% of sales) ...................... Gross profit ................. $ 220,000 Selling and administrative expense

$ 780,000

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(12% of sales) .................. $ 120,000 Depreciation .................. $ 11,000 Operating profit .................. $ 89,000 Interest expense ...................$ 8,000 Earnings before taxes .................. $ 81,000 Taxes @ 30% .................. $ 24,300 Earnings after taxes ................. $ 56,700 b. Sales ............... $1,050,900 Cost of goods sold (74% of sales) ..................... Gross profit ................. $ 273,234 Selling and administrative expense (14% of sales) ................. $ 147,126 Depreciation ................. $ 11,000 Operating profit ................. $ 115,108 Interest expense ................. $ 15,800 Earnings before taxes ................. $ 99,308 Taxes @ 30% ................. $ 29,792 Earnings after taxes ................ $ 69,516

$ 777,666

Ms. Carr’s ideas will increase profitability.

13.

Balance sheet (LO3) Classify the following balance sheet items as current or noncurrent: Retained earnings

Bonds payable

Accounts payable

Accrued wages payable

Prepaid expenses

Accounts receivable

Plant and equipment

Capital in excess of par

Inventory

Preferred stock

Common stock

Marketable securities

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2-13. Solution: Retained earnings – noncurrent Accounts payable – current Prepaid expense – current Plant and equipment – noncurrent Inventory – current Common stock – noncurrent Bonds payable – noncurrent Accrued wages payable – current Accounts receivable – current Capital in excess of par – noncurrent Preferred stock – noncurrent Marketable securities – current

14.

Balance sheet and income statement classification (LO1 & 3) Fill in the blank spaces with categories 1 through 7: 1.

Balance sheet (BS)

Current liabilities (CL)

Income statement (IS)

Long-term liabilities (LL)

Current assets (CA)

Stockholders’ equity (SE)

Fixed assets (FA)

Indicate Whether Item Is on Balance Sheet (BS) or Income

If on Balance Sheet, Designate Which Category

Item

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Statement (IS) _____ _____ _____ _____ _____ _____ _____ _____ _____ _____

_____ _____ _____ _____ _____ _____ _____ _____ _____ _____

Accounts receivable Retained earnings Income tax expense Accrued expenses Cash Selling and administrative expenses Plant and equipment Operating expenses Marketable securities Interest expense

_____ _____ _____ _____ _____ _____ _____ _____ _____

Sales Notes payable (6 months) Bonds payable, maturity 2045 Common stock Depreciation expense Inventories Capital in excess of par value Net income (earnings after taxes) Income tax payable

2-14. Solution: 1. Balance Sheet (BS) 2. Income Statement (IS) 3. Current Assets (CA) 4. Fixed Assets (FA) 5. Current Liabilities (CL) 6. Long-Term Liabilities (LL) 7. Stockholders Equity (SE)

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Indicate Whether Item is on Income Statement or Balance Sheet

If Item Is on Balance Sheet, Designate Which Category

Accounts Receivable

Retained Earnings

Item

Income Tax Expense

Accrued Expenses

Cash

IS BS

Selling and Administrative expenses FA

IS BS

Plant & Equipment Operating Expenses

Marketable Securities

Interest Expense

Sales

Notes Payable (6 Months)

Bonds Payable (Maturity 2045)

Common Stock

Depreciation Expense

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Inventories

Capital in Excess of Par Value

IS BS

15.

Net Income (Earnings after Taxes) CL

Income Tax Payable

Development of balance sheet (LO3) Arrange the following items in proper balance sheet presentation:

Accumulated depreciation.............................................................

$309,000

Retained earnings.................................... ......................................

187,000

Cash................................................. ..............................................

14,000

Bonds payable................................................................................

136,000

Accounts receivable.................................. .....................................

54,000

Plant and equipment—original cost.................... ..........................

775,000

Accounts payable..................................... ......................................

35,000

Allowance for bad debts.............................. ..................................

9,000

Common stock, $1 par, 100,000 shares outstanding..... ...............

100,000

Inventory........................................................................................

70,000

Preferred stock, $59 par, 1,000 shares outstanding......................

59,000

Marketable securities................................ ....................................

24,000

Investments.......................................... .........................................

20,000

Notes payable........................................ ........................................

34,000

Capital paid in excess of par (common stock)......... ......................

88,000

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Assets Current Assets: Cash ............................................

$ 14,000

Marketable securities ..................

24,000

Accounts receivable .................... Less: Allowance for bad debts

$ 54,000 9,00045,000

Inventory .....................................

70,000

Total current assets ............. $153,000 Other Assets: Investments ................................. Fixed Assets: Plant and equipment ...................

$775,000

Less: Accumulated depreciation

309,000

Net plant and equipment ............ Total assets

20,000

466,000

............. $ 639,000

Liabilities and Stockholders’ Equity Current Liabilities: Accounts payable ...................................................... Notes payable ............................................................ Total current liabilities Long-term liabilities Bonds payable ........................................................... Total liabilities ....................................................... Stockholders’ equity:

$ 35,000 34,000 $ 69,000

136,000

Preferred stock, $59 par, 1,000 shares outstanding .. Common stock, $1 par, 100,000 shares outstanding © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Capital paid in excess of par (common stock) ......... Retained earnings ...................................................... Total stockholders’ equity ..................................... Total liabilities and stockholders’ equity...........

$205,000

59,000 100,000 88,000 187,000 $434,000 $639,000

16.

Earnings per share and retained earnings (LO1 and 3) Elite Trailer has an operating profit or $250,000. Interest expense for the year was $32,000; preferred dividends paid were $32,700; and common dividends paid were $38,300. The tax was $63,500. The firm has 24,100 shares of common stock outstanding. a.

Calculate the earnings per share and the common dividends per share for Elite Trailer.

What was the increase in retained earnings for the year?

2-16. Solution: Elite Trailer a. Operating profit (EBIT) ....................................... $250,000 Interest expense ....................................... 32,000 Earnings before taxes (EBT) ................................... $218,000 Taxes ....................................... 63,500 Earnings after taxes (EAT) ..................................... $154,500

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Preferred dividends ....................................... 32,700 Available to common stockholders ....................... $121,800 Common dividends ....................................... 38,300 Increase in retained earnings……………………… $83,500

= $121,800/ 24,100 shares = $5.05 per share Dividends per share = $38,300/24,100 shares

= $1.59 per share b. Increase in retained earnings = $83,500 17.

Earnings per share and retained earnings (LO1 and 3) Quantum Technology had $669,000 of retained earnings on December 31, 20X2. The company paid common dividends of $35,500 in 20X2 and had retained earnings of $576,000 on December 31, 20X1. How much did Quantum Technology earn during 20X2, and what would earnings per share be if 47,400 shares of common stock were outstanding?

2-17. Solution: Quantum Technology Retained earnings, December 31, 20X2 ....................... $669,000 Less: Retained earnings, December 31, 20X1 .............. 576,000 Change in retained earnings ............................... $93,000

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Add: Common stock dividends.....................................

35,500

Earnings available to common stockholders ................ $128,500 Earnings per share

18.

Price/earning ratio (LO2) Botox Facial Care had earnings after taxes of $370,000 in 20X1 with 200,000 shares of stock outstanding. The stock price was $31.50. In 20X2, earnings after taxes increased to $436,000 with the same 200,000 shares outstanding. The stock price was $42.00. a.

Compute earnings per share and the P/E ratio for 20X1. (The P/E ratio equals the stock price divided by earnings per share.)

Compute earnings per share and the P/E ratio for 20X2.

Give a general explanation of why the P/E ratio changed.

2-18. Solution: Botox Facial Care a. EPS (20X1) P/E ratio (20X1) b. EPS (20X2)

 $370,000

= $1.85

= Price/EPS

= $31.50 = 17.03x

 $436,000

= $2.18

200,000

$1.85

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P/E ratio (20X2) c.

19.

= Price/EPS

= $42.00 = 19.27x $2.18

The stock price increased by 33.33% while EPS only increased 17.84%.

Price/earning ratio (LO2) Stilley Corporation had earnings after taxes of $436,000 in 20X2 with 200,000 shares outstanding. The stock price was $42.00. In 20X3, earnings after taxes declined to $206,000 with the same 200,000 shares outstanding. The stock price declined to $27.80. a.

Compute earnings per share and the P/E ratio for 20X2.

Compute earnings per share and the P/E ratio for 20X3.

Give a general explanation of why the P/E changed. You might want to consult the textbook to explain this surprising result.

2-19. Solution: Stilley Corporation a. EPS (20X2) P/E ratio (20X2) b. EPS (20X3)

P/E ratio (20X3) c.

20.

 $436,000 = $2.18

200,000

= Price/EPS = $42.00 = 19.27x $2.18  $206,000  $1.03 200,000

= Price/EPS = $27.80  26.99x $1.03

As explained in the text, when EPS drops rapidly, the stock price might not decline as much, and the P/E ratio rises. A higher P/E ratio under adverse conditions is not a positive.

Cash flow (LO4) Identify whether each of the following items increases or decreases cash flow: Increase in accounts receivable

Decrease in prepaid expenses

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Increase in notes payable

Increase in inventory

Depreciation expense

Dividend payment

Increase in investments

Increase in accrued expenses

Decrease in accounts payable

2-20. Solution: Increase in accounts receivable – decreases cash flow (use) Increase in notes payable – increases cash flow (source) Depreciation expense – increases cash flow (source) Increase in investments – decreases cash flow (use) Decrease in accounts payable – decreases cash flow (use) Decrease in prepaid expense – increases cash flow (source) Increase in inventory – decreases cash flow (use) Dividend payment – decreases cash flow (use) Increase in accrued expenses – increases cash flow (source)

21.

Depreciation and cash flow (LO5) The Rogers Corporation has a gross profit of $880,000 and $360,000 in depreciation expense. The Evans Corporation also has $880,000 in gross profit, with $60,000 in depreciation expense. Selling and administrative expense is $120,000 for each company. Given that the tax rate is 40 percent, compute the cash flow for both companies. Explain the difference in cash flow between the two firms.

2-21. Solution: Rogers Corporation – Evans Corporation

Gross profit ...................................... Selling and adm. expense ............

Rogers

Evans

$880,000

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Depreciation ....................................

120,000

360,000

60,000

Operating profit................................ Taxes (40%) ......................................

$400,000

$700,000

160,000

280,000

Earnings after taxes .......................... Plus depreciation expense ................

$240,000

$420,000

$360,000

$60,000

Cash flow .........................................

$600,000

$480,000

Rogers had $300,000 more in depreciation which provided $120,000 (0.40  $300,000) more in cash flow.

22.

Free cash flow (LO4) Nova Electrics anticipates cash flow from operating activities of $13 million in 20X1. It will need to spend $8.5 million on capital investments to remain competitive within the industry. Common stock dividends are projected at $1.1 million and preferred stock dividends at $1.3 million. a.

What is the firm’s projected free cash flow for the year 20X1?

What does the concept of free cash flow represent?

2-22. Solution: Nova Electronics a. Cash flow from operations activities

$13 million

– Capital expenditures

8.5

– Common stock dividends

1.1

– Preferred stock dividends

1.3

Free cash flow

$2.1 million

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b. Free cash flow represents the funds that are available for special financial activities, such as a leveraged buyout, increased dividends, common stock repurchases, acquisitions, or repayment of debt.

23.

Book value (LO3) Landers Nursery and Garden Stores has current assets of $220,000 and fixed assets of $170,000. Current liabilities are $80,000 and long-term liabilities are $140,000. There is $40,000 in preferred stock outstanding and the firm has issued 25,000 shares of common stock. Compute book value (net worth) per share.

2-23. Solution: Landers Nursery and Garden Stores Current assets Fixed assets Total assets – Current liabilities – Long-term liabilities Stockholders’ equity – Preferred stock obligation Net worth assigned to common ...................... Common shares outstanding Book value (net worth) per share ...................

$220,000 170,000 $390,000 80,000 140,000 $170,000 40,000 $130,000 25,000

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$ 24.

5.20

Book value and market value (LO2 and 3) The Holtzman Corporation has assets of $400,000, current liabilities of $50,000, and long-term liabilities of $100,000. There is $40,000 in preferred stock outstanding; 20,000 shares of common stock have been issued. a.

Compute book value (net worth) per share.

If there is $22,000 in earnings available to common stockholders, and Holtzman’s stock has a P/E of 18 times earnings per share, what is the current price of the stock?

What is the ratio of market value per share to book value per share?

2-24. Solution: Holtzman Corporation a. Total assets...............................................

$400,000

– Current liabilities ...................................

50,000

– Long-term liabilities ...............................

100,000

– Stockholders’ equity ..............................

$250,000

– Preferred stock ......................................

40,000

Net worth assigned to common ............

$210,000

Common shares outstanding .............

20,000

Book values (net worth) per share ........

$10.50

b. Earnings available to common .................

$22,000

Shares outstanding..................................... Earnings per share .....................................

20,000

P/E ratio × 18

$1.10

earnings per share

price

$1.10

$19.80

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25.

Market value per share (price) to book value per share $19.80/$10.50 = 1.89

Book value and market value (LO2 and 3) Amigo Software Inc. has total assets of $889,000, current liabilities of $192,000, and long-term liabilities of $154,000. There is $87,000 in preferred stock outstanding. Thirty thousand shares of common stock have been issued. a.

Compute book value (net worth) per share.

If there is $56,300 in earnings available to common stockholders, and the firm’s stock has a P/E of 23 times earnings per share, what is the current price of the stock?

What is the ratio of market value per share to book value per share? (Round to two places to the right of the decimal point.)

2-25. Solution: Amigo Software, Inc. a. Total assets...............................................

$889,000

– Current liabilities ...................................

192,000

– Long-term liabilities ...............................

154,000

Stockholders’ equity ..............................

$543,000

– Preferred stock ......................................

87,000

Net worth assigned to common ............

$456,000

Common shares outstanding ................

30,000

Book value (net worth) per share ..........

$ 15.20

b. Earnings available to common ................. Shares outstanding ...................................

$ 56,300

Earnings per share .....................................

30,000

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P/E ratio × 23 c.

26.

1.88

earnings per share

price

$1.88

$43.24

Market value per share (price) to book value per share $43.24/$15.20 = 2.84

Book value and P/E ratio (LO2 and 3) Vriend Software Inc.’s book value per share is $15.20. Earnings per share is $1.88, and the firm’s stock trades in the stock market at 3.5 times book value per share, what will the P/E ratio be? (Round to the nearest whole number.)

2-26. Solution: Vriend Software Inc. 3.5 × book value per share = price 3.5 × $15.20 = $53.20

round to 28x

27.

Construction of income statement and balance sheet (LO1 and 3) For December 31, 20X1, the balance sheet of Baxter Corporation was as follows: ________________________________________________________________________ Current Assets Cash .................................................

Liabilities $ 15,000

Accounts payable ...................

$ 17,000

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Accounts receivable ........................

20,000

Notes payable ........................

25,000

Inventory .........................................

30,000

Bonds payable ........................

55,000

Prepaid expenses ............................

12,500

Fixed Assets Plant and equipment (gross)…. .......

Stockholders’ Equity $255,000

Less: Accumulated ........................

Preferred stock .......................

$25,000

Common stock .......................

60,000

depreciation .................................

51,000

Paid-in capital .........................

30,000

Net plant and equipment ................

$204,000

Retained earnings ..................

69,500

......................................................... Total assets......................................

Total liabilities and $281,500

stockholders’ equity ...............

$281,500

________________________________________________________________________

Sales for 20X2 were $245,000, and the cost of goods sold was 60 percent of sales. Selling and administrative expense was $24,500. Depreciation expense was 8 percent of plant and equipment (gross) at the beginning of the year. Interest expense for the notes payable was 10 percent, while the interest rate on the bonds payable was 12 percent. This interest expense is based on December 31, 20X1 balances. The tax rate averaged 20 percent. $2,500 in preferred stock dividends were paid, and $5,500 in dividends were paid to common stockholders. There were 10,000 shares of common stock outstanding.

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During 20X2, the cash balance and prepaid expenses balances were unchanged. Accounts receivable and inventory increased by 10 percent. A new machine was purchased on December 31, 20X2, at a cost of $40,000. Accounts payable increased by 20 percent. Notes payable increased by $6,500 and bonds payable decreased by $12,500, both at the end of the year. The preferred stock, common stock, and paid-in capital in excess of par accounts did not change. a.

Prepare an income statement for 20X2.

Prepare a statement of retained earnings for 20X2.

Prepare a balance sheet as of December 31, 20X2.

2-27. Solution: Baxter Corporation 20X2 Income Statement a. Sales .................................$245,000 Cost of goods sold (60%) ................................. 147,000 Gross profit .................................$ 98,000 Selling and administrative expense ................. 24,500 Depreciation expense (8%).............................. 20,4001 Operating profit (EBIT) ................................ $ 53,100 Interest expense ................................. 9,1002 Earnings before taxes .................................$ 44,000 Taxes (20%) ................................. 8,800 Earnings after taxes (EAT) ........................... $ 35,200 Preferred stock dividends................................ 2,500 Earnings available to common stockholder ..... $ 32,700 Shares outstanding ................................. 10,000 Earnings per share ................................. $ 3.27 b. 20X2 Statement of Retained Earnings Retained earnings balance, January 1, 20X2 ... 1

8% × $255,000 = $20,400

(10% × $25,000) + (12% × $55,000) = $9,100

$ 69,500

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Add: Earnings available to common stockholders, 20X2 .................................32,700 Deduct: Cash dividend declared in 20X2 ......... 5,500

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Retained earnings balance, December 31, 20X2 .................................$96,700 c.

20X2 Balance Sheet Liabilities

Current Assets Cash…………..

$ 15,000

Accounts payable

Accounts receivable……..

22,000 Notes payable….

31,500

Inventory………

33,000 Bonds payable…

42,500

Prepaid expenses

12,500

_______

$82,500

$94,400 Stockholders’ Equity

Fixed Assets Gross plant…... Accumulated depreciation…

Net plant……..

$20,400

$295,000

(71,400)

223,600

Preferred stock... $ 25,000 Common stock... 60,000 Paid in capital in excess of par… 3 Retained earnings

30,000

96,700

$51,000 + $20,400 = $71,400

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Total assets…..

$306,100

Total liability & equity………..

$306,100

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28.

Statement of cash flows (LO4) Refer to the following financial statements for Crosby Corporation:

a) Prepare a statement of cash flows for the Crosby Corporation using the general procedures indicated in Table 2–10. b) Describe the general relationship between net income and net cash flows from operating activities for the firm. c) Has the buildup in plant and equipment been financed in a satisfactory manner? Briefly discuss. d) Compute the book value per common share for both 20X1 and 20X2 for the Crosby Corporation. e) If the market value of a share of common stock is 3.3 times book value for 20X1, what is the firm’s P/E ratio for 20X2?

_______________________________________________________________________ CROSBY CORPORATION Income Statement For the Year Ended December 31, 20X2

Sales ..................................................................................................

$2,200,000

Cost of goods sold .............................................................................

1,300,000

Gross profits ...............................................................................

900,000

Selling and administrative expense...................................................

420,000

Depreciation expense .......................................................................

150,000

Operating income .......................................................................

330,000

Interest expense................................................................................

90,000

Earnings before taxes .................................................................

240,000

Taxes..................................................................................................

80,000

Earnings after taxes ....................................................................

160,000

Preferred stock dividends ....................................................................

10,000

Earnings available to common stockholders ....................................

$ 150,000

Shares outstanding............................................................................

120,000

Earnings per share.............................................................................

1.25

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Statement of Retained Earnings For the Year Ended December 31, 20X2 Retained earnings, balance, January 1, 20X2....................................

$500,000

Add: Earnings available to common stockholders, 20X2 ...............

150,000

Deduct: Cash dividends declared and paid in 20X2 .......................

50,000

Retained earnings, balance, December 31, 20X2 .............................

$600,000

Comparative Balance Sheets For 20X1 and 20X2 Year-End Assets

Year-End

20X1

20X2

Cash ............................................................................................

$ 70,000

$100,000

Accounts receivable (net) ...........................................................

300,000

350,000

Inventory ...........................................................................................

410,000

430,000

Prepaid expenses ..............................................................................

50,000

30,000

Total current assets ....................................................................

830,000

910,000

Investments (long-term securities) ...................................................

80,000

70,000

Plant and equipment.........................................................................

2,000,000

2,400,000

Less: Accumulated depreciation .................................................

1,000,000

1,150,000

Net plant and equipment ..................................................................

1,000,000

1,250,000

Total assets........................................................................................

$1,910,000

$2,230,000

Current assets:

Liabilities and Stockholders’ Equity

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Current liabilities: Accounts payable........................................................................

$ 250,000

$ 440,000

Notes payable .............................................................................

400,000

Accrued expenses .......................................................................

70,000

50,000

Total current liabilities.............................................................

720,000

890,000

Bonds payable, 20X2 ..................................................................

70,000

120,000

Total liabilities .........................................................................

790,000

1,010,000

Preferred stock, $100 par value .................................................

90,000

Common stock, $1 par value ......................................................

120,000

Capital paid in excess of par .......................................................

410,000

Retained earnings .......................................................................

500,000

600,000

Total stockholders’ equity .......................................................

1,120,000

1,220,000

Total liabilities and stockholders’ equity...........................................

$1,910,000

$2,230,000

Long-term liabilities:

Stockholders’ equity:

_______________________________________________________________________

(The following questions apply to the Crosby Corporation, as presented in Problem 27.)

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Solution 2-28 a): Crosby Corporation Statement of Cash Flows For the Year Ended December 31, 20X2 Cash flows from operating activities: Net income (earnings after taxes) .........

$160,000

Adjustments to determine cash flow from operating activities: ............ Add back depreciation ......................... Increase in accounts receivable ........... Increase in inventory ........................... Decrease in prepaid expenses .............. Increase in accounts payable ............... Decrease in accrued expenses ............. Total adjustments ............................. Net cash flows from operating activities.................................................

$150,000 (50,000) (20,000) 20,000 190,000 (20,000) $270,000

Cash flows from investing activities: Decrease in investments ........................

$430,000

Increase in plant and equipment ........... Net cash flows from investing activities Cash flows from financing activities: Increase in bonds payable .....................

10,000 (400,000) (390,000)

Preferred stock dividends paid .............. Common stock dividends paid ............... 50,000

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Net cash flows from financing ............... Net increase (decrease) in cash flows ......

(10,000) (50,000)

(10,000) $ 30,000 The student should observe that the increase in cash flows of $30,000 equals the $30,000 change in the cash account on the balance sheet. This indicates the statement is correct.

Solution 2-28 b): Cash flows from operating activities far exceed net income. This occurs primarily because we add back depreciation of $319,000 and accounts payable increase by $248,000. Thus, the reader of the cash flow statement gets important insights as to how much cash flow was developed from daily operations.

Solution 2-28 c): The buildup in plant and equipment of $690,000 (gross) and $371,000 (net) has been financed, in part, by the large increase in accounts payable (248,000). This is not a very satisfactory situation. Short-term sources of funds can always dry up, while fixed asset needs are permanent in nature. This firm may wish to consider more long-term financing, such as a mortgage, to go along with profits, the increase in bonds payable, and the add© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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back of depreciation.

Solution 2-28 d): Book value

per share

Book value

Stockholders' equity  Preferred stock Common shares outstanding

 $1,120,000  $90,000  = $1,030,000 = $8.58

 $1, 220,000  $90,000  = $1,130,000 = $9.42

120,000

per share (20X1)

120,000

Book value per share (20X2)

Solution 2-28 e): Market value

= 3.3 × $9.42 = $31.09

P / E ratio

= Market value / Earnings per share = $31.09 / $1.25 = 24.87

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Chapter 3 Financial Analysis Discussion Questions 3-1.

If we divide users of ratios into short-term lenders, long-term lenders, and stockholders, in which ratios would each group be most interested, and for what reasons?

Short-term lenders—Liquidity ratios because their concern is with the firm’s ability to pay short-term obligations as they come due.

Long-term lenders—Leverage ratios because they are concerned with the relationship of debt to total assets. They also will examine profitability to ensure that interest payments can be made.

Stockholders—Profitability ratios, with secondary consideration given to debt utilization, liquidity, and other ratios. Since stockholders are the ultimate owners of the firm, they are primarily concerned with profits or the return on their investment.

3-2.

Explain how the DuPont system of analysis breaks down return on assets. Also explain how it breaks down return on stockholders’ equity.

The DuPont system of analysis breaks out the return on assets between the profit margin and asset turnover.

Return on assets

Net income Total assets

Profit margin



Net income Sales



Asset turnover

Sales Total assets

In this fashion, we can assess the joint impact of profitability and asset turnover on the overall return on assets. This is a particularly useful analysis because we can determine the source of strength and weakness for a given firm. For example, a

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company in the capital goods industry may have a high profit margin and a low asset turnover, while a food processing firm may suffer from low profit margins, but enjoy a rapid turnover of assets.

The modified form of the DuPont formula shows:

Return on equity =

Return on assets  investment  1  Debt/Assets 

This indicates that return on stockholders’ equity may be influenced by return on assets, the debt-to-assets ratio or a combination of both. Analysts or investors should be particularly sensitive to a high return on stockholders’ equity that is influenced by large amounts of debt.

3-3.

If the accounts receivable turnover ratio is decreasing, what will be happening to the average collection period?

If the accounts receivable turnover ratio is decreasing, accounts receivable will be on the books for a longer period of time. This means the average collection period will be increasing.

3-4.

What advantage does the fixed charge coverage ratio offer over simply using times interest earned?

The fixed charge coverage ratio measures the firm’s ability to meet all fixed obligations rather than interest payments alone, on the assumption that failure to meet any financial obligation will endanger the position of the firm.

3-5.

Is there any validity in rule-of-thumb ratios for all corporations (for example, a current

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ratio of 2 to 1 or debt to assets of 50 percent)?

No rule-of-thumb ratio is valid for all corporations. There is simply too much difference between industries or time periods in which ratios are computed. Nevertheless, rules-of-thumb ratios do offer some initial insight into the operations of the firm, and when used with caution by the analyst can provide information.

3-6.

Why is trend analysis helpful in analyzing ratios?

Trend analysis allows us to compare the present with the past and evaluate our progress through time. A profit margin of 5 percent may be particularly impressive if it has been running only 3 percent in the last 10 years. Trend analysis must also be compared to industry patterns of change.

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3-7.

Inflation can have significant effects on income statements and balance sheets, and therefore on the calculation of ratios. Discuss the possible impact of inflation on the following ratios, and explain the direction of the impact based on your assumptions. a. b. c. d.

Return on investment. Inventory turnover. Fixed asset turnover. Debt-to-assets ratio.

Return on investment 

Net income Total assets

Inflation may cause net income to be overstated and total assets to be understated causing an artificially high ratio that is misleading.

Inventory turnover 

Sales Inventory

Inflation may cause sales to be overstated. If the firm uses FIFO accounting, inventory will also reflect “inflation-influenced” dollars and the net effect will be nil.

If the firm uses LIFO accounting, inventory will be stated in old dollars and too high a ratio could be reported.

Fixed asset turnover 

Sales Fixed assets

Fixed assets will be understated relative to their replacement cost and to sales and too high a ratio could be reported.

Debt to total assets 

Total debt Total assets

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Since both are based on historical costs, no major inflationary impact will take place in the ratio.

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3-8.

What effect will disinflation following a highly inflationary period have on the reported income of the firm?

Disinflation tends to lower reported earnings as inflation-induced income is squeezed out of the firm’s income statement. This is particularly true for firms in highly cyclical industries where prices tend to rise and fall quickly.

3-9.

Why might disinflation prove to be favorable to financial assets? Because it is possible that prior inflationary pressures will no longer seriously impair the purchasing power of the dollar, lessening inflation also means that the required return that investors demand on financial assets will be going down, and with this lower demanded return, future earnings or interest should receive a higher current evaluation.

3-10.

Comparisons of income can be very difficult for two companies even though they sell the same products in equal volume. Why?

There are many different methods of financial reporting accepted by the accounting profession as promulgated by the Financial Accounting Standards Board. Though the industry has continually tried to provide uniform guidelines and procedures, many options remain open to the reporting firm. Every item on the income statement and balance sheet must be given careful attention. Two apparently similar firms may show different values for sales, research and development, extraordinary losses, and many other items.

Problems 1.

Profitability ratios (LO2) Low Carb Diet Supplement Inc. has two divisions. Division A has a profit of $156,000 on sales of $2,010,000. Division B is able to make only $28,800 on sales of $329,000. Based on the profit margins (returns on sales), which division is superior?

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3-1.

Solution: Low Carb Diet Supplements Division A Net income Sales

Division B

$156, 000  7.76% 2, 010, 000

$28,800  8.75% $329, 000

Division B is superior.

3-2.

Profitability ratios (LO2) Database Systems is considering expansion into a new product line. Assets to support expansion will cost $380,000. It is estimated that Database can generate $1,410,000 in annual sales, with an 8 percent profit margin. What would net income and return on assets (investment) be for the year?

Solution: Database Systems Net income = Sales  profit margin = $1,410,000  0.08 = $112,800

Return on assets (investment)

Net income Total assets $112,800  $380,000  29.7% 

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3-3.

Profitability ratios (LO2) Polly Esther Dress Shops Inc. can open a new store that will do an annual sales volume of $865,800. It will turn over its assets 1.8 times per year. The profit margin on sales will be 9 percent. What would net income and return on assets (investment) be for the year?

Solution: Polly Esther Dress Shops Inc. Assets = Sales / Total asset turnover

= $865,800 / 1.8 = $481,000

Net income = Sales × Profit Margin = $865,800 × 0.09 = $77,922

Return on assets (investment) = Net income / Total assets = $77,922 /$481,000 = 16.2%

3-4.

Profitability ratios (LO2) Billy’s Crystal Stores Inc. has assets of $5,960,000 and turns over its assets 1.9 times per year. Return on assets is 8 percent. What is the firm’s profit margin (return on sales)?

Solution:

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Billy’s Crystal Stores Inc.

Sales  Assets  total asset turnover $11,324,000  $5,960,000  1.9 Net income  Assets  Return on assets $476,800  $5,960,000  8% Net income  $476,800/$11,324,000 = 4.21% Sales 5.

3-5.

Profitability ratios (LO2) Elizabeth Tailors Inc. has assets of $8,540,000 and turns over its assets 1.8 times per year. Return on assets is 16.5 percent. What is the firm’s profit margin (returns on sales)?

Solution: Elizabeth Tailors Inc. Sales = Assets × Total asset turnover $15,372,000 = $8,540,000 × 1.8

Net income = Assets × Return on assets $1,409,100 = $8,540,000 × 16.5%

Net income / Sales = $1,409,100 / 15,372,000 = 9.17

Profitability ratios (LO2) Dr. Zhivàgo Diagnostics Corp. income statements for 20X1 are as follows:

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Sales ............................................................................................... $2,790,000 Cost of goods sold .......................................................................... 1,790,000 Gross profit .................................................................................... 1,000,000 Selling and administrative expense ...............................................

302,000

Operating profit .............................................................................

698,000

Interest expense ............................................................................

54,800

Income before taxes ......................................................................

643,200

Taxes (30%) ....................................................................................

192,960

Income after taxes ......................................................................... $ 450,240

a. Compute the profit margin for 20X1. b. Assume that in 20X2, sales increase by 10 percent and cost of goods sold increases by 20 percent. The firm is able to keep all other expenses the same. Assume a tax rate of 30 percent on income before taxes. What is income after taxes and the profit margin for 20X2?

3-6.

Solution: Dr. Zhivàgo Diagnostics a. Profit margin for 20X1 Net income $450, 240   16.14% Sales $2, 790, 000

b. Sales ............................. $3,069,000* Cost of goods sold ....................................... 2,148,000** Gross profit .................................................

921,000

Selling and administrative expense .............

302,000

Operating profit ..........................................

619,000

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Interest expense ..........................................

54,800

Income before taxes ....................................

564,200

Taxes (30%) .................................................

169,260

Income after taxes (20X2) ...........................

$ 394,940

* $2,790,000 × 1.10 = $3,069,000

** $1,790,000 × 1.20 = $2,148,000

Profit margin for 20X2 Net income $394,940   12.87% Sales $3, 069, 000 7.

Profitability ratios (LO2) The Haines Corp. shows the following financial data for 20X1 and 20X2.

Sales Cost of goods sold Gross profit Selling & administrative expense Operating profit Interest expense Income before taxes Taxes (35%) Income after taxes

20X1 $ 3,230,000 2,130,000 1,100,000 298,000 802,000 47,200 754,800 264,180 $490,620

20X2 $3,370,000 2,850,000 520,000 227,000 293,000 51,600 241,400 84,490 $156,910

For each year, compute the following and indicate whether it is increasing or decreasing profitability in 20X2 as indicated by the ratio. a.

Cost of goods sold to sales.

Selling and administrative expense to sales.

Interest expenses to sales.

3-7.

Solution: Haines Corp.

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20X1 a.

Cost of goods sold Sales

$2,130, 000  65.9% 3, 230, 000

20X2 $2,850, 000  84.6% 3,370, 000

It is decreasing profitability. b.

Selling & admin. expense Sales

$298, 000 $227, 000  9.2%  6.7% 3, 230, 000 3,370, 000

It is increasing profitability. Interest expense $47, 200 $51, 600  1.5%  1.5% Sales 3, 230, 000 3,370, 000 It is not changing profitability.

Profitability ratios (LO2) Easter Egg and Poultry Company has $1,840,000 in assets and $625,000 of debt. It reports net income of $145,000. a. What is the firm’s return on assets? b. What is its return on stockholders’ equity? c. If the firm has an asset turnover ratio of 2.4 times, what is the profit margin (return on sales)?

3-8.

Solution: Easter Egg and Poultry Company a.

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b. Stockholders’ equity = Total assets – Total debt = $1,840,000 – $625,000 = $1,215,000

Sales = Total assets × Total assets turnover = $1,840,000 × 2.4 = $4,416,000

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3-9.

Profitability ratios (LO2) Network Communications has total assets of $1,500,000 and current assets of $612,000. It turns over its fixed assets three times a year. It has $319,000 of debt. Its return on sales is 8 percent. What is its return on stockholders’ equity?

Solution: Network Communications Total assets – Current assets Fixed assets

$1,500,000 612,000 $ 888,000

Sales = Fixed assets × Fixed asset turnover $2,664,000 = $888,000 × 3 Total assets $1,500,000 – Debt 319,000 Stockholders’ equity $1,181,000

Net income = Sales  Profit margin = $2,664,000  8% = $213,120

Net income Stockholders' equity $213,120   18.05% $1,181, 000

Return on stockholders' equity 

10.

Profitability ratios (LO2) Fondren Machine Tools has total assets of $3,310,000 and current assets of $879,000. It turns over its fixed assets 3.6 times per year. Its return on sales is 4.8 percent. It has $1,750,000 of debt. What is its return on stockholders’ equity?

3-10. Solution: Fondren Machine Tools Total assets

$3,310,000

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– Current assets Fixed assets

879,000 $2,431,000

Sales  Fixed assets  Fixed asset turnover $8,751,600  $2,431,000  3.6 Net income = Sales  Profit margin $8,751,600  4.8% = $420,076.80 Total assets – Debt Stockholders’ equity

$3,310,000 1,750,000 $1,560,000

Return on stockholders' equity 



11.

Net income Stockholders' equity $420,076.80  26.93% $1,560,000

Profitability ratios (LO2) Baker Oats had an asset turnover of 1.9 times per year. a.

If the return on total assets (investment) was 10.6 percent, what was Baker’s profit margin?

The following year, on the same level of assets, Baker’s assets turnover increased to 2 times and its profit margin was 5.3 percent. How did the return on total assets change from that of the previous year?

3-11. Solution: Baker Oats a. Total asset turnover × Profit margin = Return on total assets 1.9 × ? = 10.6%

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b. 2

5.3% = 10.6%

It did not change at all because the increase in profit margin made up for the decrease in the asset turnover. 12.

DuPont system of analysis (LO3) AllState Trucking Co. has the following ratios compared to its industry for last year.

Return on sales………..

AllState Trucking 3%

Industry 8%

Return on assets………

15%

10%

Explain why the return-on-assets ratio is so much more favorable than the return-on-sales ratio compared to the industry. No numbers are necessary; a one-sentence answer is all that is required.

3-12. Solution: AllState Trucking Company AllState Trucking Company has a higher asset turnover ratio than the industry. Calculations are not necessary to answer the question, but just in case a student did the calculations here is the comparison. Return on assets =Asset turnover Return on sales

15% 10% vs 3% 8%

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AllState’s turnover 5x versus 1.25x Industry turnover

13.

DuPont system of analysis (LO3) Front Beam Lighting Company has the following ratios compared to its industry for last year.

Return on assets……………

Front Beam Lighting 12%

Industry 5%

Return on equity……………

16%

20%

Explain why the return-on-equity ratio is so much less favorable than the return-on-assets ratio compared to the industry. No numbers are necessary; a one-sentence answer is all that is required.

3-13. Solution: Front Beam Lighting Company Front Beam has a lower debt-to-total-assets ratio than the industry. For those who did a calculation, Front Beam’s debt-to-assets was 75 percent versus 25 percent for the industry.

14.

DuPont system of analysis (LO3) Jin’s Appliances has a return-on-assets (investment) ratio of 8 percent. a.

If the debt-to-total-assets ratio is 40 percent, what is the return on equity?

If the firm had no debt, what would the return-on-equity ratio be?

3-14. Solution:

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Jin’s Appliances a.

Return on equity 

Return on assets (investment) (1  Debt/Assets)



8% (1  0.40)



8% 0.60

 13.33%

b. The same as return on assets (8%). 15.

DuPont system of analysis (LO3) Using the DuPont method, evaluate the effects of the following relationships for the Butters Corporation:

a. Butters Corporation has a profit margin of 6.5 percent and its return on assets (investment) is 16.5 percent. What is its assets turnover? b. If the Butters Corporation has a debt-to-total-assets ratio of 50 percent, what would the firm’s return on equity be? c. What would happen to return on equity if the debt-to-total-assets ratio decreased to 35 percent?

3-15. Solution: Butters Corporation a. Profit margin × Total asset turnover = Return on assets (investment)

6.5

= 16.5%

= 2.5x

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= 33%

= 25.4%

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16.

DuPont system of analysis (LO3) Jerry Rice and Grain Stores has $4,780,000 in yearly sales. The firm earns 4.5 percent on each dollar of sales and turns over its assets 2.7 times per year. It has $123,000 in current liabilities and $349,000 in long-term liabilities. a. b.

What is its return on stockholders’ equity? If the asset base remains the same as computed in part a, but total asset turnover goes up to 3, what will be the new return on stockholders’ equity? Assume that the profit margin stays the same as do current and long-term liabilities.

3-16. Solution: Jerry Rice and Grain Stores a.

Net income  Sales  profit margin  $4,780,000  4.5%  $215,100 Stockholders' equity  Total assets  Total liabilities Total assets  Sales/Total asset turnover  $4,780,000/2.7  $1,770,370.37 Total liabilities  Current liabilities  Long-term liabilities  $123,000  $349,000  $472,000

Stockholders' equity  $1,770,370.37  $472,000  $1,298,370.37 Net income Stockholders' equity $215,100   16.57% $1, 298,370.37

Return on stockholders' equity 

b. The new level of sales will be:

Sales  Total assets  Total asset turnover  $1,770,370.37  3  $5,311,111.11

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Net income  Sales  Profit margin  $5,31,111.11  4.5%  $239,000

Return on stockholders' equity  

17.

Net income Stockholders' equity $239, 000  18.41% $1, 298,370.37

Interpreting results from the DuPont system of analysis (LO3) Assume the following data for Cable Corporation and Multi-Media Inc. Cable

Multi-

Corporation

Media Inc.

Net income ....................................

$ 31,200

$ 140,000

Sales ...............................................

317,000

2,700,000

Total assets ....................................

402,000

965,000

Total debt ......................................

163,000

542,000

Stockholders’ equity ......................

239,000

423,000

a. Compute the return on stockholders’ equity for both firms using ratio 3a. Which firm has the higher return? b. Compute the following additional ratios for both firms: Net income/Sales Net income/Total assets Sales/Total assets Debt/Total assets c. Discuss the factors from part b that added or detracted from one firm having a higher return on stockholders’ equity than the other firm as computed in part a.

3-17. Solution: Cable Corporation and Multi-Media Inc. a.

Cable

Multi-

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Corporation

Media Inc.

Net income $31, 200   13.05% Stockholders' equity $239, 000

$140, 000  33.1% $423, 000

Multi-Media Inc. has a much higher return on stockholders’ equity than Cable Corporation.

Cable Corporation

Net income  Sales Net income  Total assets Sales  Total assets Debt  Total assets

MultiMedia Inc.

$31, 200 $140, 000  9.84%  5.19% $317, 000 $2, 700, 000 $31, 200 $140, 000  7.76%  14.51% $402, 000 $965, 000 $317, 000 $2,700,000  .79x  2.8x $402, 000 $965, 000 $163, 000 $542, 000  40.55%  56.17% $402, 000 $965, 000

c. As previously indicated, Multi-Media Inc. has a substantially higher return on stockholders’ equity than Cable Corporation (33.1 percent versus 13.05 percent). The reason is certainly not to be found on return on the sales dollar where Cable Corporation has a higher return than Multi-Media Inc. (9.84 percent versus 5.19 percent).

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However, Multi-Media Inc. has a higher return than Cable Corporation on total assets (14.51 percent versus 7.76 percent). The reason is clearly to be found in total asset turnover, which strongly favors Multi-Media Inc. over Cable Corporation (2.8x versus 0.79x). This factor alone leads to the higher return on total assets. Multi-Media Inc.’s superior return on stockholders’ equity is further enhanced by a higher debt ratio than Cable Corporation (56.17 percent versus 40.55 percent). This means that a smaller percentage of Multi-Media Inc.’s total assets are being financed by stockholders’ equity and thus the potentially higher return on stockholders’ equity. Although not requested in the question, one could show the following:

Net income Net income / Total assets  Stockholders' equity (1  Debt/Assets) Multi-Media Inc. = 14.51%/(1 – 0.5617) = 14.51%/0.4383 = 33.1% Cable Corporation = 7.76%/(1 – 0.4055) = 7.76%/0.5945 = 13.05% 18.

Average collection period (LO2) A firm has sales of $3 million, and 10 percent of the sales are for cash. The year-end accounts receivable balance is $285,000. What is the average collection period? (Use a 360-day year.)

3-18. Solution:

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Accounts receivable Average daily credit sales ($3,000,000  90%)  $285,000 / 360 days $285,000  $7,500 per day  38 days

Average collection period 

19.

Average daily sales (LO2) Martinez Electronics has an accounts receivable turnover equal to 15 times. If accounts receivable are equal to $80,000, what is the value for average daily credit sales?

3-19. Solution: Martinez Electronics Average daily credit sales 

Credit sales 360

To determine credit sales, multiply accounts receivable by accounts receivable turnover.

$80,000  15  $1,200,000 Average daily credit sales 

20.

$1,200,000  $3,333 360

Inventory turnover (LO2) Perez Corporation has the following financial data for the years 20X1 and 20X2:

20X1

20X2

Sales…………………………

$8,000,000

$10,000,000

Cost of goods sold……………

6,000,000

9,000,000

Inventory……………………..

800,000

1,000,000

a. Compute inventory turnover based on Ratio 6, Sales/Inventory, for each year.

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b. Compute inventory turnover based on an alternative calculation that is used by many financial analysts, Cost of goods sold/Inventory, for each year. c. What conclusions can you draw from part a and part b?

3-20. Solution: Perez Corporation 20X1

20X2

Sales $8,000,000   10x Inventory 8,00,000

$10,000,000  10x 1,000,000

Cost of goods sold $6,000,000 $9,000,000   7.5x  9x Inventory 800,000 1,000,000

c. Based on the sales-to-inventory ratio, the turnover has remained constant at 10x. However, based on the cost of goods sold to inventory ratio, it has improved from 7.5x to 9x. The latter ratio may be providing a false picture of improvement in this example simply because cost of goods sold has gone up as percentage of sales has (from 75 percent to 90 percent). Inventory is not really turning over any faster. 21.

Turnover ratios (LO2) Jim Short’s Company makes clothing for schools. Sales in 20X1 were $4,820,000. Assets were as follows:

Cash………………………………………. Accounts receivable………………………. Inventory………………………………….. Net plant and equipment………………….. Total assets……………………………

$ 163,000 889,000 411,000 520,000 $1,983,000

a. Compute the following: 1. Accounts receivable turnover. 2. Inventory turnover.

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3. Fixed asset turnover. 4. Total asset turnover. b. In 20X2, sales increased to $5,740,000 and the assets for that year were as follows: Cash………………………………………... $ 163,000 Accounts receivable……………………….. 924,000 Inventory…………………………………... 1,063,000 Net plant and equipment…………………... 520,000 Total assets…………………………….. $2,670,000 Once again, compute the four ratios. c.

Indicate if there is an improvement or decline in total asset turnover, and based on the other ratios, indicate why this development has taken place.

3-21. Solution: Jim Short’s Company a. 1. Accounts receivable turnover = Sales/Accounts Receivable $4,820, 000  5.42 x 889, 000

2. Inventory turnover = Sales/Inventory $4,820, 000  11.73 x 411, 000

3. Fixed asset turnover = Sales/(Net Plant & Equipment) $4,820, 000  9.27 x 520, 000

4. Total asset turnover = Sales/Total assets $4,820, 000  2.43 x 1,983, 000

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b. 1. Accounts receivable turnover $5, 740, 000  6.21x 924, 000

2. Inventory turnover $5, 740, 000  5.4 x 1, 063, 000

3. Fixed asset turnover $5, 740, 000  11.04 x 520, 000

4. Total asset turnover $5, 740, 000  2.15 x 2, 670, 000

c. There is a decline in total asset turnover from 2.43 to 2.15. This development has taken place because of the slowdown in inventory turnover (11.73 down to 5.4). The other two ratios are slightly improved. 22.

Overall ratio analysis (LO2) The balance sheet for Revolution Clothiers is shown next. Sales for the year were $2,400,000, with 90 percent of sales sold on credit.

REVOLUTION CLOTHIERS Balance Sheet 20X1 Assets Cash……………………

Liabilities and Equity $

60,000

Accounts payable……………..

$ 220,000

Accounts receivable…...

240,000

Accrued taxes…………………

30,000

Inventory………………

350,000

Bonds payable

150,000

(long-term)……………………

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Plant and equipment…...

410,000

Total assets………...

$1,060,000

Common stock………………..

80,000

Paid-in capital…………………

200,000

Retained earnings……………..

380,000

Total liabilities and equity…

$1,060,000

Compute the following ratios: a. b. c. d. e.

Current ratio. Quick ratio. Debt-to-total-assets ratio. Asset turnover. Average collection period.

3-22. Solution:

Revolution Clothiers a.

Current ratio  

Current assets Current liabilities $650,000 $250,000

 2.6x b.

Quick ratio 

(Current assets  inventory) Current liabilities



$650,000  $350,000 $250,000



$300,000 $250,000

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Debt to total assets 

Total debt Total assets



$400,000 $1,060,000

 37.74% d.

Asset turnover 

Sales Total assets



$2, 400,000 $1,060,000

 2.26x e.

23.

Accounts receivable Average daily credit sales ($2,400,000  0.90)  $240,000 / 360 days $240,000  $6,000 per day  40 days

Average collection period 

Debt utilization ratios (LO2) The Lancaster Corporation’s income statement is given next. a.

What is the times-interest-earned ratio?

What would be the fixed-charge-coverage ratio? LANCASTER CORPORATION

Sales .............................................................................. Cost of goods sold ......................................................... Gross profit ................................................................... Fixed charges (other than interest) ................................ Income before interest and taxes................................... Interest........................................................................... Income before taxes ...................................................... Taxes (35%) ..................................................................

$246,000 122,000 124,000 27,500 96,500 21,800 74,700 26,145

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Income after taxes .........................................................

$ 48,555

3-23. Solution: Lancaster Corporation a.

Times interested earned  

Income before interest and taxes Interest $96,500 21,800

 4.43x b.

Fixed charge coverage 

Income before fixed charges and taxes Fixed charges



$96, 500  27, 500 $21,800  27, 500



$124, 000 $49, 300

 2.52x 24.

Debt utilization and DuPont system of analysis (LO3) Using the income statement for Times Mirror and Glass Co., compute the following ratios: a.

The interest coverage.

The fixed charge coverage.

The total assets for this company equal $80,000. Set up the equation for the DuPont system of ratio analysis, and compute c, d, and e. c.

Profit margin.

Total asset turnover.

Return on assets (investment).

TIME MIRROR AND GLASS COMPANY

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Sales .............................................................................. Less: Cost of goods sold ............................................... Gross profit ................................................................... Less: Selling and administrative expense ..................... Less: Lease expense ...................................................... Operating profit* ........................................................... Less: Interest expense ................................................... Earnings before taxes .................................................... Less: Taxes (30%)......................................................... Earnings after taxes ....................................................... *Equals income before interest and taxes.

$126,000 93,000 33,000 11,000 4,000 $ 18,000 3,000 $ 15,000 4,500 $ 10,500

3-24. Solution:

Times Mirror and Glass Co. a.

Times interest earned  

Income before interest and taxes Interest $18,000 $3,000

 6x b.

Fixed charge coverage 

Income before fixed charges and taxes Fixed charges



$18,000  4,000 $3,000  $4,000



$22,000 $7,000

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Profit margin  

Net income Sales $10,500 $126,000

 8.33% d.

Total asset turnover  

Sales Total assets $126,000 $80,000

 1.575x

Return on assets (investments) 

Net income Sales  Sales Total assets

 8.33%  1.575x  13.12%

25.

Debt utilization (LO2) A firm has net income before interest and taxes of $193,000 and interest expense of $28,100. a.

What is the times-interest-earned ratio?

If the firm’s lease payments are $48,500, what is the fixed charge coverage?

3-25. Solution:

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Times interest earned  

Income before interest and taxes Interest $193, 000 $28,100

 6.87x b.

Fixed charge coverage 

IBIT + Before tax fixed charges Interest + Fixed charges



$193,000  $48,500 $28,100  $48,500



$241,500 $76,600

 3.15x 26.

Return on assets analysis (LO2) In January 2009, the Status Quo Company was formed. Total assets were $544,000, of which $306,000 consisted of depreciable fixed assets. Status Quo uses straight-line depreciation of $30,600 per year, and in 2009 it estimated its fixed assets to have useful lives of 10 years. Aftertax income has been $29,000 per year each of the last 10 years. Other assets have not changed since 2009. a.

Compute return on assets at year-end for 2009, 2011, 2014, 2016, and 2018. (Use $29,000 in the numerator for each year.)

To what do you attribute the phenomenon shown in part a?

Now assume income increased by 10 percent each year. What effect would this have on your preceding answers? (A comment is all that is necessary.)

3-26. Solution: Status Quo Company a.

Return on assets (investment) =

Income after taxes Total assets

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The return on assets for Status Quo will increase over time as the assets depreciate and the denominator gets smaller. Fixed assets at the beginning of 2009 equal $306,000 with a 10-year life, which means the depreciation expense will be $30,600 per year. Book values at year-end are as follows: 2009 = $275,400; 2011 = $214,200; 2014 = $122,400; 2016 = $ 61,200; 2018 = $ 0 Return on assets (investment) =

Income after taxes Current assets + Fixed assets

2009 = $29,000/$513,400 = 5.65% 2011 = $29,000/$452,200 = 6.41% 2014 = $29,000/$360,400 = 8.05% 2016 = $29,000/$299,200 = 9.69% 2018 = $29,000/$238,000 = 12.18% b. The increasing return on assets over time is due solely to the fact that annual depreciation charges reduce the amount of investment. The increasing return is in no way due to operations. Financial analysts should be aware of the effect of overall asset age on the return-on-investment ratio and be able to search elsewhere for indications of operating efficiency when ROI is very high or very low. c.

27.

As income rises, return on assets will be higher than in part (b) and would indicate an increase in return partially from more profitable operations.

Trend analysis (LO4) Jolie Foster Care Homes Inc. shows the following data:

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Year 20X1 20X2 20X3 20X4

Net Income $155,000 191,000 208,000 192,000

Total Assets $2,390,000 2,700,000 2,730,000 2,470,000

Stockholders’ Equity $ 761,000 966,000 1,770,000 2,220,000

Total Debt $1,629,000 1,734,000 960,000 250,000

Compute the ratio of net income to total assets for each year and comment on the trend.

Compute the ratio of net income to stockholders’ equity and comment on the trend. Explain why there may be a difference in the trends between parts a and b.

3-27. Solution: Jolie Foster Care Homes Inc. a.

Net income Total assets

20X1 20X2 20X3 20X4

$155,000/$2,390,000 = 6.49% $191,000/$2,700,000 = 7.07 $208,000/$2,730,000 = 7.62 $192,000/$2,470,000 = 7.77

Comment: There is a strong upward movement in return on assets over the four-year period. b.

Net income Stockholders' equity 20X1 20X2 20X3 20X4

$155,000/$761,000 = 20.37% $191,000/$966,000 = 19.77% $208,000/$1,770,000 = 11.75% $192,000/$2,220,000 = 8.65%

Comment: The return on stockholders’ equity ratio is going down each year. The difference in trends between a and b is due to the larger portion of assets that are financed by stockholders’ equity as opposed to debt.

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Optional: This can be confirmed by computing total debt to total assets for each year. Total debt Total assets

20X1 20X2 20X3 20X4 28.

68.2% 64.2% 35.2% 10.1%

Trend analysis (LO4) Quantum Moving Company has the following data. Industry information also is shown.

Industry Data on Net Income/Total Assets

Year 20X1 20X2 20X3

Company Data Net Income $424,000 428,000 412,000

Total Assets $2,843,000 3,267,000 3,834,000

Year 20X1 20X2 20X3

Debt $1,722,000 1,732,000 1,950,000

Total Assets $2,843,000 3,267,000 3,834,000

14.0% 9.8 3.9 Industry Data on Debt/Total Assets 56.6% 42.0 38.0

As an industry analyst comparing the firm to the industry, are you likely to praise or criticize the firm in terms of the following: a.

Net income/Total assets.

Debt/Total assets.

3-28. Solution:

Quantum Moving Company a. Net income/total assets

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Year 20X1 20X2 20X3

Quantum Ratio 14.9% 13.1% 10.7%

Industry Ratio 14.0% 9.8% 3.9%

Although the company has shown a declining return on assets since 20X1, it has performed much better than the industry. Praise may be more appropriate than criticism. b. Debt/total assets Year 20X1 20X2 20X3

Quantum Ratio 60.6% 53.0% 50.9%

Industry Ratio 56.6% 42.0% 38.0%

While the company’s debt ratio is declining, it is not declining nearly as rapidly as the industry ratio. Criticism may be more appropriate than praise.

29.

Analysis by divisions (LO2) The Global Products Corporation has three subsidiaries.

Medical Supplies Heavy Machinery Sales ....................................... Net income (after taxes) ......... Assets .....................................

$20,040,000 1,700,000 8,340,000

$5,980,000 592,000 8,760,000

Electronics $4,730,000 402,000 3,570,000

Which division has the lowest return on sales?

Which division has the highest return on assets?

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Compute the return on assets for the entire corporation.

If the $8,760,000 investment in the heavy machinery division is sold off and redeployed in the medical supplies subsidiary at the same rate of return on assets currently achieved in the medical supplies division, what will be the new return on assets for the entire corporation?

3-29. Solution: Global Products Corporation a. Net income/Sales

Medical Supplies 8.48%

Heavy Machinery Electronics 9.90% 8.50%

The medical supplies division has the lowest return on sales. b. Net income/ Total assets

Medical Heavy Supplies Machinery Electronics 20.38% 6.76% 11.26%

The medical supplies division has the highest return on assets.

Corporate net income $1, 700, 000  $592, 000  $402, 000  Corporate total assets $8,340, 000  $8, 760, 000  $3,570, 000 

$2, 694, 000 $20, 670, 000

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20.38% × $8,760,000 = $1,785,288 Return on assets for the entire corporation:

Corporate net income $1, 700, 000  $1, 785, 288  $402, 000  Corporate total assets $20, 670, 000 

$3,887, 288 $20, 670, 000

 18.81% 30.

Analysis by affiliates (LO1) Omni Technology Holding Company has the following three affiliates:

Sales ................................. Net income (after taxes) ... Assets ............................... Stockholders’ equity ........

Software

Personal Computers

Foreign Operations

$40,200,000 2,086,000 5,820,000 4,090,000

$60,080,000 2,880,000 25,790,000 10,170,000

$100,680,000 8,510,000 60,630,000 50,950,000

Which affiliate has the highest return on sales?

Which affiliate has the lowest return on assets?

Which affiliate has the highest total asset turnover?

Which affiliate has the highest return on stockholders’ equity?

Which affiliate has the highest debt ratio? (Assets minus stockholders’ equity equals debt.)

Returning to question b, explain why the software affiliate has the highest return on total assets.

Returning to question d, explain why the personal computer affiliate has a higher return on stockholders’ equity than the foreign operations affiliate even though it has a lower return on total assets.

3-30. Solution:

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Omni Technology Holding Company

Personal Foreign Software Computers Operations 5.19% 4.79% 8.45%

Net income/Sales

The foreign operation affiliate has the highest return on sales. b. Net income/Total assets

Software 35.84%

Personal Computers 11.17%

Foreign Operations 14.04%

The personal computer affiliate has the lowest return on assets.

Sales/Total assets

Software 6.91x

Personal Computers 2.33x

Foreign Operations 1.66x

The software affiliate has the highest return on total asset turnover.

Personal Foreign Software Computers Operations 51.0% 28.32% 16.70%

d. Net income/ Stockholders’ equity The software affiliate has the highest return on stockholders’ equity.

Debt/Total assets

Personal Foreign Software Computers Operations 29.73% 60.57% 15.97%

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This is because of its high total asset turnover ratio of 6.91x in part c.

g. This is because the personal computer affiliate has a higher debt ratio (60.57%) than the foreign operations affiliate (15.97%). 31.

Inflation and inventory accounting effect (LO5) The Canton Corporation shows the following income statement. The firm uses FIFO inventory accounting.

CANTON CORPORATION Income Statement for 20X1 Sales ..................................................................... Cost of goods sold ................................................ Gross profit .......................................................... Selling and administrative expense ...................... Depreciation ......................................................... Operating profit .................................................... Taxes (30%) ......................................................... Aftertax income ...................................................

$272,800 (17,600 units at $15.50) 123,200 (17,600 units at $7.00) 149,600 13,640 15,900 120,060 36,018 $ 84,042

Assume in 20X2 that the same 17,600-unit volume is maintained, but that the sales price increases by 10 percent. Because of FIFO inventory policy, old inventory will still be charged off at $7 per unit. Also assume selling and administrative expense will be 5 percent of sales and depreciation will be unchanged. The tax rate is 30 percent. Compute aftertax income for 20X2.

In part a, by what percent did aftertax income increase as a result of a 10 percent increase in the sales price? Explain why this impact took place.

Now assume that in 20X3 the volume remains constant at 17,600 units, but the sales price decreases by 15 percent from its year 20X2 level. Also, because of FIFO inventory policy, cost of goods sold reflects the inflationary conditions of the prior year and is $7.50 per unit. Further, assume selling and administrative expense will be 5 percent of sales and depreciation will be unchanged. The tax rate is 30 percent. Compute the aftertax income.

3-31. Solution: Canton Corporation

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a. 20X2 Sales .................................. Cost of goods sold ............ Gross profit .................... Selling and adm. expense Depreciation ..................... Operating profit ............. Taxes (30%) ..................... Aftertax income .............

$300,080 (17,600 units at $17.05) 123,200 (17,600 units at $7) $ 176,880 15,004 (5% of sales) 15,900 $ 145,976 $ 43,793 $ 102,183

b. Gain in aftertax income 20X2 20X1 Increase

$102,183 84,042 $18,141

Increase $18,141   21.59% Base value (2010) $84, 042 Aftertax income increased much more than sales because of FIFO inventory policy (in this case, the cost of old inventory did not go up at all), and because of historical cost depreciation (which did not change).

c. 20X3 Sales .................................. $255,024 (17,600 units at $14.49*) Cost of goods sold ............ 132,000 (17,600 units at $7.50) Gross profit .................... $123,024 Selling and adm. expense 12,751 (5% of sales) Depreciation ..................... 15,900 Operating profit ............. $ 94,373 Taxes (30%) ..................... $ 28,312 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Aftertax income ............. $66,061 *$17.05 × 0.85 = $14.49 The low profits indicate the effect of inflation followed by disinflation. 32.

Using ratios to construct financial statements (LO2) Construct the current assets section of the balance sheet from the following data. (Use cash as a plug figure after computing the other values.)

Yearly sales (credit) ..................................................................... Inventory turnover ....................................................................... Current liabilities ......................................................................... Current ratio ................................................................................. Average collection period ............................................................ Current assets: $ Cash......................................................................... ______ Accounts receivable ................................................ ______ Inventory ................................................................. ______ Total current assets ............................................. ______

$420,000 7 times $80,000 2 36 days

3-32. Solution: Inventory

= $420,000/7 = $60,000

Current assets

= 2 × $80,000 = $160,000

Account rec.

= ($420,000/360) × 36 = $42,000

Cash

= $160,000 – $60,000 – $42,000 = $ 58,000

Cash ................................ Accounts receivable ....... Inventory ........................

$ 58,000 42,000 60,000

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Total current assets 33.

$160,000

Using ratios to construct financial statements (LO2) The Griggs Corporation has credit sales of $1,200,000. Given these ratios, fill in the following balance sheet.

Total assets turnover ................................... Cash to total assets ...................................... Accounts receivable turnover ..................... Inventory turnover ...................................... Current ratio ................................................ Debt to total assets ......................................

2.4 times 2.0% 8.0 times 10.0 times 2.0 times 61.0%

GRIGGS CORPORATION Balance Sheet Liabilities and Stockholders’ Equity

Assets Cash .............................. Accounts receivable ...... Inventory ....................... Total current assets Fixed assets .................. Total assets .............

_____ _____ _____ _____ _____ _____

Current debt ............................................. Long-term debt......................................... Total debt ........................................... Equity ....................................................... Total debt and stockholders’ equity

_____ _____ _____ _____ _____

3-33. Solution: Griggs Corporation Sales/Total assets Total assets Total assets

= 2.4 times = $1,200,000/2.4 = $500,000

Cash Cash Cash

= 2% of total assets = 2% × $500,000 = $10,000

Sales/Accounts receivable Accounts receivable Accounts receivable

= 8 times = $1,200,000/8 = $150,000

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Sales/Inventory Inventory Inventory

= 10 times = $1,200,000/10 = $120,000

Fixed assets Current asset

= Total assets – Current assets = $10,000 + $150,000 + $120,000 = $280,000 = $500,000 – $280,000 = $220,000

Fixed assets Current assets/Current debt Current debt Current debt Current debt

=2 = Current assets/2 = $280,000/2 = $140,000

Total debt/Total assets Total debt Total debt

= 61% = 0.61 × $500,000 = $305,000

Long-term debt Long-term debt Long-term debt

= Total debt – Current debt = $305,000 – 140,000 = $165,000

Equity Equity Equity

= Total assets – Total debt = $500,000 – $305,000 = $195,000

Griggs Corporation Balance Sheet Cash ..................... A/R ...................... Inventory ............. Total current

$ 10,000 Current debt .......... 150,000 Long-term debt ..... $120,000 Total debt .......... 280,000

$140,000 165,000 $305,000

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assets Fixed assets ......... Total assets ..........

34.

220,000 Equity ................... $500,000 Total debt and stockholders’ equity

195,000 $500,000

Using ratios to determine account balances (LO2) We are given the following information for the Pettit Corporation.

Sales (credit) ............................................................. Cash .......................................................................... Inventory .................................................................. Current liabilities ...................................................... Asset turnover .......................................................... Current ratio ............................................................. Debt-to-assets ratio ................................................... Receivables turnover ................................................

$3,549,000 179,000 911,000 788,000 1.40 times 2.95 times 40% 7 times

Current assets are composed of cash, marketable securities, accounts receivable, and inventory. Calculate the following balance sheet items. a.

Accounts receivable.

Marketable securities.

Fixed assets.

Long-term debt.

3-34. Solution:

Pettit Corporation

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a. Accounts receivable

= Sales/Receivable turnover = $3,549,000/7x = $507,000

b. Marketable securities = Current assets – (Cash + Accounts rec. + Inventory) Current assets

= Current ratio × Current liabilities = 2.95 × $788,000 = $2,324,600

Marketable securities = $2,324,600 – ($179,000 + $507,000 + $911,000) = $2,324,600 – $1,597,000 = $727,600 c.

Fixed assets

= Total assets – Current assets

Total assets

= Sales/Asset turnover = $3,549,000/1.40x = $2,535,000

Fixed assets

= $2,535,000 – $2,324,600 = $210,400

d. Long-term debt

= Total debt – Current liabilities

Total debt

= Debt to assets × Total assets = 40% × $2,535,000 = $1,014,000

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Long-term debt

= $1,014,000 – $788,000 = $226,000

35.

Using ratios to construct financial statements (LO2) The following information is from Harrelson Inc.’s, financial statements. Sales (all credit) were $28.50 million for last year.

Sales to total assets......................................... 1.90 times Total debt to total assets ................................. 35% Current ratio ................................................... 2.50 times Inventory turnover ......................................... 10.00 times Average collection period .............................. 20 days Fixed asset turnover ....................................... 5.00 times

Fill in the balance sheet: Cash..................................... Accounts receivable ............ Inventory ............................. Total current assets ........... Fixed assets ......................... Total assets ........................

______ ______ ______ ______ ______ ______

Current debt .......................................... Long-term debt...................................... Total debt ............................................ Equity .................................................... Total debt and equity ..........................

______ ______ ______ ______ ______

3-35. Solution: Harrelson Inc. Sales/Total assets Total assets Total assets

= 1.90 = $28.50 million/1.90 = $15 million

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Total debt/Total assets Total debt Total debt

= 35% = $15 million × 0.35 = $5.25 million

Sales/inventory Inventory Inventory

= 10x = $28.50 million/10x = $2.85 million

Average daily sales

= $28.50 million/360 days = $79,166.67 per day

Accounts receivable

= 20 days × $79,166.67 = $1.58 million (or)

Accounts receivable =

$28.50 million  $1,583,333 360 20

Fixed assets

= $28.50 million/5x = $5.70 million

Current assets

= Total assets – Fixed assets = $15.00 million – $5.70 million = $9.30 million

Cash

= Current assets – Accounts receivable – Inventory = $9.30 mil. – $1.58 mil. – $2.85 mil. = $4.87 million

Current liabilities

= Current assets/2.50 = $9.30 million/2.50 = $3.72 million

Long-term debt

= Total debt – Current debt = $5.25 million – $3.72 million = $1.53 million

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= Total assets – Total debt = $15.00 million – $5.25 million = $9.75 million

Equity

Cash................ Accounts receivable........ Inventory......... Total current assets............... Fixed assets..... Total assets..... 36.

$ 4.87 million Current debt...........

$ 3.72 million

$ 1.58 $ 2.85

$ 1.53 $ 5.25 $ 9.75

Long-term debt....... Total debt....... Equity.............

$ 9.30 $ 5.70 $15.00 million Total debt and equity...........

$15.00 million

Comparing all the ratios (LO2) Using the financial statements for the Jackson Corporation, calculate the 13 basic ratios found in the chapter.

JACKSON CORPORATION Balance Sheet December 31, 20X1 Assets Current assets: Cash...................................................... Marketable securities ........................... Accounts receivable (net) .................... Inventory .............................................. Total current assets ........................... Investments ............................................. Plant and equipment................................ Less: Accumulated depreciation .......... Net plant and equipment ...................... Total assets ..............................................

$ 52,200 24,400 222,000 238,000 $536,000 65,900 615,000 (271,000) 344,000 $946,500

Liabilities and Stockholders’ Equity Current liabilities Accounts payable ................................. Notes payable ....................................... Accrued taxes .......................................

$93,400 70,600 17,000

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Total current liabilities ...................... Long-term liabilities: Bonds payable ...................................... Total liabilities ..................................... Stockholders’ equity Preferred stock, $50 per value ............. Common stock, $1 par value ............... Capital paid in excess of par ................ Retained earnings ................................. Total stockholders’ equity................. Total liabilities and stockholders’ equity

181,000 $153,200 $334,200 100,000 80,000 190,000 242,300 612,300 $946,500

JACKSON CORPORATION Income statement For the Year Ending December 31, 20X1 Sales (on credit)................................................................................. Less: Cost of goods sold ............................................................... Gross profit ....................................................................................... Less: Selling and administrative expenses .................................... Operating profit (EBIT) .................................................................... Less: Interest expense ................................................................... Earnings before taxes (EBT) ............................................................. Less: Taxes.................................................................................... Earnings after taxes (EAT)................................................................ *Includes $36,100 in lease payments.

$2,064,000 1,313,000 751,000 496,000* 255,000 26,900 228,100 83,300 $ 144,800

3-36. Solution: Jackson Corporation Profitability ratios Profit margin = $144,800/$2,064,000 = 7.02% Return on assets (investment) = $144,800/$946,500 = 15.3% Return on equity = $144,800/$612,300 = 23.65% Assets utilization ratios Receivable turnover = $2,064,000 /$222,000 = 9.30x © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Average collection period = $222,000/$5,733 = 38.72 days Inventory turnover = $2,064,000 /$238,000 = 8.67x Fixed asset turnover = $2,064,000 /$344,000 = 6.00x Total asset turnover = $2,064,000 /$946,500 = 2.18x Liquidity ratio Current ratio = $536,600/$181,000 = 2.96x Quick ratio = $298,600/$181,000 = 1.65x Debt utilization ratios Debt to total assets = $334,200/$946,500 = 35.31% Times interest earned = $255,000/$26,900 = 9.48x Fixed charge coverage = $291,100/$63,000 = 4.62x 37.

Ratio computation and analysis (LO2) Given the financial statements for Jones Corporation and Smith Corporation shown here: a.

To which one would you, as credit manager for a supplier, approve the extension of (shortterm) trade credit? Why? Compute all ratios before answering.

In which one would you buy stock? Why?

JONES CORPORATION Current Assets Cash.............................................. Accounts receivable ..................... Inventory ...................................... Long-Term Assets Fixed assets .................................. Less: Accumulated depreciation Net fixed assets* .......................... Total assets ...............................

$ 20,000 80,000 50,000 $500,000 (150,000) 350,000 $500,000

Liabilities Accounts payable .................. Bonds payable (long-term) ....

$100,000 80,000

Stockholders’ Equity Common stock ....................... $150,000 Paid-in capital ........................ 70,000 Retained earnings .................. 100,000 Total liab. and equity ........ $500,000

Sales (on credit) ....................................................................................... $1,250,000 Cost of goods sold ................................................................................... 750,000 Gross profit .............................................................................................. 500,000 Selling and administrative expense† ..................................................... 257,000 Less: Depreciation expense .................................................................. 50,000 Operating profit ....................................................................................... 193,000 Interest expense ....................................................................................... 8,000 Earnings before taxes .............................................................................. 185,000 Tax expense ............................................................................................. 92,500 Net income .............................................................................................. $ 92,500

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*Use net fixed assets in computing fixed asset turnover. †Includes $7,000 in lease payments. SMITH CORPORATION Current Assets Cash ................................. $ 35,000 Marketable securities ...... 7,500 Accounts receivable ........ 70,000 Inventory ......................... 75,000

Liabilities Accounts payable .................. Bonds payable (long-term) ....

Long-Term Assets Fixed assets ..................... $500,000 Less: Accum. dep.......... (250,000) Net fixed assets* ............. 250,000 Total assets ................. $437,500

Stockholders’ Equity Common stock....................... $ 75,000 Paid-in capital ........................ 30,000 Retained earnings .................. 47,500 Total liab. and equity ........... $437,500

$ 75,000 210,000

*Use net fixed assets in computing fixed asset turnover. SMITH CORPORATION Sales (on credit)....................................................................................... $1,000,000 Cost of goods sold ................................................................................... 600,000 Gross profit ............................................................................................. 400,000 Selling and administrative expense†..................................................... 224,000 Less: Depreciation expense .................................................................. 50,000 Operating profit ....................................................................................... 126,000 Interest expense ....................................................................................... 21,000 Earnings before taxes .............................................................................. 105,000 Tax expense............................................................................................. 52,500 Net income .............................................................................................. $ 52,500 †Includes $7,000 in lease payments.

3-37. Solution: Jones and Smith Comparison One way of analyzing the situation for each company is to compare the respective ratios for each. Examining those ratios which would be most important to a supplier or short-term lender and a stockholder.

Profit margin Return on assets (investments)

Jones Corp. 7.4% 18.5%

Smith Corp. 5.25% 12.00%

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Return on equity 28.9% 34.4% Receivable turnover 15.63x 14.29x Average collection period 23.04 days 25.2 days Inventory turnover 25x 13.3x Fixed asset turnover 3.57x 4x Total asset turnover 2.5x 2.29x Current ratio 1.5x 2.5x Quick ratio 1.0x 1.5x Debt to total assets 36% 65.1% Times interest earned 24.13x 6x Fixed charge coverage 13.33x 4.75x Fixed charge coverage (200/15) (133/28) calculation a. Since suppliers and short-term lenders are most concerned with liquidity ratios, Smith Corporation would get the nod as having the best ratios in this category. One could argue, however, that Smith had benefited from having its debt primarily long term rather than short term. Nevertheless, it appears to have better liquidity ratios. b. Stockholders are most concerned with profitability. In this category, Jones has much better ratios than Smith. Smith does have a higher return on equity than Jones, but this is due to its much larger use of debt. Its return on equity is higher than Jones’ because it has taken more financial risk. In terms of other ratios, Jones has its interest and fixed charges well covered and in general its long-term ratios and outlook are better than Smith’s. Jones has asset utilization ratios equal to or better than Smith and its lower liquidity ratios could reflect better shortterm asset management. This point was covered in part a. Note: Remember that, in order to make actual financial decisions, more than one year’s comparative data is usually required. Industry comparisons should also be made.

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SMITH CORPORATION Sales (on credit) .........................................

$1,000,000

Cost of goods sold ......................................

600,000

Gross profit.................................................

400,000

Selling and administrative expense .........

224,000

Less: Depreciation expense ......................

50,000

Operating profit..........................................

126,000

Interest expense .........................................

21,000

Earnings before taxes .................................

105,000

Tax expense ................................................

52,500

Net income .................................................

52,500



Includes $7,000 in lease payments.

COMPREHENSIVE PROBLEM Comprehensive Problem 1. Lamar Swimwear (trend analysis and industry comparisons) (LO3) Bob Adkins has recently been approached by his first cousin, Ed Lamar, with a proposal to buy a 15 percent interest in Lamar Swimwear. The firm manufactures stylish bathing suits and sunscreen products.

Mr. Lamar is quick to point out the increase in sales that has taken place over the last three years as indicated in the income statement, Exhibit 1. The annual growth rate is 25 percent. A balance sheet for a similar time period is shown in Exhibit 2, and selected industry ratios are presented in Exhibit 3. Note the industry growth rate in sales is only 10 to 12 percent per year.

There was a steady real growth of 3 to 4 percent in gross domestic product during the period under study.

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Exhibit 1 LAMAR SWIMWEAR Income Sheet 20X1

20X2

20X3

Sales (all on credit).....................................................

$1,200,000

$1,500,000

$1,875,000

Cost of goods sold......................................................

800,000

1,040,000

1,310,000

Gross profit ................................................................

$ 400,000

$ 460,000

$ 565,000

Selling and administrative expense* ..........................

239,900

274,000

304,700

Operating profit (EBIT)...............................................

$ 160,100

$ 186,000

$ 260,300

Interest expense ........................................................

35,000

45,000

85,000

Net income before taxes ...........................................

$ 125,100

$ 141,000

$ 175,300

Taxes ..........................................................................

36,900

49,200

55,600

91,800

$ 119,700

Net income ................................................................

88,200

Shares ........................................................................

30,000

38,000

Earnings per share .....................................................

$ 2.94

$ 3.06

$ 3.15

Includes $15,000 in lease payments for each year.

Exhibit 2 LAMAR SWIMWEAR Balance Sheet Assets

20X1

Cash ...........................................................................

30,000

20X2 $

40,000

20X3 $

30,000

Marketable securities ...............................................

20,000

25,000

30,000

Accounts receivable ..................................................

170,000

259,000

360,000

Inventory ...................................................................

230,000

261,000

290,000

Total current assets ...............................................

$ 450,000

$ 585,000

$ 710,000

Net plant and equipment..........................................

650,000

765,000

1,390,000

Total assets ...............................................................

$1,100,000

$1,350,000

$ 2,100,000

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Liabilities and Stockholders’ Equity Accounts payable ......................................................

$ 200,000

$ 310,000

$ 505,000

Accrued expenses .....................................................

20,400

30,000

35,000

Total current liabilities ..........................................

$ 220,400

$ 340,000

$ 540,000

Long-term liabilities ..................................................

325,000

363,600

703,900

Total liabilities .......................................................

$ 545,400

$ 703,600

$ 1,243,900

Common stock ($2 par).............................................

60,000

76,000

Capital paid in excess of par .....................................

190,000

264,000

Retained earnings .....................................................

304,600

396,400

516,100

Total stockholders’ equity .....................................

$ 554,600

$ 646,400

$ 856,100

Total liabilities and stockholders’ equity ..................

$1,100,000

$1,350,000

$2, 100,000

Exhibit 3 Selected Industry Ratios 20X1

20X2

20X3

Growth in sales ........................................

—

10.00%

12.00%

Profit margin ............................................

7.71%

7.82%

7.96%

Return on assets (investment) .................

7.94%

8.86%

8.95%

Return on equity ......................................

14.31%

15.26%

16.01%

Receivable turnover .................................

9.02x

8.86x

9.31x

Average collection period ........................

39.9 days

40.6 days

38.7 days

Inventory turnover ...................................

4.24x

5.10x

5.11x

Fixed asset turnover.................................

1.60x

1.64x

1.75x

Total asset turnover .................................

1.05x

1.10x

1.12x

Current ratio ............................................

1.96x

2.25x

2.40x

Quick ratio ................................................

1.37x

1.41x

1.38x

Debt to total assets ..................................

43.47%

43.11%

44.10%

Times interest earned ..............................

6.50x

5.99x

6.61x

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Fixed charge coverage .............................

4.70x

4.69x

4.73x

Growth in EPS...........................................

—

10.10%

13.30%

The stock in the corporation has become available due to the ill health of a current stockholder, who is in need of cash. The issue here is not to determine the exact price for the stock, but rather whether Lamar Swimwear represents an attractive investment situation. Although Mr. Adkins has a primary interest in the profitability ratios, he will take a close look at all the ratios. He has no fast and firm rules about required return on investment, but rather wishes to analyze the overall condition of the firm. The firm does not currently pay a cash dividend, and return to the investor must come from selling the stock in the future. After doing a thorough analysis (including ratios for each year and comparisons to the industry), what comments and recommendations do you offer to Mr. Adkins?

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CP 3-1.

