CHAPTER 2 – REVIEWING FINANCIAL STATEMENTS questions LG2-1
1. List and describe the four major financial statements. The four basic financial statements are: 1. The balance sheet reports a firm’s assets, liabilities, and equity at a particular point in time. 2. The income statement shows the total revenues that a firm earns and the total expenses the firm incurs to generate those revenues over a specific period of time—generally one year. 3. The statement of cash flows shows the firm’s cash flows over a given period of time. This statement reports the amounts of cash the firm generated and distributed during a particular time period. The bottom line on the statement of cash flows―the difference between cash sources and uses―equals the change in cash and marketable securities on the firm’s balance sheet from the previous year’s balance. 4. The statement of retained earnings provides additional details about changes in retained earnings during a reporting period. This financial statement reconciles net income earned during a given period minus any cash dividends paid within that period to the change in retained earnings between the beginning and ending of the period.
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2. On which of the four major financial statements (balance sheet, income statement, statement of cash flows, or statement of retained earnings) would you find the following items? a. earnings before taxes - income statement b. net plant and equipment - balance sheet c. increase in fixed assets - statement of cash flows d. gross profits - income statement e. balance of retained earnings, December 31, 20xx - statement of retained earnings and balance sheet f. common stock and paid-in surplus - balance sheet g. net cash flow from investing activities - statement of cash flows h. accrued wages and taxes – balance sheet i. increase in inventory - statement of cash flows
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3. What is the difference between current liabilities and long-term debt? Current liabilities constitute the firm’s obligations due within one year, including accrued wages and taxes, accounts payable, and notes payable. Long-term debt includes long-term loans and bonds with maturities of more than one year.
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4. How does the choice of accounting method used to record fixed asset depreciation affect management of the balance sheet? Firm managers can choose the accounting method they use to record depreciation against their fixed assets. Two choices include the straight-line method and the modified accelerated cost recovery system (MACRS). Companies often calculate depreciation using MACRS when they figure the firm’s taxes and the straight-line method when reporting income to the firm’s
Chapter 2 - Reviewing Financial Statements
stockholders. The MACRS method accelerates deprecation, which results in higher depreciation expenses, lower taxable income, and lower taxes in the early years of a project’s life. The straight-line method results in lower depreciation expenses, but also results in higher taxes in the early years of a project’s life. Firms seeking to lower their cash outflows from tax payments will favor the MACRS depreciation method. LG2-1
5. What is bonus depreciation? How did the Tax Cuts and Jobs Act of 2017 temporarily extend and modify bonus depreciation? Since 2001, businesses have had the ability to immediately deduct a percentage of the acquisition cost of qualifying assets as "bonus depreciation." This additional depreciation deduction was allowed to encourage business investment. However, bonus depreciation was a temporary provision; the rate would have been 50 percent in 2017, 40 percent in 2018, and 30 percent in 2019, before phasing out in 2020. The Tax Cuts and Jobs Act of 2017 extended and modified bonus depreciation, allowing businesses to immediately deduct 100 percent of the cost of eligible property in the year it is placed in service, through 2022. The amount of allowable bonus depreciation will then be phased down over four years: 80 percent will be allowed for property placed in service in 2023, 60 percent in 2024, 40 percent in 2025, and 20 percent in 2026. MACRS or straight-line depreciation is applied to any costs that do not qualify for bonus depreciation.
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6. What are the costs and benefits of holding liquid securities on a firm’s balance sheet? The more liquid assets a firm holds, the less likely the firm will be to experience financial distress. However, liquid assets generate little or no profits for a firm. For example, cash is the most liquid of all assets, but it earns little, if any, return for the firm. In contrast, fixed assets are illiquid, but provide the means to generate revenue. Thus, managers must consider the trade-off between the advantages of liquidity on the balance sheet and the disadvantages of having money sit idle rather than generating profits.
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7. Why can the book value and market value of a firm differ? A firm’s balance sheet shows its book (or historical cost) value based on Generally Accepted Accounting Principles (GAAP). Under GAAP, assets appear on the balance sheet at what the firm paid for them, regardless of what assets might be worth today if the firm were to sell them. Inflation and market forces make many assets worth more now than they were when the firm bought them. So in most cases, book values differ widely from the market values for the same assets—the amount that the assets would fetch if the firm actually sold them. For the firm’s current assets—those that mature within a year―the book value and market value of any particular asset will remain very close. For example, the balance sheet lists cash and marketable securities at their market value. Similarly, firms acquire accounts receivable and inventory and then convert these short-term assets into cash fairly quickly, so the book value of these assets is generally close to their market value.
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8. From a firm manager’s or investor’s point of view, which is more important―the book value of a firm or the market value of the firm?
Chapter 2 - Reviewing Financial Statements
Balance sheet assets are listed at historical cost. Managers would thus see little relation between the total asset value listed on the balance sheet and the current market value of the firm’s assets. Similarly, the stockowners’ equity listed on the balance sheet generally differs from the true market value of the equity—in this case, the market value may be higher or lower than the value listed on the firm’s accounting books. So, financial managers and investors often find that balance sheet values are not always the most relevant numbers. LG2-3
9. How did the Tax Cuts and Jobs Act of 2017 change corporate tax laws? The Tax Cuts and Jobs Act (TCJA) of 2017 is the most recent revision of corporate tax laws and represents one of the most significant changes in more than 30 years. The Act permanently lowers corporate taxes from a progressive schedule that saw tax rates as high as 35 percent to a flat 21 percent starting in 2018.
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10. What is the difference between an average tax rate and a marginal tax rate? A firm can figure the average tax rate as the percentage of each dollar of taxable income that the firm pays in taxes. From your economics classes, you can probably guess that the firm’s marginal tax rate is the amount of additional taxes a firm must pay out for every additional dollar of taxable income it earns.
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11. How did the Tax Cuts and Jobs Act of 2017 change the tax deductibility of corporate interest in debt? The Tax Cuts and Jobs Act of 2017 contains a new limitation on the deductibility of net interest expense (interest expense minus interest income) that exceeds 30 percent of a firm’s “adjusted taxable income” starting in 2018. For tax years beginning before January 1, 2022, “adjusted taxable income” is measured as a business’ EBITDA. For subsequent tax years, “adjusted taxable income” is measured as EBIT, no longer including an add-back for depreciation and amortization. Thus, beginning in 2022, the new limitation will become more severe. Prior corporate tax laws generally allowed full deduction of interest paid or accrued by businesses.
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12. How does the payment of interest on debt affect the amount of taxes the firm must pay? Corporate interest payments appear on the balance sheet as an expense item, so we deduct the allowable portion of interest payments from operating income when the firm calculates taxable income. But, any dividends paid by corporations to their shareholders are not tax deductible. This is one factor that encourages managers to finance projects with debt financing rather than to sell more stock. Suppose one firm uses mainly debt financing and another firm, with identical operations, uses mainly equity financing. The equity-financed firm will have very little interest expense to deduct for tax purposes. Thus, it will have higher taxable income and pay more taxes than the debt-financed firm. The debt-financed firm will pay fewer taxes and be able to pay more of its operating income to asset funders, i.e., its bondholders and stockholders. So, as long as interest on debt is under the 30 percent allowable cap for tax deduction, even stockholders prefer that firms finance assets primarily with debt rather than with stock.
Chapter 2 - Reviewing Financial Statements
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13. The income statement is prepared using GAAP. How does this affect the reported revenue and expense measures listed on the balance sheet? Company accountants must prepare firm income statements following GAAP principles. GAAP procedures require that the firm recognize revenue at the time of sale, but sometimes the company receives the cash before or after the time of sale. Likewise, GAAP counsels the firm to show production and other expenses on the balance sheet as the sales of those goods take place. So production and other expenses associated with a particular product’s sale only appear on the income statement (for example, cost of goods sold and depreciation) when that product sells. Of course, just as with the revenue recognition, actual cash outflows incurred with production may occur at a very different point in time—usually much earlier than GAAP principles allow the firm to formally recognize the expenses. Further, income statements contain several non-cash entries, the largest of which is depreciation. Depreciation attempts to capture the non-cash expense incurred as fixed assets deteriorate from the time of purchase to the point when those assets must be replaced. Let’s illustrate the effect of depreciation: Suppose a firm purchases a machine for $100,000. The machine has an expected life of five years and at the end of those five years, the machine will have no expected salvage value. The firm lays out a $100,000 cash outflow at the time of purchase. But the entire $100,000 does not appear on the income statement in the year that the firm purchases the machine—in accounting terms, the machine is not expensed in the year of purchase. Rather, if the firm’s accounting department uses the straightline depreciation method, it deducts only $100,000/5, or $20,000, each year as an expense. This $20,000 equipment expense is not a cash outflow for the firm. The person in charge of buying the machine knows that the cash flow occurred at the time of purchase—and it totaled $100,000 rather than $20,000. So, figures shown on an income statement may not represent the actual cash inflows and outflows for a firm during a particular period.
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14. Why do financial managers and investors find cash flows to be more important than accounting profit? Financial managers and investors are far more interested in actual cash flows than they are in the somewhat artificial, backward-looking accounting profit listed on the income statement. This is a very important distinction between the accounting point of view and the finance point of view. Finance professionals know that the firm needs cash, not accounting profit, to pay the firm’s obligations as they come due, to fund the firm’s operations and growth, and to compensate the firm’s ultimate owners: its shareholders. Thus, the statement of cash flows is a financial statement that shows the firm’s cash flows over a given period of time. This statement reports the amounts of cash that the firm generated and distributed during a particular time period.
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15. Which of the following activities result in an increase (decrease) in a firm’s cash? a. Decrease fixed assets – increase in cash b. Decrease accounts payable – decrease in cash c. Pay dividends – decrease in cash d. Sell common stock – increase in cash e. Decrease accounts receivable – increase in cash
Chapter 2 - Reviewing Financial Statements
f. Increase notes payable – increase in cash
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16. What is the difference between cash flows from operating activities, cash flows from investing activities, and cash flows from financing activities? Cash flows from operations are those cash inflows and outflows that result directly from producing and selling the firm’s products. These cash flows include: net income, depreciation, and working capital accounts other than cash and operations-related short-term debt. Cash flows from investing activities are cash flows associated with buying or selling of fixed or other longterm assets. This section of the statement of cash flows shows cash inflows and outflows from long-term investing activities—most significantly the firm’s investment in fixed assets. Cash flows from financing activities are cash flows that result from debt and equity financing transactions. These include raising cash by: issuing short-term debt, issuing long-term debt, issuing stock, using cash to pay dividends, using cash to pay off debt, and using cash to buy back stock.
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17. What are free cash flows for a firm? What does it mean when a firm’s free cash flow is negative? Free cash flows are the cash flows available to pay the firm’s stockholders and debtholders after the firm has made the necessary working capital investments, fixed asset investments, and developed the necessary new products to sustain the firm’s ongoing operations. If free cash flow is negative, the firm's operations produce no cash flows available for investors.
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18. What is earnings management? Managers and financial analysts have recognized for years that firms use considerable latitude in using accounting rules to manage their reported earnings in a wide variety of contexts. Indeed, within the GAAP framework, firms can “smooth” earnings. That is, firms often take steps to over- or understate earnings at various times. Managers may choose to smooth earnings to show investors that firm assets are growing steadily. Similarly, one firm may be using straight-line depreciation for its fixed assets, while another is using a modified accelerated cost recovery method (MACRS), which causes depreciation to accrue quickly. If the firm uses MACRS accounting methods, its managers write fixed asset values down quickly; assets will thus have lower book value than if the firm used straight line depreciation methods. This process of controlling a firm’s earnings is called earnings management.
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19. What does the Sarbanes-Oxley Act require of firm managers? The Sarbanes-Oxley Act, passed in June 2002, requires public companies to ensure that their corporate boards’ audit committees have considerable experience applying generally accepted accounting principles (GAAP) for financial statements. The Act also requires that any firm’s senior management must sign off on the financial statements of the firm, certifying the statements as accurate and representative of the firm’s financial condition during the period covered. If a firm’s board of directors or senior managers fails to comply with Sarbanes-Oxley (SOX), the firm may be delisted from stock exchanges.
Chapter 2 - Reviewing Financial Statements
problems basic 2-1 Balance Sheet You are evaluating the balance sheet for Goodman’s Bees Corporation. problems From the balance sheet you find the following balances: cash and marketable securities = LG2-1 $400,000, accounts receivable = $1,200,000, inventory = $2,100,000, accrued wages and taxes = $500,000, accounts payable = $800,000, and notes payable = $600,000. Calculate Goodman Bees’ net working capital. Net working capital = Current assets - Current liabilities. Goodman’s Bees’ current assets = Cash and marketable securities Accounts receivable Inventory Total current assets
= $400,000 = 1,200,000 = 2,100,000 $3,700,000
and current liabilities = Accrued wages and taxes Accounts payable Notes payable Total current liabilities
= = =
$500,000 800,000 600,000 $1,900,000
So the firm’s net working capital was $1,800,000 ($3,700,000 - $1,900,000).
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2-2 Balance Sheet Casello Mowing & Landscaping’s year-end 2021 balance sheet lists current assets of $435,200, fixed assets of $550,800, current liabilities of $416,600, and long-term debt of $314,500. Calculate Casello’s total stockholders’ equity. Recall the balance sheet identity in Equation 2-1: Assets = Liabilities + Equity. Rearranging this equation: Equity = Assets – Liabilities. Thus, the balance sheets would appear as follows: Book value Assets
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Book value Liabilities and Equity
Current assets Fixed assets
$ 435,200 550,800
Total
$ 986,000
Current liabilities Long-term debt Stockholders’ equity Total
$ 416,600 314,500 254,900 $ 986,000
2-3 Income Statement The Fitness Studio, Inc.’s 2021 income statement lists the following income and expenses: EBITDA = $650,000, EBIT = $538,000, interest expense = $63,000, and net income = $435,000. Calculate the 2021 taxes reported on the income statement. With $650,000 of EBITDA, The Fitness Studio is allowed to deduct $195,000 ($650,000 x 30 percent) in net interest expense. The recorded interest expense of $63,000 is under this limit and is thus all tax deductible. EBIT Interest expense EBT
$538,000 -63,000 $ 475,000
Chapter 2 - Reviewing Financial Statements
Taxes Net income
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-40,000 $435,000
2-4 Income Statement The Fitness Studio, Inc.’s 2021 income statement lists the following income and expenses: EBITDA = $923,000, EBIT = $773,500, interest expense = $100,000, and taxes = $234,500. The firm has no preferred stock outstanding and 100,000 shares of common stock outstanding. Calculate the 2018 earnings per share. With $923,000 of EBITDA, The Fitness Studio is allowed to deduct $276,900 ($923,000 x 30 percent) in net interest expense. The recorded interest expense of $100,000 is under this limit and is thus all tax deductible. EBIT Interest expense EBT Taxes Net income
$773,500 -100,000 $ 673,500 -234,500 $439,000
Thus, $439,000 Earnings per share (EPS) = —————— = $4.39 per share 100,000 shares
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2-5 Income Statement Consider a firm with an EBIT of $850,000. The firm finances its assets with $2,500,000 debt (costing 7.5 percent and is all tax deductible) and 400,000 shares of stock selling at $5.00 per share. To reduce firm’s risk associated with this financial leverage, the firm is considering reducing its debt by $1,000,000 by selling an additional 200,000 shares of stock. The firm’s tax rate is 21 percent. The change in capital structure will have no effect on the operations of the firm. Thus, EBIT will remain at $850,000. Calculate the change in the firm’s EPS from this change in capital structure. The EPS before and after this change in capital structure is illustrated below: Before capital structure change After capital structure change EBIT $850,000 $850,000 Less: Interest ($2,500,000 x 0.075) 187,500 ($1,500,000 x 0.075) 112,500 EBT 662,500 737,500 Less: Taxes (21%) 139,125 154,875 Net income $523,375 $582,625 Divide by # of shares 400,000 600,000 EPS $1.3084 $0.9710 The change in capital structure would decrease the stockholders EPS by $0.3374.
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2-6 Income Statement Consider a firm with an EBIT of $550,000. The firm finances its assets with $1,000,000 debt (costing 5.5 percent and is all tax deductible) and 200,000 shares of stock selling at $12.00 per share. The firm is considering increasing its debt by $900,000, using the proceeds to buy back 75,000 shares of stock. The firm’s tax rate is 21 percent. The change in capital structure will have no effect on the operations of the firm. Thus, EBIT will remain at $550,000. Calculate the change in the firm’s EPS from this change in capital structure.
Chapter 2 - Reviewing Financial Statements
The EPS before and after this change in capital structure is illustrated below: Before capital structure change After capital structure change EBIT $550,000 $550,000 Less: Interest ($1,000,000 x 0.055) 55,000 ($1,900,000 x 0.055) 104,500 EBT 495,000 445,500 Less: Taxes (21%) 103,950 93,555 Net income $391,050 $351,945 Divide by # of shares 200,000 125,000 EPS $1.9552 $2.8156 The change in capital structure increases the stockholders EPS by $0.8604.
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2-7 Corporate Taxes Oakdale Fashions, Inc., 2021 Income Statement is reported below. 2021 Net sales (all credit) $565,000 Less: Cost of goods sold 215,000 Gross profits 350,000 Less: Other operating expenses 90,000 Earnings before interest, taxes, depreciation, and amortization (EBITDA) 260,000 Less: Depreciation and amortization 15,000 Earnings before interest and taxes (EBIT) 245,000 Less: Interest 80,000 Earnings before taxes (EBT) 165,000 Less: Taxes Net income $ Determine the firm’s 2021 tax liability, net income, average tax rate, and marginal tax rate. (LG2-3) With $260,000 of EBITDA, Oakdale Fashions is allowed to deduct only $78,000 ($260,000 x 30 percent) of its $80,000 in net interest expense. Thus, Taxable income = EBIT – Allowable interest deduction = $245,000 - $78,000 = $167,000 Tax liability = 0.21x Taxable income = 0.21($167,000) = $35,070 The 30 percent cap on the allowable interest deduction results in an increase in Oakdale Fashions’ tax liability of $420 (0.21($80,000 - $78,000)). Net income = EBT – Tax liability = $165,000 - $35,070 = $129,930 The average tax rate for Oakdale Fashions Inc. comes to: $35,070 Average tax rate = ———— $167,000
= 21.00%
Chapter 2 - Reviewing Financial Statements
If Oakdale Fashions, Inc. earned $1 more of taxable income, it would pay 21 cents (its tax rate of 21 percent) more in taxes. Thus, the firm’s marginal tax rate is 21 percent.
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2-8 Corporate Taxes Everybody’s Fitness 2021 Income Statement is reported below (in millions of dollars). 2021 Net sales (all credit) $885 Less: Cost of goods sold 440 Gross profits 445 Less: Other operating expenses 215 Earnings before interest, taxes, depreciation, and amortization (EBITDA) 230 Less: Depreciation and amortization 52 Earnings before interest and taxes (EBIT) 178 Less: Interest 75 Earnings before taxes (EBT) 103 Less: Taxes Net income $ Determine the firm’s 2021 tax liability, net income, average tax rate, and marginal tax rate. (LG2-3) With $230,000,000 of EBITDA, Everybody’s Fitness is allowed to deduct only $69,000,000 ($230,000,000 x 30 percent) of its $75,000,000 in net interest expense. Thus, Taxable income = EBIT – Allowable interest deduction = $178,000,000 - $69,000,000 = $109,000,000 Tax liability = 0.21x Taxable income = 0.21($109,000,000) = $22,890,000 The 30 percent cap on the allowable interest deduction results in an increase in Everybody’s Fitness’ tax liability of $1,260,000 (0.21($75,000,000 - $69,000,000)). Net income = EBT – Tax liability = $103,000,000 - $22,890,000 = $80,110,000 The average tax rate for Everybody’s Fitness comes to: $22,890,000 Average tax rate = —————— = 21.00% $109,000,000 If Oakdale Fashions, Inc. earned $1 more of taxable income, it would pay 21 cents (its tax rate of 21 percent) more in taxes. Thus, the firm’s marginal tax rate is 21 percent.
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2-9 Corporate Taxes Hunt Taxidermy, Inc., is concerned about the taxes paid by the company in 2021. In addition to $42.4 million of taxable income, the firm received $2,975,000 of interest
Chapter 2 - Reviewing Financial Statements
on state-issued bonds and $1,000,000 of dividends on common stock it owns in Oakdale Fashions, Inc. Calculate Hunt Taxidermy’s tax liability, average tax rate, and marginal tax rate. In this case, interest on the state-issued bonds is not taxable and should not be included in taxable income. Further, the first 50 percent of the dividends received from Oakdale Fashions is not taxable. Thus, only 50 percent of the dividends received are taxed, so: Taxable income = $42,400,000 + (0.5)$1,000,000 = $42,900,000 Now Hunt Taxidermy’s tax liability will be: Tax liability = 0.21 ($42,900,000) = $9,009,000 The $1,000,000 of dividend income increased Hunt Taxidermy’s tax liability by $105,000 (0.5 x $1,000,000 x 0.21). Hunt Taxidermy’s resulting average tax rate is: Average tax rage = $9,009,000/$42,900,000 = 21.00% Finally, if Hunt Taxidermy earned $1 more of taxable income, it would pay 21 cents (based upon its tax rate of 21 percent) more in taxes. Thus, the firm’s marginal tax rate is 21 percent.
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2-10 Corporate Taxes Chapman & Power Inc., is concerned about the taxes paid by the company in 2021. In addition to $135,000,000 of taxable income, the firm received $15,500,000 of interest on state-issued bonds and $12,000,000 of dividends on common stock it owns in Hunt Taxidermy. Calculate Chapman & Power’s tax liability, average tax rate, and marginal tax rate. In this case, interest on the state-issued bonds is not taxable and should not be included in taxable income. Further, the first 50 percent of the dividends received from Hunt Taxidermy is not taxable. Thus, only 50 percent of the dividends received are taxed, so: Taxable income = $135,000,000 + (0.5)$12,000,000 = $141,000,000 Now Hunt Taxidermy’s tax liability will be: Tax liability = 0.21 ($141,000,000) = $29,610,000 The $12,000,000 of dividend income increased Chapman & Power’s tax liability by $1,260,000 (0.5 x $12,000,000 x 0.21). Hunt Taxidermy’s resulting average tax rate is: Average tax rage = $29,610,000/$141,000,000 = 21.00% Finally, if Chapman & Power earned $1 more of taxable income, it would pay 21 cents (based upon its tax rate of 21 percent) more in taxes. Thus, the firm’s marginal tax rate is 21 percent.
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2-11 Statement of Cash Flows Ramakrishnan Inc. reported 2021 net income of $15 million and depreciation of $2,650,000. The top part of Ramakrishnan, Inc.’s 2021 and 2020 balance sheets is listed below (in millions of dollars). Current assets: Cash and marketable securities Accounts receivable Inventory
2021
2020
$ 20 84 121
$ 15 75 110
Current liabilities: Accrued wages and taxes Accounts payable Notes payable
2021
2020
$ 19 51 45
$ 18 45 40
Chapter 2 - Reviewing Financial Statements
Total
$225
$200
Total
$115
$103
Calculate the 2021 net cash flow from operating activities for Ramakrishnan, Inc.
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Cash Flows from Operating Activities Net income Additions (sources of cash): Depreciation Increase in accrued wages and taxes Increase in accounts payable Subtractions (uses of cash): Increase in accounts receivable Increase in inventory
-9,000,000 -11,000,000
Net cash flow from operating activities:
$4,650,000
$15,000,000 2,650,000 1,000,000 6,000,000
2-12 Statement of Cash Flows In 2021, Usher Sports Shop had cash flows from investing activities of -$4,364,000 and cash flows from financing activities of -$5,880,000. The balance in the firm’s cash account was $1,615,000 at the beginning of 2021 and $1,742,000 at the end of the year. Calculate Usher Sports Shop’s cash flow from operations for 2021. Net change in cash and marketable securities = $1,742,000 - $1,615,000 = $127,000 Cash flows from operating activities Cash flows from investing activities Cash flows from financing activities Net change in cash and marketable securities
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= $10,371,000 = - 4,364,000 = - 5,880,000 = $127,000
2-13 Free Cash Flow You are considering an investment in Fields and Struthers, Inc., and want to evaluate the firm’s free cash flow. From the income statement, you see that Fields and Struthers earned an EBIT of $62 million, had a tax rate of 30 percent, and its depreciation expense was $5 million. Fields and Struthers’ gross fixed assets increased by $32 million from 2020 to 2020. The firm’s current assets increased by $20 million and spontaneous current liabilities increased by $12 million. Calculate Fields and Struthers’ NOPAT, operating cash flow, investment in operating capital, and free cash flow for 2021. Fields and Struthers’ NOPAT was: NOPAT = EBIT(1 – Tax rate) = $62m.(1 – 0.21) = $48.98m. Operating cash flow for 2021 was: OCF = NOPAT + Depreciation = $48.98m. + $5m. = $53.98m. Investment in operating capital for 2021 was: IOC = ΔGross fixed assets + ΔNet operating working capital = $32m. + ($20m. - $12m.) = $40 m. Accordingly, Fields and Struthers’ free cash flow for 2021 was: FCF = Operating cash flow – Investment in operating capital = $53.98m. - $40m. = $13.98m.
Chapter 2 - Reviewing Financial Statements
In other words, in 2021, Fields and Struthers had cash flows of $13.98 million available to pay its stockholders and debtholders.
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2-14 Free Cash Flow Tater and Pepper Corp. reported free cash flows for 2021 of $39.1 million and investment in operating capital of $22.1 million. Tater and Pepper incurred $13.6 million in depreciation expense and paid $28.9 million in taxes on EBIT in 2021. Calculate Tater and Pepper’s 2021 EBIT. Tater and Pepper’s free cash flow for 2021 was: FCF = Operating cash flow – Investment in operating capital $39.1m. = Operating cash flow - $22.1m. So, operating cash flow = $39.1m. + $22.1m. = $61.2m. Tater and Pepper’s operating cash flow was: OCF = EBIT(1 – Tax rate) + Depreciation = EBIT – Taxes on EBIT + Depreciation $61.2m. = EBIT – $28.9m. + $13.6m. So, EBIT = $61.2m. + $28.9m. - $13.6m. = $76.5m.
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2-15 Statement of Retained Earnings Mr. Husker’s Tuxedos, Corp. began the year 2021 with $256 million in retained earnings. The firm earned net income of $33 million in 2021 and paid dividends of $5 million to its preferred stockholders and $10 million to its common stockholders. What is the yearend 2021 balance in retained earnings for Mr. Husker’s Tuxedos? The statement of retained earnings for 2021 is as follows: Balance of retained earnings, December 31, 2020 Plus: Net income for 2021 Less: Cash dividends paid Preferred stock Common stock Total cash dividends paid Balance of retained earnings, December 31, 2021
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$256m. 33m. $5m. 10m. 15m. $274m.
2-16 Statement of Retained Earnings Use the following information to find dividends paid to common stockholders during 2021. Balance of retained earnings, December 31, 2020 Plus: Net income for 2021 Less: Cash dividends paid Preferred stock $1m. _6m. Common stock Total cash dividends paid Balance of retained earnings, December 31, 2021
$462m. 15m.
7m. $470m.
Total cash dividends paid = $470m. - $15m. - $462m. = -$7m. Thus, common stock dividends paid = $7m. - $1m = $6m.
intermediate 2-17 Balance Sheet Mikey’s Bar and Grill has total assets of $15 million of which $5 million
Chapter 2 - Reviewing Financial Statements
problems
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are current assets. Cash makes up 10 percent of the current assets and accounts receivable makes up another 40 percent of current assets. Mikey’s gross plant and equipment has a book value of $11.5 million and other long-term assets have a book value of $500,000. Using this information, what is the balance of inventory and the balance of depreciation on Mikey’s Bar and Grill’s balance sheet? Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment Other long-term assets Total
(in millions)
step 1.
$11.5 2.0
step 3.
$9.5 ($10.0 - $0.5)
step 2.
0.5 $10.0 ($15.0 - $5.0)
($11.5 - $9.5)
$15.0
2-18 Balance Sheet Sophie’s Tobacco Shop has total assets of $91.8 million. Fifty percent of these assets are financed with debt of which $28.9 million is current liabilities. The firm has no preferred stock, but the balance in common stock and paid-in surplus is $20.4 million. Using this information what is the balance for long-term debt and retained earnings on Sophie’s Tobacco Shop’s balance sheet? (in millions) $28.9
Total current liabilities Long-term debt: Total debt:
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(0.1 x $5) (0.4 x $5) ($5 - $0.5 - $2.0)
step 4.
Total assets
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$ 0.5 2.0 2.5 $5.0
step 3. step 2.
17.0 (= $45.9 - $28.9) $45.9 (= 0.5 x $91.8)
Stockholders’ equity: Preferred stock Common stock and paid-in surplus (20 million shares) Retained earnings Total
step 5. step 4
25.5 $45.9
Total liabilities and equity
step 1.
$91.8 (= Total Assets)
$ 0.0 20.4 (= $45.9 - $20.4) (= $91.8 - $45.9)
2-19 Market Value versus Book Value Muffin’s Masonry, Inc’s balance sheet lists net fixed asset as $14 million. The fixed assets could currently be sold for $19 million. Muffin’s current balance sheet shows current liabilities of $5.5 million and net working capital of $4.5 million. If all the current accounts were liquidated today, the company would receive $7.25 million cash after paying the $5.5 million in current liabilities. What is the book value of Muffin’s Masonry’s assets today? What is the market value of these assets?
Chapter 2 - Reviewing Financial Statements
BOOK VALUE
MARKET VALUE
Assets Current assets Step 1. Fixed assets
$10m. 14m.
Step 3.
$12.75m. 19.00m.
Total
$24m.
Step 4.
$31.75m.
Step 2.
Step 1. Net working capital (book value) = Current assets (book value) – Current liabilities (book value) = $4.5m. = Current assets (book value) - $5.5m. => Current assets (book value) = $4.5m. + $5.5m. = $10m. Step 2. Total assets (book value) = $10m. + $14m. = $24m. Step 3. Net working capital (market value) = Current assets (market value) – Current liabilities (market value) = $7.25m. = Current assets (market value) - $5.5m. => Current assets (market value) = $7.25m. + $5.5m. = $12.75m. Step 4. Total assets (market value) = $12.75m. + $19m. = $31.75m.
LG2-2
2-20 Market Value versus Book Value Ava’s SpinBall Corp. lists fixed assets of $12 million on its balance sheet. The firm’s fixed assets have recently been appraised at $16 million. Ava’s SpinBall Corp.’s balance sheet also lists current assets at $5 million. Current assets were appraised at $6 million. Current liabilities’ book and market values stand at $3 million and the firm’s book and market values of long-term debt are $7 million. Calculate the book and market values of the firm’s stockholders’ equity. Construct the book value and market value balance sheets for Ava’s SpinBall Corp. (LG2) Recall the balance sheet identity in Equation 2-1: Assets = Liabilities + Equity. Rearranging this equation: Equity = Assets – Liabilities. Thus, the balance sheets would appear as follows:
LG2-1
BOOK VALUE
MARKET VALUE
Assets Current assets Fixed assets
$ 5m. 12m.
$ 6m. 16m.
Total
$17m.
$22m.
Liabilities and Equity Current liabilities Long-term debt Stockholders’ equity Total
BOOK VALUE
MARKET VALUE
$ 3m. 7m. 7m. $17m.
$ 3m. 7m. 12m. $22m.
2-21 Debt versus Equity Financing You are considering a stock investment in one of two firms (NoEquity, Inc., and NoDebt, Inc.), both of which operate in the same industry and have identical EBITDA of $37.7 million and operating income of $32.5 million. NoEquity, Inc., finances its $65 million in assets with $64 million in debt (on which it pays 10 percent interest annually) and $1 million in equity. NoDebt, Inc., finances its $65 million in assets with no debt and $65 million in equity. Both firms pay a tax rate of 21 percent on their taxable income. Calculate the net income and return on asset-funders’ investment for the two firms. With $37.7 million of EBITDA AllDebt Inc., may deduct up to $11.31 million ($37.7 x 30 percent) of interest expense for tax purposes. Thus, AllDebt Inc., is allowed to deduct all of its interest expense.
Operating income Less: Interest Taxable income Less: Taxes (21%) Net income
($64m. x 0.1)
NoEquity
NoDebt
$32.500m 6.400m $26.100m 5.481m $20.619m
$32.500m 0.000m $32.500m 6.825m $25.675m
Chapter 2 - Reviewing Financial Statements
Income available for asset funders (= Operating income - Taxes) Return on asset-funders’ investment
LG2-1
$10.379m
$27.019m/$65m = 41.57%
$25.675m
$25.675m/$65m = 39.50%
2-22 Debt versus Equity Financing You are considering a stock investment in one of two firms (AllDebt, Inc., and AllEquity, Inc.), both of which operate in the same industry and have identical EBITDA of $14.7 million and operating income of $12.5 million. AllDebt, Inc., finances its $25 million in assets with $24 million in debt (on which it pays 10 percent interest annually) and $1 million in equity. AllEquity, Inc., finances its $25 million in assets with no debt and $25 million in equity. Both firms pay a tax rate of 21 percent on their taxable income. Calculate the income available to pay the asset funders (the debt holders and stockholders) and resulting return on asset-funders’ investment for the two firms. With $14.7 million of EBITDA AllDebt Inc., may deduct up to $4.41 million ($14.7 x 30 percent) of interest expense for tax purposes. Thus, AllDebt Inc., is allowed to deduct all of its interest expense.
Operating income Less: Interest Taxable income Less: Taxes (21%) Net income Income available for asset funders (= Operating income - Taxes) Return on asset-funders’ investment
LG2-1
($24m. x 0.1)
AllDebt
AllEquity
$12.500m 2.400m $10.100m 2.121m $7.979m $10.379m
$12.500m 0.000m $12.500m 2.625m $9.875m $9.875m
$10.379m./$25m. = 41.516%
$9.875m./$25m. = 39.500%
2-23 Income Statement You have been given the following information for Corky’s Bedding Corp.: a. Net sales = $11,250,000. b. Cost of goods sold = $7,500,000. c. Other operating expenses = $250,000. d. Addition to retained earnings = $1,000,000. e. Dividends paid to preferred and common stockholders = $495,000. f. Interest expense = $850,000, all of which is tax deductible. The firm’s tax rate is 35 percent. Calculate the depreciation expense for Corky’s Bedding Corp. Net sales Less: Cost of goods sold Gross profits Step 4. Less: Other operating expenses Earnings before interest, taxes, depreciation, and amortization (EBITDA) Step 5. Less: Depreciation Step 6. Earnings before interest and taxes (EBIT) Step 3. Less: Interest Earnings before taxes (EBT) Step 2. Less: Taxes (21%)
$11,250,000 7,500,000 $3,750,000 250,000 $3,500,000 350,000 $3,150,000 850,000 $2,300,000
Chapter 2 - Reviewing Financial Statements
Net income
Step 1.
Less: Common and preferred stock dividends Addition to retained earnings
$1,817,000 $ 817,000 $1,000,000
Step 1. Net income = Common and preferred stock dividends + Addition to retained earnings = $817,000 + $1,000,000 = $1,817,000 Step 2. EBT (1 – Tax rate) = Net income => EBT = Net income/(1 – Tax rate) = $1,817,000/(1 - 0.21) = $2,300,000 Step 3. EBIT – Interest = EBT => EBIT = EBT + Interest = $2,300,000 + $850,000 = $3,150,000 Step 4. Gross profits = Net sales – Cost of goods sold = $11,250,000 – 7,500,000 = $3,750,000 Step 5. EBITDA = Gross profits – Other operating expenses = $3,750,000 – 250,000 = $3,500,000 Step 6. EBITDA – Depreciation = EBIT => Depreciation = EBITDA – EBIT = $3,500,000 - $3,150,000 = $350,000
LG2-1
2-24 Income Statement You have been given the following information for Moore’s HoneyBee Corp.: a. Net sales = $32,000,000. b. Gross profits = $18,700,000. c. Other operating expenses = $2,500,000. d. Addition to retained earnings = $4,700,000. e. Dividends paid to preferred and common stockholders = $2,900,000. f. Depreciation expense = $2,800,000. The firm’s tax rate is 35 percent. The firm’s interest expense is all tax deductible. Calculate the cost of goods sold and the interest expense for Moore’s HoneyBee Corp. Net sales Less: Cost of goods sold Step 1. Gross profits Less: Other operating expenses Earnings before interest, taxes, depreciation, and amortization (EBITDA) Step 4. Less: Depreciation Earnings before interest and taxes (EBIT) Step 5. Less: Interest Step 6. Earnings before taxes (EBT) Step 3. Less: Taxes (21%) Net income Step 2. Less: Common and preferred stock dividends Addition to retained earnings
$32,000,000 13,300,000 $18,700,000 2,500,000 $16,200,000 2,800,000 $13,400,000 1,700,000 $11,700,000 $ 9,243,000 $2,900,000 $6,343,000
Step 1. Net sales - Cost of goods sold = Gross profits => Cost of goods sold = Net sales – Gross Profits = $32,000,000 – $18,700,000 = $13,300,000 Step 2. Net income = Common and preferred stock dividends + Addition to retained earnings = $2,900,000 + $6,343,000 = $9,243,000 Step 3. EBT (1 – Tax rate) = Net income => EBT = Net income/(1 – Tax rate) = $9,243,000/(1 - 0.21) = $11,700,000 Step 4. EBITDA = Gross profits – Other operating expenses = $18,700,000 – 2,500,000 = $16,200,000 Step 5. EBITDA – Depreciation = EBIT = $16,200,000 - $2,800,000 = $13,400,000 Step 6. EBIT – Interest = EBT => Interest = EBIT - EBT = $13,400,000 - $11,7000,000 = $1,700,000
LG2-1
2-25 Income Statement Consider a firm with an EBITDA of $1,100,000 and an EBIT of $1,000,000. The firm finances its assets with $4,500,000 debt (costing 8 percent, all of which is
Chapter 2 - Reviewing Financial Statements
tax deductible) and 200,000 shares of stock selling at $16.00 per share. To reduce risk associated with this financial leverage, the firm is considering reducing its debt by $2,500,000 by selling additional shares of stock. The firm’s tax rate is 21 percent. The change in capital structure will have no effect on the operations of the firm. Thus, EBIT will remain at $1,000,000. Calculate the change in the firm’s EPS from this change in capital structure. With $1,100,000 of EBITDA, the firm may deduct up to $330,000 ($1,100,000 x 30 percent) of interest expense for tax purposes. Thus, given the current capital structure, the firm may deduct only $330,000 of its $360,000 interest expense ($4,500,000 x 0.08) for tax purposes. Thus, Taxable income = EBIT – Allowable interest deduction = $1,000,000 - $330,000 = $670,000 Tax liability = 0.21x Taxable income = 0.21($670,000) = $140,700 With the proposed change in capital structure, the firm may deduct all of its $160,000 ($2,000,000 x 0.08) interest expense for tax purposes. Number of shares of stock that must be sold to raise $2,500,000: $2,500,000/$16 = 156,250 => number of shares of stock outstanding after refinancing = 200,000 + 156,250 = 356,250 The EPS before and after this change in capital structure is illustrated below: Before capital structure change After capital structure change EBIT $1,000,000 $1,000,000 Less: Interest ($4,500,000 x 0.08) 360,000 ($2,000,000 x 0.08) 160,000 EBT 640,000 840,000 Less: Taxes (21%) 140,700 176,400 Net income $499,300 $663,600 Divide by # of shares 200,000 356,250 EPS $2.4965 $1.8627 The change in capital structure will result in a decrease in the stockholders EPS by $0.6338.
LG2-1
2-26 Income Statement Consider a firm with an EBITDA of $13,00,000 and an EBIT of $10,500,000. The firm finances its assets with $50,000,000 debt (costing 6.5 percent) and 10,000,000 shares of stock selling at $10.00 per share. The firm is considering increasing its debt by $25,000,000, using the proceeds to buy back shares of stock. The firm’s tax rate is 21 percent. The change in capital structure will have no effect on the operations of the firm. Thus, EBIT will remain at $10,500,000. Calculate the change in the firm’s EPS from this change in capital structure. With $13,000,000 of EBITDA, the firm may deduct up to $3,900,000 ($13,000,000 x 30 percent) of interest expense for tax purposes. Thus, given the current capital structure, the firm may deduct the full $3,250,000 ($50,000,000 x 0.065) of its interest expense for tax purposes. With the proposed change in capital structure, the firm may deduct only $3,900,000 of its $4,875,000 interest expense ($75,000,000 x 0.065) for tax purposes. Thus, Taxable income = EBIT – Allowable interest deduction = $10,500,000 - $3,900,000 = $6,600,000
Chapter 2 - Reviewing Financial Statements
Tax liability = 0.21x Taxable income = 0.21($6,600,000) = $1,386,000 Number of shares of stock that can be repurchased with $25,000,000: $25,000,000/$10 = 2,500,000 => number of shares of stock outstanding after refinancing = 10,000,000 – 2,500,000 = 7,500,000 The EPS before and after this change in capital structure is illustrated below: Before capital structure change After capital structure change EBIT $10,500,000 $10,500,000 Less: Interest ($50,000,000 x 0.065) 3,250,000 ($75,000,000 x 0.065) 4,875,000 EBT 7,250,000 5,625,000 Less: Taxes (21%) 1,522,500 1,386,000 Net income $5,727,500 $4,239,000 Divide by # of shares 10,000,000 7,500,000 EPS $0.57275 $0.56520 The change in capital structure decreases the stockholders EPS by $0.00755. While interest on debt is tax deductible up to 30 percent of EBITDA, in this case the change in the capital structure causes the firm to hit the tax deductible cap. The tax benefits of additional debt do not apply once the firm hits the cap, causing debt to no longer be an attractive option from stockholders viewpoint.
LG2-3
2-27 Corporate Taxes The Dakota Corporation had a 2021 taxable income of $33,365,000 from operations after all operating costs but before (1) interest charges of $8,500,000, all of which is tax deductible; (2) dividends received of $750,000; (3) dividends paid of $5,250,000; and (4) income taxes. The firm’s EBITDA is $tax rate is 21 percent. a. Calculate Dakota’s income tax liability. The first 50 percent of the dividends received is not taxable. Thus, only 50 percent of the dividends received are taxed, so: Taxable income = $33,365,000 - $8,500,000 + (0.5)$750,000 = $25,240,000 Now Dakota Corp.’s tax liability will be: Tax liability = 0.21 ($25,240,000) = $5,300,400
b. What are Dakota’s average and marginal tax rates on taxable income? Dakota Corp.’s average tax rate is: Average tax rate = $5,300,400/$25,240,000 = 21.00% Finally, if Dakota Corp earned $1 more of taxable income, it would pay 21 cents (based on its tax rate of 21 percent) more in taxes. Thus, the marginal tax rate is 21 percent.
LG2-3
2-26 Corporate Taxes Suppose that in addition to $17.85 million of taxable income, Texas Taco, Inc., received $1,105,000 of interest on state-issued bonds and $760,000 of dividends on common stock it owns in ArizonaTaco, Inc. a. Calculate Texas Taco’s income tax liability.
Chapter 2 - Reviewing Financial Statements
Interest on the state-issued bonds is not taxable and should not be included in taxable income. Further, the first 50 percent of the dividends received from ArizonaTaco is not taxable. Thus, only 50 percent of the dividends received are taxed, so: Taxable income = $17,850,000 + (0.5)$760,000 = $18,230,000 Texas Taco’s tax liability will be: Tax liability = 0.21 ($18,230,000) = $3,828,300
b. What are Texas Taco’s average and marginal tax rates on taxable income? Texas Taco’s resulting average tax rate is: Average tax rate = $3,828,300/$18,230,000= 21.00% Finally, if Texas Taco earned $1 more of taxable income, it would pay 21 cents (based upon its tax rate of 21 percent) more in taxes. Thus, the marginal tax rate is 21 percent.
LG2-5
2-29 Statement of Cash Flows Use the balance sheet and income statement below to construct a statement of cash flows for Clancy’s Dog Biscuit Corporation.
2021 Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Accumulated depreciation Net plant and equipment Other long-term assets Total Total assets
$
5 20 36 $ 61
Clancy’s Dog Biscuit Corporation Balance Sheet as of December 31, 2021and 2020 (in millions of dollars) 2020 Liabilities and Equity Current liabilities : Accrued wages and $ 5 taxes 19 Accounts payable 29 Notes payable $ 53 Total
2021
2020
$ 10 16 14 $ 40
$ 6 15 13 $ 34
Long-term debt:
$ 57
$ 53
$ 2
$ 2
11
11
57 $ 70
45 $ 58
$167
$145
$106
$ 88
15
11
$ 91
$ 77
15 $106
15 $ 92
Stockholders’ equity: Preferred stock (2 million shares) Common stock and paid-in surplus (5 million shares) Retained earnings Total
$167
$145
Total liabilities and equity
Clancy’s Dog Biscuit Corporation Income Statement for Years Ending December 31, 2021 and 2020 (in millions of dollars) 2021 2020 Net sales $ 76 $ 80 Less: Cost of goods sold 38 35 Gross profits $ 38 $ 45 Less: Other operating expenses 6 5 Earnings before interest, taxes, depreciation, and
Chapter 2 - Reviewing Financial Statements
amortization (EBITDA) Less: Depreciation Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes Net income
$ 32 4 $ 28 5 $ 23 5 $18
$ 40 4 $ 36 5 $ 31 7 $24
Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
$ 1 $17 5 $12
$ 1 $23 5 $18
$3.00 $1.00 $13.60 $14.25
$4.20 $1.00 $11.20 $14.60
Per (common) share data: Earnings per share (EPS) Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
SOLUTION:
Statement of Cash Flows for Year Ending December 31, 2021 (in millions of dollars) 2021 A. Cash flows from operating activities Net income $18 Additions (sources of cash): Depreciation 4 Increase accrued wages and taxes 4 Increase in accounts payable 1 Subtractions (uses of cash): Increase in accounts receivable -1 Increase in inventory ------------------------------------------------- 7 Net cash flow from operating activities: B. Cash flows from investing activities Subtractions: Increase fixed assets Increase in other long-term assets Net cash flow from investing activities:
$19
-$18 0 -$18
C. Cash flows from financing activities Additions: Increase in notes payable $1 Increase in long-term debt 4 Increase in common and preferred stock 0 Subtractions: Preferred stock dividends -1 Common stock dividends -------------------------------------------- 5 Net cash flow from financing activities:
- $1
D. Net change in cash and marketable securities
-$ 0
Chapter 2 - Reviewing Financial Statements
LG2-5
2-30 Statement of Cash Flows Use the balance sheet and income statement below to construct a statement of cash flows for Valium’s Medical Supply Corporation.
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Accumulated depreciation Net plant and equipment Other long-term assets Total Total assets
Valium’s Medical Supply Corporation Balance Sheet as of December 31, 2021 and 2020 (in thousands of dollars) 2021 2020 Liabilities and Equity Current liabilities : Accrued wages and $ 74 $ 73 taxes 199 189 Accounts payable 322 291 Notes payable $ 595 $ 553 Total Long-term debt: $1,084
$ 886
153
116
$ 931 $ 770 130 $1,061
130 $ 900
$1,656
$1,453
2021
$
58 $ 45 159 145 131 131 $ 348 $ 321
$ 565
Per (common) share data:
$549
Stockholders’ equity: Preferred stock (6 thousand shares) $ 6 $ 6 Common stock and paid-in surplus 120 120 (100 thousand shares) Retained earnings 617 457 Total $ 743 $ 583 Total liabilities and equity
$1,656 $1,453
Valium’s Medical Supply Corporation Income Statement for Years Ending December 31, 2021 and 2020 (in thousands of dollars) 2021 2020 Net sales $ 888 $ 798 Less: Cost of goods sold 387 350 Gross profits $ 501 $ 448 Less: Other operating expenses 48 42 Earnings before interest, taxes, depreciation, and amortization (EBITDA) $ 453 $ 406 Less: Depreciation and amortization 37 35 Earnings before interest and taxes (EBIT) $ 416 $ 371 Less: Interest 46 40 Earnings before taxes (EBT) $ 370 $ 331 Less: Taxes 78 70 Net income $ 292 $ 261 Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
2020
$ 6 $ 286 126 $ 160
$ 6 $ 255 126 $ 129
Chapter 2 - Reviewing Financial Statements
Earnings per share (EPS) Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
SOLUTION:
$2.86 $1.26 $7.37 $8.40
$2.55 $1.26 $5.77 $6.25
Statement of Cash Flows for Year Ending December 31, 2021 (in thousands of dollars)
A. Cash flows from operating activities Net income $292 Additions (sources of cash): Depreciation and amortization 37 Increase in accrued wages and taxes 13 Increase in accounts payable 14 Subtractions (uses of cash): Increase in accounts receivable -10 Increase in inventory ------------------------------------------------ 31 Net cash flow from operating activities:
$315
B. Cash flows from investing activities Subtractions: Increase in fixed assets Increase in other long-term assets
-$198 0
Net cash flow from investing activities:
-$198
C. Cash flows from financing activities Additions: Increase in notes payable Increase in long-term debt Increase in common and preferred stock Subtractions: Preferred stock dividends Common stock dividends
LG2-5
$
0 16 0
- 6 -126
Net cash flow from financing activities:
-$116
D. Net change in cash and marketable securities
$
1
2-31 Statement of Cash Flows Chris’ Outdoor Furniture, Inc., has net cash flows from operating activities for the last year of $340 million. The income statement shows that net income is $315 million and depreciation expense is $46 million. During the year, the change in inventory on the balance sheet was $38 million, change in accrued wages and taxes was $15 million and change in accounts payable was $20 million. At the beginning of the year the balance of accounts receivable was $50 million. Calculate the end-of-year balance for accounts receivable. A. Cash flows from operating activities Net income Additions (sources of cash): Depreciation
(in millions) $315 46
Chapter 2 - Reviewing Financial Statements
Increase accrued wages and taxes 15 Increase in accounts payable 20 Subtractions (uses of cash): Increase in accounts receivable -18 (=$340 - $315 - $46 - $15 - $20 + $38) Increase in inventory --------------------------------- 38 Net cash flow from operating activities:
$340
End-of-year balance for accounts receivable = $50m. + $18m. = $68m.
LG2-5
2-32 Statement of Cash Flows Dogs 4 U Corporation has net cash flow from financing activities for the last year of $34 million. The company paid $178 million in dividends last year. During the year, the change in notes payable on the balance sheet was $39 million, and change in common and preferred stock was $0. The end-of-year balance for long-term debt was $315 million. Calculate the beginning-of-year balance for long-term debt. C. Cash flows from financing activities Additions: Increase in notes payable Increase in long-term debt Increase in common and preferred stock Subtractions: Stock dividends
(in millions)
Net cash flow from financing activities:
$34
$ 39 173 (=$34 + $178 - $39) 0 -178
Beginning-of-year balance for long-term debt = $315m. - $173m = $142m.
LG2-5
2-31 Free Cash Flow The 2021 income statement for Duffy’s Pest Control shows that depreciation expense was $197 million, EBIT was $440 million, and the tax rate was 21 percent. At the beginning of the year, the balance of gross fixed assets was $1,562 million and net operating working capital was $417 million. At the end of the year, gross fixed assets was $1,803 million. Duffy’s free cash flow for the year was $424 million. Calculate the end-of-year balance for net operating working capital. Duffy’s Pest Control’s operating cash flow was: OCF = EBIT(1 – Tax rate) + Depreciation = ($440m.(1 - 0.21) + $197m.) = $544.6m. Duffy’s Pest Control’s free cash flow for 2021 was: FCF = Operating cash flow – Investment in operating capital $424m. = $544.6m. - Investment in operating capital => Investment in operating capital = $544.6m. - $424m. = $120.6m. Accordingly, investment in operating capital for 2021 was: IOC = ΔGross fixed assets + ΔNet operating working capital $120.6m. = ($1,803m. - $1,562m.) + (Ending net operating working capital - $417m.) => Ending net operating working capital = $120.6m. - ($1,803m. - $1,562m.) + $417m. = $296.6m.
LG2-5
2-34 Free Cash Flow The 2021 income statement for Egyptian Noise Blasters shows that depreciation expense is $85 million, NOPAT is $246 million. At the end of the year, the balance
Chapter 2 - Reviewing Financial Statements
of gross fixed assets was $655 million. The change in net operating working capital during the year was $73 million. Egyptian’s free cash flow for the year was $190 million. Calculate the beginning-of-year balance for gross fixed assets. Egyptian Noise Blasters’ operating cash flow was: OCF = NOPAT + Depreciation = = ($246m. + $85m.) = $331m. Egyptian Noise Blasters’ free cash flow for 2021 was: FCF = Operating cash flow – Investment in operating capital $190m. = $331m. - Investment in operating capital = > Investment in operating capital = $331m. - $190m. = $141m. Accordingly, investment in operating capital for 2021 was: IOC = ΔGross fixed assets + ΔNet operating working capital $141m. = ($655m. – Beginning of year gross fixed assets) + $73m. => Beginning of year gross fixed assets = $655m. - $141m. + $73m. = $587m.
LG2-1
2-35 Statement of Retained Earnings Thelma and Louie, Inc., started the year with a balance of retained earnings of $543 million and ended the year with retained earnings of $589 million. The company paid dividends of $35 million to the preferred stockholders and $88 million to common stockholders. Calculate Thelma and Louie’s net income for the year. Statement of Retained Earnings as of December 31, 2021 (in millions of dollars) Balance of retained earnings, December 31, 2020 Plus: Net income for 2021 Less: Cash dividends paid Preferred stock Common stock Total cash dividends paid Balance of retained earnings, December 31, 2021
LG2-1
$543 169 (= $589 + $123 - $543) $35 88 123 $589
2-36 Statement of Retained Earnings Jamaica Tours, Inc., started the year with a balance of retained earnings of $1,780 million. The company reported net income for the year of $284 million and paid dividends of $17 million to the preferred stockholders and $59 million to common stockholders. Calculate Jamaica Tour’s end-of-year balance in retained earnings. Statement of Retained Earnings as of December 31, 2018 (in millions of dollars) Balance of retained earnings, December 31, 2017 Plus: Net income for 2018 Less: Cash dividends paid Preferred stock Common stock Total cash dividends paid Balance of retained earnings, December 31, 2018
$1,780 284 $17 59 76 $1,988
Chapter 2 - Reviewing Financial Statements
advanced 2-37 Income Statement Listed below is the 2021 income statement for Tom and Sue Travels, Inc. problems LG2-1 Tom and Sue Travels, Inc. Income Statement for Year Ending December 31, 2021 (in millions of dollars) Net sales Less: Cost of goods sold Gross profits Less: Other operating expenses Earnings before interest, taxes, depreciation, and amortization (EBITDA) Less: Depreciation Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes Net income
$16.500 7.100 9.400 3.200 6.200 2.900 3.300 0.950 2.350 0.495 $ 1.855
The CEO of Tom and Sue’s wants the company to earn a net income of $2.250 million in 2022. Cost of goods sold is expected to be 60 percent of net sales, depreciation and other operating expenses are not expected to change, interest expense is expected to increase to $1.416 million, and the firm’s tax rate will be 21 percent. Calculate the net sales needed to produce net income of $2.250 million. Tom and Sue Travels, Inc. Income Statement for Year Ending December 31, 2022 (in millions of dollars) Net sales Step 5. $25.910 Less: Cost of goods sold Step 6. 15.546 Gross profits Step 4. 10.364 Less: Other operating expenses 3.200 Earnings before interest, taxes, depreciation, and amortization (EBITDA) Step 3. 7.164 Less: Depreciation 2.900 Earnings before interest and taxes (EBIT) Step 2. 4.264 Less: Interest 1.416 Earnings before taxes (EBT) Step 1. 3.214 Less: Taxes Net income $ 2.250
Step 1. EBT (1-t) = Net income = $2.250m = EBT (1 - 0.21) => EBT = $2.250m./(1 - 0.21) = $2.848m. Step 2. EBIT = EBT + Interest = $2.848m. + $1.416m. = $4.264m. Step 3. EBITDA = EBIT + Depreciation = $4.264m. + $2.900m. = $7.164m Step 4. Gross profits = EBITDA + Other operating expenses = $7.164m. + $3.200m. = $10.364m Step 4. Net sales = Gross profits/(1-Cost of goods sold percent) = $10.364m./(1 - 0.6) = $25.910m.
Chapter 2 - Reviewing Financial Statements Step 5. Cost of goods sold = Net sales – Gross profits = $25.910m. - $10.364 = $15.546m.
LG2-1
2-38 Income Statement You have been given the following information for PattyCake’s Athletic Wear Corp. for the year 2021: a. Net sales = $38,250,000. b. Cost of goods sold = $22,070,000. c. Other operating expenses = $5,300,000. d. Addition to retained earnings = $2,195,500. e. Dividends paid to preferred and common stockholders = $1,912,000. f. Interest expense = $1,785,000. g. The firm’s tax rate is 21 percent. In 2022: h. net sales are expected to increase by $9.75 million. i. Cost of goods sold is expected to be 60 percent of net sales. j. Depreciation and other operating expenses are expected to be the same as in 2021. k. Interest expense is expected to be $2,004,367. l. The tax rate is expected to be 21 percent of EBT. m. Dividends paid to preferred and common stockholders will not change. Calculate the addition to retained earnings expected in 2022. Income Statement for Year Ending December 31, 2021 (in millions of dollars) Net sales Less: Cost of goods sold Gross profits Less: Other operating expenses Earnings before interest, taxes, depreciation, and amortization (EBITDA) Less: Depreciation $10,880,000 - $6,984,367 Earnings before interest and taxes (EBIT) $5,199,367 + $1,785,000 Less: Interest $4,107,500 / (1 - 0.21) Earnings before taxes (EBT) Less: Taxes Net income
$38,250,000 22,070,000 16,180,000 5,300,000
Less: Preferred and common stock dividends Addition to retained earnings
$1,912,000 $2,195,500
10,880,000 3,895,633 6,984,367 1,785,000 5,199,367 $4,107,500
Income Statement for Year Ending December 31, 2022 (in millions of dollars) Net sales (all credit) $38,250,000 + $9,750,000 Less: Cost of goods sold 0.6 x $48,000,000 Gross profits Less: Other operating expenses
$48,000,000 28,800,000 19,200,000 5,300,000
Chapter 2 - Reviewing Financial Statements
LG2-5
Earnings before interest, taxes, depreciation, and amortization (EBITDA) Less: Depreciation Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes (21%) Net income
13,900,000 3,895,633 10,004,367 2,004,367 8,000,000 1,680,000 $6,320,000
Less: Preferred and common stock dividends Addition to retained earnings
$1,912,000 $4,408,000
2-39 Free Cash Flow Rebecky’s Flowers 4U, Inc., had free cash flows during 2021 of $43 million, NOPAT of $85 million, and depreciation of $14 million. Using this information, fill in the blanks on Rebecky’s balance sheet below. Rebecky’s operating cash flow for 2021 was: OCF = NOPAT + Depreciation = ($85m. + $14m.) = $99m. Rebecky’s free cash flow was: FCF = Operating cash flow – Investment in operating capital $43m. = $99m. - Investment in operating capital So, Investment in operating capital = $99m. - $43m. = $56m. IOC = ΔGross fixed assets + ΔNet operating working capital $56m. = ($333m. - $300m.) + ΔNet operating working capital => ΔNet operating working capital = $56m. - ($333m. - $300m.) = $23m. ΔNet operating working capital = $23m. = ∆Current assets - ∆Current liabilities $23m. = ($221m. - $190m.) - ∆Current liabilities => ∆Current liabilities = ($221m. - $190m.) - $23m. = $8m. => 2021 Current liabilities = $110m. + $8m. = $118m. and 2021 Current liabilities = Accrued wages and taxes + Accounts payable + Notes payable $118m. = $17m. + Accounts payable + $45m. => Accounts payable = $118m. - $17m. - $45m. = $56m. => Long-term debt = $550m. - $118m. - $237m. = $195m.
2021 Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment
$ 28 75 118 $221
$333
Rebecky’s Flowers 4U, Inc. Balance Sheet as of December 31, 2021 and 2020 (in millions of dollars) 2020 Liabilities and Equity
$ 25 65 100 $190
$300
2021
2020
Current liabilities : Accrued wages and taxes Accounts payable Notes payable Total
$ 17 56 45 $118
$ 15 50 45 $110
Long-term debt:
$195
$190
Chapter 2 - Reviewing Financial Statements
Less: Accumulated depreciation Net plant and equipment Other long-term assets Total Total assets
LG2-5
54
40
$279
$260
50 $329
50 $310
Stockholders’ equity: Preferred stock (5 million shares) Common stock and paid-in surplus (20 million shares) Retained earnings Total
$550
$500
Total liabilities and equity
$ 5
$
5
40
40
192 $237
155 $200
$550
$500
2-38 Free Cash Flow Vinny’s Overhead Construction had free cash flow during 2021 of $25.4 million. The change in gross fixed assets on Vinny’s balance sheet during 2021 was $7.0 million and the change in net operating working capital was $8.4 million. Using this information, fill in the blanks on Vinny’s income statement below. =>
IOC = ΔGross fixed assets + ΔNet operating working capital IOC = $7.0m. + $8.4m. = $15.4m.
=> =>
FCF = Operating cash flow – Investment in operating capital $25.4m. = OCF – $15.4m. OCF = $25.4m. + $15.4m. = $40.8m.
OCF = EBIT(1 – 0.21) + Depreciation Using the numbers below: $40.8m. = EBIT(1 – 0.21) + $10.2m. => EBIT = ($40.8m. - $10.2m.)/(1 – 0.21) = $38.73m Vinny’s Overhead Construction, Corp. Income Statement for Year Ending December 31, 2021 (in millions of dollars) Net sales Less: Cost of goods sold Gross profits Less: Other operating expenses Earnings before interest, taxes, depreciation, and amortization (EBITDA) Less: Depreciation Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes (21% from above) Net income
$ 182.10 116.10 $ 66.00 17.07 48.93 10.20 $ 38.73 3.73 $ 35.00 7.35 $27.65
Step 1. (= $66.00 + $116.10)
Step 7. (= $66.00 - $48.93) Step 6. (= $38.73 + $10.20) Step 2. (from above) Step 5. (= $38.73 - $35.00) Step 3. (= $27.65 / (1 – 0.21) Step 4. (= $35.00 - $27.65)
research it! Reviewing Financial Statements Go the web site of Wal-Mart Stores, Inc. at www.walmartstores.com and get the latest financial statements from the annual report using the following steps.
Chapter 2 - Reviewing Financial Statements
Go to Wal-Mart Stores, Inc.’s Web site at www.walmartstores.com. Click on Investors, then select Annual Reports; next choose Annual Reports & Proxies. This will bring the file onto your computer that contains the relevant data. Locate the total assets, total equity, net sales, net income, dividends paid, cash flows from operating activities, and cash flows from investing activities for the last two years. How have these items changed over the last two years? SOLUTION: The solution will vary with the year annual report is accessed. However, the annual report for each year summarizes the financial information necessary to evaluate key information used by firm managers, who make financial decisions, and by investors, who decide whether or not to invest in the firm.
Chapter 2 - Reviewing Financial Statements
integrated mini-case: Working with Financial Statements Shown below are partial financial statements for Garners’ Platoon Mental Health Care, Inc. Fill in the blanks on the four financial statements.
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total
Garners’ Platoon Mental Health Care, Inc. Balance Sheet as of December 31, 2021 and 2020 (in millions of dollars) 2021 2020 Liabilities and Equity Current liabilities : Accrued wages and taxes $ 421 $ 1,020 Accounts payable Notes payable 1,760 1,581 $3,290 $ Total
Fixed assets: Gross plant and equipment $ $4,743 Less: Accumulated 840 640 depreciation Net plant and $4,972 $ equipment Other long-term assets 790 Total $5,864 $4,893 Total assets
$
Long-term debt:
2021
2020
$ 316 867
$ 242 791 714 $2,055 $1,747 $3,090 $
Stockholders’ equity: Preferred stock (30 million shares) $ 60 $ 60 Common stock and paid-in surplus 637 (200 million shares) Retained earnings 3,312 2,440 Total $4,009 $3,137
$7,889 Total liabilities and equity
$9,154 $7,889
Garners’ Platoon Mental Health Care, Inc. Income Statement for Years Ending December 31, 2021 and 2020 (in millions of dollars) 2021 2020 $ Net sales $4,980 Less: Cost of goods sold 2,035 Gross profits $2,313 $2,734 Less: Other operating expenses 125 100 Earnings before interest, taxes, depreciation, and 2,609 2,213 amortization (EBITDA) Less: Depreciation 200 191 $ Earnings before interest and taxes (EBIT) $2,409 Less: Interest (21 percent) 285 $1,737 Earnings before taxes (EBT) $2,094 Less: Taxes Net income $1,372 $1,654
Chapter 2 - Reviewing Financial Statements
Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
$ 60 $1,594 722 $ 872
$ $1,312 722 $
Per (common) share data: Earnings per share (EPS) Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
$ $ $ $26.850
$ $ $ $22.500
Garners’ Platoon Mental Health Care, Inc. Statement of Cash Flows for Year Ending December 31, 2021 (in millions of dollars) A. Cash flows from operating activities Net income Additions (sources of cash): Depreciation Increase in accrued wages and taxes Increase in accounts payable Subtractions (uses of cash): Increase in accounts receivable Increase in inventory Net cash flow from operating activities: B. Cash flows from investing activities Subtractions: Increase in fixed assets Increase in other long-term assets Net cash flow from investing activities: C. Cash flows from financing activities Additions: Increase in notes payable Increase in long-term debt Increase in common and preferred stock Subtractions: Dividends Net cash flow from financing activities:
$
$
$
$
$
$
Chapter 2 - Reviewing Financial Statements
D. Net change in cash and marketable securities
$ 26
Garners’ Platoon Mental Health Care, Inc. Statement of Retained Earnings as of December 31, 2021 (in millions of dollars) Balance of retained earnings, December 31, 2020 Plus: Net income for 2021 Less: Cash dividends paid Preferred stock Common stock Total cash dividends paid Balance of retained earnings, December 31, 2021
$2,440
$
$
SOLUTION:
2021 Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total
Garners’ Platoon Mental Health Care, Inc. Balance Sheet as of December 31, 2021 and 2020 (in millions of dollars) 2020 Liabilities and Equity
$ 421 $_395 1,109 1,020 1,581 1,760 $3,290 $2,996
Fixed assets: Gross plant and $5,812 $4,743 equipment Less: Accumulated 640 depreciation 840 Net plant and equipment $4,972 $4,103 790 Other long-term assets 892 Total $5,864 $4,893 Total assets
2021
2020
Current liabilities : Accrued wages and taxes Accounts payable Notes payable Total
$ 316 $ 242 867 791 _872 714 $1,747 $2,055
Long-term debt:
$3,090 $3,005
Stockholders’ equity: Preferred stock (25 million shares) $ 60 $ 60 Common stock and 637 paid-in surplus 637 (200 million shares) Retained earnings 3,312 2,440 Total $4,009 $3,137
$9,154 $7,889 Total liabilities and equity
$9,154 $7,889
Garners’ Platoon Mental Health Care, Inc. Income Statement for Years Ending December 31, 2021 and 2020 (in millions of dollars) 2020 2021 $4,348 Net sales $4,980 Less: Cost of goods sold 2,246 2,035
Chapter 2 - Reviewing Financial Statements
Gross profits Less: Other operating expenses Earnings before interest, taxes, depreciation, and amortization (EBITDA) Less: Depreciation Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes (21 percent) Net income
$2,734 125
$2,313 100
2,609 200 $2,409 315 $2,094 440 $1,654
2,213 191 $ 2,022 285 $1,737 365 $1,372
Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
$ 60 $1,594 722 $ 872
$ 60 $1,312 722 $ 590
Per (common) share data: Earnings per share (EPS) Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
$ 7.970 $ 3.610 $ 19.745 $26.850
$ 6.560 $ 3.610 $ 15.385 $22.500
Garners’ Platoon Mental Health Care, Inc. Statement of Cash Flows for Year Ending December 31, 2021 (in millions of dollars) A. Cash flows from operating activities Net income Additions (sources of cash): Depreciation Increase in accrued wages and taxes Increase in accounts payable Subtractions (uses of cash): Increase in accounts receivable Increase in inventory Net cash flow from operating activities: B. Cash flows from investing activities Subtractions: Increase in gross fixed assets Increase in other long-term assets
$1,654 200 74 76 -89 -179 $1,736
$ -1,069 -102
Net cash flow from investing activities:
$-1,171
C. Cash flows from financing activities Additions: Increase in notes payable Increase in long-term debt Increase in common and preferred stock Subtractions:
$ 158 85 0
Chapter 2 - Reviewing Financial Statements
-782
Dividends Net cash flow from financing activities:
$ -539
D. Net change in cash and marketable securities
$ 26
Garners’ Platoon Mental Health Care, Inc. Statement of Retained Earnings as of December 31, 2021 (in millions of dollars) Balance of retained earnings, December 31, 2020 Plus: Net income for 2021 Less: Cash dividends paid Preferred stock Common stock Total cash dividends paid Balance of retained earnings, December 31, 2021
$2,440 1,654 $ 60 722 $ 782 $3,312
Chapter 03 - Analyzing Financial Statements
CHAPTER 3 – ANALYZING FINANCIAL STATEMENTS Questions LG3-1 through LG3-5
1. Classify each of the following ratios according to a ratio category (liquidity ratio, asset management ratio, debt management ratio, profitability ratio, or market value ratio). a. Current ratio – liquidity ratio b. Inventory turnover – asset management ratio c. Return on assets – profitability ratio d. Average payment period – asset management ratio e. Times interest earned – debt management ratio f. Capital intensity – asset management ratio g. Equity multiplier – debt management ratio h. Basic earnings power – profitability ratio
LG3-1
2. For each of the following actions, determine what would happen to the current ratio. Assume nothing else on the balance sheet changes and that net working capital is positive. a. Accounts receivable are paid in cash – Current ratio does not change b. Notes payable are paid off with cash – Current ratio increases c. Inventory is sold on account – Current ratio does not change d. Inventory is purchased on account– Current ratio decreases e. Accrued wages and taxes increase – Current ratio decreases f. Long-term debt is paid with cash – Current ratio decreases g. Cash from a short-term bank loan is received – Current ratio decreases
LG3-1 through LG3-5
3. Explain the meaning and significance of the following ratios a. Quick ratio - Inventories are generally the least liquid of a firm’s current assets. Further, inventory is the current asset for which book values are the least reliable measures of market value. In practical terms, what this means is that if the firm must sell inventory to pay upcoming bills, the firm is most likely to have to discount inventory items in order to liquidate them, and therefore, they are the current assets on which losses are most likely to occur. Therefore, the quick (or acid-test) ratio measures a firm’s ability to pay off short-term obligations without relying on inventory sales. The quick ratio measures the dollars of more liquid assets (cash and marketable securities and accounts receivable) available to pay each dollar of current liabilities. b. Average collection period - The average collection period (ACP) measures the number of days accounts receivable are held before the firm collects cash from the sale. In general, a firm wants to produce a high level of sales per dollar of accounts receivable; that is, it wants to collect its accounts receivable as quickly as possible to reduce any cost of financing inventories and accounts receivable, including interest expense on liabilities used to finance inventories and accounts receivable, and defaults associated with accounts receivable.