Solution:

Lamar Swimwear 20X1 Growth in sales (Company) (Industry) Profit margin (Company) 7.35% (Industry) 7.71% Return on assets (Company) 8.02% (Industry) 7.94% Return on equity (Company) 15.90% (Industry) 14.31% Receivable turnover (Company) 7.06x (Industry) 9.02x Average collection (Company) 51.0 days period (Industry) 39.9 days Inventory turnover (Company) 5.22x (Industry) 4.24x Fixed asset turnover (Company) 1.85x (Industry) 1.60x Total asset turnover (Company) 1.09x (Industry) 1.05x Current ratio (Company) 2.04x (Industry) 1.96x Quick ratio (Company) 1.00x (Industry) 1.37x Debt to total assets (Company) 49.58% (Industry) 43.47% Times interest (Company) 4.57x earned (Industry) 6.50x Fixed charge (Company) 3.50x coverage (Industry) 4.70x Growth in E.P.S. (Company) ---(Industry) ----

20X2 25% 10% 6.12% 7.82% 6.80% 8.68% 14.20% 15.26% 5.79x 8.86x 62.2 days 40.6 days 5.75x 5.10x 1.96x 1.64 1.11x 1.10x 1.72x 2.25x .95x 1.41x 52.12% 43.11% 4.13x 5.99x 3.35x 4.69x 4.1% 10.1%

20X3 25% 12% 6.38% 7.96% 5.70% 8.95% 13.98% 16.01% 5.21x 9.31x 69.1 days 38.7 days 6.47x 5.11x 1.35x 1.75x 0.89x 1.12x 1.31x 2.40x 0.78x 1.38x 59.23% 44.10% 3.06x 6.61x 2.75x 4.73x 2.9% 13.3%

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Discussion of Ratios While Lamar Swimwear is expanding its sales much more rapidly than others in the industry, there are some clear deficiencies in their performance. These can be seen in terms of a trend analysis over time as well as a comparative analysis with industry data. In terms of profitability, the profit margin is declining over time. This is surprising in light of the 56.25 percent increase in sales over two years (25 percent per year). There obviously are no economies of scale for this firm. Higher costs of goods sold and interest expense appear to be causing the problem. The return-on-asset ratio starts out in 20X1 above the industry average (8.02 percent versus 7.94 percent) and ends up well below it (5.70 percent versus 8.95 percent) in 20X3. The decline of 2.32 percent for return on assets is serious and can be attributed to the previously mentioned declining profit margin as well as a slowing total asset turnover (going from 1.09x to 0.89x). Return on equity is higher than the industry average the first year, and then also falls far below it. This decline is particularly significant in light of the progressively larger debt that the firm is using. High debt utilization tends to contribute to high return on equity, but not in this case. There is simply too much deterioration in return on assets translating into low return on equity. The previously mentioned slower turnover of assets can be analyzed through the turnover ratios. A problem can be found in accounts receivable where turnover has gone from 7.06x to 5.21x. This can also be stated in terms of an average collection period that has increased from 51 days to 69.1 days. While inventory turnover has been and remains superior to the industry, the same cannot be said for fixed asset turnover. A decline from 1.85x to 1.35x was caused by an increase in 113.8 percent in fixed assets (representing $740,000). We can summarize the discussion of the turnover ratios by saying that despite a 56.25 percent increase in sales, assets grew even more rapidly causing a decline in total asset turnover from 1.09x to 0.89x. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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The liquidity ratios also are not encouraging. Both the current and quick ratios are falling against a stable industry norm of approximately two to one and one to one, respectively. The debt-to-total-assets ratio is particularly noticeable in regard to industry comparisons. Lamar Swimwear has gone from being only 6.11 percent over the industry average to 15.13 percent above the norm (59.23 percent versus 44.10 percent). Their heavy debt position is clearly out of line with their competitors. Their downtrend in times interest earned and fixed charge coverage confirms the heavy debt burden on the company. Finally, we see that the firm has a slower growth rate in earnings per share than the industry. This is a function of less rapid growth in earnings as well as an increase in shares outstanding (with the sale of 8,000 shares in 20X3). Once again, we see that the rapid growth in sales is not being translated down into significant earnings gains. This is true in spite of the fact that there is a very stable economic environment. Investment Comments: He would probably have difficulty justifying such an investment based on the performance of the firm. There are no dividend payouts, so return to the investor would have to come in the form of capital appreciation if and when he was able to resell the shares. The prospects, at this point, would not appear to justify the purchase. This is particularly true when one considers that Mr. Adkins would be buying a minority interest (15 percent) and would not have control of the firm.

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Comprehensive Problem 2 Sun Microsystems (trends, ratios stock performance) (LO3) Sun Microsystems is a leading supplier of computer-related products, including servers, workstations, storage devices, and network switches.

In the letter to stockholders as part of the 2001 annual report, President and CEO Scott G. McNealy offered the following remarks:

Fiscal 2001 was clearly a mixed bag for Sun, the industry, and the economy as a whole. Still, we finished with revenue growth of 16 percent—and that’s significant. We believe it’s a good indication that Sun continued to pull away from the pack and gain market share. For that, we owe a debt of gratitude to our employees worldwide, who aggressively brought costs down— even as they continued to bring exciting new products to market.

The statement would not appear to be telling you enough. For example, McNealy says the year was a mixed bag with revenue growth of 16 percent. But what about earnings? You can delve further by examining the income statement in Exhibit 1. Also, for additional analysis of other factors, consolidated balance sheet(s) are presented in Exhibit 2 on page 92.

1. Referring to Exhibit 1, compute the annual percentage change in net income per common sharediluted (second numerical line from the bottom) for 1998–1999, 1999–2000, and 2000–2001. 2. Also in Exhibit 1, compute net income/net revenue (sales) for each of the four years. Begin with 1998. 3. What is the major reason for the change in the answer for Question 2 between 2000 and 2001? To answer this question for each of the two years, take the ratio of the major income statement accounts to net revenues (sales). Cost of sales Research and development Selling, general and administrative expense Provision for income tax 4. Compute return on stockholders’ equity for 2000 and 2001 using data from Exhibits 1 and 2.



In 2009, Sun Microsystems was acquired by Oracle Corporation.

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Exhibit 1 SUN MICROSYSTEMS INC. Summary Consolidated Statement of Income (in millions)

Net revenues ....................................................

2001

2000

1999

1998

Dollars

$18,250

$15,721

$11,806

$9,862

Cost of sales...............................................

10,041

7,549

5,670

4,713

Research and development ......................

2,016

1,630

1,280

1,029

Selling, general and administrative ...........

4,544

4,072

3,196

2,826

Goodwill amortization...............................

261

In-process research and development ......

121

176

Total costs and expenses ..................................

16,939

13,328

10,286

8,748

Operating Income .............................................

1,311

2,393

1,520

1,114

Gain (loss) on strategic investments.................

(90)

208

–

Interest income, net .........................................

363

170

Litigation settlement ........................................

–

Income before taxes .........................................

1,584

2,771

1,605

1,162

Provision for income taxes ...............................

603

917

575

407

Cumulative effect of change in accounting principle, net ..........................

(54)

–

Net income .......................................................

$ 927

$ 1,854

$ 1,030

$ 755

Net income per common share—diluted .........

$ 0.27

$ 0.55

$ 0.31

$ 0.24

Shares used in the calculation of net income per common share—diluted.............................

3,417

3,379

3,282

3,180

Costs and expenses:

5. Analyze your results to Question 4 more completely by computing ratios 1, 2a, 2b, and 3b (all from this chapter) for 2000 and 2001. Actually, the answer to ratio 1 can be found as part of the answer to question 2, but it is helpful to look at it again. What do you think was the main contributing factor to the change in return on stockholders’ equity between 2000 and 2001? Think in terms of the DuPont system of analysis.

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6. The average stock prices for each of the four years shown in Exhibit 1 were as follows: 1998 11¼ 1999

16¾

2000

28½

2001

9½

a. Compute the price/earnings (P/E) ratio for each year. That is, take the stock price shown above and divide by net income per common stock-dilution from Exhibit 1. b. Why do you think the P/E has changed from its 2000 level to its 2001 level? A brief review of P/E ratios can be found under the topic of Price-Earnings Ratio Applied to Earnings per Share in Chapter 2.

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Exhibit 2 SUN MICROSYSTEMS, INC Consolidated Balance Sheets (in millions) Assets

2001

2000

Cash and cash equivalents ..............................................................................

$ 1,472

$ 1,849

Short-term investments ..................................................................................

387

626

2,955

2,690

Inventories.......................................................................................................

1,049

557

Deferred tax assets ..........................................................................................

1,102

673

Prepaids and other current assets ..................................................................

969

482

Total current assets ......................................................................................

$7,934

$6,877

Property, plant and equipment, net....................................................................

2,697

2,095

Long-term investments .......................................................................................

4,677

4,496

2,041

163

832

521

$18,181

$14,152

Current assets:

Accounts receivable, net allowances of $410 in 2001 and $534 in 2000 .................................................................................................

Goodwill, net of accumulated amortization of $349 in 2001 and $88 in 2000 ...................................................................................................... Other assets, net .................................................................................................

Liabilities and Stockholders’ Equity Current liabilities: Short-term borrowings ....................................................................................

Accounts payable ............................................................................................

1,050

924

Accrued payroll-related liabilities....................................................................

488

751

Accrued liabilities and other............................................................................

1,374

1,155

Deferred revenues and customer deposits .....................................................

1,827

1,289

Warranty reserve.............................................................................................

314

211

Income taxes payable ......................................................................................

209

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Total current liabilities .................................................................................

$5,146

$4,546

Deferred income taxes ........................................................................................

744

577

Long-term debt and other obligations ................................................................

1,705

1,720

Total debt .....................................................................................................

$ 7,595

$ 6,843

–

6,238

2,728

Treasury stock, at cost: 288 shares in 2001 and 301 shares in 2000 ..................

(2,435)

(1,438)

Deferred equity compensation ...........................................................................

(73)

(15)

Retained earnings ................................................................................................

6,885

5,959

Accumulated other comprehensive income (loss) ..............................................

(29)

Total stockholders’ equity .................................................................................

$10,586

$7,309

$18,181

$14,152

Commitments and contingencies Stockholders’ equity: Preferred stock, $0.001 par value, 10 shares authorized (1 share which has been designated as Series A Preferred participating stock): no shares issued and outstanding ........................................................................................... Common stock and additional paid-in-capital, $0.00067 par value, 7,200 shares authorized; issued: 3,536 shares in 2001 and 3,495 shares in 2000 .......................

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The book values per share for the same four years discussed in the preceding question were: 1998 1999 2000 2001

$1.18 $1.55 $2.29 $3.26

a. Compute the ratio of price to book value for each year. b. Is there any dramatic shift in the ratios worthy of note?

CP 3-2.

Solution Sun Microsystems

1. Percentage change in net income per common share—diluted 1999 1998

$ 0.31 $ 0.24 $ 0.07 +29.2%

2000 1999

$ 0.55 $ 0.31 $ 0.24 +77.4%

2001 2000

1998

1999

2000

2001

Net income $755 = Net revenues 9,862

$1,030 11,806

$1,854 15,721

$927 18,250

7.66%

8.72%

11.79%

5.08%

$ 0.27 $ 0.55 $–0.28 –50.9%

2. Profit margin

3. Percent of net revenue 2000 Net revenues Cost of sales Research and development S, G, and A Provision for income taxes

$15,721 7,549

2001 48.02%

$18,250 10,041

55.02%

1,630 4,072

10.37 25.90

2,016 4,544

11.05 24.90

917

5.83

603

3.30

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The main problem between 2000 and 2001 was the increase in cost of sales as a percentage of net revenue (48.02 percent to 55.02 percent). 4. Return on stockholders’ equity

Net income  Stockholders' equity

2000

2001

$1,854 7,309

$ 927 10,586

25.37%

8.76%

2000

2001

Net income Net revenues (sales)

11.79%

5.08%

2.a.

Net income Total assets

13.1%

5.10%

2.b.

Net income Sales  Sales Total assets

3.b.

Return on assets 1  Debt/Assets 

11.79%  1.11 5.08%  1.00

13.09%

5.08%

13.09% 1  .484 

5.08% 1  .418

25.37%

8.73%

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The main contributing factor to the decline in the return on stockholders’ equity (25.37 percent to 8.73 percent) was the decline in the profit margin (11.79 percent versus 5.08 percent). The decrease in asset turnover (1.11 to 1.00) made a small contribution to the decline, as did the decline in the debt ratio (48.4 percent to 41.8 percent). 6.a. P/E = Stock price/Net income per common share—diluted (EPS) 1998

1999

2000

2001

Share prices EPS

$11.25 .24

$16.75 .31

$28.50 .55

$9.50 .27

P/E

46.9

54.0

51.8

35.2

b. The sharp decline in performance caused investors to pay a lower multiple for the stock. 7.a. Price to book value = Stock price/book value 1998

1999

2000

2001

Share prices Book value

$11.25 1.18

$16.75 1.55

$28.50 2.29

$9.50 3.26

P/BV

9.53

12.45

2.91

10.81

b. Once again, the sharp falloff in price to book value between 2000 and 2001 can be attributed to the decline in performance (and the impact on the stock prices). Book value was going up, but the ratio declined sharply due to the declining stock prices. Chapter 4 Financial Forecasting

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Discussion Questions 4-1.

What are the basic benefits and purposes of developing pro forma statements and a cash budget?

The pro forma financial statements and cash budget enable the firm to determine its future level of asset needs and the associated financing that will be required. Furthermore, one can track actual events against the projections. Bankers and other lenders also use these financial statements as a guide in credit decisions.

4-2.

Explain how the collections and purchases schedules are related to the borrowing needs of the corporation.

The collections and purchase schedules measure the speed at which receivables are collected and purchases are paid. To the extent collections do not cover purchasing costs and other financial requirements, the firm must look to borrowing to cover the deficit.

4-3.

With inflation, what are the implications of using LIFO and FIFO inventory methods? How do they affect the cost of goods sold?

LIFO inventory valuation assumes the latest purchased inventory becomes part of the cost of goods sold, while the FIFO method assigns inventory items that were purchased first to the cost of goods sold. In an inflationary environment, the LIFO method will result in a higher cost of goods sold figure and one that more accurately matches the sales dollars recorded at current dollars.

4-4.

Explain the relationship between inventory turnover and purchasing needs.

The more rapid the turnover of inventory, the greater the need for purchase and replacement. Rapidly turning inventory makes for somewhat greater ease in foreseeing future requirements and reduces the cost of carrying inventory.

4-5.

Rapid corporate growth in sales and profits can cause financing problems. Elaborate on this statement.

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Rapid growth in sales and profits is often associated with rapid growth in asset commitment. A $100,000 increase in sales may cause a $50,000 increase in assets, with perhaps only $10,000 of the new financing coming from profits. It is very seldom that incremental profits from sales expansion can meet new financing needs.

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4-6.

Discuss the advantage and disadvantage of level production schedules in firms with cyclical sales.

Level production in a cyclical industry has the advantage of allowing for the maintenance of a stable workforce and reducing inefficiencies caused by shutting down production during slow periods and accelerating work during crash production periods. A major drawback is that a large stock of inventory may be accumulated during the slow sales period. This inventory may be expensive to finance, with an associated danger of obsolescence.

4-7.

What conditions would help make a percent-of-sales forecast almost as accurate as pro forma financial statements and cash budgets?

The percent-of-sales forecast is only as good as the functional relationship of assets and liabilities to sales. To the extent that past relationships accurately depict the future, the percent-of-sales method will give values that reasonably represent the values derived through the pro forma statements and the cash budget.

Problems 1.

Growth and financing (LO4) Mr. Miyagi is very excited because sales for his nursery and plant company are expected to double from $600,000 to $1,200,000 next year. Mr. Miyagi notes that net assets (Assets — Liabilities) will remain at 50 percent of sales. His firm will enjoy an 8 percent return on total sales. He will start the year with $120,000 in the bank and is bragging about the Jaguar and luxury townhouse he will buy. Does his optimistic outlook for his cash position appear to be correct? Compute his likely cash balance or deficit for the end of the year. Start with beginning cash and subtract the asset buildup (equal to 50 percent of the sales increase) and add in profit.

4-1. Solution: Mr. Miyagi Beginning cash

$120,000

– Asset buildup

(300,000)

(1/2 × $600,000)

Profit

96,000

(8% × $1,200,000)

Ending cash

($84,000)

Deficit

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No, he will actually end up with a negative cash balance.

4-2.

Growth and financing (LO4) Franck Eggelhoffer expects the sales for his clothing company to be $650,000 next year. Franck notes that net assets (Assets – Liabilities) will remain unchanged. His clothing firm will enjoy a 12 percent return on total sales. He will start the year with $250,000 in the bank. What will Franck's ending cash balance be?

Solution: Franck Eggelhoffer Beginning cash No asset buildup Profit Ending cash

$250,000 ----78,000(12% × $650,000) $328,000

The lesson to be learned is that increased sales can increase the financing requirements and reduce cash even for a profitable firm.

Growth and financing (LO4) Galehouse Gas Stations Inc. expects sales to increase from $1,550,000 to $1,750,000 next year. Galehouse believes that net assets (Assets  Liabilities) will represent 50 percent of sales. Her firm has an 8 percent return on sales and pays 45 percent of profits out as dividends. a. What effect will this growth have on funds? b. If the dividend payout is only 25 percent, what effect will this growth have on funds?

4-3.

Solution: Galehouse Gas Stations Inc. a. Asset buildup Profit Dividends

($100,000)(50% × $200,000) 140,000 (8% × $1,750,000) (63,000)(45% × $140,000)

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Change in cash

($23,000)

The cash balance will reduce by $23,000. b. Dividends would only be $35,000 (25% × $140,000). The change in cash would be a positive $5,000. Asset buildup Profit Dividends Change in cash

($100,000) 140,000 (35,000) $5,000

The cash balance will increase by $5,000. 4.

Sales projections (LO2) The Alliance Corp. expects to sell the following number of units of copper cables at the prices indicated, under three different scenarios in the economy. The probability of each outcome is indicated. What is the expected value of the total sales projection?

Outcome A B C

4-4.

Probability 0.70 0.10 0.20

Units 225 370 510

Price $20 35 45

Solution: Alliance Corporation (1)

(2)

(3)

(4)

(5)

(6) Expected Value (2 × 5)

Outcome

Probability

Units

Price

Total Value

0.70

225

$20

$4,500 $3,150

0.10

370

$35

12,950

1,295

0.20

510

$45

22,950

4,590

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Total expected value

Sales projections (LO2) Bronco Truck Parts expects to sell the following number of units at the prices indicated under three different scenarios in the economy. The probability of each outcome is indicated. What is the expected value of the total sales projection?

Outcome A B C

4-5.

$9,035

Probability 0.40 0.10 0.50

Units 350 600 1,050

Price $21 $30 $35

Solution: Bronco Truck Parts (1)

(2)

(3)

(4)

4-6.

(6) Expected Value (2 × 5)

Outcome

Probability

Units

Price

Total Value

0.40

350

$21

$7,350

$ 2,940

0.10

600

18,000

1,800

0.50

1,050

36,750

18,375

Total expected value

(5)

$23,115

Sales projections (LO2) Cyber Security Systems had sales of 3,500 units at $75 per unit last year. The marketing manager projects a 30 percent increase in unit volume sales this year with a 40 percent price increase. Returned merchandise will represent 8 percent of total sales. What is your net dollar sales projection for this year?

Solution:

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Cyber Security Systems

4-7.

Unit volume 3,500 × 1.30 .........................

4,550

Price

$75 × 1.40………………… ..........

× $105

Total sales…………………………. ......................

$477,750

Returns (8%)……………………….. ....................

38,220

Net Sales…………………………….......................

$439,530

Sales projections (LO2) Dodge Ball Bearings had sales of 15,000 units at $35 per unit last year. The marketing manager projects a 15 percent increase in unit volume sales this year with a 20 percent price decrease (due to a price reduction by a competitor). Returned merchandise will represent 3 percent of total sales. What is your net dollar sales projection for this year?

Solution: Dodge Ball Bearings

Unit volume 15,000 × 1.15 .......................

17,250

Price

$35 × 0.80 .............................

× $28

Total sales ..................................................

$483,000

Returns (3%)...............................................

14,490

Net Sales ....................................................

$468,510

Production requirements (LO2) Sales for Gonzales Pro’s Sports Equipment are expected to be 4,800 units for the coming month. The company likes to maintain 10 percent of unit sales for each month in ending inventory. Beginning inventory is 300 units. How many units should the firm produce for the coming month?

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4-8.

Solution: Gonzales Pro’s Sports Equipment + Projected sales ..................

4-9.

4,800 units

+ Desired ending inventory ..

480 (10% × 4,800)

– Beginning inventory...........

300

Units to be produced .........

4,980

Production requirements (LO2) Vitale Hair Spray had sales of 13,000 units in March. A 70 percent increase is expected in April. The company will maintain 30 percent of expected unit sales for April in ending inventory. Beginning inventory for April was 650 units. How many units should the company produce in April?

Solution: Vitale Hair Spray + Projected sales ............................ 22,100 units (13,000 × 1.70) + Desired ending inventory ............ 6,630 (30% × 22,100) – Beginning inventory ....................

650

Units to be produced ..................... 28,080

10.

Production requirements (LO2) Mario & Luigi Plumbing Company has beginning inventory of 22,500 units, will sell 67,000 units for the month, and desires to reduce ending inventory to 25 percent of beginning inventory. How many units should they produce?

4-10. Solution:

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Mario & Luigi Plumbing Company

11.

+ Projected sales ............................

67,000 units

+ Desired ending inventory ............

5,625 (25% × 22,500)

– Beginning inventory ....................

22,500

Units to be produced .....................

50,125

Cost of goods sold—FIFO (LO2) On December 31 of last year, Wolfson Corporation had an inventory of 450 units of its product, which cost $22 per unit to produce. During January, the company produced 850 units at a cost of $25 per unit. Assuming that Wolfson Corporation sold 800 units in January, what was the cost of goods sold? (Assume FIFO inventory accounting.)

4-11. Solution: Wolfson Corporation Cost of goods sold on 800 units Old inventory: Quantity (units)................... 450 Cost per unit .......................$ 22 Total....................................$ 9,900 New inventory: Quantity (units)................... 350 Cost per unit .......................$ 25 Total $ 8,750 Total cost of goods sold ........$18,650

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12.

Cost of goods sold—FIFO (LO2) At the end of January, Higgins Data Systems had an inventory of 650 units, which cost $16 per unit to produce. During February, the company produced 950 units at a cost of $19 per unit. If the firm sold 1,150 units in February, what was its cost of goods sold? (Assume LIFO inventory accounting.)

4-12. Solution: Higgins Data System Cost of goods sold on 1,150 units New inventory: Quantity (units) ............... 950 Cost per unit .................... $ 19 Total ................................ $18,050 Old inventory: Quantity (units) ............... 200 Cost per unit .................... $ 16 Total ................................ $ 3,200 Total cost of goods sold .... $21,250

13.

Cost of goods sold—LIFO and FIFO (LO2) At the end of January, Mineral Labs had an inventory of 775 units, which cost $12 per unit to produce. During February, the company produced 900 units at a cost of $16 per unit. If the firm sold 1,500 units in February, what was the cost of goods sold? a. Assume LIFO inventory accounting. b. Assume FIFO inventory accounting.

4-13. Solution:

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Mineral Labs a. LIFO Accounting Cost of goods sold on 1,500 units New inventory: Quantity (units) ............... 900 Cost per unit ............... $ 16 Total .............. $14,400 Old inventory: Quantity (units) ............... 600 Cost per unit ............... $ 12 Total ...............$ 7,200 Total cost of goods sold .............. $21,600 b. FIFO Accounting Cost of goods sold on 1,000 units Old inventory: Quantity (units) ................. 775 Cost per unit ............... $ 12 Total ...............$ 9,300 New inventory: Quantity (units) ............... 725 Cost per unit ............... $ 16 Total .............. $11,600 Total cost of goods sold .............. $20,900 14.

Gross profit and ending inventory (LO2) Convex Mechanical Supplies produces a product with the following costs as of July 1, 20X1:

Material ............................

Labor .................................

Overhead ..........................

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$12 Beginning inventory at these costs on July 1 was 5,000 units. From July 1 to December 1, Convex produced 15,000 units. These units had a material cost of $10 per unit. The costs for labor and overhead were the same. Convex uses FIFO inventory accounting. Assuming that Convex sold 17,000 units during the last six months of the year at $20 each, what would gross profit be? What is the value of ending inventory?

4-14. Solution: Convex Mechanical Supplies Sales (17,000 @ $20)

$340,000

Cost of goods sold: Old inventory: Quantity (units) ................. Cost per unit......................

5,000 $

Total ....................................

$ 60,000

New inventory: Quantity (units) .................

12,000

Cost per unit......................

Total .................................... Total cost of goods sold.................................... Gross profit .........................

$192,000

$252,000 $ 88,000

Value of ending inventory:

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Beginning inventory (5,000 @ $12)....................

$ 60,000

+ Total production (15,000 @ $16)..................

$240,000

Total inventory available for sale ...............

$300,000

– Cost of goods sold ............

$252,000

Ending inventory .................

$ 48,000

or 3,000 units @ $16 = $48,000

15.

Gross profit and ending inventory (LO2) The Bradley Corporation produces a product with the following costs as of July 1, 20X1: Material ...................

$5 per unit

Labor ........................

3 per unit

Overhead

1 per unit

Beginning inventory at these costs on July 1 was 3,700 units. From July 1 to December 1, 20X1, Bradley produced 13,400 units. These units had a material cost of $2, labor of $3, and overhead of $4 per unit. Bradley uses LIFO inventory accounting. Assuming that Bradley sold 15,800 units during the last six months of the year at $14 each, what is its gross profit? What is the value of ending inventory?

4-15. Solution: Bradley Corporation (Continued) Sales (15,800 @ $14) Cost of goods sold:

$221,200

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New inventory: Quantity (units)............ Cost per unit ................ Total .............................. Old inventory: Quantity (units)............ Cost per unit ................ Total .............................. Total cost of goods sold............................. Gross profit .................... Value of ending inventory: Beginning inventory (3,700  $9) ................. + Total production (13,400  $9) ............... Total inventory available for sale .......... – Cost of goods sold ..... Ending inventory ...........

13,400 $ 9 $120,600 2,400 $ 9 $ 21,600 $142,200 $ 79,000

$ 33,300

$120,600 $153,900 $142,200 $ 11,700

OR 1,300 units  $9 = $11,700

16.

Gross profit and ending inventory (LO2) Sprint Shoes Inc. had a beginning inventory of 9,250 units on January 1, 20X1. Costs associated with the inventory: Material ...................

$15.00 per unit

Labor ........................

8.00 per unit

Overhead .................

7.10 per unit

During 20X1, the firm produced 43,000 units with the following costs: Material ...................

$17.50 per unit

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Labor ........................

8.80 per unit

Overhead .................

10.30 per unit

Sales for the year were 47,350 units at $44.60 each. Sprint Shoes uses LIFO accounting. What was the gross profit? What was the value of ending inventory?

4-16. Solution: Sprint Shoes Inc. Sales (47,350 @ $44.60) Cost of goods sold: New inventory: Quantity (units) Cost per unit ................ $ Total .............................. Old inventory: Quantity (units) ........... Cost per unit ................ $ Total .............................. Total cost of goods sold .............................. Gross profit ................... Value of ending inventory: Beginning inventory (9,250  $30.10) .......... + Total production (43,000  $36.60)......... Total inventory available for sale .......... – Cost of goods sold ..... Ending inventory ...........

$2,111,810

43,000 36.60 $1,573,800 4,350 30.10 $ 130,935 $1,704,735 $ 407,075

$ 278,425

$1,573,800 $1,852,225 $1,704,735 $ 147,490

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4,900 units  $30.10 = $147,490 17.

Schedule of cash receipts (LO2) J. Lo’s Clothiers has forecast credit sales for the fourth quarter of the year as: September (actual) ................................. Fourth Quarter

$70,000

October ...................................................

$60,000

November ...............................................

55,000

December ...............................................

80,000

Experience has shown that 30 percent of sales are collected in the month of sale, 60 percent in the following month, and 10 percent are never collected. Prepare a schedule of cash receipts for J. Lo’s Clothiers covering the fourth quarter (October through December).

4-17. Solution: J. Lo’s Clothiers Septembe October November December r Credit sales 30% collected in month of sales 60% collected in month after sales Total cash receipts

$70,000 $60,000

$55,000

$80,000

18,000

16,500

24,000

42,000

36,000

33,000

$60,000

$52,500

$57,000

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18.

Schedule of cash receipts (LO2) Simpson Glove Company has made the following sales projections for the next six months. All sales are credit sales.

March ..................................

$41,000

April.....................................

50,000

May .....................................

32,000

June .....................................

47,000

July ......................................

58,000

August .................................

62,000

Sales in January and February were $41,000 and $39,000, respectively. Experience has shown that of total sales receipts 10 percent are uncollectible, 40 percent are collected in the month of sale, 30 percent are collected in the following month, and 20 percent are collected two months after sale. Prepare a monthly cash receipts schedule for the firm for March through August.

18.

Solution: Simpson Glove Company Cash Receipts Schedule March $41,000

April $50,000

May June July August $32,000 $47,000 $58,000 $62,000

Collections (40% of current sales)

16,400

20,000

12,800

18,800

23,200

24,800

Collections (30% of prior month’s sales)

11,700

12,300

15,000

9,600

14,100

17,400

Collections (20% of sales 2 months earlier)

8,200

7,800

8,200

10,000

6,400

9,400

Total cash receipts

$36,300

$40,100

Sales

Jan $41,000

Feb $39,000

$36,000 $38,400 $43,700 $51,600

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Schedule of cash receipts (LO2) Watt’s Lighting Stores made the following sales projection for the next six months. All sales are credit sales. March ..................................

$35,000

April.....................................

41,000

May .....................................

30,000

June .....................................

39,000

July ......................................

47,000

August .................................

49,000

Sales in January and February were $38,000 and $37,000, respectively. Experience has shown that of total sales, 10 percent are uncollectible, 30 percent are collected in the month of sale, 40 percent are collected in the following month, and 20 percent are collected two months after sale. Prepare a monthly cash receipts schedule for the firm for March through August. Of the sales expected to be made during the six months from March through August, how much will still be uncollected at the end of August? How much of this is expected to be collected later?

4-19. Solution: Watt’s Lighting Stores Cash Receipts Schedule March

April

May

June

July

August

$35,00 0

$41,00 0

$30,00 0

$39,00 0

$47,00 0

$49,00 0

Collection s (30% of current sales)

10,500

12,300

9,000

11,700

14,100

14,700

Collection s (40% of prior month’s

14,800

14,000

16,400

12,000

15,600

18,800

Sales

Januar Februar y y $38,00 $37,000 0

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sales) Collection s (20% of sales 2 months earlier)

7,600

7,400

7,000

8,200

6,000

7,800

Total cash receipts

$32,90 0

$33,70 0

$32,40 0

$31,90 0

$35,70 0

$41,30 0

Still due (uncollected) in August: Bad debts: ($35,000 + 41,000 + 30,000 + 39,000 + 47,000 + 49,000) × 0.1 = (241,000) × 0.1 = $24,100 To be collected from July sales: ($47,000 × 0.20) = $9,400 To be collected from August sales: ($49,000 × 0.60) = $29,400 $24,100 + $9,400 + $29,400 = $62,900 due Expected to be collected: $62,900 due – $24,100 bad debts = $38,800 20.

Schedule of cash payments (LO2) Ultravision Inc. anticipates sales of $290,000 from January through April. Materials will represent 50 percent of sales, and because of level production, material purchases will be equal for each month during the four months of January, February, March, and April. Materials are paid for one month after the month purchased. Materials purchased in December of last year were $25,000 (half of $50,000 in sales). Labor costs for each of the four months are slightly different due to a provision in the labor contract in which bonuses are paid in February and April. Here are the labor figures: January ................................

$15,000

February ..............................

18,000

March ..................................

15,000

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April.....................................

20,000

Fixed overhead is $11,000 per month. Prepare a schedule of cash payments for January through April.

4-20. Solution:

Ultravision Inc. Cash Payment Schedule Dec.

Jan.

Feb.

March

April

$25,000

$36,250

** Payment to material purchases

25,000

36,250

Labor

15,000

18,000

15,000

20,000

Fixed overhead

11,000

Total cash payments

$51,000

$65,250

$62,250

$67,250

* Purchases

For January through April

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* Monthly purchases equal ($290,000  50%)/4 or $145,000/4  $36,250 ** Payment is equal to prior month’s purchases.

21.

Schedule of cash payments (LO2) The Denver Corporation has forecast the following sales for the first seven months of the year: January………..............

$15,000

May………

$15,000

February………............

17,000

June………

21,000

March………................

19,000

July……..

23,000

April……… ..................

25,000

Monthly material purchases are set equal to 40 percent of forecast sales for the next month. Of the total material costs, 50 percent are paid in the month of purchase and 50 percent in the following month. Labor costs will run $4,500 per month, and fixed overhead is $4,500 per month. Interest payments on the debt will be $3,500 for both March and June. Finally, the Denver salesforce will receive a 3.00 percent commission on total sales for the first six months of the year, to be paid on June 30. Prepare a monthly summary of cash payments for the six-month period from January through June. (Note: Compute prior December purchases to help get total material payments for January.)

4-21. Solution: Denver Corporation Cash Payments Schedule Dec. Sales Purchases (40% of next month’s sales) Payment (50% of current purchases)

6,000

Jan.

Feb.

March

April

May

June

July

$15,000

$17,000 $19,000

$25,000

$15,000

$21,000

$23,000

6,800

7,600

10,000

6,000

8,400

9,200

3,400

3,800

5,000

3,000

4,200

4,600

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Material payment (50% of previous month’s purchases)

3,000

3,400

3,800

5,000

3,000

4,200

Total payment for materials

6,400

7,200

8,800

8,000

7,200

8,800

Labor costs

4,500

Fixed overhead

4,500

3,500

Interest payments

3,500 3,360

Sales commission (3.00% of $112,000) Total payments

$15,400

$16,200 $21,300

$17,000

$16,200

$24,660

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22.

Schedule of cash payments (LO2) Wright Lighting Fixtures forecasts its sales in units for the next four months as follows: March

4,000

April

10,000

May

8,000

June

6,000

Wright maintains an ending inventory for each month in the amount of one and one-half times the expected sales in the following month. The ending inventory for February (March’s beginning inventory) reflects this policy. Materials cost $7 per unit and are paid for in the month after production. Labor cost is $3 per unit and is paid for in the month incurred. Fixed overhead is $10,000 per month. Dividends of $14,000 are to be paid in May. Eight thousand units were produced in February. Complete a production schedule and a summary of cash payments for March, April, and May. Remember that production in any one month is equal to sales plus desired ending inventory minus beginning inventory.

4-22. Solution: Wright Lighting Fixtures Production Schedule March

April

May

June

Forecasted unit sales

4,000

10,000

8,000

+ Desired ending inventory

15,000

12,000

9,000

– Beginning inventory

6,000

15,000

12,000

Units to be produced

13,000

7,000

5,000

6,000

Cash Payments Feb Units produced Materials ($7/unit) month after production

8,000

March

April

May

13,000

7,000

5,000

$56,000

$91,000

$49,000

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Labor ($3/unit) month of production Fixed overhead

39,000

21,000

15,000

10,000

Dividends

14,000

Total cash payments

23.

$105,000

$122,000

$88,000

Schedule of cash payments (LO2) The Volt Battery Company has forecast its sales in units as follows: January………..............

1,300

May………

1,850

February………............

1,150

June………

2,000

March………................

1,100

July………

1,700

April……… ..................

1,600

Volt Battery always keeps an ending inventory equal to 110 percent of the next month’s expected sales. The ending inventory for December (January’s beginning inventory) is 1,460 units, which is consistent with this policy. Materials cost $14 per unit and are paid for in the month after purchase. Labor cost is $7 per unit and is paid in the month the cost is incurred. Overhead costs are $8,500 per month. Interest of $8,500 is scheduled to be paid in March, and employee bonuses of $13,700 will be paid in June. Prepare a monthly production schedule and a monthly summary of cash payments for January through June. Volt produced 1,100 units in December.

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4-23. Solution: Volt Battery Company Production Schedule Jan.

Feb.

March

April

May

June

Forecasted unit sales

1,300

1,150

1,100

1,600

1,850

2,000

+ Desired ending inventory

1,265

1,210

1,760

2,035

2,200

1,870

– Beginning inventory

1,460

1,265

1,210

1,760

2,035

2,200

= Units to be produced

1,105

1,095

1,650

1,875

2,015

1,670

July 1,700

Summary of Cash Payments Jan. 1,105

Feb. 1,095

Material cost ($12/unit) month after purchase

$ 15,400

$ 15,470

Labor cost ($5/unit) month incurred

7,735

7,665

11,550

13,125

14,105

11,690

Overhead cost

8,500

Units produced

Dec. 1,100

March 1,650

April 1,875

May 2,015

June 1,670

$ 15,330 $23,100 $26,250

$28,210

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Interest

8,500

Employee bonuses Total cash payments

13,700 $31,635

$31,635

$43,880 $44,725 $48,855

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$62,100

24.

Cash Budget (LO2) Graham Potato Company has projected sales of $12,000 in September, $15,000 in October, $22,000 in November, and $18,000 in December. Of the company’s sales, 30 percent are paid for by cash and 70 percent are sold on credit. Experience shows that 40 percent of accounts receivable are paid in the month after the sale, while the remaining 60 percent are paid two months after. Determine collections for November and December. Also assume Graham’s cash payments for November and December are $18,500 and $11,000, respectively. The beginning cash balance in November is $5,000, which is the desired minimum balance. Prepare a cash budget with borrowing needed or repayments for November and December. (You will need to prepare a cash receipts schedule first.)

4-24. Solution: Graham Potato Company Cash Receipts Schedule September

October

November

December

Sales

$12,000

$15,000

$22,000

$18,000

Credit sales (70%)

8,400

10,500

15,400

12,600

Cash sales (30%)

3,600

4,500

6,600

5,400

Collections in month after sales (40%)

4,200

6,160

Collections two months after sales (60%)

5,040

6,300

Total cash

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receipts

$15,840

$17,860

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Graham Potato Company (Continued) Cash Budget November

December

Cash receipts

$ 15,840

$17,860

Cash payments

18,500

11,000

Net cash flow

(2,660)

6,860

Beginning cash balance

5,000

Cumulative cash balance

2,340

11,860

Monthly loan (or repayment)

2,660

(2,660)

Ending cash balance

$ 5,000

$ 9,200

2,660

-0-

Cumulative loan balance

25.

Complete cash budget (LO2) Jayden’s Carryout Stores has eight locations. The firm wishes to expand by two more stores and needs a bank loan to do this. Mrs. Wilson, the banker, will finance construction if the firm can present an acceptable three-month financial plan for January through March. The following are actual and forecasted sales figures: Actual

Forecast

November ............. $260,000

January.............. $400,000

December .............

February............ 440,000

340,000

Additional Information April forecast......... $400,000

March……… ....... 410,000

Of the firm’s sales, 60 percent are for cash and the remaining 40 percent are on credit. Of credit sales, 20 percent are paid in the month after sale and 80 percent are paid in the second month after the sale. Materials cost 20 percent of sales and are purchased and received each month in an amount sufficient to cover the following month’s expected sales. Materials are paid for in the

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month after they are received. Labor expense is 50 percent of sales and is paid for in the month of sales. Selling and administrative expense is 15 percent of sales and is also paid in the month of sales. Overhead expense is $31,000 in cash per month. Depreciation expense is $10,600 per month. Taxes of $8,600 will be paid in January, and dividends of $5,000 will be paid in March. Cash at the beginning of January is $92,000, and the minimum desired cash balance is $87,000. For January, February, and March, prepare a schedule of monthly cash receipts, monthly cash payments, and a complete monthly cash budget with borrowings and repayments.

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4-25. Solution: Jayden’s Carry-Out Stores Cash Receipts Schedule November December

January

Sales

$260,000

$340,000

$ $440,000 $410,000 $400,000 400,000

Cash sales (60%)

156,000

204,000

240,000

264,000

246,000

240,000

Credit sales (40%)

104,000

136,000

160,000

176,000

164,000

160,000

20,800

27,200

32,000

35,200

32,800

83,200

108,800

128,000

140,800

Collections (month after credit sales) 20% Collections (two months after credit sales) 80% Total cash receipts

February

March

$350,400 $404,800 $409,200

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April

Jayden’s Carry-Out Stores Cash Payments Schedule January

Februar y

March

Payments for purchases (20% of next $ $ 88,000 $82,000 month’s sales paid in month after 80,000 purchases—equivalent to 20% of current sales) ....................................................... Labor expense (50% of sales) .............................. 200,000 220,000 205,000 Selling and Admin. Exp. (15% of sales) ................ 60,000

66,000

61,500

Overhead ............................................................. 31,000

31,000

Taxes ................................................................... 8,600 Dividends .............................................................

5,000

Total cash payments* .......................................... $379,60 $405,00 $384,50 0 0 0

*The $10,600 of depreciation is excluded because it is not a cash expense. Jayden’s Carry-Out Stores Cash Budget January

February

March

Total cash receipts .............................. $350,400

$404,800

$409,200

Total cash payments ........................... 379,600

405,000

384,500

Net cash flow ...................................... (29,200)

(200)

24,700

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Beginning cash balance ....................... 92,000

87,000

Cumulative cash balance .................... 62,800

86,800

111,700

Monthly loan (or 24,200 repayment) .........................................

200

(24,400)

Cumulative loan balance ..................... 24,200

24,400

-0-

Ending cash balance ............................ $ 87,000

$ 87,000

$ 87,300

26.

Complete cash budget (LO2) Archer Electronics Company’s actual sales and purchases for April and May are shown here, along with forecast sales and purchases for June through September.

April (actual) .................................... May (actual)...................................... June (forecast) .................................. July (forecast) ................................... August (forecast) .............................. September (forecast) .........................

Sales

Purchases

$370,000 350,000 325,000 325,000 340,000 380,000

$155,000 145,000 145,000 205,000 225,000 220,000

The company makes 20 percent of its sales for cash and 80 percent on credit. Of the credit sales, 50 percent are collected in the month after the sale, and 50 percent are collected two months later. Archer pays for 20 percent of its purchases in the month after purchase and 80 percent two months after. Labor expense equals 15 percent of the current month’s sales. Overhead expense equals $12,500 per month. Interest payments of $32,500 are due in June and September. A cash dividend of $52,500 is scheduled to be paid in June. Tax payments of $25,500 are due in June and September. There is a scheduled capital outlay of $350,000 in September. Archer Electronics’ ending cash balance in May is $22,500. The minimum desired cash balance is $10,500. Prepare a schedule of monthly cash receipts, monthly cash payments, and a complete monthly cash budget with borrowing and repayments for June through September. The maximum desired cash balance is $50,500. Excess cash (above $50,500) is used to buy marketable securities. Marketable securities are sold before borrowing funds in case of a cash shortfall (less than $10,500).

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4-26. Solution: Archer Electronics Cash Receipts Schedule April Sales  Cash Sales (20%) Credit Sales (80%)

May

June

July

Aug.

Sept.

$370,00 $350,00 $ $325,00 $340,00 $380,00 0 0 325,000 0 0 0 74,000

70,000

65,000

68,000

76,000

296,000 280,000 260,000 260,000 272,000 304,000

 Collectio ns (month after sale) 50%

148,000 140,000 130,000 130,000 136,000

 Collectio ns (second month after sale) 50%

148,000 140,000 130,000 130,000

Total cash receipts

$353,00 $335,00 $328,00 $342,00 0 0 0 0

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Archer Electronics Cash Payments Schedule April

May

June

July

Aug.

Sept.

Purchases $155,00 $145,00 $145,00 $205,00 $225,00 $220,00 0 0 0 0 0 0 Payments (month after purchase —20%)

31,000

29,000

41,000

45,000

Payments (second month after purchase —80%)

124,000 116,000 116,000 164,000

Labor expense (15% of sales)

48,750

51,000

57,000

Overhead

12,500

Interest payments

32,500

Cash dividend

52,500

Taxes

25,500

32,500

25,500

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Capital outlay Total cash payments

350,000 $324,75 $206,25 $220,50 $686,50 0 0 0 0

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Archer Electronics Cash Budget June

July

August

Septembe r

Cash receipts .......................................... $353,00 $335,00 0 0

$328,00 $342,000 0

Cash payments ....................................... 324,750 206,250

220,500

686,500

Net cash flow .......................................... 28,250 128,750

107,500

(344,500)

Beginning cash balance .......................... 22,500 50,500

50,500

Cumulative cash balance ........................ 50,750 179,250

158,000

(294,000)

Monthly borrowing (or -repayment) ............................................

*68,000

Cumulative loan balance ........................ --

68,000

Marketable securities 250 128,750 purchased ...............................................

107,500

(236,500)

Cumulative marketable 250 129,000 securities ................................................

236,500

Ending cash balance ............................... 50,500 50,500

50,500

10,500

(Sold)

*Cumulative Marketable Sec. (Aug) $236,500 Cumulative Cash Balance (Sept) –294,000 Required (ending) Cash Balance –10,500 Monthly Borrowing –$68,000

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Chapter 06: Working Capital and the Financing Decision

27.

Percent-of-sales method (LO3) Owen’s Electronics has nine operating plants in seven Southwestern states. Sales for last year were $100 million, and the balance sheet at yearend is similar in percentage of sales to that of previous years (and this will continue in the future). All assets (including fixed assets) and current liabilities will vary directly with sales. The firm is working at full capacity. Balance Sheet (in $ millions) Assets

Liabilities and Stockholders’ Equity

Cash............................................

Accounts payable .......................

$20

Accounts receivable ...................

Accrued wages ...........................

Inventory ....................................

Accrued taxes .............................

Current assets ...........................

$60

Current liabilities ......................

$40

Fixed assets ................................

Notes payable .............................

Common stock ............................

Retained earnings .......................

Total liabilities and stockholders’ equity .................

$105

Total assets .................................

$105

Owen’s has an after-tax profit margin of 10 percent and a dividend payout ratio of 45 percent. If sales grow by 20 percent next year, determine how many dollars of new funds are needed to finance the growth.

4-27. Solution: Owen’s Electronics At Full Capacity

Spontaneous Assets = Current Assets  Fixed Assets Spontaneous Liabilities = Acc. Pay. + Accrued Wages & Taxes Required New Funds =

A L  S   S  PS2 1  D  S S

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Chapter 06: Working Capital and the Financing Decision

RNF (millions) =

105 40  $20, 000, 000    $20, 000, 000   .10 100 100  $120, 000, 000 1  .45

 1.05  $20, 000, 000   .40  $20, 000, 000   .10  $120, 000, 000 .55   $21, 000, 000  $8, 000, 000  $6, 600, 000 RNF = $6,400,000 28.

Percent-of-sales method (LO3) The Manning Company has financial statements as shown next, which are representative of the company’s historical average. The firm is expecting a 35 percent increase in sales next year, and management is concerned about the company’s need for external funds. The increase in sales is expected to be carried out without any expansion of fixed assets, but rather through more efficient asset utilization in the existing store. Among liabilities, only current liabilities vary directly with sales. Using the percent-of-sales method, determine whether the company has external financing needs, or a surplus of funds. (Hint: A profit margin and payout ratio must be found from the income statement.) Income Statement Sales....................................................................

$250,000

Expenses .............................................................

192,000

Earnings before interest and taxes ....................

$ 58,000

Interest ...............................................................

7,500

Earnings before taxes .........................................

$ 50,500

Taxes...................................................................

15,500

Earnings after taxes ............................................

$ 35,000

Dividends ............................................................

$ 7,000

Balance Sheet Assets

Liabilities and Stockholders’ Equity

Cash ...................................................

$ 8,500

Accounts payable ..............................

$ 26,400

Accounts receivable ..........................

63,000

Accrued wages ..................................

2,350

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Chapter 06: Working Capital and the Financing Decision

Inventory ...........................................

91,000

Accrued taxes ....................................

3,750

Current assets .................................

$162,500

Current liabilities .............................

$ 32,500

Fixed assets .......................................

85,000

Notes payable....................................

7,500

Long-term debt .................................

17,500

Common stock...................................

125,000

Retained earnings .............................

65,000

Total liabilities and Total assets .......................................

$247,500

stockholders’ equity ........................

$247,500

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Chapter 06: Working Capital and the Financing Decision

4-28. Solution: Manning Company

Earnings after taxes $35, 000  14% Sales $250, 000 Dividends $7, 000 Payout ratio =   20% Earnings 35, 000

Profit margin =

Change in Sales  35%  $250, 000  $87,500 SpontaneousAssets  Cash  Acc. Rec.  Inventory Spontaneous Liabilities  Acc. Payable  Accrued Wages & Taxes A L  ΔS   ΔS  PS2 1  D  S S $162,500 $32,500 =  $87,500    $87,500   .14  $337,500 1  .20  $250, 000 $250, 000

RNF =

=.65  $87,500   .13  $87,500   .14  $337,500 .80  = $56,875  $11,375  $37,800 RNF = $7, 700

The firm needs $7,700 in external funds.

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Chapter 06: Working Capital and the Financing Decision

29.

Percent-of-sales method (LO3) Conn Man’s Shops, a national clothing chain, had sales of $350 million last year. The business has a steady net profit margin of 9 percent and a dividend payout ratio of 25 percent. The balance sheet for the end of last year is shown next. Balance Sheet End of Year (in $ millions)

Assets Cash................................................. Accounts receivable ........................ Inventory ......................................... Plant and equipment ........................

$ 25 40 82 133

Total assets ......................................

$280

Liabilities and Stockholders’ Equity Accounts payable ......................... $ 64 Accrued expenses ......................... 31 Other payables ............................. 45 Common stock ............................. 50 Retained earnings ......................... 90 Total liabilities and stockholders’ equity.................. $280

The firm’s marketing staff has told the president that in the coming year there will be a large increase in the demand for overcoats and wool slacks. A sales increase of 20 percent is forecast for the company. All balance sheet items are expected to maintain the same percent-of-sales relationships as last year, except for common stock and retained earnings. No change is scheduled in the number of common stock shares outstanding, and retained earnings will change as dictated by the profits and dividend policy of the firm. (Remember the net profit margin is 9 percent.) a. Will external financing be required for the company during the coming year? b.



What would be the need for external financing if the net profit margin went up to 10.5 percent and the dividend payout ratio was increased to 60 percent? Explain.

This included fixed assets since the firm is at full capacity.

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Chapter 06: Working Capital and the Financing Decision

4-29. Solution: Conn Man’s Shops a.

Required New Funds =

A L  S   S  PS2 1  D  S S

S = 20%  $350,000,000 = $70, 000, 000 RNF 

280 140  $70, 000, 000    $70, 000, 000   .09 350 350  $420, 000, 000 1  .25

 .80  $70, 000, 000   .40  $70, 000, 000   .09

 $420, 000, 000 .75  $56, 000, 000  $28, 000, 000  $28,350, 000 RNF =  $350,000 

A negative figure for required new funds indicates that an excess of funds ($0.35 mil.) is available for new investment. No external funds are needed. b.

RNF  $56,000,000  $28,000,000  .105($420,000,000)  1  .6   $56,000,000  $28,000,000  $17,640,000

= $10,360,000 external funds required The net profit margin increased slightly, from 9 percent to 10.5 percent, which decreases the need for external funding. The dividend payout ratio increased tremendously, however, from 25 percent to 60 percent, necessitating more external financing. The effect of the dividend policy change overpowered the effect of the net profit margin change.

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Chapter 06: Working Capital and the Financing Decision

COMPREHENSIVE PROBLEM Comprehensive Problem 1 Mansfield Corporation (external funds requirement) (LO4) Mansfield Corporation had 20X1 sales of $100 million. The balance sheet items that vary directly with sales and the profit margin are as follows: Percent 5% Cash .................................................................. Accounts receivable .................................................. 15 Inventory ................................................................... 20 Net fixed assets ......................................................... 40 Accounts payable ...................................................... 15 Accruals..................................................................... 10 Profit margin after taxes ............................................ 10% The dividend payout rate is 50 percent of earnings, and the balance in retained earnings at the end of 20X1 was $33 million. Notes payable are currently $7 million. Long-term bonds and common stock are constant at $5 million and $10 million, respectively. a. b.

CP 4-1.

How much additional external capital will be required for next year if sales increase 15 percent? (Assume that the company is already operating at full capacity.) What will happen to external fund requirements if Mansfield Corporation reduces the payout ratio, grows at a slower rate, or suffers a decline in its profit margin? Discuss each of these separately. Prepare a pro forma balance sheet for 20X2 assuming that any external funds being acquired will be in the form of notes payable. Disregard the information in part b in answering this question (that is, use the original information and part a in constructing your pro forma balance sheet).

Solution: Mansfield Corporation

Sales

 .15  $100 million =15 million

Spontaneous assets

 5%  15%  20%  40%  80%

Spontaneous liabilities  15%  10%  25%

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Chapter 06: Working Capital and the Financing Decision

A L  S   S  PS2 1  D  S S  .8  $15 million   .25  $15 million   .10  $115 1  .5 

RNF=

 $12 million  $3.75 million  $5.75 million = $2.5 million

b. If Mansfield reduces the payout ratio, the company will retain more earnings and need less external funds. A slower growth rate means that fewer assets will have to be financed, and in this case, less external funds would be needed. A declining profit margin will lower retained earnings and force Mansfield Corporation to seek more external funds. c.

Balance Sheet—December 31, 20X2 (Dollars in Millions)

Cash.............................. Accounts receivable ..... Inventory ...................... Net fixed assets ............

1 2

$ 5.75 Accounts payable ........ 17.25 Accruals ...................... 23.00 Notes payable .............. 46.00 Long-term bonds ......... Common stock ............ _____ Retained earnings ........ $92.00

$ 17.25 11.50 17.501 5.00 10.00 38.752 $92.00

Original notes payable plus required new funds. This is the plug figure. 20X2 retained earnings (end of 20X1) + PS2 (1 – D)

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Chapter 06: Working Capital and the Financing Decision

Comprehensive Problem 2 Marsh Corporation (financial forecasting with seasonal production) (LO5) The difficult part of solving a problem of this nature is to know what to do with the information contained within a story problem. Therefore, this problem will be easier to complete if you rely on Chapter 4 for the format of all required schedules. The Marsh Corporation makes standard-size 2-inch fasteners, which it sells for $155 per thousand. Mr. Marsh is the majority owner and manages the inventory and finances of the company. He estimates sales for the following months to be: January ............... February ............. March ................. April ................... May ....................

$263,500 (1,700,000 fasteners) $186,000 (1,200,000 fasteners) $217,000 (1,400,000 fasteners) $310,000 (2,000,000 fasteners) $387,500 (2,500,000 fasteners)

Last year Marsh Corporation’s sales were $175,000 in November and $232,500 in December (1,500,000 fasteners). Mr. Marsh is preparing for a meeting with his banker to arrange the financing for the first quarter. Based on his sales forecast and the following information he has provided, your job as his new financial analyst is to prepare a monthly cash budget, monthly and quarterly pro forma income statements, a pro forma quarterly balance sheet, and all necessary supporting schedules for the first quarter. Past history shows that Marsh Corporation collects 50 percent of its accounts receivable in the normal 30-day credit period (the month after the sale) and the other 50 percent in 60 days (two months after the sale). It pays for its materials 30 days after receipt. In general, Mr. Marsh likes to keep a two-month supply of inventory in anticipation of sales. Inventory at the beginning of December was 2,600,000 units. (This was not equal to his desired twomonth supply.) The major cost of production is the purchase of raw materials in the form of steel rods, which are cut, threaded, and finished. Last year raw material costs were $52 per 1,000 fasteners, but Mr. Marsh has just been notified that material costs have risen, effective January 1, to $60 per 1,000 fasteners. The Marsh Corporation uses FIFO inventory accounting. Labor costs are relatively constant at $20 per thousand fasteners, since workers are paid on a piecework basis. Overhead is allocated at $10 per thousand units, and selling and administrative expense is 20 percent of sales. Labor expense and overhead are direct cash outflows paid in the month incurred, while interest and taxes are paid quarterly. The corporation usually maintains a minimum cash balance of $25,000, and it puts its excess cash into marketable securities. The average tax rate is 40 percent, and Mr. Marsh usually pays out 50 percent of net income in dividends to stockholders. Marketable securities are sold before funds are borrowed when a cash shortage is faced. Ignore the interest on any short-term borrowings. Interest on the long-term debt is paid in March, as are taxes and dividends.

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Chapter 06: Working Capital and the Financing Decision

As of year-end, the Marsh Corporation balance sheet was as follows: MARSH CORPORATION Balance Sheet December 31, 20X1 Assets Current assets: Cash.............................................................. Accounts receivable ..................................... Inventory ...................................................... Total current assets ................................... Fixed assets: Plant and equipment ..................................... Less: Accumulated depreciation ............... Total assets ..................................................... Liabilities and Stockholders’ Equity Accounts payable ........................................... Notes payable ................................................. Long-term debt, 8 percent .............................. Common stock ............................................... Retained earnings ........................................... Total liabilities and stockholders’ equity .......

30,000 320,000 237,800 $ 587,800 1,000,000 200,000

800,000 $1,387,800

93,600 0 400,000 504,200 390,000 $1,387,800

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Chapter 06: Working Capital and the Financing Decision

CP 4-2.

Solution: Marsh Corporation Forecasting with Seasonal Production Dec.

Jan.

Feb.

Mar.

Projected unit sales

1,500,000

1,700,000

1,200,000

1,400,000

+ Desired ending inventory (2 months supply)

2,900,000

2,600,000

3,400,000

4,500,000

 Beginning inventory

2,600,000

2,900,000

2,600,000

3,400,000

Units to be produced

1,800,000

1,400,000

2,000,000

2,500,000

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Chapter 06: Working Capital and the Financing Decision

CP 4-2. (Continued) Monthly Cash Payments Dec.

Jan.

1,800,000

1,400,000

2,000,000 2,500,000

Materials (from previous month)

$ 93,600

$ 84,000 $ 120,000

Labor ($20 per thousand units)

$ 28,000

$ 40,000 $ 50,000

Overhead ($10 per thousand units)

$ 14,000

$ 20,000 $ 25,000

Selling & adm. expense (20% of sales)

$ 52,700

$ 37,200

Units to be produced

Feb.

Mar.

$ 43,400

Interest

$ 8,000

Taxes (40% tax rate)

$ 64,560*

Dividends

$ 48,420*

Total payments

$188,300

$181,200

$ 359,380

*See the pro forma income statement, which follows this material later on, for the development of these values.

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Chapter 06: Working Capital and the Financing Decision

Marsh Corporation Monthly Cash Receipts

Nov.

Dec.

Jan.

Feb.

Mar.

$175,000

$232,500

$263,500

$186,000

$217,000

87,500

116,250

131,750

93,000

Collections (50% of 2 months earlier)

87,500

116,250

131,750

Total collections

$203,750

$248,000

$224,750

Sales Collections (50% of previous month)

Monthly Cash Flow January

February

March

Cash receipts

$203,750

$248,000

$224,750

Cash payments

188,300

181,200

359,380

Net cash flow

15,450

66,800

(134,630)

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Chapter 06: Working Capital and the Financing Decision

Marsh Corporation Cash Budget Net cash flow Beginning cash balance Cumulative cash balance Loans (and repayments) Cumulative loans Marketable securities Cumulative marketable securities Ending cash balance

January $15,450 30,000 $45,450 -0-020,450 20,450

February $66,800 25,000 $91,800 -0-066,800 87,250

March $(134,630) 25,000 ($109,630) 47,380 47,380 (87,250) -0-

$25,000

Marsh Corporation Pro Forma Income Statement Jan.

Feb.

Mar.

Total

Sales

$263,500

$186,000

$217,000

$666,500

Cost of goods sold

139,400

98,400

126,000

363,800

Gross profit

124,100

87,600

91,000

302,700

Selling and admin. expense

52,700

37,200

43,400

133,300

Interest expense

2,667

2,666

8,000

$ 68,733

$ 47,733

$ 44,934

$161,400

27,493

19,093

17,974

64,560

$ 41,240

$ 28,640

$ 26,960

$ 96,840

Net profit before tax Taxes Net profit after tax

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Chapter 06: Working Capital and the Financing Decision

Less: common dividends

48,420

Increase in retained earnings

$ 48,420

Marsh Corporation Cost of Goods Sold

Material ........... Labor ................ Overhead .........

Unit Cost per Thousand before January 1st $52 20 10 $82

Unit Cost per Thousand after January 1st $60 20 10 $90

Ending inventory as of December 31 was 2,900,000; therefore, sales for January and February had a cost of goods sold per thousand units of $82, and March sales reflect the increased cost of $90 per thousand units using FIFO inventory methods. Pro Forma Balance Sheet (March) Assets Current assets: Cash Accounts receivable Inventory Plant & equip: net plan

Liabilities & Stockholders’ Equity Current liabilities: $ 25,000 Accounts payable 310,000 Notes payable 405,000 Long-term debt 800,000 Stockholders’ equity: common stock

$ 150,000 47,380 400,000 504,200

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Retained earnings, total liabilities, & stockholders’ equity Total assets

$1,540,000

438,420

$1,540,000

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Explanation of Changes in the Balance Sheet: Cash = Ending cash balance from cash budget in March $217,000

Accounts receivable = all of March sales plus 50% of Feb. sales

93,000 $310,000

Inventory = ending inventory in March of 4,500,000 units at $90 per thousand Plant and equipment did not change since we did not include depreciation.

RE  Old RE   NI  dividends   $390,000   $96,840  $48,240  $438,420

Chapter 5 Operating and Financial Leverage Discussion Questions 5-1.

Discuss the various uses for break-even analysis.

Such analysis allows the firm to determine at what level of operations it will break even (earn zero profit) and to explore the relationship between volume, costs, and profits.

5-2.

What factors would cause a difference in the use of financial leverage for a utility company and an automobile company?

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Chapter 06: Working Capital and the Financing Decision

A utility is in a stable, predictable industry and therefore can afford to use more financial leverage than an automobile company, which is generally subject to the influences of the business cycle. An automobile manufacturer may not be able to service a large amount of debt when there is a downturn in the economy.

5-3.

Explain how the break-even point and operating leverage are affected by the choice of manufacturing facilities (labor intensive versus capital intensive).

A labor-intensive company will have low fixed costs and a correspondingly low break-even point. However, the impact of operating leverage on the firm is small and there will be little magnification of profits as volume increases. A capitalintensive firm, on the other hand, will have a higher break-even point and enjoy the positive influences of operating leverage as volume increases.

5-4.

What role does depreciation play in break-even analysis based on accounting flows? Based on cash flows? Which perspective is longer term in nature?

For break-even analysis based on accounting flows, depreciation is considered part of fixed costs. For cash flow purposes, it is eliminated from fixed costs.

The accounting flows perspective is longer term in nature because we must consider the problems of equipment replacement.

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Chapter 06: Working Capital and the Financing Decision

5-5.

What does risk taking have to do with the use of operating and financial leverage?

Both operating and financial leverage imply that the firm will employ a heavy component of fixed cost resources. This is inherently risky because the obligation to make payments remains regardless of the condition of the company or the economy.

5-6.

Discuss the limitations of financial leverage.

Debt can only be used up to a point. Beyond that, financial leverage tends to increase the overall costs of financing to the firm as well as encourage creditors to place restrictions on the firm. The limitations of using financial leverage tend to be greatest in industries that are highly cyclical in nature.

5-7.

How does the interest rate on new debt influence the use of financial leverage? The higher the interest rate on new debt, the less attractive financial leverage is to the firm.

5-8.

Explain how combined leverage brings together operating income and earnings per share. Operating leverage primarily affects the operating income of the firm. At this point, financial leverage takes over and determines the overall impact on earnings per share. A delineation of the combined effect of operating and financial leverage is presented in Table 5-6 and Figure 5-5.

5-9.

Explain why operating leverage decreases as a company increases sales and shifts away from the break-even point. At progressively higher levels of operations than the break-even point, the percentage change in operating income as a result of a percentage change in unit volume diminishes. The reason is primarily mathematical—as we move to increasingly higher levels of operating income, the percentage change from the higher base is likely to be less.

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Chapter 06: Working Capital and the Financing Decision

5-10.

When you are considering two different financing plans, does being at the level where earnings per share are equal between the two plans always mean you are indifferent as to which plan is selected? The point of equality only measures indifference based on earnings per share. Since our ultimate goal is market value maximization, we must also be concerned with how these earnings are valued. Two plans that have the same earnings per share may call for different price-earnings ratios, particularly when there is a differential risk component involved because of debt.

Problems 1.

Break-even analysis (LO2) Shock Electronics sells portable heaters for $45 per unit, and the variable cost to produce them is $27. Ms. Amps estimates that the fixed costs are $100,350. a. b.

5-1.

Compute the break-even point in units. Fill in the following table (in dollars) to illustrate that the break-even point has been achieved.

Sales………………….

____________

– Fixed costs………….

____________

– Total variable costs…

____________

Net profit (loss)……….

____________

Solution: a.

BE 

Fixed costs Pr ice-variable cost per unit

b. Sales – Fixed costs – Total variable costs Net profit (loss) 2.

$250,875 (5,575 units × $45) 100,350 150,525 (5,575 units × $27) $ 0

Break-even analysis (LO2) The Hartnett Corporation manufactures baseball bats with Babe Ruth’s autograph stamped on them. Each bat sells for $35 and has a variable cost of $19. There are $31,200 in fixed costs involved in the production process.

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Chapter 06: Working Capital and the Financing Decision

5-2.

Compute the break-even point in units.

Find the sales (in units) needed to earn a profit of $18,400.

Solution: a. BE

units

Break-even analysis (LO2) Therapeutic Systems sells its products for $13 per unit. It has the following costs:

Rent ............................................

$145,000

Factory labor ..............................

$4.00 per unit

Executives under contract ..........

$186,500

Raw material ..............................

$1.20 per unit

Separate the expenses between fixed and variable costs per unit. Using this information and the sales price per unit of $13, compute the break-even point.

5-3.

Solution:

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Chapter 06: Working Capital and the Financing Decision

Therapeutic Systems

Rent Factory labor Executive under contract Raw materials

Variable Costs (per unit)

Fixed Costs $145,000

$4.00 $186,500 1.20 $5.20

$331,500

BE  4.

FC $331,500 $331,500    42,500 units P  VC $13  $5.20 $7.80

Break-even analysis (LO2) Draw two break-even graphs—one for a conservative firm using laborintensive production and another for a capital-intensive firm. Assuming these companies compete within the same industry and have identical sales, explain the impact of changes in sales volume on both firms’ profits.

5-4.

Solution: Labor-Intensive

Capital-Intensive

Total revenue Revenue and costs

Profits

Total costs

Total costs Profits BE

Variable Cost

Fixed costs Fixed costs

Units produced and sold

The company having the higher fixed costs will have lower variable costs than its competitor since it has substituted capital

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Chapter 06: Working Capital and the Financing Decision

for labor. With a lower variable cost, the high-fixed-cost company will have a larger contribution margin. Therefore, when sales rise, its profits will increase faster than the lowfixed-cost firm, and when the sales decline, the reverse will be true. 5.

5-5.

Break-even analysis (LO2) Eaton Tool Company has fixed costs of $255,000, sells its units for $66, and has variable costs of $36 per unit. a.

Compute the break-even point.

Ms. Eaton comes up with a new plan to cut fixed costs to $200,000. However, more labor will now be required, which will increase variable costs per unit to $39. The sales price will remain at $66. What is the new break-even point?

Under the new plan, what is likely to happen to profitability at very high volume levels (compared to the old plan)?

Solution: a.

BE  

Fixed costs Pr ice  Variable cost per unit $255,000 $255,000   8,500 units $66  $36 $30

Fixed costs Pr ice  Variable cost per unit $200,000 $200,000   7,407 units $66  $39 $27

The break-even level decreases.

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Chapter 06: Working Capital and the Financing Decision

With less operating leverage and a smaller contribution margin, profitability is likely to be less than it would have been at very high volume levels.

Break-even analysis (LO2) Shawn Pen & Pencil Sets Inc. has fixed costs of $80,000. Its product currently sells for $5 per unit and has variable costs of $2.50 per unit. Ms. Bic, the head of manufacturing, proposes to buy new equipment that will cost $400,000 and drive up fixed costs to $120,000. Although the price will remain at $5 per unit, the increased automation will reduce costs per unit to $2.00. As a result of Bic’s suggestion, will the break-even point go up or down? Compute the necessary numbers.

5-6.

Solution:

BE (before) 

BE (after) 

$80,000 $80,000   32,000 units $5.00  $2.50 $2.50

$120,000 $120,000   40,000 units $5.00  $2.00 $3.00

The break-even point will go up. 7.

5-7.

Cash break-even analysis (LO2) Calloway Cab Company determines its break-even strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $530,000, but 5 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $4.90. How many units does the firm need to sell to reach the cash break-even point?

Solution: Cash-related fixed costs = Total fixed costs – Depreciation = $530,000 – 5% ($530,000) = $530,000 – $26,500

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= $503,500

5-8.

Cash break-even analysis (LO2) Air Purifier Inc. computes its break-even point strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $2,450,000, but 15 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $40. How many units does the firm need to sell to reach the cash break-even point?

Solution: Cash-related fixed costs = Total fixed costs – Depreciation = $2,450,000 – 15% (2,450,000) = $2,450,000 – $367,500 = $2,082,500

BE 

5-9.

2,082,500  52, 063 units $40

Cash break-even analysis (LO2) Boise Timber Co. computes its break-even point strictly on the basis of cash expenditures related to fixed costs. Its total fixed costs are $6,500,000, but 10 percent of this value is represented by depreciation. Its contribution margin (price minus variable cost) for each unit is $9. How many units does the firm need to sell to reach the cash break-even point?

Solution: Cash-related fixed costs = Total fixed costs – Depreciation = $6,500,000 – 10% ($6,500,000) = $6,500,000 – $650,000 = $5,850,000

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BE 

10.

$5,850,000  650, 000 units $9

Degree of leverage (LO2 and 5) The Sterling Tire Company’s income statement for 20X1 is as follows:

STERLING TIRE COMPANY Income Statement For the Year Ended December 31, 20X1 Sales (20,000 tires at $60 each)................................... Less: Variable costs (20,000 tires at $30) ................ Fixed costs...................................................... Earnings before interest and taxes (EBIT) .................. Interest expense ........................................................... Earnings before taxes (EBT) ....................................... Income tax expense (30%) .......................................... Earnings after taxes (EAT)..........................................

$1,200,000 600,000 400,000 200,000 50,000 150,000 45,000 $ 105,000

Given this income statement, compute the following: a.

Degree of operating leverage.

Degree of financial leverage.

Degree of combined leverage.

Break-even point in units.

5-10. Solution: Q = 20,000, P = $60, VC = $30, FC = $400,000, I = $50,000

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DOL  

20,000($60  $30) 20,000($60  $30)  $400,000



20,000($30) 20,000($30)  $40,000



$600,000 $600,000   3.00x $600,000  $400,000 $200,000

DFL  

11.

DCL 

BE 

Q(P  VC) Q(P  VC)  FC

EBIT $200,000  EBIT  I $200,000  $50,000 $200,000  1.33x $150,000

Q (P  VC) Q(P  VC)  FC  I



20,000($60  $30) 20,000($60  $30)  $400,000  $50,000



$600,000 $600,000   4x $600,000  $400,000  $50,000 $150,000

$400,000 $400,000   13,333 units $60  $30 $30

Degree of leverage (LO2 and 5) The Harding Company manufactures skates. The company’s income statement for 20X1 is as follows:

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Chapter 06: Working Capital and the Financing Decision

HARDING COMPANY Income Statement For the Year Ended December 31, 20X1 Sales (10,500 skates @ $60 each) ................................. Less: Variable costs (10,500 skates at $25)................... Fixed costs ........................................................... Earnings before interest and taxes (EBIT) .................... Interest expense ............................................................. Earnings before taxes (EBT) ......................................... Income tax expense (30%) ............................................ Earnings after taxes (EAT) ............................................

$630,000 262,500 200,000 167,500 62,500 105,000 31,500 $ 73,500

Given this income statement, compute the following: a. b. c. d.

Degree of operating leverage. Degree of financial leverage. Degree of combined leverage. Break-even point in units (number of skates).

5-11. Solution: Q = 10,500, P = $60, VC = $25, FC = $200,000, I = $62,500 a.

DOL 

Q(P  VC) Q(P  VC)  FC



10,500($60  $25) 10,500($60  $25)  $200,000



10,500($35) 10,500($35)  $200,000



$367,500 $367,500   2.19x $367,500  $200,000 $167,500

EBIT $167,500  EBIT  I $167,500  $62,500 $167,500   1.60x $105,000

DFL 

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12.

DCL 

BE 

Q( P  VC) Q( P  VC)  FC  I



10,500($60  $25) 10,500($60  $25)  $200,000  $62,500



$10,500($35) $367,500   3.50x $10,500($35)  $262,500 $105,000

$200,000 $200, 000   5, 714 skates $60  $25 $35

Break-even point and degree of leverage (LO2 and 5) Healthy Foods Inc. sells 50-pound bags of grapes to the military for $10 a bag. The fixed costs of this operation are $80,000, while the variable costs of grapes are $0.10 per pound. a.

What is the break-even point in bags?

Calculate the profit or loss on 12,000 bags and on 25,000 bags.

What is the degree of operating leverage at 20,000 bags and at 25,000 bags? Why does the degree of operating leverage change as the quantity sold increases?

If Healthy Foods has an annual interest expense of $10,000, calculate the degree of financial leverage at both 20,000 and 25,000 bags.

What is the degree of combined leverage at both sales levels?

5-12. Solution: a.

BE 

$80,000 $80,000   16,000 bags $10  ($0.10  50) $5

b. Sales @ $10 per bag Less: Variables costs ($5) Fixed costs Profit or loss

12,000 bags $120,000 (60,000) (80,000) ($ 20,000)

25,000 bags $250,000 (125,000) (80,000) $ 45,000

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DOL 

DOL at 20,000   DOL at 25,000 

Q( P  VC) Q( P  VC)  FC 20,000($10  $5) 20,000 ($10  $5)  $80,000 $100,000  5.00x $20,00 25,000 ($10  $5) 25,000($10  $5)  $80,000

$125,000  2.78x $45,000 Leverage goes down because we are further away from the break-even point, thus the firm is operating on a larger profit base and leverage is reduced. 

EBIT EBIT  I First determine the profit or loss (EBIT) at 20,000 bags. As indicated in part b, the profit (EBIT) at 25,000 bags is $45,000: DFL 

Sales @ $10 per bag Less: Variable costs ($5) Fixed costs Profit or loss $20,000 DFL at 20,000  $20,000  $10,000

20,000 bags $200,000 100,000 80,000 $ 20,000

 2.0x

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Chapter 06: Working Capital and the Financing Decision

DFL at 25,000 

$45,000 $45,000  $10,000

 1.29x e.

DCL 

Q( P  VC) Q( P  VC)  FC  I

DCL at 20,000   DCL at 25,000  

13.

20,000 ($10  $5) 20,000($10  $5)  $80,000  $10,000 $100,000  10.0x $10,000

25,000 ($10  $5) 25,000($10  $5)  $80,000  $10,000 $125,000  3.57x $35,000

Break-even point and degree of leverage (LO2 and 5) United Snack Company sells 50-pound bags of peanuts to university dormitories for $20 a bag. The fixed costs of this operation are $176,250, while the variable costs of peanuts are $0.15 per pound. a. What is the break-even point in bags? b. Calculate the profit or loss on 7,000 bags and on 20,000 bags. c. What is the degree of operating leverage at 19,000 bags and at 24,000 bags? Why does the degree of operating leverage change as the quantity sold increases? d. If United Snack Company has an annual interest expense of $15,000, calculate the degree of financial leverage at both 19,000 and 24,000 bags. e.

What is the degree of combined leverage at both sales levels?

5-13. Solution: a.

BE 

$176,250 $176, 250   14,100 bags $20  ($.15  50) $12.50

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b. 7,000 bags Sales @ $20 per bag $140,000 Less: Variables costs ($7.50) (52,500) Fixed costs (176,250) Profit or loss (EBIT) ($ 88,750) DOL 

DOL at 19,000  

DOL at 24,000 

20,000 bags $400,000 (150,000) (176,250) $ 73,750

Q( P  VC) Q( P  VC)  FC 19,000($20  $7.50) 19,000 ($20  $7.50)  $176, 250 $237,500  3.88x $61, 250 24,000 ($20  $7.50) 24, 000($20  $7.50)  $176, 250

$300, 000  2.42x $123, 750 Leverage goes down because we are further away from the break-even point, thus the firm is operating on a larger profit base and leverage is reduced. 

DFL 

EBIT EBIT  I

First determine the profit or loss (EBIT) at 19,000 bags and at 24,000 bag: Sales @ $20 per bag Less: Variable costs ($7.50) Fixed costs

19,000 bags 24,000 bags $380,000 $480,000 142,500 180,000 176,250 176,250

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Profit or loss (EBIT)

DFL at 19,000 

$ 61,250

$ 123,750

$61,250 $61, 250  $15, 000

 1.32x DFL at 24,000 

$123,750 $123, 750  $15, 000

 1.14x e.

DCL 

Q( P  VC) Q( P  VC)  FC  I

DCL at 19,000   DCL at 24,000  

14.

19,000 ($20  $7.50) 19,000($20  $7.50)  $176, 250  $15, 000 $237,500  5.14x $46, 250 24,000 ($20  $7.50) 24, 000($20  $7.50)  $176, 250  $15, 000 $300, 000  2.76x $108, 750

Nonlinear breakeven analysis (LO2) International Data System’s information on revenue and costs is relevant only up to a sales volume of 105,000 units. After 105,000 units, the market becomes saturated and the price per unit falls from $14.00 to $8.80. Also, there are cost overruns at a production volume of over 105,000 units, and variable cost per unit goes up from $7.00 to $8.00. Fixed costs remain the same at $55,000. a. Compute operating income at 105,000 units. b. Compute operating income at 205,000 units.

5-14. Solution:

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Sales (105,000  $14) .................................................. $1,470,000

Total variable costs (105,000  $7) .............................

735,000

Fixed costs....................................................................

55,000

Operating income .........................................................

$680,000

b. Sales (205,000  $8.80) ............................................... $1,804,000

15.

Total variable costs (205,000  $8.00) ........................

1,640,000

Fixed costs....................................................................

55,000

Operating income .........................................................

$109,000

Use of different formulas for operating leverage (LO3) U.S. Steal has the following income statement data:

Units Sold 60,000 80,000 a.

Total Variable Costs $ 120,000 160,000

Total Costs $170,000 210,000

Total Revenue $360,000 480,000

Compute DOL based on the following formula:

DOL  b.

Fixed Costs $50,000 50,000

Operating Income (Loss) $190,000 270,000

Percent change in operating income Percent change in units sold

Confirm that your answer to part a is correct by recomputing DOL using Formula 5– 3. There may be a slight difference due to rounding.

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DOL 

Q( P  VC) Q( P  VC)  FC

Q represents beginning units sold (all calculations should be done at this level). P can be found by dividing total revenue by units sold. VC can be found by dividing total variable costs by units sold.

5-15. Solution: a.

DOL 

Percent change in operating income Percent change in units sold

$80, 000 190, 000 42%    1.27 20, 000 33% 60, 000

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DOL  b.

Q( P  VC) Q( P  VC)  FC

Q  60,000 P VC 

Total revenue $360,000   $6 Units sold 60,000 Total variable costs $120,000   $2 Units sold 60,000

FC  $50,000 DOL   16.

60,000 ($6  $2) $240,000  60,000($6  $2)  $50,000 $240,000  $50,000 $240,000  1.26 $190,000

Earnings per share and financial leverage (LO4) Lenow’s Drug Stores and Hall’s Pharmaceuticals are competitors in the discount drug chain store business. The separate capital structures for Lenow and Hall are presented next.

Lenow Debt @ 10% ......................... Common stock, $10 par ....... Total ..................................... Shares ...................................

$100,000 200,000 $300,000 20,000

Hall Debt @ 10% .......................... Common stock, $10 par ........ Total ...................................... Common shares .....................

$200,000 100,000 $300,000 10,000

Compute earnings per share if earnings before interest and taxes are $20,000, $30,000, and $120,000 (assume a 30 percent tax rate).

Explain the relationship between earnings per share and the level of EBIT.

If the cost of debt went up to 12 percent and all other factors remained equal, what would be the break-even level for EBIT?

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5-16. Solution: a. EBIT Less: Interest EBT Less: Taxes @ 30% EAT Shares EPS EBIT Less: Interest EBT Less: Taxes @ 30% EAT Shares EPS EBIT Less: Interest EBT Less: Taxes @ 30% EAT Shares EPS

Lenow $ 20,000 10,000 10,000 3,000 7,000 20,000 $ 0.35 $ 30,000 10,000 20,000 6,000 14,000 20,000 $ 0.70 $120,000 10,000 110,000 33,000 77,000 20,000 $ 3.85

Hall $ 20,000 20,000 0 0 0 10,000 0 $ 30,000 20,000 10,000 3,000 7,000 10,000 $ 0.70 $120,000 20,000 100,000 30,000 70,000 10,000 $ 7.00

b. Before-tax return on assets = 6.67 percent, 10 percent, and 40 percent at the respective levels of EBIT. When the before-tax return on assets (EBIT/Total assets) is less than the cost of debt (10 percent), Lenow does better with less debt than Hall. When before-tax return on assets is equal to the cost of debt, both firms have equal EPS. This would be where the method of financing has a neutral effect on EPS. As return on assets © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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becomes greater than the interest rate, financial leverage becomes more favorable for Hall. c. 17.

12%  $300,000 = $36,000 break-even level for EBIT.

P/E ratio (LO6) The capital structure for Cain Supplies is presented below. Compute the stock price for Cain if it sells at 19 times earnings per share and EBIT is $50,000. The tax rate is 20 percent.

Cain Debt @ 9% .......................... Common stock, $10 par ...... Total ................................ Common shares ...................

$100,000 200,000 $300,000 20,000

5-17. Solution:

EBIT Less: Interest EBT Less: Taxes @ 20% EAT Shares EPS P/E Stock price

18.

Cain $50,000 9,000 $41,000 8,200 $32,800 20,000 $1.64 19x $ 31.16

Leverage and stockholder wealth (LO4) Sterling Optical and Royal Optical both make glass frames, and each is able to generate earnings before interest and taxes of $132,000. The separate capital structures for Sterling and Royal are shown here:

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Sterling Debt @ 12%……………… Common stock, $5 par…… Total……………………… Common shares………….. a. b.