Chapter 03 - Analyzing Financial Statements
c. Return on equity - Return on equity (ROE) measures the return on the common stockholders’ investment in the assets of the firm. ROE is the net income earned per dollar of common stockholders’ equity. The value of a firm’s ROE is affected not only by net income, but also by the amount of financial leverage or debt that firm uses. d. Days’ sales in inventory - The days’ sales in inventory ratio measures the number of days that inventory is held before the final product is sold. In general, a firm wants to produce a high level of sales per dollar of inventory; that is, it wants to turn inventory over (from raw materials to finished goods to sold goods) as quickly as possible. A high level of sales per dollar of inventory implies reduced warehousing, monitoring, insurance, and any other costs of servicing the inventory. So, a high inventory turnover ratio or a low days’ sales in inventory is a sign of good management. e. Debt ratio - The debt ratio measures the percentage of total assets financed with debt. The debt-to-equity ratio measures the dollars of debt financing used for every dollar of equity financing. The equity multiplier measures the dollars of assets on the balance sheet for every dollar of equity financing. As you might suspect, all three measures are related. So, the lower the debt, debt-to-equity, or equity multiplier ratios, the less debt and more equity the firm uses to finance its assets (i.e., the bigger the firm’s equity cushion). f. Profit margin - The profit margin is the percentage of sales left after all firm expenses are paid. g. Accounts payable turnover - The accounts payable turnover measures the dollar cost of goods sold per dollar of accounts payable. In general, a firm wants to pay for its purchases as slowly as possible. The slower the firm pays for its supply purchases, the longer it can avoid obtaining other costly sources of financing such as notes payable or long-term debt. Thus, a high APP or a low accounts payable turnover is generally a sign of good management. h. Market-to-book ratio - The market-to-book ratio compares the market (current) value of the firm’s equity to its historical cost. In general, the higher the market-to-book ratio, the better the firm. LG3-2
4. A firm has an average collection period of 10 days. The industry average ACP is 25 days. Is this a good or poor sign about the management of the firm’s accounts receivable? If the ACP is extremely low, the firm’s accounts receivable policy may be so strict that customers prefer to do business with competing firms. Firms offer accounts receivable terms as an incentive to get customers to buy products from their firm rather than a competing firm. By offering customers the accounts receivable privilege, management allows them to buy (more) now and pay later. Without this incentive, customers may choose to buy the goods from the firm’s competitors who offer better credit terms. So, extremely low ACP levels may be a sign of bad firm management.
LG3-3
5. A firm has a debt ratio of 20 percent. The industry average debt ratio is 65 percent. Is this a good or poor sign about the management of the firm’s financial leverage? When a firm issues debt to finance its assets, it gives the debt holders first claim to a fixed amount of its cash flows. Stockholders are entitled to any residual cash flows―those left after debt holders are paid. When a firm does well, financial leverage increases the reward to
Chapter 03 - Analyzing Financial Statements
shareholders since the amount of cash flows promised to debt holders is constant and capped. So, when firms do well, financial leverage creates more cash flows to share with stockholders—it magnifies the return to the stockholders of the firm. This magnification is one reason that firm stockholders encourage the use of debt financing. However, financial leverage also increases the firm’s potential for financial distress and even failure. If the firm has a bad year and cannot make promised debt payments, debtholders can force the firm into bankruptcy. Thus, a firm’s current and potential debtholders (and even stockholders) look at equity financing as a safety cushion that can absorb fluctuations in the firm’s earnings and asset values and guarantee debt service payments. Clearly, the larger the fluctuations or variability of a firm’s cash flows, the greater the need for an equity cushion. Managers’ choice of capital structure―the amount of debt versus equity to issue―affects the firm’s viability as a long-term entity. In deciding the level of debt versus equity financing to hold on the balance sheet, managers must consider the trade-off between maximizing cash flows to the firm’s stockholders versus the risk of being unable to make promised debt payments. In summary, the low debt ratio could be either a good sign or a poor sign, depending upon the overall circumstances. LG3-4
6. A firm has an ROE of 20 percent. The industry average ROE is 12 percent. Is this a good or poor sign about the management of the firm? Generally, a high ROE is considered to be a positive sign of firm performance. However, if performance comes from a high degree of financial leverage, a high ROE can indicate a firm with an unacceptably high level of bankruptcy risk as well.
LG3-6
7. Why is the DuPont system of analysis an important tool when evaluating firm performance? Many of the ratios discussed in the chapter are interrelated. So, a change in one ratio may well affect the value of several ratios. Often these interrelations can help evaluate firm performance. Managers and investors often perform a detailed analysis of ROA (return on assets) and ROE (return on equity) using the DuPont analysis system. Popularized by the DuPont Corporation, the DuPont analysis system uses the balance sheet and income statement to break the ROA and ROE ratios into component pieces.
LG3-6
8. A firm has an ROE of 10 percent. The industry average ROE is 15 percent. How can the DuPont system of analysis help the firm’s managers identify the reasons for this difference? The basic DuPont equation looks at the firm’s overall profitability as a function of the profit the firm earns per dollar of sales (operating efficiency) and the dollar of sales produced per dollar of assets on the balance sheet (efficiency in asset use). With this tool, managers can see the reason for any changes in ROA in more detail. For example, if ROA increases, the DuPont equation may show that the net profit margin was constant, but the total asset turnover (efficiency in using assets) increased, or that total asset turnover remained constant, but profit margins (operating efficiency) increased. Managers can more specifically identify the reasons for an ROA change by using the ratios described in the chapter to further break down operating efficiency and efficiency in asset use.
LG3-6
9. What is the difference between the internal growth rate and the sustainable growth rate?
Chapter 03 - Analyzing Financial Statements
The internal growth rate is the growth rate a firm can sustain if it uses only internal financing—that is, retained earnings—to finance future growth. A problem arises when a firm relies only on internal financing to support asset growth. Through time, its debt ratio will fall because as asset values grow, total debt stays constant—only retained earnings finance asset growth. If total debt remains constant as assets grow, the debt ratio decreases. Shareholders often become disgruntled if, as the firm grows, a decreasing debt ratio (increasing equity financing) dilutes their return. So as firms grow, managers must often try to maintain a debt ratio that they view as optimal. In this case, managers finance asset growth with new debt and retained earnings. The maximum growth rate that can be achieved this way is the sustainable growth rate. LG3-7
10. What is the difference between time series analysis and cross-sectional analysis? Time series analysis evaluates the performance of the firm over time. Cross-sectional analysis evaluates the performance of the firm against one or more companies in the same industry.
LG3-7
11. What information do time series and cross-sectional analysis provide for firm managers, analysts, and investors? Analyzing ratio trends over time, along with absolute ratio levels, gives managers, analysts, and investors information about whether a firm’s financial condition is improving or deteriorating. For example, ratio analysis may reveal that the days’ sales in inventory is increasing. This suggests that inventories, relative to the sales they support, are not being used as well as they were in the past. If this increase is the result of a deliberate policy to increase inventories to offer customers a wider choice and if it results in higher future sales volumes or increased margins that more than compensate for increased capital tied up in inventory, the increased relative size of the inventories is good for the firm. Managers and investors should be concerned, on the other hand, if increased inventories result from declining sales but steady purchases of supplies and production. Looking at one firm’s financial ratios, even through time, give managers, analysts, and investors only a limited picture of firm performance. Ratio analysis almost always includes a comparison of one firm’s ratios relative to the ratios of other firms in the industry, or cross-sectional analysis. Key to cross-sectional analysis is identifying similar firms in that they compete in the same markets, have similar assets sizes, and operate in a similar manner to the firm being analyzed. Since no two firms are identical, obtaining such a comparison group is no easy task. Thus, the choice of companies to use in cross-sectional analysis is at best subjective.
LG3-8
12. Why is it important to know a firm’s accounting rules before making any conclusions about its performance from ratios analysis? Firms use different accounting procedures. For example, inventory methods can vary. One firm may use FIFO (first-in, first-out), transferring inventory at the first purchase price, while another uses LIFO (last-in, first-out), transferring inventory at the last purchase price. Likewise, the depreciation method used to value a firm’s fixed assets over time may vary across firms. One firm may use straight-line depreciation, while another may use an accelerated depreciation
Chapter 03 - Analyzing Financial Statements
method (e.g., MACRS). Particularly, when reviewing cross-sectional ratios, differences in accounting rules can affect balance sheet values and financial ratios. It is important to know which accounting rules the firms under consideration are using before making any conclusions about their performance from ratio analysis. LG3-8
13. What does it mean when a firm window dresses its financial statements? Firms often window dress their financial statements to make annual results look better. For example, to improve liquidity ratios calculated with year-end balance sheets, firms often delay payments for raw materials, equipment, loans, and so on to build up their liquid accounts and thus their liquidity ratios. If possible, it is often more accurate to use other than year-end financial statements to conduct ratio analysis. problems
basic 3-1 Liquidity Ratios You are evaluating the balance sheet for SophieLex Corporation. From the problems balance sheet you find the following balances: cash and marketable securities = $400,000; accounts receivable = $1,200,000; inventory = $2,100,000; accrued wages and taxes = $500,000; accounts LG3-1 payable = $800,000; and notes payable = $600,000. Calculate SophieLex’s current ratio, quick ratio, and cash ratio. $400,000 + $1,200,000 + $2,100,000 Current ratio = ———————————————— = 1.95 times $500,000 + $800,000 + $600,000 ($400,000 + $1,200,000 + $2,100,000) - $2,100,000 Quick ratio (acid-test ratio) = —————————————————————— = 0.84 times $500,000 + $800,000 + $600,000 $400,000 Cash ratio = —————————————— = 0.21 times $500,000 + $800,000 + $600,000
LG3-1
3-2 Liquidity Ratios The top part of Ramakrishnan, Inc,’s 2021 and 2020 balance sheets is listed below (in millions of dollars). Calculate Ramakrishnan, Inc.’s current ratio, quick ratio, and cash ratio for 2021 and 2020. Current assets: Cash and marketable securities Accounts receivable Inventory Total
Current ratio =
2021
2020
$ 34 143 206 $383
$ 25 128 187 $340
Current liabilities: Accrued wages and taxes Accounts payable Notes payable Total
2021 $383m. ——— = 1.96 times $195m.
2021
2020
$ 32 87 76 $195
$ 31 76 68 $175
2020 $340m. ———— = 1.94 times $175m.
$383m. - $206m. $340m. - $187m. Quick ratio (acid-test ratio) = ——————— = 0.91 times ———————— = 0.87 times
Chapter 03 - Analyzing Financial Statements
$195m. $34m. ———— = 0.17 times $195m.
Cash ratio =
LG3-2
$175m. $25m. —————— = 0.14 times $175m.
3-3 Asset Management Ratios Tater and Pepper Corp. reported sales for 2021 of $23 million. Tater and Pepper listed $5.6 million of inventory on its balance sheet. Using a 365 day year, how many days did Tater and Pepper’s inventory stay on the premises? How many times per year did Tater and Pepper’s inventory turn over? $5.6m x 365 Days’ sales in inventory = —————— = 88.87 days $23m
Inventory turnover
LG3-2
$23m = ———— = 4.11 times $5.6m
3-4 Asset Management Ratios Mr. Husker’s Tuxedos Corp. ended the year 2021 with an average collection period of 32 days. The firm’s credit sales for 2021 were $56.1 million. What is the yearend 2021 balance in accounts receivable for Mr. Husker’s Tuxedos? Accounts receivable x 365 Average collection period (ACP) = ——————————— = 32 days $56.1m => Accounts receivable = 32 days x $56.1 m / 365 = $4,918,356
LG3-3
3-5 Debt Management Ratios Tiggie’s Dog Toys, Inc. reported a debt-to-equity ratio of 1.75 times at the end of 2021. If the firm’s total debt at year-end was $25 million, how much equity does Tiggie’s have on its balance sheet? Debt-to-equity
LG3-3
Total debt $25 m = ————— = 1.75 = ————— => Total equity = $25m / 1.75 = 14.29m. Total equity Total equity
3-6 Debt Management Ratios You are considering a stock investment in one of two firms (LotsofDebt, Inc. and LotsofEquity, Inc.), both of which operate in the same industry. LotsofDebt, Inc. finances its $30 million in assets with $29 million in debt and $1 million in equity. LotsofEquity, Inc. finances its $30 million in assets with $1 million in debt and $29 million in equity. Calculate the debt ratio, equity multiplier, and debt-to-equity ratio for the two firms.
Debt ratio =
Equity multiplier
LotsofDebt $29m ——— = 96.67% $30m
Lotsof Equity $1m ——— = 3.33% $30m
$30m = ——— = 30 times $1m
$30m ——— = 1.03 times $29m
$29m
$1m
Chapter 03 - Analyzing Financial Statements
Debt-to-equity
LG3-4
=
——— = 29 times $1m
——— = .03 times $29m
3-7 Profitability Ratios Maggie’s Skunk Removal Corp.’s 2021 income statement listed net sales = $12.5 million, gross profit of $6.9 million, EBIT = $5.6 million, net income available to common stockholders = $3.2 million, and common stock dividends = $1.2 million. The 2021 year-end balance sheet listed total assets of $52.5 million and common stockholders’ equity of $21 million with 2 million shares outstanding. Calculate the gross profit margin, operating profit margin, profit margin, basic earnings power, ROA, ROE, and dividend payout. $6.9m Gross profit margin =------------ = 55.20 % $12.5m $5.6m Operating profit margin = ------------ = 44.80% $12.5m $3.2m Profit margin = ———— = 25.60% $12.5m $5.6m Basic earnings power (BEP) = ——— = 10.67% $52.5m $3.2m Return on assets (ROA) = ——— = 6.10% $52.5m $3.2m Return on equity (ROE) = ——— = 15.24% $21m $1.2m Dividend payout = ——— = 37.50% $3.2m
LG3-4
3-8 Profitability Ratios In 2021, Jake’s Jamming Music, Inc., announced an ROA of 8.56 percent, ROE of 14.5 percent, and profit margin of 20.5 percent. The firm had total assets of $9.5 million at year-end 2021. Calculate the 2021 values of net income available to common stockholders, common stockholders’ equity, and net sales for Jake’s Jamming Music, Inc. Net income available to common stockholders Return on assets (ROA) = 0.0856 = ———————————————————— $9.5m => Net income available to common stockholders = 0.0856 x $9.5 m = $813,200 $813,200 Return on equity (ROE) = 0.145 = ———————————— Common stockholders’ equity
Chapter 03 - Analyzing Financial Statements => Common stockholders’ equity = $813,200 / 0.145 = $5,608,276 $813,200 Profit margin = 0.205 = ————— => Sales = $813,200 / 0.205 = $3,966,829 Sales
LG3-5
3-9 Market Value Ratios You are considering an investment in Roxie’s Bed & Breakfast Corp. During the last year the firm’s income statement listed an addition to retained earnings of $4.8 million and common stock dividends of $2.2 million. Roxie’s year-end balance sheet shows common stockholders’ equity of $35 million with 10 million shares of common stock outstanding. The common stock’s market price per share was $9.00. What is Roxie’s Bed & Breakfast’s book value per share and earnings per share? Calculate the market-to-book ratio and PE ratio. Book value per share = $35m / 10m = $3.50 per share Earnings per share = ($4.8m + $2.2m) / 10m = $0.70 per share $9.00 Market-to-book ratio = ——— = 2.57 times $3.50 $9.00 Price-earnings (PE) ratio = ——— = 12.86 times $0.70
LG3-5
3-10 Market Value Ratios Dudley Hill Golf Club’s market-to-book ratio is currently 2.5 times and the PE ratio is 6.75 times. If Dudley Hill Golf Club’s common stock is currently selling at $22.50 per share, what is the book value per share and earnings per share? $22.50 Market-to-book ratio = 2.50 = ————————— => Book value per share = $22.50 / 2.50 = $9.00 Book value per share $22.50 Price-earnings (PE) ratio = 6.75 times = ————————— => Earnings per share = $22.50 / 6.75 = $3.33 Earnings per share
LG3-6
3-11 DuPont Analysis If Silas 4-Wheeler, Inc., has an ROE of 18 percent, equity multiplier of 2, and a profit margin of 18.75 percent, what is the total asset turnover and the capital intensity? ROE = 0.18 = 0.1875 x Total asset turnover x 2 => Total asset turnover = 0.18 / (0.1875 x 2) = 0.48 Capital intensity ratio = 1/0.48 times = 2.08 times
LG3-6
3-12 DuPont Analysis Last year, Hassan’s Madhatter, Inc., had an ROA of 7.5 percent, a profit margin of 12 percent, and sales of $25 million. Calculate Hassan’s Madhatter’s total assets. ROA = 0.075 = 0.12 x ($25m. /Total assets) => Total assets = (0.12 x $25m) / 0.075 = $40m
LG3-6
3-13 Internal Growth Rate Last year, Lakesha’s Lounge Furniture Corporation had an ROA of 7.5 percent and a dividend payout ratio of 25 percent. What is the internal growth rate?
Chapter 03 - Analyzing Financial Statements
0.075 x (1 - 0.25) Internal growth rate = ————————— = 5.96% 1 – [0.075 x (1 - 0.25)]
LG3-6
3-14 Sustainable Growth Rate Last year, Lakesha’s Lounge Furniture Corporation had an ROE of 17.5 percent and a dividend payout ratio of 20 percent. What is the sustainable growth rate? 0.175 x (1 - 0.20) Sustainable growth rate = ————————— = 16.28% 1- [0.175 x (1 - 0.20)]
intermediate problems 3-15 Liquidity Ratios Brenda’s Bar and Grill has current liabilities of $15 million. Cash makes up LG3-1 10 percent of the current assets and accounts receivable makes up another 40 percent of current assets. Brenda’s current ratio is 2.1 times. Calculate the value of inventory listed on the firm’s balance sheet. Current ratio = 2.1 = Current assets / $15m. => Current assets = 2.1 x $15m = $31.5m Cash = 0.10 x $31.5m = $3.15m Accounts receivable = 0.40 x $31.5m = $12.6m => Inventory = $31.5m - $3.15m - $12.6m = $15.75m
LG3-1 LG3-2
3-16 Liquidity and Asset Management Ratios Mandesa, Inc., has current liabilities of $8 million, current ratio of 2 times, inventory turnover ratio of 12 times, average collection period of 30 days, and credit sales of $64 million. Calculate the value of cash and marketable securities. Current assets Current ratio = 2 times = ——————— => Current assets = 2 x $8m = $16m $8m $64m Inventory turnover = 12 times = ———— => Inventory = $64m / 12 = $5,333,333 Inventory Accounts receivable x 365 days Average collection period (ACP) = 30 days = ————————————— $64m => Accounts receivable = 30 x $64m / 365 = $5,260,274 => Cash and marketable securities = $16m - $5,333,333 - $5,260,274 = $5,406,393
LG3-2 LG3-4
3-17 Asset Management and Profitability Ratios You have the following information on Els’ Putters, Inc.: sales to working capital is 4.6 times, profit margin is 20 percent, net income available to common stockholders is $5 million, and current liabilities are $6 million. What is the firm’s balance of current assets? Profit margin = 0.2 = $5m / Sales => Sales = $5m / 0.2 = $25m Sales / (Current assets – Current liabilities) = 4.6 = $25m / (Current assets - $6m) => Current assets = ($25m / 4.6) + $6m = $11.43m
Chapter 03 - Analyzing Financial Statements
LG3-2 LG3-3
3-18 Asset Management and Debt Management Ratios Use the following information to complete the balance sheet below. Sales are $8.8 million, capital intensity ratio is 2.10 times, debt ratio is 55 percent, and fixed asset turnover ratio is 1.2 times. Step 1: Capital intensity ratio = 2.10 = Total assets / $8.8m => Total assets = 2.1 x $8.8m = $18.48m and Total liabilities and equity = $18.48m Step 2: Debt ratio = 0.55 = Total debt / $18.48m => Total debt = 0.55 x $18.48m = $10.164m Step 3: Total equity = $18.48m - $10.164m = $8.316m Step 4: Fixed asset turnover = 1.2 = $8.8m / Fixed assets => Fixed assets = $8.8m / 1.2 = $7.333m Step 5: Current assets = $18.48m - $7.333m = $11.147m Assets
LG3-3
Liabilities and Equity
Current assets Step 5
$11.147m
Total liabilities
Step 2
Fixed assets Step 4
$7.333m
Total equity
Step 3
Total assets
$18.480m
Total liabilities and equity $
Step 1 $
$
$10.164m $8.316m $18.480m
3-19 Debt Management Ratios Tiggie’s Dog Toys, Inc., reported a debt-to-equity ratio of 1.75 times at the end of 2021. If the firm’s total assets at year-end were $25 million, how much of their assets are financed with debt and how much with equity? Debt to equity = 1.75 = Total debt / Total equity = Total debt / (Total assets – Total debt) 1.75 = Total debt / ($25m – Total debt) => 1.75 x ($25m – Total debt) = Total debt => (1.75 x $25m) – (1.75 x Total debt) = Total debt => $43.75m = 2.75 x Total debt => Total debt = $43.75m / 2.75 = $15.909m => Total equity = $25m - $15.909m = $9.091m
LG3-3
3-20 Debt Management Ratios Calculate the times interest earned ratio for LaTonya’s Flop Shops, Inc., using the following information. Sales are $1.5 million, cost of goods sold is $600,000, depreciation expense is $150,000, other operating expenses is $300,000, addition to retained earnings is $176,625, dividends per share is $1, tax rate is 21 percent, and number of shares of common stock outstanding is 90,000. LaTonya’s Flop Shops has no preferred stock outstanding. Net sales (all credit) Less: Cost of goods sold Gross profits Less: Depreciation Other operating expenses Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes Net income Less: Common stock dividends Addition to retained earnings
Step 4.
$1,500,000 600,000 $900,000
Step 5. Step 6. Step 3.
150,000 300,000 $450,000 112,500 $337,500
Step 2.
$266,625
Step 1.
$90,000 $176,625
Chapter 03 - Analyzing Financial Statements
Step 1. Common stock dividends = $1per share x 90,000 shares = $90,000 Step 2. Net income = Common stock dividends + Addition to retained earnings = $90,000 + $146,250 = $266,625 Step 3. EBT (1 – Tax rate) = Net income => EBT = Net income / (1 – Tax rate) = $266,625 / (1 - 0.21) = $337,500 Step 4. Gross profits = Net sales – Cost of goods sold = $1,500,000 – $600,000 = $900,000 Step 5. Gross profits – Depreciation – Other operating expenses = EBIT = $900,000 - $150,000 - $300,000 = $450,000 Step 6. EBIT – Interest = EBT => Interest = EBIT - EBT = $450,000 - $337,500 = $112,500 => Times interest earned = $450,000 / $112,500 = 4.00 times
LG3-2 LG3-4
3-21 Profitability and Asset Management Ratios You are thinking of investing in Nikki T’s, Inc. You have only the following information on the firm at year-end 2021: net income is $250,000, total debt is $2.5 million, and debt ratio is 55 percent. What is Nikki T’s ROE for 2021? Debt ratio = 0.55 = $2.5m / Total assets => Total assets = $2.5m / 0.55 = $4.545m => Total equity = $4.545m - $2.5m = $2.045m => ROE = $250,000 / $2.045m = 12.22%
LG3-4
3-22 Profitability Ratios Rick’s Travel Service has asked you to help piece together financial information on the firm for the most current year. Managers give you the following information: sales are $8.2 million, total debt is $2.1 million, debt ratio is 40 percent, and ROE is 18 percent. Using this information, calculate Rick’s ROA. Debt ratio = 0.40 = $2.1m / Total assets => Total assets = $2.1m / 0.40 = $5.25m => Total equity = $5.25m - $2.1m = $3.15m => ROE = 0.18 = Net income / $3.15m => Net income = 0.18 x $3.15m = $567,000 => ROA = $567,000 / $5.25m = 10.80%
LG3-5
3-23 Market Value Ratios Leonatti Labs’ year-end price on its common stock is $35. The firm has total assets of $50 million, debt ratio of 65 percent, no preferred stock, and 3 million shares of common stock outstanding. Calculate the market-to-book ratio for Leonatti Labs. Debt ratio = 0.65 = Total debt / $50m => Total debt = 0.65 x $50m = $32.5m => Total equity = $50m - $32.5m = $17.5m => Book value of equity = $17.5m / 3m = $5.83333 per share => Market to book ratio = $35 / $5.83333 = 6 times
LG3-5
3-24 Market Value Ratios Leonatti Labs’ year-end price on its common stock is $15. The firm has a profit margin of 8 percent, total assets of $42 million, a total asset turnover ratio of 0.75, no preferred stock, and 3 million shares of common stock outstanding. Calculate the PE ratio for Leonatti Labs. Total asset turnover = 0.75 = Sales / $42m => Sales = $42m x 0.75 = $31.50m => Profit margin = 0.08 = Net income / $31.50m => Net income = 0.08 x $31.50m = $2.52m => EPS = $2.52m / 3m shares = $0.84 per share => PE ratio = $15 / $0.84 = 17.86 times
LG3-6
3-25 DuPont Analysis Last year, Stumble-on-Inn, Inc., reported an ROE of 18 percent. The firm’s debt ratio was 55 percent, sales were $15 million, and the capital intensity was 1.25 times. Calculate the net income for Stumble-on-Inn last year. Capital intensity = 1.25 = Total assets / $15m => Total assets = 1.25 x $15m = $18.75m
Chapter 03 - Analyzing Financial Statements
=> Debt ratio = 0.55 = Total debt / $18.75m => Total debt = 0.55 x $18.75m = $10.3125m => Total equity = $18.75m - $10.3125m = $8.4375m => ROE = 0.18 = Net income / $8.4375m => Net income = 0.18 x $8.4375m = $1,518,750
LG3-6
3-26 DuPont Analysis You are considering investing in Nuran Security Services. You have been able to locate the following information on the firm: total assets are $24 million, accounts receivable are $3.3 million, ACP is 25 days, net income is $3.5 million, and debt-to-equity is 1.2 times. Calculate the ROE for the firm. Debt-to-equity = 1.2 = Total debt / Total equity = Total debt / (Total assets – Total debt) 1.2 = Total debt / ($24m – Total debt) => (1.2 x $24m) – 1.2 x Total debt = Total debt => $28.8m = 2.2 x Total debt => Total debt = $28.8m / 2.2 = $13.091m => Total equity = $24m. - $13.091m = $10.909m => ROE = $3.5m / $10.909m = 32.08%
LG3-6
3-27 Internal Growth Rate Dogs R Us reported a profit margin of 10.5 percent, total asset turnover of 0.75 times, debt-to-equity of 0.80 times, net income of $500,000, and dividends paid to common stockholders of $200,000. The firm has no preferred stock outstanding. What is Dogs R Us’s internal growth rate? ROA = Profit margin x Total asset turnover = 10.5% x 0.75 = 7.875% RR = ($500,000 - $200,000)/$500,000 = 0.60 ROA x RR Internal growth rate = —————— = 1- (ROA x RR)
LG3-6
0.07875 x 0.60 ———————— = 4.96% 1 – (0.07875 x 0.60)
3-28 Sustainable Growth Rate You have located the following information on Webb’s Heating & Air Conditioning: debt ratio is 54 percent, capital intensity ratio is 1.10 times, profit margin is 12.5 percent, and dividend payout ratio is 25 percent. Calculate the sustainable growth rate for Webb. Equity multiplier = Total assets / Total equity => 1 / Equity multiplier = Total equity / Total assets Debt ratio = Total debt / Total assets = (Total assets – Total equity) / Total assets = 1 – (Total equity / Total assets) 0.54 = 1- (Total equity / Total assets) => Total equity / Total assets = 1 - 0.54 = 0.46 = 1 / Equity multiplier => Equity multiplier = 1 / 0.46 = 2.1739 ROE = Profit margin x Total asset turnover x Equity multiplier = 0.125 x 1 / 1.10 x 2.1739 = 24.70% Retention ratio (RR) = 1 - Dividend payout ratio = 1 - 0.25 = 0.75 0.2470 x 0.75 Sustainable growth rate = ———————— = 22.74% 1 – (0.2470 x 0.75)
Use the following financial statements for Lake of Egypt Marina to answer Problems 3-29 through 3-32. Lake of Egypt Marina, Inc. Balance Sheet as of December 31, 2021 and 2020 (in millions of dollars)
Chapter 03 - Analyzing Financial Statements
Assets
2021
Current assets: Cash and marketable securities Accounts receivable Inventory Total
$
75 115 200 $ 390
2020
$
65 110 190 $ 365
Liabilities & Equity Current liabilities: Accrued wages and taxes Accounts payable Notes payable Total Long-term debt:
Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment Other long-term assets Total
$ 470 $ 371 50 49 $ 520 $ 420
Total assets
$ 910 $ 785
$ 580 $ 471 110 100
Stockholders’ equity: Preferred stock (5 million shares) Common stock and paid-in surplus (65 million shares) Retained earnings Total Total liabilities and equity
2021
2020
$
40 90 80 $ 210
$
$ 300
$ 280
$
$
5
43 80 70 $ 193
5
65
65
330 $ 400 $ 910
242 $ 312 $ 785
Lake of Egypt Marina, Inc. Income Statement for Years Ending December 31, 2021 and 2020 (in millions of dollars) 2021 2020 Net sales (all credit) $ 515 $ 432 Less: Cost of goods sold 230 175 Gross profits $285 $257 Less: Other operating expenses 30 25 Earnings before interest, taxes, depreciation, and amortization (EBITDA) $255 $232 Less: Depreciation 22 20 Earnings before interest and taxes (EBIT) $233 $212 Less: Interest 33 30 Earnings before taxes (EBT) $200 $182 Less: Taxes 57 55 Net income $ 143 $ 127
LG3-1 through LG3-7
Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
$ 5 $ 138 65 $ 73
$ 5 $ 122 65 $ 57
Per (common) share data: Earnings per share (EPS) Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
$2.123 $1.000 $6.077 $14.750
$1.877 $1.000 $4.723 $12.550
3-29 Spreading the Financial Statements Spread the balance sheets and income statements of Lake of Egypt Marina, Inc. for 2021 and 2020. Spread the balance sheet:
Chapter 03 - Analyzing Financial Statements
Lake of Egypt Marina, Inc. Balance Sheet as of December 31, 2021 and 2020 (in millions of dollars) 2021 2020 Liabilities & Equity 2021
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment Other long-term assets Total Total assets
Current liabilities: Accrued wages and 8.24% 8.28% taxes 12.64 14.01 Accounts payable 21.98 24.20 Notes payable 42.86 46.50 Total Long-term debt:
2020
4.40% 5.48% 9.89 10.19 8.79 8.92 23.08 24.59 32.97
35.67
Stockholders’ equity: Preferred stock (5 million shares) 0.55 0.64 Common stock and 51.65 47.26 paid-in surplus 7.14 8.28 5.49 6.24 (65 million shares) 57.14 53.50 Retained earnings 36.26 30.83 Total 43.96 39.75 100.00% 100.00% Total liabilities and equity 100.00% 100.00% 63.74 12.09
60.00 12.74
Spreading the income statement: Lake of Egypt Marina, Inc. Income Statement for Years Ending December 31, 2021 and 2020 (in millions of dollars) 2021 2020 Net sales (all credit) 100.00% 100.00% Less: Cost of goods sold 44.66 40.51 Gross profits 55.34 59.49 Less: Other operating expenses 5.83 5.79 Earnings before interest, taxes, depreciation, and amortization (EBITDA) 49.51 53.70 Less: Depreciation 4,27 4.63 Earnings before interest and taxes (EBIT) 45.24 49.07 Less: Interest 6.41 6.94 Earnings before taxes (EBT) 38.83 42.13 Less: Taxes 8.15 12.73 Net income 30.68% 29.40%
LG3-1 through LG3-7
3-30 Calculating Ratios Calculate the following ratios for Lake of Egypt Marina, Inc. as of year-end 2021. Lake of Egypt Marina, Inc. (dollar amounts are in millions for parts a through w.) a. Current ratio $390 / $210 = 1.86 times b. Quick ratio ($390 - $200) / $210 = 0.90 times c. Cash ratio $75 / $210 = 0.36 times d. Inventory turnover $515 / $200 = 2.58 times
Industry 2.00 times 1.20 times 0.42 times 3.60 times
Chapter 03 - Analyzing Financial Statements e. Days’ sales in inventory f. Average collection period g. Average payment period h. Fixed asset turnover i. Sales to working capital j. Total asset turnover k. Capital intensity l. Debt ratio m. Debt-to-equity n. Equity multiplier (using total equity) o. Times interest earned p. Cash coverage q. Profit margin r. Gross profit margin s. Operating profit margin t. Basic earnings power u. ROA v. ROE w. Dividend payout x. Market-to-book ratio y. PE ratio
LG3-1 through LG3-7
($200 x 365)/ $515 = 141.75 days ($115 x 365) / $515 = 81.50 days ($90 x 365) / $230 = 142.83 days $515 / $470 = 1.10 times $515 / ($390 - $210) = 2.86 times $515 / $910 = 0.57 times $910 / $515 = 1.77 times ($210 + $300) / $910 = 56.04% ($210 + $300) / $400 = 1.28 times $910 / $400 = 2.28 times
101.39 days 32.50 days 45.00 days 1.25 times 4.25 times 0.85 times 1.18 times 62.50% 1.67 times 2.67 times
$233 / $33 = 7.06 times ($233 + $22) / $33 = 7.73 times $153 / $515 = 29.71% $285 / $515 = 55.34% $233 / $515 = 45.24% $233 / $910 = 25.60% $153 / $910 = 16.81% $153 / $395 = 38.73% $65 / $153 = 42.48% $14.750 / $6.077 = 2.43 times $14.750 / $2.354 = 6.27 times
8.50 times 8.75 times 30.75% 56.45% 46.78% 32.50% 19.75% 51.35% 35.00% 2.55 times 15.60 times
3-31 DuPont Analysis Construct the DuPont ROA and ROE breakdowns for Lake of Egypt Marina, Inc. ROA = Profit margin x Total asset turnover = 29.708738% x 0.56593407 times = 16.81% ROE = Profit margin x Total asset turnover x Equity multiplier = 29.708738% x 0.56593407 times x (910m/395m) = 38.73%
LG3-1 through LG3-7
3-32 Internal and Sustainable Growth Rates Calculate the internal and sustainable growth rate for Lake of Egypt Marina, Inc. 0.1681 x (1 - 0.4248) Internal growth rate = ——————————— = 10.71% 1 – (0.1681 x (1 - 0.4248)) 0.3873 x (1 - 0.4248) Sustainable growth rate = ——————————— = 28.66% 1 – (0.3873 x (1 - 0.4248))
LG3-1 through LG3-7
3-33 Cross-sectional Analysis Using the ratios from question 3-30 for Lake of Egypt Marina, Inc. and the industry, what can you conclude about Lake of Egypt Marina’s financial performance for 2021. Lake of Egypt Marina is performing below the industry in all areas. Liquidity is lower, asset management is poorer, and profit ratios are lower.
advanced 3-34 Ratio Analysis Use the following information to complete the balance sheet below. problems
Chapter 03 - Analyzing Financial Statements
LG3-1 through LG3-5
Current ratio = 2.5 times Profit margin = 10% Sales = $1,200m ROE = 20% Long-term debt to Long-term debt and equity = 55% Current assets
$
Current liabilities
Fixed assets
$210m
Long-term debt Stockholders’ equity
Total Assets
$
Total liabilities & equity
$
Step 1: Current ratio = 2.5 times = Current assets / $210m => Current assets = 2.5 x $210m = $525m Step 2: Profit margin = 10% = Net income / $1,200m => Net income = 0.10 x $1,200m = $120m => ROE = 20% = $120m / Total equity => Total equity = $120m / 0.20 = $600m Step 3: Long-term debt / Long-term debt and equity = 55% => 0.55(Long-term debt + $600m) = Long-term debt => (0.55 x Long-term debt) + (0.55 x $600m) = Long-term debt => $330m = (1 - 0.55) x Long-term debt => Long-term debt = $330m / (1- 0.55) = $733m Step 4: Total liabilities & equity = Current liabilities + Long-term debt + Stockholders’ equity = $210m + $733m + $600m. = $1,543m = Total assets Step 5: Fixed assets = Total assets - Current assets = $1,543m - $525m = $1,018m Current Assets Step 1
$525m
Current Liabilities
Fixed Assets
1,018m
Long-term Debt
Step 5
Total Assets
LG3-1 through LG3-5
$210m Step 3
733m
Stockholders’ Equity Step 2
600m
$1,543m Step 4 Total Liabilities & Equity
$1,543m
3-35 Ratio Analysis Use the following information to complete the balance sheet below. Current ratio = 2.20 times Credit sales = $1,200m Average collection period = 60 days Inventory turnover = 1.50 times Total asset turnover = 0.75 times Debt ratio = 60% Cash Accounts receivable Inventory Current assets
$
$
$500m $
Stockholders’ equity
Fixed assets Total assets
Current liabilities Long-term debt Total debt
$
Total liabilities & equity
$
Chapter 03 - Analyzing Financial Statements
Step 1: Current ratio = 2.2 times = Current assets / $500m => Current assets = 2.2 x $500m = $1,100m Step 2: Average collection period = 60 days = (Accounts receivable x 365) / $1,200m => Accounts receivable = (60 x $1,200m) / 365 = $197m Step 3: Inventory turnover = 1.5 times = $1,200m / Inventory => Inventory = $1,200m / 1.5 = $800m Step 4: Cash = $1,100m - $197m - $800m = $103m Step 5: Total asset turnover = 0.75 times = $1,200m / Total assets => Total assets = $1,200m / 0.75 = $1,600m Step 6: Fixed assets = $1,600m - $1,100m = $500m Step 7: Debt ratio = 60% = Total debt / $1,600m => Total debt = 0.60 x $1,600m = $960m Step 8: Stockholders’ equity = Total liabilities & equity - Total debt = $1,600m - $960m = $ 640m Step 9: Long-term debt = Total debt – Current liabilities = $960m - $500m = $460m
LG3-6
Cash Step 4 Accounts receivable Step 2 Inventory Step 3 Current assets Step 1 Fixed assets Step 6
$103m 197m 800m $1,100m 500m
Current liabilities Long-term debt Total debt Stockholders’ equity
Step 9 Step 7 Step 8
$500m 460m $960m 640m
Total assets
$1,600m
Total liabilities & equity
Step 5
$1,600m
3-36 DuPont Analysis Last year, K9 WebbWear, Inc., reported an ROE of 20 percent. The firm’s debt ratio was 55 percent, sales were $20 million, and the capital intensity was 1.25 times. Calculate the net income and profit margin for K9 WebbWear last year. This year, K9 WebbWear plans to increase its debt ratio to 60 percent. The change will not affect sales or total assets; however, it will reduce the firm’s profit margin to 11 percent. By how much will the change in K9 WebbWear’s debt ratio affect its ROE? Last year: Capital intensity = 1.25 = Total assets / $20m => Total assets = 1.25 x $20m = $25m => Debt ratio = 0.55 = Total debt / $25m => Total debt = 0.55 x $25m = $13.75m => Total equity = $25m - $13.75m = $11.25m => ROE = 0.20 = Net income / $11.25m => Net income = 0.20 x $11.25m = $2.25m => Profit margin = $2.25m / $20m = 11.25% This year: Profit margin = 11% = Net income / $20m => Net income = 0.11 x $20m = $2.2m and Total debt = $25m x 0.60 = $15m => Total equity = $25m - $15m = $10m => ROE = $2.2m / $10m = 22%, an increase of 2%
LG3-6
3-37 DuPont Analysis You are considering investing in Dakota’s Security Services. You have been able to locate the following information on the firm: total assets are $32 million, accounts receivable are $4.4 million, ACP is 25 days, net income is $4.66 million, and debt-to-equity is 1.2 times. All sales are on credit. Dakota’s is considering loosening its credit policy such that ACP will increase to 30 days. The change is expected to increase credit sales by 5 percent. Any change in accounts receivable will be offset with a change in debt. No other balance sheet changes are expected. Dakota’s profit margin will remain unchanged. How will this change in accounts receivable policy affect Dakota’s net income, total asset turnover, equity multiplier, ROA, and ROE? Current: ACP = (Accounts receivable x 365) / Credit sales = 25 = ($4.4m x 365) / Credit sales => Credit sales = ($4.4m x 365) / 25 = $64.24m => Profit margin = $4.66m / $64.24m = 7.25% Total asset turnover = $64.24m / $32m = 2.0075 times
Chapter 03 - Analyzing Financial Statements Debt-to-equity = Equity multiplier – 1 =1.2 => Equity multiplier = 1 + 1.2 = 2.2 ROA = Net income / Total assets = $4.66m / $32m = 14.56% or = Profit margin x Total asset turnover = 7.25% x 2.0075 = 14.56% Equity multiplier = Total assets / Total equity = 2.2 = $32m / Total equity => Total equity = $32m / 2.2 = $14.545m and Total debt = $32m - $14.545m = $17.454m => ROE = $4.66m / $14.545m = 32.04% or = Profit margin x Total asset turnover x Equity multiplier = 7.25% x 2.0075 x 2.2 = 32.04% New: ACP = 30 = (Accounts receivable x 365) / $64.24m (1.05) => Accounts receivable = (30 x $64.24m (1.05)) / 365 = $5.544m, an increase of $5.544m - $4.4m = $1.144m => Total assets = $32m + $1.144m = $33.144m and Total debt = $17.454m + 1.144m = $18.595m so Total equity = $33.144m - $18.595m = $14.545m Equity multiplier = $33.144m / $14.545m = 2.2786 times Profit margin = 7.25% = Net income / $64.24m (1.05) => Net income = 7.25% x $64.24m (1.05) = $4.893m Total asset turnover = $64.24m(1.05) / $33.144m = 2.0351 => ROA = $4.893m / $33.144m = 14.76% or = 7.25% x 2.0351 = 14.76% => ROE = $4.893m / $14.545m = 33.64%
or
= 7.25% x 2.0351 x 2.2786 = 33.64%
Change in net income = $4.893m – $4.66 = $0.233m - net income increases Change in total asset turnover = 2.0351 times – 2.0075 times = 0.0276 times - assets are turned over faster Change in equity multiplier = 2.2786 times – 2.2 times = 0.0786 times - each $ of equity supports more $s of assets Change in ROA = 14.76% - 14.56% = 0.20% return on assets increases Change in ROE = 33.64% - 32.04% = 1.60% - return on equity increases
LG3-6
3-38 Internal Growth Rate Last year, Marly Brown, Inc., reported an ROE of 20 percent. The firm’s debt-to-equity was 1.50 times, sales were $20 million, the capital intensity was 1.25 times, and dividends paid to common stockholders were $1,000,000. The firm has no preferred stock outstanding. This year, Marly Brown plans to decrease its debt-to-equity ratio to 1.20 times. The change will not affect sales, total assets, or dividends paid; however, it will reduce the firm’s profit margin to 9.85 percent. Use the DuPont equation to determine how the change in Marly Brown’s debt ratio will affect its internal growth rate. Last year: Capital intensity = 1.25 => Total asset turnover = 1 / 1.25 = 0.80 Capital intensity = 1.25 = Total assets / $20m => Total assets = 1.25 x $20m = $25m Debt-to-equity ratio = 1.50 times => Debt ratio = 1 / [(1/Debt-to-equity) + 1] = 1 / [(1/1.50) + 1] = 0.60 or 60% => Debt ratio = 0.60 = Total debt / $25m => Total debt = 0.60 x $25m = $15.00m => Total equity = $25m - $15.00m = $10.00m => ROE = 0.20 = Net income / $10.00m => Net income = 0.20 x $10.00m = $2.00m => Profit margin = $2.00m / $20.00m = 10.00% ROA = Profit margin x Total asset turnover = 10.00% x 0.80 = 8.00% RR = ($2,000,000 - $1,000,000)/$2,000,000 = 0.50 ROA x RR Internal growth rate = —————— = 1- (ROA x RR)
0.0800 x 0.50 ———————— = 4.17% 1 – (0.0800 x 0.50)
Chapter 03 - Analyzing Financial Statements
This year: ROA = 9.85% x 0.80 = 7.88% Profit margin = 9.85% = Net income / $20m => Net income = 0.0985 x $20m = $1.97m RR = ($1,970,000 - $1,000,000)/$1,970,000 = 0.4924 0.0788 x 0.4924 Internal growth rate = ————————— = 4.04%, a decrease of 0.13% 1 – (0.0788 x 0.4924)
LG3-6
3-39 Sustainable Growth Rate You are considering investing in Annie’s Eatery. You have been able to locate the following information on the firm: total assets are $40 million, accounts receivable are $6.0 million, ACP is 30 days, net income is $4.75 million, debt-to-equity is 1.5 times, and dividend payout ratio is 45 percent. All sales are on credit. Annie’s is considering loosening its credit policy such that ACP will increase to 35 days. The change is expected to increase credit sales by 5 percent. Any change in accounts receivable will be offset with a change in debt. No other balance sheet changes are expected. Annie’s profit margin and dividend payout ratio will remain unchanged. Use the DuPont equation to determine how this change in accounts receivable policy will affect Annie’s sustainable growth rate. Current: ACP = (Accounts receivable x 365) / Credit sales = 30 = ($6.0m x 365) / Credit sales => Credit sales = ($6.0m x 365) / 30 = $73.00m => Profit margin = $4.75m / $73.00m = 6.51% Total asset turnover = $73.00m / $40m = 1.825 times Debt-to-equity = Equity multiplier – 1 =1.5 => Equity multiplier = 1 + 1.5 = 2.5 Equity multiplier = Total assets / Total equity = 2.5 = $40m / Total equity => Total equity = $40m / 2.2 = $16.00m and Total debt = $40m - $16m = 24m => ROE = $4.75m / $16.00m = 29.69% or = Profit margin x Total asset turnover x Equity multiplier = 6.51% x 1.825 x 2.5 = 29.69% Retention ratio (RR) = 1 - Dividend payout ratio = 1 - 0.45 = 0.55 0.2969 x 0.55 Sustainable growth rate = ———————— = 19.51% 1 – (0.2969 x 0.55) New: ACP = 35 = (Accounts receivable x 365) / $73m (1.05) => Accounts receivable = (35 x $73m (1.05)) / 365 = $7.35m, an increase of $7.35m - $6.0m = $1.35m => Total assets = $40m + $1.35m = $41.35m and Total debt = $24m + 1.35m = $25.35m so Total equity = $41.35m - $25.35m = $16.00m Equity multiplier = $41.35m / $16.00m = 2.5844 times Profit margin = 6.51% = Net income / $73.00m (1.05) => Net income = 6.51% x $73.00m (1.05) = $4.9875m Total asset turnover = $73.00m(1.05) / $41.35m = 1.8537 => ROE = $4.9875 / $16.00m = 31.17%
or
= 6.51% x 1.8537 x 2.5844 = 31.17%
Retention ratio (RR) = 1 - Dividend payout ratio = 1 - 0.45 = 0.55
Chapter 03 - Analyzing Financial Statements
0.3117 x 0.55 Sustainable growth rate = ———————— = 20.69%, an increase of 1.18% 1 – (0.3117 x 0.55)
Chapter 03 - Analyzing Financial Statements
research it! Analyzing Financial Statements Go the Web site of Wal-Mart Stores, Inc. at www.walmartstores.com and get the latest financial statements from the annual report using the following steps. Click on “Investors.” Click on “Annual Reports.” Click on the most recent date. This will bring the file onto your computer that contains the relevant data. Using the most recent balance sheet and income statement, calculate the financial ratios for the firm, including the internal and sustainable growth rates. SOLUTION: The solution will vary with the annual report accessed. However, these financial statements provide information on the firm’s financial position at a point in time or its operations over some past period of time. But these financial statements’ real value lies in the fact that managers, investors, and analysts can use the information the statements contain to analyze the current financial performance or condition of the firm. More importantly, managers can use this information to plan changes that will improve the firm’s future performance and, ultimately, its market value. integrated mini-case: Working with Financial Statements Listed below are the 2021 financial statements for Garners’ Platoon Mental Health Care, Inc. Spread the balance sheet and income statement. Calculate the financial ratios for the firm, including the internal and sustainable growth rates. Using the DuPont system of analysis and the industry ratios reported below, evaluate the performance of the firm. Garners’ Platoon Mental Health Care, Inc. Balance Sheet as of December 31, 2021 (in millions of dollars) Liabilities and Equity
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total
$ 421 1,109 1,760 $3,290
Fixed assets: Gross plant and equipment $5,812 Less: Depreciation 840 Net plant and equipment $4,972 Other long-term assets 892 Total $5,864 Total assets
Current liabilities : Accrued wages and taxes Accounts payable Notes payable Total
$ 316 867 872 $2,055
Long-term debt:
$3,090
Stockholders’ equity: Preferred stock (30 million shares) $ 60 Common stock and paid-in surplus 637 (200 million shares) Retained earnings 3,312 Total $4,009
$9,154 Total liabilities and equity
$9,154
Chapter 03 - Analyzing Financial Statements
Garners’ Platoon Mental Health Care, Inc. Income Statement for Year Ending December 31, 2021 (in millions of dollars) Net sales (all credit) Less: Cost of goods sold Gross profits Less: Other operating expenses Earnings before interest, taxes, depreciation, and amortization (EBITDA) Less: Depreciation Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes Net income
$4,980 2,246 $2,734 125 $2,609 200 $2,409 315 $2,094 440 $1,654
Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
$ 60 $1,594 722 $ 872
Per (common) share data: Earnings per share (EPS) Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
$ 7.970 $ 3.610 $19.745 $26.850
Garners’ Platoon Mental Health Care, Inc. Current ratio Quick ratio Cash ratio Inventory turnover Days’ sales in inventory Average collection period Average payment period Fixed asset turnover Sales to working capital Total asset turnover Capital intensity Debt ratio Debt-to-equity Equity multiplier Times interest earned Cash coverage Profit margin Gross profit margin Operating profit margin Basic earnings power ROA ROE Dividend payout
. Industry 2.00 times 1.20 times 0.25 times 2.50 times 146.00 days 91.00 days 100.00 days 1.25 times 4.00 times 0.50 times 2.00 times 50.00% 1.00 times 2.00 times 7.25 times 8.00 times 18.75% 49.16% 42.02% 19.90% 9.38% 18.75% 35.00%
Chapter 03 - Analyzing Financial Statements
Market-to-book ratio PE ratio
1.30 times 4.10 times
SOLUTION: Spreading the financial statements Spread the balance sheet: Garners’ Platoon Mental Health Care, Inc. Balance Sheet as of December 31, 2021 (in millions of dollars) Liabilities and Equity
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment Other long-term assets Total
Total assets
4.60% 12.11 19.23 35.94
63.49 9.18 54.32 9.74 64.06
100.00%
Current liabilities: Accrued wages and taxes Accounts payable Notes payable Total
3.45% 9.47 9.53 22.45
Long-term debt:
33.76
Stockholders’ equity: Preferred stock (5 million shares) Common stock and paid-in surplus (65 million shares) Retained earnings Total
36.18 43.80
Total liabilities and equity
100.00%
0.66 6.96
Spreading the income statement: Garners’ Platoon Mental Health Care, Inc. Income Statement for Years Ending December 31, 2021 (in millions of dollars) Net sales (all credit) 100.00% Less: Cost of goods sold 45.10 Gross profits 54.90 Less: Other operating expenses 2.51 Earnings before interest, taxes, depreciation, and amortization (EBITDA) 52.39 Less: Depreciation 4.02 Earnings before interest and taxes (EBIT) 48.37 Less: Interest 6.33 Earnings before taxes (EBT) 42.05 Less: Taxes 8.84 Net income...................................................................... 33.21%
Chapter 03 - Analyzing Financial Statements
Garners’ Platoon Mental Health Care, Inc. Current ratio Quick ratio Cash ratio Inventory turnover Days’ sales in inventory Average collection period Average payment period Fixed asset turnover Sales to working capital Total asset turnover Capital intensity Debt ratio Debt-to-equity Equity multiplier (common equity) Times interest earned Cash coverage Profit margin Gross profit margin Operating profit margin Basic earnings power ROA ROE Dividend payout Market-to-book ratio PE ratio
Industry 2.00 times 1.20times 0.25 times 2.50 times 146.00 days 91.00 days 100.00 days 1.25 times 4.00 times 0.50 times 2.00 times 50.00% 1.00 times 2.00 times 7.25 times 8.00 times 18.75% 49.16% 42.02% 19.90% 9.38% 18.75% 48.00% 1.30 times 3.10 times
1.60 times 0.74 times 0.20 times 2.83 times 129.00 days 81.28 days 140.90 days 1.00 times 4.03 times 0.544 times 1.84 times 56.20% 1.28 times 2.318 times 7.65 times 8.28 times 32.01% 54.90% 48.37% 26.32% 17.41% 40.36% 45.29% 1.36 times 3.37 times
The ROA and ROE DuPont equations for Garners’ are calculated as follows: ROA
=
Profit Margin
x
Total asset turnover
17.41%
=
32.01%
x
0.544 times
Industry average: 9.375%
=
18.75%
x
0.50 times
ROE
=
Profit Margin
x
Total asset turnover
40.36%
=
32.01%
x
0.544 times
x 2.318 times
Industry average: 18.75%
=
18.75%
x
0.50 times
x 2.00 times
x Equity multiplier
As we see from these ratios, Garners’ Platoon Mental Health Care, Inc. is more profitable than the average firm in the industry when it comes to overall efficiency expressed as ROA and ROE. The DuPont equation highlights that this superior performance comes from both profit margin (operating efficiency) and total asset turnover (efficiency in asset use). Further, the ROE equation highlights that Garner’s superior performance is achieved while equity is supporting more dollars of assets relative to the industry. Thus, the firm is using slightly higher levels of debt and lower levels of equity compared to the industry.
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
CHAPTER 4 – TIME VALUE OF MONEY 1: ANALYZING SINGLE CASH FLOWS QUESTIONS LG1
1. List and describe the purpose of each part of a time line with an initial cash inflow and a future cash outflow. Which cash flows should be negative and which positive? Why? The cash flow timeline is a visual depiction of inflows and outflows relative to the period under consideration. Cash flows are illustrated below the cash flow line with the corresponding periods that apply appearing above the cash flow diagram. Inflows are represented by positive numbers and outflows by negative numbers.
LG2
2. How are the present value and future value related? The measure that relates present values to future values is the interest rate i. A present value can be moved forward in time with interest to arrive at the future value ( Future value in N years = ). A future value can be discounted back to the present by rearranging the equation so that the FV is divided by the interest factor.
LG3
3. Would you prefer to have an investment earning 5 percent for 40 years or an investment earning 10 percent for 20 years? Explain. Investments of $1 will grow to $7.04 in 40 years (= $1.0540) and $1 will grow to $6.73 in 20 years (= $1.1020). The 5 percent investment for 40 years is worth more. This example illustrates the importance of time in building wealth.
LG4
4. How are present values affected by changes in interest rates? Interest rates have an inverse relationship to present values. Increases in expected interest rates result in lower present values because future values are discounted at a higher rate to become smaller present values. Decreases in expected interest rates result in higher present values because future values are discounted at a lower rate.
LG5 5. What do you think about the following statement. “I am going to receive $100 two years from now and $200 three years from now, so I am getting a $300 future value.” How could the two cash flows be compared or combined? Cash flows may only be combined when they are moved to the same point in time. The statement above is incorrect in that it compares the $100 cash flow in year 2 with the $200 cash flow in year 3. To make comparisons meaningful, the cash flows need to be considered at the same point in time. Either the $100, 2nd year cash flow could be moved to year 3, or the $200, 3rd year cash flow could be moved to year 2 for combining.
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
LG6
6. Show how the Rule of 72 can be used to approximate the number of years to quadruple an investment. The Rule of 72 is a rule of thumb that approximates the amount of time necessary for an investment to double given a certain level of interest expressed in percentage form. Therefore, an investment of 8% interest will take approximately 9 years (= 72/8) to double according to the Rule of 72. It would then take another 9 years for this amount to double. Therefore, it would take 18 years for the original investment to quadruple at an 8 percent rate.
LG7
7. Without making any computations, indicate which of each pair has a higher interest rate? a. $100 doubles to $200 in 5 years or 7 years. b. $500 increases in 4 years to $750 or to $800. c. $300 increases to $450 in 2 years or increases to $500 in 3 years. a. $100 doubling to $200 in 5 years has the higher interest rate. b. $500 increasing to $800 in 4 years has a higher interest rate. c. $300 increasing to $450 in 2 years has the higher interest rate.
LG8 8. A $1,000 investment has doubled to $2,000 in 8 years because of a 9 percent rate of return. How much longer will it take for the investment to reach $4,000 if it continues to earn a 9 percent rate? The Rule of 72 predicted that $1,000 will double to $2,000 in 8 years at 9 percent interest. Another doubling from $2,000 to $4,000 will occur in eight more years at 9 percent, again predicted by the Rule of 72. PROBLEMS Basic Problems LG1
4-1 Time Line Show the time line for a $500 cash inflow today, a $605 cash outflow in year 2, and a 10 percent interest rate. The time line for this problem is: Period 0 Cash Flow
LG1
10%
1
500
2 years -605
4-2 Time Line Show the time line for a $400 cash outflow today, a $518 cash inflow in year 3, and a 9 percent interest rate. The time line for this problem is:
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
Period 0 Cash Flow
LG2
-400
1
2 9%
3 years 518
4-3 One Year Future Value What is the future value of $500 deposited for one year earning a 8 percent interest rate annually. FVN = PV × (1 + i)N FV1 = $500 × (1 + 0.08)1 = $500 × 1.08 = $540 Or N=1, I=8, PV=−500, PMT=0, CPT FV == 540
LG2
4-4 One Year Future Value What is the future value of $400 deposited for one year earning an interest rate of 9 percent per year? FVN = PV × (1 + i)N FV1 = $400 × (1 + 0.09)1 = $400 × 1.09 = $436 Or N=1, I=9, PV=−400, PMT=0, CPT FV == 436
LG3
4-5 Multiyear Future Value How much would be in your savings account in eleven years after depositing $150 today if the bank pays 8 percent per year? FVN = PV × (1 + i)N FV8 = $150 × (1 + 0.08)11 = $150 × 2.3316 = $349.74 Or N=11, I=8, PV=−150, PMT=0, CPT FV == 349.745
LG3
4-6 Multiyear Future Value Compute the value in 25 years of a $1,000 deposit earning 10 percent per year. FVN = PV × (1 + i)N FV25 = $1,000 × (1 + 0.10)25 = $1,000 × 10.83471 = $10,834.71 Or N=25, I=10, PV=−1000, PMT=0, CPT FV == 10,834.71
LG3
4-7 Compounding with Different Interest Rates A deposit of $350 earns the following interest rates: • 8 percent in the first year, • 6 percent in the second year, and
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
• 5.5 percent in the third year. What would be the third year future value? The time line for this problem is: Period 0 Cash Flow
8%
1
6%
2
-350
5.5% 3 years X
FV = PV × (1 + i) (1 + j) (1 + k) FV = $350 × (1 + 0.08) (1 + 0.06) (1 + 0.055) = $350 × 1.08 × 1.06 × 1.055 = $422.72 LG3 4-8 Compounding with Different Interest Rates A deposit of $750 earns interest rates of 9 percent in the first year and 12 percent in the second year. What would be the second year future value? The time line for this problem is: Period 0 Cash Flow
-750
9%
1
12%
2 years X
FV = PV × (1 + i) (1 + j) FV = $750 × (1 + 0.09) (1 + 0.12) = $750 × 1.09 × 1.12 = $915.60 LG4 4-9 Discounting One Year What is the present value of a $350 payment in one year when the discount rate is 10 percent? PV = FV / (1 + i) PV = $350 / (1 + 0.10) = $350 / 1.10 = $318.18 Or N=1, I=10, PMT=0, FV=−350, CPT PV == 318.182 LG4 4-10 Discounting One Year What is the present value of a $200 payment in one year when the discount rate is 7 percent? PV = FV / (1 + i) PV = $200 / (1 + 0.07) = $200 / 1.07 = $186.92
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
Or N=1, I=7, PMT=0, FV=−200, CPT PV == 186.916 LG4 4-11 Present Value What is the present value of a $1,500 payment made in nine years when the discount rate is 8 percent? PV = FV / (1 + i)N PV = $1,500 / (1 + 0.08)9 = $1,500 / 1.999005 = $750.37 Or N=9, I=8, PMT=0, FV=−1500, CPT PV == 750.37 LG4 4-12 Present Value Compute the present value of an $850 payment made in 10 years when the discount rate is 12 percent. PV = FV / (1 + i)N PV = $850 / (1 + 0.12)10 = $850 / 3.10585 = $273.68 Or N=10, I=12, PMT=0, FV=−850, CPT PV == 273.68 LG4
4-13 Present Value with Different Discount Rates Compute the present value of $1,000 paid in three years using the following discount rates: 6 percent in the first year, 7 percent in the second year, and 8 percent in the third year.
PV = FV / [(1 + i) (1 + j) (1 + k)] PV = $1,000 / [(1 + 0.06) (1 + 0.07) (1 + 0.08)] = $1,000 / [1.06 × 1.07 × 1.08] = $1,000 / 1.22494 = $816.37 LG4
4-14 Present Value with Different Discount Rates Compute the present value of $5,000 paid in two years using the following discount rates: 8 percent in the first year and 7 percent in the second year. PV = FV / [(1 + i) (1 + j) ] PV = $5,000 / [(1 + 0.08) × (1 + 0.07)] = $5,000 / [1.08 × 1.07] = $5,000 / 1.15560 = $4,326.76
LG6 4-15 Rule of 72 Approximately how many years does it take to double a $100 investment when interest rates are 7 percent per year? N = 72 / 7 10.29 years
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
LG6
4-16 Rule of 72 Approximately how many years does it take to double a $500 investment when interest rates are 10 percent per year? N = 72 / 10
LG6
7.20 years
4-17 Rule of 72 Approximately what interest rate is needed to double an investment over five years? N = 72 / 5 14.40 percent
LG6
4-18 Rule of 72 Approximately what interest rate is earned when an investment doubles over 12 years? N = 72 / 12
LG7
6.00 percent
4-19 Rates over One Year Determine the interest rate earned on a $1,400 deposit when $1,800 is paid back in one year. $1,400 × (1 + i) = $1,800; Solving for i yields 0.2857, or 28.57% Or N=1, PV=−1400, PMT=0, FV=1800, CPT I == 28.57
LG7
4-20 Rates over One Year Determine the interest rate earned on a $2,300 deposit when $2,900 is paid back in one year. $2,300 × (1 + i) = $2,900; Solving for i yields 26.09% Or N=1, PV=−2300, PMT=0, FV=2900, CPT I == 26.09 intermediate problems
LG3
4-21 Interest-on-Interest Consider a $2,000 deposit earning 8 percent interest per year for five years. What is the future value, and how much total interest is earned on the original deposit vs. how much is interest earned on interest? The $2,000 investment will grow to a future value of $2,938.66 [= FV5 = $2,000 × (1 + 0.08)5], assuming compounded interest over the 5 years. The total interest earned is $938.66. The interest earned on the original investment is $160 per year for 5 years, or $800. The interest earned on the interest is the difference of $138.66 [= $938.66 − $800].
LG3 4-22 Interest-on-Interest Consider a $5,000 deposit earning 10 percent interest per year for 10 years. What is the future value, how much total interest is earned on the original deposit, and how much is interest earned on interest?
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
The $5,000 investment will grow to a future value of $12,968.71 [= FV10 = $5,000 × (1 + 0.10)10], assuming compounded interest over the 10 years. The total interest earned is $7,968.71. The interest earned on the original investment is $500 per year for 10 years, or $5,000. The interest earned on the interest is the difference of $2,968.71 [= $7,968.71 − $5,000]. LG5
4-23 Comparing Cash Flows What would be more valuable, receiving $500 today or receiving $625 in three years if interest rates are 7 percent? Why? PV = FV / (1 + i)N PV = $625 / (1 + 0.07)3 = $625 / 1.225043 = $510.19 Or N=3, I=7, PMT=0, FV=−625, CPT PV == 510.186 The present value of $625 to be paid in three years at 7 percent interest is $510.19. This amount is worth more than $500 received today. Therefore, the $625 payment made in 3 years is more valuable.
LG5
4-24 Comparing Cash Flows Which cash flow would you rather pay, $425 today or $500 in two years if interest rates are 10 percent? Why? PV = FV / (1 + i)N PV = $500 / (1 + 0.10)2 = $500 / 1.21 = $413.22 Or N=2, I=10, PMT=0, FV=−500, CPT PV == 413.22 The present value of $500 to be paid in two years at 10 percent interest is $413.22. This amount is lower than $425 paid today. Therefore, paying the $500 in two years is cheaper.
LG5
4-25 Moving Cash Flows What is the value in year 3 of a $700 cash flow made in year 6 if interest rates are 10 percent? PV3 = FV6 / (1 + i)N PV3 = $700 / (1 + 0.10)(6-3) = $700 / 1.3310 = $525.92 Or N=3, I=10, PMT=0, FV=−700, CPT PV == 525.92
LG5
4-26 Moving Cash Flows What is the value in year 4 of a $1,000 cash flow made in year 6 if interest rates are 8 percent? PV = FVN / (1 + i)N PV4 = FV6 / (1 + i)(6 – 4) PV4 = $1,000 / (1 + 0.08)(2)
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
= $1,000 / 1.1664 = $857.34 Or N=2, I=8, PMT=0, FV=−1000, CPT PV == 857.338 LG5
4-27 Moving Cash Flows What is the value in year 10 of a $1,000 cash flow made in year 3 if interest rates are 9 percent? FVN = PV × (1 + i)N FV10 = PV(3) × (1 + i)(10-3) FV10 = $1,000 × (1 + 0.09)7 = $1,000 × 1. 828039 = $1,828.04 Or N=7, I=9, PV=−1000, PMT=0, CPT FV == 1,828.039
LG5
4-28 Moving Cash Flows What is the value in year 15 of a $250 cash flow made in year 3 if interest rates are 11 percent? FVN = PV × (1 + i)N FV15 = PV3 × (1 + i)(15-3) FV15 = $250 × (1 + 0.11)12 = $250 × 3.49845 = $874.61 Or N=12, I=11, PV=−250, PMT=0, CPT FV == 874.61
LG7
4-29 Solving for Rates What annual rate of return is earned on a $1,000 investment when it grows to $1,800 in six years? FVN = PV × (1 + i)N $1,800 = $1,000 × (1 + i)6 (1 + i)6 = $1,800 / $1,000 (1 + i)6 = 1.8 i = (1.8)(1/6) -1 = 0.102924 or 10.29% Or N=6, PV=−1000, PMT=0, FV=1800, CPT I == 10.29
LG7
4-30 Solving for Rates What annual rate of return is earned on a $5,000 investment when it grows to $9,500 in five years? FVN = PV × (1 + i)N $9,500 = $5,000 × (1 + i)5 (1 + i)5 = $9,500 / $5,000 (1 + i)5 = 1.9 i = (1.9)(1/5) -1 = 0.1370 or 13.70% Or N=5, PV=−5000, PMT=0, FV=9500, CPT I == 13.697
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
LG8
4-31 Solving for Time How many years (and months) will it take $2 million to grow to $5 million with an annual interest rate of 7 percent? FVN = PV × (1 + i)N $5 million = $2 million × (1 + 0.07)N (1.07)N = 5 / 2 (the millions cancel) ln(1.07)N = ln2.5 N × ln1.07 = ln2.5 N = ln2.5 / ln1.07 = 0.91629 / 0.06766 = 13.54 years = 13 years, 6.5 months OR use footnote 4 formula: N = ln(FV / PV) / ln(1 + i) = ln($5,000 / $2,000) / ln1.07 = ln2.5 / ln1.07 = 13.54 years = 13 years, 6.5 months
LG8
4-32 Solving for Time How long will it take $2,000 to reach $5,000 when it grows at 10 percent per year? FVN = PV × (1 + i)N $5,000 = $2,000 × (1 + 0.10)N (1.10)N = 5 / 2 (the thousands cancel) ln(1.10)N = ln2.5 N × ln1.10 = ln2.5 N = ln2.5 / ln1.10 = 0.91629/ 0.09531 = 9.61 years = 9 years, 7.4 months OR use footnote 4 formula: N = ln(FV / PV) / ln(1 + i) = ln($5,000 / $2,000) / ln(1.10) = ln2.5 / ln1.10 = 9.61 years = 9 years, 7.4 months advanced problems
LG2
4-33 Future Value At age 30 you invest $1,000 that earns 8 percent each year. At age 40 you invest $1,000 that earns 12 percent per year. In which case would you have more money at age 60? FVAge 60 = PVAge 30 × (1 + i)Years until age 60 FVAge 60 = $1,000 × (1.08)30 = $1,000 × 10.06266 = $10,062.66 Or N=30, I=8, PV=−1000, PMT=0, CPT FV == 10,062.66 FVAge 60 = PVAge 40 × (1 + i)Years until age 60
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
FVAge 60 = $1,000 × (1.12)20 = $1,000 × 9.64629 = $9,646.29 Or N=20, I=12, PV=−1000, PMT=0, CPT FV == 9,646.29 The investment of $1,000 at age 30 yields more money at age 60, even though the interest rate is lower. This illustrates the importance of starting to invest earlier in life. LG2 4-34 Future Value At age 25 you invest $1,500 that earns 8 percent each year. At age 40 you invest $1,500 that earns 11 percent per year. In which case would you have more money at age 65? FVAge 65 = PVAge 25 × (1 + i)Years until age 65 FVAge 65 = $1,500 × (1.08)40 = $1,500 × 21.7245215 = $32,586.78 Or N=40, I=8, PV=−1500, PMT=0, CPT FV == 32,586.78 FVAge 65 = PVAge 40 × (1 + i)Years until age 65 FVAge 65 = $1,500 × (1.11)25 = $1,500 × 13.5854638 = $20,378.20 Or N=25, I=11, PV=−1500, PMT=0, CPT FV == 20,378.20 The investment of $1,500 at age 25 yields more money at age 65, even though the interest rate is lower. This illustrates the importance of starting to invest earlier in life. LG7 4-35 Solving for Rates You invested $2,000 in the stock market one year ago. Today, the investment is valued at $1,500. What return did you earn? What return would you need to get next year to break even overall? FVN = PV × (1 + i)N $1,500 = $2,000 × (1 + i)1 (1 + i) = $1,500 / $2,000 i = 0.75 -1 = −0.25, or −25% (first year return is negative) Or N=1, PV=−2000, PMT=0, FV=1500, CPT I == −25.0 FVN = PV × (1 + i)N $2,000 = $1,500 × (1 + i)1 (1 + i) = $2,000 / $1,500 i = 1.3333 -1 = 0.3333 or 33.33% (second year return needs to be higher to compensate for the loss) Or N=1, PV=−1500, PMT=0, FV=2000, CPT I == 33.333
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
LG7 4-36 Solving for Rates You invested $3,000 in the stock market one year ago. Today, the investment is valued at $3,750. What return did you earn? What return would you suffer next year for your investment to be valued at the original $3,000? FVN = PV × (1 + i)N $3,750 = $3,000 × (1 + i)1 (1 + i) = $3,750 / $3,000 i = )1.25 -1 = 0.25 or 25.00% (first year return is positive) Or N=1, PV=−3000, PMT=0, FV=3750, CPT I == 25.0 FVN = PV × (1 + i)N $3,000 = $3,750 × (1 + i)1 (1 + i) = $3,000 / $3,750 i = .80 -1 = -0.20 or −20.0% (second year return is negative) Or N=1, PV=−3750, PMT=0, FV=3000, CPT I == −20.0 LG7 4-37 Solving for Rates What annual rate of return is earned on a $4,000 investment made in year 2 when it grows to $6,500 by the end of year seven? FVN = PV × (1 + i)N FV7 = PV2×(1 + i)(7 – 2) $6,500 = $4,000 × (1 + i)5 (1 + i) 5 = $6,500 / $4,000 i = (1.625) (1/5) -1 = 1.10197 – 1 = 0.10197 or 10.20% Or N=5, PV=−4000, PMT=0, FV=6500, CPT I == 10.197 LG7 4-38 Solving for Rates What annual rate of return is implied on a $2,500 loan taken next year when $3,500 must be repaid in year 4? FVN = PV × (1 + i)N FV4 = PV1 × (1 + i)(4 – 1) $3,500 = $2,500 × (1 + i)(4 - 1) (1 + i)3 = $3,500 / $2,500 i = (1.40) (1/3) - 1 = 0.1187 or 11.87% (note, this is from the lender’s perspective) Or N=3, PV=−2500, PMT=0, FV=3500, CPT I == 11.869 LG2&4
4-39 General TVM Ten years ago, Hailey invested $2,000 and locked in a 9 percent annual interest rate for 30 years (end 20 years from now). Aidan can make a 20-year investment today and lock in a 10 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Hailey? First determine how much Hailey will have. FV20 = PV-10 × (1 + i)30
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
FV20 = $2,000 × (1 + 0.09)30 = $2,000 × 13.26768 = $26,535.36 (Hailey’s FV in 30 years) Or N=30, I=9, PV=−2000, PMT=0, CPT FV == 26,535.36 So Aidan will have to deposit: PV = FV20 / (1 + i)N PV = $26,535.36 / (1 + 0.10)20 = $26,535.36 / 6.72750 = $3,944.31 Or N=20, I=10, PMT=0, FV=26535.36, CPT PV == −3,944.31 LG2&4 4-40 General TVM Ten years ago, Hailey invested $3,000 and locked in an 8 percent annual interest rate for 30 years (end 20 years from now). Aidan can make a 20-year investment today and lock in a 10 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Hailey? First determine how much Hailey will have. FV20 = PV-10 × (1 + i)30 FV20 = $3,000 × (1 + 0.08)30 = $3,000 × 10.062657 = $30,187.97 (Hailey’s FV in 30 years) Or N=30, I=8, PV=−3000, PMT=0, CPT FV == 30,187.97 So Aidan will have to deposit: PV = FV20 / (1 + i)N PV = $30,187.97 / (1 + 0.10)20 = $30,187.97 / 6.72750 = $4,487.25 Or N=20, I=10, PMT=0, FV=30,187.97, CPT PV == −4,487.249 LG5 4-41 Moving Cash Flows You are scheduled to receive a $500 cash flow in one year, a $1,000 cash flow in two years, and pay an $800 payment in three years. If interest rates are 10 percent per year, what is the combined present value of these cash flows? The timeline of this problem is: Period 0 Cash Flow
?