$ 660,000 440,000 $1,100,000 88,000

Royal Debt @ 12%…………… Common stock, $5 par Total…………………… Common shares………...

$ 220,000 880,000 $1,100,000 176,000

Compute earnings per share for both firms. Assume a 25 percent tax rate. In part a, you should have gotten the same answer for both companies’ earnings per share. Assuming a price-earnings (P/E) ratio of 22 for each company, what would its stock price be? Now as part of your analysis, assume the P/E ratio would be 16 for the riskier company in terms of heavy debt utilization in the capital structure and 24 for the less risky company. What would the stock prices for the two firms be under these assumptions? (Note: Although interest rates also would likely be different based on risk, we will hold them constant for ease of analysis.) Based on the evidence in part c, should management be concerned only about the impact of financing plans on earnings per share, or should stockholders’ wealth maximization (stock price) be considered as well?

5-18. Solution:

a. Sterling $132,000 79,200 52,800 13,200 39,600 88,000 $0.45

EBIT Less: Interest EBT Less: Taxes @ 25% EAT Shares EPS

Royal $132,000 26,400 105,600 26,400 79,200 176,000 $0.45

b. Stock price = P/E ×EPS 22 × $0.45 = $9.90

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Sterling

Royal

16 × $0.45 = $7.20

24 × $0.45 = $10.80

d. Clearly, the ultimate objective should be to maximize the stock price. While management would be indifferent between the two plans based on earnings per share, Royal Optical, with the less risky plan, has a higher stock price. 19.

Japanese firm and combined leverage (LO5) Firms in Japan often employ both high operating and financial leverage because of the use of modern technology and close borrower–lender relationships. Assume the Mitaka Company has a sales volume of 135,000 units at a price of $30 per unit; variable costs are $9 per unit and fixed costs are $1,900,000. Interest expense is $410,000. What is the degree of combined leverage for this Japanese firm?

5-19. Solution:

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= 5.4x

20. Combining operating and financial leverage (LO5) Sinclair Manufacturing and Boswell Brothers Inc. are both involved in the production of brick for the homebuilding industry. Their financial information is as follows:

Capital Structure Debt @ 11%............................................................ Common stock, $10 per share................................ Total..................................................................... Common shares....................................................... Operating Plan Sales (55,000 units at $20 each).............................. Less: Variable costs............................................. .................................................................................. Fixed costs....... Earnings before interest and taxes (EBIT)............... a.

Sinclair 900,000 600,000 $ 1,500,000 60,000

Boswell

0 $ 1,5000,000 $ 1,500,000 150,000

$ 1,100,000 550,000 ($10 per unit) 305,000 $ 245,000

1,100,000 880,000 ($16 per unit) 0 $ 220,000

If you combine Sinclair’s capital structure with Boswell’s operating plan, what is the degree of combined leverage? (Round to two places to the right of the decimal point.) If you combine Boswell’s capital structure with Sinclair’s operating plan, what is the degree of combined leverage? Explain why you got the results you did in part b.

In part b, if sales double, by what percentage will EPS increase?

5-20. Solution: a.

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DCL 

Q( P  VC) Q( P  VC)  FC  I



55,000 ($20  $10) 55,000 ($20  $10)  $305,000  $99,000



550,000 550,000  $305,000  $99,000



$550,000 $146,000

 3.77x

DCL 

Q( P  VC) Q( P  VC)  FC  I



55,000($20  $16) 55,000($20  $16)  0  0



55,000($4) 55,000($4)



$220,000 $220,000

 1x c.

The leverage factor is only lx because Boswell has no financial leverage and Sinclair has no operating leverage.

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d. EPS will increase by 100 percent. However, there is no leverage involved. EPS merely grows at the same rate as sales.

21.

Expansion and leverage (LO5) DeSoto Tools Inc. is planning to expand production. The expansion will cost $300,000, which can be financed either by bonds at an interest rate of 14 percent or by selling 10,000 shares of common stock at $30 per share. The current income statement before expansion is as follows:

DESOTO TOOLS Inc. Income Statement 20X1 Sales ............................................................................... Less: Variable costs..................................................... Fixed costs......................................................... Earnings before interest and taxes.................................. Less: Interest expense ................................................. Earnings before taxes ..................................................... Less: Taxes @ 34% ..................................................... Earnings after taxes ........................................................ Shares ............................................................................. Earnings per share ..........................................................

$1,500,000 $450,000 550,000

1,000,000 500,000 100,000 400,000 136,000 $ 264,000 100,000 $ 2.64

After the expansion, sales are expected to increase by $1,000,000. Variable costs will remain at 30 percent of sales, and fixed costs will increase to $800,000. The tax rate is 34 percent. a.

Calculate the degree of operating leverage, the degree of financial leverage, and the degree of combined leverage before expansion. (For the degree of operating leverage, use the formula developed in footnote 2. For the degree of combined leverage, use the formula developed in footnote 3. These instructions apply throughout this problem.)

Construct the income statement for the two alternative financing plans.

Calculate the degree of operating leverage, the degree of financial leverage, and the degree of combined leverage, after expansion.

Explain which financing plan you favor and the risks involved with each plan.

5-21. Solution: a.

DOL 

S  VC S  TVC  FC

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 DFL 

$1,500,000  $450,000  2.1x $1,500,000  $450,000  $550,000 EBIT EBIT  I



$500,000 $500,000  $100,000



$500,000  1.25x $400,000

DCL 

S  TVC S  TVC  FC  I



$1,500,000  $450,000 $1,500,000  $450,000  $550,000  $100,000



$1,050,000  2.63x $400,000

b. Income Statement after Expansion

Sales Less: Variable costs (30%) Fixed costs EBIT Less: Interest EBT Less: Taxes @ 34% EAT (Net income) Common shares

Debt $2,500,000 750,000 800,000 950,000 142,0001 808,000 274,720 533,280 100,000

Equity $2,500,000 750,000 800,000 950,000 100,000 850,000 289,000 561,000 110,0002

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EPS

5.33

5.10

New interest expense level if expansion is financed with debt. $100,000 + 14% ($300,000) = $142,000

Number of common shares outstanding if expansion is financed with equity. 100,000 + 10,000 = 110,000

DOL  DOL (Debt/Equity)  

DFL 

S  TVC S  TVC  FC $2,500,000  $750,000 $2,500,000  $750,000  $800,000 $1,750,000  1.84x $950,000

EBIT EBIT  I

DFL (Debt) 

$950,000 $950,000   1.18x $950,000-$142,000 $808,000

DFL (Equity) 

$950,000 $950,000   1.12x $950,000-$100,000 $850,000

DCL (Debt) 

$2,500,000  $750,000 $2,500,000  $750,000  $800,000  $142,000



$1,750,000  2.17x $808,000

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DCL (Equity)  

$2,500,000  $750,000 $2,500,000  $750,000  $800,000  $100,000 $1,750,000  2.06x $850,000

d. The debt financing plan provides a greater earnings per share at the new sales level, but provides more risk because of the increased use of debt. However, the interest coverage ratio in both cases is certainly satisfactory and interest expense is well protected. The crucial point is expectations for future sales. If sales are expected to decline, the debt plan will not provide higher EPS at sales of less than about $2 million, so cyclical swings in sales, earnings, and profit margins need to be considered in choosing the financing plan. 22.

Leverage analysis with actual companies (LO6) Using Standard & Poor’s data or annual reports, compare the financial and operating leverage of Chevron, Eastman Kodak, and Delta Airlines for the most current year. Explain the relationship between operating and financial leverage for each company and the resultant combined leverage. What accounts for the differences in leverage of these companies?

5-22. Solution: The results for this problem change every year. This is primarily an Internet/library assignment to facilitate class discussion. 23.

Leverage and sensitivity analysis (LO6) Tyson Company has $12 million in assets. Currently half of these assets are financed with long-term debt at 10 percent and half with common stock having a par value of $8. Ms. Park, vice president of finance, wishes to analyze two refinancing plans, one with more debt (D) and one with more equity (E). The company earns a return on assets before interest and taxes of 10 percent. The tax rate is 45 percent.

Under Plan D, a $3 million long-term bond would be sold at an interest rate of 12 percent and 375,000 shares of stock would be purchased in the market at $8 per share and retired.

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Under Plan E, 375,000 shares of stock would be sold at $8 per share and the $3,000,000 in proceeds would be used to reduce long-term debt. a.

How would each of these plans affect earnings per share? Consider the current plan and the two new plans.

Which plan would be most favorable if return on assets fell to 5 percent? Increased to 15 percent? Consider the current plan and the two new plans.

If the market price for common stock rose to $12 before the restructuring, which plan would then be most attractive? Continue to assume that $3 million in debt will be used to retire stock in Plan D and $3 million of new equity will be sold to retire debt in Plan E. Also assume for calculations in part c that return on assets is 10 percent.

5-23. Solution: Tyson Company Income Statements a.

Return on assets = 10%

EBIT = $ 1,200,000

Current Plan D Plan E EBIT $1,200,000 $1,200,000 $1,200,000 Less: Interest 600,0001 960,0002 300,0003 EBT 600,000 240,000 900,000 Less: Taxes (45%) 270,000 108,000 405,000 EAT 330,000 132,000 495,000 4 Common shares 750,000 375,000 1,125,000 EPS $ .44 $ .35 $ .44 1

$6,000,000 debt @ 10%

$600,000 interest + ($3,000,000 debt @ 12%)

($6,000,000 – $3,000,000 debt retired)  10%

($6,000,000 common equity)/($8 par value) = 750,000 shares

Plan E and the original plan provide the same earnings per share because the cost of debt at 10 percent is equal to the operating return on assets of 10 percent. With Plan D, the cost of increased debt rises to 12 percent, and the firm incurs © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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negative leverage reducing EPS and also increasing the financial risk to Tyson. b. Return on assets = 5% EBIT = $600,000 EBIT Less: Interest EBT Less: Taxes @ 45% EAT Common shares EPS

Current $600,000 600,000 0 --0 750,000 0

Plan D $600,000 960,000 (360,000) (162,000) $(198,000) 375,000 $ (.53)

Plan E $ 600,000 300,000 300,000 135,000 $ 165,000 1,125,000 $ .15

Return on assets = 15% EBIT = $1,800,000 EBIT Less: Interest EBT Less: Taxes @ 45% EAT Common shares EPS

Current $1,800,000 600,000 1,200,000

Plan D $1,800,000 960,000 840,000

Plan E $1,800,000 300,000 1,500,000

540,000 $ 660,000 750,000 $ .88

378,000 $ 462,000 375,000 $ 1.23

675,000 $ 825,000 1,125,000 $ .73

If the return on assets decreases to 5 percent, Plan E provides the best EPS, and at 15 percent return, Plan D provides the best EPS. Plan D is still risky, having an interest coverage ratio of less than 2.0.

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Return on Assets = 10% EBIT = $1,200,000 EBIT EAT Common shares EPS

Current $1,200,000 330,000 750,000 $ .44

Plan D Plan E $1,200,000 $1,200,000 132,000 495,000 1 500,000 1,000,0002 $ .26 $ .50

750,000 – ($3,000,000/$12 per share) = 750,000 – 250,000 = 500,000 shares

750,000 + ($3,000,000/$12 per share) = 750,000 + 250,000 = 1,000,000 shares As the price of the common stock increases, Plan E becomes more attractive because fewer shares can be retired under Plan D and, by the same logic, fewer shares need to be sold under Plan E.

24.

Leverage and sensitivity analysis (LO6) Edsel Research Labs has $27 million in assets. Currently, half of these assets are financed with long-term debt at 5 percent and half with common stock having a par value of $10. Ms. Edsel, the vice president of finance, wishes to analyze two refinancing plans, one with more debt (D) and one with more equity (E). The company earns a return on assets before interest and taxes of 5 percent. The tax rate is 30 percent. Under Plan D, a $6.75 million long-term bond would be sold at an interest rate of 11 percent and 675,000 shares of stock would be purchased in the market at $10 per share and retired. Under Plan E, 675,000 shares of stock would be sold at $10 per share and the $6,750,000 in proceeds would be used to reduce long-term debt. a. How would each of these plans affect earnings per share? Consider the current plan and the two new plans. Which plan(s) would produce the highest EPS? Note that due to tax loss carry-forwards and carry-backs, taxes can be a negative number. b. Which plan would be most favorable if return on assets increased to 8 percent? Compare the current plan and the two new plans. What has caused the plans to give different EPS numbers? c. Assuming return on assets is back to the original 5 percent, but the interest rate on new debt in Plan D is 7 percent, which of the three plans will produce the highest EPS? Why?

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5-24. Solution: Edsel Research Labs Income Statement a.

Return on assets = 5% Current EBIT $1,350,000 Less: Interest 675,0001 EBT 675,000 L Less: Taxes (30%) 202,500 EAT 472,500 Common shares 1,350,0004 EPS $0.35

EBIT = $1,350,000 Plan D

Plan E

$1,350,000 $1,350,000 1,417,5002 337,5003 1,012,500 67,500 20,250 303,750 708,750 47,250 5 675,000 2,025,0006 $0.35 $0.07

$13,500,000 debt @ 5% = $675,000

$675,000 interest + ($6,750,000 new debt @ 11%) = $1,417,500

($13,500,000  $6,750,000 debt retired)  5% = $337,500

($13,500,000 common equity / $10 par value) = 1,350,000 shares

($6,750,000 common equity / $10 par value) = 675,000 shares

($20,250,000 common equity / $10 par value) = 2,025,000 shares

The current plan and Plan E provide the highest return of $0.35.

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b. Return on assets = 8%

EBIT = $2,160,000

Current

Plan D

Plan E

$2,160,000

Less: Interest

675,000

1,417,500

337,500

EBT

1,485,000

742,500

1,822,500

Less: Taxes (30%)

445,500

222,750

546,750

EAT

1,039,500

519,750

1,275,750

Common shares

1,350,000

675,000

2,025,000

EPS

$0.77

$0.63

EBIT

The current plan and Plan D provides the highest return. The % EBIT (12%) is higher than the interest rate (8% and 10%). Thus, the more debt the firm takes on, the higher the EPS. c. Return on assets = 5%

EBIT = $1,350,000

Current

Plan D

Plan E

$1,350,000

Less: Interest

675,000

1,147,5001

337,500

EBT

675,000

202,500

1,012,500

Less: Taxes (30%)

202,500

60,750

303,750

EAT

472,500

141,750

708,750

Common shares

1,350,000

675,000

2,025,000

EPS

$0.35

$0.21

$0.35

EBIT

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$675,000 + (6,750,000  7%) = 1,147,500

The current plan and Plan E provides the highest return. The % EBIT (8%) is higher than the cost of new debt (6%).

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25.

Leverage and sensitivity analysis (LO6) The Lopez-Portillo Company has $10.6 million in assets, 80 percent financed by debt, and 20 percent financed by common stock. The interest rate on the debt is 9 percent and the par value of the stock is $10 per share. President Lopez-Portillo is considering two financing plans for an expansion to $18 million in assets. Under Plan A, the debt-to-total-assets ratio will be maintained, but new debt will cost a whopping 12 percent! Under Plan B, only new common stock at $10 per share will be issued. The tax rate is 40 percent. a. If EBIT is 9 percent on total assets, compute earnings per share (EPS) before the expansion and under the two alternatives. b. What is the degree of financial leverage under each of the three plans? c. If stock could be sold at $20 per share due to increased expectations for the firm’s sales and earnings, what impact would this have on earnings per share for the two expansion alternatives? Compute earnings per share for each. d.

Explain why corporate financial officers are concerned about their stock values.

5-25. Solution: a. Return on Assets = 20% EBIT Less: Interest EBT Less: Taxes (40%)

Current $954,000 763,200(a) 190,800 76,320

Plan A Plan B $1,620,000 $1,620,000 1,473,600(c) 763,200(e) 146,400 856,800 58,560 342,720

EAT $114,480 $ 87,840 $ 514,080 Common shares 212,000(b) 360,000(d) 952,000(f) EPS $0.54 $0.24 $0.54 (a) (80%  $10,600,000)  9% = $8,480,000  9% = $763,200 (b) (20%  $10,600,000)/$10 = $2,120,000/$10 = 212,000 shares (c) $763,200 (current)  (80%  $7,400,000)  12% = $763,200  $710,400 = $1,473,600 (d) 212,000 shares (current) + (20%  $7,400,000)/$10 = 212,000 + 148,000 = 360,000 shares (e) Unchanged (f) 212,000 shares (current) + $7,400,000/$10 = 212,000 + 740,000 = 952,000 shares

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DFL 

EBIT EBIT  I

DFL (Current) 

$954,000  5.00x $954, 000  $763, 200

DFL (Plan A) 

$1,620,000  11.07x $1, 620, 000  $1, 473, 600

DFL (Plan B) 

$1,620,000  1.89x $1, 620, 000  $763, 200

c. EAT Common shares EPS

Plan A $87,840 286,0001 $ 0.31

Plan B $514,080 582,0002 $ 0.88

212,000 shares (current) + (20%  $7,400,000)/$20 = 212,000 + 74,000 = 286,000 shares

212,000 shares (current) + $7,400,000/$20 = 212,000 + 370,000 = 582,000 shares

Plan B would continue to provide the higher earnings per share. The difference between plans A and B is even greater than that indicated in part (a). d. Not only does the price of the common stock create wealth to the shareholder, which is the major objective of the financial manager, but it greatly influences the ability to finance projects at a high or low cost of capital. Cost of capital will be discussed in Chapter 10, and one will see the impact that the cost of capital has on capital budgeting decisions.

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26.

Operating leverage and ratios (LO6) Ms. Gold is in the widget business. She currently sells 1.5 million widgets a year at $6 each. Her variable cost to produce the widgets is $4 per unit, and she has $1,550,000 in fixed costs. Her sales-to-assets ratio is six times, and 30 percent of her assets are financed with 10 percent debt, with the balance financed by common stock at $10 par value per share. The tax rate is 35 percent. Her sister-in-law, Ms. Silverman, says Ms. Gold is doing it all wrong. By reducing her price to $5.00 a widget, she could increase her volume of units sold by 60 percent. Fixed costs would remain constant, and variable costs would remain $4 per unit. Her sales-toassets ratio would be 7.5 times. Furthermore, she could increase her debt-to-assets ratio to 50 percent, with the balance in common stock. It is assumed that the interest rate would go up by 1 percent and the price of stock would remain constant. a. Compute earnings per share under the Gold plan. b. Compute earnings per share under the Silverman plan. c.

Ms. Gold’s, chief financial officer does not think that fixed costs would remain constant under the Silverman plan but that they would go up by 15 percent. If this is the case, should Ms. Gold shift to the Silverman plan, based on earnings per share?

5-26. Solution: a. Gold Plan Sales ($1,500,000 units  $6)

$9,000,000

 Fixed costs

1,550,000

 Variable costs

6,000,000

Operating income (EBIT)

$ 1,450,000

 Interest1

45,000

EBT

$ 1,405,000

 Taxes @ 35%

491,750

EAT

$ 913,250

Shares2

105,000

Earnings per share

8.70

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Assets 

Sales $9,000,000   $1,500,000 Asset turnover 6

Debt = 30% of Assets = 30% × $1,500,000 = $450,000 Interest = 10% × $450,000 = $45,000 2 Stock = 70% of $1,500,000 = $1,050,000 Shares = $1,050,000/$10 = 105,000 shares b. Silverman Plan Sales ($2,400,000 units at $5.00)  Fixed costs  Variable costs (2,400,000 units  $4) Operating income (EBIT)  Interest3 EBT Taxes @ 35% EAT Shares4 Earnings per share

Assets 

$12,000,000 1,550,000 9,600,000 $ 850,000 88,000 $ 762,000 266,700 $ 495,300 80,000 $ 6.19

Sales $12,000,000   $1,600,000 Asset turnover 7.50

Debt = 50% of Assets = 50% × $1,600,000 = $800,000 Interest = 11% × $800,000 = $88,000

Stock = 50% of $1,600,000 = $800,000 Shares = $800,000/$10 = 80,000 shares

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c. Silverman Plan (based on Ms. Gold’s Assumption) Sales ($2,400,000 units at $5.00)

$12,000,000

 Fixed costs ($1,550,000  1.15)

1,782,500

 Variable costs (2,400,000 units  $4)

9,600,000

Operating income (EBIT)

$ 617,500

 Interest

104,000

EBT

$ 513,500

 Taxes @ 35%

179,725

EAT

$ 333,775

80,000

Earnings per share

4.17

No! Gold should not shift to the Silverman Plan if the chief financial officer’s assumption is correct. 27.

Expansion, break-even analysis, and leverage (LO2, 3, and 4) Delsing Canning Company is considering an expansion of its facilities. Its current income statement is as follows: Sales .................................................................. Less: Variable expense (50% of sales) ........... Fixed expense ....................................... Earnings before interest and taxes (EBIT) ........ Interest (10% cost) ............................................ Earnings before taxes (EBT) ............................. Tax (40%) .......................................................... Earnings after taxes (EAT) ................................ Shares of common stock—250,000 .................. Earnings per share .............................................

$5,500,000 2,750,000 1,850,000 900,000 300,000 600,000 240,000 $ 360,000 $1.44

The company is currently financed with 50 percent debt and 50 percent equity (common stock, par value of $10). In order to expand the facilities, Mr. Delsing estimates a need for

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$2.5 million in additional financing. His investment banker has laid out three plans for him to consider: 1. Sell $2.5 million of debt at 13 percent.

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2. 3.

Sell $2.5 million of common stock at $20 per share. Sell $1.25 million of debt at 12 percent and $1.25 million of common stock at $25 per share. Variable costs are expected to stay at 50 percent of sales, while fixed expenses will increase to $2,350,000 per year. Delsing is not sure how much this expansion will add to sales, but he estimates that sales will rise by $1.25 million per year for the next five years. Delsing is interested in a thorough analysis of his expansion plans and methods of financing. He would like you to analyze the following: a. The break-even point for operating expenses before and after expansion (in sales dollars). b. The degree of operating leverage before and after expansion. Assume sales of $5.5 million before expansion and $6.5 million after expansion. Use the formula in footnote 2 of the chapter. c. The degree of financial leverage before expansion and for all three methods of financing after expansion. Assume sales of $6.5 million for this question. d. Compute EPS under all three methods of financing the expansion at $6.5 million in sales (first year) and $10.5 million in sales (last year). e. What can we learn from the answer to part d about the advisability of the three methods of financing the expansion?

5-27. Solution: a.

At break-even before expansion:

PQ  FC  VC where PQ equals sales volume at break-even point Sales

 Fixed costs  Variable costs (Variable costs  50% of sales)

Sales

 $1,850,000  .50 Sales

.50 Sales  $1,850,000 Sales

 $3,700,000

At break-even after expansion: Sales  $2,350,000  .50 Sales

.50 Sales  $2,350,000 Sales

 $4,700,000

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b. Degree of operating leverage, before expansion, at sales of $5,500,000

DOL =

Q  P  VC 

Q  P  VC   FC



S  TVC S  TVC  FC

$5,500,000  $2,750,000 $5,500,000  $2,750,000  $1,850,000 $2,750,000   3.06x $900,000 Degree of operating leverage after expansion at sales of $6,500,000 

$6,500, 000  $3, 250, 000 $6,500, 000  $3, 250, 000  $2,350, 000 $3, 250, 000   3.61x $900, 000

DOL =

This could also be computed for subsequent years. c. DFL before expansion: DFL =

EBIT EBIT  1



$900, 000 $900, 000  $300, 000



$900, 000  1.50x $600, 000

DFL after expansion: Compute EBIT and I for all three plans: (100% Debt)

(100%

(50% Debt

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Sales – TVC (.50) – FC EBIT I – Old debt I – New debt Total interest DFL =

(1)

Equity) (2)

$6,500,000 3,250,000 2,350,000 $ 900,000 300,000 325,000 $ 625,000

$6,500,000 3,250,000 2,350,000 $ 900,000 300,000 0 $ 300,000

and 50% Equity) (3) $6,500,000 3,250,000 2,350,000 $ 900,000 300,000 150,000 $ 450,000

EBIT EBIT  I

(1)

(2)

(3)

$900, 000 $900, 000 $900, 000  $900, 000  $625, 000   $900, 000  $300, 000   $900, 000  $450, 000 

DFL = 3.27x

1.50x

2.00x

d. EPS @ sales of $6,500,000 (refer back to part c to get the values for EBIT and Total I) (50% Debt (100% (100% and 50% Debt) (1) Equity) (2) Equity) (3) EBIT $900,000 $900,000 $900,000 Total I 625,000 300,000 450,000 EBT $275,000 $600,000 $450,000 Taxes (40%) 110,000 240,000 180,000 EAT $165,000 $360,000 $270,000 Shares (old) 250,000 250,000 250,000 Shares (new) 0 125,000 50,000 Total shares 250,000 375,000 300,000 EPS (EAT/Total $0.66 $0.96 $0.90

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shares) EPS @ sales of $10,500,000

Sales – TVC – FC EBIT Total I EBT Taxes (40%) EAT Total shares EPS (EAT/Total shares) e.

(100% Debt) (1) $10,500,000 5,250,000 2,350,000 $ 2,900,000 625,000 $ 2,275,000 910,000 $1,365,000 250,000

(100% Equity) (2) $10,500,000 5,250,000 2,350,000 $ 2,900,000 300,000 $ 2,600,000 1,040,000 $1,560,000 375,000

(50% Debt and 50% Equity) (3) $10,500,000 5,250,000 2,350,000 $ 2,900,000 450,000 $2,450,000 980,000 $1,470,000 300,000

$5.46

$4.16

$4.90

In the first year, when sales and profits are relatively low, plan 2 (100% equity) appears to be the best alternative. However, as sales expand up to $10.5 million, financial leverage begins to produce results as EBIT increases and Plan 1 (100% debt) is the highest yielding alternative.

COMPREHENSIVE PROBLEM Comprehensive Problem 1

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Ryan Boot Company (review of Chapters 2 through 5) (multiple LO’s from Chapters 2 through 5)

Assets Cash........................................... Marketable securities ................ Accounts receivable .................. Inventory ................................... Gross plant and equipment Less ........................................ Accumulated depreciation .. Total assets ................................

RYAN BOOT COMPANY Balance Sheet December 31, 20X1 Liabilities and Stockholders’ Equity $ 50,000 Accounts payable ................... $2,200,000 80,000 Accrued expenses .................. 150,000 3,000,000 Notes payable (current) .......... 400,000 1,000,000 Bonds (10%) .......................... 2,500,000 6,000,00 Common stock (1.7 million 1,700,000 shares, par value $1) ........... 2,000,000 Retained earnings ................... 1,180,000 Total liabilities and $8,130,000 $8,130,000 stockholders’ equity ............

Income Statement—20X1 Sates (credit) ........................................................................... Fixed costs* ............................................................................ Variable costs (0.60) .............................................................. Earnings before interest and taxes .......................................... Less: Interest ....................................................................... Earnings before taxes ............................................................. Less: Taxes @ 35% ............................................................. Earnings after taxes ................................................................ Dividends (40% payout)...................................................... Increased retained earnings ....................................................

$7,000,000 2,100,000 4,200,000 700,000 250,000 450,000 157,500 $ 292,500 117,000 $ 175,500

*Fixed costs include (a) lease expense of $200,000 and (b) depreciation of $500,000. Note: Ryan Boots also has $65,000 per year in sinking fund obligations associated with its bond issue. The sinking fund represents an annual repayment of the principal amount of the bond. It is not tax-deductible.

Ratios

Profit margin ................................... Return on assets .............................. Return on equity ............................. Receivables turnover ...................... Inventory turnover ..........................

Ryan Boot (to be filled in) _____________ _____________ _____________ _____________ _____________

Industry 5.75% 6.90% 9.20% 4.35X 6.50X

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Fixed-asset turnover ....................... Total-asset turnover ........................ Current ratio .................................... Quick ratio ...................................... Debt to total assets .......................... Interest coverage ............................. Fixed charge coverage .................... a.

_____________ _____________ _____________ _____________ _____________ _____________ _____________

1.85X 1.20X 1.45X 1.10X 25.05% 5.35X 4.62X

Analyze Ryan Boot Company, using ratio analysis. Compute the ratios on the prior page for Ryan and compare them to the industry data that is given. Discuss the weak points, strong points, and what you think should be done to improve the company’s performance. In your analysis, calculate the overall break-even point in sales dollars and the cash break-even point. Also compute the degree of operating leverage, degree of financial leverage, and degree of combined leverage. (Use footnote 2 for DOL and footnote 3 in the chapter for DCL.) Use the information in parts a and b to discuss the risk associated with this company. Given the risk, decide whether a bank should lend funds to Ryan Boot.

Ryan Boot Company is trying to plan the funds needed for 20X2. The management anticipates an increase in sales of 20 percent, which can be absorbed without increasing fixed assets. d.

CP 5-1.

What would be Ryan’s needs for external funds based on the current balance sheet? Compute RNF (required new funds). Notes payable (current) and bonds are not part of the liability calculation. What would be the required new funds if the company brings its ratios into line with the industry average during 20X2? Specifically examine receivables turnover, inventory turnover, and the profit margin. Use the new values to recompute the factors in RNF (assume liabilities stay the same). Do not calculate, only comment on these questions. How would required new funds change if the company (1) Were at full capacity? (2) Raised the dividend payout ratio? (3) Suffered a decreased growth in sales? (4) Faced an accelerated inflation rate?

Solution: Ryan Boot Company

a. Ratio analysis Profit margin Return on assets

$292,500/$7,000,000 $292,500/$8,130,000

Ryan Industry 4.18% 5.75% 3.60% 6.90%

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Return on equity Receivable turnover Inventory turnover Fixed asset turnover Total asset turnover Current ratio Quick ratio Debt to total assets Interest coverage Fixed charge coverage

$292,500/$2,880,000 $7,000,000/$3,000,000 $7,000,000/$1,000,000 $7,000,000/$4,000,000 $7,000,000/$8,130,000 $4,130,000/$2,750,000 $3,130,000/$2,750,000 $5,250,000/$8,130,000 $700,000/$250,000 See calculation below*

10.16% 2.33x 7.00x 1.75x .86x 1.50x 1.14x 64.58 2.80x 1.64x

9.20% 4.35x 6.50x 1.85x 1.20x 1.45x l.l0x 25.05 5.35x 4.62x

$700,000+200,000(Lease)  1.64x $250,000  200,000  65,000 / (1  .35)

Lease expense of $200,000 and sinking fund of $65,000 a.

The company has a lower profit margin than the industry and the problem is further compounded by the slow turnover of assets (.86x versus an industry norm of 1.20x). This leads to a much lower return on assets. The company has a higher return on equity than the industry, but this is accomplished through the firm’s heavy debt ratio rather than through superior profitability. The slow turnover of assets can be directly traced to the unusually high level of accounts receivable. The firm’s accounts receivable turnover ratio is only 2.33x, versus an industry norm of 4.35x. Actually, the firm does quite well with inventory turnover and it is only slightly below the industry in fixed asset turnover.

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The previously mentioned heavy debt position becomes more apparent when we examine times interest earned and fixed charge coverage. The latter is particularly low due to lease expenses and sinking fund obligations. b. Break-even in sales Sales  Fixed costs  Variable costs (variable costs are expressed as a percentage of sales) Sales BE  $2,100,000  .60 Sales

.40 S

 $2,100,000

 $2,100,000 / .40

 $5,250,000

Cash break-even Sales  (Fixed costs  Noncash expenses*) + Variable costs Sales BE  ($2,100,000  $500,000) + .60 Sales

Sales BE  $1,600,000  .60 Sales  $1,600,000

.40 S S

 $1,600,000 / .40

 $4,000,000 *Depreciation

DOL 

S  TVC S  TVC  FC



$7,000,000  $4, 200,000 $7,000,000  $4, 200,000  $2,100,000



$2,800,000  4x $700,000

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DFL 

EBIT $700,000  EBIT  I $700,000  $250,000



$700,000  1.56x $450,000

DCL 

S  TVC S  TVC  FC  I



$7,000,000  $4, 200,000 $7,000,000  $4, 200,000  $2,100,000  $250,000



$2,800,000  6.22x $450,000

Ryan is operating at a sales volume that is $1,750,000 above the traditional break-even point and $3,000,000 above the cash break-even point. This can be viewed as somewhat positive. However, the firm has a high degree of leverage, which indicates any reduction in sales volume could have a very negative impact on profitability. The DOL of 4x is associated with heavy fixed assets and relatively high fixed costs. The DFL of 1.56x is attributed to high debt reliance. Actually, if we were to include the lease payments of $200,000 with the interest payments of $250,000, the DFL would be almost 3x. The banker would have to question the potential use of the funds and the firm’s ability to pay back the loan. Actually, the firm already appears to have an abundant amount of assets, so hopefully a large expansion would not take place here. There appears to be a need to reduce accounts receivable rather than increase the level.

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One possible use of the funds might be to pay off part of the current notes payable of $400,000. This might be acceptable if the firm can demonstrate the ability to meet its future obligations. The banker should request to see pro forma financial statements and projections of future cash flow generation. The loan might only be acceptable if the firm can bring down its accounts receivable position back in line and improve its profitability. d. Required new funds =

A L  S   S  PS2 1  D  S S

Change in Sales = 20%  $7,000,000= $1,400,000 RNF 

$4,130,000 $2,350,000  $1, 400,000    $1, 400,000  $7,000,000 $7,000,000  4.18%  $8, 400,000  (1  .4)

RNF = .590  $1,400,000   .336  $1, 400,000   $351,120 .6   $826,000  $470, 400  $210,672  $144,928

e. Required funds if selected industry ratios were applied Receivables = Sales/Receivable turnover Receivables = $7,000,000/4.35 Receivables = $1,609,195 Revised A (assets)

 $50,000  $80,000  $1,609,195  $1,000,000  $2,739,195 Profit Margin = 5.75%

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A L  S   S  PS2 1  D  S S $2,739,195 $2,350,000 RNF=  $1,400,000    $1,400,000  $7,000,000 $7,000,000

RNF =

 5.75%  $8,400,000 1  .4  RNF  .391 $1,400,000   .336  $1, 400,000   $483,000 .6   $547, 400  $470, 400  $289,800   $212,800

Required new funds (RNF) is negative, indicating there will actually be an excess of funds equal to $212,180. This is due to the much more rapid turnover of accounts receivable and the higher profit margin. f.

(1)

If Ryan Boots was at full capacity, more funds would be needed to expand plant and equipment.

(2)

More funds would be needed to offset the larger payout of earnings to dividends.

(3)

Fewer funds would be required as sales grow less rapidly. Fewer new assets would be needed to support sales growth.

(4)

As inflation increased, so would the cost of new assets, especially inventory and plant and equipment. Even if sales prices could be increased, more assets would be required to support the same physical level of sales. Increased profits alone would not make up for the higher level of assets required and more funds would be needed. Chapter 6 Working Capital and the Financing Decision

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Discussion Questions 6-1.

Explain how rapidly expanding sales can drain the cash resources of a firm.

Rapidly expanding sales will require a buildup in assets to support the growth. In particular, more and more of the increase in current assets will be permanent in nature. A non-liquidating aggregate stock of current assets will be necessary to allow for floor displays, multiple items for selection, and other purposes. All of these “asset” investments can drain the cash resources of the firm.

6-2.

Discuss the relative volatility of short- and long-term interest rates.

Figure 6-10 shows the long-run view of short- and long-term interest rates. Normally, short-term rates are much more volatile than long-term rates.

6-3.

What is the significance to working capital management of matching sales and production?

If sales and production can be matched, the level of inventory and the amount of current assets needed can be kept to a minimum; therefore, lower financing costs will be incurred. Matching sales and production has the advantage of maintaining smaller amounts of current assets than level production, and therefore less financing costs are incurred. However, if sales are seasonal or cyclical, workers will be laid off in a declining sales climate and machinery (fixed assets) will be idle. Here lies the trade-off between level and seasonal production: Full utilization of fixed assets with skilled workers and more financing of current assets versus unused capacity, training and retraining workers, with lower financing for current assets.

6-4.

How is a cash budget used to help manage current assets?

A cash budget helps minimize current assets by providing a forecast of inflows and outflows of cash. It also encourages the development of a schedule as to when inventory is produced and maintained for sales (production schedule), and accounts receivables are collected. The cash budget allows us to forecast the level of each current asset and the timing of the buildup and reduction of each.

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6-5.

“The most appropriate financing pattern would be one in which asset buildup and length of financing terms is perfectly matched.” Discuss the difficulty involved in achieving this financing pattern. Only a financial manager with unusual insight and timing could design a plan in which asset buildup and the length of financing terms are perfectly matched. One would need to know exactly what current assets are temporary and which ones are permanent. Furthermore, one is never quite sure how much short-term or long-term financing is available at all times. Even if this were known, it would be difficult to change the financing mix on a continual basis.

6-6.

By using long-term financing to finance part of temporary current assets, a firm may have less risk but lower returns than a firm with a normal financing plan. Explain the significance of this statement. By establishing a long-term financing arrangement for temporary current assets, a firm is assured of having necessary funding in good times as well as bad, thus we say there is low risk. However, long-term financing is generally more expensive than short-term financing and profits may be lower than those which could be achieved with a synchronized or normal financing arrangement for temporary current assets.

6-7.

A firm that uses short-term financing methods for a portion of permanent current assets is assuming more risk but expects higher returns than a firm with a normal financing plan. Explain. By financing a portion of permanent current assets on a short-term basis, we run the risk of inadequate financing in tight money periods. However, since short-term financing is less expensive than long-term funds, a firm tends to increase its profitability over the long run (assuming it survives). In answer to the preceding question, we stressed less risk and less return. Here the emphasis is on risk and high return.

6-8.

What does the term structure of interest rates indicate? The term structure of interest rates shows the relative level of short-term and longterm interest rates at a point in time on U.S. treasury securities. It is often referred to as a yield curve.

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6-9.

What are three theories for describing the shape of the term structure of interest rates (the yield curve)? Briefly describe each theory. Liquidity premium theory, the market segmentation theory, and the expectations theory. The liquidity premium theory indicates that long-term rates should be higher than short-term rates. This premium of long-term rates over short-term rates exists because short-term securities have greater liquidity, and therefore higher rates have to be offered to potential long-term bond buyers to entice them to hold these less liquid and more price-sensitive securities. The market segmentation theory states that Treasury securities are divided into market segments by the various financial institutions investing in the market. The changing needs, desires, and strategies of these investors tend to strongly influence the nature and relationship of short- and long-term rates. The expectations hypothesis maintains that the yields on long-term securities are a function of short-term rates. The result of the hypothesis is that when long-term rates are much higher than short-term rates, the market is saying that it expects short-term rates to rise. Conversely, when long-term rates are lower than short-term rates, the market is expecting short-term rates to fall.

6-10.

Since the mid-1960s, corporate liquidity has been declining. What reasons can you give for this trend? The decrease in liquidity can be traced in part to more efficient inventory management such as just-in-time inventory and point of sales terminals that provide better inventory control. The decline in working capital can also be attributed to electronic cash flow transfer systems, and the ability to sell accounts receivables through securitization of assets (this is more fully explained in the next chapter). It might also be that management is simply willing to take more liquidity risk as interest rates declined.

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Chapter 06: Working Capital and the Financing Decision

Problems 1.

Expected value (LO6) Taylor’s Pipe and Steel Company expects sales next year to be $1,000,000 if the economy is strong, $700,000 if the economy is steady, and $385,000 if the economy is weak. Taylor believes there is a 20 percent probability the economy will be strong, a 65 percent probability of a steady economy, and a 15 percent probability of a weak economy. What is the expected level of sales for next year?

6-1.

Solution:

Taylor’s Pipe and Steel Company

State of Economy

Sales

Probability

Expected Outcome

Strong

$1,000,000

0.20

$200,000

Steady

700,000

0.65

455,000

Weak

385,000

0.15

57,750

Expected level of sales =

$712,750

Expected value (LO6) Sharpe Knife Company expects sales next year to be $1,550,000 if the economy is strong, $825,000 if the economy is steady, and $550,000 if the economy is weak. Mr. Sharpe believes there is a 30 percent probability the economy will be strong, a 40 percent probability of a steady economy, and a 30 percent probability of a weak economy. What is the expected level of sales for the next year?

6-2.

Solution:

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Chapter 06: Working Capital and the Financing Decision

Sharpe Knife Company State of Economy

Sales

Probability

Expected Outcome

Strong

$1,550,000

0.30

$465,000

Steady

825,000

0.40

330,000

Weak

550,000

0.30

165,000

Expected level of sales =

$960,000

External financing (LO1) Tobin Supplies Company expects sales next year to be $500,000. Inventory and accounts receivable will increase $90,000 to accommodate this sales level. The company has a steady profit margin of 12 percent with a 40 percent dividend payout. How much external financing will Tobin Supplies Company have to seek? Assume there is no increase in liabilities other than that which will occur with the external financing.

6-3.

Solution:

Net income = 0.12 × $500,000 = $60,000 Dividends = 0.40 × $60,000 = $24,000

Tobin Supplies Company

60,000 – 24,000 $ 36,000

Net income Dividends (40%) Increase in retained earnings

$ 90,000 – 36,000 $ 54,000

Increase in assets Increase in retained earnings External funds needed

External financing (LO1) Antivirus Inc. expects its sales next year to be $3,500,000. Inventory and accounts receivable will increase $580,000 to accommodate this sales level. The company has a steady profit margin of 10 percent with a 25 percent dividend payout. How much external

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financing will the firm have to seek? Assume there is no increase in liabilities other than that which will occur with the external financing.

6-4.

Solution:

Net income = 0.10 × $3,500,000 = $350,000 Dividends = 0.25 × $350,000 = $87,500

Antivirus Inc.

350,000 – 87,500 $ 262,500

Net income Dividends (25%) Increase in retained earnings

$ 580,000 – 262,500 $317,500

Increase in assets Increase in retained earnings External funds needed

Level versus seasonal production (LO1) Antonio Banderos & Scarves makes headwear that is very popular in the fall-winter season. Units sold are anticipated as:

October .........................................................

1,250

November .....................................................

2,250

December......................................................

4,500

January ..........................................................

3,500 11,500 units

If seasonal production is used, it is assumed that inventory will directly match sales for each month and there will be no inventory buildup. However, Antonio decides to go with level production to avoid being out of merchandise. He will produce the 11,500 items over four months at a level of 2,875 per month.

a. What is the ending inventory at the end of each month? Compare the unit sales to the units produced and keep a running total. b. If the inventory costs $8 per unit and will be financed at the bank at a cost of 12 percent, what are the monthly financing cost and the total for the four months? (Use 1 percent or the monthly rate.)

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6-5.

Solution:

Antonio Banderos and Scarves a.

Units Sold

Units Produced

Change in Inventory

Ending Inventory

October November December January

1,250 2,250 4,500 3,500

2,875 2,875 2,875 2,875

+1,625 + 625 –1,625 – 625

1,625 2,250 625 0

b. Total Cost per Unit ($8 per unit) 1,625 13,000 2,250 18,000 625 5,000 0 0 Total Financing Cost =

Ending Inventory October November December January

Inventory Financing Cost (at 1% per month) 130 180 50 0 $360

Level versus seasonal production (LO1) Bambino Sporting Goods makes baseball gloves that are very popular in the spring and early summer season. Units sold are anticipated as follows:

March ............................................................

3,250

April ...............................................................

7,250

May ............................................................... 11,500 June ...............................................................

9,500

31,500 If seasonal production is used, it is assumed that inventory will directly match sales for each month and there will be no inventory buildup.

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The production manager thinks the preceding assumption is too optimistic and decides to go with level production to avoid being out of merchandise. He will produce the 31,500 units over four months at a level of 7,875 per month.

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a. What is the ending inventory at the end of each month? Compare the unit sales to the units produced and keep a running total. b. If the inventory costs $12 per unit and will be financed at the bank at a cost of 12 percent, what are the monthly financing cost and the total for the four months? (Use 0.01 as the monthly rate.)

6-6.

Solution:

Bambino Sporting Goods a.

Units Sold

Units Produced

Change in Inventory

Ending Inventory

March April May June

3,250 7,250 11,500 9,500

7,875 7,875 7,875 7,875

+4,625 + 625 –3,625 –1,625

4,625 5,250 1,625 0

b. Ending Inventory March April May June

Total Cost ($12 per unit)

4,625 55,500 5,250 63,000 1,625 19,500 0 0 Total Financing Cost =

Inventory Financing Cost (at 1% per month) $ 555 630 195 0 $1,380

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Short-term versus longer-term borrowing (LO3) Boatler Used Cadillac Co. requires $950,000 in financing over the next two years. The firm can borrow the funds for two years at 12 percent interest per year. Mr. Boatler decides to do forecasting and predicts that if he utilizes short-term financing instead, he will pay 7.75 percent interest in the first year and 13.55 percent interest in the second year. Determine the total two-year interest cost under each plan. Which plan is less costly?

6-7.

Solution:

Boatler Used Cadillac Co. Cost of Two-Year Fixed Cost Financing $950,000 borrowed @ 12% per annum × 2 years = $228,000 interest cost Cost of Two-Year Variable Short-Term Financing 1st year $950,000 × 7.75% per annum 2nd year $950,000 × 13.55% per annum

= $ 73,625 interest cost = $128,725 interest cost $202,350 total interest cost

The short-term plan is less costly. 8.

Short-term versus longer-term borrowing (LO3) Biochemical Corp. requires $550,000 in financing over the next three years. The firm can borrow the funds for three years at 10.60 percent interest per year. The CEO decides to do a forecast and predicts that if she utilizes short-term financing instead, she will pay 8.75 percent interest in the first year, 13.25 percent interest in the second year, and 10.15 percent interest in the third year. Determine the total interest cost under each plan. Which plan is less costly?

6-8.

Solution:

Biochemical Corp. Cost of Three-Year Fixed Cost Financing $550,000 borrowed × 10.60% per annum × 3 years = $174,900

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Cost of Three-Year Variable Short-Term Financing 1st year $550,000 × 8.75% per annum = $ 48,125 Interest cost 2nd year $550,000 × 13.25% per annum = 72,875 Interest cost 3rd year $550,000 × 10.15% per annum = 55,825 Interest cost $176,825 3-year total The fixed cost plan is less costly.

Short-term versus longer-term borrowing (LO3) Sauer Food Company has decided to buy a new computer system with an expected life of three years. The cost is $150,000. The company can borrow $150,000 for three years at 10 percent annual interest or for one year at 8 percent annual interest. How much would Sauer Food Company save in interest over the three-year life of the computer system if the one-year loan is utilized and the loan is rolled over (reborrowed) each year at the same 8 percent rate? Compare this to the 10 percent three-year loan. What if interest rates on the 8 percent loan go up to 13 percent in year 2 and 18 percent in year 3? What would be the total interest cost compared to the 10 percent, three-year loan?

6-9.

Solution:

Sauer Food Company If Rates Are Constant $150,000 borrowed × 8% per annum × 3 years = $36,000 interest cost $150,000 borrowed × 10% per annum × 3 years = $45,000 interest cost $45,000 – $36,000 = $9,000 interest savings borrowing short-term If Short-Term Rates Change 1st year 2nd year 3rd year

$150,000 × 0.08 = $12,000 $150,000 × 0.13 = $19,500 $15,000 × 0.18 = $27,000 Total = $58,500

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$58,500 – $45,000 = $13,500 extra interest costs borrowing short-term.

10.

Optimal policy mix (LO5) Assume that Hogan Surgical Instruments Co. has $2,500,000 in assets. If it goes with a low-liquidity plan for the assets, it can earn a return of 18 percent, but with a highliquidity plan, the return will be 14 percent. If the firm goes with a short-term financing plan, the financing costs on the $2,500,000 will be 10 percent, and with a long-term financing plan, the financing costs on the $2,500,000 will be 12 percent. (Review Table 6-11 for parts a, b, and c of this problem.)

6-10. Solution: Hogan Surgical Instruments Company a. Most aggressive Low liquidity Short-term financing Anticipated return

$2,500,000 × 18% = 2,500,000 × 10% =

$450,000 –250,000 $200,000

$2,500,000 × 14% = 2,500,000 × 12% =

$350,000 –300,000 $ 50,000

$2,500,000 × 18% = 2,500,000 × 12% =

$450,000 –300,000 $150,000

b. Most conservative High liquidity Long-term financing Anticipated return c.

Moderate approach Low liquidity Long-term financing

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OR High liquidity Short-term financing

$2,500,000 × 14% = 2,500,000 × 10% =

$350,000 –250,000 $ 100,000

d. You may not necessarily select the plan with the highest return. You must also consider the risk inherent in the plan. Of course, some firms are better able to take risks than others. The ultimate concern must be for maximizing the overall valuation of the firm through a judicious consideration of risk-return options. 11.

Optimal policy mix (LO5) Assume that Atlas Sporting Goods Inc. has $840,000 in assets. If it goes with a low-liquidity plan for the assets, it can earn a return of 15 percent, but with a high-liquidity plan the return will be 12 percent. If the firm goes with a short-term financing plan, the financing costs on the $840,000 will be 9 percent, and with a long-term financing plan, the financing costs on the $840,000 will be 11 percent. (Review Table 6-11 for parts a, b, and c of this problem.)

a. Compute the anticipated return after financing costs with the most aggressive assetfinancing mix. b. Compute the anticipated return after financing costs with the most conservative assetfinancing mix. c. Compute the anticipated return after financing costs with the two moderate approaches to the asset-financing mix. d. If the firm used the most aggressive asset-financing mix described in part a and had the anticipated return you computed for part a, what would earnings per share be if the tax rate on the anticipated return was 30 percent and there were 20,000 shares outstanding? e. Now assume the most conservative asset-financing mix described in part b will be utilized. The tax rate will be 30 percent. Also assume there will only be 5,000 shares outstanding. What will earnings per share be? Would it be higher or lower than the earnings per share computed for the most aggressive plan computed in part d?

6-11. Solution: Atlas Sporting Goods Inc. a. Most aggressive

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Low liquidity Short-term financing Anticipated return

$840,000 × 15% = 840,000 × 9% =

$126,000 –75,600 $ 50,400

$840,000 × 12% = 840,000 × 11% =

$ 100,800 –92,400 $ 8,400

$840,000 × 15% = 840,000 × 11% =

$126,000 –92,400 $ 33,600

$840,000 × 12% = 840,000 × 9% =

$ 100,800 –75,600 $ 25,200

b. Most conservative High liquidity Long-term financing Anticipated return c. Moderate approach Low liquidity Long-term financing Anticipated return OR High liquidity Short-term financing Anticipated return

d. Anticipated return $ 50,400 – Taxes (30%) 15,120 Earnings after taxes 35,280 Shares 20,000 Earnings per share $1.76 e. Anticipated return $ 8,400 – Taxes (30%) 2,520 Earnings after taxes 5,880 Shares 5,000 Earnings per share $1.18 It is higher ($1.18 vs. $1.76)

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Chapter 06: Working Capital and the Financing Decision

12.

Matching asset mix and financing plans (LO3) Colter Steel has $5,250,000 in assets.

Temporary current assets .............................

$2,500,000

Permanent current assets.............................

1,575,000

Fixed assets ...................................................

1,175,000

Total assets .............................................

$5,250,000

Short-term rates are 9 percent. Long-term rates are 14 percent. Earnings before interest and taxes are $1,110,000. The tax rate is 40 percent. If long-term financing is perfectly matched (synchronized) with long-term asset needs, and the same is true of short-term financing, what will earnings after taxes be? For a graphical example of perfectly matched plans, see Figure 6-5.

6-12. Solution: Colter Steel Long-term financing equals: Permanent current assets Fixed assets 1,175,000 $2,750,000

$1,575,000

Short-term financing equals: Temporary current assets Long-term interest expense = 14% × $2,750,000 = Short-term interest expense = 9% × 2,500,000 = Total interest expense $ 610,000 Earnings before interest and taxes Interest expense 610,000 Earnings before taxes $ 500,000 Taxes (40%) 200,000 Earnings after taxes $ 300,000

$2,500,000 $ 385,000 $225,000

$ 1,110,000

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13.

Impact of term structure of interest rates on financing plans (LO4) In Problem 12, assume the term structure of interest rates becomes inverted, with short-term rates going to 11 percent and long-term rates 5 percentage points lower than short-term rates. If all other factors in the problem remain unchanged, what will earnings after taxes be?

6-13. Solution: Colter Steel (Continued) Long-term interest expense = 6% × $2,750,000 = Short-term interest expense = 11% × 2,500,000 = Total interest expense $440,000 Earnings before interest and taxes Interest expense 440,000 Earnings before taxes $670,000 Taxes (40%) 268,000 Earnings after taxes $402,000

14.

$165,000 275,000 $1,110,000

Conservative versus aggressive financing (LO5) Guardian Inc. is trying to develop an assetfinancing plan. The firm has $400,000 in temporary current assets and $300,000 in permanent current assets. Guardian also has $500,000 in fixed assets. Assume a tax rate of 40 percent.

a. Construct two alternative financing plans for Guardian. One of the plans should be conservative, with 75 percent of assets financed by long-term sources, and the other should be aggressive, with only 56.25 percent of assets financed by long-term sources. The current interest rate is 15 percent on long-term funds and 10 percent on short-term financing. b. Given that Guardian’s earnings before interest and taxes are $200,000, calculate earnings after taxes for each of your alternatives. c. What would happen if the short- and long-term rates were reversed?

6-14. Solution: Guardian Inc. a. Temporary current assets Permanent current assets Fixed assets 500,000 Total assets $1,200,000

$ 400,000 300,000

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Conservative % of Interest Interest Amount Total Rate Expense $1,200,000 × 0.75 = $900,000 × 0.15 = $135,000 Long-term $1,200,000 × 0.25 = $300,000 × 0.10 = 30,000 Short-term Total interest charge $165,000 Aggressive $1,200,000 × 0.5625 = $675,000 × 0.15 = $101,250 Long-term $1,200,000 × 0.4375 = $525,000 × 0.10 = 52,500 Short-term Total interest charge b. EBIT – Int EBT Tax 40% EAT

$153,750 Conservative $200,000 165,000 35,000 14,000 $ 21,000

Aggressive $200,000 153,750 46,250 18,500 $ 27,750

c. Reversed: Conservative $1,200,000 × 0.75 = $900,000 × 0.10 = $ 90,000 Long-term $1,200,000 × 0.25 = $300,000 × 0.15 = 45,000 Short-term Total interest charge $135,000 Aggressive $1,200,000 × 0.5625 = $675,000 × 0.10 = $67,500 Long-term $1,200,000 × 0.4375 = $525,000 × 0.15 = 78,750 Short-term Total interest charge $146,250 Reversed

Conservative

Aggressive

EBIT

$200,000

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– Int EBT Tax 40% EAT

15.

135,000 65,000 26,000 $ 39,000

146,250 53,750 21,500 $ 32,250

Alternative financing plans (LO5) Lear Inc. has $840,000 in current assets, $370,000 of which are considered permanent current assets. In addition, the firm has $640,000 invested in fixed assets.

a. Lear wishes to finance all fixed assets and half of its permanent current assets with long-term financing costing 8 percent. The balance will be financed with short-term financing, which currently costs 7 percent. Lear’s earnings before interest and taxes are $240,000. Determine Lear’s earnings after taxes under this financing plan. The tax rate is 30 percent. b. As an alternative, Lear might wish to finance all fixed assets and permanent current assets plus half of its temporary current assets with long-term financing and the balance with short-term financing. The same interest rates apply as in part a. Earnings before interest and taxes will be $240,000. What will be Lear’s earnings after taxes? The tax rate is 30 percent. c. What are some of the risks and cost considerations associated with each of these alternative financing strategies?

6-15. Solution: Lear Inc. a. Current assets – Permanent current assets = Temporary current assets $840,000 – $370,000 = $470,000 Long-term interest expense = 8% [$640,000 + ½($370,000)] = 8% ($825,000) = $66,000 Short-term interest expense = 7% [$470,000 + ½($370,000)] = 7% × ($655,000) © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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= $45,850 Total interest expense

= $66,000 + $45,850 = $111,850

Earnings before interest and taxes $240,000 Interest expense 111,850 Earnings before taxes $128,150 Taxes (30%) 38,445 Earnings after taxes $ 89,705 b. Alternative financing plan Long-term interest expense = 8% [$640,000 + $370,000 + ½($470,000)] = 8% ($1,245,000) = $99,600 Short-term interest expense = 7% [½($470,000)] = 7% (235,000) = $16,450 Total interest expense

=$99,600 + $16,450 =$116,050

Earnings before interest and taxes $240,000 Interest 116,050 Earnings before taxes $123,950 Taxes (30%) 37,185 Earnings after taxes $ 86,765 c. The alternative financing plan, which calls for more financing by high-cost debt, is more expensive and reduces aftertax income by $2,940. However, we must not automatically reject this plan because of its higher cost since it has less

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risk. The alternative provides the firm with long-term capital which at times will be in excess of its needs and invested in marketable securities. It will not be forced to pay higher short-term rates on a large portion of its debt when shortterm rates rise and will not be faced with the possibility of no short-term financing for a portion of its permanent current assets when it is time to renew the short-term loan. 16.

Expectations hypothesis and interest rates (LO4) Using the expectations hypothesis theory for the term structure of interest rates, determine the expected return for securities with maturities of two, three, and four years based on the following data. Do an analysis similar to that in Table 66.

1-year T-bill at beginning of year 1

1-year T-bill at beginning of year 2

1-year T-bill at beginning of year 3

1-year T-bill at beginning of year 4

11%

6-16. Solution: 2-year security 3-year security 4-year security 17.

(6% + 7%)/2 = 6.50% (6% + 7% + 9%)/3 = 7.33% (6% + 7% + 9% + 11%)/4 = 8.25%

1-year T-bill at beginning of year 1……

1-year T-bill at beginning of year 2……

1-year T-bill at beginning of year 3……

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1-year T-bill at beginning of year 4……

10%

6-17. Solution: 2-year security 3-year security 4-year security 18.

(5% + 8%)/2 = 6.50% (5% + 8% + 7%)/3 = 6.67% (5% + 8% + 7% + 10%)/4 = 7.50%

Interest costs under alternative plans (LO3) Carmen’s Beauty Salon has estimated monthly financing requirements for the next six months as follows: January ...................

$8,500

April.....................

$8,500

February .................

2,500

May .....................

9,500

March .....................

3,500

June .....................

4,500

Short-term financing will be utilized for the next six months. Projected annual interest rates: January ...................

9.0%

April.....................

16.0%

February .................

10.0%

May .....................

12.0%

March .....................

13.0%

June .....................

12.0%

a. Compute total dollar interest payments for the six months. To convert an annual rate to a monthly rate, divide by 12. Then, multiply this value times the monthly balance. To get your answer, add up the monthly interest payments. b. If long-term financing at 12 percent had been utilized throughout the six months, would the total-dollar interest payments be larger or smaller? Compute the interest owed over the six months and compare your answer to that in part a.

6-18. Solution: Carmen’s Beauty Salon a. Short-term financing Month

Rate

On Monthly Amount

Actual

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Basis January February March April May June

9% 10% 13% 16% 12% 12%

0.75% 0.83% 1.08% 1.33% 1.00% 1.00%

Interest $8,500 $2,500 $3,500 $8,500 $9,500 $4,500

$ 63.75 $ 20.75 $ 37.80 $113.05 $ 95.00 $ 45.00 $375.35

On Monthly Basis Amount

Actual Interest

b. Long-term financing

Month

Rate

January February March April

12% 12% 12% 12%

1% 1% 1% 1%

$8,500 $2,500 $3,500 $8,500

$ 85.00 $ 25.00 $ 35.00 $ 85.00

May June

12% 12%

1% 1%

$9,500 $4,500

$ 95.00 $ 45.00 $370.00

Total dollar interest payments would be larger under the short-term financing plan as described in part b. 19.

Break-even point in interest rates (LO3) In Problem 18, what long-term interest rate would represent a break-even point between using short-term financing as described in part a and longterm financing? (Hint: Divide the interest payments in 18a by the amount of total funds provided for the six months and multiply by 12.)

6-19. Solution: Carmen’s Beauty Salon (Continued)

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Divide the total interest payments in part (a) of $375.35 by the total amount of funds extended $37,000 ($8,500 + 2,500 + 3,500 + 8,500 + 9,500 + 4,500) and multiply by 12.

Interest $375.35   1.014% Monthly rate Principal $37,000 12  1.014%  12.17% Annual rate

20.

Cash receipts schedule (LO1) Eastern Auto Parts Inc. has 15 percent of its sales paid for in cash and 85 percent on credit. All credit accounts are collected in the following month. Assume the following sales: January $65,000 February 55,000 March

100,000

April

45,000

Sales in December of the prior year were $75,000. Prepare a cash receipts schedule for January through April.

6-20. Solution:

Eastern Auto Parts

Sales 15% Cash sales 85% Prior month’s sales* Total cash receipts

Jan

Feb

Mar

Apr

$65,000 9,750 63,750 $73,500

$55,000 8,250 55,250 $63,500

$100,000 15,000 46,750 $61,750

$45,000 6,750 85,000 $91,750

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Based on December sales of $75,000

21.

Level production and related financing effects (LO3) Bombs Away Video Games Corporation has forecasted the following monthly sales:

January ................

$100,000

July................

$ 45,000

February ..............

93,000

August ..........

45,000

March ..................

25,000

September ....

55,000

April .....................

25,000

October ........

85,000

May .....................

20,000

November ....

105,000

June .....................

35,000

December .....

123,000

Total annual sales = $756,000 Bombs Away Video Games sells the popular Strafe and Capture video game. It sells for $5 per unit and costs $2 per unit to produce. A level production policy is followed. Each month’s production is equal to annual sales (in units) divided by 12. Of each month’s sales, 30 percent are for cash and 70 percent are on account. All accounts receivable are collected in the month after the sale is made.

a. Construct a monthly production and inventory schedule in units. Beginning inventory in January is 25,000 units. (Note: To do part a, you should work in terms of units of production and units of sales.) b. Prepare a monthly schedule of cash receipts. Sales in the December before the planning year are $100,000. Work part b using dollars. c. Determine a cash payments schedule for January through December. The production costs of $2 per unit are paid for in the month in which they occur. Other cash payments, besides those for production costs, are $45,000 per month. d. Prepare a monthly cash budget for January through December using the cash receipts schedule from part b and the cash payments schedule from part c. The beginning cash balance is $5,000, which is also the minimum desired.

6-21. Solution: Bombs Away Video Games Corporation a. Production and inventory schedule in units Beginning + Production1 – Sales2

Ending

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Jan. Feb.

Inventory 25,000 17,600

+ +

12,600 12,600

– –

20,000 18,600

= =

Inventory 17,600 11,600

Mar.

11,600

12,600

–

5,000

19,200

Apr. May June July Aug. Sept. Oct. Nov. Dec.

19,200 26,800 35,400 41,000 44,600 48,200 49,800 45,400 37,000

+ + + + + + + + +

12,600 12,600 12,600 12,600 12,600 12,600 12,600 12,600 12,600

– – – – – – – – –

5,000 4,000 7,000 9,000 9,000 11,000 17,000 21,000 24,600

= = = = = = = = =

26,800 35,400 41,000 44,600 48,200 49,800 45,400 37,000 25,000

Total annual sales = $756,000 $756,000/$5 per unit = 151,200 units 151,200 units/12 months = 12,600 per month 2 Monthly dollar sales/$5 price = unit sales

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b. Bombs Away Video Games Corporation Cash Receipts Schedule Jan.

Feb.

Sales (in dollars) $100,000 $93,000 30% Cash sales 30,000 27,900 70% Prior month’s sales 70,000* 70,000 Total cash receipts $100,000 $97,900 *Based on December sales of $100,000

Sales (in dollars) 30% Cash sales 70% Prior month’s sales Total cash receipts

July $45,000 13,500 24,500 $38,000

Aug. $45,000 13,500 31,500 $45,000

Mar.

Apr.

May

June

$25,000 7,500 65,100 $72,600

$25,000 7,500 17,500 $25,000

$20,000 6,000 17,500 $23,500

$35,000 10,500 14,000 $24,500

Sept. $55,000 16,500 31,500 $48,000

Oct. Nov. Dec. $85,000 $105,000 $123,000 25,500 31,500 36,900 38,500 59,500 73,500 $64,000 $ 91,000 $110,400

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c. Bombs Away Video Games Corporation Cash Payments Schedule Constant Production

12,600 units × $2 Other cash payments Total cash payments

Jan.

Feb.

Mar.

Apr.

May

June

$25,200 45,000 $70,200

July

Aug.

Sept.

Oct.

Nov.

Dec.

$25,200 45,000 $70,200

$25,200 $25,200 45,000 45,000 $70,200 $70,200

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d. Bombs Away Video Games Corporation Cash Budget

Net cash flow Beginning cash Cumulative cash balance Monthly loan or (repayment) Cumulative loan Ending cash balance

Jan.

Feb.

Mar.

$29,800 5,000 34,800 -0-034,800

$27,700 34,800 62,500 -0-062,500

$ 2,400 62,500 64,900 -0-064,900

July

Aug.

Sept.

($32,200) ($25,200) ($22,200) 5,000 5,000 5,000 (27,200) (20,200) (17,200) 32,200 25,200 22,200 109,900 135,100 157,300 5,000 5,000 5,000

Apr.

June

($45,200) ($46,700) ($45,700) 64,900 19,700 5,000 19,700 (27,000) (40,700) -032,000 45,700 -032,000 77,700 19,700 5,000 5,000

Oct.

Nov.

Dec.

($6,200) 5,000 (1,200) 6,200 163,500 5,000

$20,800 5,000 25,800 (20,800) 142,700 5,000

$40,200 5,000 45,200 (40,200) 102,500 5,000

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22.

Level production and related financing effects (LO3) Esquire Products Inc. expects the following monthly sales:

January ..............

$28,000

May .............

$8,000

September .........

$29,000

February ............

19,000

June .............

6,000

October ..............

34,000

March ................

12,000

July ..............

22,000

November ..........

42,000

April ..................

14,000

August .........

26,000

December ..........

24,000

Total sales = $264,000 Cash sales are 40 percent in a given month, with the remainder going into accounts receivable. All receivables are collected in the month following the sale. Esquire sells all of its goods for $2 each and produces them for $1 each. Esquire uses level production, and average monthly production is equal to annual production divided by 12.

a. Generate a monthly production and inventory schedule in units. Beginning inventory in January is 12,000 units. (Note: To do part a, you should work in terms of units of production and units of sales.) b. Determine a cash receipts schedule for January through December. Assume that dollar sales in the prior December were $20,000. Work part b using dollars. c. Determine a cash payments schedule for January through December. The production costs ($1 per unit produced) are paid for in the month in which they occur. Other cash payments (besides those for production costs) are $7,400 per month. d. Construct a cash budget for January through December using the cash receipts schedule from part b and the cash payments schedule from part c. The beginning cash balance is $3,000, which is also the minimum desired. e. Determine total current assets for each month. Include cash, accounts receivable, and inventory. Accounts receivable equal sales minus 40 percent of sales for a given month. Inventory is equal to ending inventory (part a) times the cost of $1 per unit.

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6-22. Solution: Esquire Products Inc. a. Production and inventory schedule in units

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Beginning Inventory 12,000 9,000 10,500 15,500 19,500 26,500 34,500 34,500 32,500 29,000 23,000 13,000

+ + + + + + + + + + + + +

Production 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000 11,000

– – – – – – – – – – – – –

Sales 14,000 9,500 6,000 7,000 4,000 3,000 11,000 13,000 14,500 17,000 21,000 12,000

= = = = = = = = = = = = =

Ending Inventory 9,000 10,500 15,500 19,500 26,500 34,500 34,500 32,500 29,000 23,000 13,000 12,000

$264,000 sales/$2 price = 132,000 units 132,000 units/12 months = 11,000 units per month 2 Monthly dollar sales/$2 = number of units

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b. Esquire Products Inc. Cash Receipts Schedule (take dollar values from problem statement) Jan.

Feb.

Mar.

Apr.

May

June

Sales (in dollars) $28,000 $19,000 30% Cash sales 11,200 7,600 70% Prior month’s sales 12,000 16,800 Total receipts $23,200 $24,400 *Based on December sales of $100,000

$12,000 4,800 11,400 $16,200

$14,000 5,600 7,200 $12,800

$8,000 3,200 8,400 $11,600

$6,000 2,400 4,800 $7,200

Sales (in dollars) 30% Cash sales 70% Prior month’s sales Total receipts

July

Aug.

Sept.

Oct.

Nov.

Dec.

$22,000 8,800 3,600 $12,400

$26,000 10,400 13,200 $23,600

$29,000 11,600 15,600 $27,200

$34,000 13,600 17,400 $31,000

$42,000 16,800 20,400 $37,200

$24,000 9,600 25,200 $34,800

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c. Esquire Products Inc. Cash Payments Schedule Constant Production

12,600 units × $2 Other cash payments Total payments

12,600 units × $2 Other cash payments Total cash payments

Jan.

Feb.

Mar.

Apr.

May

June

$11,000 7,400 $18,400

July

Aug.

Sept.

Oct.

Nov.

Dec.

$11,000 7,400 $18,400

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d. Esquire Products Inc. Cash Budget

Cash flow Beginning cash Cumulative cash balance Monthly loan (or repayment) Cumulative loan Ending cash balance

Jan.

Feb.

Mar.

Apr.

May

$4,800 3,000 7,800 -0-0$7,800

$6,000 7,800 13,800 -0-0$13,800

($2,200) 13,800 11,600 -0-0$11,600

($5,600) 11,600 6,000 0 0 $6,000

($6,800) ($11,200) 6,000 3,000 (800) (8,200) 3,800 11,200 3,800 15,000 $3,000 $3,000

July

Aug.

Sept.

Oct.

Nov.

Dec.

($6,000) $5,200 $8,800 3,000 3,000 3,000 ($3,000) $8,200 $11,800 6,000 (5,200) (8,800)

$12,600 3,000 $15,600 (7,000)

$18,800 8,600 $27,400 0

$16,400 27,400 $43,800 0

21,000 $3,000

0 $8,600

0 $27,400

0 $43,800

15,800 $3,000

7,000 $3,000

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June

Chapter 12: The Capital Budgeting Decision

e. Esquire Products Inc. Assets

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Cash

Accounts Receivable Inventory

Total Current

$7,800 13,800 11,600 6,000 3,000 3,000 3,000 3,000 3,000 8,600 27,400 43,800

$16,800 11,400 7,200 8,400 4,800 3,600 13,200 15,600 17,400 20,400 25,200 14,400

$33,600 35,700 34,300 33,900 34,300 41,100 50,700 51,100 49,400 52,000 65,600 70,200

$9,000 10,500 15,500 19,500 26,500 34,500 34,500 32,500 29,000 23,000 13,000 12,000

The instructor may wish to point out how current assets are at relatively high levels and illiquid during June through October. In November and particularly December, the asset levels remain high, but they become increasingly more liquid as inventory diminishes relative to cash. Chapter 7 Current Asset Management Discussion Questions 7-1.

In the management of cash and marketable securities, why should the primary concern be for safety and liquidity rather than maximization of profit?

Cash and marketable securities are generally used to meet the transaction needs of

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Chapter 12: The Capital Budgeting Decision

the firm and for contingency purposes. Because the funds must be available when needed, the primary concern should be with safety and liquidity rather than the maximum profits.

7-2.

Explain the similarities and differences of lockbox systems and regional collection offices.

Both lockbox systems and regional collection offices allow for the rapid processing of checks that originate at distant points. The difference is that a regional collection center requires the commitment of corporate resources and personnel to staff an office, while a lockbox system requires only the use of a post office box and the assistance of a local bank. Clearly, the lockbox system is less expensive.

7-3.

Why would a financial manager want to slow down disbursements?

By slowing down disbursements or the processing of checks against the corporate account, the firm is able to increase float and also to provide a source of short-term financing.

7-4.

Use The Wall Street Journal or some other financial publication to find the going interest rates for the list of marketable securities in Table 7-1 on page 199. Which security would you choose for a short-term investment? Why? The answer to this question may well depend upon the phase of the business cycle at the time the question is considered. In normal times, small CDs and savings accounts may prove adequate. However, in a tight money period, wide differentials may be established between the various instruments and maximum returns may be found in Treasury bills, large CDs, commercial paper, and money market funds.

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Chapter 12: The Capital Budgeting Decision

7-5.

Why are Treasury bills a favorite place for financial managers to invest excess cash? Treasury bills are popular because of the large and active market in which they trade. Because of this, the investor may literally pinpoint the maturity desired choosing anywhere from one day to a year. The “T-bill” market provides maximum liquidity and can absorb almost any dollar amount of business.

7-6.

Explain why the bad debt percentage or any other similar credit-control percentage is not the ultimate measure of success in the management of accounts receivable. What is the key consideration? An investment in accounts receivable requires a commitment of funds as is true of any other investment. The key question is: Will the dollar returns from the resource commitment provide a sufficient rate of return to justify the investment? There is no such thing as too many or too few bad debts, only too low a return on capital.

7-7.

What are three quantitative measures that can be applied to the collection policy of the firm? The average collection period, the ratio of bad debts to credit sales, and the aging of accounts receivable.

7-8.

What are the 5 Cs of credit that are sometimes used by bankers and others to determine whether a potential loan will be repaid? The 5 Cs of credit are character, capital, capacity, conditions, and collateral.

7-9.

What does the EOQ formula tell us? What assumption is made about the usage rate for inventory? The EOQ or economic order point tells us at what size order point we will minimize the overall inventory costs to the firm, with specific attention to inventory ordering costs and inventory carrying costs. It does not directly tell us the average size of inventory on hand and we must determine this as a separate calculation. It is generally assumed, however, that inventory will be used up at a constant rate over time, going from the order size to zero and then back again. Thus, average inventory is half the order size.

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7-10.

Why might a firm keep a safety stock? What effect is it likely to have on carrying cost of inventory? A safety stock protects against the risk of losing sales to competitors due to being out of an item. A safety stock will guard against late deliveries due to weather, production delays, equipment breakdowns and many other things that can go wrong between the placement of an order and its delivery. With more inventory on hand, the carrying cost of inventory will go UP.

7-11.

If a firm uses a just-in-time inventory system, what effect is that likely to have on the number and location of suppliers? A just-in-time inventory system usually means there will be fewer suppliers, and they will be more closely located to the manufacturer they supply.

Problems 1.

7-1.

Cost-benefit analysis of cash management (LO2) City Farm Insurance has collection centers across the country to speed up collections. The company also makes its disbursements from remote disbursement centers. Collection time has been reduced by two days and disbursement time increased by one day because of these policies. Excess funds are being invested in short-term instruments yielding 12 percent per annum. a.

If City Farm has $5 million per day in collections and $3 million per day in disbursements, how many dollars has the cash management system freed up?

How much can City Farm earn in dollars per year on short-term investments made possible by the freed-up cash?

Solution: a.

$5,000,000 daily collections × 2.0 days speedup = $10,000,000 additional collections $3,000,000 daily disbursements × 1.0 days slowdown = $ 3,000,000 delayed disbursements $13,000,000 freed-up funds

$13,000,000 freed-up funds  12% interest rate $ 1,560,000 interest on freed-up cash

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7-2.

Cost-benefit analysis of cash management (LO2) Neon Light Company of Kansas City ships lamps and lighting appliances throughout the country. Ms. Neon has determined that through the establishment of local collection centers around the country, she can speed up the collection of payments by three days. Furthermore, the cash management department of her bank has indicated to her that she can defer her payments on her accounts by one-half day without affecting suppliers. The bank has a remote disbursement center in Florida. a.

If Neon Light Company has $2.5 million per day in collections and $1.1 million per day in disbursements, how many dollars will the cash management system free up?

If Neon Light Company can earn 6 percent per annum on freed-up funds, how much will the income be?

If the total cost of the new system is $425,000, should it be implemented?

Solution: a.

$2,500,000 daily collections × 3.0 days speedup = $7,500,000 additional collections $1,100,000 daily disbursements × 0.5 days slowdown = $550,000 delayed disbursements $8,050,000 freed-up funds

7-3.

$8,050,000 × 6% $ 483,000

freed-up funds interest rate interest on freed-up cash

Yes. The income of $483,000 is $58,000 more than the cost of $425,000.

International cash management (LO2) Orbital Communications has operating plants in over 100 countries. It also keeps funds for transactions purposes in many foreign countries. Assume in 2010 it held 150,000 kronas in Norway worth $40,000. The funds drew 13 percent interest, and the krona increased 6 percent against the dollar. What is the value of the holdings, based on U.S. dollars, at year-end (Hint: multiply $40,000 times 1.13 and then multiply the resulting value by 106 percent.)

Solution:

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Chapter 12: The Capital Budgeting Decision

7-4.

$40,000 × 1.13

= $45,200

$45,200 × 106%

= $47,912

International cash management (LO2) Postal Express has outlets throughout the world. It also keeps funds for transactions purposes in many foreign countries. Assume in 2010 it held 240,000 reals in Brazil worth 170,000 dollars. It drew 12 percent interest, but the Brazilian real declined 24 percent against the dollar. a.

What is the value of its holdings, based on U.S. dollars, at year-end? (Hint: Multiply $170,000 times 1.12 and then multiply the resulting value by 76 percent.)

What is the value of its holdings, based on U.S. dollars, at year-end if instead it drew 9 percent interest and the real went up by 13 percent against the dollar?

Solution: a.

$170,000 × 1.12

= $190,400

$190,400 × 76% holdings

= $144,704 dollar value of real

b. $170,000 × 1.09

= $185,300

$185,300 × 113%

= $209,389 dollar value of real

holdings 5.

7-5.

Average collection period (LO4) Thompson Wood Products has credit sales of $2,160,000 and accounts receivable of $288,000. Compute the value of the average collection period.

Solution: Average collection period 

Accounts receivable Average daily credit sales



$288,000 $2,160,000 / 360



$288,000  48days $6,000

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Chapter 12: The Capital Budgeting Decision

7-6.

Average collection period (LO4) Oral Roberts Dental Supplies has annual sales of $5,520,000. Ninety percent are on credit. The firm has $703,800 in accounts receivable. Compute the value of the average collection period.

Solution:

Average collection period 

Accounts receivable Average daily credit sales

Credit Sales = 90% × $5,520,000 = $4,968,000

7-7.

Accounts receivable balance (LO4) Knight Roundtable Co. has annual credit sales of $1,080,000 and an average collection period of 32 days in 2018. Assume a 360-day year. What is the company’s average accounts receivable balance? Accounts receivable are equal to the average daily credit sales times the average collection period.

Solution:

$1,080,000annual credit sales  $3,000credit sales a day 360days per year $3,000 average  32 average  $96,000 average accounts daily credit sales collection period receivable balance

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Chapter 12: The Capital Budgeting Decision

Accounts receivable balance (LO4) Darla’s Cosmetics has annual credit sales of $1,440,000 and an average collection period of 45 days in 2018. Assume a 360-day year.

What is the company’s average accounts receivable balance? Accounts receivable are equal to the average daily credit sales times the average collection period.

7-8.

Solution: $1,440,000 annual credit sales/360 = $4,000 per day credit sales $4,000 credit sales × 45 average collection period = $180,000 average accounts receivable balance

Credit policy (LO4) Barney’s Antique Shop has annual credit sales of $1,620,000 and an accounts receivable balance of $157,500. Calculate the average collection period (use 360 days in a year).

7-9.

Solution:

Average collection period 

Accounts receivable Average daily credit sales



$157,500 $1, 620, 000 / 360



$157,500 $4,500

 35 days

Since the firm has a shorter average collection period, it appears that the firm does not have a more lenient credit policy.

10.

Determination of credit sales (LO4) Mervyn’s Fine Fashions has an average collection period of 30 days. The accounts receivable balance is $78,000. What is the value of its credit sales?

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Chapter 12: The Capital Budgeting Decision

7-10. Solution:

Credit sales = $2,600 × 360 = $936,000 11.

Aging of accounts receivable (LO4) Route Canal Shipping Company has the following schedule for aging of accounts receivable:

Age of Receivables April 30, 20X1 (1)

(2)

Month of Sales April ................................. March ............................... February ........................... January ............................. Total receivables ...........

Age of Account 0–30 31–60 61–90 91–120

(3) Amounts $ 131,250 93,750 112,500 37,500 $ 375,000

(4) Percent of Amount Due ____ ____ ____ ____ 100%

Fill in column (4) for each month.

If the firm had $1,500,000 in credit sales over the four-month period, compute the average collection period. Average daily sales should be based on a 120-day period.

If the firm likes to see its bills collected in 35 days, should it be satisfied with the average collection period?

Disregarding your answer to part c and considering the aging schedule for accounts receivable, should the company be satisfied?

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Chapter 12: The Capital Budgeting Decision

What additional information does the aging schedule bring to the company that the average collection period may not show?