1 500
10%
2
3 years
1000
-800
First, discount the $500 to year 0: PV = $500 / (1 + 0.10) = $454.545 Or N=1, I=10, PMT=0, FV=−500, CPT PV == 454.545 Then discount the $1,000 to year 0: PV = $1,000 / (1 + 0.10)2 = $826.446
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
Or N=2, I=10, PMT=0, FV=−1000, CPT PV == 826.446 Discount the -$800 to year 0: PV = -$800 / (1 + 0.10)3 = -$601.052 Or N=3, I=10, PMT=0, FV=800, CPT PV == −601.052 Now sum up the cash flows: $454.545 + $826.446 – $601.052 = $679.94 4-42 Spreadsheet Problem Oil prices have increased a great deal in the last decade. The table below shows the average oil price for each year since 1949. Many companies use oil products as a resource in their own business operations (like airline firms and manufacturers of plastic products). Managers of these firms will keep a close watch on how rising oil prices will impact their costs. The interest rate in the PV / FV equations can also be interpreted as a growth rate in sales, costs, profits, and so on (see Example 4-5). Average Oil Prices
Year 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
per barrel $2.54 $2.51 $2.53 $2.53 $2.68 $2.78 $2.77 $2.79 $3.09 $3.01 $2.90 $2.88 $2.89 $2.90 $2.89 $2.88 $2.86 $2.88 $2.92 $2.94
Year 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988
per barrel $3.09 $3.18 $3.39 $3.39 $3.89 $6.87 $7.67 $8.19 $8.57 $9.00 $12.64 $21.59 $31.77 $28.52 $26.19 $25.88 $24.09 $12.51 $15.40 $12.58
Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
per barrel $15.86 $20.03 $16.54 $15.99 $14.25 $13.19 $14.62 $18.46 $17.23 $10.87 $15.56 $26.72 $21.84 $22.51 $27.54 $38.93 $46.47 $58.30 $64.67 $91.48
Year 2009 2010 2011 2012 2013 2014 2015 2016 2017
per barrel $53.48 $71.21 $87.04 $93.02 $97.91 $93.26 $48.69 $43.14 $50.88
a. Using the 1949 oil price and the 1969 oil price, compute the annual growth rate in oil prices during those 20 years. =RATE(20,0,-2.54,3.09) = 0.98%
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
b. Compute the annual growth rate between 1969 and 1989 and between 1989 and 2017. =RATE(20,0,-3.09,15.86) = 8.52% for 1969 to 1989 =RATE(28,0,-15.86,50.88) = 4.25% for 1989 to 2017 c. Given the price of oil in 2017 and your computed growth rate between 1989 and 2017, compute the future price of oil in 2020 and 2025. =FV(4.25%,3,0,50.88,0) = $57.65 in 2020 =FV(4.25%,8,0,50.88,0) = $70.99 in 2025
4-43 Spreadsheet Problem Consider that you are the marketing manager of a firm. You need to have approximately 1 additional salesperson for every $10 million in sales. You currently have $50 million in sales and have 5 employees handling the sales accounts. In order to plan ahead, you want to get an idea of when you may need to hire more salespeople. Build a table that shows the sales for each of the next ten years for sales growth of 5%, 10%, 15%, and 20%.
Comment on when new sales staff should be hired for each growth rate. Answer: Growth Rate
Today
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
5%
$50
$52.50
$55.13
$57.88
$60.78
$63.81
$67.00
$70.36
$73.87
$77.57
$81.44
10%
$50
$55.00
$66.55
$73.21
$80.53
$88.58
$97.44
$107.18
$117.90
$129.69
$142.66
15% 20%
$50 $50
$57.50 $60.00
$76.04 $86.40
$87.45 $103.68
$100.57 $124.42
$115.65 $149.30
$133.00 $179.16
$152.95 $214.99
$175.89 $257.99
$202.28 $309.59
$232.62 $371.50
Year 10
For a 5% growth rate, new staff must be hired in year 4, 7, and 10. For a 10% growth rate, new staff need to be hired in year 2 and nearly every year after that. For 15% and 20%, there are many years in which multiple new salespeople should by hired.
Research It! What kind of returns might you expect in the stock market? One way to measure how the stock market has performed is to examine the rate of return of the S&P 500 Index. To see historical prices of the S&P 500 Index, go to Yahoo! Finance (finance.yahoo.com) and click on the “S&P 500” link on the left hand side. Then click “Historical Prices” on the left menu, select “Monthly”
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
prices and click the “Get Prices” button. You can download to a spreadsheet using the buttom at the bottom of the data page. Compute the 1-year, 5-year, and 10-year returns over time. What do you conclude about the returns during each of these periods? SOLUTION: The actual data shown will depend on the date the exercise is conducted. However, the top portion may look like:
The 1-year returns are highly volatile. They can be very large and positive and very large and negative. The returns for 5-year periods are much less volatile, but can still be quite negative during some periods. The returns for 10-year periods are rarely, if ever, negative.
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
Integrated Minicase: Investing in Gold People have had a fascination with gold for thousands of years. Archaeologists have discovered gold jewelry in Southern Iraq dating to 3000 BC and gold ornaments in Peru dating to 1200 BC. The ancient Egyptians were masters in the use of gold for jewelry, ornaments, and economic exchange. By 1000 BC, squares of gold were a legal form of money in China. The Romans issued a popular gold coin called the Aureus (aureus is the Latin word for gold). By 1100 AD, gold coins had been issued by several European countries. Gold has been a highly sought-after asset all over the world and has always retained at least some economic value over thousands of years. The United States has had a very chaotic history with gold. For example, in the Great Depression, President Franklin D. Roosevelt banned the export of gold and ordered U.S. citizens to hand in all the gold they possessed. It was not until the end of 1974 that the ban on gold ownership by U.S. citizens was lifted. By 1986, the U.S. government’s attitude on gold ownership had completely turned around, as evidenced by the resumption of the U.S. Mint’s production of gold coins with the American Eagle. However, U.S. investors have little more than 30 years of gold-investing experience. Figure 4.5 shows how the price of gold per ounce has changed since 1974. Figure 4.5 December Gold Prices Since 1974
1,600.00 1,400.00
Gold Price per Oz. ($)
1,200.00 1,000.00
Gold peaked at
X
800.00 600.00 400.00 200.00
Data Source: Kitco (www.kitco.com)
2016
2010
2004
Year
1998
1992
1986
1980
1974
0.00
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
These end-of-December prices do not illustrate the true magnitude of the price bubble in gold prices that occurred in 1980.The price of gold increased from $512 at the end of 1979 to a top of $870 on January 21, 1980. The subsequent crash in the price of gold was just as spectacular. The annual returns of gold are shown in Table 4.5. Gold prices have been very volatile, increasing dramatically for one or two years and then experiencing significant declines the next year or two. Table 4.5 Annual Gold Returns Since 1975
Year 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
December Gold Price $175.00 $140.25 $134.50 $164.95 $226.00 $512.00 $589.75 $397.50 $456.90 $382.40 $309.00 $326.55 $396.13 $484.10 $410.25 $398.60 $392.75 $353.20 $332.90 $391.75 $383.25 $387.00 $369.25 $290.20 $287.80 $290.25 $274.45 $276.50 $347.20 $416.25 $435.60 $513.00 $632.00 $833.75 $869.75 $1,087.50
Annual Gold Return -19.86% -4.10% 22.64% 37.01% 126.55% 15.19% -32.60% 14.94% -16.31% -19.19% 5.68% 21.31% 22.21% -15.26% -2.84% -1.47% -10.07% -5.75% 17.68% -2.17% 0.98% -4.59% -21.41% -0.83% 0.85% -5.44% 0.75% 25.57% 19.89% 4.65% 17.77% 23.20% 31.92% 4.32% 25.04%
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
2010 2011 2012 2013 2014 2015 2016 2017
$1,405.50 $1,531.00 $1,657.50 $1,204.50 $1,206.00 $1,062.85 $1,145.90 $1,291.00
29.24% 8.93% 8.26% -27.33% 0.12% -11.87% 7.81% 12.66%
a. Compute the rate of return in gold prices that occurred during the three weeks between the last day of 1979 and the January 21, 1980 peak. SOLUTION: solve for i, $870 = $512 × (1 + i) i $870 / $512 – 1 = 0.6992 = 69.92% Or N=1, PV=−512, PMT=0, FV=870, CPT I == 69.92 b. By the end of 1980, gold had dropped to $589.75 per ounce. Compute the rate of return from the peak to the end of 1980. SOLUTION: solve for i, $589.75 = $870 × (1 + i) i = $589.75 / $870 – 1 = -0.3221 = −32.21% Or N=1, PV=−870, PMT=0, FV=589.75, CPT I == −32.21 c. Imagine that you invested $1,000 in gold at the end of 1999. Use the returns in Table 4.5 to determine the value of the investment at the end of 2017. SOLUTION:
Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Annual Gold Return 0.85% -5.44% 0.75% 25.57% 19.89% 4.65% 17.77% 23.20% 31.92% 4.32% 25.04% 29.24% 8.93% 8.26% -27.33%
Factor 0.0000 0.9456 1.0075 1.2557 1.1989 1.0465 1.1777 1.2320 1.3192 1.0432 1.2504 1.2924 1.0893 1.0826 0.7267
Investment Value $1,000.00 945.56 952.63 1196.21 1434.11 1500.78 1767.44 2177.43 2872.52 2996.55 3746.77 4842.38 5274.76 5710.59 4149.87
Chapter 04 - Time Value of Money 1: Analyzing Single Cash Flows
2014 2015 2016 2017
0.12% -11.87% 7.81% 12.66%
1.0012 0.8813 1.0781 1.1266
4155.04 3661.84 3947.98 4447.89
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
CHAPTER 5 – TIME VALUE OF MONEY 2: ANALYZING ANNUITY CASH FLOWS QUESTIONS LG1
5-1 How can you add a cash flow in year 2 and a cash flow in year 4 in year 7? To add cash flows, they need to be moved to the same time period. The cash flows in years 2 and 4 should be moved forward with interest to year 7, then they can be added together.
LG2
5-2 People can become millionaires in their retirement years quite easily if they start saving early in employer 401(k) or 403(b) programs (or even if their employers don’t offer such programs). Demonstrate the growth of a $250 monthly contribution for 40 years earning 9 percent APR. Using equation 5-2, we have: (1 + 0.09 /12)
480
FVA 40 = $250
LG3
0.09/12
−1
= $1,170,330.07
5-3 When you discount multiple cash flows, how does the future period that a cash flow is paid affect its present value and its contribution to the value of all the cash flows? Discounting reduces a future cash flow to a smaller present value. Cash flows far into the future become very small when discounted to the present. Thus, cash flows in distant future periods have small impacts on present values.
LG4
5-4 How can you use the present value of an annuity concept to determine the price of a house you can afford? Mortgages are typically for a large enough amount of money that borrowing is required to purchase a home. The amount that one can afford for a home is a function of their current state of wealth. Mortgages allow consumers to spread the expense of a home over a longer period, typically 15 or 30 years. This allows consumers to put a smaller portion of wealth into the home (for example, a 20 percent down payment) and borrow the balance over the life of the loan. Due to the effect of annuity compounding, the payments for such a long- lived debt make the monthly payments of a manageable nature so that they can be paid from current income.
LG5
5-5 Since perpetuity payments continue forever, how can a present value be computed? Why isn’t the present value infinite? Equation 5-5 is used to calculate the present value of a perpetuity. It is a limiting version of equation 5-4 in which the period N grows infinitely large. As this occurs the expression following the “1” in equation 5-4 drives to the value 0 and the numerator simply become
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
“1.” The present value is not infinite since the terms following the PMT in equation 5-4 converge to a finite limit of 1/i. This also demonstrates how payments far into the future have infinitesimal value today. LG6 5-6 Explain why you use the same adjustment factor, (1 + i), when you adjust annuity due payments for both future value and present value. Adjusting an annuity due calculation involves shifting the entire series of payments forward one period. This is accomplished by multiplying by (1 + i) irrespective of whether it is a future value or present value calculation. LG7
5-7 Use the idea of compound interest to explain why EAR is larger than APR. The annual percentage rate does not take into account the frequency of interest compounding. Equation 5-8 illustrates the conversion from APR to EAR. The effective annual rate converts the annual percentage rate to a rate that can be compared to other annual rates.
LG8
5-8 Would you rather pay $10,000 for a 5-year $2,500 annuity or a 10-year $1,250 annuity? Why? The effective annual rates for these two payment streams are 7.93 percent and 4.28% percent respectively. I would rather pay $10,000 for a 5-year $2,500 annuity as it earns a higher effective annual rate of interest.
LG9 5-9 The interest on your home mortgage is tax deductible. Why are the early years of the mortgage more helpful in reducing taxes than in the later years? Mortgage payments at the beginning of the amortization schedule are predominantly interest with little principal. In later years, interest payments decline and principal payments make up an ever increasing part of the payments. Thus, the tax deductible part (the interest payment) is larger in the beginning years. LG10 5-10 How can you use the concepts illustrated in computing the number of payments in an annuity to figure how to pay off a credit card balance? How does the magnitude of the payment impact the number of months? Utilizing equation 5-4, you can declare the present balance for the credit card and set that equal to the PVA. The interest is the APR, which is the value to put into “i” in equation 5-4. You then decide when you want to have the credit card paid off and convert this to a monthly value of N in equation 5-4. Solving for PMT will yield the amount needed to pay the credit card off in the time frame you desire, assuming that no additional charges are made to the credit card and that the interest rate remains level. The higher the payment amount, the fewer the number of months required to pay off the balance.
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
PROBLEMS basic problems LG1
5-1 Future Value Compute the future value in year 9 of a $2,000 deposit in year 1 and another $1,500 deposit at the end of year 3 using a 10 percent interest rate. Use equation 5-1: FV8 = $2,000 × (1 + 0.10)8 + $1,500× (1 + 0.10)6 = $4,287.18 + $2,657.34 = $6,944.52 Or N=8, I=10, PV=−2000, PMT=0, CPT FV == 4,287.18 and N=6, I=10, PV=−1500, PMT=0, CPT FV == 2,657.34 then $4,287.18 + $2,657.34 = $6,944.52
LG1
5-2 Future Value Compute the future value in year 7 of a $2,000 deposit in year 1 and another $2,500 deposit at the end of year 4 using an 8% interest rate. Use equation 5-1: FV7 = $2,000 × (1 + 0.08)6 + $2,500 × (1 + 0.08)3 = $3,173.75 + $3,149.28 = $6,323.03 Or N=6, I=8, PV=−2000, PMT=0, CPT FV == 3,173.75 and N=3, I=8, PV=−2500, PMT=0, CPT FV == 3,149.28 then $3,173.75 + $3,149.28 = $6,323.03
LG2
5-3 Future Value of an Annuity What is the future value of a $900 annuity payment over five years if interest rates are 8 percent? Use equation 5-2: FVA 5 = $900
(1+ 0.08)5 −1 = $900 5.8666 = $5,279.94 0.08
Or N=5, I=8, PV=0, PMT=−900, CPT FV == 5,279.94
LG2
5-4 Future Value of an Annuity What is the future value of a $700 annuity payment over six years if interest rates are 10 percent? Use equation 5-2: (1 + 0.10) − 1 = $700 7.7156 = $5,400.93 6
FVA 6 = $700
0.10
Or N=6, I=10, PV=0, PMT=−700, CPT FV == 5,400.93
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
LG3
5-5 Present Value Compute the present value of a $2,000 deposit in year 1 and another $1,500 deposit at the end of year 3 if interest rates are 10 percent. Use equation 5-3: PV = $2,000 ÷ (1 + 0.10)1 + $1,500 ÷ (1 + 0.10)3 = $1,818.18 + $1,126.97 = $2,945.15 Or N=1, I=10, PMT=0, FV=−2000, CPT PV == 1,818.18 and N=3, I=10, PV=−1500, PMT=0, CPT FV == 1,126.97 then $1,818.18+ $1,126.97= $2,945.15
LG3
5-6 Present Value Compute the present value of a $2,000 deposit in year 1 and another $2,500 deposit at the end of year 4 using an 8 percent interest rate. Use equation 5-3: PV = $2,000 ÷ (1 + 0.08)1 + $2,500 ÷ (1 + 0.08)4 = $1,851.85 + $1,837.57 = $3,689.43 Or N=1, I=8, PMT=0, FV=−2000, CPT PV == 1,851.85 and N=4, I=8, PV=−2500, PMT=0, CPT FV == 1,837.57 then $1,851.85+ $1,837.57= $3,689.43
LG4
5-7 Present Value of an Annuity What’s the present value of a $900 annuity payment over five years if interest rates are 8 percent? Use equation 5-4: 1 1 − (1 + 0.08) 5 = $900 3.9927 = $3,593.44 PVA 5 = $900 0.08
Or N=5, I=8, PMT=−900, FV=0, CPT PV == 3,593.44 LG4
5-8 Present Value of an Annuity What’s the present value of a $700 annuity payment over six years if interest rates are 10 percent? Use equation 5-4: 1 1− (1+ 0.10)6 PVA = $700 = $700 4.355261 = $3,048.68 6 0.10
Or N=4, I=10, PMT=−700, FV=0, CPT PV == 3,048.68 LG5
5-9 Present Value of a Perpetuity What’s the present value, when interest rates are 7.5 percent, of a $50 payment made every year forever?
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
Use equation 5-5: PV of a perpetuity =
LG5
$50 = $666.67 0.075
5-10 Present Value of a Perpetuity What’s the present value, when interest rates are 8.5 percent, of a $75 payment made every year forever? Use equation 5-5: PV of a perpetuity =
LG6
$75 = $882.35 0.085
5-11 Present Value of an Annuity Due If the present value of an ordinary, 7-year annuity is $6,500 and interest rates are 7.5 percent, what’s the present value of the same annuity due? Use equation 5-7: PVA7 due = $6,500 × (1 + 0.075) = $6,987.50
LG6
5-12 Present Value of an Annuity Due If the present value of an ordinary, 6-year annuity is $8,500 and interest rates are 9.5 percent, what’s the present value of the same annuity due? Use equation 5-7: PVA6 due = $8,500 × (1 + 0.095) = $9,307.50
LG6
5-13 Future Value of an Annuity Due If the future value of an ordinary, 7-year annuity is $6,500 and interest rates are 8.5 percent, what is the future value of the same annuity due? Use equation 5-6: FVA7 due = $6,500 × (1 + 0.075) = $6,987.50 (Note this is the same answer as problem 5-11, as expected) LG6 5-14 Future Value of an Annuity Due If the future value of an ordinary, 6-year annuity is $8,500 and interest rates are 9.5 percent, what’s the future value of the same annuity due? Use equation 5-6: FVA6 due = $8,500 × (1 + 0.095) = $9,307.50 (Note this is the same answer as problem 5-12, as expected)
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
LG7
5-15 Effective Annual Rate A loan is offered with monthly payments and a 10 percent APR. What’s the loan’s effective annual rate (EAR)? Use equation 5-8: 0.10 EAR = 1+ −1 = 0.1047 = 10.47% 12 12
LG7
5-16 Effective Annual Rate A loan is offered with monthly payments and a 13 percent APR. What’s the loan’s effective annual rate (EAR)? Use equation 5-8: 0.13 EAR = 1+ −1 = 0.1380 = 13.80% 12 12
intermediate problems LG1
5-17 Future Value Given a 4 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,100, $1,200, $1,200, and $1,500. Use equation 5-1: FV6 = $1,100 × (1 + 0.04)5 + $1,200 × (1 + 0.04)4 + $1,200 × (1 + 0.04)3 + $1,500 × (1 + 0.04)2 FV6 = $1,338.32 + $1,403.83 + $1,349.84 + $1,622.40 = $5,714.39 Or N=5, I=4, PV=−1100, PMT=0, CPT FV == 1,338.32 and N=4, I=4, PV=−1200, PMT=0, CPT FV == 1,403.83 and N=3, I=4, PV=−1200, PMT=0, CPT FV == 1,349.84 and N=2, I=4, PV=−1500, PMT=0, CPT FV == 1,622.40 then sum the FVs = $1,338.32 + $1,403.83 + $1,349.84 + $1,622.40 = $5,714.39
LG1
5-18 Future Value Given a 5 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400. Use equation 5-1: FV6 = $1,000 × (1 + 0.05)5 + $1,300 × (1 + 0.05)4 + $1,300 × (1 + 0.05)3 + $1,400 × (1 + 0.05)2 FV6 = $1,276.28 + $1,580.16 + $1,504.91 + $1,543.50 = $5,904.85 Or N=5, I=5, PV=−1000, PMT=0, CPT FV == 1,276.28 and N=4, I=5, PV=−1300, PMT=0, CPT FV == 1,580.16 and N=3, I=5, PV=−1300, PMT=0, CPT FV == 1,504.91
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
and N=2, I=5, PV=−1400, PMT=0, CPT FV == 1,543.50 then sum the FVs = $1,276.28 + $1,580.16 + $1,504.91 + $1,543.50 = $5,904.85 LG2 5-19 Future Value of Multiple Annuities Assume that you contribute $200 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $300 per month for another 30 years. Given a 7 percent interest rate, what is the value of your retirement plan after the 50 years? Break the annuity streams into a level stream of payments of $200 for 50 years and another level stream of payments of $100 for the last 30 years. Use equation 5-2 for each payment stream and add the results: FVA 50 + FVA 30 = $200
(1 + 0.07 /12)600 −1 + $100 (1 + 0.07 /12)360 −1 = $200 5,448.0709 + $100 1,219.9710 = $1,211,611.28 0.07/12
0.07/12
Or N=50x12, I=7/12, PV=0, PMT=−200, CPT FV == 1,089,614.18 and N=30x12, I=7/12, PV=0, PMT=−100, CPT FV == 121,997.10 sum the FVs to get $1,211,611.28 LG2 5-20 Future Value of Multiple Annuities Assume that you contribute $150 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $350 per month for the next 25 years. Given an 8 percent interest rate, what is the value of your retirement plan after the 40 years? Break the annuity streams into a level stream of payments of $150 for 40 years and another level stream of payments of $200 for the last 25 years. Use equation 5-2 for each payment stream and add the results: FVA40 + FVA25 = $150
(1+ 0.08 / 12)480 −1 + $200 (1+ 0.08 / 12)300 −1 = $150 3,491.0078 + $200 951.0264 = $713,856.45 0.08/12
0.08/12
Or N=40x12, I=8/12, PV=0, PMT=−150, CPT FV == 523,651.17 and N=25x12, I=8/12, PV=0, PMT=−200, CPT FV == 190,205.28 sum the FVs to get $713,856.45 LG3
5-21 Present Value Given a 6 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,500. Use equation 5-3: PV = $1,000 ÷ (1 + 0.06)1 + $1,200 ÷ (1 + 0.06)2 + $1,200 ÷ (1 + 0.06)3 + $1,500 ÷ (1 + 0.06)4 PV = $943.40 + $1,068.00 + $1,007.54 + $1,188.14 = $4,207.08 Or N=1, I=6, PMT=0, FV=−1000, CPT PV == 943.40
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
and N=2, I=6, PMT=0, FV=−1200, CPT PV == 1,068.00 and N=3, I=6, PMT=0, FV=−1200, CPT PV == 1,007.54 and N=4, I=6, PMT=0, FV=−1500, CPT PV == 1,188.14 then sum the PVs = $943.40 + $1,068.00 + $1,007.54 + $1,188.14 = $4,207.08 LG3
5-22 Present Value Given a 7 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,000, $1,300, $1,300, and $1,400. Use equation 5-3: PV = $1,000 ÷ (1 + 0.07)1 + $1,300 ÷ (1 + 0.07)2 + $1,300 ÷ (1 + 0.07)3 + $1,400 ÷ (1 + 0.07)4 PV = $934.58 + $1,135.47 + $1,061.19 + $1,068.05 = $4,199.29 Or N=1, I=7, PMT=0, FV=−1000, CPT PV == 934.58 and N=2, I=7, PMT=0, FV=−1300, CPT PV == 1,135.47 and N=3, I=7, PMT=0, FV=−1300, CPT PV == 1,061.19 and N=4, I=7, PMT=0, FV=−1400, CPT PV == 1,068.05 then sum the PVs = $934.58 + $1,135.47 + $1,061.19 + $1,068.05 = $4,199.29
LG4 5-23 Present Value of Multiple Annuities A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $1,000 per month for the next three years and then $2,000 per month for two years after that. If the bank is charging customers 7.5 percent APR, how much would it be willing to lend the business owner? Break the annuity streams into a level stream of payments of $2,000 for 5 years and another level stream of payments of $1,000 for the first 3 years. Use equation 5-4 for each payment stream and subtract the results: 1 1 1 − (1 + 0.075 / 12)60 1 − (1 + 0.075 / 12)36 = $99,810.6164 − $32,147.9132 = $67,662.70 − $1,000 PVA − PVA = $2,000 60 36 0.075/12 0.075/12
Or N=5x12, I=7.5/12, PMT=−2000, FV=0, CPT PV == 99,810.616 and N=3x12, I=7.5/12, PMT=1000, FV=0, CPT PV == −32,147.913 sum the FVs to get $67,662.70 LG4 5-24 Present Value of Multiple Annuities A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $1,500 per month for the next three years and then $500 per month for two years after that. If the bank is charging customers 8.5 percent APR, how much would it be willing to lend the business owner? Break the annuity into two streams of payments: $500 monthly for five years and $1,000 for three years. Use equation 5-4 for each annuity and add the results:
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows 1 1 1− 1− (1+ 0.085 / 12)60 (1+ 0.085 / 12)36 = $24,370.59 + $31,678.11 = $56,048.70 + $1,000 PVA + PVA = $500 60 36 0.085/12 0.085/12
Or N=5x12, I=8.5/12, PMT=−500, FV=0, CPT PV == 24,370.59 and N=3x12, I=8.5/12, PMT=−1000, FV=0, CPT PV == 31,678.11 sum the FVs to get $56,048.70 LG4 5-25 Present Value You are looking to buy a car. You can afford $450 in monthly payments for four years. In addition to the loan, you can make a $1,000 down payment. If interest rates are 5% APR, what price of car can you afford? Find the loan value of the monthly payments and add the down payment: 1 1 − 48 PVA 48 = $450 (1 + 0.05 /12) + $1,000 = $19,540.33 + $1,000 = $20,540.33 0.05/12
Or N=4x12, I=5/12, PMT=−450, FV=0, CPT PV == 19,540.33 Add the downpayment of $1,000 to get $20,540.33 LG4
5-26 Present Value You are looking to buy a car. You can afford $650 in monthly payments for five years. In addition to the loan, you can make a $750 down payment. If interest rates are 8% APR, what price of car can you afford?
Find the loan value of the monthly payments and add the down payment: 1 1 − (1 + 0.08 /12)60
PVA 60 = $650
0.08/12
+ $750 = $32,056.98 + $750 = $32,806.98
Or N=5x12, I=8/12, PMT=−650, FV=0, CPT PV == 32,056.98 Add the downpayment of $750 to get $32,806.98 LG5 5-27 Present Value of a Perpetuity A perpetuity pays $100 per year and interest rates are 7.5 percent. How much would its value change if interest rates increased to 9 percent? Did the value increase or decrease? Use equation 5-5: PV of a perpetuity =
$100
= $1,333.33
0.075 PV of a perpetuity =
$100 0.09
= $1,111.11
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
The difference between these perpetuities is $222.22. The value of the perpetuity decreased with an increase in the interest rate. LG5 5-28 Present Value of a Perpetuity A perpetuity pays $50 per year and interest rates are 9 percent. How much would its value change if interest rates decreased to 7.5 percent? Did the value increase or decrease? Use equation 5-5: PV of a perpetuity =
$50
= $555.56
0.09
PV of a perpetuity =
$50 = $666.67 0.075
The difference between these perpetuities is $111.11. The value of the perpetuity increased with a decrease in the interest rate. LG6 5-29 Future and Present Value of an Annuity Due If you start making $50 monthly contributions today and continue them for five years, what’s their future value if the compounding rate is 10 percent APR? What is the present value of this annuity? Compute the future value using equation 5-2: (1 + 0.10 /12) − 1 (1 + 0.10 /12) = $50 77.437072 1.008333 = $3,904.12 60
FVA 60 = $50
0.10/12
Compute the present value using equation 5-4: 1 1− 60 ( 1 + 0.10 / 12 ) 1.008333 = $50 47.065369 1.008333 = $2,372.88 = $50 PVA 60 0.10/12
Or N=5x12, I=10/12, PV=0, PMT=−50, CPT FV == 3,904.12 use DUE or BGN setting and N=5x12, I=10/12, PMT=−50, FV=0, CPT PV == 2,372.88 use DUE or BGN setting LG6 5-30 Future and Present Value of an Annuity Due If you start making $75 monthly contributions today and continue them for four years, what is their future value if the compounding rate is 12 percent APR? What is the present value of this annuity? First calculate the future values and present values, using equations 5-2 and 5-4, respectively. Using these results, the annuity due values can be computed using equations 5-6 and 5-7, respectively. (1 + 0.12 /12) − 1 = $75 61.2226 = $4,591.695 = $4,591.70 48
FVA 48 = $75
0.12/12
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows 1 1− (1+ 0.12 / 12)48 PVA = $75 = $75 37.973959 = $2,848.05 48 0.12/12
Or N=4x12, I=12/12, PV=0, PMT=−75, CPT FV == 4,591.70 use DUE or BGN setting and N=4x12, I=12/12, PMT=−75, FV=0, CPT PV == 2,848.05 use DUE or BGN setting LG7 5-31 Compound Frequency Payday loans are very short-term loans that charge very high interest rates. You can borrow $225 today and repay $300 in two weeks. What is the compounded annual rate implied by this 33.33 percent rate charged for only two weeks? 33.33 percent for two weeks needs to be compounded 26 times to form a year: (1 + i)26 – 1 = (1 + 0.3333)26 – 1 = 1770.77 = 177,077% Note: Use the unrounded percent of increase in the computation. LG7 5-32 Compound Frequency Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $590 in two weeks. What is the compounded annual rate implied by this 18 percent rate charged for only two weeks? 18 percent for two weeks needs to be compounded 26 times to form a year: (1 + i)26 – 1 = (1 + 0.18)26 – 1 = 72.9490 = 7,294.90% LG8 5-33 Annuity Interest Rate What’s the interest rate of a 6-year, annual $5,000 annuity with present value of $20,000? Use equation 5-4 and solve for i: 1
1− $20,000 = $5,000
(1 + i)6 i = 12.98% i
or: N=6, PV=-20,000, PMT=5,000, FV=0, CPT I = 12.98% LG8
5-34 Annuity Interest Rate What’s the interest rate of a 7-year, annual $4,000 annuity with present value of $20,000? Use equation 5-2 and solve for i: 1− $20,000 = $4,000
1 (1+ i)7 i = 9.20% i
or: N=7, PV=-20,000, PMT=4,000, FV=0, CPT I = 9.20%
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
LG8
5-35 Annuity Interest Rate What annual interest rate would you need to earn if you wanted a $1,000 per month contribution to grow to $75,000 in six years? Use equation 5-2 and solve for i:
(1 + i /12) − 1 72
$75,000 = $1,000
i/12
i = 1.37%
or: N=72, PV=0, PMT=-1,000, FV=75,000, CPT I = 0.1143% Now convert the monthly interest rate to an annual rate by multiplying by 12 which yields 1.37 percent.
LG8
5-36 Annuity Interest Rate What annual interest rate would you need to earn if you wanted a $600 per month contribution to grow to $45,000 in six years? Use equation 5-2 and solve for i: (1 + i /12) − 1 72
$45,000 = $600
i/12
i = 1.37.%
or: N=72, PV=0, PMT=-600, FV=45,000, CPT I = 0.1143% Now convert the monthly interest rate to an annual rate by multiplying by 12 which yields 1.37 percent. LG8
5-37 Add-on Interest Payments To borrow $500, you are offered an add-on interest loan at 8 percent. Two loan payments are to be made, one at six months and the other at the end of the year. Compute the two equal payments. The total interest to be paid is $500 x 0.08 = $40. Add this to the principle to get $540. Each of the two payments will be $540 / 2 = $270
LG8 5-38 Add-on Interest Payments To borrow $800, you are offered an add-on interest loan at 7 percent. Three loan payments are to be made, one at four months, another at eight months, and the last one at the end of the year. Compute the three equal payments. The total interest to be paid is $800 x 0.07 = $56. Add this to the principle to get $856. Each of the three payments will be $856 / 3 = $285.33.
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
LG9
5-39 Loan Payments You wish to buy a $25,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be? Use equation 5-9: .09 /12 = $25,000 0.0248850 = $622.13 PMT48 = $25,000 1 1− (1 + .09 /12)48
or: N=4x12, I=9/12, PV=25,000, FV=0, CPT PMT = −622.13 If you only paid interest over the length of the loan and your principal balance was repaid at the end of the 48 months, your payment would be $187.50 per month (= $25,000 × 0.09 ÷ 12) for interest only and you would owe $25,000 at the end of the 48 months, too. LG9
5-40 Loan Payments You wish to buy a $10,000 dining room set. The furniture store offers you a 3-year loan with an 11 percent APR. What are the monthly payments? How would the payment differ if you paid interest only? What would the consequences of such a decision be? Use equation 5-9: .11/ 12 = $10,000 0.03279 = $327.39 PMT = $10,000 36 1 1− (1+ .11/ 12)36
or: N=3x12, I=11/12, PV=10,000, FV=0, CPT PMT = −327.39 If you only paid interest over the length of the loan and your principal balance was repaid at the end of the 36 months, your payment would be $91.67 per month (= $10,000 × 0.11 ÷ 12) for interest only and you would owe $10,000 at the end of the 36 months, too. LG10 5-41 Number of Annuity Payments Joey realizes that he has charged too much on his credit card and has racked up $5,000 in debt. If he can pay $150 each month and the card charges 17 percent APR (compounded monthly), how long will it take him to pay off the debt? Rewrite equation 5-9 in terms of N: N=
ln $150 $(150 − $5,000 0.17 /12) = 45.43 months ln(1 + 0.17 /12)
or: PV = 5,000, PMT = -150, FV = 0, I = 1.417; CPT N = 45.43 months
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
LG10 5-42 Number of Annuity Payments Phoebe realizes that she has charged too much on her credit card and has racked up $6,000 in debt. If she can pay $200 each month and the card charges 18 percent APR (compounded monthly), how long will it take her to pay off the debt? Rewrite equation 5-9 in terms of N: N=
ln $200 ($200 − $6,000 0.18/12) = 40.15 months ln(1 + 0.18/12)
or: PV = 6,000, PMT = -200, FV = 0, I = 1.50; CPT N = 40.15 months advanced problems LG1
5-43 Future Value Given an 8 percent interest rate, compute the year 7 future value if deposits of $1,000 and $2,000 are made in years 1 and 3, respectively, and a withdrawal of $700 is made in year 4. Use equation 5-1: FV7 = $1,000 × (1 + 0.08)6 + $2,000 × (1 + 0.08)4 - $700 × (1 + 0.08)3 = $1,586.87 + $2,720.98 – $881.80 = $3,426.05 or N=6, I=8, PV=−1000, PMT=0, CPT FV == 1,586.87 and N=4, I=8, PV=−2000, PMT=0, CPT FV == 2,720.98 and N=3, I=8, PV=700, PMT=0, CPT FV == −881.80 sum them to get $3,426.05
LG1
5-44 Future Value Given a 9 percent interest rate, compute the year 6 future value if deposits of $1,500 and $2,500 are made in years 2 and 3, respectively, and a withdrawal of $600 is made in year 5. Use equation 5-1: FV6 = $1,500 × (1 + 0.09)4 + $2,500 × (1 + 0.09)3 - $600 × (1 + 0.09)1 = $2,117.37 + $3,237.57 – $654.00 = $4,700.94 or N=4, I=9, PV=−1500, PMT=0, CPT FV == 2,117.37 and N=3, I=9, PV=−2500, PMT=0, CPT FV == 3,237.57 and N=1, I=9, PV=600, PMT=0, CPT FV == −654.00 sum them to get $4,700.94
LG7 – LG8 5-45 EAR of Add-on Interest Loan To borrow $2,000, you are offered an add-on interest loan at 10 percent with 12 monthly payments. First, compute the 12 equal payments and then compute the EAR of the loan:
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
The total interest cost is $2,000 x 0.10 = $200. Added to the principle, this becomes $2,200. The 12 monthly payments are therefore $2,200 / 12 = $183.33. The APR of the loan is N = 12, PV = 2,000, PMT = -183.33, FV=0; CPT I = 1.4977% So APR = 1.4977% x 12 = 17.97% (not the 10% advertised!) The EAR is:
12
0.1797 EAR = 1+ −1 = 0.1953 = 19.53% 12
LG7-LG8 5-46 EAR of Add-on Interest Loan To borrow $700, you are offered an add-on interest loan at 9 percent with 12 monthly payments. First, compute the 12 equal payments and then compute the EAR of the loan: The total interest cost is $700 x 0.09 = $63. Added to the principle, this becomes $763. The 12 monthly payments are therefore $763 / 12 = $63.58. The APR of the loan is N = 12, PV = 700, PMT = -63.58, FV = 0; CPT I = 1.3505% So APR = 1.3505% x 12 = 16.21% (not the 9% advertised!) The EAR is:
12
0.1621 EAR = 1+ −1 = 0.1747 = 17.47% 12
LG4 LG9
5-47 Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $500 cash back on the purchase, or a 3 percent APR, 4-year loan. The price of the car is $15,000 and you could obtain a 4-year loan from your credit union, at 6 percent APR. Which deal is cheaper? Compare two cases. The first case is to elect the 3 percent APR and fully finance $15,000 over 48 months. Using equation 5-9, the payment under this scenario would be: 0.03 / 12 = $332.01 PMT = $15,000 48 1 1− 48 (1+ 0.03/12)
or: N=4x12, I=3/12, PV=15,000, FV=0, CPT PMT = −332.01 The second case is to take the $500 cash back, apply it to the purchase and finance only $14,500 through your credit union at 6 percent. The payment under this scenario would be:
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
0.06 /12 = $340.53 PMT48 = $14,500 1 1− (1 + 0.06/12)48
or: N=4x12, I=6/12, PV=14,500, FV=0, CPT PMT = −340.53 The lower payment represents the more advantageous scenario that you should choose, electing the 3 percent financing through the car dealer. LG4 LG9
5-48 Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $1,000 cash back on the purchase, or a 2 percent APR, 5-year loan. The price of the car is $20,000 and you could obtain a 5-year loan from your credit union, at 7 percent APR. Which deal is cheaper? Compare two cases. The first case is to elect the 2 percent APR and fully finance $20,000 over 60 months. Using equation 5-9, the payment under this scenario would be: 0.02 / 12 = $350.56 PMT = $20,000 60 1 1− (1+ 0.02/12)60
or: N=5x12, I=2/12, PV=20,000, FV=0, CPT PMT = −350.56 The second case is to take the $1,000 cash back, apply it to the purchase and finance only $19,000 through your credit union at 7 percent. The payment under this scenario would be: 0.07 / 12 = $376.22 PMT = $19,000 60 1 1− (1+ 0.07/12)60
or: N=5x12, I=7/12, PV=19,000, FV=0, CPT PMT = −376.22 The lower payment represents the more advantageous scenario that you should choose, electing the 2 percent financing through the car dealer. LG9
5-49 Amortization Schedule Create the amortization schedule for a loan of $15,000, paid monthly over three years using a 9 percent APR. 0.09 /12 PMT36 = $15,000 = $477.00 1− 1 36 (1+ 0.09 /12)
Month 1
Beginning Balance $15,000.00
Total Payment $477.00
Interest Paid $112.50
Principal Paid $364.50
Ending Balance $14,635.50
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
LG9
14,635.50 14,268.27 13,898.29 13,525.53 13,149.98 12,771.61 12,390.40 12,006.33 11,619.38 11,229.53 10,836.76 10,441.03 10,042.35 9,640.67 9,235.98 8,828.25 8,417.47 8,003.60 7,586.63 7,166.54 6,743.29 6,316.87 5,887.25 5,454.41 5,018.32 4,578.96 4,136.31 3,690.33 3,241.02 2,788.33 2,332.24 1,872.74 1,409.79 943.37 473.45
477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00 477.00
109.77 107.01 104.24 101.44 98.62 95.79 92.93 90.05 87.15 84.22 81.28 78.31 75.32 72.31 69.27 66.21 63.13 60.03 56.90 53.75 50.57 47.38 44.15 40.91 37.64 34.34 31.02 27.68 24.31 20.91 17.49 14.05 10.57 7.08 3.55
367.23 369.98 372.76 375.55 378.37 381.21 384.07 386.95 389.85 392.77 395.72 398.69 401.68 404.69 407.73 410.78 413.86 416.97 420.10 423.25 426.42 429.62 432.84 436.09 439.36 442.65 445.97 449.32 452.69 456.08 459.50 462.95 466.42 469.92 473.45
14,268.27 13,898.29 13,525.53 13,149.98 12,771.61 12,390.40 12,006.33 11,619.38 11,229.53 10,836.76 10,441.03 10,042.35 9,640.67 9,235.98 8,828.25 8,417.47 8,003.60 7,586.63 7,166.54 6,743.29 6,316.87 5,887.25 5,454.41 5,018.32 4,578.96 4,136.31 3,690.33 3,241.02 2,788.33 2,332.24 1,872.74 1,409.79 943.37 473.45 0.00
5-50 Amortization Schedule Create the amortization schedule for a loan of $5,000, paid monthly over two years using an 8 percent APR. 0.08 /12 PMT24 = $5,000 = $226.14 1 − 1 24 (1+ 0.08 /12)
Month 1
Beginning Balance $5,000.00
Total Payment $226.14
Interest Paid $33.33
Principal Paid $192.80
Ending Balance $4,807.20
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
4,807.20 4,613.11 4,417.73 4,221.04 4,023.04 3,823.73 3,623.08 3,421.10 3,217.77 3,013.09 2,807.04 2,599.62 2,390.81 2,180.61 1,969.01 1,756.00 1,541.57 1,325.71 1,108.42 889.67 669.46 447.79 224.64
$226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14 $226.14
$32.05 $30.75 $29.45 $28.14 $26.82 $25.49 $24.15 $22.81 $21.45 $20.09 $18.71 $17.33 $15.94 $14.54 $13.13 $11.71 $10.28 $8.84 $7.39 $5.93 $4.46 $2.99 $1.50
194.09 195.38 196.68 198.00 199.32 200.64 201.98 203.33 204.68 206.05 207.42 208.81 210.20 211.60 213.01 214.43 215.86 217.30 218.75 220.21 221.67 223.15 224.64
4,613.11 4,417.73 4,221.04 4,023.04 3,823.73 3,623.08 3,421.10 3,217.77 3,013.09 2,807.04 2,599.62 2,390.81 2,180.61 1,969.01 1,756.00 1,541.57 1,325.71 1,108.42 889.67 669.46 447.79 224.64 0.00
LG4 5-51 Investing for Retirement Monica has decided that she wants to build enough LG9 retirement wealth that, if invested at 8 percent per year, will provide her with $3,500 of monthly income for 20 years. To date, she has saved nothing, but she still has 30 years until she retires. How much money does she need to contribute per month to reach her goal? First, calculate the amount you would need to have in 30 years time to yield the $3,500 monthly payments for an additional 20 years. Use equation 5-4 to calculate this present value: 1 1 − 240 PVA = $3,500 (1 + 0.08 /12) = $418,440.02 0.08/12
or: N=20x12, I=8/12, PMT=−3500, FV=0, CPT PV = 418,440.02 This amount will become the future value in the next calculation, assuming 8 percent interest and 360 level monthly payments. Use equation 5-2 and solve for the monthly payment: $418,440.02 = PMT
(1 + 0.08 /12)360 −1 0.08/12
PMT = $280.76
or: N=30x12, I=8/12, PV=0, FV=418,440.02, CPT PMT = −280.76 LG4
5-52 Investing for Retirement Ross has decided that he wants to build enough retirement
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
LG9
wealth that, if invested at 7 percent per year, will provide him with $3,000 of monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires. How much money does he need to contribute per month to reach his goal? First, calculate the amount you would need to have in 20 years time to yield the $3,000 monthly payments for an additional 30 years. Use equation 5-4 to calculate this present value: 1 1 − 360 PVA = $3,000 (1 + 0.07 /12) = $450,922.70 0.07/12
or: N=30x12, I=7/12, PMT=−3000, FV=0, CPT PV = 450,922.70 This amount will become the future value in the next calculation, assuming 7 percent interest and 240 level monthly payments. Use equation 5-2 and solve for the monthly payment: $450,922.70 = PMT
(1+ 0.07 /12)240 −1 0.07/12
PMT = $865.62
or: N=20x12, I=7/12, PV=0, FV=450,922.70, CPT PMT = −865.62 LG9 5-53 Loan Balance Rachel purchased a $15,000 car three years ago using an 8 percent, 4-year loan. She has decided that she would sell the car now, if she could get a price that would pay off the balance of her loan. What is the minimum price Rachel would need to receive for her car? First calculate the monthly payment that she has been paying using equation 5-9: 0.08 /12 = $366.19 PMT48 = $15,000 1 1− (1 + 0.08/12)48
or: N=4x12, I=8/12, PV=15000, FV=0, CPT PMT = −366.19 The loan balance is the principal amount outstanding. The duration of remaining payments is 12, the interest rate is 8 percent annual and the monthly payment is $366.19 from the previous calculation. Use these values to calculate the present value of the loan using equation 5-4: 1 1− 12 ( 1 + 0.08 /12 ) = $4,209.64 PVA = $366.19 0.08/12
or: N=1x12, I=8/12, PMT = −366.19, FV=0, CPT PV = 4,209.64 This is the minimum price the car needs to be sold for and it represents her break even price.
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
LG9
5-54 Loan Balance Hank purchased a $20,000 car two years ago using a 9 percent, 5-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What’s the minimum price Hank would need to receive for his car? First calculate the monthly payment that he has been paying using equation 5-9: 0.09 /12 = $415.17 PMT60 = $20,000 1 1− (1 + 0.09/12)60
or: N=5x12, I=9/12, PV=20000, FV=0, CPT PMT = −415.17 The loan balance is the principal amount outstanding. The duration of remaining payments is 36, the interest rate is 9 percent annual and the monthly payment is $415.17 from the previous calculation. Use these values to calculate the present value of the loan using equation 5-4: 1 1 − (1 + 0.09 /12)36
PVA = $415.17
0.09/12
= $13,055.77
or: N=3x12, I=9/12, PMT = −415.17, FV=0, CPT PV = 13,055.77 This is the minimum price the car needs to be sold for and it represents his break even price. LG9
5-55 Teaser Rate Mortgage A mortgage broker is offering a $183,900, 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 4 percent APR interest rate. After the second year, the mortgage interest rate charged increases to 7 percent APR. What are the monthly payments in the first two years? What are the monthly payments after the second year? Use equation 5-9 to calculate the payment using the teaser rate: PMT360 = $183,900 1−
0.04 /12 = $877.97 1 (1 + 0.04 /12)360
or: N=30x12, I=4/12, PV=183,900, FV=0, CPT PMT = −877.97 Now calculate the outstanding loan balance after the first 24 payments using equation 5-4: 1 1− 336 ( 1 + 0.04 /12 ) = $177,291.63 PVA336 = $877.97 0.04/12
or: N=28x12, I=4/12, PMT = −877.97, FV=0, CPT PV = 177,291.63
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
Now use this amount for the present value, the new interest rate of 7% over the remaining 336 payments in equation to calculate the new payment amount after expiration of the teaser rate, using equation 5-9: PMT336 = $177,291.63 1−
= $1,204.89 336 (1 + 0.07 /12) 0.07 /12 1
or: N=28x12, I=7/12, PV=177,291.63, FV=0, CPT PMT = −1204.89 LG9
5-56 Teaser Rate Mortgage A mortgage broker is offering a $279,000, 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 4.5 percent APR interest rate. After the second year, the mortgage interest rate charged increases to 7.5 percent APR. What are the monthly payments in the first two years? What are the monthly payments after the second year? Use equation 5-9 to calculate the payment using the teaser rate: PMT360 = $279,000 1−
0.045 /12 = $1,413.65 1 360 (1 + 0.045 /12)
or: N=30x12, I=4.5/12, PV=279,000, FV=0, CPT PMT = −1413.65 Now calculate the outstanding loan balance after the first 24 payments using equation 5-4: 1 − PVA336 = $1,413.65
1
(1 + 0.045 /12)336 0.045/12
= $269,791.04
or: N=28x12, I=4.5/12, PMT = −1413.65, FV=0, CPT PV = 269,791.04 Now use this amount for the present value, the new interest rate of 7.5 percent over the remaining 336 payments in equation to calculate the new payment amount after expiration of the teaser rate, using equation 5-9: PMT336 = $269,791.04 1−
= $1,923.25 336 (1 + 0.075 /12) 0.075 /12 1
or: N=28x12, I=7.5/12, PV=269,791.04, FV=0, CPT PMT = −1923.25
LG2 LG95-57 Spreadsheet Problem Consider a person who begins contributing to a retirement plan at age 25 and contributes for 40 years until retirement at age 65. For the first ten years, she contributes $3,000 per year. She increases the contribution rate to $5,000 per year in years 11
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
through 20. This is followed by increases to $10,000 per year in years 21 through 30 and to $15,000 per year for the last ten years. This money earns a 9 percent return. First compute the value of the retirement plan when she turns age 65. Then compute the annual payment she would receive over the next 40 years if the wealth was converted to an annuity payment at 8 percent. End of Age 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
Contribution $3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 3,000.00 5,000.00 5,000.00 5,000.00 5,000.00 5,000.00 5,000.00 5,000.00 5,000.00 5,000.00 5,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00 15,000.00 15,000.00 15,000.00 15,000.00 15,000.00 15,000.00 15,000.00 15,000.00 15,000.00 15,000.00
Total Wealth $3,000.00 6,270.00 9,834.30 13,719.39 17,954.13 22,570.00 27,601.30 33,085.42 39,063.11 45,578.79 54,680.88 64,602.16 75,416.35 87,203.83 100,052.17 114,056.87 129,321.98 145,960.96 164,097.45 183,866.22 210,414.18 239,351.45 270,893.08 305,273.46 342,748.07 383,595.40 428,118.99 476,649.70 529,548.17 587,207.50 655,056.18 729,011.23 809,622.25 897,488.25 993,262.19 1,097,655.79 1,211,444.81 1,335,474.84 1,470,667.58 $1,618,027.66
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
PMT =
($135,688.06)
LG5-9 5-58 Spreadsheet Problem When paying off a home mortgage, extra principle payments can have a dramatic impact on the time needed to pay off the mortgage. (a) Create an amortization schedule for a $200,000, 3-year mortgage with a 6% APR. (b) After the 5th year, add an extra $100 to each monthly payment. When is the loan payed off? First, use the annuity function to compute the payment for the loan. Answer= $1,199.10. The amortization schedule looks like this:
Increasing the payment by $100 each month after the 5th year leads to:
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
Research it! Retirement Income Calculators The Internet provides some excellent retirement income calculators. You can find one by Googling “retirement income calculator.” Many of the calculators allow you to determine your predicted annual income from a retirement nest egg under different assumptions. For example, you can spend only the investment income generated from the nest egg. Most retirees try not to touch the principal. Or, you can spend both the income and the nest egg itself. These calculators let you input the size of the retirement wealth and the investment return to be earned. They then make time value computations to determine the annual income the nest egg will provide. Go to a retirement income calculator like the one at MSN Money. Use the calculator to create a retirement scenario. Use the TVM equations or a financial calculator to check the Internet results. http://money.msn.com/retirement/retirement-calculator.aspx SOLUTION: Assuming the principal amount is exhausted and the amount of savings at my retirement at age 65, here is what the calculator gives. Summary Given a certain amount of savings, how much can I spend annually during retirement? Your annual income is estimated to be $70,000.
Information entered
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
1. Savings Amount saved Rate of return Inflation rate Average effective tax rate 2. Retirement years Retirement age Life expectancy Estate amount
$1,000,000 7% 3.8% 22.6%
65 years 85 years $0
Using a financial calculator, the following inputs are needed to determine the projected annual payment: N = 20 years I = 1.07/1.038 -1 = 3.083% PV = $1,000,000 CPT PMT = $67,732.56 (The retirement income calculator rounds this amount to the nearest $10,000 for an estimate of $70,000 gross annually.)
Integrated Minicase: Paying on your Stafford loan Consider Gavin, a new freshman who has just received a Stafford student loan and started college. He plans to obtain the maximum loan from Stafford at the beginning of each year. Although Gavin does not have to make any payments while he is in school, the unsubsidized 6.8 percent interest owed (compounded monthly) accrues and is added to the balance of the loan. UNSUBSIDIZED Stafford loan limits: Freshman $6,000 Sophomore 6,000 Junior 7,000 Senior 7,000 After graduation, Gavin gets a 6-month grace period. This means that monthly payments are still not required, but interest is still accruing. After the grace period, the standard repayment plan is to amortize the debt using monthly payments for ten years. a. Show a time line of when the loans will be taken. b. What will be the loan balance when Gavin graduates after his fourth year of school? c. What is the loan balance six months after graduation?
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
d.Using the standard repayment plan and a 6.8 percent APR interest rate, compute the monthly payments Gavin owes after the grace period. SOLUTION: a. Show a time line of when the loans will be taken. Period 0
6.8%
Cash Flows $6,000
1
6.8% 2
6.8% 3
$6,000
$7,000
$7,000
6.8% 4 6.8%
5 years
b. What will be the loan balance when Gavin graduates after his fourth year of school? Each payment needs to be moved forward with 6.8 percent interest to the middle of years 4 and 5 to calculate the outstanding accrued loan balance as of the date payments are set to begin: FV4 = $6,000 × (1.068)4 + $6,000 × (1.068)3 + $7,000 × (1.068)2 + $7,000 × (1.068)1 FV4 = $7,806.14 + $7,309.12 + $7,984.37 + $7,476.00 = $30,575.63 c. What is the loan balance six months after graduation? Each payment needs to be moved forward with 6.8 percent interest to the middle of years 4 and 5 to calculate the outstanding accrued loan balance as of the date payments are set to begin: Add interest for half a year, $30,575.63 × (1 + 0.068 / 12)6 = $31,630.04 d.Using the standard repayment plan and a 6.8 percent APR interest rate, compute the monthly payments Gavin owes after the grace period. Using equation 5-9, the monthly payments will be: PMT120 = $31,630.04 1−
0.068 /12 = $364.00 1 (1 + 0.068 /12)120
Combined Chapter 4 and Chapter 5 Problems 4&5-1 Future Value Consider that you are 35 years old and have just changed to a new job. You have $80,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $3,600 each year into
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
your new employer’s plan. If the rolled-over money and the new contributions both earn a 7 percent return, how much should you expect to have when you retire in 30 years? The future value can be calculated by adding the accumulated value of $80,000 brought forward with interest for 30 years to a 30-year annuity of $3,600 per year, both using the 7 percent interest assumption. Use equations 5-1 and 5-2 and add the results: FVA Age 65 = $80,000 (1+ 0.07) + $3,600 30
(1+ 0.07)30 −1 = $608,980.40 + $340,058.83 = $949,039.23 0.07
or N=30, I=7, PV=−80000, PMT=−3600, CPT FV == 949,039.23
4&5-2 Future Value Consider that you are 45 years old and have just changed to a new job. You have $150,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $7,200 each year into your new employer’s plan. If the rolled-over money and the new contributions both earn an 8 percent return, how much should you expect to have when you retire in 20 years? The future value can be calculated by adding the accumulated value of $150,000 brought forward with interest for 20 years to a 20-year annuity of $7,200 per year, both using the 8 percent interest assumption. Use equations 5-1 and 5-2 and add the results: FVA Age 65 = $150,000 (1+ 0.08) + $7,200 20
(1+ 0.08)20 −1 = $699,143.57 + $329,486.14 = $1,028,629.71 0.08
or N=20, I=8, PV=−150000, PMT=−7200, CPT FV == 1,028,629.71 4&5-3 Future Value and Number of Annuity Payments Your client has been given a trust fund valued at $1 million. He cannot access the money until he turns 65 years old, which is in 25 years. At that time, he can withdrawal $25,000 per month. If the trust fund is invested at a 5.5 percent rate, how many months will it last your client once he starts to withdraw the money? Using equation 5-1, $1 million will accumulate for 25 more years at 5.5 percent interest for a future value: FVA Age 65= $1,000,000 (1+ 0.055) = $3,813,392.35 25
or N=25, I=5.5, PV=−1,000,000, PMT=0, CPT FV == 3,813,392.35 Now, rewrite equation 5-9 in terms of N: N=
ln$25,000($25,000 − $3,813,392.35 0.055 /12) = 262.65 months ln(1 + 0.055 /12)
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
Or: PV = 3,813,392.35, PMT = −25,000, FV = 0, I = 0.458333; CPT N = 262.65 months
4&5-4 Future Value and Number of Annuity Payments Your client has been given a trust fund valued at $1.5 million. She cannot access the money until she turns 65 years old, which is in 15 years. At that time, she can withdraw $20,000 per month. If the trust fund is invested at a 5 percent rate, how many months will it last your client once she starts to withdraw the money? Using equation 5-1, $1.5 million will accumulate for 15 more years at 5 percent interest for a future value: FVA Age 65 = $1,500,000 (1 + 0.05) 15 = $3,118,392.27
or N=15, I=5, PV=−1,500,000, PMT=0, CPT FV == 3,118,392.27 Now, rewrite equation 5-9 in terms of N: ln$20,000($20,000 − $3,118,392.27 0.05 /12) = 252.25 months N= ln(1 + 0.05 /12)
Or: PV=3,118,392.27, PMT = −20,000, FV = 0, I = 0.416667; CPT N = 252.25 months 4&5-5 Present Value and Annuity Payments A local furniture store is advertising a deal in which you buy a $3,000 dining room set and do not need to pay for two years (no interest cost is incurred). How much money would you have to deposit now in a savings account earning 5 percent APR, compounded monthly, to pay the $3,000 bill in two years? Alternatively, how much would you have to deposit in the savings account each month to be able to pay the bill? Use equation 5-3 and solve for the lump sum payment: PV = $3,000 (1+ 0.05 / 12) = $2,715.08 24
or N=24, I=5/12, PMT=0, FV=−3,000, CPT PV == 2,715.08 Use equation 5-2 and solve for the annuity payment: $3,000 = PMT
(1+ 0.05/12)24 −1 0.05/12
PMT = $119.11per month
or: N=2x12, I=5/12, PV=0, FV=3000, CPT PMT = −119.11 4&5-6 Present Value and Annuity Payments A local furniture store is advertising a deal in which you buy a $5,000 living room set with three years before you need to make any payments (no interest cost is incurred). How much money would you have to deposit now in a savings account earning 4 percent APR, compounded monthly, to pay the $5,000 bill in three years? Alternatively, how much would you have to deposit in the savings account each month to be able to pay the bill?
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
Use equation 5-3 and solve for the lump sum payment: PV = $5,000 (1+ 0.04 / 12) = $4,435.49 36
or N=36, I=4/12, PMT=0, FV=−5,000, CPT PV == 4,435.49 Use equation 5-2 and solve for the annuity payment: $5,000 = PMT
(1+ 0.04/12)36 −1 0.04/12
PMT = $130.95
or: N=3x12, I=4/12, PV=0, FV=5000, CPT PMT = −130.95 4&5-7 House Appreciation and Mortgage Payments Say that you purchase a house for $200,000 by getting a mortgage for $180,000 and paying a $20,000 down payment. If you get a 30-year mortgage with a 7 percent interest rate, what are the monthly payments? What would the loan balance be in ten years? If the house appreciates at 3 percent per year, what will be the value of the house in ten years? How much of this value is your equity? Use equation 5-9 to calculate your monthly payment: PMT360 = $180,000 1−
0.07 /12 = $1,197.54 1 (1 + 0.07 /12)360
or: N=30x12, I=7/12, PV=180000, FV=0, CPT PMT = −1197.54 In ten years, you will have 240 payments of $1,197.54 left to pay. The present value can be calculated using equation 5-4: 1 − PVA 240 = $1,197.54
1
(1 + 0.07 /12)240 0.07/12
= $154,461.71
or N=20x12, I=7/12, PMT=−1197.54, FV=0, CPT PV == 154,461.71 An appreciation of 3 percent per year will result in a forecast future value of the home using the original purchase price in equation 5-1: FV10 years = $200,000 (1+ .03)
10
= $268,783.28
or N=10, I=3, PV=−200,000, PMT=0, CPT FV == 268,783.28 The amount of equity is the difference between the home’s value and the outstanding balance on the mortgage: Equity = $268,783.28 - $154,461.71 = $114,321.57
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows
4&5-8 House Appreciation and Mortgage Payments Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-year mortgage with a 7 percent interest rate, what are the monthly payments? What would the loan balance be in five years? If the house appreciates at 4 percent per year, what will be the value of the house in five years? How much of this value is your equity? Use equation 5-9 to calculate your monthly payment: PMT180 = $135,000 1−
0.07 /12 = $1,213.42 1 (1 + 0.07 /12)180
or: N=15x12, I=7/12, PV=135000, FV=0, CPT PMT = −1213.42 In 5 years, you will have 120 payments of $1,213.42 left to pay. The present value can be calculated using equation 5-4: 1 1 − (1 + 0.07 /12)120
PVA120 = $1,213.42
0.07/12
= $104,507.44
or N=10x12, I=7/12, PMT=−1213.42, FV=0, CPT PV == 104,507.44 An appreciation of 4 percent per year will result in a forecast future value of the home using the original purchase price in equation 5-1: FV5years = $150,000 (1+ .04) = $182,497.94 5
or N=5, I=4, PV=−150,000, PMT=0, CPT FV == 182,497.94 The amount of equity is the difference between the home’s value and the outstanding balance on the mortgage: Equity = $182,497.94 - $104,507.44 = $77,990.50
4&5-9 Construction Loan You have secured a loan from your bank for two years to build your home. The terms of the loan are that you will borrow $200,000 now and an additional $100,000 in one year. Interest of 10 percent APR will be charged on the balance monthly. Since no payments will be made during the 2-year loan, the balance will grow at the 10 percent compounded rate. At the end of the two years, the balance will be converted to a traditional 30year mortgage at a 6 percent interest rate. What will you be paying as monthly mortgage payments (principal and interest only)? Use equation 5-1 to calculate the capitalized value of your mortgage at the end of year 2:
Chapter 05 - Time Value of Money 2: Analyzing Annuity Cash Flows FV2 = $200,000 (1+ 0.10 /12) + $100,000 (1+ 0.10/12 ) = $354,549.50 24
12
or N=2x12, I=10/12, PV=−200,000, PMT=0, CPT FV == 244,078.19 and N=1x12, I=10/12, PV=−100,000, PMT=0, CPT FV == 110,471.31 sum to get $354,549.50 This is the amount that you will need to finance over 30 years at 6 percent. Use equation 5-9 to compute the monthly payment: PMT360 = $354,549.50 1−
0.06 /12 = $2,125.70 1 360 (1 + 0.06 /12)
or: N=30x12, I=6/12, PV=354,549.50, FV=0, CPT PMT = −2125.70 4&5-10 Construction Loan You have secured a loan from your bank for two years to build your home. The terms of the loan are that you will borrow $100,000 now and an additional $50,000 in one year. Interest of 9 percent APR will be charged on the balance monthly. Since no payments will be made during the 2-year loan, the balance will grow. At the end of the two years, the balance will be converted to a traditional 15-year mortgage at a 7 percent interest rate. What will you pay as monthly mortgage payments (principal and interest only)? Use equation 5-1 to calculate the capitalized value of your mortgage at the end of year 2: FV2 = $100,000 (1+ 0.09 /12) + $50,000 (1+ 0.09/12 ) = $174,331.70 24
12
or N=2x12, I=9/12, PV=−100,000, PMT=0, CPT FV == 119,641.35 and N=1x12, I=9/12, PV=−50,000, PMT=0, CPT FV == 54,690.34 sum to get $174,331.70 This is the amount that you will need to finance over 15 years at 7 percent. Use equation 5-9 to compute the monthly payment: PMT180 = $174,331.70 1−
0.07 /12 = $1,566.94 1 (1 + 0.07 /12)180
or: N=15x12, I=7/12, PV=174,331.70, FV=0, CPT PMT = −1566.94
Chapter 06 - Understanding Financial Markets and Institutions
1CHAPTER 6 – UNDERSTANDING FINANCIAL MARKETS AND INSTITUTIONS questions LG6-1
1. Classify the following transactions as taking place in the primary or secondary markets: a. IBM issues $200 million of new common stock – primary market b. The New Company issues $50 million of common stock in an IPO – primary market c. IBM sells $5 million of GM preferred stock out of its marketable securities portfolio – secondary market d. The Magellan Fund buys $100 million of previously issued IBM bonds – secondary market e. Prudential Insurance Co. sells $10 million of GM common stock – secondary market
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2. Classify the following financial instruments as money market securities or capital market securities: a. Federal funds – money market security b. Common stock – capital market security c. Corporate bonds – capital market security d. Mortgages – capital market security e. Negotiable certificates of deposit – money market security f. U.S. Treasury bills – money market security g. U.S. Treasury notes – capital market security h. U.S. Treasury bonds – capital market security i. State and government bonds – capital market security
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3. What are the different types of financial institutions? Include a description of the main services offered by each. The different types of financial institutions are: Commercial banks: depository institutions whose major assets are loans and whose major liabilities are deposits. Commercial bank loans cover a broader range, including consumer, commercial, and real estate loans, than do loans from other depository institutions. Because they are larger and more likely to have access to public securities markets, commercial bank liabilities generally include more nondeposit sources of funds, such as subordinate notes and debentures, than do those of other depository institutions. Thrifts: depository institutions including savings associations, savings banks, and credit unions. Thrifts generally perform services similar to commercial banks, but they tend to concentrate their loans in one segment, such as real estate loans or consumer loans. Credit unions operate on a notfor-profit basis for particular groups of individuals, such as a labor union or a particular company’s employees. Insurance companies: protect individuals and corporations (policyholders) from financially adverse events. Life insurance companies provide protection in the event of untimely death or
Chapter 06 - Understanding Financial Markets and Institutions
illness, and help in planning retirement. Property casualty insurance protects against personal injury and liability due to accidents, theft, fire, and so on. Securities firms and investment banks: underwrite securities and engage in related activities such as securities brokerage, securities trading, and making markets in which securities trade. Finance companies: make loans to both individuals and businesses. Unlike depository institutions, finance companies do not accept deposits, but instead rely on short- and long-term debt for funding, and many of their loans are collateralized with some kind of durable good, such as washer/dryers, furniture, carpets and the like. Mutual funds: pool many individuals’ and companies’ financial resources and invest those resources in diversified asset portfolios. Pension funds: offer savings plans through which fund participants accumulate savings during their working years. Participants then withdraw their pension resources (which have presumably earned additional returns in the interim) during their retirement years. Funds originally invested in and accumulated in a pension fund are exempt from current taxation. Participants pay taxes on distributions taken after age 55, when their tax brackets are (presumably) lower. LG6-3
4. How would economic transactions between suppliers of funds (e.g., households) and users of funds (e.g., corporations) occur in a world without FIs? In such a world, suppliers of funds (e.g., households), generating excess savings by consuming less than they earn, would have a basic choice. They could either hold cash as an asset or directly transfer that cash by investing in the securities issued by users of funds (e.g., corporations, governments, or retail borrowers). In general, demanders (users) of funds issue financial claims (e.g., equity and debt securities) to finance the gap between their investment expenditures and their internally generated funds, such as retained earnings or tax receipts. In a world without financial institutions, we would have direct transfers of funds from fund suppliers to fund users. In return, financial claims would flow directly from fund users to fund suppliers.