7-11. Solution:

Route Canal Shipping Company Age of Receivables, April 30, 20X1 a. (1)

(2) Age of Month of Sales Account April 0–30 March 31–60 February 61–90 January 91–120 Total receivables

(3) Amounts $131,250 93,750 112,500 37,500 $375,000

(4) Percent of Amount Due 35% 25% 30% 10% 100%

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Chapter 12: The Capital Budgeting Decision

Average collection period 

Accounts receivable Average daily credit sales



$375,000 $1,500,000 / 120



$375,000 $12,500

 30 days c.

Yes, the average collection of 30 days is less than 35 days.

d. No. The aging schedule provides additional insight that at least 40 percent of the accounts receivable are over 35 days old. e.

12.

It goes beyond showing how many days of credit sales accounts receivables represent to indicate the distribution of accounts receivable between various time frames.

Economic ordering quantity (LO5) Nowlin Pipe & Steel has projected sales of 84,000 pipes this year, an ordering cost of $3 per order, and carrying costs of $1.40 per pipe. a.

What is the economic ordering quantity?

How many orders will be placed during the year?

What will the average inventory be?

7-12. Solution: a.

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Chapter 12: The Capital Budgeting Decision

b. 84,000 units/600 units = 140 orders c. EOQ/2 = 600/2 = 300 units (average inventory) 13.

Economic ordering quantity (LO5) Fisk Corporation is trying to improve its inventory control system and has installed an online computer at its retail stores. Fisk anticipates sales of 49,000 units per year, an ordering cost of $8 per order, and carrying costs of $1.60 per unit. a.

What is the economic ordering quantity?

How many orders will be placed during the year?

What will the average inventory be?

What is the total cost of ordering and carrying inventory?

7-13. Solution: a.

EOQ 

2SO 2  49, 000  $8   700 units C $1.60

b. 49,000 units/700 units = 70 orders c.

EOQ/2 = 700/2 = 350 units (average inventory)

d. 70 orders × $8 ordering cost 350 units × $1.60 carrying cost per unit Total costs

= $ 560 = 560 = $1,120

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14.

Economic ordering quantity (LO5) Fisk Corporation is trying to improve its inventory control system and has installed an online computer at its retail stores. Fisk anticipates sales of 49,000 units per year, an ordering cost of $2 per order, and carrying costs of $1.60 per unit. a.

What is the economic ordering quantity?

How many orders will be placed during the year?

What will the average inventory be?

What is the total cost of ordering and carrying inventory?

7-14. Solution: a.

EOQ  

2SO 2  49, 000  $2  C $1.60 $196, 000  122,500  350 units $1.60

b. 49,000 units/350 units = 140 orders c. EOQ/2 = 350/2 = 175 units (average inventory) d. 140 orders × $2 ordering cost 175 units × $1.60 carrying cost per unit Total costs 15.

= $280 = 280 = $560

Economic ordering quantity with safety stock (LO5) Diagnostic Supplies has expected sales of 84,100 units per year, carrying costs of $5 per unit, and an ordering cost of $10 per order. a.

What is the economic order quantity?

What is the average inventory? What is the total carrying cost?

Assume an additional 80 units of inventory will be required as safety stock. What will the new average inventory be? What will the new total carrying cost be?

7-15. Solution:

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Chapter 12: The Capital Budgeting Decision

EOQ 



2SO 2  84,100  $10  C $5 $1, 682, 000  $336, 400  580 units $5

b. EOQ/2 = 580/2 = 290 units (average inventory) 290 units × $5 carrying cost/unit = $1,450 total carrying cost c.

Average inventory  

EOQ  Safety Stock 2 580  80  290  80  370 2

370 inventory × $5 carrying cost per year = $1,850 total carrying cost 16.

Level versus seasonal production (LO5) Wisconsin Snowmobile Corp. is considering a switch to level production. Cost efficiencies would occur under level production, and aftertax costs would decline by $36,000, but inventory would increase by $360,000. Wisconsin Snowmobile has to finance the extra inventory at a cost of 11 percent. a.

Determine the extra cost or savings of switching over to level production. Should the company go ahead and switch to level production?

How low would interest rates need to fall before level production would be feasible?

7-16. Solution: a.

Inventory increases by × Interest expense Increased costs

$360,000 11% $ 39,600

Savings Less: Increased costs

$36,000 ($39,600)

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Chapter 12: The Capital Budgeting Decision

Loss

($ 3,600)

Don’t switch to level production. b. If interest rates fall to 10 percent or less, the switch would be feasible.

However, the decision is more complicated because it depends on expectations for interest rates. If the extra inventory were considered permanent current assets and was financed by locking in long-term interest rates below 10 percent, then it would make sense to switch. However, given that short-term rates are volatile, this decision can’t be made on a dip in short-term interest rates below 10 percent.

17.

Credit policy decision (LO4) Johnson Electronics is considering extending trade credit to some customers previously considered poor risks. Sales would increase by $150,000 if credit is extended to these new customers. Of the new accounts receivable generated, 5 percent will prove to be uncollectible. Additional collection costs will be 2 percent of sales, and production and selling costs will be 74 percent of sales. The firm is in the 35 percent tax bracket. a.

Compute the incremental income after taxes.

What will Johnson’s incremental return on sales be if these new credit customers are accepted?

If the receivable turnover ratio is 3 to 1, and no other asset buildup is needed to serve the new customers, what will Johnson’s incremental return on new average investment be?

7-17. Solution: a.

Additional sales .................................................... $150,000 Accounts uncollectible (5% of new sales) ........... – 7,500 Annual incremental revenue ................................ $ 142,500

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Chapter 12: The Capital Budgeting Decision

Collection costs (2% of new sales) ...................... – 3,000 Production and selling costs (74% of new sales) .......................................... – 111,000 Annual income before taxes ................................. $ 28,500 Taxes (35%) ......................................................... – 9,975 Incremental income after taxes ............................ $ 18,525 b.

Incremental return on sales 

Incremental income Incremental sales

 $18,525 / $150, 000  12.35% c.

18.

Receivable turnover = Sales/Receivable turnover = 3x Receivables = Sales/Receivable turnover = $150,000/3 = $50,000.00 Incremental return on new average investment = $18,525/$50,000.00 = 37.05%

Credit policy decision-receivables and inventory (LO4 and 5) Henderson Office Supply is considering a more liberal credit policy to increase sales, but expects that 9 percent of the new accounts will be uncollectible. Collection costs are 6 percent of new sales, production and selling costs are 74 percent, and accounts receivable turnover is four times. Assume income taxes of 20 percent and an increase in sales of $65,000. No other asset buildup will be required to service the new accounts. a.

What is the level of accounts receivable to support this sales expansion?

What would be Henderson’s incremental aftertax return on investment?

Should Henderson liberalize credit if a 16 percent aftertax return on investment is required?

Assume that Henderson also needs to increase its level of inventory to support new sales and that inventory turnover is two times. d.

What would be the total incremental investment in accounts receivable and inventory to support a $65,000 increase in sales?

Given the income determined in part b and the investment determined in part d, should Henderson extend more liberal credit terms?

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Chapter 12: The Capital Budgeting Decision

7-18. Solution: a.

Investment in accounts receivable 

$65,000  $16, 250 4

b. Added sales .......................................................... Accounts uncollectible (9% of new sales) ........... Annual incremental revenue ................................ Collection costs (6% of new sales) ...................... Production and selling costs (74% of new sales) Annual income before taxes ................................. Taxes (20%) ......................................................... Incremental income after taxes ............................ Return on incremental investment 

c. d.

$ 65,000 – 5,850 $ 59,150 – 3,900 – 48,100 $ 7,150 – 1,430 $ 5,720

$5,720  35.20% 16,250

Yes! 35.20 percent exceeds the required return of 16 percent. $65,000  $32,500 2 Total incremental investment Investment in inventory =

Inventory Accounts receivable Incremental investment

$32,500 16,250 $48,750

$5,720/$48,750 = 11.73% return on investment e.

No! 11.73 percent is less than the required return of 16 percent.

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Chapter 12: The Capital Budgeting Decision

19.

Credit policy decision with changing variables (LO4) Fast Turnstiles Co. is evaluating the extension of credit to a new group of customers. Although these customers will provide $180,000 in additional credit sales, 12 percent are likely to be uncollectible. The company will also incur $16,200 in additional collection expense. Production and marketing costs represent 72 percent of sales. The firm is in a 34 percent tax bracket and has a receivables turnover of four times. No other asset buildup will be required to service the new customers. The firm has a 10 percent desired return. a.

Calculate the incremental income after taxes and the return on incremental investment. Should Fast Turnstiles Co. extend credit to these customers?

Calculate the incremental income after taxes and the return on incremental investment if 15 percent of the new sales prove to be uncollectible. Should credit be extended if 15 percent of the new sales prove uncollectible?

Calculate the return on incremental investment if the receivables turnover drops to 1.6, and 12 percent of the accounts are uncollectible. Should credit be extended if the receivables turnover drops to 1.6, and 12 percent of the accounts are uncollectible (as in part a)?

7-19. Solution: Fast Turnstiles Co. a.

Added sales ............................................................. $180,000 Accounts uncollectible (12% of new sales) ............ 21,600 Annual incremental revenue ................................... 158,400 Collection costs ....................................................... 16,200 Production and selling costs (72% of new sales) ................................................ 129,600 Annual income before taxes .................................... 12,600 Taxes (34%) ............................................................ 4,284 Incremental income after taxes ............................... $ 8,316

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Chapter 12: The Capital Budgeting Decision

Re ceivable turnover 

$180,000  $45, 000 new receivables 4.0

Return on incremental investment 

$8,316  18.48% $45, 000

Yes, extend credit to these customers since the incremental return of 18.48 percent is greater than 10 percent. b. Added sales .......................................................... $180,000 Accounts uncollectible (15% of new sales) ......... 27,000 Annual incremental revenue ................................ $153,000 Collection costs .................................................... 16,200 Production and selling costs (72% of new sales) .............................................. 129,600 Annual income before taxes ................................. 7,200 Taxes (34%) ......................................................... 2,448 Incremental income after taxes ............................ $ 4,752 Return on incremental investment 

$4,752  10.56% $45,000

Yes, extend credit. c.

If receivable turnover drops to 1.6x, the investment in accounts receivable would equal $180,000/1.6 = $112,500. Return on incremental investment 

$8,316  7.39% $112,500

Credit should not be extended because 7.39 percent is less than the desired 10 percent. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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20.

Credit policy decision with changing variables (LO4) Slow Roll Drum Co. is evaluating the extension of credit to a new group of customers. Although these customers will provide $180,000 in additional credit sales, 12 percent are likely to be uncollectible. The company will also incur $16,200 in additional collection expense. Production and marketing costs represent 72 percent of sales. The firm is in a 34 percent tax bracket. No other asset buildup will be required to service the new customers. The firm has a 10 percent desired return. Assume the average collection period is 120 days. a. Compute the return on incremental investment b. Should credit be extended?

7-20. Solution: Slow Roll Drum Co. a.

First compute the accounts receivable balance. Accounts receivable = average collection × average daily period sales

120 days 

$180,000  120  $500  $60,000 360 days

Then, compute return on incremental investment. $8,316  13.86% $60, 000

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Yes, extend credit. 13.86 percent is greater than 10 percent.

21.

Credit policy and return on investment (LO4) Global Services is considering a promotional campaign that will increase annual credit sales by $450,000. The company will require investments in accounts receivable, inventory, and plant and equipment. The turnover for each is as follows:

Accounts receivable .................................... Inventory ..................................................... Plant and equipment ....................................

2x 6x 1x

All $450,000 of the sales will be collectible. However, collection costs will be 6 percent of sales, and production and selling costs will be 71 percent of sales. The cost to carry inventory will be 4 percent of inventory. Depreciation expense on plant and equipment will be 5 percent of plant and equipment. The tax rate is 30 percent. a.

Compute the investments in accounts receivable, inventory, and plant and equipment based on the turnover ratios. Add the three together.

Compute the accounts receivable collection costs and production and selling costs and then add the two figures together.

Compute the costs of carrying inventory.

Compute the depreciation expense on new plant and equipment.

Add together all the costs in parts b, c, and d.

Subtract the answer from part e from the sales figure of $450,000 to arrive at income before taxes. Subtract taxes at a rate of 30 percent to arrive at income after taxes.

Divide the aftertax return figure in part f by the total investment figure in part a. If the firm has a required return on investment of 8 percent, should it undertake the promotional campaign described throughout this problem.

7-21. Solution: Global Services a.

Accounts receivable = Sales/Accounts receivable turnover $225,000  $450,000/2 Inventory = Sales/Inventory turnover

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$75,000  $450,000/6

Plant and equipment = Sales/(Plant and equipment turnover) $450, 000  $450, 000 / 1 $750,000

Total investment

b. Collection cost = 6% × $450,000 $ 27,000 Production and selling costs = 71% × $450,000 = 319,500 Total costs related to accounts receivable $346,500 c.

Cost of carrying inventory 4% × inventory 4% × $75,000

d. Depreciation expense 5% × $450,000 e.

$3,000

$22,500

Total costs related to accounts receivable $346,500 Cost of carrying inventory Depreciation expense Total costs

3,000 22,500 $372,000

Sales – Total costs Income before taxes Taxes (30%) Income after taxes

$450,000 372,000 78,000 23,400 $ 54,600

Income after taxes $54, 600   7.28% Total investment 750, 000

No, it should not undertake the campaign.

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The aftertax return of 7.28 percent exceeds the required rate of return of 8 percent. (Problems 22–25 are a series and should be completed in order.) 22.

Credit policy decision with changing variables (LO4) Dome Metals has credit sales of $180,000 yearly with credit terms of net 60 days, which is also the average collection period. Dome does not offer a discount for early payment, so its customers take the full 60 days to pay. What is the average receivables balance? Receivables turnover?

7-22. Solution: Sales/360 days = Average daily sales $180,000/360 = $500 Accounts receivable balance = $500 × 60 days = $30,000 Receivable turnover =

Sales $180, 000  6 Receivables $30, 000

or 360 days/60 = 6x 23.

Dome Metals had credit sales of $180,000 yearly. If Dome offers a 3 percent discount for payment in 18 days, what will the new average receivables balance be? Use the credit sales of $180,000 for your calculations of receivables.

7-23. Solution: Sales/360 days = Average daily sales $180,000/360 = $500 $500 × 18 days = $9,000 new receivable balance 24.

Dome Metals had credit sales of $180,000 yearly with credit terms of net 60 days, which is also the average collection period. What will be the net gain or loss if Dome offered a 3 percent

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Chapter 12: The Capital Budgeting Decision

discount for payment in 18 days, every customer takes advantage of the new terms, and Dome reduces its bank loans, which cost 12 percent, by the cash generated from its reduced receivables? Should it offer the discount? Use the credit sales of $180,000 yearly with credit terms of net 60 days for your calculation.

7-24. Solution: Sales / 360 days = Average daily sales $180,000 / 360 = $500 Old receivable balance = $500 × 60 days = $30,000 New receivable balance = $500 × 18 days = $9,000 Old receivables – New receivables = Funds freed by with discount discount $30,000

–

$9,000

= $21,000 discount

Savings on loan = 12% × $21,000 .......... Discount on sales = 3% × $180,000 ........ Net change in income from discount ......

= $ 2,520 = (5,400) $(2,880)

No! Don’t offer the discount since the income from reduced bank loans does not offset the loss on the discount. 25.

Dome Metals has credit sales of $180,000 yearly with credit terms of net 60 days, which is also the average collection period. Dome offered a 3 percent discount for payment in 18 days, and Dome reduced its bank loans, which cost 12 percent. Now assume that the new trade terms of 3/18, net 60 will increase sales by 15 percent because the discount makes the Dome’s price competitive. If Dome earns 20 percent on sales before discounts, what will be the net change in income? Should it offer the discount?

7-25. Solution: New sales = $180,000 × 1.15 = $207,000 Change in sales = $207,000 – $180,000 = $ 27,000 Sales per day = $207,000/360 = $575 Average receivables balance = $575 × 18 = $ 10,350

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Increase profit on new sales = 20% × $27,000 Reduced profit because = 3% × $207,000 of discount Savings in interest cost ($30,000 – $10,350) × 12% Net change in income............................................

= $ 4,320 = (6,210) =

2,358 $ 1,548

Yes, offer the discount because total profit increases.

COMPREHENSIVE PROBLEM Logan Distributing Company (receivables and inventory policy) (LO4 and 5) Logan Distributing Company of Atlanta sells fans and heaters to retail outlets throughout the Southeast. Joe Logan, the president of the company, is thinking about changing the firm’s credit policy to attract customers away from competitors. The present policy calls for a 1/10, net 30 cash discount. The new policy would call for a 3/10, net 50 cash discount. Currently, 30 percent of Logan customers are taking the discount, and it is anticipated that this number would go up to 50 percent with the new discount policy. It is further anticipated that annual sales would increase from a level of $400,000 to $600,000 as a result of the change in the cash discount policy. The increased sales would also affect the inventory level. The average inventory carried by Logan is based on a determination of an EOQ. Assume sales of fans and heaters increase from 15,000 to 22,500 units. The ordering cost for each order is $200 and the carrying cost per unit is $1.50 (these values will not change with the discount). The average inventory is based on EOQ/2. Each unit in inventory has an average cost of $12. Cost of goods sold is equal to 65 percent of net sales; general and administrative expenses are 15 percent of net sales, and interest payments of 14 percent will only be necessary for the increase in the accounts receivable and inventory balances. Taxes will be 40 percent of beforetax income. a.

Compute the accounts receivable balance before and after the change in the cash discount policy. Use the net sales (total sales minus cash discounts) to determine the average daily sales.

Determine EOQ before and after the change in the cash discount policy. Translate this into average inventory (in units and dollars) before and after the change in the cash discount policy.

Complete the following income statement.

Before Policy Change

After Policy Change

Net sales (Sales – Cash discounts) ...............

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Cost of goods sold ........................................ Gross profit .................................................. General and administrative expense............. Operating profit ............................................ Interest on increase in accounts receivable and inventory (14%) ................ Income before taxes ..................................... Taxes ............................................................ Income after taxes ........................................ d.

Should the new cash discount policy be utilized? Briefly comment.

CP 7-1. Solution: a.

Accounts receivable = Average collection × Average daily period sales Before Average collection period 0.30 × 10 days = 3 0.70 × 30 days = 21 24 days (Avg. acc. receivables) Average daily sales Credit sales  Discount $400,000  .01.30  $400,000   360 days 360 days 

$400,000  $1, 200 360 days



$398,800 360 days

Average daily sales  $1,107.78

Accounts receivable = 24 days × $1,107.78 = $26,586.72 before policy change © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

After Average collection period 0.50 × 10 days = 5 0.50 × 50 days = 25 30 days (Avg. acc. receivables) Average daily sales

Credit sales  discount $600,000  .03.50  $600,000   360 days 360 days 

$600,000  $9,000 360 days



$591,000 360 days

Average daily sales  $1,641.67 Accounts receivable = 30 days × $1,641.67 = $49,250.10 after policy change b.

Before EOQ 

2SO C

2  15,000  $200 $6,000,000   4,000,000  2,000 units $1.50 $1.50

After 2  22,000  $200 $9,000,000   6,000,000  2, 449.49 $1.50 $1.50

Average inventory Before

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2,000  1,000 units 1,000 units  $12  $12,000 2 After 2,449.49 1,224.75 units 1,224.75 units × $12 =  2 or 1,225 (rounded) $14,697 or $14,700 (rounded)

Net sales (Sales – Cash discount) Cost of goods sold (65%) Gross profit General and admin. expense (15%) Operating profit *Interest on increase in accounts receivable and inventory (14%) Income before taxes Taxes (40%) Income after taxes

*14%  AR

Before Policy Change $398,800 259,220 139,580

After Policy Change $591,000 384,150 206,850

59,820

88,650

79,760

118,200

79,760 31,904 $ 47,856

3,550.45 114,649.55 45,859.82 $ 68,789.73

 14%   $49,250.10  $26,586.72 

 14%  $22,663.38 14%  INV

 $3,172.87

=14%   $14,697  $12,000 

 14%  $2.697

 $ 377.58 $3,550.45

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Chapter 12: The Capital Budgeting Decision

The new cash discount policy should be utilized. The interest cost on the increased accounts receivable and inventory is small in comparison to the increased operating profit from the policy change. Chapter 8 Sources of Short-Term Financing

Discussion Questions 8-1.

Under what circumstances would it be advisable to borrow money to take a cash discount?

It is advisable to borrow in order to take a cash discount when the cost of borrowing is less than the cost of foregoing the discount. If it cost us 36 percent to miss a discount, we would be much better off finding an alternate source of funds for 8 to 10 percent.

8-2.

Discuss the relative use of credit between large and small firms. Which group is generally in the net creditor position, and why?

Larger firms tend to be in a net creditor position because they have the financial resources to be suppliers to credit. The smaller firm must look to the larger manufacturer or wholesaler to help carry the firm’s financing requirements.

8-3.

How have new banking laws influenced competition?

New banking laws allowed more competition and gave banks the right to expand across state lines to create larger, more competitive markets. They also increased bank mergers.

8-4.

What is the prime interest rate? How does the average bank customer fare in regard to the prime interest rate?

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The prime rate is the rate that a bank charges its most creditworthy customers. The average customer can expect to pay one or two percent (or more) above prime.

8-5.

What does LIBOR mean? Is LIBOR normally higher or lower than the U.S. prime interest rate?

LIBOR stands for London Interbank Offered Rate. As indicated in Figure 8-1, it is consistently below the prime rate.

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Chapter 12: The Capital Budgeting Decision

8-6.

What advantages do compensating balances have for banks? Are the advantages to banks necessarily disadvantages to corporate borrowers?

The use of a compensating balance or minimum required account balance allows the banker to generate a higher return on a loan because not all funds are actually made available to the borrower. A $125,000 loan with a $25,000 compensating balance requirement means only $100,000 is being provided on a net basis. This benefit to the lender need not be a disadvantage to the borrower. The borrower may, in turn, receive a lower quoted interest rate and certain gratuitous services because of the compensating balance requirement.

8-7.

Commercial paper may show up on corporate balance sheets as either a current asset or a current liability. Explain this statement. Commercial paper can be either purchased or issued by a corporation. To the extent one corporation purchases another corporation’s commercial paper as a short-term investment, it is a current asset. Conversely, if a corporation issues its own commercial paper, it is a current liability.

8-8.

What are the advantages of commercial paper in comparison with bank borrowing at the prime rate? What is a disadvantage? In comparison to bank borrowing, commercial paper can generally be issued at below the prime rate. Furthermore, there are no compensating balance requirements, though the firm is required to maintain approved credit lines at a bank. Finally, there is a certain degree of prestige associated with the issuance of commercial paper. The drawback is that commercial paper may be an uncertain source of funds. When money gets tight or confidence in the commercial paper market diminishes, funds may not be available. There is no loyalty factor such as that which exists between a bank and its best borrowers.

8-9.

What is the difference between pledging accounts receivable and factoring accounts receivable? Pledging accounts receivable means receivables are used as collateral for a loan; factoring account receivables means they are sold outright to a finance company.

8-10.

What is an asset-backed public offering? A public offering is backed by an asset (accounts receivable) as collateral. Essentially a

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firm sells its receivables into the securities markets. 8-11.

Briefly discuss three types of lender control used in inventory financing. Three types of lender control used in inventory financing are: a. Blanket inventory—Lien-general claim against inventory or collateral. No specific items are marked or designated. b. Trust receipt—Borrower holds the inventory in trust for the lender. Each item is marked and has a serial number. When the inventory is sold, the trust receipt is canceled and the funds go into the lender’s account. c. Warehousing—The inventory is physically identified, segregated, and stored under the direction of an independent warehouse company that controls the movement of the goods. If done on the premises of the warehousing firm, it is termed public warehousing. An alternate arrangement is field warehousing, whereby the same procedures are conducted on the borrower’s property.

8-12.

What is meant by hedging in the financial futures market to offset interest rate risks? Hedging means to engage in a transaction that partially or fully reduces a prior risk exposure. In selling a financial futures contract, if interest rates go up, one is able to buy back the contract at a profit. This will help to offset the higher interest charges to a corporation or other business entity.

Problems 1.

8-1.

Cash discount (LO1) Compute the cost of not taking the following cash discounts. a.

2/10, net 40.

2/15, net 30.

2/10, net 45.

3/10, net 90.

Solution: Cost of not Discount % 360 taking a cash =  100%  Disc.% Final due date  discount Discount period

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Chapter 12: The Capital Budgeting Decision

a. Cost of 2% 360    2.04%  12.00  24.48% lost discount 98% 40  10 b. Cost of 2% 360 =   2.04%  24.00  48.96% lost discount 98% 30  15 c. Cost of 2% 360 =   2.04%  10.29  20.99% lost discount 98% 45  10 d. Cost of 3% 360 =   3.09%  4.50  13.91% lost discount 97% 90  10 2.

8-2.

Cash discount decision (LO1) Regis Clothiers can borrow from its bank at 16 percent to take a cash discount. The terms of the cash discount are 3/16, net 55. Should the firm borrow the funds?

Solution: First, compute the cost of not taking the cash discount and compare this figure to the cost of the loan.

= 3.09% × 9.23 = 28.52% The cost of not taking the cash discount is greater than the cost of the loan (42.82 percent vs. 16 percent). The firm should borrow the money and take the cash discount.

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Chapter 12: The Capital Budgeting Decision

Cash discount decision (LO1) Simmons Corp. can borrow from its bank at 17 percent to take a cash discount. The terms of the cash discount are 1.5/10, net 45. Should the firm borrow the funds?

8-3.

Solution: First, compute the cost of not taking the cash discount and compare this figure to the cost of the loan. Cost of not Discount% 360 taking a cash =  100%  Disc.% Final due date  Discount period discount



1.5% 360  98.5% 45  10

1.52%  10.29  15.64% The cost of not taking the cash discount is less than the cost of the loan (15.64 percent vs. 17 percent). The firm should not borrow the money to take the cash discount. 4.

8-4.

Effective rate of interest (LO2) Your bank will lend you $4,000 for 45 days at a cost of $50 interest. What is your effective rate of interest?

Solution: Interest Days in the year (360)  Principal Days loan is outstanding $50 360   $4, 000 45  1.25%  8  10%

Effective rate =

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Chapter 12: The Capital Budgeting Decision

Effective rate of interest (LO2) A pawnshop will lend $3,500 for 45 days at a cost of $30 interest. What is the effective rate of interest?

8-5. Solution:

8-6.

Effective rate on discounted loan (LO2) Sol Pine borrows $6,500 for one year at 8 percent interest. What is the effective rate of interest if the loan is discounted?

Solution: Sol Pine

= 8.7%

Effective rate on discounted loan (LO2) Mary Ott is going to borrow $10,400 for 120 days and pay $150 interest. What is the effective rate of interest if the loan is discounted?

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Chapter 12: The Capital Budgeting Decision

8-7.

Solution: Effective rate on a = Interest  Days per year (360) discounted loan Princ.  Int. Days loan is outstanding $150 360 $150   3 $10, 400  $150 120 $10, 250  1.46%  3  4.38% 

8-8.

Prime vs. LIBOR (LO2) Dr. Ruth is going to borrow $5,000 to help write a book. The loan is for one year and the money can either be borrowed at the prime rate or the LIBOR rate. Assume the prime rate is 11 percent and LIBOR 1.5 percent less. Also assume there will be a $45 transaction fee with LIBOR (this amount must be added to the interest cost with LIBOR). Which loan has the lower effective interest cost?

Solution:

Effective interest = (9.5%  $5,000)+$45=$475+$45=$520 $520 360  10.40%  1  10.40% $5, 000 360

LIBOR is cheaper than prime (10.40 percent vs. 11 percent).

8-9.

Foreign borrowing (LO2) Gulliver Travel Agencies thinks interest rates in Europe are low. The firm borrows euros at 9 percent for one year. During this time period the dollar falls 12 percent against the euro. What is the effective interest rate on the loan for one year? (Consider the 12 percent fall in the value of the dollar as well as the interest payment.)

Solution: 9% Interest 12% Decline in the dollar (increased cost in euros) 21% Total effective cost

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Chapter 12: The Capital Budgeting Decision

10.

Dollar cost of a loan (LO2) Talmud Book Company borrows $24,900 for 60 days at 12 percent interest. What is the dollar cost of the loan?

Dollar cost of loan = Amount borrowed × Interest rate ×

Days loan is outstanding

 

Days in the year 360

8-10. Solution:

Dollar cost of loan = Amount borrowed  Interest rate 

Days loan is outstanding Days per year (360)

60 360 1  $24,900  12%  6  $24,900  2.00%  $498  $24,900  12% 

11.

Net credit position (LO1) McGriff Dog Food Company normally takes 27 days to pay for average daily credit purchases of $9,530. Its average daily sales are $10,680, and it collects accounts in 32 days. a.

What is its net credit position? That is, compute its accounts receivable and accounts payable and subtract the latter from the former.

Accounts receivable = Average daily credit sales × Average collection period Accounts payable = Average daily credit purchases × Average payment period b.

If the firm extends its average payment period from 27 days to 37 days (and all else remains the same), what is the firm’s new net credit position? Has it improved its cash flow?

8-11. Solution: a.

Net credit position = Accounts receivable – Accounts payable

Average Accounts receivable = Average daily  credit sales collection period $341,760



$10,680



32days

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Chapter 12: The Capital Budgeting Decision

Average Accounts payable = Average daily  credit purchases payment period $257,310 

$9,530



Net credit position  $341,760 – $257,310  $84,450 b. Accounts receivable will remain at $341,760 Accounts payable = $9,530 × 37 = 352,610 Net credit position ($ 10,850) The firm has improved its cash flow position. Instead of extending $84,450 more in credit (funds) than it is receiving, it has reversed the position and is the net recipient of $10,850 in credit.

12.

Compensating balances (LO2) Maxim Air Filters Inc. plans to borrow $300,000 for one year. Northeast National Bank will lend the money at 10 percent interest and requires a compensating balance of 20 percent. What is the effective rate of interest?

8-12. Solution: Effective rate of interest with 20% compensating balance = Interest rate 10% 10%    12.5% 1  C  1  .2  .8 or

Interest Days of the year (360)  Principal  Compensating balance Days loan is outstanding $30, 000 $30, 000  1   1  12.5% $300, 000  $60, 000 $240, 000

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Chapter 12: The Capital Budgeting Decision

13.

Compensating balances (LO2) Digital Access Inc. needs $400,000 in funds for a project. a.

With a compensating balance requirement of 20 percent, how much will the firm need to borrow?

Given your answer to part a and a stated interest rate of 9 percent on the total amount borrowed, what is the effective rate on the $400,000 actually being used?

8-13. Solution: a.

Amount to be borrowed = 

Amount needed 1  C  $400, 000 $400, 000  1  .20 .80  

 $500, 000 $500,000 Total amount borrowed 9% Interest rate $ 45,000 Interest $45, 000  11.5% $400, 000

14.

Compensating balances and installment loans (LO2) Carey Company is borrowing $200,000 for one year at 12 percent from Second Intrastate Bank. The bank requires a 20 percent compensating balance. What is the effective rate of interest? What would the effective rate be if Carey were required to make 12 equal monthly payments to retire the loan? The principal, as used in Formula 8–6, refers to funds the firm can effectively utilize (Amount borrowed – Compensating balance).

8-14. Solution:

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Chapter 12: The Capital Budgeting Decision

Effective rate of interest with 20% compensating balance =

Interest Days in the year (360)  Principal  Compensating balance Days loan is outstanding $24,000 360 $24,000 360      15% $200,000  $40,000 360 $160,000 360 Installment loan with compensating balance 2  Annual no. payments  Interest  Total no. of payments + 1  Principal

15.



2  12  $24,000 12  1   $200,000  $40,000 



$576,000 $576,000   27.69% 13  $160,000 $2,080,000

Compensating balances with idle cash balances (LO2) Randall Corporation plans to borrow $276,000 for one year at 19 percent from the Waco State Bank. There is a 28 percent compensating balance requirement. Randall Corporation keeps minimum transaction balances of $9,000 in the normal course of business. This idle cash counts toward meeting the compensating balance requirement. What is the effective rate of interest?

8-15. Solution: Effective rate of interest =

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Chapter 12: The Capital Budgeting Decision

* Required compensating balance Minimum balance on deposit  Additional funds needed at bank ($77,280 – $9,000) = $68,280 16.

Compensating balances with idle cash balances (LO2) The treasurer for the Macon Blue Sox baseball team is seeking a $23,600 loan for one year from the 4th National Bank of Macon. The stated interest rate is 10 percent, and there is a 15 percent compensating balance requirement. The treasurer always keeps a minimum of $2,280 in the baseball team’s checking accounts. These funds count toward meeting any compensating balance requirements. What will be the effective rate of interest on this loan?

8-16. Solution: Effective rate of interest =

* Required compensating balance  Minimum balance on deposit  Additional funds needed at bank ($3,540 – $2,280) = $1,260 17.

Effective rate under different terms (LO2) Your company plans to borrow $13 million for 12 months, and your banker gives you a stated rate of 24 percent interest. You would like to know the effective rate of interest for the following types of loans. (Each of the following parts stands alone.) a.

Simple 24 percent interest with a 10 percent compensating balance.

Discounted interest.

An installment loan (12 payments).

Discounted interest with a 5 percent compensating balance.

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Chapter 12: The Capital Budgeting Decision

8-17. Solution: a.

Simple interest with a 10% compensating balance $3,120, 000 $3,120, 000 1   26.67% $13, 000, 000  $1,300, 000 $11, 700, 000

b. Discounted interest $3,120, 000 $3,120, 000 1   31.58% $13, 000, 000  $3,120, 000 $9,880, 000

An installment loan with 12 payments

2  12  $3,120, 000 $74,880, 000   44.31% 13  $13, 000, 000 $169, 000, 000 d. Discounted interest with a 5% compensating balance $3,120, 000 /  $13, 000, 000 – $3,120, 000 – $650, 000  

$3,120,000/$9,230,000 = 33.80% 18.

Effective rate under different terms (LO2) If you borrow $5,300 at $400 interest for one year, what is your effective interest rate for the following payment plans? a.

Annual payment.

Semiannual payments.

Quarterly payments.

Monthly payments.

8-18. Solution: a. $400/$5,300 = 7.55% Use formula 8-6 for b, c, and d. Rate on installment loan =

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Chapter 12: The Capital Budgeting Decision

2  Annual no. of payments  Interest  Total no. of payments + 1  Principal

19.

b. (2 × 2 × $400)/(3 × $5,300) = $1,600/$15,900

= 10.06%

c. (2 × 4 × $400)/(5 × $5,300) = $3,200/$26,500

= 12.08%

d. (2 × 12 × $400)/(13 × $5,300) = $9,600/$68,900

= 13.93%

Effective rate under different terms (LO2) Zerox Copying Company plans to borrow $172,000. New Jersey National Bank will lend the money at one-half percentage point over the prime rate at the time of 17½ percent (18 percent total) and requires a compensating balance of 21 percent. The principal in this case will be funds that the firm can effectively use in the business. This loan is for one year. What is the effective rate of interest? What would the effective rate be if Zerox were required to make four quarterly payments to retire the loan?

8-19. Solution: Effective rates of interest with compensating balance First determine interest 17½% (prime rate) + ½% = 18% 18%  $172,000  $30,960 Then determine the rate $30,960 $30,960 1   22.78% $172, 000  36,120 $135,880

Effective rate of interest with compensating balance and four quarterly payments.

2  4  $30,960 $247, 680   36.46% (4  1)  $135,880 $679, 400

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Chapter 12: The Capital Budgeting Decision

20.

Installment loan for multiyears (LO2) Lewis and Clark Camping Supplies Inc. is borrowing $59,000 from Western State Bank. The total interest is $20,400. The loan will be paid by making equal monthly payments for the next three years. What is the effective rate of interest on this installment loan?

8-20. Solution: Rate on installment loan =

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Chapter 12: The Capital Budgeting Decision

21.

Cash discount under special circumstance (LO2) Mr. Hugh Warner is a very cautious businessman. His supplier offers trade credit terms of 3/15, net 85. Mr. Warner never takes the discount offered, but he pays his suppliers in 75 days rather than the 85 days allowed so he is sure the payments are never late. What is Mr. Warner’s cost of not taking the cash discount?

8-21. Solution: 360 Cost of not taking = Discount %  a cash discount 100%  Disc.% Final due date  Discount period 

3% 360  100%  3% (75  15)

 3.09%  6  18.54%

In this problem, Mr. Warner has the use of funds for 60 extra days (75 – 15), instead of 70 extra days allowed by the credit terms (85 – 15). Mr. Warner’s suppliers are offering terms of 3/15, net 85. Mr. Warner is effectively accepting terms of 3/15, net 75. If he took the full 85 days to pay, his cost of not taking the discount would be 15.89 percent. 22.

Bank loan to take cash discount (LO1 and 2) The Reynolds Corporation buys from its suppliers on terms of 3/17, net 45. Reynolds has not been utilizing the discounts offered and has been taking 45 days to pay its bills. Ms. Duke, Reynolds Corporation vice president, has suggested that the company begin to take the discounts offered. Duke proposes that the company borrow from its bank at a stated rate of 16 percent. The bank requires a 27 percent compensating balance on these loans. Current account balances would not be available to meet any of this compensating balance requirement. Do you agree with Duke’s proposal?

8-22. Solution:

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Chapter 12: The Capital Budgeting Decision

360 Cost of not taking a cash = Discount %  discount 100%  Disc.% Final due date  Discount period 3% 360    3.09%  12.86  39.74% 97% (45  17) Effective rate of interest with a 27 percent compensating balance requirement: = Interest rate/(1 – C) = 16%/(1 – 0.27) = 16%/(0.73) = 21.92% The effective cost of the loan, 21.92 percent, is less than the cost of passing up the discount, 39.74 percent. Reynolds Corporation should borrow funds from the bank and pay the invoice early in order to take advantage of the discount. 23.

Bank loan to take cash discount (LO1 and 2) The Reynolds Corporation buys from its suppliers on terms of 3/17, net 45. Reynolds has not been utilizing the discounts offered and has been taking 45 days to pay its bills. Ms. Duke, Vice President of Reynolds Corporation, has suggested that the company begin to take the discounts offered. Duke proposes that the company borrow from its bank at a stated rate of 16 percent. The bank requires a 20 percent compensating balance on these loans. Current account balances would not be available to meet any of this compensating balance requirement. Do you agree with Duke’s proposal?

8-23. Solution:

360 Cost of not taking a cash = Discount %  discount 100%  Disc.% Final due date  Discount period 3% 360    3.09%  12.86  39.74% 97% (45  17)

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Chapter 12: The Capital Budgeting Decision

Effective rate of interest with a 20 percent compensating balance requirement: Interest rate 16% 16%     20.00% 1  C  1  .20  .8 The answer now changes. The effective cost of the loan, 20.00 percent, is less than the cost of passing up the discount, 39.74 percent. Reynolds Corporation should borrow the funds and pay early to take the discount. 24.

Bank loan to take cash discount (LO1 and 2) Neveready Flashlights Inc. needs $340,000 to take a cash discount of 3/17, net 72. A banker will lend the money for 55 days at an interest cost of $10,400. a.

What is the effective rate on the bank loan?

How much would it cost (in percentage terms) if the firm did not take the cash discount, but paid the bill in 72 days instead of 17 days?

Should the firm borrow the money to take the discount?

If the banker requires a 20 percent compensating balance, how much must the firm borrow to end up with the $340,000?

What would be the effective interest rate in part d if the interest charge for 55 days were $13,000? Should the firm borrow with the 20 percent compensating balance? (The firm has no funds to count against the compensating balance requirement.)

8-24. Solution:

$10,400 360  $340, 000 55  3.06%  6.55  20.04%

Effective rate of interest =

Cost of lost discount =

3% 360  97%  72  17 

 3.09%  6.55  20.24%

Yes, because the cost of borrowing is less than the cost of losing the discount.

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Chapter 12: The Capital Budgeting Decision

Amount d. $340, 000 $340, 000 $340, 000    $425, 000 needed to be .80 1  C  1  .20  borrowed e. $13,000 360  $425, 000  $85, 000 55 $13, 000   6.55  3.82%  6.55 $340, 000  25.02%

Effective interest rate =

No, do not borrow with a compensating balance of 20 percent since the effective rate is greater than the savings from taking the cash discount.

25.

Bank loan to take cash discount (LO1 and 2) Harper Engine Company needs $631,000 to take a cash discount of 2.5/20, net 75. A banker will lend the money for 55 days at an interest cost of $13,300. a. What is the effective rate on the bank loan? b. How much would it cost (in percentage terms) if Harper did not take the cash discount, but paid the bill in 75 days instead of 20 days? c. Should Harper borrow the money to take the discount? d. If another banker requires a 10 percent compensating balance, how much must Harper borrow to end up with $631,000? e. What would be the effective interest rate in part d if the interest charge for 55 days were $10,100? Should Harper borrow with the 10 percent compensating balance? (There are no funds to count against the compensating balance requirement.)

8-25. Solution: a.

$13,300 360  631, 000 55  2.11%  6.55  13.82%

Effective rate of interest =

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Chapter 12: The Capital Budgeting Decision

Cost of lost discount =

2.50% 360  97.50%  75  20 

360 55  2.56%  6.55  16.77%  2.56% 

Yes, because the cost of borrowing is less than the cost of losing the discount.

Amount $631, 000 $631, 000 $631, 000    $701,111 needed to be 1  C 1  .10 .90     borrowed

Effective interest rate =

$10,100 360  $701,111  70,111 55 $10,100   6.55  $631, 000  1.60%  6.55 10.48%

Yes, because the cost of borrowing is less than the cost of losing the discount. 26.

Competing terms from banks (LO2) Summit Record Company is negotiating with two banks for a $151,000 loan. Fidelity Bank requires a 28 percent compensating balance, discounts the loan, and wants to be paid back in four quarterly payments. Southwest Bank requires a 14 percent compensating balance, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for both banks is 10 percent. Compensating balances will be subtracted from the $151,000 in determining the available funds in part a. a. Calculate the effective interest rate for Fidelity Bank and Southwest Bank. Which loan should Summit accept? b. Recompute the effective cost of interest, assuming that Summit ordinarily maintains $42,280 at each bank in deposits that will serve as compensating balances. c. Does your choice of banks change if the assumption in part b is correct?

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Chapter 12: The Capital Budgeting Decision

8-26. Solution: a. Fidelity Bank Effective interest rate

2  4  $15,100  $151, 000  $42, 280  $15,100    4  1

 $120,800 / $468,100  25.81% Southwest Bank

Effective interest rate =

2  12  $15,100  $151, 000  $21,140   12  1

 $362, 400 / $1, 688,180  21.47% Choose Southwest Bank since it has the lowest effective interest rate. b. The numerators stay the same as in part (a) but the denominator increases to reflect the use of more money because compensating balances are already maintained at both banks. Fidelity Bank

Effective interest rate = $120,800/($151,000  $15,100)  5 = $120,800/$679,500 =17.78% Southwest Bank

Effective interest rate = $362,400/($151,000  13) = $362,400/$1,963,000 = 18.46% c. Yes. If compensating balances are maintained at both banks in the normal course of business, then Fidelity Bank should

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Chapter 12: The Capital Budgeting Decision

be chosen over Southwest Bank. The effective cost of its loan will be less. 27.

Accounts receivable financing (LO1) Charming Paper Company sells to the 12 accounts listed here.

Account A.................................... B .................................... C .................................... D.................................... E .................................... F .................................... G.................................... H.................................... I ..................................... J ..................................... K.................................... L ....................................

Receivable Balance Outstanding $ 60,800 168,000 78,300 24,300 58,900 238,000 30,400 374,000 41,400 96,500 292,000 67,700

Average Age of the Account over the Last Year 22 43 19 55 42 39 16 72 32 58 17 37

Capital Financial Corporation will lend 90 percent against account balances that have averaged 30 days or less; 80 percent for account balances between 31 and 40 days; and 70 percent for account balances between 41 and 45 days. Customers that take over 45 days to pay their bills are not considered acceptable accounts for a loan. The current prime rate is 15.5 percent, and Capital charges 4.5 percent over prime to Charming as its annual loan rate. a. Determine the maximum loan for which Charming Paper Company could qualify. b. Determine how much one month’s interest expense would be on the loan balance determined in part a.

8-27. Solution: a. 0–30 days A C G K Total Loan % Loan

Amount $ 60,800 78,300 30,400 292,000 461,500 90% $415,350

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Chapter 12: The Capital Budgeting Decision

31–40 days F I L Total Loan% Loan

Amount $ 238,000 41,400 67,700 $ 347,100 80% $ 277,680

Total Loan % Loan

Amount $168,000 58,900 $226,900 70% $158,830

41–45 days B E

Maximum Loan = $415,350 + $277,680 + $158,830 = $851,860 b. Loan balances

28.

$ 851,860

Interest, 20% annual (15.5% prime  4.5%)

(1.67%)

One month’s interest

$ 14,226.06

1.67% per month

Hedging to offset risk (LO5) The treasurer for Pittsburgh Iron Works wishes to use financial futures to hedge her interest rate exposure. She will sell five Treasury futures contracts at $138,000 per contract. It is July and the contracts must be closed out in December of this year. Long-term interest rates are currently 13.3 percent. If they increase to 14.5 percent, assume the value of the contracts will go down by 5 percent. Also, if interest rates do increase by 1.2 percent, assume the firm will have additional interest expense on its business loans and other commitments of $53,000. This expense, of course, will be separate from the futures contracts. a. What will be the profit or loss on the futures contract if interest rates go to 14.5 percent by December when the contract is closed out? b. Explain why a profit or loss took place on the futures contracts. c. After considering the hedging in part a, what is the net cost to the firm of the increased interest expense of $53,000? What percent of this $53,000 cost did the treasurer effectively hedge away? d. Indicate whether there would be a profit or loss on the futures contracts if interest rates dropped.

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Chapter 12: The Capital Budgeting Decision

8-28. Solution: a. Sales price, December Treasury bond contract (Sale takes place in July) $138,000 Purchase price, December Treasury bond contract (5% price decline) .95 × $138,000 = 131,100 Gain per contract $ 6,900 Number of contracts 5 Profit on futures contracts $ 34,500 b. A profit took place because the value of the bond went down due to increasing rates. This meant the subsequent purchase price was less than the initial sales price. c.

Increased interest cost $53,000 Profit from hedging 34,500 Net cost $18,500 Net cost $18,500   34.91% Increased interest cost $53,000 The net cost is 34.91 percent. This means 65.09 percent of the increased interest cost was hedged away.

d. If interest rates dropped, there would be a loss on the futures contracts. The lower interest rates would lead to higher bond prices and a purchase price that exceeded the original sales price. Chapter 9 Time Value of Money Discussion Questions 9-1.

How is the future value related to the present value of a single sum?

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Chapter 12: The Capital Budgeting Decision

The future value represents the expected worth of a single amount, whereas the present value represents the current worth. FV = PV (1 + i)n future value

9-2.

 1  Present value PV  FV n    1  i  

How is the present value of a single sum related to the present value of an annuity? The present value of a single amount is the discounted value for one future payment, whereas the present value of an annuity represents the discounted value of a series of consecutive future payments of equal amount.

9-3.

Why does money have a time value? Money has a time value because funds received today can be invested to reach a greater value in the future. A person would rather receive $1 today than $1 in 10 years, because a dollar received today, invested at 6 percent, is worth $1.791 after 10 years.

9-4.

Does inflation have anything to do with making a dollar today worth more than a dollar tomorrow? Inflation makes a dollar today worth more than a dollar in the future. Because inflation tends to erode the purchasing power of money, funds received today will be worth more than the same amount received in the future.

9-5.

Adjust the annual formula for a future value of a single amount at 12 percent for 10 years to a semiannual compounding formula. What are the interest factors (FVIF) before and after? Why are they different? FV  PV  FVIF  Appendix A  i  12%, n  10 3.106 Annual i  6%, n  20

3.207 Semiannual

The more frequent compounding under the semiannual compounding assumption increases the future value so that semiannual compounding is worth 0.101 more per dollar. 9-6.

If, as an investor, you had a choice of daily, monthly, or quarterly compounding, which would you choose? Why? The greater the number of compounding periods, the larger the future value. The investor should choose daily compounding over monthly or quarterly.

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Chapter 12: The Capital Budgeting Decision

9-7.

What is a deferred annuity? A deferred annuity is an annuity in which the equal payments will begin at some future point in time.

9-8.

List five different financial applications of the time value of money. Different financial applications of the time value of money: Equipment purchase or new product decision Present value of a contract providing future payments Future value of an investment Regular payment necessary to provide a future sum Regular payment necessary to amortize a loan Determination of return on an investment Determination of the value of a bond

Problems 1.You invest $3,000 for three years at 12 percent.

a. b.

What is the value of your investment after one year? Multiply $3,000 × 1.12. What is the value of your investment after two years? Multiply your answer to part a by 1.12. What is the value of your investment after three years? Multiply your answer to part b by 1.12. This gives your final answer. n Combine these three steps by using the formula FV  PV  1  i  to find the future value of $3,000 in 3 years at 12 percent interest.

c. d.

9-1.

Solution: a. FV  PV  (1  i ) n FV  $3,000  (1.12)1 FV  $3,360

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Chapter 12: The Capital Budgeting Decision

b. FV  PV  (1  i ) n FV  $3,360  (1.12)1 FV  $3,763.20

c. FV  PV  (1  i ) n FV  $3,763.20  (1.12)1 FV  $4, 214.78

d. FV  PV (1  i ) n FV  $3, 000  (1.12)3 FV  $4, 214.78 Calculator Solution: (d) N 3

I/Y 12

PV 3,000

PMT 0

FV CPT FV −4,214.78

Answer: $4,214.78

Solution using TVM Tables:

a. b. c. d. 2.

9-2.

$3,000 × 1.12 $3,360 × 1.12 $3,763.20 × 1.12 $3,000 × 1.405

= = = =

$3,360.00 $3,763.20 $4,214.78 $4,215.00 (Appendix A)

Present value (LO9-3) What is the present value of a. $7,900 in 10 years at 11 percent? b. $16,600 in 5 years at 9 percent? c. $26,000 in 14 years at 6 percent?

Solution: a.

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Chapter 12: The Capital Budgeting Decision

PV  FV 

1 (1  i ) n

1 (1.11)10 PV  $2,788.86 PV  $7,900 

PV  FV 

1 (1  i ) n

1 (1.09)5 PV  $10,788.86 PV  $16,600 

PV  FV 

1 (1  i ) n

1 (1.06)14 PV  $11, 499.82 PV  $26,000 

Calculator Solution: (a) N 10

I/Y 11

PV CPT PV −2,782.26

PMT 0

FV 7,900

I/Y 9

PV CPT PV −10,788.86

PMT 0

FV 16,600

I/Y

PMT

Answer: $2,782.26 (b) N 5 Answer: $10,788.86 (c) N

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Chapter 12: The Capital Budgeting Decision

CPT PV −11,499.83

26,000

Answer: $11,499.83

Appendix B PV = FV × PVIF a. $ 7,900 × 0.352 = $2,781 b. $16,600 × 0.650 = $10,790 c. $26,000 × 0.442 = $11,492 3.

9-3.

Present Value (LO9-3) a. What is the present value of $140,000 to be received after 30 years with a 14 percent discount rate? b. Would the present value of the funds in part a be enough to buy a $2,900 concert ticket?

Solution: (a)

PV  FV 

1 (1  i ) n

PV  $140, 000  PV  $2, 747.78 (b)

1 1.1430

No, $2,747.78 isn’t enough.

Calculator Solution: (a) N I/Y 30 14 Answer: $2747.78 (b) No. You only have $2747.78.

PV CPT PV -2747.78

PMT 0

FV 140,000

Appendix B PV = FV × PVIF (14%, 30 periods)

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Chapter 12: The Capital Budgeting Decision

a. $140,000 × 0.02 = $2,800 b. NO. You only have $2,800 in present value. 4.

Present Value (LO9-4) You will receive $6,800 three years from now. The discount rate is 10 percent.

c. d.

9-4.

What is the value of your investment two years from now? Multiply $6,800 by  1    or divide by 1.10 (one year’s discount rate at 10 percent).  1.10  What is the value of your investment one year from now? Multiply your answer to  1  part a by  .  1.10   1  What is the value of your investment today? Multiply the part b answer by  .  1.10  1 Use the formula PV  FV  to find the present value of $6,800 received (1  i ) n three years from now at 10 percent interest.

Solution: a.

1 (1  i ) n 1 PV  $6,800  (1.10)1 PV  $6,181.82 PV  FV 

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Chapter 12: The Capital Budgeting Decision

PV  FV 

1 (1  i ) n 1 (1.1)1

PV  $6,181.82  PV  $5,619.83 c.

PV  FV 

1 (1  i ) n

PV  $5,619.83 

1 (1.1)1

PV  $5,108.94 d. 1 (1  i ) n 1 PV  $6,800  (1.1)3 PV  $5,108.94 PV  FV 

Calculator Solution: (d) N 3 Answer: $5,108.94

I/Y 10

PV CPT −5,108.94

PMT 0

FV FV 6,800

Solution using TVM Tables:

a. b. c. d.

$6,800 × 0.909 = $6,181.20 $6,181.20 × 0.909 = $5,618.71 $5,618.71 × 0.909 = $5,107.41 Appendix B (10%, 3 periods) PV= FV × PVIF $6,800 × 0.751 = $5,106.80

If you invest $9,000 today, how much will you have

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Chapter 12: The Capital Budgeting Decision

a. b. c. d.

9-5.

In 2 years at 9 percent? In 7 years at 12 percent? In 25 years at 14 percent? In 25 years at 14 percent (compounded semiannually)?

Solution: a. FV  PV  (1  i ) n FV  $9,000  (1.09) 2 FV  $10,692.90

b. FV  PV  (1  i ) n FV  $9,000  (1.12) 2 FV  $19,896.13

c. FV  PV  (1  i ) n FV  $9,000  (1.14) 25 FV  $235,157.24

d. FV  PV  (1  i ) n FV  $9,000  (1.07)50 FV  $265,113.23 Calculator Solution: (a) N 2

I/Y 9

PV 9,000

PMT 0

FV CPT FV −10,692.90

I/Y 12

PV 9,000

PMT 0

FV CPT FV −19,896.13

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Chapter 12: The Capital Budgeting Decision

I/Y 14

PV 9,000

PMT 0

FV CPT FV −238,157.24

I/Y 7

PV 9,000

PMT 0

FV CPT FV −265,113.23

Answer: $238,157.24 (d) N 50 Answer: $265,113.23

Appendix A FV = PV × FVIF a. $9,000 × 1.188 b. $9,000 × 2.211 c. $9,000 × 26.462 d. $9,000 × 29.457 6.

9-6.

= = = =

$ 10,692 $ 19,899 $238,158 $265,113 (7%, 50 periods)

Present value (LO9-3) Your aunt offers you a choice of $21,600 in 30 years or $200 today. If money is discounted at 17 percent, which should you choose?

Solution:

PV = $194.48 Take the $200 today instead of $21,600 in 30 years.

Calculator Solution:

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Chapter 12: The Capital Budgeting Decision

N 30

I/Y 17

PV −194.48

PMT 0

FV 21,600

Answer: $869.92

Appendix B PV = FV × PVIF (17%, 30 periods) PV = $21,600 × 0.009 = $194 Choose $200 today. 7.

9-7.

Present Value (LO9-3) Your uncle offers you a choice of $105,000 in 10 years or $47,000 today. If money is discounted at 9 percent, which should you choose?

Solution:

PV  FV 

1 (1  i ) n

PV  $105,000 

1 (1.09)10

PV  $44,353.13 Take the $47,000 today instead of $105,000 in 10 years. Calculator Solution: N 10

I/Y 9

PV CPT PV −44,353.13

PMT 0

FV 105,000

Answer: $44,353.13

Appendix B PV = FV × PVIF (9%, 10 periods) PV = $105,000 × 0.422 = $44,310 Choose $47,000 today. 8.

Present Value (LO9-3) Your father offers you a choice of $105,000 in 12 years or $47,000 today.

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Chapter 12: The Capital Budgeting Decision

a. b.

9-8.

If money is discounted at 8 percent, which should you choose? If money is still discounted at 8 percent, but your choice is between $105,000 in 9 years or $47,000 today, which should you choose?

Solution: a.

PV  FV 

1 (1  i ) n

PV  $105,000 

1 (1.08)12

PV  $41,696.94 Take $47,000 today instead of $105,000 in 12 years. b.

PV  FV 

1 (1  i ) n

PV  $105,000 

1 (1.08)9

PV  $52,526.14 Take the $105,000 in 9 years because it is worth $52,526.14, which is more than $47,000 today. Calculator Solution: (a) & (b) N

I/Y

PV CPT PV −41,696.94

PMT

105,000

PV CPT PV −52,526.14

PMT

105,000

Answer: $41,696.94 (c) & (d) N

I/Y

Answer: $52,526.14

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Chapter 12: The Capital Budgeting Decision

Appendix B PV = FV × PVIF (8%, 12 periods) FV = $105,000 × 0.397 = $41,685 Choose $47,000 today.

b. Appendix B PV = FV × PVIF (8%, 9 periods) FV = $105,000 × 0.500 = $52,500 Choose $105,000 in 9 years. 9.

9-9.

Present Value (LO9-3) You are going to receive $205,000 in 18 years. What is the difference in present value between using a discount rate of 12 percent versus 9 percent?

Solution: 9% Rate

PV  FV 

1 (1  i ) n

PV  $205,000 

1 (1.09)18

PV  $43,458.72 12% Rate

PV  FV 

1 (1  i ) n

PV  $205,000 

1 (1.12)18

PV  $26,658.12 The Difference $43,458.12 –26,658.12 $16,800.60

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Chapter 12: The Capital Budgeting Decision

Calculator Solution: At 12% N

I/Y

Answer: $26,658.12 At 9% N 18 Answer: $43,458.72

I/Y 9

CPT

PV CPT PV −26,658.12

PMT

205,000

PV PV −43,458.72

PMT 0

FV 205,000

The difference is 43,458.72 – 26,658.12 = $16,800.60

Appendix B $205, 000 .130

$205, 000 (12%,18)

$26, 650

.212

(9%,18)

$43, 460

The difference is $16,810 $43, 460 26, 650 $16,810

10.

How much would you have to invest today to receive a. $15,000 in 8 years at 10 percent? b. $20,000 in 12 years at 13 percent? c. $6,000 each year for 10 years at 9 percent? d. $50,000 each year for 50 years at 7 percent?

9-10. Solution:

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Chapter 12: The Capital Budgeting Decision

PV  FV 

1 (1  i ) n

PV  $15,000 

1 (1.10)8

PV  $6,997.61 b.

PV  FV 

1 (1  i ) n

PV  $20,000 

1 (1.13)12

PV  $4,614.12 c. 1 PVA  A 

1 (1  i ) n i 1 (1.09)10 .09

1 PVA  $6,000  PVA  $38,505.95

d. 1 PVA  A 

1 (1  i ) n i 1

PVA  $50,000 

1 (1.07)50 .07

PVA  $690,037.31

Calculator Solution:

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Chapter 12: The Capital Budgeting Decision

(a) N 8

I/Y 10

PV CPT PV −6,997.61

PMT 0

FV 15,000

I/Y 13

PV CPT PV −4,614.12

PMT 0

FV 20,000

I/Y 9

CPT

PV PV −38,505.95

PMT 6,000

FV 0

I/Y 7

PV CPT PV −690,037.31

PMT 50,000

FV 0

Answer: $6,997.61 (b) N 12 Answer: $4,614.12 (c) N 10 Answer: $38,505.95 (d) N 50 Answer: $690,037.31

Appendix B (a and b) PV = FV × PVIF a. $15,000 × 0.467 = $7,005 b. $20,000 × 0.231 = $4,620 Appendix D (c and d) c. $ 6,000 × 6.418 = d. $50,000 × 13.801 = 11.

$38,508 $690,050

Future value (LO9-2) If you invest $9,500 per period for the following number of periods, how much would you have? a. 13 years at 10 percent. b. 50 years at 9 percent.

9-11. Solution:

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Chapter 12: The Capital Budgeting Decision

FVA = $232,965.77 b.

FVA = $7,743,293.79 Calculator Solution: (a) N 13

I/Y 10

PV 0

PMT 9,500

FV CPT FV −232,965.77

I/Y

PMT

9,500

FV CPT FV −7,743,293.79

Answer: $232,965.77 (b)

Answer: $7,743,293.79

Appendix C FVA = A × FV IFA a. $9,500 × 24.523 = $ 232,968.50 b. $9,500 × 815.084 = $ 7,743,298 12.

You invest a single amount of $10,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years?

9-12. Solution:

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Chapter 12: The Capital Budgeting Decision

After 5 Years

FV  PV  (1  i ) n FV  $10, 000  (1.10)5 FV  $16,105.10 After 17 Years FV  PV  (1  i ) n

FV  $16,10.10  (1.15)12 FV  $86,166.31 Calculator Solution: First step: N 5

I/Y 10

PV 10,000

PMT 0

FV CPT FV −16,105.10

I/Y 15

PV 16,105.10

PMT 0

FV CPT FV −86,166.31

Answer: $16,105.10 Second step: N 12 Answer: $86,166.31

Appendix A FV = PV × FVIF $10,000 × 1.611 = $16,110 Appendix A FV = PV × FVIF $16,110 × 5.350 = $86,188 13.

Present value (LO9-3) Mrs. Crawford will receive $7,600 a year for the next 19 years from her trust. If a 14 percent interest rate is applied, what is the current value of the future payments?

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Chapter 12: The Capital Budgeting Decision

9-13. Solution: 1 PVA  A 

1 (1  i ) n i 1

PVA  $7, 600 

1 (1.14)19 .14

PVA  $49, 782.80 Calculator Solution: N 19

I/Y 14

CPT

PV PV −49,782.80

PMT 7,600

FV 0

Answer: $49,782.80

Appendix D PVA = A × PVIFA (14%, 19 periods) = $7,600 × 6.550 = $49,780 14.

Phil Goode will receive $175,000 in 50 years. His friends are very jealous of him. If the funds are discounted back at a rate of 14 percent, what is the present value of his future ―pot of gold‖?

9-14. Solution: PV  FV 

1 (1  i ) n

PV  $175, 000 

1 (1.14)50

PV  $249.92

Calculator Solution: N 50

I/Y 14

CPT

PV PV −249.92

PMT 0

FV 175,000

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Chapter 12: The Capital Budgeting Decision

Answer: $249.92

Appendix B PV = FV × PVIF (14%, 50 periods) = $175,000 × 0.001 = $175 15.

Present value (LO9-3) Sherwin Williams will receive $18,500 a year for the next 25 years as a result of a picture he has painted. If a discount rate of 12 percent is applied, should he be willing to sell out his future rights now for $165,000?

9-15. Solution: 1 PVA  A 

1 (1  i ) n i 1

PVA  $18,500 

1 (1.12) 25 .12

PVA  $145, 098.07

Sherwin Williams should take the $165,000 for his future rights now. Calculator Solution: N

I/Y

PV CPT PV −145,098.07

PMT

18,500

Answer: $145,098.07

Appendix D PVA = A × PVIFA (12%, 25 periods) PVA = $18,500 × 7.843 = $145,096 Yes, the present value of the annuity is worth less than $165,000. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

16.

Carrie Tune will receive $19,500 for the next 20 years as a payment for a new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for $160,000?

9-16. Solution:

1 PVA  A 

1 (1  i ) n i 1

PVA  $19,500 

1 (1.10) 20 .10

PVA  $166, 014.49 Carrie Tune should not accept $160,000 for the future rights because they are worth more than that. Calculator Solution: N 20

I/Y 10

PV CPT PV −166,014.49

PMT 19,500

FV 0

Answer: $166,014.49

Appendix D PVA = A × PVIFA (10%, 20 periods) PVA = $19,500 × 8.514 = $166,023 No, the present value of the annuity is worth more than $160,000. 17.

The Clearinghouse Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $20,000 a year for the next 50 years. With a discount rate of 10 percent, what is the present value of your winnings?

9-17. Solution:

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Chapter 12: The Capital Budgeting Decision

1 PVA  A 

1 (1  i ) n i 1

PVA  $20, 000 

1 (1.10)50 .10

PVA  $198, 296.29 Calculator Solution: N 50

I/Y 10

PV CPT PV −198,296.29

PMT 20,000

FV 0

Answer: $198,296.29

Appendix D PVA = A × PVIFA (10%, 50 periods) PVA = $20,000 × 9.915 = $198,300 18.

Present value (LO9-3) Rita Gonzales won the $41 million lottery. She is to receive $1.5 million a year for the next 19 years plus an additional lump sum payment of $12.5 million after 19 years. The discount rate is 14 percent. What is the current value of her winnings?

9-18. Solution:

Annuity Part

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Chapter 12: The Capital Budgeting Decision

1 PVA  A 

1 (1  i ) n i 1

PVA  $1,500, 000 

1 (1.14)19 .14

PVA  $9,825,553.24 Lump Sum Part

PV  FV 

1 (1  i ) n

PV  $12,500, 000 

1 (1.14)19

PV  $1, 036,854.55 Total Value $ 9,825,553.24 + 1,036,854.55 $10,862,407.79

Present value of annuity Present value of lump sum Total value

Calculator Solution: First part: N

I/Y

Answer: $9,825,553.24 Second part: N I/Y 19

PV CPT PV −9,825,553.24

PV CPT PV −1,036,854.55

PMT

1,500,000

PMT

12,500,000

Answer: $1,036,854.55

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Chapter 12: The Capital Budgeting Decision

Total = 9,825,553.24 + 1,036,854.55 = $10,862,407.79

Appendix D PVA = A × PVIFA (14%, 19 periods) PVA = $1,500,000 × 6.550 = $9,825,000 Appendix B PV = FV × PVIF (14%, 19 periods) PV = $12,500,000 × 0.083 = $1,037,500 $ 9,825,000 1,037,500 $10,862,500 19.

Al Rosen invests $30,000 in a mint condition 1952 Mickey Mantle Topps baseball card. He expects the card to increase in value 8 percent per year for the next 15 years. How much will his card be worth after 15 years?

9-19. Solution: FV = PV × (1+ i)n FV = $30,000 × (1.08)15 FV = $95,165.07 Calculator Solution: Part one: N 15

I/Y 8

PV 30,000

PMT 0

FV CPT FV −95,165.07

Answer: $95,165.07

Appendix A FV = PV × FVIF (8%, 15 periods) = $30,000 × 3.172 = $95,160

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Chapter 12: The Capital Budgeting Decision

20.

Future value (LO9-2) Kai Chang made a $2,000 deposit in her savings account on her 21st birthday, and she has made another $2,000 deposit on every birthday since then. Her account earns 7 percent compounded annually. How much will she have in her account after she makes the deposit on her 32nd birthday?

9-20. Solution:

(1  i ) n  1 FVA  A  i (1.07)12  1 FVA  $2, 000  .07 FVA  $35, 776.90 Calculator Solution: N 12

I/Y 7

PV 0

PMT 2,000

FV CPT FV −35,776.90

Answer: $35,776.90

Appendix C FVA = A × FVIFA (7%, n = 12) FVA = $2,000 × 17.888 = $35,776.00 21.

Future value (LO9-2) At a growth (interest) rate of 10 percent annually, how long will it take for a sum to double? To triple? Select the year that is closest to the correct answer.

9-21. Solution: The key to solving this problem algebraically is to know that ln x n  n  ln x

To Double

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Chapter 12: The Capital Budgeting Decision

FV  PV  (1  i ) n 2  1 (1.10) n 2  (1.10) n ln(2)  n  ln(1.1) ln(2) ln(1.1) n  7.27 years n

To Triple FV  PV  (1  i ) n

3  1 (1.10) n 3  (1.10) n ln(3)  n  ln(1.1) ln(3) ln(1.1) n  11.53 years n

Calculator Solution: To double: N CPT N 7.2725

I/Y 10

PV 1.00

PMT 0

FV −2.00

I/Y 10

PV 1.00

PMT 0

FV −3.00

Answer: 7.27 years To triple: N CPT N 11.5267 Answer: 11.53 years

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Chapter 12: The Capital Budgeting Decision

If the sum is doubling, then the tabular value must equal 2. In Appendix A, looking down the 10% column, we find the factor closest to 2 (1.949) in the 7-year row. The factor closest to 3 (3.138) is in the 12-year row. 22.

Present value (LO9-3) If you owe $35,000 payable at the end of eight years, what amount should your creditor accept in payment immediately if she could earn 13 percent on her money?

9-22. Solution: PV  FV 

1 (1  i ) n

1 (1.13)8 PV  $13,165.60 PV  $35, 000 

Calculator Solution: N 8

I/Y 13

PV CPT PV −13,165.60

PMT 0

FV 35,000

Answer: $13,165.60

Appendix B PV = FV × PVIF (13%, 8 periods) PV = $35,000 × 0.376 = $13,160 23.

Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year; $2.20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes that at the end of the third year he will be able to sell the stock for $33. What is the present value of all future benefits if a discount rate of 11 percent is applied? (Round all values to two places to the right of the decimal point.)

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Chapter 12: The Capital Budgeting Decision

First Dividend

1 (1  i ) n 1 PV  $2  (1.11)1 PV  $1.80 PV  FV 

Second Dividend

1 (1  i ) n 1 PV  $2.20  (1.11) 2 PV  $1.79 PV  FV 

Third Dividend

1 (1  i ) n 1 PV  $2.40  (1.11)3 PV  $1.75 PV  FV 

Selling Price

1 (1  i ) n 1 PV  $33  (1.11)3 PV  $24.13 PV  FV 

Present Value Total $24.13 Selling price + 1.80 First dividend + 1.79 Second dividend + 1.75 Third dividend $29.47 Present total value

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Chapter 12: The Capital Budgeting Decision

First dividend: N 1

I/Y 11

PV CPT PV −1.80

PMT 0

FV 2.00

I/Y 11

PV CPT PV −1.79

PMT 0

FV 2.20

I/Y 11

PV CPT PV −1.75

PMT 0

FV 2.40

I/Y 11

PV CPT PV −24.13

PMT 0

FV 33.00

Answer: $1.80 Second dividend: N 2 Answer: $1.79 Third dividend: N 3 Answer: $1.75 Selling price: N 3 Answer: $24.13 Total = 1.80 + 1.79 + 1.75 + 24.13 = $29.47

Appendix B PV = FVIF Discount rate = 11 percent $ 2.00 × 0.901 2.20 × 0.802 2.40 × 0.731 33.00 × 0.731

= $ 1.80 = 1.79 = 1.75 = 24.12 $29.46

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Chapter 12: The Capital Budgeting Decision

24.

Les Moore retired as president of Goodman Snack Foods Company but is currently on a consulting contract for $35,000 per year for the next 10 years. a. If Mr. Moore’s opportunity cost (potential return) is 10 percent, what is the present value of his consulting contract? b. Assuming Mr. Moore will not retire for two more years and will not start to receive his 10 payments until the end of the third year, what would be the value of his deferred annuity?

9-24. Solution: a.

1 PVA  A 

1 (1  i ) n i 1

PVA  $35, 000 

1 (1.10)10 .10

PVA  $215, 059.85 b. Present Value of the Annuity

1 PVA  A 

1 (1  i ) n i 1

PVA  $35, 000 

1 (1.10)10 .10

PVA  $215, 059.85 Discount two years off

PV  FV 

1 (1  i ) n

PV  $215, 059.85 

1 (1.10) 2

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Chapter 12: The Capital Budgeting Decision

Calculator Solution: (a) N

I/Y

PV CPT PV −215,059.85

PMT

35,000

PMT

35,000

PMT

215,059.85

Answer: $215,059.85 (b) First part: Find the PV of the 10 payments of annuity: N I/Y PV CPT PV 10 10 −215,059.85 Answer: $215,059.85 Second part: Find the PV of the above FV lump sum: N I/Y PV CPT PV 2 10 −177,735.41 Answer: $177,735.41

Appendix D a. PVA = A × PVIFA (10%, 10 periods) PVA = $35,000 × 6.145 = $215,075 b. Deferred annuity—Appendix D PVA = A × PVIFA (i = 10%, 10 periods) PVA = $35,000 × 6.145 = $215,075 Now, discount back this value for two periods. PV = FV × PVIF (i = 10%, 2 periods) Appendix B = $215,075 × 0.826 = $177,652 OR

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Chapter 12: The Capital Budgeting Decision

Appendix D PVA = $35,000 (6.814 – 1.7360, where n = 12, n = 2, and i = 10%) = $35,000(5.078) = $177,730 The answer is slightly different from the preceding answer due to rounding in the tables.

25.

Juan Garza invested $110,000 10 years ago at 8 percent, compounded quarterly. How much has he accumulated?

9-25. Solution: Ten years with quarterly compounding means

n = 10 × 4 = 40

FV = PV × (1 + i)n FV = $110,000 × (1.02)40 FV = $242,884.36 Calculator Solution: N 40

I/Y 2

PV 110,000

PMT 0

FV CPT FV −242,884.36

Answer: $242,884.36

Appendix A FV = PV × FVIF (2%, 40 periods) FV = $110,000 × 2.208 = $242,880

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Chapter 12: The Capital Budgeting Decision

26.

Special compounding (LO9-5) Determine the amount of money in a savings account at the end of 10 years, given an initial deposit of $5,500 and a 12 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly.

9-26. Solution: a. Annually

FV  PV  (1  i ) n FV  $5,500  (1.12)10 FV  $17, 082.17 b. Semiannually

i FV  PV  (1  ) 2 n 2 FV  $5,500  (1.06) 20 FV  $17, 639.25 c. Quarterly

i FV  PV  (1  ) 4 n 4 FV  $5,500  (1.03)40 FV  $17,941.21 Calculator Solution: (a) N 10

I/Y 12

PV 5,500

PMT 0

FV CPT FV −17,082.17

I/Y 6

PV 5,500

PMT 0

FV CPT FV −17,639.25

I/Y 3

PV 5,500

PMT 0

FV CPT FV −17,941.21

Answer: $17,082.17 (b) N 20 Answer: $17,639.25 (c) N 40

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Chapter 12: The Capital Budgeting Decision

Answer: $17,941.21

Appendix A FV = PV × FVIF a. $5,500 × 3.106 = $17,083 (n = 10; i = 12%) b. $5,500 × 3.207 = $17,639 (n = 20; i = 6%) c. $5,500 × 3.262 = $17,941 (n = 40; i = 3%) 27.

Annuity due (LO9-4) As stated in the chapter, annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come at the beginning of each period (termed an annuity due). To find the present value of an annuity due, subtract 1 from n and add 1 to the tabular value. To find the present value of an annuity due, the annuity formula must be adjusted to the following:

1    1  (1  i ) n 1  PVAD  A    1 i       Likewise, the formula for the future value of an annuity due requires a modification:

 (1  i)n1  1  FVAD  A    1 i   What is the future value of a 15-year annuity of $1,800 per period where payments come at the beginning of each period? The interest rate is 12 percent.

9-27. Solution:

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Chapter 12: The Capital Budgeting Decision

 (1  i ) n1  1  FVAD  A    1 i    (1.12)16  1  FVAD  $1,800    1 .12   FVAD  $1,800  (41.75328) FVAD  $75,155.90 Calculator Solution: Set calculator beginning N I/Y 15 12

PV 0

PMT 1,800

FV CPT FV 75,155.90

Answer: $75,155.90

Appendix C FVA = A × FVIFA n = 16, i = 12% 42.753 – 1 = 41.753 FVA = $1,800 × 41.753 = $75,155 28.

Annuity due (LO9-4) What is the present value of a 10-year annuity of $3,000 per period in which payments come at the beginning of each period? The interest rate is 12 percent.

1   1  n  1   (1  i ) PVAD  A    1 i      

9-28. Solution:

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Chapter 12: The Capital Budgeting Decision

1   1  n  1   (1  i ) PVAD  A    1 i       1   1    (1.12)9 PVAD  $3,000    1 .12       PVAD  $3,000  (6.32825) PVAD  $18,984.75 Calculator Solution: Set calculator to beginning N I/Y 10 12

CPT

PV PV −18,984.75

PMT 3,000

FV 0

Answer: $18,984.75

Appendix D PVA = A × PVIFA n = 9, i = 12% 5.328 + 1 = 6.328 PVA = $3,000 × 6.328 = $18,984 29.

Present value alternative (LO9-3) Your grandfather has offered you a choice of one of the three following alternatives: $7,500 now, $2,200 a year for nine years, or $31,000 at the end of nine years. Assuming you could earn 10 percent annually, which alternative should you choose? If you could earn 11 percent annually, would you still choose the same alternative?

9-29. Solution:

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Chapter 12: The Capital Budgeting Decision

10% annually Option 1

PV  $7,500

Option 2

1 PVA  A 

1 (1  i ) n i 1

PVA  $2, 200 

1 (1.10)9 .10

PVA  $12, 669.85 Option 3

PV  FV 

1 (1  i ) n

1 (1.10)9 PV  $13,147.03 PV  $31, 000 

At a rate of 10 percent annually, the best deal is $31,000 in nine years because it has the highest present value. 11% annually Option 1

PV  $7,500

Option 2

1 PV  A 

1 (1  i ) n i 1

PV  $2, 200 

1 (1.11)9 .11

PV  $12,181.50

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Chapter 12: The Capital Budgeting Decision

Option 3

PV  FV 

1 (1  i ) n

1 (1.11)9 PV  $12,118.67 PV  $31, 000 

At a rate of 11 percent annually, the best option is Option 2 because $2,200 a year for nine years is the best deal.

Calculator Solution: (a-1) (first alternative) Present value of $7,500 received now: $7,500 (second alternative) Present value of annuity of $2,200 for nine years: N I/Y PV PMT 9 10 CPT PV –12,669.85 2,200

FV 0

Answer: $12,669.85 (third alternative) Present value of $31,000 received in nine years: N I/Y PV PMT 9 10 CPT PV –13,147.03 0

FV 31,000

Answer: $13,147.03 (a-2) Select $31,000 received at end of nine years. (b-1) (first alternative) Present value of $7,500 received today: $7,500 (second alternative) Present value of annuity of $2,200 at 11 percent for nine years: N I/Y PV PMT 9 11 CPT PV –12,181.50 2,200

FV 0

Answer: $12,181.50 (third alternative) Present value of $31,000 received in nine years at 11 percent: N I/Y PV PMT 9 11 CPT PV –12,118.67 0

FV 31,000

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Chapter 12: The Capital Budgeting Decision

Answer: $12,118.67 (b-2) Select $2,200 received for nine years.

(first alternative) Present value of $7,500 received now: $7,500 (second alternative) Present value of annuity of $2,200 for nine years: Appendix D PVA  A×PVIFA  $2, 200  PVIFA (10%, 9 years)  $2, 200  5.759  $12, 670 (third alternative) Present value of $31,000 received in nine years: Appendix B PV  FV×PVIF  $31,000×PVIF (10%, 9 years)  $31,000×.424  $13,144 Select $31,000 to be received in nine years. Revised answers based on 11 percent. (first alternative) Present value of $7,500 received today: $7,500 (second alternative) Present value of annuity of $2,200 at 11 percent for nine years: Appendix D

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Chapter 12: The Capital Budgeting Decision

PVA  A  PVIFA  $2, 200  PVIFA (11%, 9 years)  $2, 200  5.537  $12,181

(third alternative) Present value of $31,000 received in nine years at 11 percent: Appendix B PV = FV×PVIF = $31,000×PVIF (11%, 9 years) = $31,000×.391 = $12,121

Select $2,200 a year for nine years. As the interest rate (discount rate) increases, the present value declines. 30.

You need $25,456 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year. a. What single payment could be made at the beginning of the first year to achieve this objective? b. What amount could you pay at the end of each year annually for 10 years to achieve this same objective?

9-30. Solution: a.

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Chapter 12: The Capital Budgeting Decision

A = $1,757.21 Calculator Solution: (a) N 10

I/Y 8

CPT

PV PV −11,791.05

PMT 0

FV 25,456

Answer: $13,420.57 (b) N

I/Y

PMT CPT PMT −1,757.21

FV 25,456

Answer: $2,000.06

a. Appendix B PV = FV × PVIF (8%, 10 periods) = $25,456 × .463 = $11,786.13 b. Appendix C A = FVA/FVIFA (8%, 10 periods) = $25,456/14.487 = $1,757.16 31.

Quarterly compounding (LO9-5) Beverly Hills started a paper route on January 1. Every three months, she deposits $550 in her bank account, which earns 8 percent annually but is

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Chapter 12: The Capital Budgeting Decision

compounded quarterly Four years later, she used the entire balance in her bank account to invest in an investment at 7 percent annually. How much will she have after three more years?

9-31. Solution: Quarterly deposits for four years 4n

 i 1    1 4 FV  A   i (1.02)16  1 FV  $550  .02 FV  $10, 251.61 Investment growth over three years

FV  PV  (1  i ) n FV  $10, 251.61 (1.07)3 FV  $12,558.66 Calculator Solution: Step one: N 16

I/Y 2

PV 0

PMT 550.00

I/Y 7

PV 10,251.61

PMT 0

CPT

FV FV −10,251.61

CPT

FV FV −12,558.66

Answer: $10,251.61 Step two: N 3 Answer: $12,558.66

Appendix C FVA = A × FVIFA (2%, 16 periods) FVA = $550 × 18.639 = $10,251.45 after four years Appendix A FV = PV × FVIF (7%, 3 periods) © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

FV = $10,251.45 × 1.225 FV = $12,558.03 after three more years 32.

Yield (LO9-4) Franklin Templeton has just invested $9,260 for his son (age one). This money will be used for his son’s education 18 years from now. He calculates that he will need $71,231 by the time the boy goes to school. What rate of return will Mr. Templeton need in order to achieve this goal?

9-32. Solution:

1 PV  (1  i ) n FV 1 $9,260  (1  i )18 $71,231 (1  i )18  7.692 1 18 18

1 18

(1  i )    7.692 1  i  1.12 i  .12

Franklin Templeton needs a 12 percent rate to achieve his goal of $71,231.

Calculator Solution: N 18

I/Y CPT I/Y 12.00

PV 9,260.00

PMT 0

FV −71,231.00

Answer: 12.00

Appendix B PV PVIF = (18 periods) FV $9, 260 PVIF =  .130 Rate of return 12% $71, 231

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Chapter 12: The Capital Budgeting Decision

or Alternative solution Appendix A FV FVIF  (18 periods) PV $71, 231 FVIF   7.69 Rate of return  12% $9, 260 33.

Yield with interpolation (LO9-4) Mr. Dow bought 100 shares of stock at $14 per share. Three years later, he sold the stock for $20 per share. What is his annual rate of return?

9-33. Solution:

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Chapter 12: The Capital Budgeting Decision

Calculator Solution: N 3

I/Y CPT I/Y 12.62

PV 14.00

PMT 0

FV −20.00

Answer: 12.62%

Appendix B PV PVIF  FV $14 PVIF   .700 Return is between 12–13 percent for three $20 years. PVIF at 12%

.712

PVIF at 13%

 .693 .019

PFIF at 12%

.712

PVIF computed

 .700 .012

12% + (.012/.019) (1%) 12% + .632 (1%) 12.63%

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Chapter 12: The Capital Budgeting Decision

34.

Yield with interpolation (LO9-4) C. D. Rom has just given an insurance company $35,000. In return, he will receive an annuity of $3,700 for 20 years. At what rate of return must the insurance company invest this $35,000 in order to make the annual payments? Interpolate.

9-34. Solution: Calculator Solution: N 20

I/Y CPT I/Y 8.51

PV −35,000.00

PMT 3,700.00

FV 0

Answer: 8.51%

Appendix D PVIFA  PVA / A (20 periods)  $35,000 / $3,700  9.459 is between 8% and 9% for 20 periods PVIFA at 8%

9.818

PVIFA at 9%

9.129 .689

PVIFA at 8%

9.818

PVIFA computed

9.459 .359

8% + (.359/.689) (1%) 8% + 0.521 (1%) = 8.52% 35.

Betty Bronson has just retired after 25 years with the electric company. Her total pension funds have an accumulated value of $180,000, and her life expectancy is 15 more years. Her pension fund manager assumes he can earn a 9 percent return on her assets. What will be her yearly annuity for the next 15 years?

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Chapter 12: The Capital Budgeting Decision

1   1   (1  i ) n  PVA  A    i       PVA A 1   1   (1  i ) n    i       $180,000 A 1   1   (1.09)15    .09       A  $22,330.60 Calculator Solution: N 15

I/Y 9

PV 180,000

PMT CPT −22,330.60

FV 0

Answer: $22,330.60

Appendix D A  PVA / PVIFA (9%, 15periods)  $180,000 / 8.061  $22,329.74

36.

Morgan Jennings, a geography professor, invests $50,000 in a parcel of land that is expected to increase in value by 12 percent per year for the next five years. He will take the

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Chapter 12: The Capital Budgeting Decision

proceeds and provide himself with a 10-year annuity. Assuming a 12 percent interest rate, how much will this annuity be?

9-36. Solution: Part 1

FV  PV  (1  i ) n FV  $50,000  (1.12)5 FV  $88,117.08 Part 2

1   1   (1  i ) n  PVA  A    i       PVA A 1   1   (1  i ) n    i       $88,117.08 A 1   1   (1.12)10    .12       A  $15,595.33 Calculator Solution: Step one: N 5 Answer: $88,117.08

I/Y 12

PV 50,000.00

PMT 0

FV CPT FV −88,117.08

Step two:

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Chapter 12: The Capital Budgeting Decision

N 10

I/Y 12

PV 88,117.08

PMT CPT PMT −15,595.33

FV 0

Answer: $15,595.33

Appendix A FV = PV × FVIF (12%, 5 periods) FV = $50,000 × 1.762 = $88,100 Appendix D A = PVA/PVIFA (12%, 10 periods) A = $88,100/5.650 = $15,593 37.

Solving for an annuity (LO9-4) You wish to retire in 14 years, at which time you want to have accumulated enough money to receive an annual annuity of $17,000 for 19 years after retirement. During the period before retirement you can earn 8 percent annually, while after retirement you can earn 10 percent on your money. What annual contributions to the retirement fund will allow you to receive the $17,000 annuity?

9-37. Solution: Part 1 1   1   (1  i ) n  PVA  A    i       1   1  19  (1.10)  PVA  $17,000    .10       PVA  $142, 203.64

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Chapter 12: The Capital Budgeting Decision

 (1  i ) n  1  FVA  A    i   FVA A  (1  i ) n  1    i   A

$142, 203.64  (1.08)14  1    .08  

A  $5,872.56 Calculator Solution: Determine the present value of a 14-year annuity during retirement: N I/Y PV PMT 19 10 CPT PV −142,203.64 17,000

FV 0

Answer: $142,203.64 To determine the annual deposit into an account earning 8% that is necessary to accumulate $142,203.64 after 14 years, solve for the annuity: N I/Y PV PMT FV 14 8 0 CPT PMT −5,872.56 142,203.64 Answer: $5,872.56 Annual contribution

Determine the present value of an annuity during retirement: Appendix D PVA  A  PVIFA (10%, 19 years)  $17,000  8.365  $142,205

To determine the annual deposit into an account earning 8 percent that is necessary to accumulate $142,205 after 14 years, use the future value of an annuity table. See Appendix C.

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Chapter 12: The Capital Budgeting Decision

A  FVA / FVIFA (8%, 14 years)  $142,205 = $5,872.60 annual contribution 24.215 38.

Del Monty will receive the following payments at the end of the next three years: $2,000, $3,500, and $4,500. Then, from the end of the 4th through the end of the 10th year, he will receive an annuity of $5,000 per year. At a discount rate of 9 percent, what is the present value of all three future benefits?

9-38. Solution: Payment #1  1  PV  FV   n   (1  i )  1 PV  $2,000  (1.09)1 PV  $1,834.86 Payment #2  1  PV  FV   n   (1  i )  1 (1.09) 2 PV  $2,945.88 Payment #3  1  PV  FV   n   (1  i )  PV  $3,500 

1 (1.09)3 PV  $3, 474.83 PV  $4,500 

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Chapter 12: The Capital Budgeting Decision

Annuity Value after three years 1   1   (1  i ) n  PVA  A    i       1   1   (1.09)7  PVA  $5,000    .09       PVA  $25,164.76 Annuity Value at Time Zero 1 PV  FV  (1  i ) n 1 PV  $25,164.76  (1.09)3 PV  $19,431.81 Total Present Value $ 1,834.86 Payment #1 + 2,945.88 Payment #2 + 3,474.83 Payment #3 +19,431.81 Annuity value $27,687.38 Total present value Calculator Solution: First find the present value of the first three payments. N I/Y PV 1 9 CPT PV −1,834.86 Answer: $1,834.86 N 2 Answer: $2,945.88

I/Y 9

PV CPT PV −2,945.88

PMT 0

FV 2,000

PMT 0

FV 3,500

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Chapter 12: The Capital Budgeting Decision

N 3

I/Y 9

PV CPT PV −3,474.83

PMT 0

FV 4,500

PMT 5,000

FV 0

PMT 0

FV 25,164.76

Answer: $3,474.83 Total = 1,834.86 + 2,945.88 + 3,474.83 = $8,255.57 as of now Then find the present value of the deferred annuity. N I/Y PV 7 9 CPT PV −25,164.76 Answer: $25,164.76 as of the end of year 3. Then, find its PV as of now: N I/Y 3 9

PV CPT PV −19,431.81

Answer: $19,431.81 as of now Finally, find the total present value of all future payments. 8,255.57 + 19,431.81 = $27,687.38

First find the present value of the first three payments. PV = FV × PVIF (Appendix B) i = 9% 1) $2,000 × 0.917 = $1,834 2) 3,500 × 0.842 = 2,947 3) 4,500 × 0.772 = 3,474 $8,255 Then find the present value of the deferred annuity. Appendix D will give a factor for a seven-period annuity (4th year through the 10th year) at a discount rate of 9 percent. The value of the annuity at the beginning of the fourth year is: PVA  A  PVIFA (9%,7 periods)  $5,000  5.033  $25,165

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Chapter 12: The Capital Budgeting Decision

This value at the beginning of year 4 (end of year 3) must now be discounted back for three years to get the present value of the deferred annuity. Use Appendix B. PV  FV  PVIF (9%,3periods)  $25,165  .772  $19.427.38

Finally, find the total present value of all future payments. Present value of first three payments Present value of the deferred annuity

39.

$ 8,225.00 19,427.38 $27,682.38

Bridget Jones has a contract in which she will receive the following payments for the next five years: $1,000, $2,000, $3,000, $4,000, and $5,000. She will then receive an annuity of $8,500 a year from the end of the 6th through the end of the 15th year. The appropriate discount rate is 14 percent. If she is offered $30,000 to cancel the contract, should she do it?

9-39. Solution: First Five Payments 1 PV  FV  (1  i ) n 1: 1 PV  $1,000   $877.19 (1.14)1 1  $1,538.94 2 : PV  $2,000  (1.14)2 1  $2,024.91 3 : PV  $3,000  (1.14)3 1  $2,368.32 4 : PV  $4,000  (1.14)4 1  $2,596.84 5 : PV  $5,000  (1.14)5 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

Present Value of the Annuity 1   1   (1  i ) n  PVA  A    i       1   1  10  (1.14)  PVA  $8,500    .14       PVA  $44,336.98 Discount five years for PV of deferred annuity $ 877.19 + 1,538.94 + 2,024.91 + 2,368.32 + 2,596.84 +23,027.24 $32,433.44 Since the present value of all future benefits under the contract is greater than $30,000, Bridget Jones should not accept this deal. Calculator Solution: First find the present value of the first five payments. N I/Y PV 1 14 CPT PV −877.19

PMT 0

FV 1,000

Answer: $877.19 N 2

PMT 0

FV 2,000

I/Y 14

PV CPT PV −1,538.94

Answer: $1,538.94

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Chapter 12: The Capital Budgeting Decision

N 3

I/Y 14

PV CPT PV −2,024.91

PMT 0

FV 3,000

I/Y 14

PV CPT PV −2,368.32

PMT 0

FV 4,000

I/Y 14

PV CPT PV −2,596.84

PMT 0

FV 5,000

Answer: $2,024.91 N 4 Answer: $2,368.32 N 5 Answer: $2,596.84 Total = 877.19 + 1,538.94 + 2,024.91 + 2,368.32 + 2,596.84 = $9,406.20 Then find the present value of the deferred annuity. N I/Y PV 10 14 CPT PV −44,336.98

PMT 8,500

FV 0

PMT 0

FV 44,336.98

Answer: $44,336.98 as of the end of year 5 Then find it PV as of now: N I/Y 5 14

PV CPT PV −23,027.24

Answer: $23,027.2 4 as of now Finally, find the total present value of all future payments. 9,406.20 + 23,027.24 = $32,433.44 Since the present value of all future benefits under the contract is greater than $30,000, Bridget Jones should not accept this amount to cancel the contract.

First find the present value of the first five payments. PV = FV × PVIF (Appendix B) i = 14% 1) $1,000 × 0.877 = $ 877 2) 2,000 × 0.769 = 1,538 3) 3,000 × 0.675 = 2,025 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

4) 5)

4,000 × 0.592 = 2,368 5,000 × 0.519 = 2,595 $9,403

Then, find the present value of the deferred annuity. Appendix D will give a factor for a 10-period annuity (6th year through the 15th year) at a discount rate of 14 percent. The value of the annuity at the beginning of the 6th year is: PVA  A  PVIFA (14%, 10 periods)  $8,500  5.216  $44,336

This value at the beginning of year 6 (end of year 5) must now be discounted back for five years to get the present value of the deferred annuity. Use Appendix B. PV = FV × PVIF (14%, 5 periods) = $44,336 × .516 = $23,010.38

Next, find the total present value of all future payments. Present value of first five payments $ 9,403.00 Present value of the deferred annuity 23,010.38 $32,413.38 40.

Mark Ventura has just purchased an annuity to begin payment two years from today. The annuity is for $8,000 per year and is designed to last 10 years. If the interest rate for this problem calculation is 13 percent, what is the most he should have paid for the annuity?

9-40. Solution:

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Chapter 12: The Capital Budgeting Decision

Annuity

1   1   (1  i ) n  PVA  A    i       1   1  10  (1.13)  PVA  8,000    .13       PVA  $8,000  (5.426) PVA  $43, 409.95 Discount off two years 1 V  FV  (1  i ) n

PV  $43, 409.95 

1 (1.13) 2

PV  $33,996.36 Calculator Solution: N 10

I/Y 13

PV CPT PV −43,409.95

PMT 8,000

FV 0

PMT 0

FV 43,409.95

Answer: $43,409.95 as of the end of year 2 Then, find its PV as of now: N I/Y 2 13

PV CPT PV −33,996.36

Answer: $33,996.36 as of now The maximum that should be paid for the annuity is $33,996.36.

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Chapter 12: The Capital Budgeting Decision

Appendix D will give a factor for a 10-year annuity when the appropriate discount rate is 13 percent (5.426). The value of the annuity at the beginning of the year it starts (2011) is: PVA  A  PVIFA (13%, 10 periods)  $8,000  5.426  $43,408

The present value at the beginning of 2014 is found using Appendix B (two years at 13 percent). The factor is .783. Note we are discounting from the beginning of 2016 to the beginning of 2014.

PV = FV × PVIF (13%, 2periods) = $43,408 × .783 = $33,988 The maximum that should be paid for the annuity is $33,988.

41.

Yield (LO9-4) If you borrow $8,599 and are required to pay back the loan in five equal annual installments of $2,750, what is the interest rate associated with the loan?

9-41. Solution: Calculator Solution: N 5

I/Y CPT I/Y 18.00

PV −8,599

PMT 2,750.00

FV 0

Answer: 18.00%

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Chapter 12: The Capital Budgeting Decision

Appendix D PVIFA = PVA / A (5 periods) = $8,599/ $2,750 = 3.127 Interest rate = 18% Go across period 5 until you find 3.127. Go up to the percentage at the top of the column and find 18 percent. 42.

Cal Lury owes $10,000 now. A lender will carry the debt for five more years at 10 percent interest. That is, in this particular case, the amount owed will go up by 10 percent per year for five years. The lender then will require that Cal pay off the loan over the next 12 years at 11 percent interest. What will his annual payment be?

9-42. Solution: Part 1 FV  PV  (1  i ) n FV  $10,000  (1.10)5 FV  $16,105.10

Part 2 1    1  (1  i ) n  PVA  A    i       PVA A 1 1 (1.11)12 .11 $16,105.10 A 1 1 (1.11)12 .11 $16,105.10 A 6.492 A  $2, 480.62

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Chapter 12: The Capital Budgeting Decision

Calculator Solution: Step one: N 5

I/Y 10

PV 10,000

PMT 0

FV CPT FV −16,105.10

Answer: $16,105.10 is the amount owed after five years. Step two: N 12

I/Y 11

PV 16,105.10

PMT CPT PMT −2,480.62

FV 0

Answer: $2,480.62 is the annual payment to retire the loan.

Appendix A FV = PV × FVIF (10%, 5 periods) = $10,000 × 1.611 = $16,110 Amount owed after 5 years

Appendix D A = PVA /PVIFA (11%, 12 periods) = $16,110/6.492 = $2, 482 43.

Annual payments to retire the loan

If your uncle borrows $60,000 from the bank at 10 percent interest over the seven-year life of the loan, what equal annual payments must be made to discharge the loan, plus pay the bank its required rate of interest (round to the nearest dollar)? How much of his first payment will be applied to interest? To principal? How much of his second payment will be applied to each?

9-43. Solution: Annual Payment

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Chapter 12: The Capital Budgeting Decision

1   1   (1  i ) n  PVA  A    i       $60,000 A 1 1 (1.10) 7 .10 $60,000 A 6.868 A  $12,324.33

Amount of first payment applied to interest and principal $60,000  (.10)  $6,000 First year interest Applied to principal $12,324.33  $6,000  $6,324.33 Amount of second payment applied to interest and principal $60,000  $6,324.33  $53,675.67 $53,675.67  (.10)  $5,367.57 $12,324.33  $5,367.57  $6,956.76

After one year Second year interest Applied to principal

Calculator Solution: N 7

I/Y 10

PV 60,000.00

PMT CPT PMT −12,324.33

FV 0

Answer: $12,324.33 is the annual payment to retire the loan. First payment: $60,000 × 0.10 = $6,000 first year interest $12,324.33 – $6,000 = $6,324.33 applied to principal Second payment: First determine remaining principal $60,000 – $6,324.33 = $53,675.67 $53,675.67 × 0.10 = $5,367.57 second year interest $12,324.33 – $5,367.57 = $6,956.76 applied to principal

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Chapter 12: The Capital Budgeting Decision

Appendix D A = PVA /PVIFA (10%,7 periods) = $60,000/4.868 = $12,325 annual payment

First payment: $60,000 × 0.10 = $6,000 interest $12,325 – $6,000 = $6,325 applied to principal Second payment: First determine remaining principal and then the interest and principal payment. $60,000 – $6,325 = $53,675 remaining principal $53,675 × 0.10 = $ 5,368 interest $12,325 – $5,368 = $ 6,957 applied to principal 44.

Larry Davis borrows $80,000 at 14 percent interest toward the purchase of a home. His mortgage is for 25 years. a. How much will his annual payments be? (Although home payments are usually on a monthly basis, we shall do our analysis on an annual basis for ease of computation. We will get a reasonably accurate answer.) b. How much interest will he pay over the life of the loan? c. How much should he be willing to pay to get out of a 14 percent mortgage and into a 10 percent mortgage with 25 years remaining on the mortgage? Assume current interest rates are 10 percent. Carefully consider the time value of money. Disregard taxes.

9-44. Solution: a.

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Chapter 12: The Capital Budgeting Decision

1   1   (1  i ) n  PVA  A    i       PVA A 1 1 (1  i ) n i $80,000 A 1 1 (1.14) 25 .14 $80,000 A 6.873 A  $11,639.87

$11,639.87  25  $290,996.82 $290,996.82  $80,000  $210,996.82

Total payments Total interest paid

PVA 1 1 (1  i ) n i $80,000 A 1 1 (1.10) 25 .10 $80,000 A 9.077 A  $8,813.45 A

New annual payments

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Chapter 12: The Capital Budgeting Decision

Difference between 14 percent and 10 percent interest $11,639.87 – 8,813.45 $ 2,826.42 1 1 (1  i ) n PV  $2,826.42  i 1 1 (1.10) 25 PV  $2,826.42  .10 PV  $2,826.42  (9.077) Amount that could be paid to refinance PV  $25,655.53 Calculator Solution: (a) N 25

I/Y 14

PV 80,000

PMT CPT PMT −11,639.87

FV 0

PMT CPT PMT −8,813.45

FV 0

Answer: Annual payment $11,639.87 (b) Total payments = 11,639.87 × 25 = $290,996.82 Total interest paid = 290,996.82 – 80,000 = 210,996.82 (c) N 25

I/Y 10

PV 80,000

Answer: Annual Payment $8,813.45 Difference between old and new payments = 11,639.87 – 8,813.45 = $2,826.42 P.V. of difference at 10 percent: N 25

I/Y 10

PV CPT PV −25,655.53

PMT 2,826.42

FV 0

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Chapter 12: The Capital Budgeting Decision

Answer: $25,655.53 is the amount that could be paid to refinance.

Appendix D a. A = PVA /PVIFA (14%, 25periods) = $80,000/6.873 = $11,639.75

$11,639.75 ×

Annual payments Years

$290,993.75

Total payment

 80,000.00

Repayment of principal

$210,993.75

Total interest paid

Appendix D c.

New payments at 10 percent A = PVA /PVIFA (10%, 25periods) = $80,000/9.077 = $8,813.48

Difference between old and new payments

$11,639.75 Old 8,813.48 New $ 2,826.27 Difference PV of difference – Appendix D

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Chapter 12: The Capital Budgeting Decision

PVA  A  PVIFA (assumes 10% discount rate, 25 periods)  $ 2,826.27  9.077  $25,654.05 Amount that could be paid to refinance 45.

Annuity with changing interest rates (LO9-4) You are chairperson of the investment fund for the Continental Soccer League. You are asked to set up a fund of semiannual payments to be compounded semiannually to accumulate a sum of $250,000 after nine years at a 10 percent annual rate (18 payments). The first payment into the fund is to take place six months from today, and the last payment is to take place at the end of the ninth year. a. Determine how much the semiannual payment should be. (Round to whole numbers.) On the day after the sixth payment is made (the beginning of the fourth year), the interest rate goes up to a 12 percent annual rate, and you can earn a 12 percent annual rate on funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded semiannually on all funds. b. Determine how much the revised semiannual payments should be after this rate change (there are 12 payments and compounding dates). The next payment will be in the middle of the fourth year. (Round all values to whole numbers.)

9-45. Solution: a. (1  i ) n  1 FVA  A  i FVA A (1  i ) n  1 i $250,000 A (1.05)18  1 .05 $250,000 A 28.132 A  $8,886.68

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Chapter 12: The Capital Budgeting Decision

b. Part 1: Value of first six payments at the beginning of year 4 (1  i ) n  1 FVA  A  i (1.05)6  1 FVA  $8,886.68  .05 FVA  $8,886.68  (6.802) FVA  $60, 446.42

Part 2 : FV of first six payments at the end of year 9 FV  PV  (1  i ) n

FV  $60, 446.42  (1.06)12 FV  $60, 446.42  (2.012) FV  $121,630.10 Part 3: Additional amount required $ 250,000.00 – 121,630.10 $ 128,369.90 Part 4 : New payment level

FVA (1  i ) n  1 i $128,369.90 A (1.06)12  1 .06 $128,369.90 A 16.870 A  $7,609.39 A

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Chapter 12: The Capital Budgeting Decision

Calculator Solution: (a) N 18

I/Y 5

PV 0

PMT CPT PV −8,886.68

FV 250,000

Answer: $8,886.68 (b) First determine how much the old payments are equal to after 6 periods at 5%. N I/Y PV PMT FV 6 5 0 8,886.68 CPT FV −60,446.40 Answer: $60,446.40 Then, determine how much this value will grow to after 12 periods at 6 percent (semiannual rate). N I/Y PV PMT FV 12 6 60,446 0 CPT FV −121,629.23 Answer: $121,629.23 Subtract this value ($121,629.00) from $250,000 to determine how much you need to accumulate on the next 12 payments. 250,000 – 121,629 = $128,371 Determine the revised semiannual payment necessary to accumulate this sum after 12 periods at 6 percent. N I/Y PV PMT FV CPT 12 6 0 128,371 PV −7,609.45 Answer: $7,609.39 is the revised semiannual payment.

Appendix C a. A  FVA / FVIFA  $250,000 / 28.132 (5%, 18 periods)  $8,887

b. First determine how much the old payments are equal to after six periods at 5 percent. Use Appendix C.

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Chapter 12: The Capital Budgeting Decision

FVA = A × FVIFA (5%, 6 periods) = $8,887 × 6.802 = $60, 449

Then, determine how much this value will grow to after 12 periods at 6 percent (semiannual rate). Appendix A FV = PV × FVIF (6%, 12 periods) = $60, 449 × 2.012 = $121, 623 Subtract this value from $250,000 to determine how much you need to accumulate on the next 12 payments.

$250, 000  121, 623 $128,377 Determine the revised semiannual payment necessary to accumulate this sum after 12 periods at 6 percent. Appendix C A = FVA/FVIFA A = $128,377 /16.870 A = $7,610 46.

Your younger sister, Linda, will start college in five years. She has just informed your parents that she wants to go to Hampton University, which will cost $17,000 per year for four years (cost assumed to come at the end of each year). Anticipating Linda’s ambitions, your parents started investing $2,000 per year five years ago and will continue to do so for five more years. How much more will your parents have to invest each year (A?) for the next five years to have the necessary funds for Linda’s education? Use 10 percent as the

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Chapter 12: The Capital Budgeting Decision

appropriate interest rate throughout this problem (for discounting or compounding). This timeline depicts the cash flows described (in thousands of dollars.)

9-46. Solution: PV of college costs five years from today (Part 1) 1 1 (1  i ) n PVA  A  i 1 1 (1.10) 4 PVA  $17,000  .10 PVA  $17,000  (3.170)

PVA  $53,887.71 Accumulation of $2,000 per year for 10 years (Part 2) (1  i ) n  1 FVA  A  i (1.10)10  1 FVA  $2,000  .10 FVA  $2,000  (15.937) FVA  $31,874.85 Part 1 minus Part 2 $53,887.71 –31,874.85 $22,012.86 Additional funds required in five years

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Chapter 12: The Capital Budgeting Decision

Additional contribution required for next five years (1  i ) n  1 FVA  A  i FVA A (1  i ) n  1 i $22,012.86 A (1.10)5  1 .10 $22,012.86 A 6.105 A  $3,605.65 Calculator Solution: Present value of college costs N I/Y 4 10

PV CPT PV −53,887.71

PMT 17,000

FV 0

Answer: $53,887.71 Accumulation based on investing $2,000 per year for 10 years. N I/Y PV PMT 10 10 0 2,000

FV CPT FV −31,874.85

Answer: $31,874.85 Additional funds required five years from now when Brittany starts college: PV of college costs − Accumulation based on $2,000 per year = 53,887.71 – 31,874.85 = $22,012.86 Added contribution for the next five years N I/Y PV 5 10 0

PMT CPT PV −3,605.65

FV 22,012.86

Answer: $3,605.65

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Chapter 12: The Capital Budgeting Decision

Appendix D PVA = A × PVIFA (10%, 4 periods) = $17,000 × 3.170 = $53,890

Accumulation based on investing $2,000 per year for 10 years. Appendix C FVA = A × FVIFA (10%, 10 periods) = $2,000 × 15.937 = $31,874

Additional funds required five years from now. $53,890 31,874 $22,016

PV of college costs Accumulation based on $2,000 per year investment Additional funds required

Added contribution for the next five years Appendix C

A = FVA /FVIFA (10%, 5 periods) = $22,016/6.105 = $3,606.22

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Chapter 12: The Capital Budgeting Decision

Connect-Only Problem 47.

Special consideration of annuities and time periods (LO9-4) Your parents have accumulated a $120,000 nest egg. They have been planning to use this money to pay college costs to be incurred by you and your sister, Courtney. However, Courtney has decided to forgo college and start a nail salon. Your parents are giving Courtney $15,000 to help her get started, and they have decided to take year-end vacations costing $10,000 per year for the next four years. How much money will your parents have at the end of four years to help you with graduate school, which you will start then? You plan to work on a master’s and perhaps a PhD. If graduate school costs $26,353 per year, approximately how long will you be able to stay in school based on these funds? Use 9 percent as the appropriate interest rate throughout this problem. Round all values to whole numbers.

9-47. Solution: Funds available after Nail Salon $120,000 – 15,000 $105,000 PV of vacations

1 PVA  A 

1 (1  i ) n i

1 (1.09)4 PVA  $10,000  .09 PVA  $10,000  (3.2397) 1

PVA  $32,397 Funds available after vacations $105,000 – 32,397 $ 72,603

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Chapter 12: The Capital Budgeting Decision

Funds four years later for graduate school FV  PV  (1  i ) n

FV  $72,603  (1.09) 4 FV  $102, 485 Number of years of graduate school 1 1 (1  i ) n PVA  A  i 1 1 (1  i ) n PVA  i A 1 1 (1.09) n $102, 485  .09 $26,353 1 1  .3500 (1.09) n 1   .6500 (1.09) n (1.09) n  1.538 n  ln(1.09)  ln(1.538) ln(1.538) ln(1.09) n5 n

Calculator Solution: N 4

I/Y 9

PV CPT PV −32,397.20

PMT 10,000

FV 0

Answer: $32,397.20

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Chapter 12: The Capital Budgeting Decision

Less present value of vacation Funds available four years later for graduate school: N I/Y PV 4 9 72,603

PMT 0

FV CPT FV −102,485.05

PMT –26,353

FV 0

Answer: $102,485 Number of years of graduate education N I/Y CPT N 5.00 9

PV 102,485

Answer: Three years

$120,000 Funds available Funds available after the nail salon $120,000 Funding available before the nail salon – 15,000 Nail salon 105,000 Funds available after the nail salon Less present value of vacation Appendix D PVA  A  PVIFA (9%, 4 periods)  $10,000  3.240 = $32,400

$105,000 – 32,400 $72,600

Remaining funds for graduate school

Available funds after four years.

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Chapter 12: The Capital Budgeting Decision

Appendix A FV  PV  FVIF (9%, 4 periods)  $72,600  1.412  $102,511 Funds available for starting graduate school

Number of years of graduate education Appendix D

PVA (9%) A $102,511   3.890 (rounded) $26,353

PVIFA 

with i = 9%, n = 5 for 3.890, the answer is five years. COMPREHENSIVE PROBLEM Medical Research Corporation (Comprehensive time value of money) Dr. Harold Wolf of Medical Research Corporation (MRC) was thrilled with the response he had received from drug companies for his latest discovery, a unique electronic stimulator that reduces the pain from arthritis. The process had yet to pass rigorous Federal Drug Administration (FDA) testing and was still in the early stages of development, but the interest was intense. He received the three offers described following this paragraph. (A 10 percent interest rate should be used throughout this analysis unless otherwise specified.) Offer I - $1,000,000 now plus $200,000 from year 6 through 15. Also, if the product did over $100 million in cumulative sales by the end of year 15, he would receive an additional $3,000,000. Dr. Wolf thought there was a 70 percent probability this would happen. Offer II - Thirty percent of the buyer’s gross profit on the product for the next four years. The buyer in this case was Zbay Pharmaceutical. Zbay’s gross profit margin was 60 percent. Sales in year one were projected to be $2 million and then expected to grow by 40 percent per year. Offer III - A trust fund would be set up for the next eight years. At the end of that period, Dr. Wolf would receive the proceeds (and discount them back to the present at 10 percent). The trust fund called for semiannual payments for the next eight years of $200,000 (a total of $400,000 per year).

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Chapter 12: The Capital Budgeting Decision

The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. To look up the future value of an annuity due in the tables, add 1 to n (16 + 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 10 percent annually (5 percent semiannually). Determine the present value of the trust fund’s final value. Hint: See page 280for a discussion of calculating an annuity due. Required: Find the present value of each of the three offers and indicate which one has the highest present value.

CP 9-1. Solution: Offer I $1,000,000 now plus: + $200,000 from year 6 through 15 (deferred annuity) Appendix D PVA = A × PVIFA (10%, 10 years) = $200,000 × 6.145 = $1, 229,000 (percent value at the beginning of year 6; i.e., the end of year 5)

Appendix B PV  FV  PVIF (10%, 5 years)  $1,229,000  .621  $763,209

+ .70 × $3,000,000 = $2,100,000 Appendix B PV  FV  PVIF (10%, 15 years)  $2,100,000  .239  $501,900

Total value of Offer I

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Chapter 12: The Capital Budgeting Decision

$1,000,000 763,209 501,900 $2,265,109

Payment today Present value of deferred annuity Present value of $3 million bonus

Offer II Gross Profit

Payment 30%

Year

Sales

(60% of Sales) of Gross Profit

1 2 3

$2,000,000 2,800,000 3,920,000

$1,200,000 1,680,000 2,352,000

$360,000 504,000 705,600

5,488,000

3,292,800

987,600

Year

Payment

Appendix B PV Factor

1 2 3 4

$360,000 504,000 705,600 987,600

0.909 0.826 0.751 0.683

$327,240 416,304 529,906 674,531

Total value of Offer II

$1,947,981

Offer III Future value of an annuity due (Appendix C) 8 years – semiannually n = 16 + 1 = 17 i = 10%/2 = 5% FVIFA = 25.840 – 1 = 24.840 (Appendix C)

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Chapter 12: The Capital Budgeting Decision

FVA  A  FVIFA  $200,000  24.840  $4,968,000 value of trust fund after eight years

Present value of trust fund (Appendix B)

PV  A  PVIF (10%, 8 years)  $4,968,000  .467  $2,320,056 Total value of offer III Summary Value of Offer I

$2,265,109

Value of Offer II

$1,947,981

Value of Offer III

$2,320,056

Select Offer III Chapter 10 Valuation and Rates of Return

Discussion Questions 10-1.

How is valuation of any financial asset related to future cash flows?

The valuation of a financial asset is equal to the present value of future cash flows.

10-2.

Why might investors demand a lower rate of return for an investment in Microsoft as compared to United Airlines?

Because Microsoft has less risk than United Airlines, Microsoft has relatively high

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Chapter 12: The Capital Budgeting Decision

returns and a strong market position; United Airlines has had financial difficulties and emerged from bankruptcy in 2006.

10-3.

What are the three factors that influence the required rate of return by investors?

The three factors that influence the demanded rate of return are:

a. The real rate of return b. The inflation premium c. The risk premium 10-4.

If inflationary expectations increase, what is likely to happen to yield to maturity on bonds in the marketplace? What is also likely to happen to the price of bonds?

If inflationary expectations increase, the yield to maturity (the required rate of return) will increase. This will mean a lower bond price.

10-5.

Why is the remaining time to maturity an important factor in evaluating the impact of a change in yield to maturity on bond prices? The longer the time period remaining to maturity, the greater the impact of a difference between the rate the bond is paying and the current yield to maturity (required rate of return). For example, a 2 percent ($20) differential is not very significant for one year, but very significant for 20 years. In the latter case, it will have a much greater effect on the bond price.

10-6.

What are the three adjustments that have to be made in going from annual to semiannual bond analysis?

The three adjustments in going from annual to semiannual bond analysis are:

1. Divide the annual interest rate by two. 2. Multiply the number of years by two.

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Chapter 12: The Capital Budgeting Decision

3. Divide the annual yield to maturity by two. 10-7.

Why is a change in required yield for preferred stock likely to have a greater impact on price than a change in required yield for bonds? The longer the life of an investment, the greater the impact of a change in the required rate of return. Since preferred stock has a perpetual life, the impact is likely to be at a maximum.

10-8.

What type of dividend pattern for common stock is similar to the dividend payment for preferred stock? The no-growth pattern for common stock is similar to the dividend on preferred stock.

10-9.

What two conditions must be met to go from Formula 10-7 to Formula 10-8 in using the dividend valuation model?

P0 

D1 Ke  g

To go from Formula (10-7) to Formula (10-8): The firm must have a constant growth rate (g). The discount rate (Ke) must exceed the growth rate (g). 10-10.

What two components make up the required rate of return on common stock? The two components that make up the required rate of return on common stock are: a. The dividend yield D1/P0. b. The growth rate (g). This actually represents the anticipated growth in dividends, earnings, and stock price over the long term.

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10-8

Chapter 12: The Capital Budgeting Decision

10-11.

What factors might influence a firm’s price-earnings ratio? The price-earnings ratio is influenced by the earnings and sales growth of the firm, the risk (or volatility in performance), the debt-equity structure of the firm, the dividend policy, the quality of management, and a number of other factors. Firms that have bright expectations for the future tend to trade at high P/E ratios while the opposite is true of low P/E firms.

10-12.

How is the supernormal growth pattern likely to vary from the normal, constant growth pattern? A supernormal growth pattern is represented by very rapid growth in the early years of a company or industry that eventually levels off to more normal growth. The supernormal growth pattern is often experienced by firms in emerging industries, such as in the early days of electronics or microcomputers.

10-13.

What approaches can be taken in valuing a firm’s stock when there is no cash dividend payment? In valuing a firm with no cash dividend, one approach is to assume that at some point in the future a cash dividend will be paid. You can then take the present value of future cash dividends. A second approach is to take the present value of future earnings as well as a future anticipated stock price. The discount rate applied to future earnings is generally higher than the discount rate applied to future dividends.

Problems (For the first 20 bond problems, assume interest payments are on an annual basis.) 1.

Bond value (LO10-3) The Lone Star Company has $1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is

a. 6 percent. b. 9 percent. c. 13 percent.

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Chapter 12: The Capital Budgeting Decision

Calculator Solution:

(a) 6 percent yield to maturity N 20

I/Y 6

PV CPT PV −1,458.80

PMT 100

FV 1,000

PV CPT PV −1,091.29

PMT 100

FV 1,000

PV CPT PV −789.26

PMT 100

FV 1,000

Answer: $1,458.80 Current bond price

(b) 9 percent yield to maturity N 20

I/Y 9

Answer: $1,091.29 Current bond price

I/Y 13

Answer: $789.26 Current bond price

a. 6 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 20, i = 6%) PVA = 100 × 11.470 = $1,147.00

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20, i = 6%) Appendix B PV = 1,000 × 0.312 = $312 Total Present Value Present Value of Interest Payments

$1,147.00

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Chapter 12: The Capital Budgeting Decision

Present Value of Principal Payment Total Present Value or Price of the Bond

312.00 $1,459.00

b. 9 percent yield to maturity PVA = A × PVIFA (n = 20, i = 9%) PVA = $100 × 9.129 = $912.90 PV = FV × PVIF (n = 20, i = 9%) PV = $1,000 × 0.178 = $178.00

Appendix D Appendix B $ 912.90 178.00 $1,090.90

13 percent yield to maturity PVA = A × PVIFA (n = 20, i = 13%) PVA = $100 × 7.025 = $702.50

Appendix D

PV = FV × PVIF (n = 20, i = 13%) PV = $1,000 × 0.087 = $87.00

Appendix B $702.50 87.00 $789.50

Midland Oil has $1,000 par value bonds outstanding at 8 percent interest. The bonds will mature in 25 years. Compute the current price of the bonds if the present yield to maturity is

a. 7 percent. b. 10 percent. c. 13 percent.

10-2. Solution: Calculator Solution:

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Chapter 12: The Capital Budgeting Decision

(a) 7 percent yield to maturity

I/Y

PMT

CPT PV −1,116.54

1,000

Answer: $1,116.54 Current bond price

(b) 10 percent yield to maturity N

I/Y

PMT

CPT PV −818.46

1,000

Answer: $ 818.46 Current bond price

I/Y

PMT

CPT PV −633.50

1,000

Answer: $633.50 Current bond price

a. 7 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 25, i = 7%) PVA = $80 × 11.654 = $932.32

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 25, i = 7%) Appendix B PV = $1,000 × 0.184 = $184 Total Present Value

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Chapter 12: The Capital Budgeting Decision

Present Value of Interest Payments Present Value of Principal Payments Total Present Value or Price of the Bond b. 10 percent yield to maturity PVA = A × PVIFA (n = 25, i = 10%) PVA = $80 × 9.077 = $726.16 PV = FV × PVIF (n = 25, i = 10%) PV = $1,000 × 0.092 = $92

$ 932.32 184.00 $1,116.32 Appendix D

Appendix B $726.16 92.00 $818.16

c. 13 percent yield to maturity PVA = A × PVIFA (n = 25, i = 13%) PVA = $80 × 7.330 = $586.40 PV = FV × PVIF (n = 25, i = 13%) PV = $1,000 × 0.047 = $47

Appendix D Appendix B $586.40 47.00 $633.40

Exodus Limousine Company has $1,000 par value bonds outstanding at 10 percent interest. The bonds will mature in 50 years. Compute the current price of the bonds if the percent yield to maturity is

a. 5 percent. b. 15 percent.

10-3. Solution: Calculator Solution:

(a) 5 percent yield to maturity

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Chapter 12: The Capital Budgeting Decision

I/Y

PMT

CPT PV −1,912.80

100

1,000

Answer: $1,912.80 Current bond price

(b) 15 percent yield to maturity N

I/Y

PMT

CPT PV −666.97

100

1,000

Answer: $666.97 Current bond price

a. 5 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 50, i = 5%) PVA = $100 × 18.256 = $1,825.60

Appendix D

Present Value of Principal Payment PV = FV × PVIF (n = 50, i = 5%) PV = $1,000 × 0.087 = $87

Appendix B

Present Value of Interest Payment Present Value of Principal Payment Total Present Value or Price of the Bond

$1,825.60 87.00 $1,912.60

b. 15 percent yield to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 50, i = 15%) PVA = $1,000 × 6.661 = $666.10

Appendix D

PV = FV × PVIF (n = 50, i = 15%)

Appendix B

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Chapter 12: The Capital Budgeting Decision

PV = $1,000 × 0.001 = $1 Present Value of Interest Payment Present Value of Principal Payment Total Present Value or Price of the Bond

$666.10 1.00 $667.10

Bond value (LO10-3) Barry’s Steroids Company has $1,000 par value bonds outstanding at 16 percent interest. The bonds will mature in 40 years. If the percent yield to maturity is 13 percent, what percent of the total bond value does the repayment of principal represent?

10-4. Solution: Calculator Solution:

13 percent yield to maturity N

I/Y

PMT

CPT PV −1,229.03

160.0

1,000

Answer: $1,229.03 Total present value of the bond

I/Y

PMT

CPT PV −7.53

1,000

Answer: $7.53 Present value of the principal payment

PV of principal payment $7.53 = = 0.613% Bond value $1,229.03

Present Value of Interest Payments PVA = A × PVIFA (n = 40, i = 13%) PVA = $160 × 7.634 = $1,221.44

Appendix D

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Chapter 12: The Capital Budgeting Decision

Present Value of Principal Payment PV = FV × PVIF (n = 40, i = 13%) PV = $1,000 × 0.008 = $8.00

Appendix B

Present Value of Interest Payments Present Value of Principal Payment Total Present Value or Price of the Bond

$1,221.44 8.00 $1,229.44

PV of Principal Payment $8.00   .651% Bond Value $1,229.44 5.

Bond value (LO10-3) Essex Biochemical Co. has a $1,000 par value bond outstanding that pays 15 percent annual interest. The current yield to maturity on such bonds in the market is 17 percent. Compute the price of the bonds for the following maturity dates:

a. 30 years b. 20 years c. 4 years

10-5. Solution: Calculator Solution:

(a) 30 years to maturity N 30

I/Y 17

PV CPT PV −883.41

PMT 150.0

FV 1,000

PV CPT PV −887.44

PMT 150.0

FV 1,000

Answer: $883.41 Bond price

(b) 20 years to maturity N 20

I/Y 17

Answer: $887.44 Bond price

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Chapter 12: The Capital Budgeting Decision

I/Y 17

PV CPT PV −945.14

PMT 150.0

FV 1,000

Answer: $945.14 Bond price

a. 30 years to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 17%) PVA = $150 × 5.829 = $874.35 PV = FV × PVIF (n = 30, i = 17%) PV = $1,000 × 0.009 = $9.00

Appendix D

Appendix B

Total Present Value Present Value of Interest Payments Present Value of Principal Payment Total Present Value or Price of the Bond

$874.35 9.00 $883.35

b. 20 years to maturity PVA = A × PVIFA (n = 20, i = 17%) PVA = $150 ×5.628 = $844.20

Appendix D

PV = FV × PVIF (n = 20, i = 17%) PV = $1,000 × 0.043 = $43.00

Appendix B $ 844.20 43.00 $887.20

4 years to maturity PVA = A × PVIFA (n = 4, i = 17%)

Appendix D

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Chapter 12: The Capital Budgeting Decision

PVA = $150 × 2.743 = $411.45 PV = FV × PVIF PV = $1,000 × 0.534 = $534

Appendix B $ 411.45 534.00 $945.45

Kilgore Natural Gas has a $1,000 par value bond outstanding that pays 9 percent annual interest. The current yield to maturity on such bonds in the market is 12 percent. Compute the price of the bonds for the following maturity dates:

a. 30 years b. 15 years c. 1 year

10-6. Solution: Calculator Solution:

(a) 30 years to maturity N

I/Y

PMT

CPT PV −758.34

1,000

Answer: $758.34 Bond price

(b) 15 years to maturity N

I/Y

PMT

CPT PV −795.67

1,000

Answer: $795.67 Bond price

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Chapter 12: The Capital Budgeting Decision

I/Y

1 12 Answer: $973.21 Bond price

PMT

CPT PV −973.21

1,000

a. 30 years to maturity Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 12%) PVA = $90 × 8.055 = $724.95 PV = FV × PVIF (n = 30, i = 12%) PV = $1,000 × 0.033 = $33

Appendix D Appendix B

Total Present Value Present Value of Interest Payments Present Value of Principal Payment Total Present Value or Price of the Bond

$724.95 33.00 $757.95

b. 15 years to maturity PVA = A × PVIFA (n = 15, i = 12%)

Appendix D

PVA = $90 × 6.811 = $612.99 PV = FV × PVIF (n = 15, i = 12%) PV = $1,000 × .183 = $183

Appendix B $612.99 183.00 $795.99

1 year to maturity PVA = A × PVIFA PVA = $90 × .893 = $80.37

Appendix D

PV = FV × PVIF PV = $1,000 × .893 = $893.00

Appendix B

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Chapter 12: The Capital Budgeting Decision

$ 80.37 893.00 $973.37 7.

Bond maturity effect (LO10-3) Toxaway Telephone Company has a $1,000 par value bond outstanding that pays 6 percent annual interest. If the yield to maturity is 8 percent, and remains so over the remaining life of the bond, the bond will have the following values over time: Remaining Maturity

Bond Price

$795.67

$830.49

$891.86

$973.21

Graph the relationship in a manner similar to the bottom half of Figure 10-2. Also explain why the pattern of price change takes place.

10-7. Solution: Toxaway Telephone Company

As the time to maturity becomes less and less, the importance of the difference between the rate the bond pays and the yield © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

to maturity becomes less significant. Therefore, the bond trades closer to par value. 8.

Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 11 percent to 8 percent:

a. What is the bond price at 11 percent? b. What is the bond price at 8 percent? c. What would be your percentage return on investment if you bought when rates were 11 percent and sold when rates were 8 percent?

10-8. Solution: a. $920.30 b. $1,196.80 c. Sales price (8%) $1,196.36 Purchase price (11%) 920.30 Profit $ 275.99

Profit $275.99   29.99% Purchase Pr ice $920.37

Interest rate effect (LO10-3) Go to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) increase from 9 to 12 percent.

a. What is the bond price at 9 percent? b. What is the bond price at 12 percent? c. What would be your percentage return on the investment if you bought when rates were 9 percent and sold when rates were 12 percent?

10-9. Solution: a. $1,091.29 b. $850.61 c. Purchase price (9%) Sales Price (12%) Loss

.............. $1,091.29 850.61 .............. ($240.68)

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Chapter 12: The Capital Budgeting Decision

Loss $240.68    22.05% Purchase Price $1,091.29

10.

Interest rate effect (LO10-3) Using Table 10-1, assume interest rates in the market (yield to maturity) are 14 percent for 20 years on a bond paying 10 percent.

a. What is the price of the bond? b. Assume five years have passed and interest rates in the market have gone down to 12 percent. Now, using Table 10-2 for 15 years, what is the price of the bond? c. What would your percentage return be if you bought the bonds when interest rates in the market were 14 percent for 20 years and sold them 5 years later when interest rates were 12 percent?

10-10. Solution: a. $735.07 b. $863.78 c. Sales price (12%) .............. $863.78 Purchase Price (14%) 735.07 Profit .............. $128.71

Profit $128.71   17.51% Purchase Price $735.07

11.

Effect of maturity on bond price (LO10-3) Using Table 10-2:

a. Assume the interest rate in the market (yield to maturity) goes down to 8 percent for the 10 percent bonds. Using column 2, indicate what the bond price will be with a 10-year, a 15-year, and a 20-year time period. b. Assume the interest rate in the market (yield to maturity) goes up to 12 percent for the 10 percent bonds. Using column 3, indicate what the bond price will be with a 10-year, a 15-year, and a 20-year period. c. Based on the information in part a, if you think interest rates in the market are going down, which bond would you choose to own? d. Based on information in part b, if you think interest rates in the market are going up, which bond would you choose to own?

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Chapter 12: The Capital Budgeting Decision

10-11. Solution: a.

Maturity 10 year 15 year 20 year

Bond price $1,134.20 1,171.19 1,196.36

Maturity 10 year 15 year 20 year

Bond price $887.00 863.78 850.61

c. Based on information in part a, you would want to own the longest-term bond possible to maximize your gain. d. Based on information in part b, you would want to own the shortest-term bond possible to minimize your loss. 12.

Jim Busby calls his broker to inquire about purchasing a bond of Disk Storage Systems. His broker quotes a price of $1,180. Jim is concerned that the bond might be overpriced based on the facts involved. The $1,000 par value bond pays 14 percent interest, and it has 25 years remaining until maturity. The current yield to maturity on similar bonds is 12 percent. Compute the new price of the bond and comment on whether you think it is overpriced in the marketplace.

10-12. Solution: Calculator Solution:

(a) N

I/Y

PMT

CPT PV −1,156.86

140

1,000

Answer: $1,156.86 New bond price

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Chapter 12: The Capital Budgeting Decision

(b) The bond has a value of $1,156.86. This indicates his broker is quoting a higher price at $1,180.

Present Value of Interest Payments PVA = A × PVIFA (n = 25, i = 12%) PVA = $140 × 7.843 = $1,098.02

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 25, i = 12%) Appendix B PV = $1,000 × 0.059 = $59 $1,098.02 59.00 $1,157.02 The bond has a value of $1,157.02. This indicates his broker is quoting too high a price at $1,180. 13.

Effect of yield to maturity on bond price (LO10-3) Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point as described next:

Real rate of return ............ Inflation premium ............ Risk premium ................... Total return ...................

4% 6 5 15%

Assume that 5 years later the inflation premium is only 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 20 years remaining until maturity. Compute the new price of the bond.

10-13. Solution: First compute the new required rate of return (yield to maturity). Real rate of return Inflation premium Risk premium

4% 3 5

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Chapter 12: The Capital Budgeting Decision

Total return

12%

Then, use this value to find the price of the bond.

Calculator Solution:

Present value of interest payments N

I/Y

PMT

CPT PV −1,224.08

150

1,000

Answer: $1,224.08 New bond price

Present Value of Interest Payments PVA = A × PVIFA (n = 20, i = 12%) PVA = $150 × 7.469 = $1,120.35

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20, i = 12%) Appendix B PV = $1,000 × 0.104 = $104 $1,120.35 104.00 $1,224.35

14.

Analyzing bond price changes (LO10-3) Katie Pairy Fruits Inc. has a $1,000, 20-year bond outstanding with a nominal yield of 15 percent (coupon equals 15% × $1,000 = $150 per year). Assume that the current market-required interest rate on similar bonds is now only 12 percent.

a. Compute the current price of the bond. b. Find the present value of 3 percent × $1,000 (or $30) for 20 years at 12 percent. The $30 is assumed to be an annual payment. Add this value to $1,000. c. Explain why the answers in parts a and b are basically the same. (There is a slight difference due to rounding in the tables.)

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Chapter 12: The Capital Budgeting Decision

10-14. Solution: Calculator Solution:

I/Y

PMT

CPT PV −1,224.08

150

1,000

PMT

Answer: $1,224.08 Bond price

I/Y

20 12 CPT PV −224.08 Answer: $224.08 + 1,000 = 1,224.08 Bond price

a. Present Value of Interest Payments PVA = A × PVIFA (n = 20, i = 12%) PVA = $150 × 7.469 = $1,120.35

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20, i = 12%) Appendix B PV = $1,000 × 0.104 = $104 $1,120.35 104.00 $1,224.35 b. PVA = A × PVIFA (n = 20, i = 12%) PVA = $30 × 7.469 = $224.07

Appendix D $1,000.00 224.07 $1,224.07

The answer to part a of $1,224.35 and part b of $1,224.07 are basically the same because in both cases we are valuing the present value of a $30 differential between actual return and required return for 20 years.

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Chapter 12: The Capital Budgeting Decision

In part b, we take the present value of the $30 differential to arrive at $224.07. We then add this value to the $1,000 par value that is exactly equal to its market value because the remaining 12 percent coupon ($150 – $30 = $120 coupon) equals the 12 percent market rate. When the coupon rate equals the required rate, the market value equals the par value. In part a, we accomplish the same goal by valuing all future benefits at a three percent differential between stated return (coupon = 12%) and required return (10%) to arrive at $1,224.35.

15.

Effect of yield to maturity on bond price (LO10-2 and 3) Media Bias Inc. issued bonds 10 years ago at $1,000 per bond. These bonds had a 40-year life when issued and the annual interest payment was then 12 percent. This return was in line with the required returns by bondholders at that point in time as described next:

Real rate of return ............ Inflation premium ............ Risk premium ................... Total return ...................

2% 5 5 12%

Assume that 10 years later, due to good publicity, the risk premium is now 2 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 30 years remaining until maturity. Compute the new price of the bond.

10-15. Solution: First compute the new required rate of return (yield to maturity) Real rate of return Inflation premium Risk premium

2% 5% 2% 9% Total required return Then, use this value to find the price of the bond.

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Chapter 12: The Capital Budgeting Decision

Calculator Solution:

I/Y

PMT

CPT PV −1,308.21

120

1,000

Answer: $1,308.21 Bond price

Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 9%) PVA = $120 × 10.274 = $1,232.88

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 30, i = 9%) Appendix B PV = $1,000 × 0.075 = $75.00 Total Present Value Present Value of Interest Payments Present Value of Principal Payment Total Present Value or Price of the Bond 16.

$1,232.88 75.00 $1,307.88

Effect of yield to maturity on bond price (LO10-2 and 3) Wilson Oil Company issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then 15 percent. This return was in line with the required returns by bondholders at that point in time as described next:

Real rate of return ............ Inflation premium ............ Risk premium ................... Total return ..................

8% 3 4 15%

Assume that 10 years later, due to bad publicity, the risk premium is now 7 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 15 years remaining until maturity. Compute the new price of the bond.

10-16. Solution: First compute the new required rate of return (yield to maturity). © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

Real rate of return Inflation premium Risk premium

8% 3% 7% 18% Total required return

Then, use this value to find the price of the bond. Calculator Solution:

N 15

I/Y 18

PV CPT PV −847.25

PMT 150

FV 1,000

Answer: $847.25 Bond Price

Present Value of Interest Payments PVA = A × PVIFA (n = 15, i = 18%) PVA = $150 × 5.092 = $763.80

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 15, i = 18%) Appendix B PV = $1,000 × 0.084 = $84.00 $763.80 84.00 Bond Price = $847.80

17.

Deep discount bonds (LO10-3) Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond pays 4 percent annual interest and has 18 years remaining to maturity. The current yield to maturity on similar bonds is 14 percent.

a. What is the current price of the bonds? b. By what percent will the price of the bonds increase between now and maturity? c. What is the annual compound rate of growth in the value of the bonds? (An approximate answer is acceptable.)

10-17. Solution:

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Chapter 12: The Capital Budgeting Decision

Calculator Solution:

(a) N 18

I/Y 14

PV CPT PV −353.26

PMT 40

FV 1,000

Answer: $353.26 Bond price

a. Current price of the bonds Present Value of Interest Payments PVA = A × PVIFA (n = 18, i = 14) PVA = $40 × 6.467 = $258.68

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 18, i = 14%) Appendix B PV = $1,000 × 0.095 = $95.00 $258.68 95.00 $353.68 b. Percent increase at maturity Maturity Value $1,000.00 Current price – 353.68 Dollar increase $ 646.32

Percent increase 

Dollar increase $646.32   182.74% Current price 353.68

c. Compound rate of growth The bond will grow by 182.74 percent over 18 years. Using Appendix A, the future value of $1, and the interest factor of 2.828 (1 + 1.8274), we see the growth rate is between 5 and 6 percent.

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Chapter 12: The Capital Budgeting Decision

18.

Yield to maturity – A calculator or Excel is required (LO10-3) Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, which, of course, is also the amount of principal to be paid at maturity. The bonds are currently selling for $690. They have 10 years remaining to maturity. The annual interest payment is 13 percent ($130). Compute the approximate yield to maturity.

10-18. Solution: Calculator Solution:

I/Y

PMT

CPT I/Y 20.53

−690

130

1,000

Answer: 20.53%

19.

Yield to maturity – A calculator or Excel is required (LO10-3) Stilley Resources bonds have 4 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 5 percent. If the price of the bond is $841.51, what is the yield to maturity?

10-19. Solution: N

I/Y

CPT I/Y 10

PV −841.51

PMT 50

FV 1,000

Answer: 10%

20.

Yield to maturity – A calculator or Excel is required (LO10-3) Evans Emergency Response bonds have 6 years to maturity. Interest is paid semiannually. The bonds have a $1,000 par value and a coupon rate of 8 percent. If the price of the bond is $1,073.55, what is the annual yield to maturity?

10-20. Solution:

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Chapter 12: The Capital Budgeting Decision

Semiannual: Payment: $1000 × 0.08 = $80/2 = $40 n: 6 years × 2 payments per year = 12 N

I/Y

PMT

CPT I/Y 3.25

−1,073.55

1,000

3.25% × 2 = 6.5% annual rate (For the next two problems, assume interest payments are on a semiannual basis.) 21.

Bond value––semiannual analysis (LO10-3) Heather Smith is considering a bond investment in Locklear Airlines. The $1,000 par value bonds have a quoted annual interest rate of 11 percent and the interest is paid semiannually. The yield to maturity on the bonds is 14 percent annual interest. There are seven years to maturity. Compute the price of the bonds based on semiannual analysis.

10-21. Solution: 11%/2 = 5.5% semiannual interest rate 5.5% × $1,000 = $55 semiannual interest 7 × 2 = 14 number of periods (n)14%/2 = 7% yield to maturity expressed on a semiannual basis

Calculator Solution:

I/Y

PMT

CPT PV −868.82

1,000

Answer: $868.82 Bond price

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Chapter 12: The Capital Budgeting Decision

Present Value of Interest Payments PVA = A × PVIFA (n = 14, i = 7%) PVA = $55 × 8.745 = $480.98

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 14, i = 7%) Appendix B PV = $1,000 × 0.388 = $388 Present Value of Interest Payments Present Value of Principal Payment Total Present Value or Price of the Bond 22.

$480.98 388.00 $868.98

Bond value––semiannual analysis (LO10-3) You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 10 percent, which is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 15 years to maturity.

a. Compute the price of the bonds based on semiannual analysis. b. With 10 years to maturity, if yield to maturity goes down substantially to 8 percent, what will be the new price of the bonds?

10-22. Solution: Calculator Solution:

(a) N

I/Y

PMT

CPT PV −1,000.00

1,000

PMT

CPT PV −1,135.90

1,000

Answer: $1,000.00 Bond price

(b) N

I/Y

20 4 Answer: $1,135.90 Bond price

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Chapter 12: The Capital Budgeting Decision

a. Present Value of Interest Payments PVA = A × PVIFA (n = 30, i = 5%) PVA = $50 × 15.372 = $768.60

Appendix D

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 30, i = 5%) Appendix B PV = $1,000 × 0.231 = $231 $768.60 231.00 $999.60 b. PVA = A × PVIFA (n = 20, i = 4%) PVA = $50 × 13.590 = $679.50 PV = FV × PVIF (n = 20, i = 4%) PV = $1,000 × .456 = $456

Appendix D Appendix B $679.50 456.00 $1,135.50

23.

Preferred stock value (LO10-4) The preferred stock of Denver Savings and Loan pays an annual dividend of $8.10. It has a required rate of return of 9 percent. Compute the price of the preferred stock.

10-23. Solution:

24.

North Pole Cruise Lines issued preferred stock many years ago. It carries a fixed dividend of $6 per share. With the passage of time, yields have soared from the original 6 percent to 14 percent (yield is the same as required rate of return).

a. What was the original issue price? b. What is the current value of this preferred stock?

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Chapter 12: The Capital Budgeting Decision

c. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will the price of the preferred stock be affected?

10-24. Solution: a. Original price D p $6.00 Pp    $100 Kp .06 b. Current value $6.00  $42.86 .14 c. The price of preferred stock will increase as yields decline. Since preferred stock is a fixed income security, its price is inversely related to yields as would be true with bond prices. The present value of an income stream has a higher present value as the discount rate declines, and a lower present value as the discount rate increases. 25.

Preferred stock value (LO10-4) X-Tech Company issued preferred stock many years ago. It carries a fixed dividend of $12 per share. With the passage of time, yields have soared from the original 10 percent to 17 percent (yield is the same as required rate of return).

a. What was the original issue price? b. What is the current value of this preferred stock? c. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will the price of the preferred stock be affected?

10-25. Solution:

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Chapter 12: The Capital Budgeting Decision

Pp 

Dp Kp



$12.00  $120 0.10

b. Current value $12.00  $70.59 0.17 c. The price of preferred stock will increase as yields decline. Since preferred stock is a fixed income security, its price is inversely related to yields as would be true with bond prices. The present value of an income stream has a higher present value as the discount rate declines, and a lower present value as the discount rate increases. 26.

Analogue Technology has preferred stock outstanding that pays a $9 annual dividend. It has a price of $76. What is the required rate of return (yield) on the preferred stock?

10-26. Solution:

Kp 

Dp Pp



$9  11.84% $76

(All of the following problems pertain to the common stock section of the chapter.) 27.

Common stock value (LO10-5) Stagnant Iron and Steel currently pays a $12.25 annual cash dividend (D0). The company plans to maintain the dividend at this level for the foreseeable future as no future growth is anticipated. If the required rate of return by common stockholders (Ke) is 18 percent, what is the price of the common stock?

10-27. Solution:

P0 

D0 $12.25   $68.06 Ke 0.18

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Chapter 12: The Capital Budgeting Decision

28.

BioScience Inc. will pay a common stock dividend of $3.20 at the end of the year (D1). The required return on common stock (Ke) is 14 percent. The firm has a constant growth rate (g) of 9 percent. Compute the current price of the stock (P0).

10-28. Solution: P0 

29.

D1 $3.20 $3.20    $64.00 K e g .14  .09 .05

Common stock value under different market conditions (LO10-5) Ecology Labs Inc. will pay a dividend of $6.40 per share in the next 12 months (D1). The required rate of return (Ke) is 14 percent and the constant growth rate is 5 percent.

a. Compute P0. (For parts b, c, and d in this problem, all variables remain the same except the one specifically changed. Each question is independent of the others.)

b. Assume Ke, the required rate of return, goes up to 18 percent. What will be the new value of P0? c. Assume the growth rate (g) goes up to 9 percent. What will be the new value of P0? Ke goes back to its original value of 14 percent. d. Assume D1 is $7.00. What will be the new value of P0? Assume Ke is at its original value of 14 percent and g goes back to its original value of 5 percent.

10-29. Solution:

P0 

D1 Ke  g

$6.40 $6.40   $71.11 0.14  0.05 0.09

$6.40 $6.40   $49.23 0.18  0.05 0.13

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Chapter 12: The Capital Budgeting Decision

30.

$6.40 $6.40   $128.00 0.14  0.09 0.05

$7.00 $7.00   $77.78 0.14  0.05 0.09

Maxwell Communications paid a dividend of $3 last year. Over the next 12 months, the dividend is expected to grow at 8 percent, which is the constant growth rate for the firm (g). The new dividend after 12 months will represent D1. The required rate of return (Ke) is 14 percent. Compute the price of the stock (P0).

10-30. Solution:

P0 

D1 Ke  g

D1  D0 (1  g )  $3.00 (1.08)  $3.24 P0 

31.

$3.24 $3.24   $54 .14  .08 0.06

Common stock value based on determining growth rate (LO10-5) Justin Cement Company has had the following pattern of earnings per share over the last five years:

Year Earnings per Share 20X1 ........................... $5.00 20X2 ........................... 5.30 20X3 ........................... 5.62 20X4 ........................... 5.96 20X5 ........................... 6.32 The earnings per share have grown at a constant rate (on a rounded basis) and will continue to do so in the future. Dividends represent 40 percent of earnings. Project earnings and dividends for the next year (20X6). If the required rate of return (Ke) is 13 percent, what is the anticipated stock price (P0) at the beginning of 20X6?

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Chapter 12: The Capital Budgeting Decision

10-31. Solution: Earnings have been growing at a rate of 6 percent per year. Base Period (20X2/20X1)

–

(20X3/20X2)

–

(20X4/20X3)

–

(20X5/20X4)

–

The projected EPS for 20X6 is $6.70 = ($6.32 × 1.06). Dividends for 20X6 represent 40 percent of earnings or $2.68 ($6.70 × 40%). This is the value for D1. Ke (required rate of return) is 13 percent and the growth rate is 6 percent. P0 (20X6) 

32.

D1 $2.68 $2.68    $38.29 K e  g 0.13  0.06 0.07

Common stock required rate of return (LO10-5) A firm pays a $4.80 dividend at the end of year one (D1), has a stock price of $80, and has a constant growth rate (g) of 5 percent. Compute the required rate of return (Ke).

10-32. Solution:

Ke 

D1 g P0

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Chapter 12: The Capital Budgeting Decision

Ke 

33.

$4.80  5%  6%  5%  11.00% $80.00

Common stock required rate of return (LO10-5) A firm pays a $1.50 dividend at the end of year one (D1), has a stock price of $155 (P0), and has a constant growth rate (g) of 10 percent.

a. Compute the required rate of return (Ke). Indicate whether each of the following changes would make the required rate of return (Ke) go up or down. (Each question is separate from the others. That is, assume only one variable changes at a time.) No actual numbers are necessary. b. The dividend payment increases. c. The expected growth rate increases. d. The stock price increases.

10-33. Solution: a.

Ke 

D1 g P0

Ke 

$1.50 10%  .97%  10%  10.97% $155.00

b. If the dividend payment increases, the dividend yield (D1/P0) will go up, and the required rate of return (Ke) will also go up. This assumes that the stock price doesn’t rise in response to the increased dividend. If the market demands the same required return as before the dividend increase, the stock price will rise to a new level. c.

If the expected growth rate (g) increases, the required rate of return (Ke) will go up.

d. If the stock price increases, the dividend yield (D1/P0) will go down, and the required rate of return (Ke) will also go down.

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Chapter 12: The Capital Budgeting Decision

34.

Martin Office Supplies paid a $3 dividend last year. The dividend is expected to grow at a constant rate of 7 percent over the next four years. The required rate of return is 14 percent (this will also serve as the discount rate in this problem). Round all values to three places to the right of the decimal point where appropriate.

a. Compute the anticipated value of the dividends for the next four years. That is, compute D1, D2, D3, and D4—for example, D1 is $3.21 ($3.00 × 1.07). b. Discount each of these dividends back to the present at a discount rate of 14 percent and then sum them. c. Compute the price of the stock at the end of the fourth year (P4).

P4 

D5 Ke  g

(D5 is equal to D4 times 1.07) d. After you have computed P4, discount it back to the present at a discount rate of 14 percent for four years. e. Add together the answers in part b and part d to get P0, the current value of the stock. This answer represents the present value of the four periods of dividends, plus the present value of the price of the stock after four periods (which, in turn, represents the value of all future dividends). f. Use Formula 10-8 to show that it will provide approximately the same answer as part e. P0 

D1 Ke  g

For Formula 10-8, use D1 = $3.21, Ke = 14 percent, and g = 7 percent. (The slight difference between the answers to part e and part f is due to rounding.) g. If current EPS is equal to $5.32 and the P/E ratio is 1.1 times higher than the industry average of 8, what would the stock price be? h. By what dollar amount is the stock price in part g different from the stock price in part f? i. In regard to the stock price in part f, indicate which direction it would move if (1) D1 increases, (2) Ke increases, and (3) g increases.

10-34. Solution: a. D1 D2 D3 D4

$3.00 (1.07) = $3.21 3.21 (1.07) = 3.435 3.435 (1.07) = 3.675 3.675 (1.07) = 3.932

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Chapter 12: The Capital Budgeting Decision

b. D1 D2 D3 D4

Dividends

PV(14%)

PV of Dividends

$3.21 3.435 3.675 3.932

0.877 0.769 0.675 0.592

$ 2.815 2.642 2.481 2.328 $10.266

P4 

D5 D5  3.932 (1.07)  $4.207 Ke  g

P4 

$4.207 $4.207   $60.10 .14  .07 .07

d. PV of P4 for n = 4, i = 14% $60.10 × 0.592 = 35.579 e. Answer to part b (PV of dividends) Answer to part d (PV of P4) Current value of the stock f.

P0 

10.266 35.579 $45.845

D1 $3.21 $3.21    $45.857 K e  g 14.07 .07

g. Price = P/E × EPS P/E = 8 × 1.1 = 8.8 Price = 8.8 × $5.32 = $46.816 h. Part g Part f i.

$46.816 45.857 0.959

1) D1 increases, stock price increases 2) Ke increases, stock price decreases 3) g increases, stock price increases

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Chapter 12: The Capital Budgeting Decision

Calculator Solution:

(b) N

I/Y

PMT

CPT PV −2.816

3.210

I/Y

PMT

CPT PV −2.643

3.435

I/Y

PMT

CPT PV −2.481

3.675

I/Y

PMT

CPT PV −2.328

3.932

Answer: $2.82 PV of D1

Answer: $2.64 PV of D2

Answer: $4.83 PV of D3

Answer: $2.33 PV of D4

Total = 2.82 + 2.64 + 2.48 + 2.33 = $10.27. (d) N

I/Y

PMT

CPT PV −35.584

60.10

Answer: $35.58 PV of P4

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Chapter 12: The Capital Budgeting Decision

35.

Common stock value based on PV calculations (LO10-5) Beasley Ball Bearings paid a $4 dividend last year. The dividend is expected to grow at a constant rate of 2 percent over the next four years. The required rate of return is 15 percent (this will also serve as the discount rate in this problem). Round all values to three places to the right of the decimal point where appropriate.

a. Compute the anticipated value of the dividends for the next four years. That is, compute D1, D2, D3, and D4—for example, D1 is $4.08 ($4 × 1.02). b. Discount each of these dividends back to present at a discount rate of 15 percent and then sum them. c. Compute the price of the stock at the end of the fourth year (P4). P4 

D5 Ke  g

(D5 is equal to D4 times 1.02.) d. After you have computed P4, discount it back to the present at a discount rate of 15 percent for four years. e. Add together the answers in part b and part d to get P0, the current value of the stock. This answer represents the present value of the four periods of dividends, plus the present value of the price of the stock after four periods, (which, in turn, represents the value of all future dividends). f. Use Formula 10-8 to show that it will provide approximately the same answer as part e. P0 

D1 Ke  g

For Formula 10-8, use D1 = $4.08, Ke = 15 percent, and g = 2 percent. (The slight difference between the answers to part e and part f is due to rounding.) g. If current EPS were equal to $4.98 and the P/E ratio is 1.2 times higher than the industry average of 6, what would the stock price be? h. By what dollar amount is the stock price in part g different from the stock price in part f? i. In regard to the stock price in part f, indicate which direction it would move if (1) D1 increases, (2) Ke increases, and (3) g increases.

10-35. Solution: a. D1 D2 D3 D4

$4.000 (1.02) = $4.08 $4.080 (1.02) = 4.162 $4.162 (1.02) = 4.245 $4.245 (1.02) = 4.330

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Chapter 12: The Capital Budgeting Decision

b. D1 D2 D3 D4

Dividends

PV(15%)

PV of Dividends

$4.080 4.162 4.245 4.330

0.870 0.756 0.658 0.572

$ 3.550 3.146 2.793 2.477 $11.966

P4 

D5 Ke  g

P4 

$4.417 $4.417   $33.977 .15  .02 .13

D5  4.330 (1.02)  $4.417

d. PV of P4 for n = 4, i = 15% $33.977 × 0.572 = $19.435 e. Answer to part b (PV of dividends) Answer to part d (PV of P4) Current value of the stock f.

P0 

$11.966 19.435 $31.401

D1 $4.08 $4.08    $31.385 K e  g .15  .02 .13

g. Price = P/E × EPS P/E = 6 × 1.2 = 7.20 Price = 7.20 × $4.98 = $35.86 h. Part g Part f i.

$35.86 –31.39 $ 4.47

1) D1 increases, stock price increases 2) Ke increases, stock price decreases 3) g increases, stock price increases

Calculator Solution:

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Chapter 12: The Capital Budgeting Decision

(b) N

I/Y

PMT

CPT PV −3.550

4.080

I/Y

PMT

CPT PV −3.146

4.162

I/Y

PMT

CPT PV −2.793

4.245

I/Y

PMT

CPT PV −2.477

4.330

1 Answer: $3.550 PV of D1

N 2 Answer: $3.146 PV of D2

Answer: $2.793 PV of D3

Answer: $2.477 PV of D4

Total = 3.550 + 3.146 + 2.793 + 2.477 = $11.966 (d) N

I/Y

PMT

CPT PV −19.426

33.977

Answer: $19.426 PV of P4

COMPREHENSIVE PROBLEM

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Chapter 12: The Capital Budgeting Decision

Preston Products (Dividend valuation model, P/E ratio) (LO10-5) Mel Thomas, the chief financial officer of Preston Resources, has been asked to do an evaluation of Dunning Chemical Company by the president and Chair of the Board, Sarah Reynolds. Preston Resources was planning a joint venture with Dunning (which was privately traded), and Sarah and Mel needed a better feel for what Dunning’s stock was worth because they might be interested in buying the firm in the future. Dunning Chemical paid a dividend at the end of year one of $1.30, the anticipated growth rate was 10 percent, and the required rate of return was 14 percent. a. What is the value of the stock based on the dividend valuation model (Formula 10-8)? b. Indicate that the value you computed in part a is correct by showing the value of D1, D2, and D3 and discounting each back to the present at 14 percent. D1 is $1.30 and it increases by 10 percent (g) each year. Also discount back the anticipated stock price at the end of year three to the present and add it to the present value of the three dividend payments. The value of the stock at the end of year three is: P3 

D4 Ke  g

D4  D3 1  g 

If you have done all these steps correctly, you should get an answer approximately equal to the answer in part a. c. As an alternative measure, you also examine the value of the firm based on the priceearnings (P/E) ratio times earnings per share. Since the company is privately traded (not in the public stock market), you will get your anticipated P/E ratio by taking the average value of five publicly traded chemical companies. The P/E ratios were as follows during the time period under analysis:

Dow Chemical ........... DuPont ....................... Georgia Gulf .............. 3M .............................. Olin Corp ...................

P/E Ratio 15 18 7 19 21

Assume Dunning Chemical has earnings per share of $2.10. What is the stock value based on the P/E ratio approach? Multiply the average P/E ratio you computed times earnings per share. How does this value compare to the dividend valuation model values that you computed in parts a and b? d. If, in computing the industry average P/E, you decide to weight Olin Corp. by 40 percent and the other four firms by 15 percent, what would be the new weighted average industry P/E? (Note: You decided to weight Olin Corp. more heavily because it

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Chapter 12: The Capital Budgeting Decision

is similar to Dunning Chemical.) What will the new stock price be? Earnings per share will stay at $2.10. e. By what percent will the stock price change as a result of using the weighted average industry P/E ratio in part d as opposed to that in part c? Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 20, i = 11%) (Appendix B) PV = $1,000 × .124 = $124 Total Present Value Present value of interest payments ............................... $ 939.63 Present value of principal payment at maturity ............

124.00

Total present value, or price, of the bond .................. $1,063.63

The discount rate of 11 percent gives us a value slightly lower than the bond price of $1,085. The rate for the bond must fall between 10 and 11 percent. Using linear interpolation, the answer is 10.76 percent $1,153.65 PV @ 10% 1,063.63 PV @ 11% $ 90.02

10% 

$1,153.65 PV @ 10% 1,085.00 bond price $ 68.65

$68.65 1%   10%  .76 1%   10.76% $90.02

CP 10-1. Solution: a.

P10 

D1 $1.30 $1.30    $32.50 K e  g .14  .10 .04

b. Future Value of Dividends D1 D2 D3

$1.30 (1.00) = $1.30 $1.30 (1.10) = $1.43 $1.30 (1.10) = $1.573

Present Value of Dividends D1

Dividends $1.30

PV (14%) 0.877

(PV of Dividend) $1.14

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Chapter 12: The Capital Budgeting Decision

D2 D3

$1.43 $1.573

0.769 0.675

$1.10 $1.06 $3.30

Value of Stock Price at the end of Year 3

P3 

D4 Ke  g

P3 

$1.730 $1.730   $43.25 .14  .10 .04

D4  D3 (1  g )  1.573 (1.10)  $1.730

Present Value of Future Stock Price P3 = $43.25 n = 3, i = 14% (Appendix B) PV = $43.25 × 0.675 = $29.19 Total stock prices: PV of Dividends $ 3.30 PV of Stock Price 29.19 $32.49 c. Average P/E Ratio of Five Chemical Firms Dow Chemical 15 DuPont 18 Georgia Gulf 7 3M 19 Olin Corp. 21 Total 80 80  16 Average P/E 5

Stock Price = P/E × EPS 16 × $2.10 = $33.60

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Chapter 12: The Capital Budgeting Decision

The stock price using the P/E ratio approach is slightly higher than the value using the dividend valuation model approach ($33.60 versus $32.50). d. Dow Chemical DuPont Georgia Gulf 3M Olin Corp.

Weighted P/E Ratio Weights Average 15 0.15 2.25 18 0.15 2.70 7 0.15 1.05 19 0.15 2.85 21 0.40 8.40 17.25

Stock price = P/E × EPS $17.25 × $2.10 = $36.23 e. Stock price (d) Stock price (c) Change

$36.23 33.60 $2.63  7.83% Beginning amount $33.60

Appendix: Valuation of Supernormal Growth Firm 10A–1.

Valuation of supernormal growth firm (LO10-5) Surgical Supplies Corporation paid a dividend of $1.12 per share over the last 12 months. The dividend is expected to grow at a rate of 25 percent over the next three years (supernormal growth). It will then grow at a normal, constant rate of 7 percent for the foreseeable future. The required rate of return is 12 percent (this will also serve as the discount rate).

a. Compute the anticipated value of the dividends for the next three years (D1, D2, and D3). b. Discount each of these dividends back to the present at a discount rate of 12 percent and then sum them. c. Compute the price of the stock at the end of the third year (P3). P3 

D4 Ke  g

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Chapter 12: The Capital Budgeting Decision

d. After you have computed P3, discount it back to the present at a discount rate of 12 percent for three years. e. Add together the answers in part b and part d to get the current value of the stock. (This answer represents the present value of the first three periods of dividends plus the present value of the price of the stock after three periods.)

10A–1. Solution a. D1 D2 D3

b. D1 D2 D3

$1.12 (1.25) = $1.40 $1.40 (1.25) = $1.75 $1.75 (1.25) = $2.19

Supernormal Dividends $1.40 $1.75 $2.19

P3 

Discount Rate Ke = 12% 0.893 0.797 0.712

Present Value of Dividends During the Supernormal Growth Period $1.25 1.39 1.56 $4.20

D4 Ke  g

D4  D3 (1.07)  $2.19 (1.07)  $2.34 P3 

$2.34 $2.34   $46.80 .12  .07 0.05

d. PV of P3 for n = 3, i = 12% $46.80 × 0.712 = $33.32 e. Answer to part b (PV of dividends) Answer to part d (PV of P3) Current value of the stock

$ 4.20 33.32 $37.52

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Chapter 12: The Capital Budgeting Decision

Chapter 11 Cost of Capital Discussion Questions 11-1.

Why do we use the overall cost of capital for investment decisions even when only one source of capital will be used (e.g., debt)?

Though an investment financed by low-cost debt might appear acceptable at first glance, the use of debt could increase the overall risk of the firm and eventually make all forms of financing more expensive. Each project must be measured against the overall cost of funds to the firm.

11-2.

How does the cost of a source of capital relate to the valuation concepts presented previously in Chapter 10?

The cost of a source of financing directly relates to the required rate of return for that means of financing. Of course, the required rate of return is used to establish valuation.

11-3.

In computing the cost of capital, do we use the historical costs of existing debt and equity or the current costs as determined in the market? Why?