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5. Why would a world limited to the direct transfer of funds from suppliers of funds to users of funds likely result in quite low levels of fund flows? In this economy without FIs, the amount of funds flowing between fund suppliers and fund users through financial markets would likely to be quite low for several reasons. First, once they have lent money in exchange for financial claims, fund suppliers would need to continually monitor the use of their funds. Fund suppliers must ensure that fund users neither steal the funds outright nor waste the funds on projects that have low or negative returns, since either theft or waste would lower fund suppliers’ chances of being repaid and/or earning a positive return on their investments (such as through the receipt of dividends or interest). Monitoring against theft, misuse, or underuse of their funds would cost any given fund supplier a lot of time and effort, and of course each fund supplier, regardless of the dollar value of the investment, would have to carry out the same costly and time-consuming process. Further, many investors do not have the
Chapter 06 - Understanding Financial Markets and Institutions
issuer is making the best use of their funds. In fact, so many investment opportunities are available to fund suppliers, that even those trained in financial analysis rarely have the time to monitor how their funds are used in all of their investments. The resulting lack of monitoring increases the risk of directly investing in financial claims. Given these challenges, fund suppliers would likely prefer to delegate the task of monitoring fund borrowers to ensure good performance to others. Second, many financial claims feature a long-term commitment (e.g., mortgages, corporate stock, and bonds) for fund suppliers, thus creating another disincentive for fund suppliers to hold direct financial claims that fund users may issue. Specifically, given the choice between holding cash or holding long-term securities, fund suppliers may well choose to hold cash for its liquidity, especially if they plan to use their savings to finance consumption expenditures before their creditors expect to be repaid. Fund suppliers may also fear that they will not find anyone to purchase their financial claim and free up their funds. When financial markets are not very developed, or deep, in terms of the number of active buyers and sellers in the market, such liquidity concerns arise. Finally, even though real-world financial markets provide some liquidity services by allowing fund suppliers to trade financial securities among themselves, fund suppliers face price risk when they buy securities—fund suppliers may not get their principal back, let alone any return on their investment. Trading securities on secondary markets involves various transaction costs. The price at which investors can sell a security on secondary markets such as the New York Stock Exchange (NYSE) or NASDAQ may well differ from the price they initially paid for the security. The investment community as a whole may change the security’s valuation between the time the fund supplier bought it and when the fund supplier sold it. Further, dealers, acting as intermediaries between buyers and sellers, charge transaction costs for completing a trade. So even if an investor bought a security and then sold it the next day, the investor would likely lose money from transaction and other costs. LG6-3
6. How do FIs reduce monitoring costs associated with the flow of funds from fund suppliers to fund users? Financial institutions’ aggregation of funds from fund suppliers resolves a number of problems. First, large FIs now have much greater incentive to collect information and monitor the ultimate fund user’s actions, because the FI has far more at stake than any small individual fund supplier would have. Second, the FI performs the necessary monitoring function via its own internal experts, alleviating the “free-rider” problem that arises when small fund suppliers leave it to each other to collect information and monitor a fund user. In an economic sense, fund suppliers appoint the FI as a delegated monitor to act on their behalf. For example, full-service securities firms, such as Merrill Lynch, carry out investment research on new issues and make investment recommendations for their retail clients (investors), while commercial banks collect deposits from fund suppliers and lend these funds to ultimate users, such as corporations. An important part of these FIs’ functions is their ability and incentive to monitor ultimate fund users.
Chapter 06 - Understanding Financial Markets and Institutions
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7. How do FIs alleviate the problem of liquidity risk faced by investors wishing to invest in securities of corporations? Financial intermediaries provide additional liquidity to fund suppliers, acting as asset transformers as follows: FIs purchase the financial claims that fund users issue―primary securities such as mortgages, bonds, and stocks―and finance these purchases by selling financial claims to household investors and other fund suppliers as deposits, insurance policies, or other secondary securities. The secondary securities—packages or pools of primary claims—that FIs collect and then issue are often more liquid than are the primary securities themselves.
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8. Who are the suppliers of loanable funds? The household sector (consumers) is the largest supplier of loanable funds. Households supply funds when they have excess income or want to reinvest a part of their wealth. For example, during times of high growth households may replace part of their cash holdings with earning assets. As the total wealth of the consumer increases, the total supply of funds from that household will also generally increase. Households determine their supply of funds not only on the basis of the general level of interest rates and their total wealth, but also on the risk on financial securities change. The greater a security’s risk, the less households are willing to invest at each interest rate. Further, the supply of funds provided from households will depend on the future spending needs. For example, near term educational or medical expenditures will reduce the supply of funds from a given household. Higher interest rates will also result in higher supplies of funds from the business sector. When businesses mismatch inflows and outflows of cash to the firm they have excess cash that they can invest for a short period of time in financial markets. In addition to interest rates on these investments, the expected risk on financial securities and the business’ future investment needs will affect the supply of funds from businesses. Loanable funds are also supplied by some government units that temporarily generate more cash inflows (e.g., taxes) than they have budgeted to spend. These funds are invested until they are needed by the governmental agency. Additionally, the federal government (i.e., the Federal Reserve) implements monetary policy by influencing the availability of credit and the growth in the money supply. Monetary policy implementation in the form of increases in the money supply will increase the amount of loanable funds available. Finally, foreign investors increasingly view U.S. financial markets as alternatives to their domestic financial markets. When expected risk-adjusted returns are higher on U.S. financial securities than on comparable securities in their home countries, foreign investors increase the supply of funds to U.S. markets. Indeed the high savings rates of foreign households combined with relatively high U.S. interest rates compared to foreign rates, has resulted in foreign market participants as major suppliers of funds in U.S. financial markets. Similar to domestic suppliers of loanable funds, foreign suppliers assess not only the interest rate offered on financial securities, but also their total wealth, the risk on the security, and their future spending needs. Additionally, foreign investors alter their investment decisions as financial conditions in their
Chapter 06 - Understanding Financial Markets and Institutions
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9. Who are the demanders of loanable funds? Households (although they are net suppliers of funds) borrow funds in financial markets. The demand for loanable funds by households comes from their purchases of homes, durable goods (e.g., cars, appliances), and nondurable goods (e.g., education expenses, medical expenses). In addition to the interest rate on borrowed funds, the greater the utility the household receives from the purchased good, the higher the demand for funds. Additionally, nonprice conditions and requirements affect a household=s demand for funds at every level of interest rates. Businesses often finance investments in long-term (fixed) assets (e.g., plant and equipment) and in short-term assets (e.g., inventory and accounts receivable) with debt market instruments. Higher borrowing costs also reduce the demand for borrowing from the business sector. Rather when interest rates are high, businesses will finance investments with internally generated funds (i.e., retained earnings). In addition to interest rates, nonprice conditions also affect business’ demand for funds. The more restrictive the conditions on borrowed funds, the less businesses borrow at any interest rate. Further, the greater the number of profitable projects available to businesses, or the better the overall economic conditions, the greater the demand for loanable funds. Governments also borrow heavily in financial markets. State and local governments often issue debt to finance temporary imbalances between operating revenues (e.g., taxes) and budgeted expenditures (e.g., road improvements, school construction). Higher interest rates cause state and local governments to postpone such capital expenditures. Similar to households and businesses, state and local governments’ demand for funds vary with general economic conditions. In contrast, the federal government’s borrowing is not influenced by the level of interest rates. Expenditures in the federal government’s budget are spent regardless of the interest cost. Finally, foreign participants might also borrow in U.S. financial markets. Foreign borrowers look for the cheapest source of funds globally. Most foreign borrowing in U.S. financial markets comes from the business sector. In addition to interest costs, foreign borrowers consider nonprice terms on loanable funds as well as economic conditions in the home country.
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10. What factors cause the supply of funds curve to shift? Factors that affect the supply of funds include total wealth, risk of the financial security, nearterm spending needs, monetary policy objectives, and foreign economic conditions. Wealth. As the total wealth of financial market participants (households, business, etc.) increases the absolute dollar value available for investment purposes increases. Accordingly, at every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the supply of funds due to an increase in the total wealth of market participants results in a decrease in the equilibrium interest rate and an increase in the equilibrium quantity of funds traded.
Chapter 06 - Understanding Financial Markets and Institutions
Conversely, as the total wealth of financial market participants decreases the absolute dollar value available for investment purposes decreases. Accordingly, at every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve again creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the supply of funds due to a decrease in the total wealth of market participants results in an increase in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded. Risk. As the risk of a financial security increases, it becomes less attractive to suppliers of funds. Accordingly, at every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the supply of funds due to an increase in the financial security’s risk results in an increase in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded. Conversely, as the risk of a financial security decreases, it becomes more attractive to suppliers of funds. At every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The shift in the supply curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the supply of funds due to a decrease in the risk of the financial security results in a decrease in the equilibrium interest rate and an increase in the equilibrium quantity of funds traded. Near-term Spending Needs. When financial market participants have few near-term spending needs, the absolute dollar value of funds available to invest increases. Accordingly, at every interest rate the supply of loanable funds increases, or the supply curve shifts down and to the right. The financial market, holding all other factors constant, reacts to this increased supply of funds by decreasing the equilibrium interest rate and increasing the equilibrium quantity of funds traded. Conversely, when financial market participants have near-term spending needs, the absolute dollar value of funds available to invest decreases. At every interest rate the supply of loanable funds decreases, or the supply curve shifts up and to the left. The shift in the supply curve creates a disequilibrium in this financial market that, when corrected results in an increase in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded. Monetary Expansion. One method used by the Federal Reserve to implement monetary policy is to alter the availability of credit and thus, the growth in the money supply. When monetary policy objectives are to enhance growth in the economy, the Federal Reserve increases the supply of funds available in the financial markets. At every interest rate the supply of loanable funds increases, the supply curve shifts down and to the right and the equilibrium interest rate falls, while the equilibrium quantity of funds traded increases. Conversely, when monetary policy objectives are to contract economic growth, the Federal Reserve decreases the supply of funds available in the financial markets. At every interest rate the supply of loanable funds decreases, the supply curve shifts up and to the left, and the
Chapter 06 - Understanding Financial Markets and Institutions
Economic Conditions. Finally, as economic conditions improve in a country relative to other countries, the flow of funds to that country increases. The inflow of foreign funds to U.S. financial markets increases the supply of loanable funds at every interest rate and the supply curve shifts down and to the right. Accordingly, the equilibrium interest rate falls and the equilibrium quantity of funds traded increases. LG6-5
11. What factors cause the demand for funds curve to shift? Factors that affect the demand for funds include the utility derived from the asset purchased with borrowed funds, restrictiveness of nonprice conditions of borrowing, domestic economic conditions, and foreign economic conditions. Utility Derived from Asset Purchased With Borrowed Funds. As the utility derived from an asset purchased with borrowed funds increases the willingness of market participants (households, business, etc.) to borrow increases and the absolute dollar value borrowed increases. Accordingly, at every interest rate the demand for loanable funds increases, or the demand curve shifts up and to the right. The shift in the demand curve creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the increase in the demand for funds due to an increase in the utility from the purchased asset results in an increase in the equilibrium interest rate and an increase in the equilibrium quantity of funds traded. Conversely, as the utility derived from an asset purchased with borrowed funds decreases the willingness of market participants (households, business, etc.) to borrow decreases and the absolute dollar value borrowed decreases. Accordingly, at every interest rate the demand of loanable funds decreases, or the demand curve shifts down and to the left. The shift in the demand curve again creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the demand for funds due to a decrease in the utility from the purchased asset results in a decrease in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded. Restrictiveness on Nonprice Conditions on Borrowed Funds. As the nonprice restrictions put on borrowers as a condition of borrowing increase the willingness of market participants to borrow decreases and the absolute dollar value borrowed decreases. Accordingly, at every interest rate the demand of loanable funds decreases, or the demand curve shifts down and to the left. The shift in the demand curve again creates a disequilibrium in this financial market. As competitive forces adjust, and holding all other factors constant, the decrease in the demand for funds due to an increase in the restrictive conditions on the borrowed funds results in a decrease in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded. Conversely, as the nonprice restrictions put on borrowers as a condition of borrowing decrease market participants willingness to borrow increases and the absolute dollar value borrowed increases. Accordingly, at every interest rate the demand for loanable funds increases, or the demand curve shifts up and to the right. The shift in the demand curve results in an increase in
Chapter 06 - Understanding Financial Markets and Institutions
Economic Conditions. When the domestic economy is experiencing a period of growth, market participants are willing to borrow more heavily. Accordingly, at every interest rate the demand of loanable funds increases, or the demand curve shifts up and to the right. As competitive forces adjust, and holding all other factors constant, the increase in the demand for funds due to economic growth results in an increase in the equilibrium interest rate and an increase in the equilibrium quantity of funds traded. Conversely, when economic growth is stagnant market participants reduce their borrowings increases. Accordingly, at every interest rate the demand for loanable funds decreases, or the demand curve shifts down and to the left. The shift in the demand curve results in a decrease in the equilibrium interest rate and a decrease in the equilibrium quantity of funds traded. LG6-6
12. What are six factors that determine the nominal interest rate on a security? Specific factors that affect nominal interest rates for any particular security include: expected inflation, the real risk-free rate, default risk, liquidity risk, special provisions regarding the use of funds raised by a particular security issuer, and the security’s term to maturity.
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13. What should happen to a security’s equilibrium interest rate as the security’s liquidity risk increases? The interest rate on a security reflects its relative liquidity, with highly liquid assets carrying the lowest interest rates (all other characteristics remaining the same). Likewise, if a security is illiquid, investors add a liquidity risk premium (LRP) to the interest rate on the security.
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14. Discuss and compare the three explanations for the shape of the yield curve. Explanations for the yield curve’s shape fall predominantly into three categories: the unbiased expectations theory, the liquidity premium theory, and the market segmentation theory. According to the unbiased expectations theory of the term structure of interest rates, at any given point in time, the yield curve, reflects the market's current expectations of future short-term rates. The second popular explanation―the liquidity premium theory of the term structure of interest rates—builds on the unbiased expectations theory. The liquidity premium idea is as follows: Investors will hold long-term maturities only if these securities with longer term maturities are offered at a premium to compensate for future uncertainty in the security’s value. The liquidity premium theory states that long-term rates are equal to geometric averages of current and expected short-term rates (like the unbiased expectations theory), plus liquidity risk premiums that increase with the security’s maturity (this is the extension of the liquidity premium added to the unbiased expectations theory). The market segmentation theory does not build on the unbiased expectations theory or the liquidity premium theory, but rather argues that individual investors and FIs have specific maturity preferences, and convincing them to hold securities with maturities other than their most preferred requires a higher interest rate (maturity premium). The main thrust of the market segmentation theory is that investors do not consider
Chapter 06 - Understanding Financial Markets and Institutions
have distinctly preferred investment horizons dictated by the dates when their liabilities will come due. LG6-7
15. Are the unbiased expectations and liquidity premium theories explanations for the shape of the yield curve completely independent theories? Explain why or why not. No. The two theories are related. Specifically, the liquidity premium theory states that long-term rates are equal to geometric averages of current and expected short-term rates (like the unbiased expectations theory), plus liquidity risk premiums that increase with the security’s maturity (this is the extension of the liquidity premium added to the unbiased expectations theory).
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16. What is a forward interest rate? A forward rate is an expected or implied rate on a short-term security that will originate at some point in the future.
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17. If we observe a one-year Treasury security rate that is higher than the two-year Treasury security rate, what can we infer about the one-year rate expected one year from now? A downward-sloping yield curve implies that the market expects future short-term interest rates to fall. problems
basic problems LG6-6
6-1 Determinants of Interest Rates for Individual Securities A particular security’s default risk premium is 2 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. The security’s liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the security’s equilibrium rate of return. ij* = 1.75% + 3.50% + 2.00% + 0.25% + 0.85% = 8.35%
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6-2 Determinants of Interest Rate for Individual Securities You are considering an investment in 30-year bonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Journal reports that one-year T-bills are currently earning 1.25 percent. Your broker has determined the following information about economic activity and Moore Corporation bonds: Real risk-free rate = 0.75% Default risk premium = 1.15% Liquidity risk premium = 0.50% Maturity risk premium = 1.75% a. What is the inflation premium?
Chapter 06 - Understanding Financial Markets and Institutions
b. What is the fair interest rate on Moore Corporation 30-year bonds? ij* = 0.50% + 0.75% + 1.15% + 0.50% + 1.75% = 4.65% LG6-6
6-3 Determinants of Interest Rates for Individual Securities Dakota Corporation 15-year bonds have an equilibrium rate of return of 8 percent. For all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.50 percent. The security’s liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the bond’s default risk premium. 8.00% = 1.75% + 3.50% + DRP + 0.25% + 0.85% => DRP = 8.00% - (1.75% + 3.50% + 0.25% + 0.85%) = 1.65%
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6-4 Determinants of Interest Rates for Individual Securities A two-year Treasury security currently earns 1.94 percent. Over the next two years, the real risk-free rate is expected to be 1.00 percent per year and the inflation premium is expected to be 0.50 percent per year. Calculate the maturity risk premium on the two-year Treasury security. 1.94% = 0.50% + 1.00% + 0.00% + 0.00% + MP => MP = 1.94% - (0.50% + 1.00% + 0.00% + 0.00%) = 0.44%
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6-5 Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: E(2r1) = 7%, E(3r1) = 7.5% E(4r1) = 7.85% 1R1 = 6%, Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve. 1R1 = 6% 1/2 - 1 = 6.50% 1R2 = [(1 + 0.06)(1 + 0.07)] 1/3 - 1 = 6.83% 1R3 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)] 1/4 - 1 = 7.09% 1R4 = [(1 + 0.06)(1 + 0.07)(1 + 0.075)(1 + 0.0785)]
Chapter 06 - Understanding Financial Markets and Institutions
Yield to Maturity 7.09% 6.83% 6.50%
6.00% 0 LG6-7
1
2
3
4
Term to Maturity (in years)
6-6 Unbiased Expectations Theory Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: E(2r1) = 3.75%, E(3r1) = 4.25% E(4r1) = 5.75% 1R1 = 1%, Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve. 1R1 = 1% 1/2 - 1 = 2.37% 1R2 = [(1 + 0.01)(1 + 0.0375)] 1/3 - 1 = 2.99% 1R3 = [(1 + 0.01)(1 + 0.0375)(1 + 0.0425)] R = [(1 + 0.01)(1 + 0.0375)(1 + 0.0425)(1 + 0.0575)]1/4 - 1 = 3.67% 1 4
Yield to Maturity 3.67% 2.99% 2.37%
1.00% 0 LG6-7
1
2
3
4
Term to Maturity (in years)
6-7 Unbiased Expectations Theory One-year Treasury bills currently earn 1.45 percent. You
Chapter 06 - Understanding Financial Markets and Institutions
unbiased expectations theory is correct, what should the current rate be on two-year Treasury securities? 1R2 = [(1 + 0.0145)(1 + 0.0165)]
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1/2
- 1 = 1.55%
6-8 Unbiased Expectations Theory One-year Treasury bills currently earn 2.15 percent. You expect that one year from now, one-year Treasury bill rates will increase to 2.65 percent and that two years from now, one-year Treasury bill rates will increase to 3.05 percent. If the unbiased expectations theory is correct, what should the current rate be on three-year Treasury securities? 1/3 - 1 = 2.62% 1R3 = [(1 + 0.0215)(1 + 0.0265)(1 + 0.0305)]
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6-9 Liquidity Premium Theory One-year Treasury bills currently earn 3.45 percent. You expect that one year from now, one-year Treasury bill rates will increase to 3.65 percent. The liquidity premium on two-year securities is 0.05 percent. If the liquidity premium theory is correct, what should the current rate be on two-year Treasury securities? 1/2 - 1 = 3.58% 1R2 = [(1 + 0.0345)(1 + 0.0365 + 0.0005)]
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6-10 Liquidity Premium Theory One-year Treasury bills currently earn 2.25 percent. You expect that one year from now, one-year Treasury bill rates will increase to 2.45 percent and that two years from now, one-year Treasury bill rates will increase to 2.95 percent. The liquidity premium on two-year securities is 0.05 percent and on three-year securities is 0.15 percent. If the liquidity premium theory is correct, what should the current rate be on three-year Treasury securities? 1/3 - 1 = 2.62% 1R2 = [(1 + 0.0225)(1 + 0.0245 + 0.0005)(1 + 0.0295 + 0.0015)]
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6-11 Liquidity Premium Theory Based on economists’ forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows: R1 = 0.65% E(2r1) = 1.75%
L2 = 0.05%
E(3r1) = 1.85%
L3 = 0.10%
E(4r1) = 2.15%
L4 = 0.12%
Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. 1R1 = 0.65% 1/2 - 1 = 1.22% 1R2 = [(1 + 0.0065)(1 + 0.0175 + 0.0005)]
R = [(1 + 0.0065)(1 + 0.0175 + 0.0005)(1 + 0.0185 + 0.0010)]1/3 - 1 = 1.47%
Chapter 06 - Understanding Financial Markets and Institutions 1/4 -1= 1R4 = [(1 + 0.0065)(1 + 0.0175 + 0.0005)(1 + 0.0185 + 0.0010)(1 + 0.0215 + 0.0012)]
1.67% Yield to Maturity 1.67% 1.47% 1.22%
0.65% 0 LG6-7
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Term to Maturity (in years)
6-12 Liquidity Premium Theory Based on economists’ forecasts and analysis, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows: R1 = 1.25% E(2r1) = 2.15%
L2 = 0.08%
E(3r1) = 2.55%
L3 = 0.10%
E(4r1) = 3.00%
L4 = 0.15%
Using the liquidity premium theory, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. 1R1 = 1.25% 1/2 - 1 = 1.74% 1R2 = [(1 + 0.0125)(1 + 0.0215 + 0.0008)] 1/3 - 1 = 2.04% 1R3 = [(1 + 0.0125)(1 + 0.0215 + 0.0008)(1 + 0.0255 + 0.0010)] 1/4 -1= 1R4 = [(1 + 0.0125)(1 + 0.0215 + 0.0008)(1 + 0.0255 + 0.0010)(1 + 0.0300 + 0.0015)]
2.32%
Chapter 06 - Understanding Financial Markets and Institutions
Yield to Maturity 2.32% 2.04% 1.74%
1.25% 0
1
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Term to Maturity (in years)
intermediate 6-13 Determinants of Interest Rates for Individual Securities Tom and Sue’s Flowers, problems Inc.’s, 15-year bonds are currently yielding a return of 8.25 percent. The expected LG6-6 inflation premium is 2.25 percent annually and the real risk-free rate is expected to be 3.50 percent annually over the next 15 years. The default risk premium on Tom and Sue’s Flowers’ bonds is 0.80 percent. The maturity risk premium is 0.75 percent on five-year securities and increases by 0.04 percent for each additional year to maturity. Calculate the liquidity risk premium on Tom and Sue’s Flowers, Inc.’s, 15-year bonds. 8.25% = 2.25% + 3.50% + 0.80 + LRP + (0.75% + (0.04% x 10)) => LRP = 8.25% - (2.25% + 3.50% + 0.80% + (0.75% + (0.04% x 10))) = 0.55% LG6-6
6-14 Determinants of Interest Rates for Individual Securities Nikki G’s Corporation’s 10year bonds are currently yielding a return of 6.05 percent. The expected inflation premium is 1.00 percent annually and the real risk-free rate is expected to be 2.10 percent annually over the next ten years. The liquidity risk premium on Nikki G’s bonds is 0.25 percent. The maturity risk premium is 0.10 percent on 2-year securities and increases by 0.05 percent for each additional year to maturity. Calculate the default risk premium on Nikki G’s 10-year bonds. 6.05% = 1.00% + 2.10% + DRP + 0.25% + (0.10% + (0.05% × 8)) => DRP = 6.05% - (1.00% + 2.10% + 0.25% + (0.10% + (0.05% x 8))) = 2.20%
LG6-6
6-15 Unbiased Expectations Theory Suppose we observe the following rates: 1R1 = 8%, 1R2 = 10%. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now, E(2r1)? 1 + 1R2 = {(1 + 1R1)(1 + E(2r1))}1/2 1.10 = {1.08(1 + E(2r1))}1/2 1.21= 1.08 (1 + E(2r1)) 1.21/1.08 = 1 + E(2r1)
Chapter 06 - Understanding Financial Markets and Institutions
E(2r1) = 12% LG6-7
6-16 Unbiased Expectations Theory The Wall Street Journal reports that the rate on four-year Treasury securities is 1.60 percent and the rate on five-year Treasury securities is 2.15 percent. According to the unbiased expectations theory, what does the market expect the one-year Treasury rate to be four years from today, E(5r1)? 1 + 1R5 = {(1 + 1R4)4(1 + E(5r1))}1/5 1.0215 = {(1.016)4(1 + E(5r1))}1/5 (1.0215)5 = (1.016)4 (1 + E(5r1)) (1.0215)5 / (1.016)4 = 1 + E(5r1) 1 + E(5r1) = 1.0438 E(5r1) = 4.38%
LG6-7
6-17 Liquidity Premium Theory The Wall Street Journal reports that the rate on three-year Treasury securities is 5.25 percent and the rate on four-year Treasury securities is 5.50 percent. The one-year interest rate expected in three years, E(4r1), is 6.10 percent. According to the liquidity premium theories, what is the liquidity premium on the 4-year Treasury security, L4? 1 + 1R4 = {(1 + 1R3)3(1 + E(4r1) + L4)}1/4 1.0550 = {(1.0525)3(1 + 0.0610 + L4)}1/4 (1.0550)4 = (1.0525)3(1 + 0.0610 + L4) (1.0550)4 / (1.0525)3 = 1 + 0.0610 + L4 (1.0550)4 / (1.0525)3 – 1.0610 = L4 = 0.1536%
LG6-7
6-18 Liquidity Premium Theory Suppose we observe the following rates: 1R1 = 0.75%, 1R2 = 1.20%, and E(2r1) = 0.907%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2, L2? 1 + 1R2 = {(1 + 1R1)(1 + E(2r1) + L2)}1/2 1.012 = {(1.0075)(1 + 0.00907 + L2)}1/2 (1.012)2 = (1.0075)(1 + 0.00907 + L2) (1.012)2/(1.0075) = 1 + 0.00907 + L2 (1.012)2/(1.0075) – 1.00907 = L2 = 0.745%
LG6-8
6-19 Forecasting Interest Rates You note the following yield curve in The Wall Street Journal. According to the unbiased expectations theory, what is the one-year forward rate for the period beginning one year from today, 2f1? Maturity One day One year Two years Three years R = 0.065 = [(1 + 0.055)(1 + f )]1/2 - 1
Yield 2.00% 5.50 6.50 9.00
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=> [(1.065)2 / (1.055)] - 1 = 2f1 = 7.51% LG6-8
6-20 Forecasting Interest Rates On March 11, 20XX, the existing or current (spot) one-, two-, three-, and four-year zero-coupon Treasury security rates were as follows: 1R1 = 0.75%,
1R2 = 1.35%,
1R3 = 1.75%,
1R4 = 1.90%
Using the unbiased expectations theory, calculate the one-year forward rates on zero coupon Treasury bonds for years 2, 3, and 4 as of March 11, 20XX. = [(1 + 1R2)2/(1 + 1R1)] - 1 = [(1 + 0.0135)2/(1 + 0.0075)] - 1 = 1.95% 3 2 3 2 3f1 = [(1 + 1R3) /(1 + 1R2) ] - 1 = [(1 + 0.0175) /(1 + 0.0135) ] - 1 = 2.55% 4 3 4 3 4f1 = [(1 + 1R4) /(1 + 1R3) ] - 1 = [(1 + 0.0190) /(1 + 0.0175) ] - 1 = 2.35% 2f1
advanced problems LG6-6
6-21 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 10-year Treasury bonds is 7.25 percent, on 20-year Treasury bonds is 7.85 percent, and on a 20-year corporate bond issued by MHM Corp. is 8.75 percent. Assume that the maturity risk premium is zero. If the default risk premium and liquidity risk premium on a 10-year corporate bond issued by MHM Corp. are the same as those on the 20year corporate bond, calculate the current rate on MHM Corp.’s 10-year corporate bond. 20-year corporate bond: 8.75% = 7.85% + DRP + LRP + 0.00% => DRP + LRP = 8.75% 7.85% = 0.90% 10-year corporate bond: ij* = 7.25% + 0.90% = 8.15%
LG6-6
6-22 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 8-year Treasury bonds is 5.85 percent, on 15-year Treasury bonds is 6.25 percent, and on a 15-year corporate bond issued by MHM Corp. is 7.35 percent. Assume that the maturity risk premium is zero. If the default risk premium and liquidity risk premium on an 8year corporate bond issued by MHM Corp. are the same as those on the 15-year corporate bond, calculate the current rate on MHM Corp.’s 8-year corporate bond. 15-year corporate bond: 7.35% = 6.25% + DRP + LRP + 0.00% => DRP + LRP = 7.35% 6.25% = 1.10% 8-year corporate bond: ij* = 5.85% + 1.10% = 6.95%
LG6-6
6-23 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports that the current rate on 5-year Treasury bonds is 1.85 percent and on 10-year Treasury bonds is 3.35 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 5year Treasury bond purchased five years from today, E(5r5). 1 + 1R10 = {(1 + 1R5)5(1 + E(5r5))5}1/10 = 1.0335 = {(1 + 0.0185)5(1 + E(5r5))5}1/10 => E(5r5) = {(1.0335)10 / (1 + 0.0185)5}1/5 – 1 = 4.87%
LG6-6
6-24 Determinants of Interest Rates for Individual Securities The Wall Street Journal reports
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bonds is 4.50 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a 10-year Treasury bond purchased ten years from today, E(10r10). 1 + 1R20 = {(1 + 1R10)10(1 + E(10r10))10}1/20 = 1.0450 = {(1 + 0.0225)10(1 + E(10r10))10}1/20 => E(10r10) = {(1.0450)20 / (1 + 0.0225)10}1/10 – 1 = 6.80% LG6-7
6-25 Unbiased Expectations Theory Suppose we observe the three-year Treasury security rate (1R3) to be 8 percent, the expected one-year rate next year−E(2r1)−to be 4 percent, and the expected one-year rate the following year−E(3r1)−to be 6 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate, 1R1? 1.08 = {(1 + 1R1)(1 + E(2r1))(1 + E(3r1))}1/3 1.08 = {(1 + 1R1) × 1.04 × 1.06}1/3 (1.08)3 = (1 + 1R1 ) × 1.04 × 1.06 1 + 1R1 = 1.2597 / (1.04 × 1.06) 1R1 = 14.27%
LG6-7
6-26 Unbiased Expectations Theory The Wall Street Journal reports that the rate on three-year Treasury securities is 1.20 percent and the rate on five-year Treasury securities is 2.15 percent. According to the unbiased expectations theories, what does the market expect the two-year Treasury rate to be three years from today, E(3r2)? 1 + 1R5 = {(1 + 1R3)3(1 + E(3r2))2}1/5 = 1.0215 = {(1 + 0.0120)3(1 + E(3r2))2}1/5 => E(3r2) = {(1.0215)5 / (1 + 0.0120)3}1/2 – 1 = 3.59%
LG6-8
6-27 Forecasting Interest Rates Assume the current interest rate on a one-year Treasury bond (1R1) is 4.50 percent, the current rate on a two-year Treasury bond (1R2) is 5.25 percent, and the current rate on a three-year Treasury bond (1R3) is 6.50 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the one-year forward rate expected on Treasury bills during year 3, 3f1? 1R1 = 4.50% 1/2 - 1 => 2f1 = 6.01% 1R2 = 5.25% = [(1 + 0.045)(1 + 2f1)] R = 6.50% = [(1 + 0.045)(1 + 0.0601)(1 + 3f1)]1/3 - 1 => 3f1 = 9.04% 1 3
LG6-8
6-28 Forecasting Interest Rates A recent edition of The Wall Street Journal reported interest rates of 1.25 percent, 1.60 percent, 1.98 percent, and 2.25 percent for three-, four-, five-, and sixyear Treasury security yields, respectively. According to the unbiased expectation theory of the term structure of interest rates, what are the expected one-year forward rates for years 4, 5, and 6? 1 + 1R4 = {(1 + 1R3)(1 + 4f1)}1/4 1.016 = {(1.0125)3(1 + 4f1)}1/4 (1.016)4 = (1.0125)3(1 + 4f1)) (1.016)4 / (1.0125)3 = 1 + 4f1
Chapter 06 - Understanding Financial Markets and Institutions
4f1 = 2.66%
1 + 1R5 = {(1 + 1R4)4(1 + 5f1)}1/5 1.0198 = {(1.016)4(1 + 5f1)}1/5 (1.0198)5 = (1.016)4(1 + 5f1) (1.0198)5/(1.016)4 = 1+5f1 1 + 5f1 = 1.03514 5f1 = 3.51% 1 + 1R6 = {(1 + 1R5)5(1 + 6f1)}1/6 1.0225 = {(1.0198)5(1 + 6f1)}1/6 (1.0225)6 = (1.0198)5(1 + 6f1) (1.0225)6/(1.0198)5 = 1 + 6f1 1 + 6f1 = 1.03611 6f1 = 3.61%
research it! Spreads Go to the Federal Reserve Bank of St. Louis’s Web site at fred.stlouisfed.org and get the latest rates on 10-year T-bills and AAA and BAA rated corporate bonds using the following steps. Go to the Federal Reserve Bank of St. Louis’s Web site at fred.stlouisfed.org. Search for “10Year Treasury Constant Maturity Rate.” Chose monthly data. This will bring the file onto your computer that contains the relevant data. Search for “AAA corporate” and then on “BAA.” Chose monthly data. This will bring the files onto your computer that contains the relevant data. Calculate the current spread of AAA and BAA rated bonds over the 10-year Treasury-bond rate. How have these spreads changed over the last two years? SOLUTION: The solution will vary with the year the data are accessed. However, these spreads help investors determine how much they must charge issuers other than the U.S. government as a premium for any perceived probability of default. The difference between a quoted interest rate on a security and a Treasury security with similar maturity, liquidity, tax, and other features is called a default or credit risk premium.
integrated mini-case: Calculating Interest Rates From discussions with your broker, you have determined that the expected inflation premium is 1.35 percent next year, 1.50 percent in year 2, 1.75 percent in year 3, and 2.00 percent in year 4 and beyond. Further, you expect that real risk-free rates will be 3.20 percent next year, 3.30 percent in year 2, 3.75 percent in year 3, and 3.80 percent in year 4 and beyond. You are considering an investment in either five-year Treasury securities or five-year bonds issued by PeeWee Corporation. The bonds have no special covenants. Your broker has determined the following information about economic activity and PeeWee Corporation five-year bonds: Default risk premium = 2.10% Liquidity risk premium = 1.75%
Chapter 06 - Understanding Financial Markets and Institutions
Maturity risk premium = 0.75% Further, the maturity risk premium on PeeWee bonds is 0.1875 percent per year starting in year 2. PeeWee’s default risk premium and liquidity risk premium do not change with bond maturity. a. What is the fair interest rate on five-year Treasury securities? b. What is the fair interest rate on PeeWee Corporation five-year bonds? c. Plot the five-year yield curve for the Treasury securities. d. Plot the five-year yield curve for the PeeWee Corporation bonds. SOLUTION: a. What is the fair interest rate on 5-year Treasury securities? 1R5 = [(1 + 0.0135 + 0.032)(1 + 0.015 + 0.033)(1 + 0.0175 + 0.0375)(1 + 0.02 + 0.038) (1 + 0.02 + 1/5
0.038)]
- 1 = 5.2887%
b. What is the fair interest rate on PeeWee Corporation 5-year bonds? Rate on 5-year PeeWee bonds = 5.2887% + 2.10% + 1.75% + 0.75% = 9.89% c. Plot the 5-year yield curve for the Treasury securities. 1R1 = 1.35% + 3.20% = 4.55% 1/2 – 1] = 4.67% 1R2 = [[(1 + 0.0455)(1 + 0.015 + 0.033)] 1/3 – 1] = 4.95% 1R3 = [[(1 + 0.0455)(1 + 0.015 + 0.033)(1 + 0.0175 + 0.0375)] 1/4 – 1] = 5.16% 1R4 = [[(1 + 0.0455)(1 + 0.015 + 0.033)(1 + 0.0175 + 0.0375)(1 + 0.02 + 0.038)] 1R5 = [[(1 + 0.0455)(1 + 0.015 + 0.033)(1 + 0.0175 + 0.0375)(1 + 0.02 + 0.038) (1 + 0.02 + 1/5
0.038)]
– 1] = 5.29%
yield to maturity 5.29% 5.16%
4.95%
4.67%
4.55% term to maturity
Chapter 06 - Understanding Financial Markets and Institutions
d. Plot the 5-year yield curve for the PeeWee Corporation bonds. 1R1 = 1.35% + 3.20% + 2.10% + 1.75%
= 8.40% – 1] + 0.0210 + 0.0175 + 0.001875 = 8.71% 1R2 = [[(1 + 0.0455)(1 + 0.015 + 0.033)] R = [[(1 + 0.0455)(1 + 0.048)(1 + 0.0175 + 0.0375)]1/3 – 1] + 0.0210 + 0.0175 + 0.00375= 9.17% 1 3 1/4 – 1] + 0.0210 + 0.0175 + 0.005625 = 9.57% 1R4 = [[(1 + 0.0455)(1 + 0.048)(1 + 0.055)(1 + 0.02 + 0.038)] 1/5 – 1] + 0.0210 + 0.0175 + .0075 = 1R5 = [[(1 + 0.0455)(1 + 0.048)(1 + 0.055)(1 + 0.058) (1 + 0.02 + 0.038)] 9.89% 1/2
Yield to Maturity 9.89% 9.57%
9.17%
8.71%
8.40% 0
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Chapter 07 - Valuing Bonds
CHAPTER 7 – VALUING BONDS Questions LG1 1. What does a call provision allow issuers to do, and why would they do it? A call provision on a bond issue allows the issuer to pay off the bond debt early at a cost of the principal plus any call premium. Most of the time when a bond issue is called, it is because interest rates have substantially declined in the economy. The issuer calls the existing bonds and issues new bonds at the lower interest rate. This reduces the interest payments the issuer must pay each year. LG2 2. List the differences between the new TIPS and traditional Treasury bonds. Traditional Treasury bonds have a fixed principal and constant interest payments. Because the principal and coupon rate are fixed, interest rate changes in the economy cause the market price of the bonds to have large fluctuations. On the other hand, the principal of a TIPS increases with the rate of inflation. Similar to a T-bond, the TIPS has a constant coupon rate. However, since the principal of the TIPS increases over time, the interest payment also increases over time. This inflation rate adjustment of a TIPS’ principal every six months reduces the amount of downward price change in the price of the bond when interest rates increase. LG2 3. Explain how mortgage-backed securities work. A large amount of home mortgages are purchased and pooled together. The homeowners pay interest and principal monthly on their mortgages. Bonds are issued from the pool of mortgages, using the mortgages as collateral. The interest payments and bond principal payments for these mortgage-backed securities (MBS) originate from the mortgage borrowers and flow through the pool of mortgages. As the homeowners pay off their mortgages over time, the MBS are also paid. LG3 4. Provide the definitions of a discount bond and a premium bond. Give examples. A discount bond is simply a bond that is selling below its par value. It would be quoted at a price that is less than 100 percent of par, like 99.05. A premium bond is a bond selling above its par value. Its price will be quoted as over 100 percent of par value, like 101.15. A bond becomes a discount bond when market interest rates rise above the bond’s coupon rate. A bond becomes a premium bond when market interest rates fall below the bond’s coupon rate.