In computing the cost of capital, we use the current costs for the various sources of financing rather than the historical costs. We must consider what these funds will cost us to finance projects in the future rather than their past costs.

11-4.

Why is the cost of debt less than the cost of preferred stock if both securities are priced to yield 10 percent in the market?

Even though debt and preferred stock may be both priced to yield 10 percent in the market, the cost of debt is less because the interest on debt is a taxdeductible expense. A 10 percent market rate of interest on debt will only cost a firm in a 35 percent tax bracket an aftertax rate of 6.5 percent. The answer is the yield

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Chapter 12: The Capital Budgeting Decision

multiplied by the difference of (one minus the tax rate).

11-5.

What are the two sources of equity (ownership) capital for the firm? The two sources of equity capital are retained earnings and new common stock.

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Chapter 12: The Capital Budgeting Decision

11-6.

Explain why retained earnings have an associated opportunity cost?

Retained earnings belong to the existing common stockholders. If the funds are paid out instead of reinvested, the stockholders could earn a return on them. Thus, we say retaining funds for reinvestment carries an opportunity cost.

11-7.

Why is the cost of retained earnings the equivalent of the firm’s own required rate of return on common stock (Ke)? Because stockholders can earn a return at least equal to their present investment. For this reason, the firm’s rate of return (Ke) serves as a means of approximating the opportunities for alternate investments.

11-8.

Why is the cost of issuing new common stock (Kn) higher than the cost of retained earnings (Ke)? In issuing new common stock, we must earn a slightly higher return than the normal cost of common equity in order to cover the distribution costs of the new security. In the case of the Baker Corporation, the cost of new common stock was six percent higher.

11-9.

How are the weights determined to arrive at the optimal weighted average cost of capital? The weights are determined by examining different capital structures and using that mix which gives the minimum cost of capital. We must solve a multidimensional problem to determine the proper weights.

11-10.

Explain the traditional, U-shaped approach to the cost of capital. The logic of the U-shaped approach to cost of capital can be explained through Figure 11-1. It is assumed that as we initially increase the debt-to-equity mix, the cost of capital will go down. After we reach an optimum point, the increased use of debt will increase the overall cost of financing to the firm. Thus, we say the weighted average cost of capital curve is U-shaped.

11-11.

It has often been said that if the company can’t earn a rate of return greater than the cost of capital, it should not make investments. Explain. If the firm cannot earn the overall cost of financing on a given project, the investment will have a negative impact on the firm’s operations and will lower the overall wealth of the shareholders.

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Chapter 12: The Capital Budgeting Decision

Clearly, it is undesirable to invest in a project yielding 8 percent if the financing cost is 10 percent. 11-12.

What effect would inflation have on a company’s cost of capital? (Hint: Think about how inflation influences interest rates, stock prices, corporate profits, and growth.) Inflation can only have a negative impact on a firm’s cost of capital, forcing it to go up. This is true because inflation tends to increase interest rates and lower stock prices, thus raising the cost of debt and equity directly and the cost of preferred stock indirectly.

11-13.

What is the concept of marginal cost of capital? The marginal cost of capital is the cost of incremental funds. After a firm reaches a given level of financing, capital costs will go up because the firm must tap more expensive sources. For example, new common stock may be needed to replace retained earnings as a source of equity capital.

Problems 1.

Cost of capital (LO11-2) In March 2021, Hertz Pain Relievers bought a massage machine that provided a return of 8 percent. It was financed by debt costing 7 percent. In August Mr. Hertz came up with a heating compound that would have a return of 14 percent. The chief financial officer, Mr. Smith, told him it was impractical because it would require the issuance of common stock at a cost of 16 percent to finance the purchase. Is the company following a logical approach to using its cost of capital?

11-1. Solution: No. Each individual project should not be measured against the specific means of financing that project, but rather against the weighted average cost of financing all projects for the firm. This principle recognizes that the availability of one source of financing is dependent on other sources. Once a common overall cost is determined, the “heating compound” yielding 14 percent is much

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Chapter 12: The Capital Budgeting Decision

more likely to be accepted than the “massage machine” only yielding 8 percent.

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Chapter 12: The Capital Budgeting Decision

Cost of capital (LO11-2) Speedy Delivery Systems can buy a piece of equipment that is anticipated to provide an 11 percent return and can be financed at 6 percent with debt. Later in the year, the firm turns down an opportunity to buy a new machine that would yield a 9 percent return but would cost 15 percent to finance through common equity. Assume debt and common equity each represents 50 percent of the firm’s capital structure. a.

Compute the weighted average cost of capital.

Which project(s) should be accepted?

11-2. Solution: Weighted a.

Cost

Weights

Cost

Debt

50%

3.0%

Common equity

15%

50%

7.5%

Weighted average cost of capital

10.5%

b. Only the piece of equipment with a return of 11 percent. The return exceeds the weighted average cost of capital of 10.5 percent.

Effect of discount rate (LO11-2) A brilliant young scientist is killed in a plane crash. It is anticipated that he could have earned $240,000 a year for the next 50 years. The attorney for the plaintiff’s estate argues that the lost income should be discounted back to the present at 4 percent. The lawyer for the defendant’s insurance company argues for a discount rate of 8 percent. What is the difference between the present value of the settlement at 4 percent and 8 percent? Compute each one separately.

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Chapter 12: The Capital Budgeting Decision

11-3. Solution: Calculator Solution:

(a) N

I/Y

PMT

CPT PV −5,155,724.31

240,000

I/Y

PMT

CPT PV −2,936,036.31

240,000

50 Answer: $5,155,724.31

(b)

Answer: $2,936,036.31

PV at 4% rate

$5,155,724.31

PV at 8% rate

2,936,036.31

Difference

Present Value at 4% PVA = A × PVIFA (4%, 50 periods) PVA = $240,000 × 21.482 = $5,155,680

2,219,687.99

Appendix D

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Chapter 12: The Capital Budgeting Decision

PVA = A × PVIFA (8%, 50 periods) PVA = $240,000 × 12.233 = $2,935,920

Appendix D

PV at 4% rate PV at 8% rate Difference

$5,155,680 2,935,920 $2,219,760

Aftertax cost of debt (LO11-3) Telecom Systems can issue debt yielding 8 percent. The company is in a 30 percent bracket. What is its aftertax cost of debt?

11-4. Solution: Kd = Yield (1 – T) = 8% (1 – 0.30) = 8% (0.70) = 5.6%

Aftertax cost of debt (LO11-3) Calculate the aftertax cost of debt under each of the following conditions: Yield

Corporate Tax Rate

8.0%

18%

12.0%

34%

10.6%

15%

11-5. Solution: Kd = Yield (1 – T)

a. b. c.

Yield 8.0% 12.0% 10.6%

(1 – T)Yield (1 – T) (1 – 0.18) 6.56% (1 – 0.34) 7.92% (1 – 0.15) 9.01%

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Chapter 12: The Capital Budgeting Decision

Aftertax cost of debt (LO11-3) Calculate the aftertax cost of debt under each of the following conditions: Yield

Corporate Tax Rate

8.0%

26%

9.0

8.0

11-6. Solution: Kd = Yield (1 – T) a. b. c.

Yield 8.0% 9.0% 8.0%

(1 – T)Yield(1 – T) (1 – 0.26) 5.92% (1 – 0.35) 5.85% (1 – 0) 8.00%

Aftertax cost of debt (LO11-3) The Goodsmith Charitable Foundation, which is taxexempt, issued debt last year at 9 percent to help finance a new playground facility in Los Angeles. This year the cost of debt is 25 percent higher—that is, firms that paid 11 percent for debt last year will be paying 13.75 percent this year. a.

If the Goodsmith Charitable Foundation borrowed money this year, what would the aftertax cost of debt be, based on its cost last year and the 25 percent increase?

If the receipts of the foundation were found to be taxable by the IRS (at a rate of 25 percent because of involvement in political activities), what would the aftertax cost of debt be?

11-7. Solution: a. Kd = Yield (1 – T) Yield = 9% × 1.25 = 11.25% Kd = 11.25% (1 – 0) = 11.25% (1) = 11.25%

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Chapter 12: The Capital Budgeting Decision

= 11.25% (1 – 0.25) = 11.25% (0.75) = 8.438%

b. Kd

Aftertax cost of debt (LO11-3) Royal Jewelers Inc. has an aftertax cost of debt of 7 percent. With a tax rate of 25 percent, what can you assume the yield on the debt is?

11-8. Solution: K d  Yield 1  T 

Yield =

Kd 1  T 

Yield =

7% 7%   9.33% 1  .25  .75

Approximate yield to maturity and cost of debt (LO11-3) Airborne Airlines Inc. has a $1,000 par value bond outstanding with 25 years to maturity. The bond carries an annual interest payment of $88 and is currently selling for $950. Airborne is in a 25 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar. a.

Compute the yield to maturity on the old issue and use this as the yield for the new issue.

Make the appropriate tax adjustment to determine the aftertax cost of debt.

11-9. Solution: Calculator Solution:

(a) N 25

I/Y CPT I/Y 9.32

PV −950

PMT 88

FV 1,000

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Chapter 12: The Capital Budgeting Decision

Answer: 9.32% The yield to maturity (b)

Kd = Yield (1 − T) = 9.32% (1 – 0.25) = 9.32% (0.75) = 6.99%

10. Approximate yield to maturity and cost of debt (LO11-3) Russell Container Corporation has a $1,000 par value bond outstanding with 30 years to maturity. The bond carries an annual interest payment of $105 and is currently selling for $880 per bond. Russell Corp. is in a 25 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar. a.

Compute the yield to maturity on the old issue and use this as the yield for the new issue.

Make the appropriate tax adjustment to determine the aftertax cost of debt.

11-10. Solution: Calculator Solution:

(a)

N 30

I/Y CPT I/Y 11.99

PV −880

PMT 105

FV 1,000

Answer: 11.99% The yield to maturity (b)

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Chapter 12: The Capital Budgeting Decision

Kd =Yield (1 − T) =11.99% (1 – 0.25) =11.99% (0.75) =8.99% 11. Changing rates and cost of debt (LO11-3) Terrier Company is in a 45 percent tax bracket and has a bond outstanding that yields 11 percent to maturity. a.

What is Terrier’s aftertax cost of debt?

Assume that the yield on the bond goes down by 1 percentage point, and due to tax reform, the corporate tax rate falls to 30 percent. What is Terrier’s new aftertax cost of debt?

Has the aftertax cost of debt gone up or down from part a to part b? Explain why.

11-11.

Solution: a. Kd = Yield (1 – T) = 11% (1 – 0.45) = 11% (0.55) = 6.05% b.

Kd(new) = Yield (1 – T) =10% (1 – 0.30) = 10% (0.70) = 7.0%

c. It has gone up. The before-tax yield is lower, but the lower tax rate reduces the tax benefit. The reduced tax benefit more than offsets the lower rate. 12. Real-world example and cost of debt (LO11-3) The Coca-Cola Company is planning to issue debt that will mature in 2093. In many respects, the issue is similar to the currently outstanding debt of the corporation.

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Using Table 11-3, identify the yield to maturity on similarly outstanding debt for the firm in terms of maturity.

Assume that because the new debt will be issued at par, the required yield to maturity will be 0.15 percent higher than the value determined in part a. Add this factor to the answer in a. (New issues sold at par sometimes require a slightly higher yield than older seasoned issues because there are fewer tax advantages and more financial leverage that increase company risk.)

If the firm is in a 25 percent tax bracket, what is the aftertax cost of debt?

11-12. Solution: a. 3.73% b. 3.73% + 0.15% = 3.88% c. Kd = Yield (1 – T) = 3.88% (1 – 0.25) = 3.88% (0.75) = 2.91% 13. Cost of preferred stock (LO11-3) Medco Corporation can sell preferred stock for $90 with an estimated flotation cost of $2. It is anticipated the preferred stock will pay $8 per share in dividends. a.

Compute the cost of preferred stock for Medco Corp.

Do we need to make a tax adjustment for the issuing firm?

11-13. Solution: a.

Kp  

Dp Pp  F $8 $8   9.09% $90  $2 $88

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b. No tax adjustment is required. Preferred stock dividends are not a tax deductible expense for the issuing firm (the dividends, of course, are 70 percent tax exempt to a corporate recipient).

14. Wallace Container Company issued $100 par value preferred stock 12 years ago. The stock provided a 9 percent yield at the time of issue. The preferred stock is now selling for $72. What is the current yield or cost of the preferred stock? (Disregard flotation costs.)

11-14. Solution:

Yield =

Dp Dp



$9  12.5% $72

15. Comparison of the costs of debt and preferred stock (LO11-3) The treasurer of Riley Coal Co. is asked to compute the cost of fixed income securities for her corporation. Even before making the calculations, she assumes the aftertax cost of debt is at least 3 percent less than that for preferred stock. Based on the following facts, is she correct? Debt can be issued at a yield of 11.0 percent, and the corporate tax rate is 21 percent. Preferred stock will be priced at $60 and pay a dividend of $6.40. The flotation cost on the preferred stock is $6.

11-15.

Solution: Aftertax cost of debt K d  Yield (1  T ) =11.0%(1  .21) = 11.0% (.79) = 8.69%

Aftertax cost of preferred stock

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Kp 

Dp Pp  F



$6.40 $6.40   11.85% $60  $6 $54

Yes, the treasurer is correct. The difference is 3.16% (8.69% versus 11.85%).

16. Murray Motor Company wants you to calculate its cost of common stock. During the next 12 months, the company expects to pay dividends (D1) of $2.50 per share, and the current price of its common stock is $50 per share. The expected growth rate is 8 percent. a.

Compute the cost of retained earnings (Ke). Use Formula 11-5.

If a $3 flotation cost is involved, compute the cost of new common stock (Kn). Use Formula 11-6.

11-16. Solution: a.

Ke  =

Kn 

D1 g P0 $2.50  8%  5%  8%  13% $50

D1 g P0  F

$2.50 $2.50  8%   8% $50  $3 $47  5.32%  8%  13.32%

17. Costs of retained earnings and new common stock (LO11-3) Compute Ke and Kn under the following circumstances: a.

D1 = $5.00, P0 = $70, g = 8%, F = $7.00.

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D1 = $0.22, P0 = $28, g = 7%, F = $2.50.

E1 (earnings at the end of period one) = $7, payout ratio equals 40 percent, P0 = $30, g = 6.0%, F = $2.20.

D0 (dividend at the beginning of the first period) = $6, growth rate for dividends and earnings (g) = 7%, P0 = $60, F = $3.

11-17. Solution: a.

Ke 

D1 g P0

$5.00  8%  7.14%  8%  15.14% $70 D1 Kn  g P0  F =

$5 $5  8%   8% $70  $7 $63

 7.94%  8%  15.94% b.

Ke 

D1 g P0

$.22  7%  .79%  7%  7.79% $28 D1 Kn  g P0  F =

$.22 $.22  7%   7% $28  $2.50 $25.50

 .86%  7%  7.86% c.

D1  40%  E1  40%  $7.00  $2.80

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Chapter 12: The Capital Budgeting Decision

Ke 

D1 g P0

$2.80  6.00%  9.33%  6.00%  15.33% $30 D1 Kn  g P0  F =

$2.80  6.00% $30  $2.20



$2.80  6.00%  10.07%  6.00%  16.07% $27.80

D1  D0 (1  g )  $6.00  (1.07)  $6.42 Ke 

D1 g P0

$6.42  7%  10.7%  7%  17.7% $60 D1 Kn  g P0  F 



$6.42 $6.42  7%   7% $60  $3 $57

 11.26%  7%  18.26% 18. Growth rates and common stock valuation (LO11-3) Business has been good for Keystone Control Systems, as indicated by the four-year growth in earnings per share. The earnings have grown from $1.00 to $1.63. a.

Determine the compound annual rate of growth in earnings (n = 4).

Based on the growth rate determined in part a, project earnings for next year (E1). Round to two places to the right of the decimal point.

Assume the dividend payout ratio is 40 percent. Compute D1. Round to two places to the right of the decimal point.

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The current price of the stock is $50. Using the growth rate (g) from part a and D1 from part c, compute Ke.

If the flotation cost is $3.75, compute the cost of new common stock (Kn).

11-18. Solution: a.

$1.63  FVIF 1.63 (n  4) i  13% 1.00

E1  E0 (1  g )  $1.63 (1.13)  $1.84

D1  E1  40%  $1.84  40%  $.74

Ke 

D1 g Po

$.74  13% $50  1.48%  13% 

 14.48%

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Chapter 12: The Capital Budgeting Decision

Kn  

D1 g Po  F $.74 13% $50  $3.75

$.74 13% $46.25  1.6%  13%  14.60% 

Calculator Solution:

(a) N

I/Y

PMT

CPT I/Y 12.99

–1.00

1.63

Answer: The growth rate is 13%.

19. Weighted average cost of capital (LO11-1) Global Technology’s capital structure is as follows:

Debt............................

35%

Preferred stock...........

Common equity..........

The aftertax cost of debt is 6.5 percent; the cost of preferred stock is 10 percent; and the cost of common equity (in the form of retained earnings) is 13.5 percent. Calculate Global Technology’s weighted average cost of capital in a manner similar to Table 11-1.

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11-19. Solution: Cost (aftertax) Weights Debt (Kd)...................................... 6.5% 35% Preferred stock (Kp) ..................... 10.0 15 Common equity (Ke) (retained earnings) .................... 13.5 50 Weighted average cost of capital (Ka) .............................

Weighted Cost 2.28% 1.50 6.75 10.53%

20. Weighted average cost of capital (LO11-1) Evans Technology has the following capital structure.

Debt............................

40%

Common equity..........

The aftertax cost of debt is 6 percent; and the cost of common equity (in the form of retained earnings) is 13 percent.

a. b.

What is the firm’s weighted average cost of capital? An outside consultant has suggested that because debt is cheaper than equity, the firm should switch to a capital structure that is 50 percent debt and 50 percent equity. Under this new and more debt-oriented arrangement, the aftertax cost of debt is 7 percent, and the cost of common equity (in the form of retained earnings) is 15 percent. Recalculate the firm’s weighted average cost of capital. Which plan is optimal in terms of minimizing the weighted average cost of capital?

11-20. Solution:

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Chapter 12: The Capital Budgeting Decision

Cost (aftertax) Weights Debt (Kd)...................................... 6% 40% Common equity (Ke) (retained earnings) .................... 13% 60 Weighted average cost of capital (Ka) .............................

Weighted Cost 2.40%

Weighted Cost 3.50%

Cost (aftertax) Weights Debt (Kd)...................................... 7% 50% Common equity (Ke) (retained earnings) .................... 15% 50 Weighted average cost of capital (Ka) .............................

7.80 10.20%

7.50 11.0%

c. The plan presented in part a is the better alternative. Even though the second plan has more relatively cheap debt, the increased costs of all forms of financing more than offset this factor. 21. Weighted average cost of capital (LO11-1) Sauer Milk Inc. wants to determine the minimum cost of capital point for the firm. Assume it is considering the following financial plans: Cost

(aftertax) Weights

Plan A Debt .......................................

4.0%

30%

Preferred stock ......................

8.0

Common equity .....................

12.0

Plan B

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Chapter 12: The Capital Budgeting Decision

Debt .......................................

4.5%

40%

Preferred stock ......................

8.5

Common equity .....................

13.0

Debt .......................................

5.0%

45%

Preferred stock ......................

18.7

Common equity .....................

12.8

Debt .......................................

12.0%

50%

Preferred stock ......................

19.2

Common equity .....................

14.5

Plan C

Plan D

Which of the four plans has the lowest weighted average cost of capital? (Round to two places to the right of the decimal point.)

Briefly discuss the results from Plan C and Plan D, and why one is better than the other.

11-21. Solution: a.

Cost (aftertax)

Weighted Cost

Weights

Plan A Debt Preferred stock Common equity

4.0% 8.0 12.0

30% 15 55

1.20% 1.20 6.60 9.00%

Plan B Debt Preferred stock Common equity

4.5% 8.5 13.0

40% 15 45

1.80% 1.28 5.85 8.93%

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Plan C Debt Preferred stock Common equity

5.0% 18.7 12.8

45% 15 40

2.25 2.81 5.12 10.18%

Plan D Debt Preferred stock Common equity

12.0% 19.2 14.5

50% 15 35

6.00% 2.88 5.08 13.96%

Plan B has the lowest weighted average cost of capital. b. Plan D is higher than Plan C because all components in the capital structure increased sharply after the firm hit the 50 percent debt level.

22. Weighted average cost of capital (LO11-1) Given the following information, calculate the weighted average cost of capital for Hamilton Corp. Line up the calculations in the order shown in Table 11-1. Percent of capital structure:

Debt............................

35%

Preferred stock...........

Common equity..........

Additional information:

Bond coupon rate ..............................

11%

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Chapter 12: The Capital Budgeting Decision

Bond yield to maturity .......................

Dividend, expected common ............. $ 5.00 Dividend, preferred ............................ $ 12.00 Price, common ................................... $ 60.00 Price, preferred .................................. $106.00 Flotation cost, preferred .................... $ 4.50 Growth rate........................................

Corporate tax rate..............................

25%

11-22. Solution: Kd = Yield (1 – T) = 9% (1 – 0.25) = 9% (.75) = 6.75% The bond yield of 9 percent is used rather than the coupon rate of 11 percent because bonds are priced in the market according to competitive yields to maturity. The new bond would be sold to reflect yield to maturity.

Kp   Ke  

Dp Pp  F $12.00 $12.00   11.82% $106  $4.50 $101.50 D1 g P0 $5  6.00%  8.33%  6.00%  14.33% $60

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Chapter 12: The Capital Budgeting Decision

Cost (aftertax) Debt (Kd)......................................6.75% Preferred stock (Kp) ..................... 11.82 Common equity (Ke) (retained earnings) ...................... 14.33 Weighted average cost of capital (Ka) ...................................

Weights 35% 20

Weighted Cost 2.36% 2.36

6.45 11.17%

23. Given the following information, calculate the weighted average cost of capital for Digital Processing Inc. Line up the calculations in the order shown in Table 11-1.

Percent of capital structure:

Preferred stock.................

20%

Common equity................

Debt..................................

Additional information:

Corporate tax rate..............................

25%

Dividend, preferred ............................

$8.50

Dividend, expected common .............

$2.50

Dividend, preferred ............................ $105.00 Growth rate........................................

Bond yield ..........................................

9.5

Flotation cost, preferred ....................

$3.60

Price, common ...................................

$75.00

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Chapter 12: The Capital Budgeting Decision

11-23. Solution: Kd = Yield (1 – T) = 9.5% (1 – .24) = 9.5% (.76) = 6.27 Kp = Dp/(Pp – F) = $8.50/($105 – 3.60) = $8.50/$101.40 = 8.38% Ke = (D1/P0) + g = ($2.50/$75) + 7% = 3.33% + 7% = 10.33% Cost (aftertax) Debt (Kd)......................................7.22% Preferred stock (Kp) .....................8.38 Common equity (Ke) (retained earnings) ...................... 10.33 Weighted average cost of capital (Ka) ...................................

Weights 40% 20

Weighted Cost 2.89% 1.68

4.13 8.70%

24. Changes in costs and weighted average cost of capital (LO11-1) Brook’s Window Shields Inc. is trying to calculate its cost of capital for use in a capital budgeting decision. Mr. Glass, the vice president of finance, has given you the following information and has asked you to compute the weighted average cost of capital. The company currently has outstanding a bond with a 12.2 percent coupon rate and another bond with a 9.5 percent coupon rate. The firm has been informed by its investment banker that bonds of equal risk and credit rating are now selling to yield 13.4 percent. The common stock has a price of $58 and an expected dividend (D1) of $5.30 per share. The firm’s historical growth rate of earnings and dividends per share has been 9.5

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percent, but security analysts on Wall Street expect this growth to slow to 7 percent in future years. The preferred stock is selling at $54 per share and carries a dividend of $6.75 per share. The corporate tax rate is 25 percent. The flotation cost is 2.1 percent of the selling price for preferred stock. The optimal capital structure is 40 percent debt, 25 percent preferred stock, and 35 percent common equity in the form of retained earnings. Compute the cost of capital for the individual components in the capital structure, and then calculate the weighted average cost of capital (similar to Table 11-1).

11-24. Solution: Kd = Yield (1 – T) = 13.4% (1 – 0.25) = 13.4% (0.75) = 10.05% Kp = Dp/(Pp – F) = $6.75/($54 – $1.13) = $6.75/$52.87 = 12.77% Ke = (D1/P0) + g = ($5.30/$58) + 7% = 9.14% + 7% = 16.14% Cost (aftertax) Debt (Kd) ...................................... 10.05% Preferred stock (Kp) ..................... 12.77 Common equity (Ke) (retained earnings) ...................... 16.14 Weighted average cost of capital (Ka) ...................................

Weighted Weights Cost 40% 4.02% 25 3.19 35

5.65 12.86%

25. Changes in cost and weighted average cost of capital (LO11-1) A-Rod Manufacturing Company is trying to calculate its cost of capital for use in making a capital budgeting decision. Mr. Jeter, the vice president of finance, has given you the following information and has asked you to compute the weighted average cost of capital. The company currently has outstanding a bond with a 10.6 percent coupon rate and another bond with an 8.2 percent rate. The firm has been informed by its investment © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

banker that bonds of equal risk and credit rating are now selling to yield 11.5 percent. The common stock has a price of $65 and an expected dividend (D1) of $1.50 per share. The historical growth pattern (g) for dividends is as follows: $1.40 1.54 1.69 1.85 Compute the historical growth rate, round it to the nearest whole number, and use it for g. The preferred stock is selling at $85 per share and pays a dividend of $8.50 per share. The corporate tax rate is 25 percent. The flotation cost is 2.6 percent of the selling price for preferred stock. The optimal capital structure for the firm is 35 percent debt, 5 percent preferred stock, and 60 percent common equity in the form of retained earnings. Compute the cost of capital for the individual components in the capital structure, and then calculate the weighted average cost of capital (similar to Table 11-1).

11-25. Solution: Kd = Yield (1 – T) = 11.5% (1 – 0.25) = 11.5% (0.75) = 8.63% Kp = Dp/(Pp – F) = $8.50/($85.00 – $2.21) = $8.50/$82.79 = 10.27% Ke = (D1/P0) + g D1 = $1.85 P0 = $65 g = 10% (see the following) $0.14/1.40 = 10.0% 0.15/1.54 = 9.7% 0.16/1.69 = 9.5% Round to 10% or = $1.85/1.40 n = 3 FVIF = 1.321 g = 10% Ke = (D1/P0) + g = $1.50/$65 + 10% = 2.31% + 10% = 12.31%

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Chapter 12: The Capital Budgeting Decision

Bring the preceding values together to compute the weighted average cost of capital. Cost (aftertax) 8.63% 10.27

Debt (Kd) .......................... Preferred stock (Kp) ......... Common equity (Ke) (retained earnings) .......... 12.31 Weighted average cost of capital (Ka)……..

Weights 35% 5%

Weighted Cost 3.02% 0.51

60%

7.39 10.92%

26. Impact of credit ratings on cost of capital (LO11-3) Northwest Utility Company faces increasing needs for capital. Fortunately, it has an Aa3 credit rating. The corporate tax rate is 25 percent. Northwest’s treasurer is trying to determine the corporation’s current weighted average cost of capital in order to assess the profitability of capital budgeting projects. Historically, the corporation’s earnings and dividends per share have increased about 8.2 percent annually and this should continue in the future. Northwest’s common stock is selling at $64 per share, and the company will pay a $6.50 per share dividend (D1). The company’s $96 preferred stock has been yielding 8 percent in the current market. Flotation costs for the company have been estimated by its investment banker to be $6.00 for preferred stock. The company’s optimal capital structure is 55 percent debt, 20 percent preferred stock, and 25 percent common equity in the form of retained earnings. Refer to the following table on bond issues for comparative yields on bonds of equal risk to Northwest:

Data on Bond Issues Issue

Moody’s Rating

Price

Yield to Maturity

$ 895.18

8.74%

Utilities: Pacific Electric Power––7¼ 2033 ......................Aa2

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Chapter 12: The Capital Budgeting Decision

Southwest Bell––7⅜ 2035.................................Aa3

891.25

8.73

970.66

8.77

Issac & Johnson––6¾ 2033 ...............................Aaa

880.24

8.55%

Wholesale Department Stores––71/8 2033 ............................................................... A2

960.92

8.22

Hotel Corp.––10 2035 .......................................B2

1,035.10

9.77

Virginia Power & Light––8½ 2032 .....................

Industrials:

Compute the answers to the following questions from the information given: a.

Cost of debt, Kd (use the accompanying table––relate to the utility bond credit rating for yield)

Cost of preferred stock, Kp

Cost of common equity in the form of retained earnings, Ke

Weighted average cost of capital

11-26. Solution: a. The student must realize that the cost of debt is related to the cost of debt for other debt issues of the same risk class. Although, in actuality, the rate Northwest might pay will not be exactly equal to Southwest Bell, it should be close enough to serve as an approximation. Both utilities are rated Aa3. Kd = Yield (1 – T) = 8.73% (1 – 0.25) = 8.73% (0.75) = 6.55% b. Kp = Dp/(Pp – F) = $7.68/($96 – $6.00) = $7.68/$90 = 8.53%

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Chapter 12: The Capital Budgeting Decision

c. Ke = (D1/P0) + g = ($6.50/$64) + 8.20% = 10.16% + 8.20% = 18.36% d. Debt (Kd) ...................... Preferred stock (Kp) ..... Common equity (Ke) (retained earnings) ... Weighted average cost of capital (Ka) ............

Cost (aftertax) 6.55% 8.53

Weighted Weights Cost 55% 3.60% 20 1.71

18.36

4.59 9.90%

27. Marginal cost of capital (LO11-5) Delta Corporation has the following capital structure: Cost (aftertax)

Weights

Weighted Cost

Debt ....................................................................................... 8.1% 35%

2.84%

Preferred stock (Kp) ............................................................... 9.6

.48

(retained earnings) ........................................................... 10.1 60

6.06

Common equity (Ke)

Weighted average cost of capital (Ka) ...................................

9.38%

If the firm has $18 million in retained earnings, at what size capital structure will the firm run out of retained earnings?

The 8.1 percent cost of debt referred to earlier applies only to the first $14 million of debt. After that, the cost of debt will go up. At what size capital structure will there be a change in the cost of debt?

11-27. Solution:

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Chapter 12: The Capital Budgeting Decision

Retained earnings % of retained earnings in the capital structure

X 

 $18 million /.60  $30million b.

Z 

Amount of lower cost debt % of debt in the capital structure

 $14 million / .35  $40 million

28. Marginal cost of capital (LO11-5) The Nolan Corporation finds it is necessary to determine its marginal cost of capital. Nolan’s current capital structure calls for 50 percent debt, 30 percent preferred stock, and 20 percent common equity. Initially, common equity will be in the form of retained earnings (Ke) and then new common stock (Kn). The costs of the various sources of financing are as follows: debt, 9.6 percent; preferred stock, 9 percent; retained earnings, 10 percent; and new common stock, 11.2 percent. a.

What is the initial weighted average cost of capital? (Include debt, preferred stock, and common equity in the form of retained earnings, Ke.)

If the firm has $18 million in retained earnings, at what size capital structure will the firm run out of retained earnings?

What will the marginal cost of capital be immediately after that point? (Equity will remain at 20 percent of the capital structure, but will all be in the form of new common stock, Kn.)

The 9.6 percent cost of debt referred to earlier applies only to the first $29 million of debt. After that, the cost of debt will be 11.2 percent. At what size capital structure will there be a change in the cost of debt?

What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)

11-28. Solution:

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Chapter 12: The Capital Budgeting Decision

Cost (aftertax) Debt (Kd).................... 9.60% Preferred stock (Kp) ..................... 9.00 Common equity (Ke) (retained earnings) ...................... 10.00 Weighted average cost of capital (Ka) ................................... b. X  

Weighted Weights Cost 50% 4.80% 30 2.70 20

2.00 9.50%

Retained earnings % of retained earnings within the capital structure $18 million  $90 million .20

c. Debt (Kd).................... Preferred stock (Kp) ... New common stock (Kn) Marginal cost of capital (Kmc) ..........................

Cost (aftertax) 9.60% 9.00 11.20

Weighted Weights Cost 50% 4.80% 30 2.70 20

2.24 9.74%

d. Z  

Amount of lower cost debt % of debt within the capital structure $29 million  $58 million .50

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Chapter 12: The Capital Budgeting Decision

Cost (aftertax) Debt (Kd) ..................................... 11.20% Preferred stock (Kp) ..................... 9.00 New common stock (Kn).............. Marginal cost of capital 11.20 (Kmc) ............................................

Weighted Weights Cost 50% 5.60% 30 2.70 20

2.24 10.54%

29. Marginal cost of capital (LO11-5) The McGee Corporation finds it is necessary to determine its marginal cost of capital. McGee’s current capital structure calls for 40 percent debt, 30 percent preferred stock, and 30 percent common equity. Initially, common equity will be in the form of retained earnings (Ke) and then new common stock (Kn). The costs of the various sources of financing are as follows: debt, 9.6 percent; preferred stock, 9.0 percent; retained earnings, 10.0 percent; and new common stock, 11.4 percent. a.

What is the initial weighted average cost of capital? (Include debt, preferred stock, and common equity in the form of retained earnings, Ke.)

If the firm has $28.5 million in retained earnings, at what size capital structure will the firm run out of retained earnings?

What will the marginal cost of capital be immediately after that point? (Equity will remain at 30 percent of the capital structure, but will all be in the form of new common stock, Kn.)

The 9.6 percent cost of debt referred to earlier applies only to the first $30 million of debt. After that, the cost of debt will be 11.2 percent. At what size capital structure will there be a change in the cost of debt?

What will the marginal cost of capital be immediately after that point? (Consider the facts in both parts c and d.)

11-29. Solution:

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Chapter 12: The Capital Budgeting Decision

Cost (aftertax) Debt (Kd) .....................................9.60% Preferred stock (Kp) .....................9.00 Common equity (Ke) (retained earnings) ..................... 10.00 Weighted average cost of capital (Ka)

X  

3.00 9.54%

$28.5 million  $95 million .30

Debt (Kd) .................... Preferred stock (Kp) ... New common stock (Kn)............................. Marginal cost of capital (Kmc) ...........................



Retained earnings % of retained earnings within the capital structure

d. Z 

Weighted Weights Cost 40% 3.84% 30 2.70

Cost (aftertax) 9.60% 9.00

Weights 40% 30

11.40

Weighted Cost 3.84% 2.70 3.42 9.96%

Amount of lower cost debt % of debt within the capital structure $30 million  $75 million .40

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Chapter 12: The Capital Budgeting Decision

e. Debt (Kd) .................... Preferred stock (Kp) ... New common stock (Kn)............................. Marginal cost of capital (Kmc) ...........................

Cost (aftertax) 11.20% 9.00

Weights 40% 30

11.40

Weighted Cost 4.48% 2.70 3.42 10.60%

30. Capital asset pricing model and dividend valuation model (LO11-3) Eaton Electronic Company’s treasurer uses both the capital asset pricing model and the dividend valuation model to compute the cost of common equity (also referred to as the required rate of return for common equity). Assume: Rf

10%

1.6

$0.70

$19

Compute Ki (required rate of return on common equity based on the capital asset pricing model).

Compute Ke (required rate of return on common equity based on the dividend valuation model).

11-30. Solution: a. Kj

= Rf. + β(Km – Rf)

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Chapter 12: The Capital Budgeting Decision

= 7% + 1.6(10% – 7%) = 7% + 1.6(3%) = 7% + 4.80% = 11.80% b.

Ke 

D1 g P0

$.70  8% $19  3.68%  8%  11.68% =

Although the values are equal in this example, that is not always the case.

COMPREHENSIVE PROBLEM Comprehensive Problem 1 Medical Research Corporation is expanding its research and production capacity to introduce a new line of products. Current plans call for the expenditure of $100 million on four projects of equal size ($25 million each), but different returns. Project A is in blood clotting proteins and has an expected return of 18 percent. Project B relates to a hepatitis vaccine and carries a potential return of 14 percent. Project C, dealing with a cardiovascular compound, is expected to earn 11.8 percent, and Project D, an investment in orthopedic implants, is expected to show a 10.9 percent return. The firm has $15 million in retained earnings. After a capital structure with $15 million in retained earnings is reached (in which retained earnings represent 60 percent of the financing), all additional equity financing must come in the form of new common stock. Common stock is selling for $25 per share and underwriting costs are estimated at $3 if new shares are issued. Dividends for the next year will be $0.90 per share (D1), and earnings and dividends have grown consistently at 11 percent per year. The yield on comparative bonds has been hovering at 11 percent. The investment banker feels that the first $20 million of bonds could be sold to yield 11 percent while additional debt

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Chapter 12: The Capital Budgeting Decision

might require a 2 percent premium and be sold to yield 13 percent. The corporate tax rate is 25 percent. Debt represents 40 percent of the capital structure. a.

Based on the two sources of financing, what is the initial weighted average cost of capital? (Use Kd and Ke.)

At what size capital structure will the firm run out of retained earnings?

What will the marginal cost of capital be immediately after that point?

At what size capital structure will there be a change in the cost of debt?

What will the marginal cost of capital be immediately after that point?

Based on the information about potential returns on investments in the first paragraph and information on marginal cost of capital (in parts a, c, and e), how large a capital investment budget should the firm use?

Graph the answer determined in part f.

CP 11-1. Solution: a. Kd = Yield (1 – T) = 11% (1 – 0.25) = 11% (0.75) = 8.25% Ke = (D1/P0) + g = ($0.90/$25.00) + 11.0% = 3.6% + 11.0% = 14.60%

Cost (aftertax) Debt (Kd) ............................. 8.25% Common equity (Ke) 14.60 (retained earnings) ...........

Weights 40% 60

Weighted Cost 3.08% 8.76

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Chapter 12: The Capital Budgeting Decision

Weighted average cost of capital (Ka) .................. b.

X  

12.06%

Retained earnings % of retained earnings in the capital structure $15 million  $25 million .60

c. First compute Kn Kn = (D1/(P0 – F) + g = ($0.90/($25 – $3)) + 11% = ($0.90/$22) + 11% = 4.09% + 11% = 15.09% Cost (aftertax)

Weights 40% 60

Debt (Kd) ............................. 8.25% New common stock 15.09 (Kn)................................... Marginal cost of capital (Kmc) ................................. Amount of lower cost debt d. Z  % of debt in the capital structure



Weighted Cost 3.30% 9.05 12.35%

$20 million  $50 million .40

e. First compute the new value for Kd. Kd = Yield (1 – T) = 13% (1 – 0.25) = 13% (0.75) = 9.75% Cost (aftertax)

Weights

Weighted Cost

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Chapter 12: The Capital Budgeting Decision

Debt (Kd) ............................. 9.75% New common stock 15.09 (Kn)................................... Marginal cost of capital (Kmc) ................................. f.

40% 60

3.90% 9.05 12.95%

The answer is $50 million.

Return on Investment st 1 $25 million 18.0% $25 million – $50 million 14.0% $50 million – $75 million 11.8% $75 million – $100 million 10.9%

> > < <

Marginal Cost of Capital 12.06% 12.35% 12.95% 12.95%

g. The top bar represents return on investment. The dotted line represents marginal cost of capital (Kmc). Invest up to $50 million.

Percent (return) 18%

14%

12.95%

Kmc

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Chapter 12: The Capital Budgeting Decision

12.35%

11.8%

12.06%

10.9%

100

Amount of Capital ($ millions) Comprehensive Problem 2 Masco Oil and Gas Company is a very large company with common stock listed on the New York Stock Exchange and bonds traded over the counter. As of the current balance sheet, it has three bond issues outstanding: $150 million of 10 percent series ......................

2046

$50 million of 7 percent series ..........................

2040

$75 million of 5 percent series ..........................

2036

The vice president of finance is planning to sell $75 million of bonds next year to replace the debt due to expire in 2036. Present market yields on similar Baa-rated bonds are 12.1 percent. Masco also has $90 million of 7.5 percent noncallable preferred stock outstanding, and it has no intentions of selling any preferred stock at any time in the future. The preferred stock is currently priced at $80 per share, and its dividend per share is $7.80. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

The company has had very volatile earnings, but its dividends per share have had a very stable growth rate of 8 percent and this will continue. The expected dividend (D1) is $1.90 per share, and the common stock is selling for $40 per share. The company’s investment banker has quoted the following flotation costs to Masco: $2.50 per share for preferred stock and $2.20 per share for common stock. On the advice of its investment banker, Masco has kept its debt at 50 percent of assets and its equity at 50 percent. Masco sees no need to sell either common or preferred stock in the foreseeable future as it has generated enough internal funds for its investment needs when these funds are combined with debt financing. Masco’s corporate tax rate is 25 percent. Compute the cost of capital for the following: a.

Bond (debt) (Kd).

Preferred stock (Kp).

Common equity in the form of retained earnings (Ke).

New common stock (Kn).

Weighted average cost of capital.

CP 11-2. Solution a. The before tax cost of debt will be equal to the market rate of 12.1 percent. The student must realize that the historical cost of the three bonds does not influence the cost of debt. Kd = Yield (1 – T) = 12.1% (1 – 0.25) = 12.1% (0.75) = 9.08% b. The fact that the preferred stock carries a coupon rate of 7.5 percent does not influence Kp, which is dependent upon current prices and the dividend. Kp = (Dp)/(Pp – F) = ($7.80)/($80 – $2.50) = ($7.80)/($77.50) = 10.06% c. Ke = (D1/P0) + g © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

= ($1.90/$40.00) + 8.0% = 4.75% + 8.0% = 12.75% d. Kn = (D1/P0 – F) + g = [$1.90/($40 – $2.20] + 8% = ($1.90/$37.80) + 8% = 5.03% + 8% = 13.03%

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Chapter 12: The Capital Budgeting Decision

e. Only those sources of capital that are expected to be used as long-run optimum components of the capital structure should be included in the weighted average cost of capital. The firm states that all their funds can be supplied by retained earnings (50 percent); therefore, we do not need to include new common stock or preferred stock in our calculation of the weighted cost of capital. Cost (aftertax) Debt (Kd) ............................. 9.08% Common equity (Ke) (retained earnings) ........... 12.75 Weighted average cost of capital (Ka) ....................

Weighted Weights Cost 50% 4.54% 50

6.37 10.91%

Appendix A–Cost of Capital and the Capital Asset Pricing Model Discussion Questions 11A-1.

How does the capital asset pricing model help explain changing costs of capital? The capital asset pricing model explains the relationship between risk and return, and the price adjustment of capital assets to changes in risk and return. As investors react to their economic environment and their willingness to take risk, they change the prices of financial assets like common stock, bonds, and preferred stock. As the prices of these securities adjust to investors’ required returns, the company’s cost of capital is adjusted accordingly.

11A-2.

How does the SML react to changes in the rate of interest, changes in the rate of inflation, and changing investor expectations?

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Chapter 12: The Capital Budgeting Decision

The SML, Security Market Line, reflects the risk-return trade-offs of securities. As interest rates increase, the SML moves up parallel to the old SML. Now investors require a higher minimum return on risk-free assets and an equally higher rate for all levels of risk. A change in the rate of inflation has a similar impact. The risk-free rate goes up to provide the appropriate inflation premium and there is an upward shift in the SML. In regard to changing investor expectations, as investors become more risk-averse, the SML increases its slope. The more risk taken, the greater the return premium that is desired (see Figure 11A-4).

Problems

11A-1.

11A-1

Capital asset pricing model (LO11-3) Assume that Rf = 5 percent and Km = 10.5 percent. Compute Kj for the following betas using Formula 11A-2. a.

0.6

1.3

1.9

Solution: a. Kj = Rf + β (Km – Rf) = 5% + 0.6 (10.5% – 5%) = 5% + 0.6 (5.5%) = 5% + 3.3% = 8.3% b. Kj = 5% + 1.3 (10.5% – 5%) = 5% + 1.3 (5.5%) = 5% + 7.15% = 12.15% c. Kj = 5% + 1.9 (10.5% – 5%)

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Chapter 12: The Capital Budgeting Decision

= 5% + 1.9 (4%) = 5% + 10.45% = 15.45%

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Chapter 12: The Capital Budgeting Decision

11A-2.

Capital asset pricing model (LO11-3) Assume that Rf = 6 percent and the market risk premium (Km – Rf) is 7.0 percent. Compute Kj for the following betas using Formula 11A-2. a.

0.6

1.3

1.9

Solution: a. Kj = 6% + 0.6 (7%) = 6% + 4.2% = 10.2% b. Kj = 6% + 1.3 (7%) = 6% + 9.1% = 15.1% c. Kj = 6% + 1.9 (7%) = 6% + 13.3% = 19.3%

Chapter 12 The Capital Budgeting Decision Discussion Questions

12-1.

What are the important administrative considerations in the capital budgeting process?

Important administrative considerations relate to the search for and discovery © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

of investment opportunities, the collection of data, the evaluation of projects, and the reevaluation of prior decisions.

12-2.

Why does capital budgeting rely on analysis of cash flows rather than on net income?

Cash flow rather than net income is used in capital budgeting analysis because the primary concern is with the amount of actual dollars generated. For example, depreciation is subtracted out in arriving at net income, but this noncash deduction should be added back in to determine cash flow or actual dollars generated.

12-3.

What are the weaknesses of the payback method?

The weaknesses of the payback method are: a. There is no consideration of inflows after payback is reached. b. The concept fails to consider the time value of money. 12-4.

What is normally used as the discount rate in the net present value method?

The cost of capital as determined in Chapter 11.

12-5.

What does the term mutually exclusive investments mean? The selection of one investment precludes the selection of other alternative investments because the investments compete with one another. For example, if a company is going to build one new plant and is considering five cities, one city will win and the others will lose.

12-6.

How does the modified internal rate of return include concepts from both the traditional internal rate of return and the net present value methods?

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Chapter 12: The Capital Budgeting Decision

The modified internal rate of return calls for the determination of the interest rate that equates future inflows to the investment, as does the traditional internal rate or return. However, it incorporates the reinvestment rate assumption of the net present value method. That is, inflows are reinvested at the cost of capital.

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Chapter 12: The Capital Budgeting Decision

12-7.

If a corporation has projects that will earn more than the cost of capital, should it ration capital?

From a purely economic viewpoint, a firm should not ration capital. The firm should be able to find additional funds and increases its overall profitability and wealth through accepting investments to the point where marginal return equals marginal cost.

12-8.

How does an asset’s ADR (asset depreciation range) relate to its MACRS category? The ADR represents the asset depreciation range or the expected physical life of the asset. Generally, the midpoint of the range or life is utilized. The longer the ADR midpoint, the longer the MACRS category in which the asset is placed. However, most assets can still be written off more rapidly than the midpoint of the ADR. For example, assets with ADR midpoints of 10 years to 15 years can be placed in the 7-year MACRS category for depreciation purposes.

Problems 1.

Cash flow (LO12-2) Assume a corporation has earnings before depreciation and taxes of $90,000, depreciation of $40,000, and a 25 percent tax bracket. Compute its cash flow using the following format:

Earnings before depreciation and taxes Depreciation Earnings before taxes Taxes @ 25% Earnings after taxes Depreciation Cash flow

_____ _____ _____ _____ _____ _____ _____

12-1. Solution: Earnings before depreciation and taxes Depreciation

$90,000 –40,000

Earnings before taxes

50,000

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Chapter 12: The Capital Budgeting Decision

Taxes @ 25%

–12,500

Earnings after taxes

$37,500

Depreciation

+40,000

Cash flow

$77,500

Cash flow (LO12-2) Assume a corporation has earnings before depreciation and taxes of $100,000, depreciation of $40,000, and that it has a 24 percent tax bracket. a.

Compute its cash flow using the following format:

Earnings before depreciation and taxes Depreciation Earnings before taxes Taxes @ 24% Earnings after taxes Depreciation

_____ _____ _____ _____ _____ _____

Compute the cash flow for the company if depreciation is only $20,000.

How much cash flow is lost due to the reduced depreciation from $40,000 to $20,000?

12-2. Solution: a. Earnings before depreciation and taxes Depreciation Earnings before taxes Taxes @ 24% Earnings after taxes Depreciation Cash flow

$100,000 – 40,000 60,000 14,400 45,600 + 40,000 $ 85,600

b. Earnings before depreciation and taxes Depreciation Earnings before taxes Taxes @ 24% Earnings after taxes

$100,000 – 20,000 80,000 19,200 60,800

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Depreciation Cash flow

+ 20,000 $ 80,800

c. Cash flow ($40,000) Cash flow ($20,000) Difference in cash flow 3.

$ 85,600 80,800 $ 4,800

Cash flow (LO12-2) Assume a firm has earnings before depreciation and taxes of $200,000 and no depreciation. It is in a 25 percent tax bracket. a. Compute its cash flow. b. Assume it has $200,000 in depreciation. Recompute its cash flow. c. How large a cash flow benefit did the depreciation provide?

12-3. Solution: a. Earnings before depreciation and taxes Depreciation

$200,000 –

Earnings before taxes

0 200,000

Taxes @ 25%

– 50,000

Earnings after taxes

150,000

Depreciation

–

Cash flow

$150,000

b. Earnings before depreciation and taxes Depreciation

$200,000 –200,000

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Chapter 12: The Capital Budgeting Decision

Earnings before taxes

Taxes @ 25%

Earnings after taxes

Depreciation

200,000

Cash flow

$200,000

c. The $200,000 in depreciation provided a cash flow benefit of $80,000. Cash flow (b) $200,000

Cash flow (a)

150,000

Cash flow benefit

$ 50,000

Cash flow (LO12-2) Assume a firm has earnings before depreciation and taxes of $440,000 and depreciation of $140,000. a.

If it is in a 35 percent tax bracket, compute its cash flow.

If it is in a 20 percent tax bracket, compute its cash flow.

12-4. Solution: a. Earnings before depreciation and taxes Depreciation Earnings before taxes Taxes @ 35% Earnings after taxes Depreciation Cash flow

$440,000 140,000 300,000 105,000 195,000 +140,000 $335,000

b. Earnings before depreciation + taxes

$440,000

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Chapter 12: The Capital Budgeting Decision

Depreciation Earnings before taxes Taxes @ 20% Earnings after taxes Depreciation Cash flow 5.

140,000 300,000 60,000 240,000 +140,000 380,000

Cash flow versus earnings (LO12-2) Al Quick, the president of a New York Stock Exchange —listed firm, is very short-term oriented and interested in the immediate consequences of his decisions. Assume a project will provide an increase of $2 million in cash flow because of favorable tax consequences, but carries a two-cent decline in earnings per share because of a write-off against first-quarter earnings. What decision might Mr. Quick make?

12-5. Solution: Being short-term oriented, he may make the mistake of turning down the project even though it will increase cash flow because of his fear of investors’ negative reaction to the more widely reported quarterly decline in earnings per share. Even though this decline will be temporary, investors might interpret it as a negative signal. 6.

Payback method (LO12-3) Assume a $250,000 investment and the following cash flows for two products: Year 1 2 3 4

Product X $90,000 90,000 60,000 20,000

Product Y $50,000 80,000 60,000 70,000

Which alternatives would you select under the payback method?

12-6. Solution: Payback for Product X

Payback for Product Y

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Chapter 12: The Capital Budgeting Decision

$250,000 – 90,000 160,000 – 90,000 70,000 – 60,000 10,000/20,000

1 year $250,000 – 50,000 1 year 2 years 200,000 – 80,000 2 years 3 years 120,000 – 60,000 3 years .5 years 60,000/70,000 .86 years

Payback Product X = 3.5 years Payback Product Y =3.86 years Product X would be selected because of the faster payback. 7.

Payback method (LO12-3) Assume a $40,000 investment and the following cash flows for two alternatives. Year 1 2 3 4 5

Investment X $ 6,000 8,000 9,000 17,000 20,000

Investment Y $15,000 20,000 10,000 — —

Which of the alternatives would you select under the payback method?

12-7. Solution:

Payback for Investment X

Payback for Investment Y

$40,000–$6,000 1 year

$40,000–$15,000

1 year

34,000–8,000

2 years

25,000–20,000

2 years

26,000–9,000

3 years

5,000/10,000

.5 years

17,000–17,000

4 years

Payback Investment X = 4.00 years

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Chapter 12: The Capital Budgeting Decision

Payback Investment Y = 2.50 years Investment Y would be selected because of the faster payback.

Payback method (LO12-3) Assume a $90,000 investment and the following cash flows for two alternatives. Year 1 ................. 2 ................. 3 ................. 4 ................. 5 .................

Investment A $25,000 30,000 25,000 19,000 25,000

Investment B $40,000 40,000 28,000 — —

a. Calculate the payback for investment A and B. b. If the inflow in the fifth year for Investment A was $25,000,000 instead of $25,000, would your answer change under the payback method?

12-8. Solution: a. Payback for Investment A $90,000 – $25,000 1 year 65,000 – 30,000 2 years 35,000 – 25,000 3 years 10,000/19,000 0.53 years

Payback for Investment B $90,000 – $40,000 50,000 – 40,000 10,000/28,000

1 year 2 years .36 years

Payback Investment A = 3.53 years Payback Investment B = 2.36 years Investment B would be selected because of the faster payback. b. The $25,000,000 inflow would still leave the payback period for Investment A at 3.53 years. It would remain inferior to Investment B under the payback method.

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Chapter 12: The Capital Budgeting Decision

Payback method (LO12-3) The Short-Line Railroad is considering a $140,000 investment in either of two companies. The cash flows are as follows: Year 1................... 2................... 3................... 4–10.............

Electric Co. $85,000 25,000 30,000 10,000

Water Works $30,000 25,000 85,000 10,000

Using the payback method, what will the decision be?

Explain why the answer in part a can be misleading.

12-9. Solution: a. Payback for Electric Co. $140,000 – $85,000 55,000 – 25,000 30,000 – 30,000

Payback for Water Works

1 year $140,000 – $30,000 2 years 110,000 – 25,000 3 years 85,000 – 85,000

1 year 2 years 3 years

Payback (Electric Co.) = 3 years Payback (Water Works) = 3 years b. The answer in part a is misleading because the two investments seem to be equal with the same payback period of three years. Nevertheless, the Electric Co. is a superior investment because it covers large cash flows in the first year, while the large recovery for Water Works is not until the third year. The problem is that the payback method does not consider the time value of money. 10. Payback and net present value (LO12-3 and 4) X-treme Vitamin Company is considering two investments, both of which cost $10,000. The cash flows are as follows: Year 1 .................... 2 .................... 3 ....................

Project A $12,000 8,000 6,000

Project B $10,000 6,000 16,000

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Chapter 12: The Capital Budgeting Decision

Which of the two projects should be chosen based on the payback method?

Which of the two projects should be chosen based on the net present value method? Assume a cost of capital of 10 percent.

Should a firm normally have more confidence in answer a or answer b.

12-10. Solution: a. Payback Method Payback for Project A 10,000  .83 years 12,000

Payback for Project B 10,000  1 year 10,000

Under the Payback Method, you should select Project A because of the shorter payback period. b. Net Present Value Method Project A Year

Cash Flow

PVIFA

Present Value

1 2 3

$12,000 $ 8,000 $ 6,000

0.909 0.826 0.751

$10,908 $ 6,608 $ 4,506

Present value of inflows Present value of outflows Net present value

$22,022 10,000 $12,022

Project B Year

Cash Flow

PVIFA

Present Value

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Chapter 12: The Capital Budgeting Decision

1 2 3

$10,000 $ 6,000 $16,000

0.909 0.826 0.751

$ 9,090 $ 4,956 $12,016

Present value of inflows Present value of outflows Net present value

$26,062 10,000 $16,062

Under the net present value method, you should select Project B because of the higher net present value. c. A company should normally have more confidence in answer b because the net present value considers all inflows as well as the time value of money. The heavy late inflow for Project B was partially ignored under the payback method. Calculator Solution: (b-1) Project A using a financial calculator: Use the NPV keys by pressing and entering the following: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 10,000 +|– key, press the Enter key. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 6,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 12,028.55, which is the net present value of Project A. (b-2) Project B Using Financial Calculator Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 10,000 +|– key, press the Enter key.

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Chapter 12: The Capital Budgeting Decision

Press down arrow, enter 10,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 6,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 16,070.62, which is the net present value of Project B.

Under the net present value method, you should select Project B because of the higher net present value.

11. Internal rate of return (LO12-4) You buy a new piece of equipment for $16,230, and you receive a cash inflow of $2,500 per year for 12 years. What is the internal rate of return?

12-11.

Solution: Appendix D PVIFA 

$16, 230  6.492 $2,500

IRR = 11% For n = 12, we find 6.492 under the 11% column. Calculator Solution:

Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 16,230 +|– key, press the Enter key. Press down arrow, enter 2,500, and press Enter. Press down arrow, enter 12, and press Enter.

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Chapter 12: The Capital Budgeting Decision

Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 11.

Answer: IRR = 11%

12. Internal rate of return (LO12-4) King’s Department Store is contemplating the purchase of a new machine at a cost of $22,802. The machine will provide $3,500 per year in cash flow for nine years. King’s has a cost of capital of 10 percent. Using the internal rate of return method, evaluate this project and indicate whether it should be undertaken.

12-12.

Solution: Appendix D PVIFA = $22,802/$3,500 = 6.515 IRR = 7% For n = 9, we find 6.515 under the 7% column. The machine should not be purchased since its return is less than the 10 percent cost of capital.

Calculator Solution:

(a) Using a financial calculator, Press the following keys: 2nd, CF, 2nd, CLR WORK. Calculator displays CFo, 22,802 +|– key, press the Enter key. Press down arrow, enter 3,500, and press Enter. Press down arrow, enter 9, and press Enter. Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 7.

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Chapter 12: The Capital Budgeting Decision

Answer: IRR = 7%

13. Internal rate of return (LO12-4) Home Security Systems is analyzing the purchase of manufacturing equipment that will cost $50,000. The annual cash inflows for the next three years will be Year 1 ......................... 2 ......................... 3 .........................

Cash Flow $25,000 23,000 18,000

Determine the internal rate of return.

With a cost of capital of 18 percent, should the machine be purchased?

12-13.

Solution: a. Step 1 Average the inflows. $25,000 23,000 18,000 $66,000 / 3  $22,000

Step 2 Divide the inflows by the assumed annuity in Step 1.

Investment $50, 000   2.273 Annuity 22, 000 Step 3 Go to Appendix D for the first approximation. The value in Step 2 (for n = 3) falls between 15 and 16 percent. Step 4 Try a first approximation of discounting back the inflows. Because the inflows are biased toward the early years, we will use the higher rate of 16 percent.

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Chapter 12: The Capital Budgeting Decision

Year 1 2 3

Cash Flow $25,000 $23,000 $18,000

PVIF at 16% Present Value 0.862 $21,550 0.743 $17,089 0.641 $11,538 $50,177

Step 5 Since the NPV is slightly over $50,000, we need to try a higher rate. We will try 17 percent.

Year 1 2 3

Cash Flow $25,000 $23,000 $18,000

PVIF at 17% Present Value 0.855 $21,375 0.731 $16,813 0.624 $11,232 $49,420

Because the NPV is now below $50,000, we know the IRR is between 16 and 17 percent. We will interpolate. $50,177 ........... PV @ 16% –49,420 ........... PV @ 17% $ 757

$50,177............. PV @ 16% –50,000............. Cost $ 177

16% + ($177/$757) (1%) 14% + 0.234 (1%) = 16.23% IRR The IRR is 16.23% If the student skipped from 16 percent to 18 percent, the calculations to find the IRR would be as follows: Year 1 2 3

Cash Flow $25,000 $23,000 $18,000

PVIF at 18% Present Value 0.847 $ 21,175 0.718 $ 16,514 0.609 $ 10,962 $ 48,651

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Chapter 12: The Capital Budgeting Decision

$50,177 ........... PV @ 16%

$50,177............. PV @ 16%

–48,651 ........... PV @ 18%

–50,000............. Cost

$ 1,526

177

16% + ($177/$1,526) (2%) 16% + (0.12)(2%) = 16.24% This answer is very close to the previous answer, the difference is due to rounding and that the differences between the numbers in the table are not linear. b. Since the IRR of 16.23 percent (or 16.24 percent) is less than the cost of capital of 18 percent, the project should not be accepted. Calculator Solution:

Alternatively, use a financial calculator as follows to obtain the correct answer rather than an approximation. Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 50,000 +|– key, press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 23,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 18,000, and press Enter. Press down arrow, enter 1, and press Enter. Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 16.23. Answer: IRR = 16.23%

14. Net present value method (LO12-4) Aerospace Dynamics will invest $110,000 in a project that will produce the following cash flows. The cost of capital is 11 percent. Should the project be undertaken? (Note that the fourth year’s cash flow is negative.)

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Chapter 12: The Capital Budgeting Decision

Year 1................. 2................. 3................. 4................. 5.................

12-14.

Cash Flow $36,000 44,000 38,000 (44,000) 81,000

Solution: Year 1 2 3 4 5

Cash Flow $36,000 44,000 38,000 (44,000) 81,000

PVIF at 11% 0.901 0.812 0.731 0.659 0.593

Present Value of Inflows Present Value of Outflows Net Present Value

Present Value $ 32,436 35,728 27,778 (28,996) 48,033 $114,979 110,000 $ 4,979

The net present value is positive and the project should be undertaken. Calculator Solution:

Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 110,000 +|– key, press Enter. Press down arrow, enter 36,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 44,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 38,000, and press Enter.

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Chapter 12: The Capital Budgeting Decision

Press down arrow, enter 1, and press Enter. Press down arrow, enter 44,000 +|–, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 81,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; the calculator shows NPV = 5,014.49, which is the net present value of the project.

The net present value is positive and the project should be undertaken.

15. Net present value method (LO12-4) The Horizon Company will invest $60,000 in a temporary project that will generate the following cash inflows for the next three years. Year 1................. 2................. 3.................

Cash Flow $15,000 25,000 40,000

The firm will also be required to spend $10,000 to close down the project at the end of the three years. If the cost of capital is 10 percent, should the investment be undertaken?

12-15.

Solution: Present Value of Inflows Year 1 2 3

Cash Flow × PVIF at 10% Present Value $15,000 0.909 $13,635 25,000 0.826 20,650 40,000 0.751 30,040 $64,325

Present Value of Outflows 0

$60,000

1.000

$60,000

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Chapter 12: The Capital Budgeting Decision

10,000

0.751

Present Value of Inflows Present Value of Outflows Net Present Value

7,510 $67,510 $64,325 67,510 ($ 3,185)

The net present value is negative and the project should not be undertaken. Note, the $10,000 outflow could have been subtracted out of the $40,000 inflow in the third year and the same answer would result. Calculator Solution:

Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 60,000 +|– key, press the Enter key Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 30,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –3,163.04, which is the net present value of the project. Note, the $10,000 outflow in year 3 has been subtracted from the $ 40,000 inflow in the third year, and thus the year 3 net cash flow is $30,000.

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Chapter 12: The Capital Budgeting Decision

16. Net present value method (LO12-4) Skyline Corp. will invest $130,000 in a project that will not begin to produce returns until after the 3rd year. From the end of the 3rd year until the end of the 12th year (10 periods), the annual cash flow will be $34,000. If the cost of capital is 12 percent, should this project be undertaken?

12-16.

Solution: Present Value of Inflows Find the present value of a deferred annuity A

= $34,000, n = 10, i = 12%

PVA

= A × PVIFA (Appendix D)

PVA

= $34,000 × 5.650 = $192,100

Discount from beginning of the third period (end of second period to present): FV

= $192,100, n = 2, i = 12%

= FV × PVIF (Appendix B)

= $192,100 × 0.797 = $153,104

Present Value of Inflows Present Value of Outflows Net Present Value

$153,104 130,000 $ 23,104

The net present value is positive and the project should be undertaken.

Calculator Solution:

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Chapter 12: The Capital Budgeting Decision

Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 130,000 +|– key, press Enter. Press down arrow, enter 0, and press Enter. Press down arrow, enter 2, and press Enter. Press down arrow, enter 34,000, and press Enter. Press down arrow, enter 10, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 23,146.99, which is the net present value of the project.

17. Net present value and internal rate of return methods (LO12-4) The Hudson Corporation makes an investment of $24,000 that provides the following cash flow: Year 1 ................. 2 ................. 3 .................

Cash Flow $ 13,000 13,000 4,000

What is the net present value at an 8 percent discount rate?

What is the internal rate of return?

In this problem, would you make the same decision under both parts a and b?

12-17.

Solution: a. Net Present Value Year 1 2 3

Cash Flow × $13,000 13,000 4,000

8% PVIF 0.926 0.857 0.794

Present Value of Inflows Present Value of Outflows Net Present Value

Present Value $ 12,038 11,141 3,176 $26,355 24,000 $ 2,355

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b. Internal Rate of Return We will average the inflows to arrive at an assumed annuity value. $13,000 13,000 4,000 $30,000/3 = $10,000 We divide the investment by the assumed annuity value. $24,000  2.400 10,000

PVIFA

Using Appendix D for n = 3, the first approximation appears to fall between 12 percent and 14 percent. Since the heavy inflows are in the early years, we will try 14 percent. Year 1 2 3

Cash Flow × 14% PVIF $13,000 0.877 13,000 0.769 4,000 0.675 Present Value of Inflows

Present Value $ 11,401 9,997 2,700 $24,098

Since 14 percent is not high enough to get $24,000 as the present value, we will try 16 percent. (We could have only gone up to 15 percent, but we wanted to be sure to include $24,000 in this calculation. Of course, students who use 15 percent are doing fine.) Year 1 2 3

Cash Flow × 16%PVIF $13,000 0.862 13,000 0.743 4,000 0.641 Present Value of Inflows

Present Value $ 11,206 9,659 2,564 $23,429

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Chapter 12: The Capital Budgeting Decision

The correct answer must fall between 14 percent and 16 percent. We interpolate. $24,098 ........... PV @ 14% 23,429 ........... PV @ 16% $ 669

$24,098............. PV @ 14% 24,000............. Cost $ 98

$98 (2%)  14%  .15 (2%)  14%  .30%  14.30% $669 As an alternative answer, students who use 15 percent as the second trial and error rate will show the following: 14% 

Year 1 2 3

Cash Flow × 15%PVIF $13,000 0.870 13,000 0.756 4,000 0.658 Present Value of Inflows

Present Value $ 11,310 9,828 2,632 $23,770

The correct answer falls between 14 percent and 15 percent. We interpolate. $24,098 23,770 328

14% 

PV @ 14% PV @ 15%

$24,098 24,000 $ 98

PV @ 14% Cost

$98 (1%)  14%  .30 (1%)  14%  .30%  14.30% $328

c. Yes. Both the NPV is greater than 0 and the IRR is greater than the cost of capital. Calculator Solution:

(a) Press the following keys: 2nd, CF, 2nd, and Clear. Calculator displays CFo, 24,000 +|– key, press Enter.

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Chapter 12: The Capital Budgeting Decision

Press down arrow, enter 13,000, and press Enter. Press down arrow, enter 2, and press Enter. Press down arrow, enter 4,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 8 and press Enter. Press down arrow; calculator shows NPV = 0.00 Press CPT; calculator shows NPV = 2,357.77, which is the net present value of the project. (b) Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 24,000 +|– key, press Enter. Press down arrow, enter 13,000 and press Enter. Press down arrow, enter 2, and press Enter. Press down arrow, enter 4,000, and press Enter. Press down arrow, enter 1, and press Enter. Press IRR; calculator shows IRR = 0.00. Press CPT; calculator shows IRR = 14.29. Answer: IRR = 14.29%

18. Net present value and internal rate of return methods (LO12-4) The Pan American Bottling Co. is considering the purchase of a new machine that would increase the speed of bottling and save money. The net cost of this machine is $60,000. The annual cash flows have the following projections: Year 1 ........... 2 ........... 3 ........... 4 ........... 5 ...........

Cash Flow $23,000 26,000 29,000 15,000 8,000

If the cost of capital is 13 percent, what is the net present value of selecting a new machine?

What is the internal rate of return?

Should the project be accepted? Why?

12-18.

Solution:

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Chapter 12: The Capital Budgeting Decision

a. Net Present Value Year 1 2 3 4 5

Cash Flow × 13% PVIF $23,000 0.885 26,000 0.783 29,000 0.693 15,000 0.613 8,000 0.543

Present Value $20,355 20,358 20,097 9,195 4,344

Present Value of Inflows Present Value of Outflows Net Present Value

$74,349 –60,000 $14,349

b. Internal Rate of Return We will average the inflows to arrive at an assumed annuity. $23,000 26,000 29,000 15,000 8,000 $101,000/5 = $20,200 We divide the investment by the assumed annuity value. $60, 000  2.97 PVIFA $20, 200

Using Appendix D for n = 5, 20 percent appears to be a reasonable first approximation (2.991). We try 20 percent. Year 1 2 3 4

Cash Flow × 20% PVIF $23,000 0.833 26,000 0.694 29,000 0.579 15,000 0.482

Present Value $19,159 18,044 16,791 7,230

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Chapter 12: The Capital Budgeting Decision

8,000 0.402 Present Value of Inflows

3,216 $64,440

Since 20 percent is not high enough, we try the next highest rate at 25 percent.

Year 1 2 3 4 5

Cash Flow × 25% PVIF $23,000 0.800 26,000 0.640 29,000 0.512 15,000 0.410 8,000 0.328 Present Value of Inflows

Present Value $18,400 16,640 14,848 6,150 2,624 $58,662

The correct answer must fall between 20 and 25 percent. We interpolate. $64,440 ........... PV @ 20% 58,662 ............ PV @ 25% $ 5,778 20% 

$64,440............. PV @ 20% 60,000............. Cost $ 4,440

$4, 440 (5%)  20%  .77 (5%)  20%  3.85%  23.85% $5,778

c. The project should be accepted because the net present value is positive and the IRR exceeds the cost of capital. Calculator Solution: Find the NPV using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 60,000 +|– key, press Enter. Press down arrow, enter 23,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter.

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Chapter 12: The Capital Budgeting Decision

Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 14,356.11, which is the net present value of the project. (b) Calculator Solution: Find the IRR using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 60,000 +|– key, press the Enter key. Press down arrow, enter 23,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press IRR; calculator shows IRR = 0. Press CPT; calculator shows IRR = 23.77%, which is the IRR of the project.

19. Use of profitability index (LO12-4) You are asked to evaluate the following two projects for the Norton Corporation. Using the net present value method combined with the profitability index approach described in footnote 2 of this chapter, which project would you select? Use a discount rate of 14 percent.

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Chapter 12: The Capital Budgeting Decision

Project X (Videotapes of the Weather Report) ($20,000 Investment)

Project Y (Slow-Motion Replays of Commercials) ($40,000 investment)

Year 1 .........................

Cash Flow $10,000

Year 1...................................

Cash Flow $20,000

2 .........................

8,000

2...................................

13,000

3 .........................

9,000

3...................................

14,000

4 .........................

8,600

4...................................

16,000

12-19.

Solution: NPV for Project X Year 1 2 3 4

Cash Flow × PVIF at 14% $10,000 0.877 8,000 0.769 9,000 0.675 8,600 0.592

Present Value $ 8,770 6,152 6,075 5,091

Present Value of Inflows $26,088 Present Value of Outflows (Cost) –20,000 Net Present Value $ 6,088 Pr ofitability index (X )  

Present value of inflows Pr esent value of outflows $26,088  1.30 $20,000

NPV for Project Y Year 1 2 3 4

Cash Flow × PVIF at 14% $20,000 0.877 13,000 0.769 14,000 0.675 16,000 0.592

Present Value $ 17,540 9,997 9,450 9,472

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Chapter 12: The Capital Budgeting Decision

Present Value of Inflows $46,459 Present Value of Outflows (Cost) –40,000 Net Present Value $ 6,459 Pr ofitability index (Y )  

Present value of inflows Pr esent value of outflows $46,459  1.16 $40,000

You should select Project X because it has the higher profitability index. This is true in spite of the fact that it has a lower net present value. The profitability index may be appropriate when you have different size investments.

Calculator Solution: (a) Find NPV using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 20,000 +|– key, press the Enter key. Press down arrow, enter 10,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 9,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 8,600, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; the calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 6,094.30, which is the net present value of Project X. Profitability index using a financial calculator: Profitability Index = Present Value of Inflows / Present Value of Outflows Present Value of Inflows = NPV + Outflows = 6,094.30 + 40,000 = $26,094.30

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Chapter 12: The Capital Budgeting Decision

Profitability Index = 26,094.30/40,000 = 1.30 (b) Find NPV using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 40,000 +|– key, press the Enter key. Press down arrow, enter 20,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 13,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 14,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 8,771.93, which is the net present value of Project Y. Profitability Index Using Financial Calculator: Profitability Index = Present Value of Inflows / Present Value of Outflows Present Value of Inflows = NPV + Outflows = 8,771.93 + 40,000 = $46,469.82 Profitability Index = $46,469.82/40,000 = 1.16

20. Reinvestment rate assumption in capital budgeting (LO12-4) Turner Video will invest $76,344 in a project. The firm’s cost of capital is 10 percent. The investment will provide the following inflows: Year 1 ................. 2 ................. 3 ................. 4 ................. 5 .................

Inflow $15,000 17,000 21,000 25,000 29,000

The internal rate of return is 11 percent.

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Chapter 12: The Capital Budgeting Decision

If the reinvestment assumption of the net present value method is used, what will be the total value of the inflows after five years? (Assume the inflows come at the end of each year.)

If the reinvestment assumption of the internal rate of return method is used, what will be the total value of the inflows after five years?

Generally is one investment assumption likely to be better than another?

12-20.

Solution: a. Reinvestment assumption of NPV Year 1 2 3 4 5

Inflows $15,000 17,000 21,000 25,000 29,000

Rate 10% 10% 10% 10% –

No. of Future Periods Value Factor Value 4 1.464 $21,960 3 1.331 22,627 2 1.210 25,410 1 1.100 27,500 0 1.000 29,000 $126,497

b. Reinvestment assumption of IRR

Year 1 2 3 4 5

Inflows $15,000 17,000 21,000 25,000 29,000

Rate 11% 11% 11% 11% –

No. of Future Periods Value Factor Value 4 1.518 $ 22,770 3 1.368 23,256 2 1.232 25,872 1 1.110 27,750 0 1.000 29,000

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$128,648 c. No. However, for investments with a very high IRR, it may be unrealistic to assume that reinvestment can take place at an equally high rate. The net present value method makes the more conservative assumption of reinvestment at the cost of capital. (a) Calculator Solution: Find PV of cash inflow using a financial calculator at 10 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 0, press the Enter key. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 17,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 21,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 78,545.62, which is the present value of the inflow. Next, find the FV of the 78,545.62 as of year 5 at a 10 percent annual rate.

I/Y

PMT

78,545.62

CPT FV - 126,498.50

Answer:

$126,498.50

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Chapter 12: The Capital Budgeting Decision

(b) Calculator Solution: Find PV of cash inflow using a financial calculator at 11 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 0, press the Enter key. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 17,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 21,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 76,344.48, which is the present value of the inflow. Next, find the FV of the 76,344.48 as of year 5 at an 11 percent annual rate.

I/Y

PMT

76,344.48

CPT FV - 128,644.88

Answer: $128,644.88

21. Modified internal rate of return (LO12-4) The Caffeine Coffee Company uses the modified internal rate of return. The firm has a cost of capital of 11 percent. The project being analyzed is as follows ($26,000 investment): Year 1 ............ 2 ............

Cash Flow $12,000 11,000

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Chapter 12: The Capital Budgeting Decision

3 ............

9,000

What is the modified internal rate of return? An approximation from Appendix B is adequate. (You do not need to interpolate.)

Assume the traditional internal rate of return on the investment is 17.5 percent. Explain why your answer in part a would be lower.

12-21.

Solution:

Terminal Value (end of year 3) a.

Year 1 Year 2 Year 3

Period of Growth $12,000 2 11,000 1 9,000 0

FV Factor (11%) (Appendix A) 1.232 1.110 1.000 Terminal Value

Future Value $14,784 12,210 9,000 $35,994

To determine the modified internal rate of return, calculate the yield on the investment. PVIF  =

PV  (Appendix B) FV $26, 000  .722 35,994

Use Appendix B for three periods, the answer is approximately 11 percent (0.731). b. The answer is lower than 17.5 percent under the Modified IRR because inflows are reinvested at the cost of capital of 11 percent. Under the traditional IRR, inflows are reinvested at the internal rate of return of 17.5 percent, which leads to a higher terminal value. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 12: The Capital Budgeting Decision

Calculator Solution: Using a financial calculator: Find the PV of cash inflow using a financial calculator at 11 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, 0, press the Enter key. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 11,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 9,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 11 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 26,319.38, which is the present value of the inflow. Next find the FV of the 26,319.38 as of year 3 at an 11 percent annual rate. (a) N 3 Answer: $35,995.20

I/Y 11

PV 26,319.38

PMT 0

FV CPT FV 35,995.20

Next, find the discount rate that produces a PV of 26,000. N 3

I/Y CPT I I/Y 11.45

PV 26,000

PMT 0

FV –35,995.20

Answer: MIRR = 11.45

22. Capital rationing and mutually exclusive investments (LO12-4) The Suboptimal Glass Company uses a process of capital rationing in its decision making. The firm’s cost of capital is 10 percent. It will only invest $77,000 this year. It has determined the internal rate of return for each of the following projects.

Project

Project Size

Internal Rate of Return

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Chapter 12: The Capital Budgeting Decision

A ..................... B ..................... C ..................... D ..................... E ..................... F ...................... G .....................

$10,500 30,500 25,500 10,500 10,500 20,500 10,500

21% 22 18 13 20 11 16

Select the projects that the firm should accept.

If Projects A and B are mutually exclusive, how would that affect your overall answer? That is, which projects would you accept in spending the $77,000?

12-22.

Solution: You should rank the investments in terms of IRR.

Project B A E C G D F

IRR 22% 21 20 18 16 13 11

Project Size $30,500 10,500 10,500 25,500 10,500 10,500 20,500

Total Budget $ 30,500 41,000 51,500 77,000 87,500 98,000 118,500

a. Because of capital rationing, only $77,000 worth of projects can be accepted. The four projects to accept are B, A, E, and C. Projects G and D provide positive benefits also, but cannot be undertaken under capital rationing. b. If Projects A and B are mutually exclusive, you would select Project B in preference to A. You would then include Project G with the freed up funds. In summary, you would accept B, E, C, and G. The last project would replace A and is of the same $10,500 magnitude.

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Chapter 12: The Capital Budgeting Decision

23. MACRS depreciation and cash flow (LO12-2) Telstar Communications is going to purchase an asset for $380,000 that will produce $180,000 per year for the next four years in earnings before depreciation and taxes. The asset will be depreciated using the three-year MACRS depreciation schedule in Table 12-12. (This represents four years of depreciation based on the half-year convention.) The firm is in a 25 percent tax bracket. Fill in the schedule below for the next four years. Earnings before depreciation and taxes Depreciation Earnings before taxes Taxes Earnings after taxes + Depreciation Cash flow

12-23.

_____ _____ _____ _____ _____ _____ _____

Solution: First, determine annual depreciation.

Year 1 2 3 4

Depreciation Base $380,000 380,000 380,000 380,000

Percentage Depreciation (Table 12-12) 0.333 0.445 0.148 0.074

Annual Depreciation $ 126,540 169,100 56,240 28,120 $380,000

Then, determine the annual cash flow. Earnings before depreciation and taxes (EBDT) will be the same for each year, but depreciation and cash flow will differ. EBDT –D EBT T (25%) EAT +D

1 2 3 4 $180,000 $180,000 $180,000 $180,000 126,540 169,100 56,240 28,120 53,460 10,900 123,760 151,880 13,365 2,725 30,940 37,970 40,095 8,175 92,820 113,910 126,540 169,100 56,240 28,120

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Chapter 12: The Capital Budgeting Decision

Cash Flow

$166,635 $177,275 $149,060 $142,030

24. MACRS depreciation categories (LO12-4) Assume $65,000 is going to be invested in each of the following assets. Using Tables 12-11 and 12-12, indicate the dollar amount of the first year’s depreciation. a.

Office furniture.

Automobile.

Electric and gas utility property.

Sewage treatment plant.

12-24.

Solution: a. Office furniture – Based on Table 12-11, this falls under 7-year MACRS depreciation. Then, examining Table 12-12, the first year depreciation rate is 0.143. Thus:

$65, 000  .143  $9, 295 b. Automobile – This falls under 5-year MACRS depreciation. This first year depreciation rate is .200.

$65, 000  .200  $13, 000 c. Electric and gas utility property – This falls under 20-year MACRS depreciation. The first year depreciation rate is .038.

$65,000  .038  $2,470 d. Sewage treatment plant – This falls under 15-year MACRS depreciation. This first year depreciation rate is .050.

$65, 000  .050  $3, 250

25. MACRS depreciation and net present value (LO12-4) The Summit Petroleum Corporation will purchase an asset that qualifies for three-year MACRS depreciation. The cost is

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Chapter 12: The Capital Budgeting Decision

$160,000 and the asset will provide the following stream of earnings before depreciation and taxes for the next four years: Year 1 ................... Year 2 ................... Year 3 ................... Year 4 ...................

$70,000 85,000 42,000 40,000

The firm is in a 35 percent tax bracket and has an 8 percent cost of capital. Should it purchase the asset? Use the net present value method.

12-25.

Solution: First, determine annual depreciation.

Year 1 2 3 4

Depreciation Base $160,000 160,000 160,000 160,000

Percentage Depreciation (Table 12-12) 0.333 0.445 0.148 0.074

Annual Depreciation $53,280 71,200 23,680 11,840 $160,000

Then, determine the annual cash flow.

EBDT –D EBT T (35%)

1 $70,000 53,280 16,720 5,852

2 $85,000 71,200 13,800 4,830

3 $42,000 23,680 18,320 6,412

4 $40,000 11,840 28,160 9,856

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EAT +D Cash Flow

10,868 53,280 $64,148

8,970 71,200 $80,170

11,908 23,680 $35,588

18,304 11,840 $30,144

Then, determine the net present value. Year 1 2 3 4

Cash Flow (inflows) $64,148 80,170 35,588 30,144

PVIF at 8% 0.926 0.857 0.794 0.735

Present Value $59,401 68,706 28,257 22,156

Present Value of Inflows Present Value of Outflows Net Present Value

$178,520 160,000 $ 18,520

The asset should be purchased based on the net present value.

Calculator Solution:

(a) Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 160,000 +|–, press the Enter key. Press down arrow, enter 64,148, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 80,170, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 35,588, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 30,144, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 8 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 18,536.79, which is the NPV of the project.

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26. MACRS depreciation and net present value (LO12-4) Oregon Forest Products will acquire new equipment that falls under the five-year MACRS category. The cost is $300,000. If the equipment is purchased, the following earnings before depreciation and taxes will be generated for the next six years. Year 1 ...................... Year 2 ...................... Year 3 ...................... Year 4 ...................... Year 5 ...................... Year 6 ......................

$112,000 105,000 82,000 53,000 37,000 32,000

The firm is in a 25 percent tax bracket and has a 14 percent cost of capital. Should Oregon Forest Products purchase the equipment? Use the net present value method.

12-26.

Solution: First, determine annual depreciation.

Year 1 2 3 4 5 6

Depreciation Base $300,000 300,000 300,000 300,000 300,000 300,000

Percentage Depreciation (Table 12-12) 0.200 0.320 0.192 0.115 0.115 0.058

Annual Depreciation $ 60,000 96,000 57,600 34,500 34,500 17,400 $300,000

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Then, determine the annual cash flow.

Annual Cash Flow 1 2 3 4 5 6 EBDT $112,000 $105,000 $82,000 $53,000 $37,000 $32,000 –D 60,000 96,000 57,600 34,500 34,500 17,400 EBT 52,000 9,000 24,400 18,500 2,500 14,600 T (25%) 13,000 2,250 6,100 4,625 625 3,650 EAT 39,000 6,750 18,300 13,875 1,785 10,950 +D 60,000 96,000 57,600 34,500 34,500 17,400 Cash Flow $ 99,000 $102,750 $75,900 $48,375 $36,375 $28,350 Then, determine the net present value. Year 1 2 3 4 5 6

Cash Flow (Inflows) PVIF @ 14% $ 99,000 0.877 102,750 0.769 75,900 0.675 48,375 0.592 36,375 0.519 28,350 0.456 Present Value of Inflows Present Value of Outflows Net Present Value

Present Value $ 86,823 79,015 51,233 28,638 18,879 12,928 $277,516 300,000 ($ 22,484)

The equipment should not be purchased. Calculator Solution: Press the following keys: 2nd, CF, 2nd, CLR WORK. Calculator displays CFo, press 300,000 +|–, press the Enter key. Press down arrow, enter 99,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 102,750, and press Enter. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Press down arrow, enter 1, and press Enter. Press down arrow, enter 75,900, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 48,375, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 36,375, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 28,350, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –24,414.97, which is the NPV of the project. The equipment should not be purchased because NPV is negative.

27. MACRS depreciation and net present value (LO12-4) Universal Electronics is considering the purchase of manufacturing equipment with a 10-year midpoint in its asset depreciation range (ADR). Carefully refer to Table 12-11 to determine in what depreciation category the asset falls. (Hint: It is not 10 years.) The asset will cost $120,000, and it will produce earnings before depreciation and taxes of $37,000 per year for three years, and then $19,000 a year for seven more years. The firm has a tax rate of 25 percent. With a cost of capital of 12 percent, should it purchase the asset? Use the net present value method. In doing your analysis, if you have years in which there is no depreciation, merely enter a zero for depreciation.

12-27.

Solution: Because the manufacturing equipment has a 10-year midpoint of its asset depreciation range (ADR), it falls into the 7-year MACRS category as indicated in Table 12-11. Furthermore, we see that most types of manufacturing equipment fall into the 7-year MACRS category. With seven-year MACRS depreciation, the asset will be depreciated over eight years (based on the half-year convention). Also, we observe that the equipment will produce earnings for 10 years, so in the last 2 years there will be no depreciation write-off.

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Chapter 12: The Capital Budgeting Decision

We first determine the annual depreciation.

Year 1 2 3 4 5 6 7 8

Depreciation Base $120,000 120,000 120,000 120,000 120,000 120,000 120,000 120,000

Percentage Depreciation (Table 12-12) 0.143 0.245 0.175 0.125 0.089 0.089 0.089 0.045

Annual Depreciation $17,160 29,400 21,000 15,000 10,680 10,680 10,680 5,400 $120,000

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Chapter 12: The Capital Budgeting Decision

12-27. (Continued) Annual Cash Flow EBDT –D EBT T (25%) EAT +D Cash Flow

1 2 3 4 5 6 7 $37,000 $37,000 $37,000 $19,000 $19,000 $19,000 $19,000 17,160 29,400 21,000 15,000 10,680 10,680 10,680 $19,840 $ 7,600 $16,000 $ 4,000 $ 8,320 $ 8,320 $ 8,320 4,960 1,900 4,000 1,000 2,080 2,080 2,080 $14,880 $5,700 $12,000 $3,000 $6,240 $6,240 $6,240 17,160 29,400 21,000 15,000 10,680 10,680 10,680 $32,040 $35,100 $33,000 $18,000 $16,920 $16,920 $16,920

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8 $19,000 5,400 $13,600 3,400 $10,200 5,400 $15,600

9 $19,000 0 $19,000 4,750 $14,250 0 $14,250

10 $19,000 0 $19,000 4,750 $14,250 0 $14,250

Chapter 13: Risk and Capital Budgeting

12-27. (Continued) Next, determine the net present value. Year 1 2 3 4 5 6 7 8 9 10

Cash Flow (Inflows) $32,040 35,100 33,000 18,000 16,920 16,920 16,920 15,600 14,250 14,250

PVIF at 12% 0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404 0.361 0.322

Present Value $ 28,612 27,975 23,496 11,448 9,594 8,578 7,648 6,302 5,144 4,589

Present Value of Inflows Present Value of Outflows Net Present Value

$133,386 120,000 $ 13,386

New asset should be purchased. Calculator Solution:

Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 120,000 +|–, press the Enter key. Press down arrow, enter 32,040, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 35,100, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 33,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 18,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 16,920, and press Enter. Press down arrow, enter 3, and press Enter.

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Chapter 13: Risk and Capital Budgeting

Press down arrow, enter 15,600, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 14,250, and press Enter. Press down arrow, enter 2, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 13,370.92, which is the NPV of the project. The asset should be purchased because NPV is positive.

28. Working capital requirements in capital budgeting (LO12-4) The Spartan Technology Company has a proposed contract with the Digital Systems Company of Michigan. The initial investment in land and equipment will be $120,000. Of this amount, $70,000 is subject to fiveyear MACRS depreciation. The balance is in nondepreciable property. The contract covers six years; at the end of six years, the nondepreciable assets will be sold for $50,000. The depreciated assets will have zero resale value. The contract will require an additional investment of $55,000 in working capital at the beginning of the first year and, of this amount, $25,000 will be returned to the Spartan Technology Company after six years. The investment will produce $50,000 in income before depreciation and taxes for each of the six years. The corporation is in a 25 percent tax bracket and has a 10 percent cost of capital. Should the investment be undertaken? Use the net present value method.

12-28.

Solution: Although there are some complicated features to this problem, we are still comparing the present value of cash flows to the total initial investment. The initial investment is: Land and equipment ......... Working capital ................ Initial investment ..............

$120,000 55,000 $175,000

In computing the present value of the cash flows, we first determine annual depreciation based on a $70,000 depreciation base. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

Year 1 2 3 4 5 6

Depreciation Base $70,000 70,000 70,000 70,000 70,000 70,000

Percentage Depreciation (Table 12-12) 0.200 0.320 0.192 0.115 0.115 0.058

Annual Depreciation $14,000 22,400 13,440 8,050 8,050 4,060 $70,000

We then determine the annual cash flow. In addition to normal cash flow from operations; we also consider the funds generated in the sixth year from the sale of the nondepreciable property (land) and from the recovery of working capital. Then, determine the annual cash flow. Annual Cash Flow 1 2 3 4 5 6 EBDT $50,000 $50,000 $50,000 $50,000 $50,000 $50,000 –D 14,000 22,400 13,440 8,050 8,050 4,060 EBT 36,000 27,600 36,560 41,950 41,950 45,940 T (25%) 9,000 6,900 9,140 10,488 10,488 11,485 EAT 27,000 20,700 27,420 31,462 31,462 34,455 +D 14,000 22,400 13,440 8,050 8,050 4,060 + Sale of Non-depreciable Assets 50,000 + Recovery of Working Capital 25,000 Cash Flow $41,000 $43,100 $40,860 $39,512 $39,512 $113,515 We then determine the net present value.

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Chapter 13: Risk and Capital Budgeting

Year 1 2 3 4 5 6

Cash Flow (Inflows) PVIF @ 10% $ 41,000 0.909 43,100 0.826 40,860 0.751 39,512 0.683 39,512 0.621 113,515 0.564 Present Value of Inflows Present Value of Outflows Net Present Value

Present Value $ 37,269 35,601 30,686 26,987 24,537 64,022 $219,102 175,000 $ 44,102

The investment should be undertaken. Calculator Solution: Using a financial calculator: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 175,000 +|–, press the Enter key. Press down arrow, enter 41,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 43,100, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 40,860, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 39,512, and press Enter. Press down arrow, enter 2 and press Enter. Press down arrow, enter 113,515, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 44,188.61, which is the NPV of the project. 29. Tax losses and gains in capital budgeting (LO12-2) An asset was purchased three years ago for $120,000. It falls into the five-year category for MACRS depreciation. The firm is in a 25 percent tax bracket. Compute the following: a.

Tax loss on the sale and the related tax benefit if the asset is sold now for $15,060.

Gain and related tax on the sale if the asset is sold now for $56,060.

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Chapter 13: Risk and Capital Budgeting

12-29.

Solution: First determine the book value of the asset. Depreciation Year Base 1 $120,000 2 120,000 3 120,000 Total Depreciation to Date

Percentage Depreciation (Table 12-12) 0.200 0.320 0.192

Annual Depreciation $24,000 38,400 23,040 $85,440

Purchase Price $120,000 – Total Depreciation to Date 85,440 Book Value $ 34,560 a. $15,060 sales price Book Value Sales Price Tax Loss on the Sale

$34,560 15,060 $19,500

Tax Loss on the Sale Tax Rate Tax Benefit

$19,500 25% $ 4,875

b. $56,060 sales price Sales Price Book Value Taxable Gain Tax Rate Tax Obligation

$56,060 34,560 21,500 25% $ 5,375

30. Capital budgeting with cost of capital computation (LO12-5) DataPoint Engineering is considering the purchase of a new piece of equipment for $240,000. It has an eight-year

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Chapter 13: Risk and Capital Budgeting

midpoint of its asset depreciation range (ADR). It will require an additional initial investment of $140,000 in nondepreciable working capital. Thirty-five thousand dollars of this investment will be recovered after the sixth year and will provide additional cash flow for that year. Here is the projected income before depreciation and taxes for the next six years: Year 1...................... 2...................... 3...................... 4...................... 5...................... 6 .....................

Amount $185,000 160,000 130,000 115,000 95,000 85,000

The tax rate is 25 percent. The cost of capital must be computed based on the following (round the final value to the nearest whole number):

Debt ............................................................ Preferred stock ........................................... Common equity (retained earnings). ..........

Kd Kp Ke

Cost (aftertax) 9.5% 13.2 18.0

Weights 25% 25 50

Determine the annual depreciation schedule.

Determine annual cash flow. Include recovered working capital in the sixth year.

Determine the weighted average cost of capital.

Determine the net present value. Should DataPoint purchase the new equipment?

12-30.

Solution: a. An eight-year midpoint of the ADR leads to five-year MACRS depreciation.

Year 1 2 3

Depreciation Base $ 240,000 240,000 240,000

Percentage Depreciation (Table 12-12) 0.200 0.320 0.192

Annual Depreciation $ 48,000 76,800 46,080

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Chapter 13: Risk and Capital Budgeting

4 5 6 b.

240,000 240,000 240,000

0.115 0.115 0.058

27,600 27,600 13,920 $240,000

Annual Cash Flow 1 2 3 4 5 $185,000 $160,000 $130,000 $115,000 $95,000 48,000 76,800 46,080 27,600 27,600 $137,000 $ 83,200 $ 83,920 87,400 $67,400 34,250 20,800 20,980 21,850 16,850 102,750 62,400 12,940 65,550 50,550 48,000 76,800 46,080 27,600 27,600

6 $85,000 13,920 71,080 17,770 53,310 13,920

EBDT –D EBT T (25%) EAT +D + Recovery of Working Capital 35,000 Cash Flow $150,750 $139,200 $109,020 $ 93,150 $78,150 $102,230 c.

Weighted Average Cost of Capital Cost (aftertax) Weights Weighted Debt Kd Preferred Stock Kp Common Equity (retained earnings) Ke Weighted Average Cost of Capital

9.5% 13.2%

25% 25%

2.38% 3.30%

18.0%

50%

9.00% 14.68%

Net Present Value Year 1 2

Cash Flow (inflows) $150,750 139,200

PVIF at 15% 0.870 0.756

Present Value $131,153 105,235

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3 4 5 6

109,020 0.658 93,150 0.572 78,150 0.497 102,230 0.432 Present Value of Inflows * Present Value of Outflows Net Present Value

71,735 53,282 38,841 44,163 $444,409 380,000 $ 64,409

*This represents the $240,000 for the equipment plus the $140,000 in initial working capital. The net present value ($64,409) is positive and DataPoint Engineering should purchase the equipment. Calculator Solution:

Using a financial calculator: (d) Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 380,000 +|–, press the Enter key. Press down arrow, enter 150,750 and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 139,200, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 109,020, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 93,150, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 78,150, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 102,230, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 15 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 64,334.60, which is the NPV of the project. The net present value 64,334.60 is positive and DataPoint Engineering should purchase

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the equipment. 31. Replacement decision analysis (LO12-4) Hercules Exercise Equipment Co. purchased a computerized measuring device two years ago for $58,000. The equipment falls into the five-year category for MACRS depreciation and can currently be sold for $24,800. A new piece of equipment will cost $148,000. It also falls into the five-year category for MACRS depreciation. Assume the new equipment would provide the following stream of added cost savings for the next six years.

Year 1 ............ 2 ............ 3 ............ 4 ............ 5 ............ 6 ............

Cash Savings $62,000 54,000 52,000 50,000 47,000 36,000

The firm’s tax rate is 25 percent and the cost of capital is 12 percent. a.

What is the book value of the old equipment?

What is the tax loss on the sale of the old equipment?

What is the tax benefit from the sale?

What is the cash inflow from the sale of the old equipment?

What is the net cost of the new equipment? (Include the inflow from the sale of the old equipment.)

Determine the depreciation schedule for the new equipment.

Determine the depreciation schedule for the remaining years of the old equipment.

Determine the incremental depreciation between the old and new equipment and the related tax shield benefits.

Compute the aftertax benefits of the cost savings.

Add the depreciation tax shield benefits and the aftertax cost savings, and determine the present value.

Compare the present value of the incremental benefits (j) to the net cost of the new equipment (e). Should the replacement be undertaken?

12-31.

Solution:

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Chapter 13: Risk and Capital Budgeting

Year 1 2

Depreciation Base $58,000 58,000

Percentage Depreciation (Table 12-12) 0.200 0.320

Total Depreciation to Date

Annual Depreciation $11,600 18,560 $30,160

Purchase Price – Total Depreciation to Date Book Value

$58,000 30,160 $27,840

b. Book Value Sales Price Tax Loss on the Sale

$27,840 24,800 $ 3,040

c. Tax Loss on the Sale Tax Rate Tax Benefit

$ 3,040 25% $ 760

d. Sales Price of the Old Equipment Tax Benefit from the Sale Cash Inflow from the Sale of the Old Equipment

$ 24,800 760 $ 25,560

e. Price of the New Equipment $148,000 – Cash Inflow from the Sale of the Old Equipment 25,560 Net Cost of the New Equipment $122,440 f.

Depreciation schedule on the new equipment

Year 1 2

Depreciation Base $148,000 148,000

Percentage Depreciation (Table 12-12) 0.200 0.320

Annual Depreciation $ 29,600 47,360

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Chapter 13: Risk and Capital Budgeting

3 4 5 6

148,000 148,000 148,000 148,000

0.192 0.115 0.115 0.058

28,416 17,020 17,020 8,584 $148,000

g. Depreciation schedule for the remaining years of the old equipment

Year* 1 2 3 4

Depreciation Base $58,000 58,000 58,000 58,000

Percentage Depreciation (Table 12-12) 0.192 0.115 0.115 0.058

Annual Depreciation $11,136 6,670 6,670 3,364

* The next four years represent the last four years on the old equipment. h. Incremental depreciation and tax shield benefits (1)

Year 1 2 3 4 5 6

(2) (3) (4) Depreciation Depreciation on new on old Incremental Equipment Equipment Depreciation $29,600 $11,136 $18,464 47,360 6,670 40,690 28,416 6,670 21,746 17,020 3,364 13,656 17,020 17,020 8,584 8,584

(5) Tax Rate 0.25 0.25 0.25 0.25 0.25 0.25

(6) Tax Shield Benefits $ 4,616 10,173 5,437 3,414 4,255 2,146

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Chapter 13: Risk and Capital Budgeting

Aftertax cost savings Year 1 2 3 4 5 6

Savings $62,000 54,000 52,000 50,000 47,000 36,000

(1 – Tax Rate) 0.75 0.75 0.75 0.75 0.75 0.75

Aftertax Savings $46,500 40,500 39,000 37,500 35,250 27,000

Present value of the total incremental benefits (1)

(2) (3) (4) (5) (6) Tax Shield Present Benefits Aftertax Total Value from Cost Annual Factor Present Year Depreciation Savings Benefits 12% Value 1 $ 4,616 $46,500 $51,116 0.893 $ 45,647 2 10,173 40,500 50,673 0.797 40,386 3 5,437 39,000 44,437 0.712 31,639 4 3,414 37,500 40,914 0.636 26,021 5 4,255 35,250 39,505 0.567 22,399 6 2,146 27,000 29,146 0.507 14,777 Present Value of Incremental Benefits $180,869 k. Present Value of Incremental Benefits $180,869 Net Cost of New Equipment 122,440 Net Present Value $ 58,429 Based on the present value analysis, the equipment should be replaced. Calculator Solution:

Using a financial calculator, Press the following keys: 2nd, CF, 2nd, Clear. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

Calculator displays CF0, press 122,440 +|–, press the Enter key. Press down arrow, enter 51,116, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 50,673, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 44,437, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 40,914, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 39,505, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 29,146, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT, calculator shows NPV = 58,416.23, which is the NPV of the project. Based on the present value analysis, the equipment should be replaced.

COMPREHENSIVE PROBLEM The Woodruff Corporation purchased a piece of equipment three years ago for $230,000. It has an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for $90,000. A new piece of equipment can be purchased for $320,000. It also has an ADR of eight years. Assume the old and new equipment would provide the following operating gains (or losses) over the next six years:

1 .............. 2 .............. 3 .............. 4 .............. 5 .............. 6 ..............

New Equipment $80,000 76,000 70,000 60,000 50,000 45,000

Old Equipment $25,000 16,000 9,000 8,000 6,000 (7,000)

The firm has a 25 percent tax rate and a 9 percent cost of capital. Should the new equipment be purchased to replace the old equipment?

CP 12-1. Solution: Book Value of Old Equipment

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(ADR of 8 years indicates the use of the 5-year MACRS schedule)

Year 1 2 3

Percentage Depreciation Depreciation Annual Base (Table 12-9) Depreciation $230,000 0.200 $ 46,000 230,000 0.320 73,600 230,000 0.192 44,160 Total Depreciation to Date $163,760

Purchase Price – Total Depreciation to Date Book Value

$230,000 163,760 $ 66,240

Tax Obligation on the Sale Sales Price Book Value Taxable Gain Tax Rate Taxes

$ 90,000 66,240 23,760 25% $ 5,940

Cash Inflow from the Sale of the Old Equipment Sales Price Taxes

$90,000 5,940 $84,060

Net Cost of the New Equipment Purchase Price $320,000 – Cash Inflow from the Sale of the Old Equipment 84,060 Net Cost $235,940 Depreciation Schedule of the New Equipment (ADR of 8 years indicates the use of the 5-year MACRS schedule) © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

Year 1 2 3 4 5 6

Depreciation Base $320,000 320,000 320,000 320,000 320,000 320,000

Percentage Depreciation

Annual (Table 12-12) Depreciation 0.200 $ 64,000 0.320 102,400 0.192 61,440 0.115 36,800 0.115 36,800 0.058 18,560 $320,000

Depreciation Schedule for the Remaining Years of the Old Equipment

Year* 1 2 3

Depreciation Base $230,000 230,000 230,000

Percentage Depreciation

Annual (Table 12-12) Depreciation 0.115 $26,450 0.115 26,450 0.058 13,340

*The next three years represent the last three years of the old equipment. Incremental Depreciation and Tax Shield Benefits (1)

Year 1 2 3 4 5 6

(2) (3) (4) Depreciation Depreciation on New on Old Incremental Equipment Equipment Depreciation $ 64,000 $26,450 $37,550 102,400 26,450 75,950 61,440 13,340 48,100 36,800 36,800 36,800 36,800 18,560 18,560

(5) Tax Rate 0.25 0.25 0.25 0.25 0.25 0.25

(6) Tax Shield Benefits $9,388 18,988 12,025 9,200 9,200 4,640

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Aftertax cost savings New Old Equipment Equipment $80,000 $25,000 76,000 16,000 70,000 9,000 60,000 8,000 50,000 6,000 45,000 (7,000)

Cost Savings $55,000 60,000 61,000 52,000 44,000 52,000

(1 – Tax Rate) 0.75 0.75 0.75 0.75 0.75 0.75

Aftertax Savings $41,250 45,000 45,750 39,000 33,000 39,000

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Chapter 13: Risk and Capital Budgeting

Present value of the total incremental benefits. (1)

(2) (3) (4) (5) Tax Shield Present Benefits Aftertax Total Value from Cost Annuity Factor Year Depreciation Savings Benefits 9% 1 $9,388 $41,250 $50,638 0.917 2 18,988 45,000 63,988 0.842 3 12,025 45,750 57,775 0.772 4 9,200 39,000 48,200 0.708 5 9,200 33,000 42,200 0.650 6 4,640 39,000 43,640 0.596 Present Value of Incremental Benefits

(6)

Present Value $ 46,435 53,879 44,602 34,126 27,430 26,009 $232,480

Net Present Value Present Value of Incremental Benefits Net Cost of New Equipment Net Present Value

$232,480 235,940 ($ 3,460)

Based on the net present value analysis, the equipment should not be replaced.

Appendix 12A–Net Present Value Profile Discussion Question 12A-1.

What is the net present value profile? What three points should be determined to graph the profile? The net present value profile allows for the graphic portrayal of the net present value of a project at different discount rates. Net present values are shown along the vertical axis and discount rates are shown along the horizontal axis. The points that must be determined to graph the profile are: a. The net present value at zero discount rate.

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Chapter 13: Risk and Capital Budgeting

b. The net present value as determined by a normal discount rate. c. The internal rate of return for the investment.

Problems 12A-1. Net present value profile (LO12-4) Keller Construction is considering two new investments. Project E calls for the purchase of earthmoving equipment. Project H represents an investment in a hydraulic lift. Keller wishes to use a net present value profile in comparing the projects. The investment and cash flow patterns are as follows: Project E

Project H

($20,000 Investment)

Year Cash Flow 1 ........................... $ 5,000 2 ........................... 6,000 3 ........................... 7.000 4 ........................... 10,000

Year 1 .................................. 2 .................................. 3 ..................................

Cash Flow $16,000 5,000 4,000

Determine the net present value of the projects based on a zero percent discount rate.

Determine the net present value of the projects based on a 9 percent discount rate.

The internal rate of return on Project E is 13.25 percent, and the internal rate of return on Project H is 16.30 percent. Graph a net present value profile for the two investments similar to Figure 12A-1. (Use a scale up to $8,000 on the vertical axis, with $2,000 increments. Use a scale up to 20 percent on the horizontal axis, with 5 percent increments.)

If the two projects are not mutually exclusive, what would your acceptance or rejection decision be if the cost of capital (discount rate) is 8 percent? (Use the net present value profile for your decision; no actual numbers are necessary.)

If the two projects are mutually exclusive (the selection of one precludes the selection of the other), what would be your decision if the cost of capital is (1) 6 percent, (2) 13 percent, and (3) 18 percent? Once again, use the net present value profile for your answer.

12A-1.

Solution: a. Zero discount rate

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Project E Inflows Outflow 8,000 = ($5,000 + $6,000 + $7,000 + $10,000) – $20,000 Project H Inflows Outflow $ 5,000 = ($16,000 + $5,000 + $4,000) – $20,000

b. 9 percent discount rate Project E Year 1 2 3 4

Cash Flow $ 5,000 6,000 7,000 10,000

PVIF at 9% 0.917 0.842 0.772 0.708

Present Value of Inflows Present Value of Outflows Net Present Value

Present Value $ 4,585 5,052 5,404 7,080 $22,121 20,000 $ 2,121

Project H Year 1 2 3

Cash Flow $16,000 5,000 4,000

PVIF at 9% 0.917 0.842 0.772

Present Value $14,672 4,210 3,088

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Present Value of Inflows Present Value of Outflows Net Present Value

$21,970 20,000 $ 1,970

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Chapter 13: Risk and Capital Budgeting

c. Net Present Value Profile d. Since the projects are not mutually exclusive, they both can be selected if they have a positive net present value. At a 9 percent cost of capital, they should both be accepted. As a side note, we can see Project E is superior to Project H. e. With mutually exclusive projects, only one can be accepted. Of course, that project must still have a positive net present value. Based on the visual evidence, we see: (i) 6 percent cost of capital—select Project E (ii) 13 percent cost of capital—select Project H (iii) Do not select either project Calculator Solution:

(b) Using a financial calculator: Project E: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 20,000 +|–, press the Enter key. Press down arrow, enter 5,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 6,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 7,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 10,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 9 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 2,126.77, which is the NPV of Project E. Project H:

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Chapter 13: Risk and Capital Budgeting

Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 20,000 +|–, press the Enter key. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 5,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 4,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 9 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 1,976.03, which is the NPV of Project H.

12A-2. Net present value profile (LO12-4) Davis Chili Company is considering an investment of $35,000, which produces the following inflows: Year 1 ................. 2 ................. 3 .................

Cash Flow $16,000 15,000 12,000

You are going to use the net present value profile to approximate the value for the internal rate of return. Please follow these steps: a.

Determine the net present value of the project based on a zero discount rate.

Determine the net present value of the project based on a 10 percent discount rate.

Determine the net present value of the project based on a 15 percent discount rate (it will be negative).

Draw a net present value profile for the investment and observe the discount rate at which the net present value is zero. This is an approximation of the internal rate of return based on the interpolation procedure presented in this chapter.

12A-2.

Solution: a. NPV @ 0% discount rate Inflows Outflow $8,000 = ($16,000 + $15,000 + $12,000) – $35,000 b.

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Year 1 2 3

Cash Flow $16,000 15,000 12,000

PVIF at 10% 0.909 0.826 0.751

Present Value of Inflows Present Value of Outflows Net Present Value

Present Value $ 14,544 12,390 9,012 $35,946 35,000 $ 946

c. Year 1 2 3

Cash Flow $16,000 15,000 12,000

PVIF at 15% 0.870 0.756 0.658

Present Value of Inflows Present Value of Outflows Net Present Value

Present Value $ 13,920 11,340 7,896 $33,156 35,000 ($ 1,844)

d. Net Present Value Profile

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Calculator Solution: (b) Using a financial calculator at 10 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 35,000 +|–, press the Enter key. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 10 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 957.93, which is the NPV of the project. (c) Using a financial calculator at 20 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, press 35,000 +|–, press the Enter key. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 12,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 20 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –1,854.61, which is the NPV of the project.

Chapter 13 Risk and Capital Budgeting Discussion Questions 13-1.

If corporate managers are risk-averse, does this mean they will not take risks? Explain.

Risk-averse corporate managers are not unwilling to take risks but will require a

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Chapter 13: Risk and Capital Budgeting

higher return from risky investments. There must be a premium or additional compensation for risk taking.

13-2.

Discuss the concept of risk and how it might be measured.

Risk may be defined in terms of the variability of outcomes from a given investment. The greater the variability, the greater the risk. Risk may be measured in terms of the coefficient of variation, in which we divide the standard deviation (or measure of dispersion) by the mean. We also may measure risk in terms of beta, in which we determine the volatility of returns on an individual stock relative to a stock market index.

13-3.

When is the coefficient of variation a better measure of risk than the standard deviation?

The standard deviation is an absolute measure of dispersion, while the coefficient of variation is a relative measure and allows us to relate the standard deviation to the mean. The coefficient of variation is a better measure of dispersion when we wish to consider the relative size of the standard deviation or compare two or more investments of different size.

13-4.

Explain how the concept of risk can be incorporated into the capital budgeting process.

Risk may be introduced into the capital budgeting process by requiring higher returns for risky investments. One method of achieving this is to use higher discount rates for riskier investments. This risk-adjusted discount rate approach specifies different discount rates for different risk categories as measured by the coefficient of variation or some other factor. Other methods, such as the certainty equivalent approach, also may be used.

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Chapter 13: Risk and Capital Budgeting

13-5.

If risk is to be analyzed in a qualitative way, place the following investment decisions in order from the lowest risk to the highest risk: a. b. c. d. e. f.

New equipment New market Repair of old machinery New product in a foreign market New product in a related market Addition to a normal product line

Referring to Table 13-3, the following order would be correct: Repair of old machinery (c) New equipment (a) Addition to a normal product line (f) New product in a related market (e) New market (b) New product in a foreign market (d) 13-6.

Assume a company, correlated with the economy, is evaluating six projects, of which two are positively correlated with the economy, two are negatively correlated, and two are not correlated with it at all. Which two projects would you select to minimize the company’s overall risk?

In order to minimize risk, the firm that is positively correlated with the economy should select the two projects that are negatively correlated with the economy.

13-7.

Assume a firm has several hundred possible investments and that it wants to analyze the risk-return trade-off for portfolios of 20 projects. How should it proceed with the evaluation? The firm should attempt to construct a chart showing the risk-return characteristics for every possible set of 20. By using a procedure similar to that indicated in Figure 13-10, the best risk-return trade-offs or efficient frontier can be determined. We then can decide where we wish to be along this line.

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Chapter 13: Risk and Capital Budgeting

13-8.

Explain the effect of the risk-return trade-off on the market value of common stock. High profits alone will not necessarily lead to a high market value for common stock. To the extent large or unnecessary risks are taken, a higher discount rate and lower valuation may be assigned to our stock. Only by attempting to match the appropriate levels for risk and return can we hope to maximize our overall value in the market.

13-9.

What is the purpose of using simulation analysis? Simulation is one way of dealing with the uncertainty involved in forecasting the outcomes of capital budgeting projects or other types of decisions. A Monte Carlo simulation model uses random variables for inputs. By programming the computer to randomly select inputs from probability distributions, the outcomes generated by a simulation are distributed about a mean, and instead of generating one return or net present value, a range of outcomes with standard deviations are provided.

Problems 1.

Risk-averse (LO13-2) Assume you are risk-averse and have the following three choices. Which project will you select? Compute the coefficient of variation for each.

Expected Value $2,200 2,730 2,250

A B C

13-1.

Solution:

V  A.

$1,440/$2,200 = 0.65

1,960/2,730 = 0.72

$1,490/$2,250 = 0.66

Standard Deviation $1,400 1,960 1,490

 D

Based on the coefficient of variation, you should select Project A because it is the least risky.

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Chapter 13: Risk and Capital Budgeting

Expected value and standard deviation (LO13-1) Myers Business Systems is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given next: Possible Market Reaction

Sales in Units

Low response..................................................

0.10

Moderate response ........................................

0.30

High response .................................................

0.40

Very high response .........................................

0.20

What is the expected value of unit sales for the new product?

What is the standard deviation of unit sales?

13-2.

Probabilities

Solution: D   DP

a. D

0.10

0.30

0.40

0.20

14 50 = D



 ( D  D) P

( D  D)

( D  D) 2

( D  D) 2 P

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Chapter 13: Risk and Capital Budgeting

–30

900

0.10

–10

100

0.30

0.40

+20

400

0.20

80 210

Expected value and standard deviation (LO13-1) Sampson Corp. is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities of their occurrence are given. Possible Market Reaction

Sales in Units

Low response..................................................

0.10

Moderate response ........................................

0.20

High response ................................................

0.40

Very high response ........................................

0.30

Probabilities

What is the expected value of unit sales for the new product?

What is the standard deviation of unit sales?

13-3.

Solution: D   DP

a. D

0.10

0.20

0.40

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0.30

27 70 = D



 ( D  D) P 2

( D  D)

( D  D) 2

( D  D) 2 P

–40

1600

0.10

160

–20

400

0.20

0.40

+20

400

0.30

120 370

Coefficient of variation (LO13-1) Shack Homebuilders Limited is evaluating a new promotional campaign that could increase home sales. Possible outcomes and probabilities of the outcomes are shown next. Compute the coefficient of variation.

Additional Sales in Units Possible Outcomes Ineffective campaign ................................. 40 Normal response........................................100 Extremely effective ...................................120

13-4.

Probabilities 0.30 0.30 0.40

Solution:

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Chapter 13: Risk and Capital Budgeting

Coefficient of Variation (V) = Standard Deviation / Expected Value D   DP D P DP 40 0.30 12 100 0.30 30 120 0.40 48 90= D

 D 40 100 120

D 90 90 90

 ( D  D) P 2

( D  D) –50 +10 +30

( D  D) 2 2,500 100 900

P 0.30 0.30 0.40

( D  D) 2 P 750 30 360 1,140

1,140  33.76   33.76 V=  .375 90 5.

Coefficient of variation (LO13-1) Al Bundy is evaluating a new advertising program that could increase shoe sales. Possible outcomes and probabilities of the outcomes are shown next. Compute the coefficient of variation.

Possible Outcomes

Additional Sales in Units

Probabilities

Ineffective campaign ......................................40

0.20

Normal response ............................................60

0.50

140 Extremely effective ........................................

0.30

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Chapter 13: Risk and Capital Budgeting

13-5.

Solution: Coefficient of Variation (V) = Standard Deviation / Expected Value D   DP

0.20

0.50

140

0.30

42 80 = D



 ( D  D) P 2

D 40

D 80

( D  D) –40

( D  D) 2 1,600

P 0.20

( D  D) 2 P 320

–20

400

0.50

200

140

+60

3,600

0.30

1,080 1,600

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Chapter 13: Risk and Capital Budgeting

40  0.5 80

Coefficient of variation (LO13-1) Possible outcomes for three investment alternatives and their probabilities of occurrence are given next.

Alternative 1 Outcomes Probability Failure ............ 50 0.2 Acceptable...... 90 0.4 Successful ...... 135 0.4

Alternative 2 Outcomes Probability 90 0.3 190 0.3 225 0.4

Alternative 3 Outcomes Probability 95 0.2 215 0.6 380 0.2

Rank the three alternatives in terms of risk from lowest to highest (compute the coefficient of variation).

13-6. Alternative 1 D × P = DP

Solution: Alternative 2

Alternative 3

D × P = P

D × P = DP

$10

$90 0.3

$27

$95 0.2

$19

90 0.4

190 0.3

215 0.6

129

135 0.4

225 0.4

380 0.2

$50 0.2

D = $100

D = $174

D = $224

Standard Deviation Alternative 1 D ( D  D) D $ 50 $100 $–50 90 100 –10 135 100 +35

( D  D) 2 $2,500 100 1,225

P 0.2 0.4 0.4

( D  D) 2 P $500 40 490 $1,030

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Chapter 13: Risk and Capital Budgeting

1,030  $32.09  

Alternative 2 $ 90 190 225

$174 174 174

$–84 +16 +51

$7,056 256 2,601

0.3 0.3 0.4

$ 2,116.80 76.80 1040.40 $3,234.00

3, 234  $56.87  

Alternative 3 $ 95 215 380

$224 224 224

$–129 –9 +156

$ 16,641 81 24,336

0.2 0.6 0.2

$3,328.20 48.60 4,867.20 $8,244.00

8, 244  $90.80  

Rank by Coefficient of Variation Coefficient of Variation (V) = Standard Deviation / Expected Value V 32.09  .321 Alternative 1 100

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Chapter 13: Risk and Capital Budgeting

Alternative 2

57.00  .328 174

Alternative 3

91.00  .406 224

Coefficient of variation (LO1) Five investment alternatives have the following returns and standard deviations of returns:

Alternative A....................................... B ....................................... C ....................................... D....................................... E .......................................

Returns— Expected Value $ 5,000 4,000 4,000 8,000 10,000

Standard Deviation $1,200 600 800 3,200 900

Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.

13-7.

Solution:

Coefficient of variation (V) = Standard deviation/Mean return

A B C D E 8.

$1,200/$5,000 = 0.24 $600/$4,000 = 0.15 $800/$4,000 = 0.20 $3,200/$8,000 = 0.40 $900/$10,000 = 0.09

Ranking from lowest to highest E (0.09) B (0.15) C (0.20) A (0.24) D (0.40)

Coefficient of variation (LO13-1) Five investment alternatives have the following returns and standard deviations of returns:

Alternative

Returns: Expected Value

Standard Deviation

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Chapter 13: Risk and Capital Budgeting

A....................................... B ....................................... C ....................................... D....................................... E .......................................

$ 1,980 820 12,700 1,140 62,700

970 1,190 3,100 630 14,100

Using the coefficient of variation, rank the five alternatives from lowest risk to highest risk.

13-8.

Solution:

Coefficient of Variation (V) = Standard deviation/Expected value

A B C D E

$970/$1,980 = 0.49 $1,190/$820 = 1.45 $3,100/$12,700 = 0.24 $630/$1,140 = 0.55 $14,100/$62,700 = 0.22

Ranking from Lowest to Highest E (0.22) C (0.24) A (0.49) D (0.55) B (1.45)

Coefficient of variation and time (LO13-1) Digital Technology wishes to determine its coefficient of variation as a company over time. The firm projects the following data (in millions of dollars): Profits: Expected Value

Year

Standard Deviation

1 .........................................

$180

$62

3 .........................................

240

104

6 .........................................

300

166

9 .........................................

400

292

Compute the coefficient of variation (V) for each time period.

Does the risk (V) appear to be increasing over a period of time? If so, why might this be the case?

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Chapter 13: Risk and Capital Budgeting

13-9.

Solution: a.

Year

Profits: Expected Value

Standard Coefficient Deviation of Variation

180

0.34

240

104

0.43

300

166

0.55

400

292

0.73

b. Yes, the risk appears to be increasing over time. This may be related to the inability to make forecasts far into the future. There is more uncertainty. 10.

Risk-averse (LO13-2) Tim Trepid is highly risk-averse, while Mike Macho actually enjoys taking a risk. a.

Which one of the four investments should Tim choose? Compute coefficients of variation to help you in your choice.

Investments Buy stocks ............................. Buy bonds ............................. Buy commodity futures ......... Buy options ........................... b.

Returns: Expected Value $ 9,140 7,680 19,100 17,700

Standard Deviation $ 6,140 2,560 26,700 18,200

Which one of the four investments should Mike choose?

13-10. Solution: Coefficient of Variation (V) = Standard Deviation / Expected Value Buy Stocks

$6,140/9,140 = 0.672

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Chapter 13: Risk and Capital Budgeting

Buy Bonds Buy Commodity Futures Buy Options

$2,560/7,680 = 0.333 $26,700/19,100 = 1.398 $18,200/17,700 = 1.028

a. Tim should buy the bonds because bonds have the lowest coefficient of variation. b. Mike should buy the commodity futures because they have the highest coefficient of variation. 11.

Risk-averse (LO13-2) Mountain Ski Corp. was set up to take large risks and is willing to take the greatest risk possible. Lakeway Train Co. is more typical of the average corporation and is riskaverse. a.

Which of the following four projects should Mountain Ski Corp. choose? Compute the coefficients of variation to help you make your decision.

Which one of the four projects should Lakeway Train Co. choose based on the same criteria of using the coefficient of variation?

Year

Returns: Expected Value

Standard Deviation

A................................................... 527,000

834,000

B ................................................... 682,000

306,000

C ................................................... 74,000

135,000

140,000 D ..................................................

89,000

13-11. Solution: Coefficient of Variation (V) = Standard Deviation / Expected Value

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Chapter 13: Risk and Capital Budgeting

Project A

$834,000/527,000 = 1.58

Project B

306,000/682,000 = 0.449

Project C

135,000/74,000 = 1.82

Project D

89,000/140,000 = 0.636

a. Mountain Ski Corp should choose Project C because it has the largest coefficient of variation.

b. Lakeway Train Co. should choose Project B because it has the smallest coefficient of variation.

12.

Coefficient of variation and investment decision (LO13-1) Karamo’s Shoe Stores Inc. is considering opening an additional suburban outlet. An aftertax expected cash flow of $130 per week is anticipated from two stores that are being evaluated. Both stores have positive net present values. Which store site would you select based on the distribution of these cash flows? Use the coefficient of variation as your measure of risk.

Site A Probability 0.3 0.3 0.1 0.3

Site B Cash Flows 80 130 160 170

Probability 0.2 0.2 0.3 0.1 0.2

Cash Flows 50 80 130 180 235

13-12. Solution: Karamo’s Shoe Stores Inc. Standard Deviations of Sites A and B Site A © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

D $ 80 130 160 170

D $130 130 130 130

( D  D) $–50 –0– +30 +40

( D  D) 2 $2,500 –0– 900 1,600

P 0.3 0.3 0.1 0.3

( D  D) 2 P $750 –0– 90 480 $1,320

P 0.2 0.2 0.3 0.1 0.2

( D  D) 2 P $ 1,280 500 –0– 250 2205 $4,235

1,320  $36.33   A

Site B D $ 50 80 130 180 235

D $130 130 130 130 130

( D  D) $–80 –50 –0– +50 +105

( D  D) 2 $6,400 2,500 –0– 2,500 11,025

4, 235  $65.08   B

VA = VB =

$36.33/$130 = 0.2795 $65.08/$130 = 0.5006

Site A is the preferred site since it has the smallest coefficient of variation. Because both alternatives have the same expected value, the standard deviation alone would have been enough for a decision. A will be just as profitable as B but with less risk. 13.

Risk-adjusted discount rate (LO13-3) Waste Industries is evaluating a $70,000 project with the following cash flows: Year

Cash Flows

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Chapter 13: Risk and Capital Budgeting

1 ........................

$11,000

2 ........................

16,000

3 ........................

21,000

4 ........................

24,000

5 ........................

30,000

The coefficient of variation for the project is 0.847. Based on the following table of risk-adjusted discount rates, should the project be undertaken? Select the appropriate discount rate and then compute the net present value. Coefficient of Variation

Discount Rate

0 – 0.25....................

0.26 – 0.50 .................

0.51 – 0.75 .................

0.76 – 1.00 ...................

1.01 – 1.25 ......................

13-13. Solution: Year

Inflows

PVIF @ 14%

$11,000

0.877

$ 9,647

16,000

0.769

12,304

21,000

0.675

14,175

24,000

0.592

14,208

30,000

0.519

15,570

PV of Inflows

$65,904

Investment

70,000

NPV

$(4,096)

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Chapter 13: Risk and Capital Budgeting

Based on the negative net present value, the project should not be undertaken. Calculator solution:

Find the PV of cash inflow using a financial calculator at 14 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, enter 70,000 and press +|–, press the Enter key. Press down arrow, enter 11,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 16,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 21,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 24,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 30,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 14 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –4074.01, which is the present value of the inflow. Solution: –$4,074. Based on the negative net present value, the project should not be undertaken.

14.

Risk-adjusted discount rate (LO13-3) Dixie Dynamite Company is evaluating two methods of blowing up old buildings for commercial purposes over the next five years. Method one (implosion) is relatively low in risk for this business and will carry a 12 percent discount rate. Method two (explosion) is less expensive to perform but more dangerous and will call for a higher discount rate of 16 percent. Either method will require an initial capital outlay of $75,000. The

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Chapter 13: Risk and Capital Budgeting

inflows from projected business over the next five years are given next. Which method should be selected using net present value analysis? Years

Method 1

Method 2

1 .......................

$18,000

$20,000

2 .......................

24,000

25,000

3 .......................

34,000

35,000

4 .......................

26,000

28,000

5 .......................

14,000

15,000

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Chapter 13: Risk and Capital Budgeting

13-14. Solution: Dixie Dynamite Co. Method 1

Year

Inflows

$18,000

Method 2

PVIF @ 12%

PVIF @ 16%

Inflows

0.893

$16,074

$20,00 0

0.862

$17,24 0

24,000

0.797

19,128

25,000 0.743

18,575

34,000

0.712

24,208

35,000 0.641

22,435

26,000

0.636

16,536

28,000 0.552

15,456

14,000

0.597

7,938

15,000 0.476

7,140

PV of Inflows

$83,884

$80,84 6

Investment

–75,000

– 75,000

NPV

$ 8,884

$ 5,846

Select Method 1 Calculator solution:

Method 1: Find the PV of cash inflow using a financial calculator at 12 percent: Press the following keys: 2nd, CF, 2nd, Clear.

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Chapter 13: Risk and Capital Budgeting

Calculator displays CFo, enter 75,000 and press +|–, press the Enter key. Press down arrow, enter 18,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 24,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 34,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 26,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 14,000, and press Enter. Press down arrow, enter 1, and press Enter. Press NPV; calculator shows I = 0; enter 12 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 8,872.06, which is the present value of the inflow.

Method 2: Find the PV of cash inflow using a financial calculator at 16 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, enter 75,000 and press +|–, press the Enter key. Press down arrow, enter 20,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 25,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 35,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 28,000, and press Enter. Press down arrow, enter 1, and press Enter. Press down arrow, enter 15,000, and press Enter. Press down arrow, enter 1, and press Enter.

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Press NPV; calculator shows I = 0; enter 16 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = 5,849.32, which is the present value of the inflow.

Solution: Select Method 1

15.

Discount rate and timing (LO13-1) Fill in the following table from Appendix B. Does a high discount rate have a greater or lesser effect on long-term inflows compared to recent ones? Discount Rate Years

20%

1 ..............................

_______

10 ..............................

_______

20 ..............................

_______

13-15. Solution: Years

20%

0.952

0.833

0.614

0.162

0.377

0.026

The impact of a high discount rate is much greater on longterm value. For example, after the first year, the high rate discount value produces an answer that is 87.5 percent of the low discount rate (0.833/0.952). However, after the 20th year, the high rate discount rate is only 6.90 percent of the low discount rate (0.026/0.377).

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16.

Expected value with net present value (LO13-1) Debby’s Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost $27,900. Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby’s cost of capital is 15 percent.

Cash Flow $4,570.............. 5,550.............. 7,400.............. 9,930..............

Probability 0.1 0.3 0.4 0.2

What is the expected value of the cash flow? The value you compute will apply to each of the five years.

What is the expected net present value?

Should Debby buy the new equipment?

13-16. Solution: a. Expected Cash Flow Cash Flow $4,570 5,550 7,400 9,930

× × × ×

P 0.1 0.3 0.4 0.2

$ 457 1,665 2,960 1,986 $7,068

b. Net Present Value (Appendix D) $7,068 × 3.352 (PVIFA @ 15%, n = 5) = $23,692 Present Value of Inflows 27,900 Present Value of Outflows $(4,208) Net Present Value

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c. Debby should not buy this new equipment because the net present value is negative. Calculator solution: b. Find the PV of cash inflow using a financial calculator at 15 percent: Press the following keys: 2nd, CF, 2nd, Clear. Calculator displays CFo, enter 27,900 and press +|–, press the Enter key. Press down arrow, enter 7,068, and press Enter. Press down arrow, enter 5, and press Enter. Press NPV; the calculator shows I = 0; enter 15 and press Enter. Press down arrow; calculator shows NPV = 0.00. Press CPT; calculator shows NPV = –4,206.97 is the present value of the inflow.

Solution: –$4,207. Based on the negative net present value, the project should not be undertaken.

17.

Deferred cash flows and risk-adjusted discount rate Highland Mining and Minerals Co. is considering the purchase of two gold mines. Only one investment will be made. The Australian gold mine will cost $1,649,000 and will produce $353,000 per year in years 5 through 15 and $503,000 per year in years 16 through 25. The U.S. gold mine will cost $2,054,000 and will produce $282,000 per year for the next 25 years. The cost of capital is 13 percent. a.

Which investment should be made? (Note: In looking up present value factors for this problem, you need to work with the concept of a deferred annuity for the Australian mine. The returns in years 5 through 15 actually represent 11 years; the returns in years 16 through 25 represent 10 years.)

If the Australian mine justifies an extra 2 percent premium over the normal cost of capital because of its riskiness and relative uncertainty of cash flows, does the investment decision change?

13-17. Solution: a. Calculate the net present value for each project. The Australian Mine © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

Years

Cash Flow

n Factor

PVIFA@13%

Present Value

5–15

$353,000 (15 – 4)

(6.462 – 2.974)

$1,231,264

16–25

$503,000 (25 – 15)

(7.330 – 6.462)

$ 436,604

Present Value of Inflows

$1,667,868

Present Value of Outflows

$1,649,000

Net Present Value

$ 18,868

The U.S. Mine Years 1–25

Cash Flow $282,000

PVIFA@13% 7.330

Present Value $2,067,060

Present Value of Inflows Present Value of Outflows Net Present Value

$2,067,060 $2,054,000 $ 13,060

n Factor (25)

Select the Australian Mine. While both mines have a positive net present value, the Australian mine adds more value to the company for a smaller investment. b. Recalculate the net present value of the Australian Mine at a 15 percent discount rate. Present Years Cash Flow n Factor PVIFA @ 15% Value 5–15 $353,000 (15 – 4) (5.847 – 2.855) $ 1,056,176 16–25 $503,000 (25 – 15) (6.464 – 5.847) $ 310,351 Present Value of Inflows Present Value of Outflows

$1,366,527 $1,649,000

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Chapter 13: Risk and Capital Budgeting

Net Present Value

$ (282,473)

Now the decision should be made to reject the purchase of the Australian Mine and purchase the U.S. Mine. 18. Coefficient of variation and investment decision (LO13-1) Mrs. Dionne Jackson desires to invest a portion of her assets in rental property. She has narrowed her choices down to two apartment complexes, Palmer Heights and Crenshaw Village. After conferring with the present owners, Mrs. Jackson has developed the following estimates of the cash flows for these properties:

Palmer Heights

Crenshaw Village

Yearly Aftertax Cash Inflow (in thousands) Probability $70 ................. 0.2 75 ................. 0.2 90 ................. 0.2 105 ............... 0.2 110 ............... 0.2

Yearly Aftertax Cash Inflow (in thousands) $75................ 80................ 90................ 100..............

Find the expected cash flow from each apartment complex.

What is the coefficient of variation for each apartment complex?

Which apartment complex has more risk?

Probability 0.2 0.3 0.4 0.1

13-18. Solution: D   DP

Palmer Heights D P DP 70 0.2 $14.0 75 0.2 15.0 90 0.2 18.0 105 0.2 21.0 110 0.2 22.0 Expected Cash $90.0 Flow (thousands)

Crenshaw Village D P DP 75 0.2 $ 15.0 80 0.3 24.0 90 0.4 36.0 100 0.1 10.0 Expected Cash $85.0 Flow (thousands)

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Chapter 13: Risk and Capital Budgeting

a. First find the standard deviation and then the coefficient of variation.

V



D Palmer Heights D $70 75 90 105 110

D $90 90 90 90 90

( D  D) $–20 –15 0 +15 +20

( D  D) 2 $400 225 0 225 400

P 0.20 0.20 0.20 0.20 0.20

( D  D) 2 P 80 45 0 45 80 250

250  $15.81(thousands)  

V = $15.81/$90 = 0.176 Crenshaw Village D $75 80 90 100

D $85 85 85 85

( D  D) $–10 –5 +5 +15

( D  D) 2 $100 25 25 225

P 0.20 0.30 0.40 0.10

( D  D) 2 P 20.0 7.5 10.0 22.5 $60.0

60  $7.75 (thousands)  

V = $7.75/$85 = 0.091 b. Based on the coefficient of variation, Palmer Heights has more risk (0.176 versus 0.091). © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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19.

Decision-tree analysis (LO13-4) Jasmine’s Dresswear Manufacturers is preparing a strategy for the fall season. One alternative is to expand its traditional ensemble of wool sweaters. A second option would be to enter the cashmere sweater market with a new line of high-quality designer label products. The marketing department has determined that the wool and cashmere sweater lines offer the following probability of outcomes and related cash flows:

Expand Wool Sweaters Line

Expected Sales Fantastic .................... Moderate ................... Low ...........................

Probability 0.5 0.2 0.3

Present Value of Cash Flows from Sales $221,000 192,000 88,600

Enter Cashmere Sweaters Line Present Value of Cash Flows Probability from Sales 0.3 $341,000 0.4 272,000 0.3 0

The initial cost to expand the wool sweater line is $142,000. To enter the cashmere sweater line, the initial cost in designs, inventory, and equipment is $102,000. a.

Diagram a complete decision tree of possible outcomes similar to Table 13-6. Note that you are dealing with thousands of dollars rather than millions. Take the analysis all the way through the process of computing expected NPV (the last column for each investment).

Given the analysis in part a, would you automatically make the investment indicated?

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13-19. Solution: Jasmine’s Dresswear Manufacturers a.

Expand Wool Sweaters

Enter Cashmere Sweaters

(1)

Expected Sales Fantastic Moderate Low

Fantastic Moderate Low

(2)

(3)

Probability 0.5 0.2 0.3

Present Value of Cash Flows from Sales $221,000 192,000 88,600

0.3 0.4 0.3

$341,000 272,000 0

(4)

Initial Cost $142,000 142,000 142,000

$102,000 102,000 102,000

(5)

NPV (3) – (4) $79,000 50,000 (53,400) Expected NPV $239,000 170,000 (102,000) Expected NPV

(6) Expected NPV (2) × (5) $39,500 10,000 (16,020) $33,480 $71,700 68,000 (30,600) $109,100

b. The indicated investment, based on the expected NPV, is in the Cashmere sweater line. However, there is more risk in this alternative so further analysis may be necessary. It is not an automatic decision.

13-577

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20.

Probability analysis with a normal curve distribution (LO13-4) When returns from a project can be assumed to be normally distributed, such as those shown in Figure 13-6 (represented by a symmetrical, bell-shaped curve), the areas under the curve can be determined from statistical tables based on standard deviations. For example, 68.26 percent of the distribution will fall within one standard deviation of the expected value ( D ± 1σ). Similarly, 95.44 percent will fall within two standard deviations ( D ± 2σ), and so on. An abbreviated table of areas under the normal curve is shown next.

Number of σ’s from Expected Value 0.5....................... 1.0....................... 1.5....................... 1.65..................... 2.0 ......................

+ or – 0.1915 0.3413 0.4332 0.4505 0.4772

+ and – 0.3830 0.6826 0.8664 0.9010 0.9544

Assume Project A has an expected value of $24,000 and a standard deviation (σ) of $4,800. a.

What is the probability that the outcome will be between $16,800 and $31,200?

What is the probability that the outcome will be between $14,400 and $33,600?

What is the probability that the outcome will be at least $14,400?

What is the probability that the outcome will be less than $31,900?

What is the probability that the outcome will be less than $19,200 or greater than $26,400?

13-20. Solution: a. Expected Value = $24,000, σ = $4,800 $16,800 > $24,000 < $31,200 Expected Value ± 1.5 σ 0.8664 b. $14,400 > $24,000 < $33,600 Expected Value ± 2.0 σ 0.9544

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c. At least $14,400

$14,400 0.4772 $14, 400  $24,000 $9,600   2 $4,800 $4,800

0.5000 0.9772 Distribution under the curve

d. Less than $31,900

$31,900 0.4505 $31,900  $24,000 $7,900   1.65 $4,800 $4,800

e. Less than $19,200 or greater than $26,400

$19,200

0.5000 0.9505 Distribution under the curve

$26,400

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Chapter 13: Risk and Capital Budgeting

$19, 200  $24,000 $4,800    1 .3413 .5000  .3413 = .1587 $4,800 $4,800 $26, 400  $24,000 $2, 400 .3085   .5 .1915 .5000  .1915 = $4,800 $4,800 .4672 Distribution under the curve is 0.4672.

21.

Increasing risk over time (LO13-1) The Oklahoma Pipeline Company projects the following pattern of inflows from an investment. The inflows are spread over time to reflect delayed benefits. Each year is independent of the others.

Year 1 Cash Inflow Probability 55 .............. 0.40 70 .............. 0.20 85 .............. 0.40

Year 5 Cash Inflow 40 ....... 70 ....... 100 .......

Probability 0.30 0.40 0.30

Year 10 Cash Inflow Probability 20 ......... 0.40 70 ......... 0.20 120 ......... 0.40

The expected value for all three years is $70. a.

Compute the standard deviation for each of the three years.

Diagram the expected values and standard deviations for each of the three years in a manner similar to Figure 13-6.

Assuming 6 percent and 12 percent discount rates, complete the following table for present value factors:

Year 1 ......... 5 ......... 10 .........

PVIF 6% 0.943 ________ ________

PVIF 12% 0.893 ________ ________

Difference 0.050 ________ ________

Is the increasing risk over time, as diagrammed in part b, consistent with the larger differences in PVIFs over time, as computed in part c?

Assume the initial investment is $135. What is the net present value of the investment at a 12 percent discount rate? Should the investment be accepted?

13-21. Solution:

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Chapter 13: Risk and Capital Budgeting

a. Standard deviation—year 1 D $55 70 85

D 70 70 70

( D  D) –15 0 +15

( D  D) 2 225 0 225

P 0.40 0.20 0.40

( D  D) 2 P 90 0 90 180

P 0.30 0.40 0.30

( D  D) 2 P 270 0 270 540

P 0.40 0.20 0.40

( D  D) 2 P 1,000 0 1,000 2,000

180  13.416   Standard deviation—year 5 D 40 70 100

D 70 70 70

( D  D) –30 0 +30

( D  D) 2 900 0 900

540  23.24   Standard deviation—year 10 D 20 70 120

D 70 70 70

( D  D) –50 0 +50

( D  D) 2 2,500 0 2,500

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b. Risk over time

$80 ($80)

c. Year 1 5 10

(1) PVIF 6% 0.943 0.747 0.558

(2) PVIF 12% 0.893 0.567 0.322

(3) PVIF Difference 0.050 0.180 0.236

d. Yes. The larger risk over time is consistent with the larger differences in the present value interest factors (PVIF) over time. In effect, future uncertainty is being penalized by a lower present value interest factor (PVIF). This is one of the consequences of using progressively higher discount rates to penalize for risk. Year 1 5 10

Inflow PVIF (12%) $70 0.893 70 0.567 70 0.322 PV of Inflows

PV $ 62.51 $ 39.69 $ 22.54 $124.74

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Investment NPV

$135.00 $ 10.26

e. Accept the investment. 22.

Portfolio effect of a merger (LO13-5) Treynor Pie Company is a food company specializing in highcalorie snack foods. It is seeking to diversify its food business and lower its risks. It is examining three companies—a gourmet restaurant chain, a baby food company, and a nutritional products firm. Each of these companies can be bought at the same multiple of earnings. The following table represents information about all the companies:

Correlation with Treynor Company Pie Company Treynor Pie Company ............. + 1.0 Gourmet restaurant .................. + 0.4 Baby food company ................ + 0.3 Nutritional products company .................................. − 0.7

Sales ($ millions) $126 63 52

Expected Earnings ($ millions) $10 9 5

Standard Deviation in Earnings ($ millions) $4.0 1.4 1.6

3.2

Using the last two columns, compute the coefficient of variation for each of the four companies. Which company is the least risky? Which company is the most risky?

Discuss which of the acquisition candidates is most likely to reduce Treynor Pie Company’s risk. Explain why.

13-22. Solution: a.

Coefficient of variation (V ) 

Standard deviation Expected value

(millions) Treynor Pie Company $4/$10 Gourmet Restaurant $1.4/$9 Baby Food $1.6/$5 Nutritional Products $3.2/$7

= 0.40 = 0.16 = 0.32 = 0.46

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Chapter 13: Risk and Capital Budgeting

The Gourmet Restaurant chain is the least risky with a coefficient of variation of .16, while the nutritional products firm has the highest risk with a coefficient of variation of 0.46 b. Because the nutritional products firm is highly negatively correlated (–0.7) with Treynor Pie Company, it is most likely to reduce risk. It would appear that the demand for high-calorie snack foods moves in the opposite direction as the demand for nutritional items. Thus, Treynor Pie Company would reduce its risk to the largest extent by acquiring the company with the highest coefficient of variation (0.46) as computed in part a. This would appear to represent a paradox, but it is not. It simply reflects the fact that the interaction between two companies is much more important than the individual risk of the companies. 23.

Portfolio effect of a merger (LO13-5) Hooper Chemical Company, a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process, is examining a plastics firm to add to its operations. Before the acquisition, the normal expected outcomes for the firm were as follows: Outcomes ($ millions)

Probability

Recession .................................

$20

0.30

Normal economy .....................

0.40

Strong economy ......................

0.30

After the acquisition, the expected outcomes for the firm would be: Outcomes ($ millions)

Probability

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Chapter 13: Risk and Capital Budgeting

Recession .................................

$10

0.3

Normal economy .....................

0.4

Strong economy ......................

0.3

Compute the expected value, standard deviation, and coefficient of variation before the acquisition.

After the acquisition, these values are as follows:

Expected value .............................................

43.0 ($ millions)

Standard deviation .......................................

27.2 ($ millions)

Coefficient of variation .................................

0.633

Comment on whether this acquisition appears desirable to you. c.

Do you think the firm’s stock price is likely to go up as a result of this acquisition?

If the firm was interested in reducing its risk exposure, which of the following three industries would you advise it to consider for an acquisition? Briefly comment on your answer. (1)

Chemical company

(2)

Oil company

(3)

Computer company

13-23. Solution: D   DP

$20

0.30

0.40

0.30

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Chapter 13: Risk and Capital Budgeting

$40 ($ million)



 ( D  D) P 2

D $20

D 40

( D  D) –20

( D  D) 2 400

P 0.30

( D  D) 2 P 120

0.40

+20

400

0 .30

120 240

V = $15.5/$40 = 0.388 b. No, it does not appear to be desirable. Although the expected value is $3 million higher, the coefficient of variation is more than twice as high (0.633 versus 0.388). The slightly added return probably does not adequately compensate for the added risk.

Probably not. There may be a higher discount rate applied to the firm’s earnings to compensate for the additional risk. The stock price may actually go down.

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d. The oil company may provide the best risk reduction benefits. Since petroleum is used as part of the firm’s production process, an increase in the price of oil would normally hurt the chemical company, but this would be offset by the increased profits for the oil company. The same type of offsetting risk reduction benefits would take place if the price of oil were going down.

24.

Efficient frontier (LO13-5) Ms. Sharp is looking at a number of different types of investments for her portfolio. She identifies eight possible investments.

(a) ................. (b) ................. (c) ................. (d) .................

Return 11% 11 13 13

Risk 2% 2.5 3.0 4.2

(e) ................. (f) .................. (g) ................. (h) .................

Return 14% 16 15 18

Risk 5.0% 5.0 5.8 7.0

Graph the data in a manner similar to Figure 13-10. Use the axes that follow for your data:

Draw a curved line representing the efficient frontier.

What two objectives do points on the efficient frontier satisfy?

Is there one point on the efficient frontier that is best for all investors?

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Chapter 13: Risk and Capital Budgeting

Return

10 0

Risk (percent)

c. Achieve the highest possible return for a given risk level. Allow the lowest possible risk at a given return level. d. No. Each investor must assess his or her own preferences about their risk and return trade-off.

25.

Certainty equivalent approach (LO13-1) Sheila Goodman recently received her MBA from the Harvard Business School. She has joined the family business, Goodman Software Products Inc., as vice president of finance.

She believes in adjusting projects for risk. Her father is somewhat skeptical but agrees to go along with her. Her approach is somewhat different than the risk-adjusted discount rate approach but achieves the same objective. She suggests that the inflows for each year of a project be adjusted downward for lack of certainty and then be discounted back at a risk-free rate. The theory is that the

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Chapter 13: Risk and Capital Budgeting

adjustment penalty makes the inflows the equivalent of risk-less inflows, and therefore a risk-free rate is justified. A table showing the possible coefficient of variation for an inflow and the associated adjustment factor is shown next: Coefficient of Variation 0 – 0.25 ............... 0 .26 – 0.50 ............. 0.51 – 0.75 ............. 0.76 – 1.00 ............. 1.01 – 1.25 ..............

Adjustment Factor 0.90 0.80 0.70 0.60 0.50

Assume a $184,000 project provides the following inflows with the associated coefficients of variation for each year:

Year 1.......................... 2.......................... 3.......................... 4.......................... 5.......................... a.

Coefficient of Variation 0.12 0.28 0.45 0.79 1.15

Fill in the following table:

Year 1 .................... 2 .................... 3 .................... 4 .................... 5 .................... b.

Inflow $32,200 59,500 79,900 59,200 65,5600

Inflow $32,200 59,500 79,900 59,200 65,600

Coefficient of Variation 0.12 0.28 0.45 0.79 1.15

Adjustment Factor ____________ ____________ ____________ ____________ ____________

Adjusted Inflow ____________ ____________ ____________ ____________ ____________

If the risk-free rate is 5 percent, should this $184,000 project be accepted? Compute the net present value of the adjusted inflows.

13-25. Solution: Adjusted Inflows

Year 1 2 3

Coefficient Adjustment Adjusted Inflow of Variation Factor Inflow $32,200 0.12 0.90 $28,980 59,500 0.28 0.80 47,600 79,900 0.45 0.80 63,920

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4 5 b.

59,200 65,600

0.79 1.15

0.60 0.50

35,520 32,800

Net Present Value

Adjusted PVIF Year Inflow at 5% 1 $28,980 0.952 2 47,600 0.907 3 63,920 0.864 4 35,520 0.823 5 32,800 0.784 Present Value of Adjusted Inflows Present Value of Outflows Net Present Value

Present Value $ 27,589 43,173 55,227 29,233 25,715 $180,937 184,000 $ (3,063)

Based on the positive net present value of –$3,063, the project should not be accepted.

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Chapter 13: Risk and Capital Budgeting

COMPREHENSIVE PROBLEMS Comprehensive Problem 1.

Gibson Appliance Co. (portfolio effect of a merger) (LO13-5) Gibson Appliance Co. is a very stable billion-dollar company with a sales growth of about 7 percent per year in good or bad economic conditions. Because of this stability (a coefficient of correlation with the economy of +0.4, and a standard deviation of sales of about 5 percent from the mean), Mr. Hoover, the vice president of finance, thinks the company could absorb a small risky company that could add quite a bit of return without increasing the company’s risk much. He is trying to decide which of the two companies he will buy, using the following figures. Gibson’s cost of capital is 12 percent. Genetic Technology Co. (cost $80 million) Cash Flow for 10 Years ($ millions) Probability $2 0.2 8 0.3 16 0.2 25 0.2 40 0.1

Silicon Microchip Co. (cost $80 million) Cash Flow for 10 Years ($ millions) Probability $5 0.2 7 0.2 18 0.3 24 0.3

What is the expected cash flow from both companies?

Which company has the lower coefficient of variation?

Compute the net present value of each company.

Which company would you pick, based on the net present values?

Would you change your mind if you added the risk dimensions to the problem? Explain.

What if Genetic Technology Co. had a coefficient of correlation with the economy of –0.2, and Silicon Microchip Co. had one of +0.5? Which of these companies would give you the best portfolio effects for risk reduction?

What might be the effect of the acquisitions on the market value of Gibson Appliance Co.’s stock?

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Chapter 13: Risk and Capital Budgeting

CP 13-1

Solution:

Portfolio Effect of a Merger Gibson Appliance Co. a. Genetic Technology Co. D P DP $2 0.2 .4 8 0.3 2.4 16 0.2 3.2 25 0.2 5.0 40 0.1 4.0 Expected Value of Cash Flows

$15.0 (million)

D $5 7 18 24

Silicon Microchip Co. P DP 0.2 1.0 0.2 1.4 0.3 5.4 0.3 7.2

Expected Value of Cash Flows

$15.0 (million)

b. Coefficient of variation for Genetic Technology Co. D $2 8 16 25 40

D $15 15 15 15 15

( D  D) $–13 –7 +1 +10 +25

( D  D) 2 $169 49 1 100 625

P 0.2 0.3 0.2 0.2 0.1

( D  D) 2 P $33.8 14.7 .2 20.0 62.5 $131.2

131.2  $11.45 (million)  

Coefficient of Variation = $11.45/$15 = 0.764 (million)

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Chapter 13: Risk and Capital Budgeting

Coefficient of variation for Silicon Microchip Co. D $5 7 18 24

D $15 15 15 15

( D  D) $–103 –8 +3 +9

( D  D) 2 $100 64 9 81

P 0.2 0.2 0.3 0.3

( D  D) 2 P $20.0 12.8 2.7 24.3 $59.8

59.8  $7.73 (million)  

Coefficient of Variation = $7.73/$15 = 0.515 Silicon Microchip has a lower coefficient of variation, 0.515 < 0.764. c. For both companies, the annual expected value is $15 million for 10 years. The cost is $80 million for either company. Gibson has a cost of capital of 12 percent. $15 million × PVIFA (n = 10, i = 12%) (Appendix D) $15 × 5.650 = $84.750 PV of Inflows 80.000 PV of Outflows $ 4.750 Net Present Value (million) d. Based on present values, you could pick either company. e. The only way one will win out over the other is if risk factors are considered. Since Genetic Technology Co. has the higher coefficient of variation, we would select the lower risk company––Silicon Microchip. If Gibson Appliance Co. uses a risk-adjusted cost of capital concepts, it would use a higher cost of capital for the cash flows generated by Genetic Technology Co. and this would reduce its NPV.

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Chapter 13: Risk and Capital Budgeting

Since Gibson Appliance Co. has a correlation coefficient with the economy of +0.4, the selection of Genetic Technology Co. would offer the most risk reduction because its correlation coefficient with the economy is –0.2.

g. Because Gibson Appliance Co. is a stable billion-dollar company, this investment of $80 million would probably not have a great impact on the stock price in the short run. There could be some positive movement in the stock price if investors perceive less risk from portfolio diversification. This would be particularly true for a merger with Genetic Technology Co. You can use this question to discuss risk-return trade-offs and market reactions. Comprehensive Problem 2.

Kennedy Trucking Company (investment decision based on probability analysis) (LO13-1) Five years ago, Kennedy Trucking Company was considering the purchase of 60 new diesel trucks that were 15 percent more fuel-efficient than the ones the firm is now using. Mr. Hoffman, the president, had found that the company uses an average of 10 million gallons of diesel fuel per year at a price of $1.25 per gallon. If he can cut fuel consumption by 15 percent, he will save $1,875,000 per year (1,500,000 gallons times $1.25). Mr. Hoffman assumed that the price of diesel fuel is an external market force that he cannot control and that any increased costs of fuel will be passed on to the shipper through higher rates endorsed by the Interstate Commerce Commission. If this is true, then fuel efficiency would save more money as the price of diesel fuel rises (at $1.35 per gallon, he would save $2,025,000 in total if he buys the new trucks). Mr. Hoffman has come up with two possible forecasts shown next—each of which he feels has about a 50 percent chance of coming true. Under assumption number 1, diesel prices will stay relatively low; under assumption number 2, diesel prices will rise considerably. Sixty new trucks will cost Kennedy Trucking $5 million. Under a special provision from the Interstate Commerce Commission, the allowable depreciation will be 25 percent in year 1, 38 percent in year 2, and 37 percent in year 3. The firm has a tax rate of 40 percent and a cost of capital of 10 percent. a. First, compute the yearly expected price of diesel fuel for both assumption 1 (relatively low prices) and assumption 2 (high prices) from the forecasts that follow. Forecast for assumption 1 (low fuel prices):

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Probability (same for each year) 0.1 0.2 0.3 0.2 0.2

Price of Diesel Fuel per Gallon Year 1 Year 2 Year 3 $ 0.80 1.00 1.10 1.30 1.40

$ 0.90 1.10 1.20 1.45 1.55

$1.00 1.10 1.30 1.45 1.60

Forecast for assumption 2 (high fuel prices):

Probability (same for each year) 0.1 0.3 0.4 0.2

Price of Diesel Fuel per Gallon Year 1 Year 2 Year 3 $1.20 1.30 1.80 2.20

$1.50 1.70 2.30 2.50

$1.70 2.00 2.50 2.80

What will be the dollar savings in diesel expenses each year for assumption 1 and for assumption 2?

Find the increased cash flow after taxes for both forecasts.

Compute the net present value of the truck purchases for each fuel forecast assumption and the combined net present value (that is, weigh the NPV by 0.5).

If you were Mr. Hoffman, would you go ahead with this capital investment?

How sensitive to fuel prices is this capital investment?

CP 13-2

Solution: Investment Decision Based on Probability Analysis Kennedy Trucking Company

a. Assumption One:

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Yr.1 Yr.2 Yr.3 Probability D DP D DP D DP 0.1 $0.80 0.08 $0.90 0.09 $1.00 0.10 0.2 1.00 0.20 1.10 0.22 1.10 0.22 0.3 1.10 0.33 1.20 0.36 1.30 0.39 0.2 1.30 0.26 1.45 0.29 1.45 0.29 0.2 1.40 0.28 1.55 0.31 1.60 0.32 Expected value $1.15/gallon $1.27/gallon $1.32/gallon Assumption Two: Yr.1 Yr.2 Yr.3 Probability D DP D DP D DP 0.1 $1.20 0.12 $1.50 0.15 $1.70 0.17 0.3 1.30 0.39 1.70 0.51 2.00 0.60 0.4 1.80 0.72 2.30 0.92 2.50 1.00 0.2 2.20 0.44 2.50 0.50 2.80 0.56 Expected value $1.67/gallon $2.08/gallon $2.33/gallon

b. Assumption One:

Yr. 1 2 3

Expected Cost/Gal. $1.15 1.27 1.32

# of Gals. % Savings Without with Total Efficiency = Cost Efficiency $ Saved 10 million $11,500,000 15% $1,725,000 12,700,000 1,905,000 13,200,000 1,980,000

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Yr. 1 2 3

Expected Cost/Gal. $1.67 2.08 2.33

# of Gals. without Efficiency = 10 million

% Savings with Cost Efficiency $16,700,000 15% 20,800,000 23,300,000

Total $ Saved $2,505,000 3,120,000 3,495,000

c. First, compute annual depreciation. Then, proceed to the analysis. Year 1 Year 2 Year 3

25% × $5 mil. = 1.25 mil. 38% × $5 mil. = 1.90 mil. 37% × $5 mil. = 1.85 mil.

Total saved equals an increase in EBDT. Assumption One: Increase in EBDT – Depreciation Increase in EBT – Taxes 40 percent Increase in EAT + Depreciation Increased Cash Flow

Year 1 $1,725,000 1,250,000 475,000 190,000 285,000 1,250,000 $1,535,000

Year 2 $1,905,000 1,900,000 5,000 2,000 3,000 1,900,000 $1,903,000

Year 3 $1,980,000 1,850,000 130,000 52,000 78,000 1,850,000 $1,928,000

Year 1 $2,505,000 1,250,000 1,255,000 502,000 753,000 1,250,000 $2,003,000

Year 2 $3,120,000 1,900,000 1,220,000 488,000 732,000 1,900,000 $2,632,000

Year 3 $3,495,000 1,850,000 1,645,000 658,000 987,000 1,850,000 $2,837,000

Assumption Two: Increase in EBDT – Depreciation Increase in EBT – Taxes 40 percent Increase in EAT + Depreciation Increased Cash Flow

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Chapter 13: Risk and Capital Budgeting

d. Present Value Assumption One: Year 1 2 3

Cash Flow PVIF @ 10% $1,535,000 0.909 1,903,000 0.826 1,928,000 0.751 PV of Inflows PV of Outflows NPV

Present Value $1,395,315 1,571,878 1,447,928 $4,415,121 5,000,000 $ (584,879)

Assumption Two: Year 1 2 3

Cash Flow PVIF @ 10% $2,003,000 0.909 2,632,000 0.826 2,837,000 0.751 PV of Inflows PV of Outflows NPV

Present Value $1,820,727 2,174,032 2,130,587 $6,125,346 5,000,000 $1,125,346

Combined NPV: Outcome Assumption One Assumption Two Expected Outcome

NPV –584,879 1,125,346

Probability 0.5 –292,440 0.5 562.673 $270,233

e. Yes—The combined expected value of the outcomes is positive. f.

Quite sensitive when that many gallons are used per year. Chapter 14 Long-Term Financing

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Chapter 13: Risk and Capital Budgeting

Discussion Questions 14-1.

In addition to U.S. corporations, what government groups compete for funds in the U.S. capital markets?

The federal government, government agencies, and state and local governments all compete for funds.

14-2.

In which foreign industry has privatization been most important?

Telecommunications

14-3.

How does foreign investment help the U.S. government?

It helps finance the deficit.

14-4.

What is a key tax characteristic associated with state and local (municipal) securities?

They are tax exempt, meaning the interest paid is normally exempt from federal income taxes and from state income taxes in the state of issue.

14-5.

What are three forms of corporate securities discussed in the chapter?

Corporate bonds, preferred stock, and common stock are the three forms of corporate securities discussed in the chapter.

14-6.

Do corporations rely more on external or internal funds as sources of financing? Corporations rely more heavily on external funds as sources of financing. Sixty percent of corporate funds came from external sources during the time period under study.

14-7.

Explain the role of financial intermediaries in the flow of funds through the three-

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sector economy.

In a three-sector economy consisting of business, households, and government, financial intermediaries such as commercial banks, mutual saving banks, insurance companies, mutual funds, pension funds, and credit unions provide the mechanism for reallocating funds from one surplus sector to a deficit sector. These institutions indirectly invest excess funds in areas of the economy where funds are needed.

14-8.

What are electronic communication networks (ECNs)? Generally speaking, are they currently part of the operations of the New York Stock Exchange and the NASDAQ Stock Market? ECNs are electronic trading systems that automatically match buy and sell orders at specific prices via computers. They are now part of the operations of the two major markets (at one time they competed with them).

14-9.

Why is secondary trading in the security markets important? It provides liquidity and keeps prices competitive among alternative investments.

14-10.

How would you define efficient security markets? Markets are efficient when (1) prices adjust rapidly to new information; (2) there is a continuous market in which each successive trade is made at a price close to the previous price; and (3) the market can absorb large dollar amounts of securities without destabilizing the price.

14-11.

The efficient market hypothesis is interpreted in a weak form, a semistrong form, and a strong form. How can we differentiate its various forms? The weak form of efficient markets simply states that past price information is unrelated to future prices and that since no trends are predictable, investors cannot take advantage of them. The semistrong form states that prices reflect all public information, while the strong form states that all information, both public and private, is reflected in the stock prices.

14-12.

What was the primary purpose of the Securities Act of 1933? The primary purpose of the Securities Act of 1933 was to provide full disclosure of all pertinent information whenever a corporation sold a new issue of securities.

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Chapter 13: Risk and Capital Budgeting

14-13.

What act of Congress created the Securities and Exchange Commission? The Securities Exchange Act of 1934 created the Securities and Exchange Commission.

14-14.

What was the purpose of the Sarbanes–Oxley Act of 2002? The intent was to restore confidence in the integrity of the financial markets through insuring accuracy in financial reporting.

Chapter 15 Investment Banking: Public and Private Placement Discussion Questions 15-1.

In what way is an investment banker a risk taker?

The investment banker is a risk taker (underwriter) in that the investment banking house agrees to buy the securities from the corporation and resell them to other security dealers and the public at an agreed upon price. If they can’t sell the securities at the initial offering price, they suffer a loss.

15-2.

What is the purpose of market stabilization activities during the distribution process?

Market stabilization activities are managed in an attempt to ensure that the market price will not fall below a desired level during the distribution process. Syndicate members committed to purchasing the stock at a given price could be in trouble if there is a rapid decline in the price of the stock.

15-3.

Discuss how an underwriting syndicate decreases risk for each underwriter and at the same time facilitates the distribution process.

By forming a syndicate of many underwriters rather than just one, the overall risk is diffused and the capabilities for widespread distribution are enhanced. A syndicate may comprise as few as two or as many as 50 investment banking houses.

15-4.

Discuss the reason for the differences between underwriting spreads for stocks and bonds.

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Chapter 13: Risk and Capital Budgeting

Common stocks often carry a larger underwriting spread than bonds because the market reaction to stocks is more uncertain.

15-5.

What is shelf registration? How does it differ from the traditional requirements for security offerings?

Shelf registration permits large companies to file one comprehensive registration statement (under SEC Rule 415). This statement outlines the firm’s plans for future long-term financing. Then, when market conditions appear to be appropriate, the firm can issue the securities without further SEC approval. Shelf registration is different from the traditional requirement that security issuers file a detailed registration statement for SEC review and approval each and every time they plan a sale.

15-6.

Discuss the benefits accruing to a company that is traded in the public securities markets.

The benefits of having a publicly traded security are: a. Greater ability to raise capital. b. Additional prestige and visibility that can be helpful in bank negotiations, executive recruitment, and the marketing of products. c. Increased liquidity for existing stockholders. d. Ease in estate planning for existing stockholders. e. An increased capability to engage in the merger and acquisition process.

15-7.

What are the disadvantages to being public?

The disadvantage of being public are: a. All information must be made available to the public through SEC and state filings. This can be very expensive for a small company. b. The president must be a public relations representative to the investment community. c. Tremendous pressure is put on the firm for short-term performance. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

d. Large downside movement in the stock can take place in a bear market. e. The initial cost of going public can be very expensive for a small firm. f. There are high reporting compliance costs. 15-8.

If a company was looking for capital by way of a private placement, where would it look for funds?

Funds for private placement can be found through insurance companies, pension funds, mutual funds, and wealthy individuals.

15-9.

How does a leveraged buyout work? What does the debt structure of the firm normally look like after a leveraged buyout? What might be done to reduce the debt?

The use of a leveraged buy-out implies that either management or some other investor group borrows the needed cash to repurchase all the shares of the company. After the repurchase, the company exits with a lot of debt and heavy interest expense. To reduce the debt load, assets may be sold off to generate cash. Also, returns from asset sales may be redeployed into higher return areas.

15-10.

How might a leveraged buyout eventually lead to high returns for companies?

Companies may restructure their companies and once again take them public at a large profit.

15-11.

What is privatization?

In the international markets, investment bankers sell companies to the public that were previously owned by the government. Since the new owners are the private sector rather than the public sector, the process of distributing the shares to the private sector is called privatization.

Problems 1.

Dilution effect of stock issue (LO15-3) Louisiana Timber Company currently has 3 million shares of stock outstanding and will report earnings of $6.5 million in the current year. The company is

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Chapter 13: Risk and Capital Budgeting

considering the issuance of 2 million additional shares that will net $34 per share to the corporation. a. What is the immediate dilution potential for this new stock issue? b. Assume the Louisiana Timber Company can earn 11.6 percent on the proceeds of the stock issue in time to include it in the current year’s results. Should the new issue be undertaken based on earnings per share?

15-1. Solution: a. Earnings per share before stock issue $6,500,000/3,000,000 = $2.17 Earnings per share after stock issue $6,500,000/5,000,000 = $1.30 Dilution

$2.17 – 1.30 $ 0.87 per share

b. Net income = $6,500,000 + 0.116 (2,000,000  $34) = $6,500,000 + 0.116 ($68,000,000) = $6,500,000 + $7,888,000 = $14,388,000 Earnings per share after additional income EPS

= $14,388,000/5,000,000 = $2.88

Yes, the EPS of $2.88 is higher than $2.17.

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Chapter 13: Risk and Capital Budgeting

Dilution effect of stock issue (LO15-3) The Hamilton Corporation Company has 4 million shares of stock outstanding and will report earnings of $6,910,000 in the current year. The company is considering the issuance of 1 million additional shares that can only be issued at $30 per share.

a. Assume the Hamilton Corporation Company can earn 7.00 percent on the proceeds. Calculate the earnings per share. b. Should the new issue be undertaken based on earnings per share?

15-2. Solution: a. Earnings per share before stock issue $6,910,000/4,000,000 = $1.73 b. Net income = $6,910,000 + 0.070 (1,000,000  $30) = $6,910,000 + 0.070 ($30,000,000) = $6,910,000 + $2,100,000 = $9,010,000 Earnings per share after additional income EPS = $9,010,000/5,000,000 = $1.80 Yes, EPS would increase by 7 cents from $1.73 to $1.80.

Dilution effect of stock issue (LO15-3) American Health Systems currently has 6,400,000 shares of stock outstanding and will report earnings of $10 million in the current year. The company is considering the issuance of 1,700,000 additional shares that will net $30 per share to the corporation.

a. What is the immediate dilution potential for this new stock issue? b. Assume that American Health Systems can earn 9 percent on the proceeds of the stock issue in time to include them in the current year’s results. Calculate earnings per share. Should the new issue be undertaken based on earnings per share?

15-3. Solution: a. Earnings per share before stock issue $10,000,000/6,400,000 = $1.56

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Chapter 13: Risk and Capital Budgeting

Earnings per share after stock issue $10,000,000/8,100,000 = $1.23 Dilution

$1.56 1.23 $0.33 per share

b. Net income = $10,000,000 + 0.09 (1,700,000  $30) = $10,000,000 + 0.09 ($51,000,000) = $10,000,000 + $4,590,000 = $14,590,000 Earnings per share after additional income EPS = $14,590,000/8,100,000 = $1.80 Yes, the EPS of $1.80 is higher than $1.56 4.

Dilution effect of stock issue (LO15-3) American Health Systems has 6,400,000 shares of stock outstanding and will report earnings of $10 million in the current year. The company is considering the issuance of 1,700,000 additional shares, which can only be issued at $18 per share.

a. Assume that American Health Systems can earn 6 percent on the proceeds. Calculate earnings per share. b. Should the new issue be undertaken based on earnings per share?

15-4. Solution: a. Earnings per share before stock issue $10,000,000/6,400,000 = $1.56 b. Net income = $10,000,000 + 0.06 (1,700,000  $18) = $10,000,000 + 0.06 ($30,600,000) = $10,000,000 + $1,836,000 = $11,836,000

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Chapter 13: Risk and Capital Budgeting

Earnings per share after additional income EPS = $11,836,000/8,100,000 = $1.46 No, the EPS of $1.46 is lower than $1.56. 5.

Dilution and pricing effect of stock issue (LO15-3) Jordan Broadcasting Company is going public at $50 net per share to the company. There also are founding stockholders that are selling part of their shares at the same price. Prior to the offering, the firm had $26 million in earnings divided over 11 million shares. The public offering will be for 5 million shares; 3 million will be new corporate shares and 2 million will be shares currently owned by the founding stockholders.

a. What is the immediate dilution based on the new corporate shares that are being offered? b. If the stock has a P/E of 30 immediately after the offering, what will the stock price be? c. Should the founding stockholders be pleased with the $50 they received for their shares?

15-5. Solution: a. Earnings per share before stock issue $26,000,000/11,000,000 = $2.36 Earnings per share after stock issue $26,000,000/14,000,000 = $1.86 Dilution

$2.36 1.86 $0.50 per share

Note only three million new corporate shares were issued. The other two million belonged to founding stockholders and do not increase the number of shares outstanding. b. EPS P/E Stock Price

$ 1.86  30 $55.80

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c. The founding stockholders will probably not be pleased. They received a net price of $50 and the stock has a value of $55.80 immediately after the offering. They may wish the initial offering price had been higher. 6.

Underwriting Spread (LO15-2) Solar Energy Corp. has $4 million in earnings with four million shares outstanding. Investment bankers think the stock can justify a P/E ratio of 21. Assume the underwriting spread is 5 percent. What should the price to the public be?

15-6.

Solution:

Earnings per share = $4 million / 4 million = $1.00 Stock price (prior to underwriting spread) P/E  EPS = 21  $1.00 = $21 Price to public (with 5% spread) $21  95% = $19.95 7.

Underwriting Spread (LO15-2) Tiger Golf Supplies has $23 million in earnings with 8 million shares outstanding. Its investment banker thinks the stock should trade at a P/E ratio of 31. Assume there is an underwriting spread of 2.5 percent. What should the price to the public be?

15-7.

Solution:

Earnings per share = $23 million / 8 million = $2.88 Price to the public (prior to underwriting spread) P/E  EPS = 31  $2.88 = $89.28 Proceeds to the firm (with 2.5% spread) $89.28  97.5% = $87.05

Underwriting Spread (LO15-2) Assume Sybase Software is thinking about three different size offerings for issuance of additional shares.

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Size of Offer

Public Price

Net to Corporation

a. 1.1 million ...........

$30

$27.50

b. 7.0 million ...........

$30

28.44

c. 28.0 million .........

$30

29.15

What is the percentage underwriting spread for each size offer?

15-8. Solution: a. Spread = $30 – $27.50 = $2.50 (on $1.1 million) % underwriting spread = $2.50/$30 = 8.33% b. Spread = $30 – $28.44 = $1.56 (on $7.0 million) % underwriting spread = $1.56/$30 = 5.20% c.

Spread = $30 – $29.15 = $0.85 (on $28 million) % underwriting spread = $0.85/$30 = 2.83%

Underwriting spread (LO15-2) Walton and Company is the managing investment banker for a major new underwriting. The price of the stock to the investment banker is $23 per share. Other syndicate members may buy the stock for $24.25. The price to the selected dealers group is $24.80, with a price to brokers of $25.20. Finally, the price to the public is $29.50.

a. If Walton and Company sells its shares to the dealer group, what will the percentage return be? b. If Walton and Company performs the dealer’s function also and sells to brokers, what will the percentage return be? c. If Walton and Company fully integrates its operation and sells directly to the public, what will its percentage return be?

15-9. Solution: a. $24.80 23.00 $ 1.80

Selected Dealer Group’s Price Managing Investing Banker’s Price Differential

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Chapter 13: Risk and Capital Budgeting

$ 1.80 $23.00 b. $25.20 23.00 $2.20 $ 2.20 23.00 c. $29.50 23.00 $ 6.50 $ 6.50 23.00

10.

= 7.83% Return Broker’s Price Managing Investing Banker’s Price Differential = 9.57% Return Public Price Managing Investing Banker’s Price Differential = 28.26% Return

Underwriting spread (LO15-2) The Wrigley Corporation needs to raise $44 million. The investment banking firm of Tinkers, Evers, & Chance will handle the transaction.

a. If stock is utilized, 2,300,000 shares will be sold to the public at $20.50 per share. The corporation will receive a net price of $19 per share. What is the percentage underwriting spread per share? b. If bonds are utilized, slightly over 43,700 bonds will be sold to the public at $1,009 per bond. The corporation will receive a net price of $994 per bond. What is the percentage of underwriting spread per bond? (Relate the dollar spread to the public price.) c. Which alternative has the larger percentage of spread? Is this the normal relationship between the two types of issues?

15-10. Solution: a. Spread = $20.50 – $19.00 = $1.50 % underwriting spread = $1.50/$20.50 = 7.32% b. Spread = $1,009 – $994 = $15 % underwriting spread = $15/$1,009 = 1.49% © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

c. The stock alternative has the larger percentage spread. This is normal because there is more uncertainty in the market associated with a stock offering and investment bankers want to be appropriately compensated.

11.

Secondary offering (LO15-2) Kevin’s Bacon Company Inc. has earnings of $9 million with 2,100,000 shares outstanding before a public distribution. Seven hundred thousand shares will be included in the sale, of which 400,000 are new corporate shares, and 300,000 are shares currently owned by Ann Fry, the founder and CEO. The 300,000 shares that Ann is selling are referred to as a secondary offering, and all proceeds will go to her.

The net price from the offering will be $16.50, and the corporate proceeds are expected to produce $1.8 million in corporate earnings. a. What were the corporation’s earnings per share before the offering? b. What are the corporation’s earnings per share expected to be after the offering?

15-11. Solution: a. Earnings per share before the stock issue $9,000,000/2,100,000 = $4.29 b. Earnings per share after the stock issue Total Earnings Before Offering $9,000,000 Incremental Earnings 1,800,000 Earnings after Offering $10,800,000

Corporate Shares Outstanding Before Offering 2,100,000 Incremental Shares 400,000* Shares after Offering 2,500,000 * The 300,000 secondary shares are not included as new corporate shares. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting Earnings/Share = $10,800,000/2,500,000

EPS = $4.32

12.

Market stabilization and risk (LO15-2) Becker Brothers is the managing underwriter for a 1.45million-share issue by Martina’s Hamburger Heaven. Becker Brothers is “handling” 10 percent of the issue. Its price is $27 per share, and the price to the public is $28.95.

Becker also provides the market stabilization function. During the issuance, the market for the stock turns soft, and Becker is forced to purchase 50,000 shares in the open market at an average price of $27.50. It later sells the shares at an average value of $27.20. Compute Becker Brothers’ overall gain or loss from managing the issue.

15-12. Original Distribution 10%  1,450,000 =

Solution:

145,000 Shares for Becker $ 1.95 Profit per Share $282,750 Profit on Original

Distribution Market Stabilization 50,000 $ 0.30 $15,000

Shares for Becker Loss per Share ($27.20 – $27.50) Loss on Market Stabilization

Gain on Original Distribution Loss on Market Stabilization Net Gain 13.

$282,750 15,000 $ 267,750

Underwriting costs (LO15-2) Trump Card Co. will issue stock at a retail (public) price of $32. The company will receive $29.20 per share.

a. What is the spread on the issue in percentage terms? b. If the firm demands receiving a new price only $2.20 below the public price suggested in part a, what will the spread be in percentage terms? c. To hold the spread down to 2.5 percent based on the public price in part a, what net amount should Trump Card Co. receive? © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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15-13.

Solution:

a. $ Spread / Public Price = $2.80/$32 = 8.75% b. $ Spread / Public Price = $2.20/$32 = 6.88% c.

14.

Public Price $32.00 2.5% Spread 0.80 Net Amount Received$31.20

Underwriting costs (LO15-2) Winston Sporting Goods is considering a public offering of common stock. Its investment banker has informed the company that the retail price will be $19.55 per share for 580,000 shares. The company will receive $17.90 per share and will incur $165,000 in registration, accounting, and printing fees.

a. What is the spread on this issue in percentage terms? What are the total expenses of the issue as a percentage of total value (at retail)? b. If the firm wanted to net $20.42 million from this issue, how many shares must be sold?

15-14.

Solution:

a. $19.55 – $17.90 = $1.65 spread $1.65/$19.55 = 8.44% spread Total Expenses = ($1.65 × 580,000 shares) + $165,000 (out-of-pocket) = $957,000 + $165,000 = $1,122,000 Total Value = 580,000 Shares  $19.55 = $11,339,000

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Total Expenses / Total Value = $1,122,000/11,339,000 = 9.9% b. Amount Needed = $20,420,000 Total shares to be sold to net $20,420,000 = ($20,420,000 + Issue Costs) / Net Price per Share = $20,585,000/$17.90 per Share = 1,150,000 Shares 15.

P/E ratio for new public issue (LO15-2) Richmond Rent-A-Car is about to go public. The investment banking firm of Tinkers, Evers, and Chance is attempting to price the issue. The car rental industry generally trades at a 20 percent discount below the P/E ratio on the Standard & Poor’s 500 Stock Index. Assume that index currently has a P/E ratio of 25. The firm can be compared to the car rental industry as follows: Richmond

Car Rental Industry

Growth rate in earnings per share .............

15%

10%

Consistency of performance ......................

Increased earnings

4 out of 5 years

3 out of 5 years

Debt to total assets ....................................

52%

39%

Turnover of product ...................................

Slightly below

Average

average Quality of management .............................

High

Average

Assume, in assessing the initial P/E ratio, the investment banker will first determine the appropriate industry P/E based on the Standard & Poor’s 500 Index. Then, a half point will be added to the P/E ratio for each case in which Richmond Rent-A-Car is superior to the industry norm, and a half point will be deducted for an inferior comparison. On this basis, what should the initial P/E be for the firm?

15-15. Solution: 80% of the S&P 500 Stock Index = 80% × 25 = 20

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Industry Comparisons Growth rate in Earnings per Share-superior + ½ Consistency of Performance-superior

+½

Debt to Total Assets-inferior

–½

Turnover of Product-inferior

–½

Quality of Management-superior

+½

Quality of Management-superior

+½

Initial P/E Ratio = 20 + ½ = 20½

16.

Dividend valuation model for new public issue (LO15-1) The investment banking firm of Einstein & Co. will use a dividend valuation model to appraise the shares of the Modern Physics Corporation. Dividends (D1) at the end of the current year will be $1.64. The growth rate (g) is 8 percent and the discount rate (Ke) is 13 percent.

a. What should be the price of the stock to the public? b. If there is a 7 percent total underwriting spread on the stock, how much will the issuing corporation receive? c. If the issuing corporation requires a net price of $31.30 (proceeds to the corporation) and there is a 7 percent underwriting spread, what should be the price of the stock to the public? (Round to two places to the right of the decimal point.)

15-16.

Solution:

a. P0 = D1 / Ke – g = $1.64/0.13 – 0.08 = $1.64/0.05 = $32.80 b. Public Price $32.80 Underwriting Spread (7%) Net Price to the Corporation c. Necessary = Public Price

2.30 $30.50

Net Price / (1 – Underwriting Spread)

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$31.30/(1 – 0.07) = $31.30/0.93 = $33.66

17.

Comparison of private and public debt offering (LO15-1) The Landers Corporation needs to raise $1.60 million of debt on a 20-year issue. If it places the bonds privately, the interest rate will be 10 percent. Twenty thousand dollars in out-of-pocket costs will be incurred. For a public issue, the interest rate will be 9 percent, and the underwriting spread will be 2 percent. There will be $120,000 in out-of-pocket costs. Assume interest on the debt is paid semiannually, and the debt will be outstanding for the full 20-year period, at which time it will be repaid.

For each plan, compare the net amount of funds initially available—inflow—to the present value of future payments of interest and principal to determine net present value. Assume the stated discount rate is 12 percent annually. Use 6 percent semiannually throughout the analysis. (Disregard taxes.)

15-17. Solution: Private Placement $1,600,000 Debt – 20,000 Out-of-Pocket Costs $ 1,580,000 Net Amount to Landers Present value of future interest payments Interest Payments (semiannually) = 10%/2 = 5.00% Interest Payments = 5.00%  $1,600,000 = $80,000 PVA = A  PVIFA (n = 40, i = 6.0%) PVA = $80,000  15.046 PVA = $1,203,680

(Appendix D)

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PV = FV  PVIF (n = 40, i = 6.0%) PV = $1,600,000  0.097 (Appendix B) PV = $155,200 Total present value of interest and maturity payments $1,203,680 + 155,200 $1,358,880 The net present value equals the net amount to Landers minus the present value of future payments. $1,580,000 –1,358,880

Net Amount to Landers Present Value of Future Payments

$ 221,120 Net Present Value (private offering) Public Issue $1,600,000

Debt

–32,000

2% Spread

–120,000

Out-of-Pocket Costs

$1,448,000

Net Amount to Landers

Present value of future interest payments Interest Payments (semiannually) = 9%/2 = 4.50% Interest Payments = 4.50%  $1,600,000 = $72,000 PVA = A  PVIFA (n = 40, i = 6%) PVA = $72,000  15.046 (Appendix D) PVA = $1,083,312 Present value of lump-sum payment at maturity © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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PV = FV  PVIF (n = 40, i = 6%) PV = $1,600,000  0.097 (Appendix B) PV = $155,200 Total present value of interest and maturity payments $1,083,312

+ 155,200 $1,238,512 Total Present Value Net present value equals the net amount to Landers minus the present value of future payments. $1,448,000

Net Amount to Landers

–1,238,512 Present Value of Future Payments $ 209,488 Net Present Value (public offering) The private placement has the higher net present value ($221,120 versus $209,488). Calculator Solution:

Private Placement N

I/Y

PMT

CPT PV −1,359,259.25

80,000

1,600,000

Answer: $1,359,259

The net present value equals the net amount to Landers minus the present value of future payments. $ 1,580,000 –1,359,259

Net Amount to Landers Present Value of Future Payments

$ 220,741 Net Present Value (private offering)

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Public issue N

I/Y

PMT

CPT PV −1,238,888.88

72,000

1,600,000

Answer:$ 1,238,889

$ 1,448,000

Net Amount to Landers

–1,238,889 Present Value of Future Payments $ 209,111 Net Present Value (public offering) The private placement has the higher net present value ($220,741 versus $209,111).

18.

Features associated with a stock distribution (LO15-3) Midland Corporation has a net income of $19 million and 4 million shares outstanding. Its common stock is currently selling for $48 per share. Midland plans to sell common stock to set up a major new production facility with a net cost of $21,120,000. The production facility will not produce a profit for one year, and then it is expected to earn a 13 percent return on the investment. Stanley Morgan and Co., an investment banking firm, plans to sell the issue to the public for $44 per share with a spread of 4 percent.

a. How many shares of stock must be sold to net $21,120,000? (Note: No out-of-pocket costs must be considered in this problem.) b. Why is the investment banker selling the stock at less than its current market price? c. What are the earnings per share (EPS) and the price-earnings ratio before the issue (based on a stock price of $48)? What will be the price per share immediately after the sale of stock if the P/E stays constant? d. Compute the EPS and the price (if the P/E stays constant) after the new production facility begins to produce a profit. e. Are the shareholders better off because of the sale of stock and the resultant investment? What other financing strategy could the company have tried to increase earnings per share?

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Determine net price to the corporation $44.00 Public Price –1.76 4% Spread $42.24 Net Price Determine number of shares to be sold $21,120,000/$42.24 = 500,000 Shares b. The new shares will increase the total number of shares outstanding and dilute EPS. This dilution effect may reduce the stock price in the market temporarily until income from the new assets becomes included in the price the market is willing to pay for the stock. By selling at below market value, the investment banker is attempting to attract investors into this temporarily dilutive situation. The investment banking firm is also reducing its own underwriting risk by pricing the issue at the lower value. c. EPS = $19,000,000/4,000,000= $4.75 P/E Ratio = Price/EPS = $48/$4.75 = 10.11x EPS after Offering = $19,000,000/4,500,000 = $4.22 Price = P/E  EPS = 10.11  $4.22 = $42.66 d. Net income

= $19,000,000 + 13% ($21,120,000) = $19,000,000 + $2,745,600 = $21,745,600

EPS after Contribution = $21,745,600/4,500,000 = $4.83 Price = P/E  EPS = 10.11  $4.83= 48.83 e. In the long run, it appears that the company is better off because of the additional investment. Earnings per share are $.27 higher and the stock price also increased. If the firm © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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had used debt financing or a combination of debt and stock, they would have increased earnings per share even more, but would have created additional financial obligations in the process. 19.

Dilution and rates of return (LO15-3) The Presley Corporation is about to go public. It currently has aftertax earnings of $7,200,000, and 2,100,000 shares are owned by the present stockholders (the Presley family). The new public issue will represent 800,000 new shares. The new shares will be priced to the public at $25 per share, with a 5 percent spread on the offering price. There will also be $260,000 in out-of-pocket costs to the corporation.

a. b. c. d.

Compute the net proceeds to the Presley Corporation. Compute the earnings per share immediately before the stock issue. Compute the earnings per share immediately after the stock issue. Determine what rate of return must be earned on the net proceeds to the corporation so there will not be a dilution in earnings per share during the year of going public. e. Determine what rate of return must be earned on the proceeds to the corporation so there will be a 5 percent increase in earnings per share during the year of going public.

15-19. Solution: a. $25 Price  95% = $23.75 Net Price $23.75 Net Price  800,000 New Shares $19,000,000 Proceeds before Out-of-Pocket Costs – 260,000 Out-of-Pocket Costs $18,740,000 Net Proceeds b. Earnings per Share before Stock Issue = $7,200,000/2,100,000 = $3.43 c. Earnings per Share after Stock Issue = $7,200,000/2,900,000 = $2.48 d. There are now 2,900,000 shares outstanding. To maintain earnings of $3.43 per share, total earnings must be

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$9,947,000. This would imply an increase in earnings of $2,747,000 ($9,947,000 – $7,200,000). Incremental Earnings / Net Proceeds = $2,747,000/$18,740,000 = 14.66% 14.66 percent must be earned on the net proceeds to produce EPS of $3.43. e. $3.43 (1.05) = $3.60 (5.00% increase in EPS) Total Earnings = $3.60 × 2,900,000 Shares = $10,440,000 Incremental Earnings = $10,440,000 – $7,200,000 = $3,240,000 Incremental Earnings / Net Proceeds = $3,240,000 / $18,740,000 = 17.29% 17.29 percent would have to be earned to produce EPS of $3.60 and the 5 percent growth in EPS.

20.

Dilution and rates of return (LO15-3) Tyson Iron Works is about to go public. It currently has aftertax earnings of $4,400,000, and 4,200,000 shares are owned by the present stockholders. The new public issue will represent 500,000 new shares. The new shares will be priced to the public at $25 per share with a 3 percent spread on the offering price. There will also be $280,000 in out-ofpocket costs to the corporation.

a. b. c. d.

Compute the net proceeds to Tyson Iron Works. Compute the earnings per share immediately before the stock issue. Compute the earnings per share immediately after the stock issue. Determine what rate of return must be earned on the net proceeds to the corporation so there will not be a dilution in earnings per share during the year of going public. e. Determine what rate of return must be earned on the proceeds to the corporation so there will be a 10 percent increase in earnings per share during the year of going public.

15-20. Solution:

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a. $25  97% = $24.25 Net Price $24.25  500,000 $12,125,000 280,000 $11,845,000

Net Price New Shares Proceeds before Out-of-Pocket Costs Out-of-Pocket Costs Net Proceeds

b. Earnings per Share before Stock Issue = $4,400,000/4,200,000 = $1.05 c. Earnings per Share after Stock Issue = $4,400,000/4,700,000 = $0.94 d. There are now 4,700,000 shares outstanding. To maintain earnings per share of $1.05, total earnings must be $4,935,000 ($1.05  4,700,000 shares). This would imply an increase in earnings of $535,000 ($4,935,000 – $4,400,000) Incremental Earnings / Net Proceeds = $535,000/$11,845,000 = 4.52%

5 percent must be earned on the net proceeds to produce EPS of $1.05. e. $1.05 (1.10) = $1.16 (10% increase in EPS) Total Earnings = $1.16  4,700,000 = $5,452,000 Incremental Earnings = $5,452,000 – 4,400,000 = $1,052,000 Incremental Earnings / Net Proceeds = $1,052,000/$11,845,000 = 8.88% 8.88 percent would have to be earned to produce EPS of $1.16.

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21.

Aftermarket for new public issue (LO15-4) I. B. Michaels has a chance to participate in a new public offering by Hi-Tech Micro Computers. His broker informs him that demand for the 700,000 shares to be issued is very strong. His broker’s firm is assigned 25,000 shares in the distribution and will allow Michaels, a relatively good customer, 1.3 percent of its 25,000 share allocation.

The initial offering price is $30 per share. There is a strong aftermarket, and the stock goes to $32 one week after issue. The first full month after issue, Mr. Michaels is pleased to observe his shares are selling for $33.50. He is content to place his shares in a lockbox and eventually use their anticipated increased value to help send his son to college many years in the future. However, one year after the distribution, he looks up the shares in The Wall Street Journal and finds they are trading at $28.50. a. Compute the total dollar profit or loss on Mr. Michaels’ shares one week, one month, and one year after the purchase. In each case, compute the profit or loss against the initial purchase price. b. Also compute the percentage gain or loss from the initial $30 price. c. Why might a new public issue be expected to have a strong aftermarket?

15-21. Solution: a. Mr. Michaels’ Purchase = 1.3%  25,000 shares = 325 shares Dollar profit or loss 1 week325 Shares  ($32 – $30) = $650.00 Profit 1 month325 Shares  ($33.50 – $30) = $1,137.5 Profit 1 year325 Shares  ($28.50 – $30) = $487.50 Loss b. Percentage profit or loss 1 week $2.00/$30= 6.67% Gain 1 month $3.50/$30= 11.67% Gain 1 year –$1.50/$30= 5% Loss c. A new public issue may be expected to have a strong aftermarket because investment bankers often underprice the issue to ensure the success of the distribution. 22.

Leveraged buyout (LO15-5) The management of Mitchell Labs decided to go private in 2002 by buying all 2.80 million of its outstanding shares at $24.80 per share. By 2006, management had

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restructured the company by selling off the petroleum research division for $10.75 million, the fiber technology division for $8.45 million, and the synthetic products division for $20 million. Because these divisions had been only marginally profitable, Mitchell Labs is a stronger company after the restructuring. Mitchell is now able to concentrate exclusively on contract research and will generate earnings per share of $1.10 this year. Investment bankers have contacted the firm and indicated that if it reentered the public market, the 2.80 million shares it purchased to go private could now be reissued to the public at a P/E ratio of 15 times earnings per share.

a. What was the initial cost to Mitchell Labs to go private? b. What is the total value to the company from (1) the proceeds of the divisions that were sold, as well as (2) the current value of the 2.80 million shares (based on current earnings and an anticipated P/E of 15)? c. What is the percentage return to the management of Mitchell Labs from the restructuring? Use answers from parts a and b to determine this value.

15-22. Solution: a. 2.80 million Shares  $24.80 = $69.44 million (cost to go private) b. Proceeds from sale of the divisions Petroleum Research Division Fiber Technology Division Synthetic Products Division $39.20

$10.75 8.45 20.0 million

million million million

Current value of the 2.80 million shares

2.80 million shares  (P/E  EPS) 2.80 million  (15  $1.10) 2.80 million  $16.50 $46.2 Total Value to the Company $85.4

million million

Total Value to the Company – Cost to Go Private Profit from Restructuring

million million million

$85.4 69.44 $ 15.96

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Profit from Restructuring / Cost to Go Private = $15.96 million / $69.44 million = 22.98%

COMPREHENSIVE PROBLEM Bailey Corporation (impact of new public offering) (LO15-4) The Bailey Corporation, a manufacturer of medical supplies and equipment, is planning to sell its shares to the general public for the first time. The firm’s investment banker, Robert Merrill and Company, is working with Bailey Corporation in determining a number of items. Information on the Bailey Corporation follows:

BAILEY CORPORATION Income Statement For the Year 20X1 Sales (all on credit) ........................................... $42,680,000 Cost of goods sold ............................................. 32,240,000 Gross profit ....................................................... 10,440,000 Selling and administrative expenses ................. 4,558,000 Operating profit ................................................. 5,882,000 Interest expense ................................................. 600,000 Net income before taxes.................................... 5,282,000 Taxes ................................................................. 2,120,000 Net income ........................................................ $ 3,162,000

BAILEY CORPORATION Balance Sheet As of December 31, 20X1 Assets Current assets Cash.............................................................. Marketable securities ................................... Accounts receivable ..................................... Inventory ......................................................

250,000 130,000 6,000,000 8,300,000

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Total current assets .................................... Net plant and equipment ................................... Total assets ........................................................ Liabilities and Stockholders’ Equity Current liabilities: Accounts payable ......................................... Notes payable ............................................... Total current liabilities ............................. Long-term liabilities.......................................... Total liabilities .................................................. Stockholders’ equity: Common stock (1,800,000 shares at $1 par). Capital in excess of par ................................. Retained earnings .......................................... Total stockholders’ equity........................... Total liabilities and stockholders’ equity ..........

$14,680,000 13,970,000 $28,650,000

$ 3,800,000 3,550,000 7,350,000 5,620,000 $12,970,000 $ 1,800,000 6,300,000 7,580,000 15,680,000 $28,650,000

a. Assume that 800,000 new corporate shares will be issued to the general public. What will earnings per share be immediately after the public offering? (Round to two places to the right of the decimal point.) Based on the price-earnings ratio of 12, what will the initial price of the stock be? Use earnings per share after the distribution in the calculation. b. Assuming an underwriting spread of 5 percent and out-of-pocket costs of $300,000, what will net proceeds to the corporation be? c. What return must the corporation earn on the net proceeds to equal the earnings per share before the offering? How does this compare with current return on the total assets on the balance sheet? d. Now assume that, of the initial 800,000-share distribution, 400,000 belong to current stockholders and 400,000 are new shares, and the latter will be added to the 1,800,000 shares currently outstanding. What will earnings per share be immediately after the public offering? What will the initial market price of the stock be? Assume a priceearnings ratio of 12, and use earnings per share after the distribution in the calculation. e. Assuming an underwriting spread of 5 percent and out-of-pocket costs of $300,000, what will net proceeds to the corporation be? f. What return must the corporation now earn on the net proceeds to equal earnings per share before the offering? How does this compare with the current return on the total assets on the balance sheet?

CP 15-1. Solution:

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Earnings Shares $3,162,000   $1.22 2,600,000

a. Earnings per share (after)  $3,162,000 1,800,000  800,000

Initial market price  P/E  EPS  12  $1.22  $14.64 b. 800,000 shares  $14.64  $11,712,000 gross proceeds  585,600 5% spread  300,000 out-of-pocket costs $10,826, 400 net proceeds

Earnings Shares $3,162,000   $1.76 1,800,000

c. Earnings per share (before) 

In order to earn $1.76 after the offering, the return on $10,826,400 must produce new earnings equal to X.

$3,162,00  X  $1.76 1,800,000  800,000 $3,162,000  X  $1.76 (2,600,00) $3,162,000  X  $1.76 2,600,000

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Proof: $3,162,000  $1,414,000 1,800,000  800,000

thus:



$4,576,000  $1.76 2,600,000

New earnings $1,414,000   13.06% New proceeds $10,826,400

The firm must earn 13.06 percent on net proceeds to equal earnings per share before the offering. This is greater than the current return on assets of 11.04 percent. Net income $3,162,000   11.04% Total assets $28,650,000

Earnings Shares $3,162,000 $3,162,000   $1.44 1,800,000  400,000 2,200,000

d. Earnings per share (after) 

Initial market price = P/E  EPS 12  $1.44 = $17.28 e. 400,000  $17.28 = $6,912,000Gross Proceeds – 345,6005% Spread – 300,000Out-of-Pocket Costs $6,266,400Net Proceeds f. © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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$3,162,000  X  $1.76 1,800,000  400,000 $3,162,000  X  $1.76 2, 200,000 $3,162,000 + X = $1.76 (2,200,000) X = $3,872,000 – $3,162,000 X = $710,000 Proof: $3,162,000  $710,000 $3,872,000   $1.76 1,800,000  400,000 2, 200,000

thus:

New earnings $710,000   11.33% Net proceeds $6,266,400 This is greater than the current return on assets of 11.04 percent. Net income $3,162,000   11.04% Total assets $28,650,000

Chapter 16 Long-Term Debt and Lease Financing Discussion Questions 16-1.

Corporate debt has been expanding very dramatically in the last three decades. What has been the impact on interest coverage, particularly since

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1977?

In 1977, the average U.S. manufacturing corporation had its interest covered almost eight times. By the 2000s, the ratio had been cut to less than half.

16-2.

What are some specific features of bond agreements?

The bond agreement specifies such basic items as the par value, the coupon rate, and the maturity date.

16-3.

What is the difference between a bond agreement and a bond indenture?

The bond agreement covers a limited number of items, whereas the bond indenture is a supplement that often contains over 100 pages of complicated legal wording and specifies every minute detail concerning the bond issue. The bond indenture covers such topics as pledged collateral, methods of repayment, restrictions on the corporation, and procedures for initiating claims against the corporation.

16-4.

Discuss the relationship between the coupon rate (original interest rate at time of issue) on a bond and its security provisions.

The greater the security provisions afforded to a given class of bondholders, the lower the coupon rate.

16-5.

Take the following list of securities and arrange them in order of their priority of claims:

Preferred stock

Senior debenture

Subordinated debenture

Senior secured debt

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Common stock

Junior secured debt

The priority of claims can be determined from Figure 16-2:

Senior secured debt Junior secured debt Senior debenture Subordinated debenture Preferred stock Common stock

16-6.

What method of “bond repayment” reduces debt and increases the amount of common stock outstanding?

Conversion of bonds to common stock through either a convertible bond or an exchange offer.

16-7.

What is the purpose of serial repayments and sinking funds?

The purpose of serial and sinking fund payments is to provide an orderly procedure for the retirement of a debt obligation. To the extend bonds are paid off over their life, there is less risk to the security holder.

16-8.

Under what circumstances would a call on a bond be exercised by a corporation? What is the purpose of a deferred call?

A call provision may be exercised when interest rates on new securities are considerably lower than those on previously issued debt. The purpose of a © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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deferred call is to ensure that the bondholder will not have to surrender the security due to a call for at least the first 5 or 10 years.

16-9.

Discuss the relationship between bond prices and interest rates. What impact do changing interest rates have on the price of long-term bonds versus short-term bonds?

Bond prices on outstanding issues and market interest rates move in opposite directions. If interest rates go up, bond prices will go down and vice versa. Long-term bonds are particularly sensitive to interest rate changes because the bondholder is locked into the interest rate for an extended period of time.

16-10.

What is the difference between the following yields: coupon rate, current yield, and yield to maturity?

The different bond yield terms may be defined as follows:

Coupon rate – Stated interest rate divided by par value.

Current yield – Stated interest rate divided by the current price of the bond. Yield to maturity – The interest rate that will equate future interest payments and payment at maturity to a current market price. 16-11.

How does the bond rating affect the interest rate paid by a corporation on its bonds?

The higher the rating on a bond, the lower the interest payment that will be required to satisfy the bondholder.

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Chapter 13: Risk and Capital Budgeting

16-12.

Bonds of different risk classes will have a spread between their interest rates. Is this spread always the same? Why?

The spread in the yield between bonds in different risk classes is not always the same. The yield spread changes with the economy. If investors are pessimistic about the economy, they will accept as much as 3 percent less return to go into very high-quality securities, whereas in more normal times the spread may only be 1½ percent.

16-13.

Explain how the bond refunding problem is similar to a capital budgeting decision.

The bond refunding problem is similar to a capital budgeting problem in that an initial investment must be made in the form of redemption and reissuing costs, and cash inflows will take place in the form of interest savings. We take the present value of the inflows to determine if they equal or exceed the outflow.

16-14.

What cost of capital is generally used in evaluating a bond refunding decision? Why?

We use the aftertax cost of new debt as the discount rate rather than the more generalized cost of capital. Because the net cash benefits are known with certainty, the refunding decision represents a riskless investment. For this reason, we use a lower discount rate.

16-15.

Explain how the zero-coupon rate bond provides a return to the investor. What are the advantages to the corporation?

The zero-coupon-rate bond is initially sold at a deep discount from par value. The return to the investor is the difference between the investor’s cost and the face value received at the end of the life of the bond. The advantages to the corporation are that there is immediate cash inflow to

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Chapter 13: Risk and Capital Budgeting

the corporation, without any outflow until the bond matures. Furthermore, the difference between the initial bond price and the maturity value may be amortized for tax purposes over the life of the bond by the corporation.

16-16.

Explain how floating rate bonds can save the investor from potential embarrassments in portfolio valuations.

Interest payments change with changing interest rates rather than with the market value of the bond. This means that the market value of a floating rate bond is almost fixed. The one exception is when interest rates dictated by the floating rate formula approach (or exceed) broadly defined limits.

16-17.

Discuss the advantages and disadvantages of debt.

The primary advantages of debt are: a. Interest payments are tax deductible. b. The financial obligation is clearly specified and of a fixed nature. c. In an inflationary economy, debt may be paid back with cheaper dollars (the dollars have less purchasing power than when received). d. The use of debt, up to a prudent point, may lower the cost of capital to the firm.

The disadvantages are: a. Interest and principal payment obligations are set by contract and must be paid regardless of economic circumstances. b. Bond indenture agreements may place burdensome restrictions on the firm. c. Debt, utilized beyond a given point, may serve as a depressant on © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

outstanding common stock.

16-18.

What is a Eurobond?

A Eurobond is a bond payable in the borrower’s currency but sold outside the borrower’s country. It is usually sold by an international syndicate.

16-19.

What do we mean by capitalizing lease payments?

Capitalizing lease payments means computing the present value of future lease payments and showing them as an asset and liability on the balance sheet.

16-20.

Explain the close parallel between a finance lease and the borrowpurchase decision from the viewpoint of both the balance sheet and the income statement.

In both cases, we create an asset and liability on the balance sheet. Furthermore, in both cases, for income statement purposes, we amortize the asset and write off interest (implied or actual) on the debt.

Problems (Assume the par value of the bonds in the following problems is $1,000 unless otherwise specified.) 1.

Bond yields (LO16-2) The Pioneer Petroleum Corporation has a bond outstanding with an $85 annual interest payment, a market price of $800, and a maturity date in five years. Find the following:

The coupon rate.

The current rate.

The yield to maturity.

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Chapter 13: Risk and Capital Budgeting

16-1. Solution: a. $85 Interest / $1,000 Par = 8.5% Coupon rate b. $85 Interest / $800 Market price = 10.625% Current yield Calculator Solution:

I/Y

PMT

CPT I/Y 14.3788

–800

1,000

Answer: 14.38

Bond yields (LO16-2) Preston Corporation has a bond outstanding with an $80 annual interest payment, a market price of $1,250, and a maturity date in 10 years. Assume the par value of the bonds is $1,000. Find the following: a.

The coupon rate.

The current rate.

The yield to maturity.

16-2. Solution: a. $80 Interest / $1,000 Par = 8.00% Coupon rate b. $80 Interest / $1,250 Market price = 6.40% Current yield (c) N

I/Y

PMT

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Chapter 13: Risk and Capital Budgeting

CPT I/Y 4.7946

–1,250

1,000

Answer: 4.79

Bond yields (LO16-2) Harold Reese must choose between two bonds: Bond X pays $95 annual interest and has a market value of $900. It has 10 years to maturity. Bond Z pays $95 annual interest and has a market value of $920. It has 2 years to maturity. a.

Compute the current yield on both bonds.

Which bond should he select based on your answer to part a?

A drawback of current yield is that it does not consider the total life of the bond. For example, the yield to maturity on Bond X is 11.21 percent. What is the yield to maturity on Bond Z?

Has your answer changed between parts b and c of this question?

16-3. Solution: a. Bond X $95 interest / $900 market price = 10.56% current yield Bond Z $95 interest / $920 market price = 10.33% current yield

b. He should select Bond X. It has a higher current yield. (c)

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Chapter 13: Risk and Capital Budgeting

I/Y

PMT

CPT I/Y 14.38223

–920

1,000

Answer: 14.38

d. Yes. Bond Z has the higher yield to maturity. This is because the discount will be recovered over only two years. With Bond X there is a $100 discount, but a 10-year recovery period.

Bond yields (LO16-2) An investor must choose between two bonds: Bond A pays $72 annual interest and has a market value of $925. It has 10 years to maturity. Bond B pays $62 annual interest and has a market value of $910. It has two years to maturity. Assume the par value of the bonds is $1,000. a. Compute the current yield on both bonds. b.

Which bond should she select based on your answer to part a?

A drawback of current yield is that it does not consider the total life of the bond. For example, the yield to maturity on Bond A is 8.33 percent. What is the yield to maturity on Bond B?

Has your answer changed between parts b and c of this question in terms of which bond to select?

16-4. Solution: a. Bond A $72 Interest / $925 Market price = 7.78% Current yield Bond B $62 Interest / $910 Market price = 6.81% Current yield

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Chapter 13: Risk and Capital Budgeting

b. Bond A. It has a higher current yield. (c) N

I/Y

PMT

CPT I/Y 11.48959

–910

1,000

Answer: 11.49%

d. Yes. Bond B now has the higher yield to maturity. This is because the $90 discount will be recovered over only two years. With Bond A there is a $75 discount, but a 10-year recovery period.

Secured vs. unsecured debt (LO16-1) Match the yield to maturity in column 2 with the security provisions (or lack thereof) in column 1. Higher returns tend to go with greater risk. (1)

(2)

Security Provision

Yield to Maturity

a. Debenture

a. 6.85%

b. Secured debt

b. 8.20%

c. Subordinated debenture

c. 7.76%

16-5. Solution: Security Provision

Yield to Maturity

a. Debenture

a. 7.76%

b. Security debt

b. 6.85%

c. Subordinated debenture

c. 8.20%

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Chapter 13: Risk and Capital Budgeting

The greater the risk, the higher the yield.

Bond value (LO16-2) The Florida Investment Fund buys 58 bonds of the Gator Corporation through a broker. The bonds pay 10 percent annual interest. The yield to maturity (market rate of interest) is 12 percent. The bonds have a 10-year maturity. Using an assumption of semiannual interest payments: a.

Compute the price of a bond (refer to “Semiannual Interest and Bond Prices” in Chapter 10 for review if necessary).

Compute the total value of the 58 bonds.

16-6. Solution: a. Present value of interest payments PVA = A × PVIFA (n = 20, i = 6%) PVA = $50 × 11.470 = $573.50

Appendix D

Present value of principal payment at maturity PV = FV × PVIF (n = 20, i = 6%) PV = $1,000 × 0.312 = $312.00

Appendix B

Total present value Present value of interest payments Present value of payment at maturity Total present value or price of the bond

$573.50 312.00 $885.50

b. Value of 58 bonds $

885.50

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Chapter 13: Risk and Capital Budgeting

$51,359.00

(a) N

I/Y

PMT

CPT PV –885.30

1,000

Answer: 885.30

Bond value (LO16-2) Cox Media Corporation pays an 11 percent coupon rate on debentures that are due in 10 years. The current yield to maturity on bonds of similar risk is 8 percent. The bonds are currently callable at $1,110. The theoretical value of the bonds will be equal to the present value of the expected cash flow from the bonds. a.

Find the market value of the bonds using semiannual analysis.

Do you think the bonds will sell for the price you arrived at in part a? Why?

16-7. Solution: a. Present value of interest payments PVA = A × PVIFA (n = 20, i = 4%) PVA = $55 × 13.590 = $747.45

Appendix D

Present value of principal payment at maturity PV = FV × PVIF (n = 20, i = 4%) PV = $1,000 × 0.456 = $456

Appendix B

Total present value Present value of interest payments

$747.45

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Chapter 13: Risk and Capital Budgeting

Present value of payment at maturity Total present value or price of the bond

456.00 $1,203.45

b. No. The call price of $1,110 will keep the bonds from getting much over $1,110. Since the bonds are currently callable, investors will not want to buy the bonds at almost $1,300 and risk having them called away at $1,110. (a) N

I/Y

PMT

CPT PV –1,203.85

1,000

Answer: 1,203.85

Effect of bond rating change (LO16-2) The yield to maturity for 10-year bonds is as follows for four different bond rating categories: Aaa

9.40% ..........................

Aa2

10.00%

Aal

9.60% ..........................

Aa3

10.60%

The bonds of Falter Corporation were rated as Aaa and issued at par a few weeks ago. The bonds have just been downgraded to Aa2. Determine the new price of the bonds, assuming a 10-year maturity and semiannual interest payments. (Refer to ―Semiannual Interest and Bond Prices‖ in Chapter 10 for a review if necessary.)

16-8. Solution: With a Aaa rating at issue, the coupon rate is 9.4 percent annually or 4.7 percent semiannually. With a downgrading to Aa2, the new yield to maturity is 10 percent or 5 percent semiannually. Present value of interest payments PVA = A × PVIFA (n = 20, i = 5%)

Appendix D

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Chapter 13: Risk and Capital Budgeting

PVA = $47 × 12.462 = $585.71 Present value of principal payment at maturity PV = FV × PVIF (n = 20, i = 5%) PV = $1,000 × 0.377 = $377

Appendix B

Total present value Present value of interest payments Present value of payment at maturity Total present value or price of the bond

$585.71 377.00 $962.71

I/Y

PMT

CPT PV –962.61

1,000

Answer: 962.61

Interest rates and bond ratings (LO16-2) Twenty-five-year B-rated bonds of Parker Optical Company were initially issued at a 12 percent yield. After 10 years, the bonds have been upgraded to Aa2. Such bonds are currently yielding 10 percent to maturity. Use Table 16-2 to determine the price of the bonds with 15 years remaining to maturity. (You do not need the bond ratings to enter the table. just use the basic facts of the problem.)

16-9. Solution: Using Table 16-2: 12 percent initial coupon rate, 10 percent yield to maturity, 15 years remaining to maturity: = $1,153.72 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

10.

Interest rates and bond ratings (LO16-2) A previously issued A2, 15-year industrial bond provides a return three-fourths higher than the prime interest rate of 11 percent. Previously issued A2 public utility bonds provide a yield of three-fourths of a percentage point higher than previously issued A2 industrial bonds of equal quality. Finally, new issues of A2 public utility bonds pay three-fourths of a percentage point more than previously issued A2 public utility bonds. What should be the interest rate on a newly issued A2 public utility bond?

16-10. Solution: Interest rate on previously issued A2 15-year industrial bonds 11% × 1.75 = 19.250% Additional return on A2 15-year public utility bond + 0.750% Additional return on new issues + 0.750% Anticipated return on newly issued A2 public utility bonds

20.750%

11. Zero-coupon rate bond (LO16-2) A 17-year, $1,000 par value zero-coupon rate bond is to be issued to yield 7 percent. a.

What should be the initial price of the bond? (Take the present value of $1,000 for 17 years at 7 percent.)

If immediately upon issue interest rates dropped to 6 percent, what would be the value of the zero-coupon rate bond?

If immediately upon issue interest rates increased to 9 percent, what would be the value of the zero-coupon rate bond?

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Chapter 13: Risk and Capital Budgeting

× .317 $ 317 b. PV of $1,000 for n = 17, i = 6%, PVIF = 0.371 $1,000 × .371 $ 371 c. PV of $1,000 for n = 17, i = 9%, PVIF = 0.231 $1,000 × .231 $ 231 (a) N

I/Y

PMT

CPT PV –316.57

1,000

I/Y

PMT

CPT PV –371.36

1,000

I/Y

PMT

CPT PV –231.07

1,000

Answer: $317 (b)

Answer: $371 (c)

Answer: $231

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Chapter 13: Risk and Capital Budgeting

12. Zero-coupon bond Yield (LO16-2) Assume a zero-coupon bond that sells for $403 and will mature in 10 years at $1,250. What is the effective yield to maturity?

16-12. Solution: PVIF = PV/FV = $403/$1,250 = 0.322 FVIF = FV/PV = $1,250/$403 = 3.102 Using Appendix A for n = 10, the yield is approximately 12 percent.

I/Y

PMT

CPT I/Y 11.985

–403

1,250

Answer: 12

13. Floating rate bond (LO16-2) You buy an 8 percent, 25-year, $1,000-par-value floating rate bond in 2025. By the year 2030, rates on bonds of similar risk are up to 11 percent. What is your one best guess as to the value of the bond?

16-13. Solution: With a floating rate bond, the rate the bond pays changes with interest rates in the market. Therefore, the price of the bond stays constant. The one best guess is $1,000.

Effect of inflation on purchasing power of bond (LO16-2) Seventeen years ago, the Archer Corporation borrowed $6,500,000. Since then, cumulative inflation has been 65 percent (a compound rate of approximately 3 percent per year).

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Chapter 13: Risk and Capital Budgeting

When the firm repays the original $6,500,000 loan this year, what will be the effective purchasing power of the $6,500,000? (Hint: Divide the loan amount by one plus cumulative inflation.)

To maintain the original $6,500,000 purchasing power, how much should the lender be repaid? (Hint: Multiply the loan amount by one plus cumulative inflation.)

If the lender knows he will receive only $6,500,000 in payment after 17 years, how might he be compensated for the loss in purchasing power? A descriptive answer is acceptable.

16-14. Solution: a. Loan amount/(1 + Cumulative inflation) = $6,500,000/1.65 = $3,939,394 b. $6,500,000 × 1.65 = $10,725,000 c. Charge a high enough interest rate to not only provide an adequate annual return on the borrowed funds, but also compensate for the loss of purchasing power. A $10,725,000 loan repayment in a 65 percent cumulative inflationary environment will provide $6,500,000 in purchasing power to the original lender.

15. Profit potential associated with margin (LO16-2) A $1,000 par value bond was issued 25 years ago at a 12 percent coupon rate. It currently has 15 years remaining to maturity. Interest rates on similar obligations are now 8 percent. a.

What is the current price of the bond? (Look up the answer in Table 16-2.)

Assume Ms. Bright bought the bond three years ago when it had a price of $1,050. What is her dollar profit based on the bond’s current price?

Further assume Ms. Bright paid 30 percent of the purchase price in cash and borrowed the rest (known as buying on margin). She used the interest payments

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Chapter 13: Risk and Capital Budgeting

from the bond to cover the interest costs on the loan. How much of the purchase price of $1,050 did Ms. Bright pay in cash? d.

What is Ms. Bright’s percentage return on her cash investment? Divide the answer to part b by the answer to part c.

Explain why her return is so high.

16-15. Solution: a. The original bond was issued at 12 percent. Yield to maturity is now 8 percent. 15 years remain to maturity. The bond price is $1,345.84. b. $1,345.84 1,050.00 $ 295.84 c. Purchase price × 30% Margin

Current price Purchase price Dollar increase $1,050.00 $ 315.00 Purchase price paid in cash

d. $295.84 $315.00 = 93.92% 93.92 percent represents Ms. Bright’s return on her investment. e. Ms. Bright has not only benefited from an increase in the price of the bond (due to lower interest rates), but she also has benefited from the use of leverage by buying on margin. She has controlled a $1,070 initial investment with only $315

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Chapter 13: Risk and Capital Budgeting

in cash. The low cash investment tends to magnify gains (as well as losses). 16. Loss exposure and profit potential (LO16-2) A $1,000 par value bond was issued 20 years ago at a 9 percent coupon rate. It currently has five years remaining to maturity. Interest rates on similar debt obligations are now 10 percent. a.

Compute the current price of the bond using an assumption of semiannual payments.

If Mr. Robinson initially bought the bond at par value, what is his percentage loss (or gain)?

Now assume Mrs. Pinson buys the bond at its current market value and holds it to maturity, what will her percentage return be?

Although the same dollar amounts are involved in part b and c, explain why the percentage gain is larger than the percentage loss.

16-16. Solution: a. Present value of interest payments PVA = A × PVIFA (n = 10*, i = 5.00%) PVA = 45 × 7.722 = $347.49

Appendix D

Present value of principal payment at maturity PV = FV × PVIF (n = 10*, i = 5.00%) PV = $1,000 × 0.614 = $614.00

Appendix B

Total present value Present value of interest payments Present value of payment at maturity Total present value or price of the bond

$347.49 614.00 $961.49

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Chapter 13: Risk and Capital Budgeting

b. Purchase price Current value Dollar loss

$1,000.00 961.49 $ 38.51

Dollar loss/Investment = $38.51/$1,000 = 3.85% c.

Maturity value $1,000.00 Purchase price 961.49 Dollar gain $ 38.51 Dollar gain/Investment = $38.51/$961.49 = 4.01%

d. The percentage gain is larger than the percentage loss because the investment is smaller ($961.49 versus $1,000). The gain/loss is the same ($38.51). Calculator Solution: (a) N

I/Y

PMT

CPT PV –961.39

1,000

Answer: 961.39

Purchase price Current value Dollar loss

$1,000.00 961.39 $ 38.61

Dollar loss/Investment = $38.61/$1,000 = 3.86%

Maturity value Purchase price Dollar gain

$1,000.00 961.39 $ 38.61

Dollar gain/Investment = $38.61 / $961.39 = 4.02% d.

The percentage gain is larger than the percentage loss because the investment is smaller ($961.39 versus $1,000). The gain/loss is the same ($38.61).

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Chapter 13: Risk and Capital Budgeting

17. Advanced refunding decision (LO16-3) The Bowman Corporation has a $18 million bond obligation outstanding, which it is considering refunding. Though the bonds were initially issued at 10 percent, the interest rates on similar issues have declined to 8.5 percent. The bonds were originally issued for 20 years and have 10 years remaining. The new issue would be for 10 years. There is a 9 percent call premium on the old issue. The underwriting cost on the new $18,000,000 issue is $530,000, and the underwriting cost on the old issue was $380,000. The company is in a 35 percent tax bracket, and it will use an 8 percent discount rate (rounded aftertax cost of debt) to analyze the refunding decision. a. Calculate the present value of total outflows. b. Calculate the present value of total inflows. c. Calculate the net present value. d. Should the old issue be refunded with new debt?

16-17. Solution: Outflows 1. Payment of call premium $18,000,000 × 9% = $1,620,000 $1,620,000 (1 – 0.35) = $1,053,000 2. Underwriting cost on new issue Amortization of costs ($530,000/10) (0.35) $53,000 × (0.35) = $18,550 tax savings per year Actual expenditure PV of future tax savings $18,550 × 6.710* Net cost of underwriting expense on new issue

$530,000 124,471 $405,529

*PVIFA for n = 10, i = 8% (Appendix D) 1. 2.

Outflows $1,053,000 405,529 $1,458,529

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Chapter 13: Risk and Capital Budgeting

Inflows 3. Cost savings in lower interest rates 10% (interest on old bond) × $18,000,000 = $ 1,800,000/year 8.5% (interest on new bond) × $18,000,000 = 1,530,000/year Savings per year before taxes = $ 270,000 Aftertax Savings $270,000 × (1 – 0.35) = $ 175,500 per yr. $ 175,500 × 6.710 $1,177,605

PVIFA (n = 10, i = 8%)

Appendix D

4. Underwriting cost on old issue Original amount Amount written off over 10 years at $19,000 per year Unamortized old underwriting cost Present value of deferred future write-off $19,000 × 6.710 (n = 10, i = 8%) Immediate gain in old underwriting cost write-off Tax rate Aftertax value of immediate gain in old Underwriting cost write-off

$380,000 190,000 $190,000 127,490 $62,510 × .35 $ 21,879

Inflows 3. $1,177,605 4. 21,879 $1,199,484

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Chapter 13: Risk and Capital Budgeting

Summary Inflows

Outflows 1.

$1,053,000

$1,177,605

405,529

21,879

$1,458,529

$1,199,484

PV of inflows

$1,199,484

PV of outflows

1,458,529

Net present value

$ –259,045

Do not refund the old issue (particularly if it is perceived that interest rates will go down even more). Calculator solution:

Summary Inflows

Outflows 1.

$1,053,000

$1,174,264**

405,528*

21,878***

$1,458,528

$1,196,142

PV of inflows

$1,196,142

PV of outflows

1,458,528

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Chapter 13: Risk and Capital Budgeting

Net present value

$ –262,386

Do not refund the old issue (particularly if it is perceived that interest rates will go down even more).

*Present value of future tax savings N

I/Y

PMT

CPT PV – 124,472.01

18,550

PV of future tax savings $124,472

Actual expenditure

$530,000

PV of future tax savings

124,472

Net cost of underwriting expense on new issue

$405,528

**Present value of future tax savings

I/Y

CPT PV – 1,177,619.285 PV of future tax savings $1,177,619 10

PMT

175,500

PMT

19,000

***Present value of deferred future write-off N

I/Y

CPT PV – 127,491.55 PV of deferred future write-off $127,492 10

Unamortized old underwriting cost Present value of deferred future write-off Immediate gain in old underwriting cost write-off

$190,000 127,492 $62,508

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Chapter 13: Risk and Capital Budgeting

Tax rate × .35 Aftertax value of immediate gain in old Underwriting cost write-off

$ 21,878

18. Refunding decision (LO16-3) The Robinson Corporation has $43 million of bonds outstanding that were issued at a coupon rate of 11¾ percent 7 years ago. Interest rates have fallen to 10¾ percent. Mr. Brooks, the vice president of finance, does not expect rates to fall any further. The bonds have 17 years left to maturity, and Mr. Brooks would like to refund the bonds with a new issue of equal amount also having 17 years to maturity. The Robinson Corporation has a tax rate of 30 percent. The underwriting cost on the old issue was 2.4 percent of the total bond value. The underwriting cost on the new issue will be 1.7 percent of the total bond value. The original bond indenture contained a five-year protection against a call, with a 9 percent call premium starting in the sixth year and scheduled to decline by one-half percent each year thereafter. (Consider the bond to be seven years old for purposes of computing the premium.) Assume the discount rate is equal to the aftertax cost of new debt rounded up to the nearest whole number. a. Compute the discount rate. b. Calculate the present value of total outflows. c. Calculate the present value of total inflows. d. Calculate the net present value.

16-18. Solution: First compute the discount rate 10.75% (1 – 0.30) = 10.75% (0.70) = 7.53%. Round to 8%. Outflows 1. Payment on call provision (7th year = 8.5% call premium) $43,000,000 × 8.5% = $3,655,000 $3,655,000 (1 – 0.30) = $2,558,500 aftertax cost 2. Underwriting cost on new issue Actual expenditure 1.7% × $43,000,000 =

$731,000

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Chapter 13: Risk and Capital Budgeting

Amortization of costs ($731,000/17) Tax savings per year = $43,000 (0.30)

= =

$ 43,000 $ 12,900

Actual expenditure PV of future tax savings $ 12,900 × 9.122* Net cost of underwriting expense on new issue

$731,000 117,674 $613,326

*PVIFA for n = 17, i = 8% (Appendix D) Outflows 1. $2,558,500 2. 613,326 $3,171,826 Inflows 3. Cost savings in lower interest rates 11 3/4% (interest on old bond) × $43,000,000 = $5,052,500 10 3/4% (interest on new bond) × 43,000,000 = 4,622,500 Savings per year $ 430,000 Savings per year $430,000 × (1 – 0.3) = $301,000 Aftertax $ 301,000 × 9.122 $2,745,722

PVIFA (n = 17, i = 8%) Present value of savings

Appendix D

4. Underwriting cost on old issue Original amount (2.40% × $43,000,000) Amount written off over last 7 years at $43,000 per year ($1,032,000/24) × 7 Unamortized old underwriting cost Present value of deferred future write-off: $43,000 × 9.122 Immediate gain in old underwriting write-off

$1,032,000 301,000 $ 731,000

392,246 $ 338,754

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Chapter 13: Risk and Capital Budgeting

Tax rate Aftertax value of immediate gain in old underwriting cost write-off

0.30 $ 101,626

Inflows 3. $2,745,722 4.

101,626 $2,847,348 Summary Inflows

Outflows 1.

$2,558,500

$2,745,722

613,326

101,626

$3,171,826

$2,847,348

PV of inflows

$2,847,348

PV of outflows

3,171,826

Net present value

$ –324,478

Based on the negative net present value, the Robinson Corporation should not refund the issue. As time passes, the call premium will decline and if interest rates stay down or decline further, the refunding decision could have a positive net present value in the future.

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Chapter 13: Risk and Capital Budgeting

Summary Inflows

Outflows 1.

$2,558,500

$2,745,613**

613,331*

101,631***

$3,171,831

$2,847,244

PV of Inflows

$2,847,244

PV of outflows

3,171,831

Net present value

$ -324,587

*Present value of future tax savings N

I/Y

PMT

CPT PV – 117,669.13

12,900

PV of future tax savings $117,669

Actual expenditure

$731,000

PV of future tax savings

117,669

Net cost of underwriting expense on new issue

$613,331

**Present value of savings

I/Y

CPT PV – 2,745,613.07 PV of future tax savings $2,745,613 17

PMT

301,000

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***Present value of deferred future write-off:

I/Y

CPT PV – 392,230.44 PV of deferred future write-off $392,230 17

PMT

43,000

Unamortized old underwriting cost

$731,000

PV of deferred future write-off

392,230

Immediate gain in old underwriting write-off

338,770

Tax rate

.30

Aftertax value of immediate gain in old Underwriting cost write-off

$101,631

19. Call premium (LO16-3) The Sunbelt Corporation has $40 million of bonds outstanding that were issued at a coupon rate of 12⅞ percent 7 years ago. Interest rates have fallen to 12 percent. Mr. Heath, the vice president of finance, does not expect rates to fall any further. The bonds have 18 years left to maturity, and Mr. Heath would like to refund the bonds with a new issue of equal amount also having 18 years to maturity. The Sunbelt Corporation has a tax rate of 36 percent. The underwriting cost on the old issue was 2.5 percent of the total bond value. The underwriting cost on the new issue will be 1.8 percent of the total bond value. The original bond indenture contained a 5-year protection against a call, with an 8 percent call premium starting in the sixth year and scheduled to decline by one-half percent each year thereafter (consider the bond to be seven years old for purposes of computing the premium). Assume the discount rate is equal to the aftertax cost of new debt rounded up to the nearest whole number. Should the Sunbelt Corporation refund the old issue?

16-19. Solution: First compute the discount rate 12% (1 – 0.36) = 12% × 0.64 = 7.68%. Round up to 8 percent.

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Chapter 13: Risk and Capital Budgeting

Outflows 1. Payment on call provision $40,000,000 × 7.5% $3,000,000 (1 – 0.36)

= $3,000,000 = $1,920,000

2. Underwriting cost on new issue Actual expenditure 1.8% × $40,000,000 = Amortization of costs ($720,000/18) (0.36) = Tax savings per year = $40,000 (0.36) = Actual expenditure $720,000 PV of future tax savings $ 14,400 × 9.372* Net cost of underwriting expense on new issue

$720,000 $ 14,400

134,957 $585,043

*PVIFA for n = 18, i = 8% (Appendix D)

Inflows 3. Cost savings in lower interest rates 12 7/8% (interest on old bond) × $40,000,000 = $5,150,000 12% (interest on new bond) × $40,000,000 = 4,800,000 Savings per year $ 350,000 Savings per year $350,000 × (1 – 0.36) = $224,000 Aftertax $ 224,000 × 9.372 $2,099,328

PVIFA (n = 18, i = 8%) Present value of savings

4. Underwriting cost on old issue Original amount (2.5% × $40,000,000) Amount written off over last 7 years at $40,000 per year ($1,000,000/25) × 7 Unamortized old underwriting cost

Appendix D

$1,000,000 280,000 $ 720,000

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Chapter 13: Risk and Capital Budgeting

Present value of deferred future write-off: $40,000 × 9.372 (n = 18, i = 8%) ... Immediate gain in old underwriting write-off Tax rate Aftertax value of immediate gain in old underwriting cost write-off Summary

374,880 $ 345,120 × 0.36 $ 124,243 Inflows

Outflows 1.

$1,920,000

$2,099,328

585,043

124,243

$2,505,043

$2,223,571

PV of inflows

$2,223,571

PV of outflows

2,505,043

Net present value

$ (281,472)

Based on the negative net present value, the Sunbelt Corporation should not refund the issue. Calculator solution: Summary Inflows

Outflows 1.

$1,920,000

$2,099,303**

585,045*

124,245***

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Chapter 13: Risk and Capital Budgeting

$2,505,045

$2,223,548

PV of inflows

$2,223,548

PV of outflows

2,505,045

Net present value

$ (281,497)

Based on the negative net present value, the Sunbelt Corporation should not refund the issue.

*Present value of future tax savings N

I/Y

PMT

CPT PV – 134,955.17

14,400

PV of future tax savings $134,955

Actual expenditure

$720,000

PV of future tax savings

134,955

Net cost of underwriting expense on new issue

$585,045

**Present value of savings

I/Y

CPT PV – 2,099,302.72 PV of future tax savings $2,099,303 18

PMT

224,000

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Chapter 13: Risk and Capital Budgeting

I/Y

CPT PV – 374,875.49 PV of deferred future write-off $374,875 18

PMT

40,000

Unamortized old underwriting cost

$720,000

PV of deferred future write-off

374,875

Immediate gain in old underwriting write-off

345,125

Tax rate

.36

Aftertax value of immediate gain in old Underwriting cost write-off

20.

$124,245

Finance lease or operating lease (LO16-4) Krawczek Company will enter into a lease agreement with Heavy Equipment Co. where Krawczek will make lease payments over the next 5 years. The lease is noncancelable and requires equal annual payments of $20,000 per year beginning on January 1 of the first year. The last payment will be January 1 of year 5, and Krawczek will continue to use the asset until December 31 of that year. Other important information includes the following:      a. b. c. d.

The fair value of the equipment is $140,000. The applicable discount rate is an 8 percent annual rate The economic life of the asset is 10 years. Krawczek does not guarantee the residual value of the asset at the end of the lease, and it does not expect to keep the asset at the end of the term. The asset is a standard piece of equipment. Is the lease an operating lease or a finance lease? What will be the lease expense shown on the income statement at the end of year 1? What will be the interest expense shown on the income statement at the end of year 1? What will be the amortization expense shown on the income statement at the end of year 1?

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Chapter 13: Risk and Capital Budgeting

Finance Lease Criteria: 1. Does the lease transfer ownership at end of lease term? - NO 2. Does the Lease grant lessee option to purchase at end of lease? - NO 3. Is the lease term is for major part of economic life of underlying asset? (Some judgment is required) (5years/10years) = 50%, not major - NO 4. Does the PV of lease payments exceed substantially all of the FV of leased asset? (Again, judgement is required) N=5, PMT=20,000, I/YR= 8%, FV=0, PV=?= 86,243 / 140,000 FV= 61.6% - NO 5. Specialized asset? - NO The lease is an operating lease because it fails all of the above five tests. b) Lease payment calculated straight line on the sum of the scheduled lease payments: (5 years × $20,000/year)/5 = $20,000 c) $0 d) $0

21.

Financial Statement effects of leases (LO16-4) The Harris Company is the lessee on a 4-year lease with the following payments at the end of each year: Year 1: $10,000 Year 2: $15,000 Year 3: $20,000 Year 4: $25,000 An appropriate discount rate is 7 percent, yielding a present value of $48,055. a)

If the lease is an operating lease

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Chapter 13: Risk and Capital Budgeting

i. ii. iii.

What will be the initial value of the right-of-use asset? What will be the initial value of the lease liability? What will be the lease expense shown on the income statement at the end of year 1? iv. What will be the interest expense shown on the income statement at the end of year 1? v. What will be the amortization expense shown on the income statement at the end of year 1? If the lease is a finance lease i. What will be the initial value of the right-of-use asset? ii. What will be the initial value of the lease liability? iii. What will be the lease expense shown on the income statement at the end of year 1? iv. What will be the interest expense shown on the income statement at the end of year 1? v. What will be the amortization expense shown on the income statement at the end of year 1?

16-21. Solution: a) Operating lease i. $48,055 ii. $48,055 iii. ($10,000 + $15,000 + $20,000 + $25,000) /4 = $17,500 iv. $0 Interest not applicable to operating leases. v. $0 amortization not applicable to operating leases. b) Finance lease i. $48,055 ii. $48,055 iii. $0 lease expense not applicable to finance leases. iv. ($48,055 × 0.07) = $3364 v. What will be the amortization expense shown on the income statement at the end of year 1? ($48,055/4) = $12,014 COMPREHENSIVE PROBLEM © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

Comprehensive Problem 1. Broadband Inc. Bond prices refunding (LO16-2 and 3) Barton Simpson, the chief financial officer of Broadband Inc. could hardly believe the change in interest rates that had taken place over the last few months. The interest rate on A2 rated bonds was now 6 percent. The $30 million, 15-year bond issue that his firm has outstanding was initially issued at 9 percent 5 years ago. Because interest rates had gone down so much, he was considering refunding the bond issue. The old issue had a call premium of 8 percent. The underwriting cost on the old issue had been 3 percent of par and on the new issue, it would be 5 percent of par. The tax rate would be 30 percent and a 4 percent discount rate will be applied for the refunding decision. The new bond would have a 10-year life. Before Barton used the 8 percent call provision to reacquire the old bonds, he wanted to make sure he could not buy them back cheaper in the open market. a. First compute the price of the old bonds in the open market. Use the valuation procedures for a bond that were discussed in Chapter 10 (use the annual analysis). Determine the price of a single $1,000 par value bond. b. Compare the price in part a to the 8 percent call premium over par value. Which appears to be more attractive in terms of reacquiring the old bonds? c. Now do the standard bond refunding analysis as discussed in this chapter. Is the refunding financially feasible? d In terms of the refunding decision, how should Barton be influenced if he thinks interest rates might go down even more?

CP 16-1.

Solution: a. Price of Old Bond Present Value of Interest Payments PVA

Appendix D

PVA = A × PVIFA (n = 10, i = 6%) = $90 × 7.360 = $662.40

Present Value of Principal Payment at Maturity PV = FV × PVIF (n = 10, i = 6%)

Appendix D

PV = $1,000 × 0.558 = $558

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Chapter 13: Risk and Capital Budgeting

Total present value Present Value of Interest Payments Present Value of Principal Payment

$ 662.40 558.00 $1,220.40

The price of $1,220.40 is more than 20 percent over par. The call price ($1080) is only 8 percent over par. Clearly, calling in the bonds is more attractive than repurchasing them in the open market.

Refunding Decision

Outflows

1. Payment of call premium $30,000,000 × 8%

= $2,400,000

$2,400,000 × (1 – 0.30) = $1,680,000 2. Underwriting cost on new issue Actual expenditure $30,000,000 × 5%

= $1,500,000

Amortization of cost = ($1,500,000/10)

= $ 150,000

Tax savings per year 150,000 × 0.30

= $

PV of future tax savings $45,000 × 8.811*

= $ 364,995

45,000

*PVIFA for n = 10, i = 5% (Appendix D)

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Chapter 13: Risk and Capital Budgeting

Actual expenditure PV of future tax savings

$1,500,000 364,995

New cost of underwriting expense on new issue

$1,135,005

3. Cost savings in lower interest rates 9% (interest on old bonds) × $30,000,000

6% (interest on new bonds) × $30,000,000

$2,700,00 0 1,800,000

Savings per year

$ 900,000

Savings per year $900,000 × (1 – 30) = $630,000 after tax

$ 630,000 8.111 PVIFA (n = 10, i = 4%) (Appendix D) $5,109,930 4. Underwriting cost on old issue Original amount (3% × $30,000,000)

$900,000

Amount written off over last 5 years at $60,000 per year ($900,000/15) 300,000 Unamortized old underwriting cost $600,000

Present value of deferred future write-off $60,000 × 8.111 (n = 10, i = 4%)

486,660

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Chapter 13: Risk and Capital Budgeting

Immediate gain in old underwriting writeTax rate After tax value of immediate gain in old

$113,340 off tax rate .30

underwriting cost write-off $ 34,002

Summary Inflows

Outflows 1.

$1,680,000

$5,109,930

1,135,005

34,002

$2,815,005

$5,143,932

PV of inflows

$5,143,932

PV of outflows

2,815,005

Net present value

$2,328,927

The refunding is financially feasible. d. If Barton thinks interest rates are going down even more, he might want to wait on the refunding because the net present value would be even higher. Of course, if he is wrong and interest rates go up, he might miss out on a highly profitable opportunity.

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Chapter 13: Risk and Capital Budgeting

Appendix–Financial Alternatives for Distressed Firms Discussion Questions 16A-1.

What is the difference between technical insolvency and bankruptcy?

Technical insolvency refers to the circumstances where a firm is unable to pay its bills as they come due. A firm may be technically insolvent even though it has a positive net worth. Bankruptcy, on the other hand, indicates that the market value of a firm’s assets is less than its liabilities and the firm has a negative net worth. Under the law, either technical insolvency or bankruptcy may be adjudged as a financial failure of the business firm.

16A-2.

What are the four types of out-of-court settlements? Briefly describe each.

Extension – Creditors agree to allow the firm more time to meet its financial obligations. Composition – Creditors agree to accept a fractional settlement on their original claims. Creditor committee – A creditor committee is set up to run the business because it is believed that management can no longer conduct the affairs of the firm. Assignment – Liquidation of assets takes place without going through formal court action.

16A-3.

What is the difference between an internal reorganization and an external reorganization under formal bankruptcy procedures?

An internal reorganization calls for an evaluation and restricting of the current affairs of the firm. Current management may be replaced and a redesign of the capital structure may be necessary. An external reorganization means that © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

an actual merger partner will be found for the firm.

16A-4.

What are the first three priority items under liquidation in bankruptcy?

(1)

Cost of administering the bankruptcy procedures.

(2)

Wages due workers if earned within three months of filing the bankruptcy petition. The maximum amount is $600 per worker.

(3)

Tax due at the federal, state, or local level.

Problems

16A–1. Settlement of claims in bankruptcy liquidation (LO16-5) The trustee in the bankruptcy settlement for Titanic Boat Co. lists the following book values and liquidation values for the assets of the corporation. Liabilities and stockholders’ claims are shown.

Liquidation Assets Accounts receivable ...........................................

Book Value $1,400,000

Value $1,200,000

Inventory..................................................1,800,000 Machinery and equipment .......................1,100,000 Building and plant ...................................4,200,000 Total assets $8,500,000

900,000 600,000 2,500,000 $ 5,200,000

Liabilities and Stockholders’ Claims Liabilities: Accounts payable .................................. $2,800,000 First lien, secured by © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

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Chapter 13: Risk and Capital Budgeting

machinery and equipment ................. 900,000 Senior unsecured debt...........................2,200,000 Subordinated debenture ........................1,700,000 Total liabilities ..................................7,600,000 Stockholders’ claims: Preferred stock ...................................... 250,000 Common stock ...................................... 650,000 Total stockholders’ claims ................ 900,000 Total liabilities and stockholders’ claims .................. $8,500,000

Compute the difference between the liquidation value of the assets and the liabilities.

Based on the answer to part a, will preferred stock or common stock participate in the distribution?

Assuming the administrative costs of bankruptcy, workers’ allowable wages, and unpaid taxes add up to $400,000, what is the total remaining asset value available to cover secured and unsecured claims?

After the machinery and equipment are sold to partially cover the first lien secured claim, how much will be available from the remaining asset liquidation values to cover unsatisfied secured claims and unsecured debt?

List the remaining asset claims of unsatisfied secured debt holders and unsecured debt holders in a manner similar to that shown in the bottom portion of Table 16A-3.

Compute a ratio of your answers in part d and e. This will indicate the initial allocation ratio.

List the remaining claims (unsatisfied secured and unsecured) and make an initial allocation and final allocation similar to that shown in Table 16A-4. Subordinated debenture holders may keep the balance after full payment is made to senior debt holders.

Show the relationship of amount received to total amount of claim in a similar fashion to that in Table 16A-5. Remember to use the sales (liquidation) value for machinery and equipment plus the allocation amount in part g to arrive at the total received on secured debt.

16A-1.

Solution: a. Liquidation value of assets

$5,200,000

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Chapter 13: Risk and Capital Budgeting

Liabilities

7,600,000

Difference

($2,400,000)

b. Preferred and common stock will not participate in the distribution because the liquidation value of the assets does not cover creditor claims. c. Asset values in liquidation Administrative costs, wages and taxes Remaining asset values

$5,200,000 – 400,000 $4,800,000

d. Remaining asset value $4,800,000 Payment to secured creditors – 600,000 Amount available to unsatisfied secured claims and unsecured debt $4,200,000 e. Remaining claims of unsatisfied secured debt and unsecured debt holder Secured debt (unsatisfied first lien) Accounts payable Senior unsecured debt Subordinated debentures

$ 300,000 2,800,000 2,200,000 1,700,000 $7,000,000

f. Amount available to unsatisfied

security claims and unsecured debt (part d) $4,200,000   60% Remaining claims of unsatisfied secured $7,000,000 debt and unsecured debt holders (part e)

Allocation procedures for unsatisfied secured claims and unsecured debt.

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Chapter 13: Risk and Capital Budgeting

(1)

(2)

Category Secured debt (unsatisfied first lien)

Amount of Claim

(3) Initial Allocation (60%)

(4)

Amount Received

$ 300,000 $ 180,000 $ 180,000

Accounts Payable

2,800,000

1,680,000

Senior unsecured debt

2,200,000

1,320,000

2,200,000

1,700,000

1,020,000

140,000*

Subordinated debentures*

$ 7,000,000 $4,200,000 $4,200,000 * The subordinated debenture holders must transfer $880,000 of their initial allocation to the senior unsecured debt holders to fully provide for their payment ($1,320,000 + $880,000 = $2,200,000). This will leave $140,000 for subordinated debentures ($1,020,000 – $880,000). h.

Payments and percent of claims