Chapter 07 - Valuing Bonds
LG4 5. Describe the differences in interest payments and bond price between a 5 percent coupon bond and a zero coupon bond. The 5 percent coupon bond pays annual interest of 5 percent of the bond’s par value. For a $1,000 par value bond, this would be $50 per year. This interest might be paid in two payments of $25 each. The price of the coupon bond tends to stay near its par value. The zero coupon bond pays no interest payments. The bondholder earns a return from the increase of the bond’s market price over time. The bond’s price is initially much lower than its par value. When the zero coupon bond finally matures, the par value is paid. LG5 6. All else equal, which bond’s price is more affected by a change in interest rates, a short-term bond or a longer-term bond? Why? All else equal, a long-term bond experiences larger price changes when interest rates change than a short-term bond. A bond’s price is the present value of all its cash flows. Changes in the discount rate (the interest rate) impact present values more for cash flows that are further out in time. LG5 7. All else equal, which bond’s price is more affected by a change in interest rates, a bond with a large coupon or a small coupon? Why? The price of the bond with the small coupon will be impacted more by a change in interest rates than the price of the large coupon bond. For a small coupon bond, the cash flows are weighted much more toward the maturity date because of the small interest payments. The large coupon bond has high interest payments, many of which occur soon. These higher cash flows made earlier dampen the impact of interest rate changes because those changes in the discount rate impact the earlier cash flows to a lesser degree than the later cash flows. LG5 8. Explain how a bond’s interest rate can change over time even if interest rates in the economy do not change. Because of the yield curve, there are different interest rates that apply to each time to maturity. So, as a bond gets closer to its maturity date, different interest rates may apply to its discounting even when interest rates in the economy have not changed. LG6 9. Compare and contrast the advantages and disadvantages of the current yield computation versus yield to maturity calculations. The current yield computation is useful because it is a very simple one. It provides a quick and easy assessment of what the bond offers the investor in return. But it measures only the return from the interest payments. The full return to an investor also includes the capital gain or loss the bond will experience if it is selling as a discount or premium bond. The yield to maturity computation is more difficult, but it incorporates the full return the bond offers to investors.
Chapter 07 - Valuing Bonds
LG6 10. What is the yield to call and why is it important to a bond investor? Many bonds do not survive until their maturity date because they get paid early through a call provision. The yield to call is the yield that would be earned if the bond is purchased at today’s price and held until it is called by the issuer. The computation incorporates the additional call premium that is paid with the principal. LG6 11. What is the purpose of computing the equivalent taxable yield of a municipal bond? Municipal bonds offer a tax advantage for the bondholder that other kinds of bonds do not offer. Thus, their yield to maturity is not directly comparable to that of other bonds. The equivalent taxable yield (ETY) is an adjustment to the yield to make it comparable to taxable bonds. Bond investors can use the ETY to assess which bond will earn them a higher after-tax return. LG6 12. Explain why high income and wealthy people are more likely to buy a municipal bond than a corporate bond. Individual bondholders do not owe taxes on interest payments received from municipal bonds. This tax advantage is more valuable to individuals who are in a higher marginal tax bracket. Because wealthy individuals are usually in a higher tax bracket, this tax advantage is more valuable to them. LG7 13. Why does a Treasury bond offer a lower yield than a corporate bond with the same time to maturity? Could a corporate bond with a different time to maturity offer a lower yield? Explain. The Treasury bond has lower credit risk than the corporate bond. Given the risk/return relationship, lower risk is associated with lower expected return. Thus, all else equal, a Treasury bond will offer a lower yield to maturity than a corporate bond. However, if the yield curve slopes upward, then shorter term to maturity bonds will require a smaller interest rate than longer term bonds. So, it is possible that a short-term corporate bond would offer a lower yield than a long-term Treasury bond. LG7 14. Describe the difference between a bond issued as a high-yield bond and one that has become a “fallen angel.” Both of these bonds would be rated as BB or below. The bond referred to as a “fallen angel” would have been issued by a a firm that was a successful, financially stable firm but one that has recently struggled. The bondholder would have purchased the bond when it was rated investment grade (BBB or above), but now holds a “fallen angel”, or junk bond, due to a decline in the issuer’s financial status. The bond issued as a high-yield, or junk, bond would
Chapter 07 - Valuing Bonds
have been issued after the firm’s financial condition had already deteriorated.. The purchaser of this bond bought the bond initially as a junk bond. LG8 15. What is the difference in the trading volume between Treasury bonds and corporate bonds? Give examples and/or evidence. There is high trading volume in Treasury bonds and low trading volume in corporate bonds.
Problems LG1 7-1 Interest Payments Determine the interest payment for the following three bonds: 3 ½ percent coupon corporate bond (paid semiannually), 4.25 percent coupon Treasury note, and a corporate zero coupon bond maturing in ten years. (Assume a $1,000 par value.) 3 ½ percent coupon corporate bond (paid semiannually): ½ × 0.035 × $1,000 = $17.50 4.25 percent coupon Treasury note: ½ × 0.0425 × $1,000 = $21.25 Corporate zero coupon bond maturing in ten years: 0.00 × $1,000 = $0 LG1 7-2 Interest Payments Determine the interest payment for the following three bonds: 4 ½ percent coupon corporate bond (paid semiannually), 5.15 percent coupon Treasury note, and a corporate zero coupon bond maturing in 15 years. (Assume a $1,000 par value.) 4 ½ percent coupon corporate bond (paid semiannually): ½ × 0.045 × $1,000 = $22.50 5.15 percent coupon Treasury note: ½ × 0.0515× $1,000 = $25.75 Corporate zero coupon bond maturing in ten years: 0.00 × $1,000 = $0 LG1
7-3 Time to Maturity A bond issued by Ford on May 15, 1997 is scheduled to mature on May 15, 2097. If today is November 16, 2014, what is this bond’s time to maturity? May 15, 2097 minus November 16, 2014 = 82 years and 6 months
LG1
7-4 Time to Maturity A bond issued by IBM on December 1, 1996 is scheduled to mature on December 1, 2096. If today is December 2, 2015, what is this bond’s time to maturity? December 1, 2096 minus December 2, 2015 = 81 years
LG1 7-5 Call Premium A 6 percent corporate coupon bond is callable in five years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond? Principal + Call premium = $1,000 + 0.06 × $1,000 = $1,060
Chapter 07 - Valuing Bonds
LG1 7-6 Call Premium A 5.5 percent corporate coupon bond is callable in ten years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond? Principal + Call premium = $1,000 + 0.055 × $1,000 = $1,055 LG2
7-7 TIPS Interest and Par Value A 2 ¾ percent TIPS has an original reference CPI of 185.4. If the current CPI is 210.7, what is the current interest payment and par value of the TIPS? Par value = 210.7 / 185.4 × $1,000 = $1,136.46 Interest payment = ½ × 0.0275 × $1,136.46 = $15.63
LG2
7-8 TIPS Interest and Par Value A 3 1/8 percent TIPS has an original reference CPI of 180.5. If the current CPI is 206.8, what is the current interest payment and par value of the TIPS? Par value = 206.8 / 180.5 × $1,000 = $1,145.71 Interest payment = ½ × 0.03125 × $1,145.71 = $17.90
LG3 7-9 Bond Quotes Consider the following three bond quotes; a Treasury note quoted at 97.844, and a corporate bond quoted at 103.25, and a municipal bond quoted at 101.90. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars? Treasury note at 97.844% × $1,000 = 0.97844 × $1,000 = $978.44 Corporate bond at 103.25: 103.25% × $1,000 = 1.0325 × $1,000 = $1,032.50 Municipal bond at 101.90: 101.90% × $5,000 = 1.019 × $5,000 = $5,095.00 LG3 7-10 Bond Quotes Consider the following three bond quotes; a Treasury bond quoted at 106.438, a corporate bond quoted at 96.55, and a municipal bond quoted at 100.95. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars? Treasury note at 106.438% × $1,000 = 1.06438 × $1,000 = $1,064.38 Corporate bond at 96.55: 96.55% × $1,000 = 0.9655 × $1,000 = $965.50 Municipal bond at 100.95: 100.95% × $5,000 = 1.0095 × $5,000 = $5,047.50 LG4 7-11 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 20 years if the market interest rate is 3.8 percent. Use semiannual compounding:
Chapter 07 - Valuing Bonds
PV =
FVN
(1 + i)N
=
$1,000 40 = $471.01 .038 1 + 2
Or N=40, I=1.9, PMT=0, FV=−1000, CPT PV == 471.01
LG4
7-12 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 15 years if the market interest rate is 5.75 percent. Use semiannual compounding: PV =
FVN
(1 + i)N
=
$1,000 30 = $427.27 .0575 1 + 2
Or N=30, I=2.875, PMT=0, FV=−1000, CPT PV == 427.27 LG6
7-13 Current Yield What’s the current yield of a 3.8 percent coupon corporate bond quoted at a price of 102.08? 3.8% / 102.08% = 0.0372 = 3.72%
LG6
7-14 Current Yield What’s the current yield of a 5.2 percent coupon corporate bond quoted at a price of 96.78? 5.2% / 96.78% = 0.05373 = 5.37%
LG6
7-15 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield to maturity of 3.5 percent for an investor in the 33 percent marginal tax bracket? Use equation 7.4: Equivalent taxable yield =
LG6
Muni yield
= 3.5% = 5.22% 1− Tax rate 1− 0.33
7-16 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield to maturity of 2.9 percent for an investor in the 28 percent marginal tax bracket? Use equation 7.4: Equivalent taxable yield =
LG7
Muni yield
= 2.9% = 4.03% 1− Tax rate 1− 0.28
7-17 Credit Risk and Yield Rank from highest credit risk to lowest risk the following bonds, with the same time to maturity, by their yield to maturity: Treasury bond with yield of 5.55
Chapter 07 - Valuing Bonds
percent, IBM bond with yield of 7.49 percent, Trump Casino bond with yield of 8.76 percent, and Banc One bond with a yield of 5.99 percent. Trump Casino bond with yield of 8.76 percent IBM bond with yield of 7.49 percent Banc One bond with yield of 5.99 percent Treasury bond with yield of 5.55 percent LG7 7-18 Credit Risk and Yield Rank the following bonds in order from lowest credit risk to highest risk, all with the same time to maturity, by their yield to maturity: Treasury bond with yield of 4.65 percent, United Airline bond with yield of 9.07 percent, Bank of America bond with a yield of 6.25 percent, and Hewlett/Packard bond with yield of 6.78 percent. Treasury bond with yield of 4.65 percent Bank of America bond with yield of 6.25 percent Hewlett/Packard bond with yield of 6.78 percent United Airline bond with yield of 9.07 percent intermediate problems LG2 7-19 TIPS Capital Return Consider a 3.5 percent TIPS with an issue CPI reference of 185.6. At the beginning of this year, the CPI was 193.5 and was at 199.6 at the end of the year. What was the capital gain of the TIPS in dollars and in percentage terms? Gain = End of year value – Beginning of year value = 199.6 / 185.6 × $1,000 − 193.5 / 185.6 × $1,000 = $1,075.43 − $1,042.56 = $32.87 As a percentage, the gain was = $32.87 / $1,042.56 = 3.15% LG2
7-20 TIPS Capital Return Consider a 2.25 percent TIPS with an issue CPI reference of 187.2. At the beginning of this year, the CPI was 197.1 and was at 203.8 at the end of the year. What was the capital gain of the TIPS in dollars and in percentage terms? Gain = End of year value – Beginning of year value = 203.8 / 187.2 × $1,000 − 197.1 / 187.2 × $1,000 = $1,088.68 − $1,052.88 = $35.80 As a percentage, the gain was = $35.80 / $1,052.88 = 3.40%
LG4 7-21 Compute Bond Price Compute the price of a 3.8 percent coupon bond with 15 years left to maturity and a market interest rate of 6.8 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? 1 1− (1 + 0.034 )30 $1,000 + Bond Price = $19.00 30 = $353.869 + $366.762 = $720.63 0.034 (1 + 0.034 )
or TVM calculator: N = 30, I = 3.4, PMT = 19.00, FV = 1,000; CPT PV = -720.63
Chapter 07 - Valuing Bonds
Since the bond’s price is less than $1,000, it is a discount bond.
Chapter 07 - Valuing Bonds
LG4
7-22 Compute Bond Price Compute the price of a 5.6 percent coupon bond with ten years left to maturity and a market interest rate of 7.0 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? 1 1− (1+ 0.035)20 $1,000 = $397.95 + $502.56 = $900.51 Bond Price = $28.00 + 20 0.035 (1+ 0.035)
or TVM calculator: N = 20, I = 3.5, PMT = 28, FV = 1,000; CPT PV = -900.51 Since the bond’s price is less than $1,000, it is a discount bond. LG4 7-23 Compute Bond Price Calculate the price of a 5.2 percent coupon bond with 18 years left to maturity and a market interest rate of 4.6 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? 1 1− (1+ 0.023)36 1,000 Bond Price = $26.00 = $631.87 + $441.04 = $1,072.91 + 36 0.023 (1+ 0.023)
or TVM calculator: N = 36, I = 2.3, PMT = 26, FV = 1,000; CPT PV = -1,072.91 Since the bond’s price is greater than $1,000, it is a premium bond. LG4 7-24 Compute Bond Price Calculate the price of a 5.7 percent coupon bond with 22 years left to maturity and a market interest rate of 6.5 percent. (Assume interest payments are semiannual.) Is this a discount or premium bond? 1 1 − (1 + 0.0325 )44 $1,000 = $662.24 + $244.81 = $907.05 Bond Price = $28.50 + 44 (1 + 0.0325 ) 0.0325
or TVM calculator: N = 44, I = 3.25, PMT = 28.50, FV = 1,000; CPT PV = -907.05 Since the bond’s price is less than $1,000, it is a discount bond. LG5 7-25 Bond Prices and Interest Rate Changes A 5.75 percent coupon bond with ten years left to maturity is priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 5.8 percent. What is the change in price the bond will experience in dollars? Compute the current bond price: 1 1− (1+ 0.0325)20 $1,000 = $418.01+ $527.47 = $945.48 Bond Price = $28.75 + 20 0.0325 (1+ 0.0325)
Chapter 07 - Valuing Bonds
or TVM calculator: N = 20, I = 3.25, PMT = 28.75, FV = 1,000; CPT PV = -945.48 Now compute the price in one year: 1 1− (1 + 0.029 )18 $1,000 + Bond Price = $28.75 18 = $398.777 + $597.755 = $996.53 0.029 (1 + 0.029 )
or TVM calculator: N = 18, I = 2.9, PMT = 28.75, FV = 1,000; CPT PV = -996.53 So, the dollar change in price is: $996.53 − $945.48 = $51.05 LG5 7-26 Bond Prices and Interest Rate Changes A 6.5 percent coupon bond with 14 years left to maturity is priced to offer a 7.2 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.8 percent. What is the change in price the bond will experience in dollars? Compute the current bond price: 1 1− (1+ 0.036)28 $1,000 = $567.42 + $371.47 = $938.89 Bond Price = $32.50 + 28 0.036 (1+ 0.036)
or TVM calculator: N = 28, I = 3.6, PMT = 32.50, FV = 1,000; CPT PV = -938.89 Now compute the price in one year: 1 1− (1+ 0.034)26 $1,000 = $555.14 + $419.24 = $974.38 Bond Price = $32.50 + 26 0.034 (1+ 0.034)
or TVM calculator: N = 26, I = 3.4, PMT = 32.50, FV = 1,000; CPT PV = -974.38 So, the dollar change in price is: $974.38 − $938.89 = $35.49 LG6 7-27 Yield to Maturity A 5.65 percent coupon bond with 18 years left to maturity is offered for sale at $1,035.25. What yield to maturity is the bond offering? (Assume interest payments are semiannual.)
Chapter 07 - Valuing Bonds
TVM calculator: N = 36, PV = -1,035.25, PMT = 28.25, FV = 1,000; CPT I = 2.671% YTM = 2.671% × 2 = 5.34% LG6 7-28 Yield to Maturity A 4.30 percent coupon bond with 14 years left to maturity is offered for sale at $943.22. What yield to maturity is the bond offering? (Assume interest payments are semiannual.) TVM calculator: N = 28, PV = -943.22, PMT = 21.5, FV = 1,000; CPT I = 2.432% YTM = 2.432% × 2 = 4.86% LG6 7-29 Yield to Call A 6.75 percent coupon bond with 26 years left to maturity can be called in six years. The call premium is one year of coupon payments. It is offered for sale at $1,135.25. What is the yield to call of the bond? (Assume interest payments are semiannual.) TVM calculator: N = 12, PV = -1,135.25, PMT = 33.75, FV = 1,067.50; CPT I = 2.541% YTC = 2.541% × 2 = 5.08% LG6 7-30 Yield to Call A 5.25 percent coupon bond with 14 years left to maturity can be called in four years. The call premium is one year of coupon payments. It is offered for sale at $1,075.50. What is the yield to call of the bond? (Assume interest payments are semiannual.) TVM calculator: N = 8, PV = -1,075.50, PMT = 26.25, FV = 1,052.50; CPT I = 2.193% YTC = 2.193% × 2 = 4.39% LG6 7-31 Comparing Bond Yields A client in the 39 percent marginal tax bracket is comparing a municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45 percent yield. Which bond will give the client more profit after taxes? First determine the ETY: Equivalent taxable yield =
Muni yield
= 4.5% = 7.38% 1 − Tax rate 1 − 0.39
Since 7.38 percent is greater than 6.45 percent, the client should take the municipal bond. LG6 7-32 Comparing Bond Yields A client in the 28 percent marginal tax bracket is comparing a municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45 percent yield. Which bond will give the client more profit after taxes? First determine the ETY: Equivalent taxable yield =
Muni yield
= 4.5% = 6.25% 1− Tax rate 1− 0.28
Since 6.25 percent is less than 6.45 percent, the client should take the corporate bond.
Chapter 07 - Valuing Bonds
advanced problems LG2
7-33 TIPS Total Return Reconsider the 3.5 percent TIPS discussed in problem 7-19. It was issued with CPI reference of 185.6. The bond is purchased at the beginning of the year (after the interest payment), when the CPI was 193.5. For the interest payment in the middle of the year, the CPI was 195.1. Now, at the end of the year, the CPI is 199.6 and the interest payment has been made. What is the total return of the TIPS in dollars and in percentage terms for the year? Capital gain = End of year value – Beginning of year value = 199.6 / 185.6 × $1,000 – 193.5 / 185.6 × $1,000 = $1,075.43 − $1,042.56 = $32.87 The mid-year interest payment was: ½ × 0.035 × 195.1 / 185.6 × $1,000 = $18.40 The end-of-year interest payment was: ½ × 0.035 × 199.6 / 185.6 × $1,000 = $18.82 Total dollar return = $32.87 + $18.40 + $18.82 = $70.09 As a percentage, the return was = $70.09 / $1,042.56 = 6.72%
LG2 7-34 TIPS Total Return Reconsider the 2.25 percent TIPS discussed in problem 7-20. It was issued with CPI reference of 187.2. The bond is purchased at the beginning of the year (after the interest payment), when the CPI was 197.1. For the interest payment in the middle of the year, the CPI was 200.1. Now, at the end of the year, the CPI is 203.8 and the interest payment has been made. What is the total return of the TIPS in dollars and in percentage terms for the year? Gain = End of year value – Beginning of year value = 203.8 / 187.2 × $1,000 − 197.1 / 187.2 × $1,000 = $1,088.68 − $1,052.88 = $35.80 The mid-year interest payment was: ½ × 0.0225× 200.1 / 187.2 × $1,000 = $12.03 The end-of-year interest payment was: ½ × 0.0225× 203.8 / 187.2 × $1,000 = $12.25 Total dollar return = $35.80 + $12.03 + $12.25 = $60.08 As a percentage, the return was = $60.08 / $1,052.88 = 5.71% LG5 7-35 Bond Prices and Interest Rate Changes A 6.25 percent coupon bond with 22 years left to maturity is priced to offer a 5.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.0 percent. If this occurs, what would be the total return of the bond in dollars and percent? (Assume interest payments are semiannual.) Compute the current bond price: 1 1− (1+ 0.0275)44 $1,000 Bond Price = $31.25 = $791.92 + $303.11 = $1,095.03 + 44 0.0275 (1+ 0.0275)
or TVM calculator: N = 44, I = 2.75, PMT = 31.25, FV = 1,000; CPT PV = -1,095.03 Now compute the price in one year:
Chapter 07 - Valuing Bonds 1 1− (1+ 0.03)42 $1,000 = $740.67 + $288.96 = $1,029.63 Bond Price = $31.25 + 42 0.03 (1+ 0.03)
or TVM calculator: N = 42, I = 3.0, PMT = 31.25, FV = 1,000; CPT PV = -1,029.63 Total return = e Dollar change in price + iInterest payments: $1,029.63 − $1,095.03 + $62.50 = -$2.90 The percentage return is: -$2.90 / $1,095.03 = -0.26% LG5 7-36 Bond Prices and Interest Rate Changes A 7.5 percent coupon bond with 13 years left to maturity is priced to offer a 6.25 percent yield to maturity. You believe that in one year, the yield to maturity will be 7.0 percent. If this occurs, what would be the total return of the bond in dollars and percentage terms? (Assume interest payments are semiannual.) Compute the current bond price: 1 1− (1+ 0.03125)26 $1,000 Bond Price = $37.50 = $660.84 + $449.30 = $1,110.14 + 26 0.03125 (1+ 0.03125)
\or TVM calculator: N = 26, I = 3.125, PMT = 37.50, FV = 1,000; CPT PV = -1,110.14 Now compute the price in one year: 1 1− (1+ 0.035)24 $1,000 = $602.19 + $437.96 = $1,040.15 Bond Price = $37.50 + 24 0.035 (1+ 0.035)
or TVM calculator: N = 24, I = 3.5, PMT = 37.50, FV = 1,000; CPT PV = -1,040.15 Total return = Dollar change in price + Interest payments: $1,040.15 − $1,110.14 + $75.00 = $5.01
Chapter 07 - Valuing Bonds
The percentage return is: $5.01 / $1,110.14 = 0.45% LG6
7-37 Yields of a Bond A 2.50 percent coupon municipal bond has 12 years left to maturity and has a price quote of 98.45. The bond can be called in four years. The call premium is one year of coupon payments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield (for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest payments are semiannual and a par value of $5,000.) Current yield = (0.025 × $5,000) / (0.9845 × $5,000) = 2.50% / 98.45% = 2.54% TVM calculator:N = 24, PV = -4,922.50, PMT = 62.50, FV = 5,000; CPT I = 1.3258% YTM = 1.3258% × 2 = 2.65% Equivalent taxable yield =
Muni yield
=
1− Tax rate
2.65%
= 4.08%
1− 0.35
TVM calculator: N = 8, PV = -4,922.50, PMT = 62.50, FV = 5,125; CPT I = 1.753% YTC = 1.753% × 2 = 3.51% The current yield is higher than the coupon rate because this is currently a discount bond. This is also shown by the YTM, which is greater than the coupon rate. The YTC is comparatively high, but it is currently unlikely that the bond will be called early since interest rates have risen. LG6
7-38 Yields of a Bond A 3.85 percent coupon municipal bond has 18 years left to maturity and has a price quote of 103.20. The bond can be called in eight years. The call premium is one year of coupon payments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield (for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest payments are semiannual and a par value of $5,000.) Current yield = (0.0385 × $5,000) / (1.0320 × $5,000) = 3.85% / 103.20% = 3.73% TVM calculator: N = 36, PV = -5,160, PMT = 96.25, FV = 5,000; CPT I = 1.803% YTM = 1.803% × 2 = 3.61% Equivalent taxable yield =
Muni yield 1− Tax rate
=
3.61%
= 5.55%
1− 0.35
TVM calculator: N = 16, PV = -5,160, PMT = 96.25, FV = 5,192.50; CPT I = 1.90% YTC = 1.90% × 2 = 3.80% The current yield is lower than the coupon rate because this is currently a premium bond. This is also shown by the YTM , which is lower than the coupon rate. The YTC is comparatively high, but it is currently unlikely that the bond will be called early since interest rates are only a little lower than the coupon rate and the call premium would have to be paid.
Chapter 07 - Valuing Bonds
LG7 7-39 Bond Ratings and Prices A corporate bond with a 6.5 percent coupon has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.2 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 8.5 percent. What will be the change in the bond’s price in dollars and percentage terms? (Assume interest payments are semiannual.) Compute the current bond price: 1 1− (1+ 0.036)30 $1,000 = $590.3223 + $346.1046 = $936.43 Bond price = $32.50 + 30 0.036 (1+ 0.036)
or TVM calculator: N = 30, I = 3.6, PMT = 32.50, FV = 1,000; CPT PV = -936.43 Now compute the price after the rating change: 1 1− (1+ 0.0425)30 $1,000 Bond price = $32.50 = $545.32 + $286.89 = $832.21 + 30 0.0425 (1+ 0.0425)
or TVM calculator: N = 30, I = 4.25, PMT = 32.50, FV = 1,000; CPT PV = -832.21 So, the dollar change in price is: $832.21 − $936.43 = -$104.22 The percentage return is: -$104.22 / $936.43 = -11.13% LG7
7-40 Bond Ratings and Prices A corporate bond with a 6.75 percent coupon has ten years left to maturity. It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm has recently become more financially stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 7.1 percent. What will be the change in the bond’s price in dollars and percentage terms? (Assume interest payments are semiannual.) Compute the current bond price: 1 1− (1+ 0.041)20 $1,000 = $454.64 + $447.70 = $902.34 Bond price = $33.75 + 20 0.041 (1+ 0.041)
or TVM calculator: N = 20, I = 4.1, PMT = 33.75, FV = 1,000; CPT PV = -902.34 Now compute the price after the rating change:
Chapter 07 - Valuing Bonds 1 1− (1+ 0.0355)20 $1,000 = $477.51+ $497.73 = $975.24 Bond price = $33.75 + 20 0.0355 (1+ 0.0355)
or TVM calculator: N = 20, I = 3.55 PMT = 33.75, FV = 1,000; CPT PV = -975.24 So, the dollar change in price is: $975.24 − $902.34 = $72.90 The percentage return is: $72.90 / $902.34 = 8.08% 7-41 Spreadsheet Problem Say that in June of this year, a company issued bonds that are scheduled to mature in three years in June. The coupon rate is 5.75 percent and is paid semiannually. The bond issue was rated AAA. a. Build a spreadsheet that shows how much money the firm pays for each interest rate payment and when those payments will occur if the bond issue sells 50,000 bonds. b. If the bond issue rating would have been BBB, then the coupon rate would have been 6.30 percent. Show the interest payments with this rating. Explain why bond ratings are important to firms issuing capital debt. c. Consider that interest rates in the economy increased in the first half of 2012. If the firm would have issued the bonds in January of this year, then the coupon rate would have only been 5.40 percent. How much extra money per year is the firm paying because it issued the bonds in June instead of January? The spreadsheet might look like: A. Coupon Rate= Par Value = Number of Bonds =
B. 6.30% $1,000
5.40% $1,000
50,000
50,000
50,000
0 $1,575,000 $1,575,000 $1,575,000 $1,575,000 $1,575,000 $1,575,000
Interest payments $1,350,000 $1,350,000 $1,350,000 $1,350,000 $1,350,000 $1,350,000 $0
Interest payments June of this year December June of next year Dec of next year June December June
C.
5.75% $1,000
0 $1,437,500 $1,437,500 $1,437,500 $1,437,500 $1,437,500 $1,437,500
Interest payments
B. The better the bond rating, the lower the interest rate a firm will have to pay. In this example, the firm saves $275,000 each year in interest payments with the higher bond rating. C. The firm is paying $175,000 per year more in interest because it issued its bonds after the rates increased.
Chapter 07 - Valuing Bonds
7-42 Spreadsheet Problem You have a portfolio of three bonds. The Long Bond will mature in 19 years and has a 5.5% coupon rate. The Midterm Bond matures in 9 years and has a 6.6% coupon rate. The Short Bond matures in only 2 years and has a 4% coupon rate. A. Construct a spreadsheet that shows the value of these three bonds and the portfolio when the discount rate is 5%. The spreadsheet can look something like this:
B. Illustrate what happens when the discount rate increases by 0.5%. What do you notice about the changes in price between the three bonds? C. Show the bond prices when the discount rate decreases by 0.5% from the discount rate in part A. What do you notice about the price change between Parts B and C? SOLUTION: A.
B.
Chapter 07 - Valuing Bonds
The price change is larger for the longer maturity bonds. This makes long term bonds more volatile. C.
The price change has a higher magnitude for the decline of 0.5% in discount rates compared to the 0.5% increase in rates.
Chapter 07 - Valuing Bonds
Research It! Bond Information Online Information on the bond market is widely available in papers like The Wall Street Journal and Barron’s. Bond information can also be found online at financial Web sites like finance.yahoo.com and http://www.finra.org. The bond credit rating agencies also maintain Web sites with their own bond market news. You can follow the bond market easily at places like the Yahoo! Finance . Web site. Click on the Bond link in the menu to go to their Bond Center. Bond yields for various maturity Treasury securities are shown for today and for previous days. The Bond Composite Rates link shows similar comparisons for municipal and corporate bonds too. Bond calculators are also available for free on the Web. Compare a bond price result from your calculator or the price equation with the online bond calculator result at Investopedia. (www.investopedia.com/calculator/BondPrice.aspx) SOLUTION: All answers will be different. Here is an example answer: An example done on the website…
1 1− (1+ 0.02)6 $1,000 = $98.03 + $887.97 = $986.00 Bond price = $17.50 + 6 0.02 (1+ 0.02)
or TVM calculator: N = 6, I = 2, PMT = 17.50, FV = 1,000; CPT PV = -986.00
Chapter 07 - Valuing Bonds
All computations are the same.
integrated minicase: Corporate Bond Credit Risk Changes and Bond Prices Land’o’Toys is a profitable, medium-sized, retail company. Several years ago, it issued a 6½ percent coupon bond, which pays interest semiannually. The bond will mature in ten years and is currently priced in the market as $1,037.19. The average yields to maturity for 10-year corporate bonds are reported in the following table by bond rating. Bond Rating AAA AA A BBB
Yield (%) 5.4 5.7 6.0 6.5
Bond Rating BB B CCC CC C D
Yield (%) 7.3 8.2 9.2 10.5 12.0 14.5
Periodically, one company will purchase another by buying all of the target firm’s stock. The bonds of the target firm continue to exist. The debt obligation is assumed by the new firm. The credit risk of the bonds often changes because of this type of an event. Suppose that the firm Treasure Toys makes an announcement that they are purchasing Land’o’Toys. Due to Treasure Toy’s projected financial structure after the purchase, Standard & Poor’s states that the bond rating for Land’o’Toys bonds will change to BB. a. Compute the yield to maturity of Land’o’Toys bonds before the purchase announcement and use it to determine the likely bond rating. b. Assume the bond’s price changes to reflect the new credit rating. What is the new price? Did the price increase or decrease? c. What is the dollar change and percentage change in the bond price? d. How do the bond investors feel about the announcement? SOLUTION: a. TVM calculator: N = 20, PV = -1,037.19, PMT = 32.50, FV = 1,000 CPT I = 3.00% YTM = 3.00% × 2 = 6.00% This bond is likely rated as an “A”. b.The new YTM will likely be 7.3percent annually, so the price will change to: TVM calculator: N = 20, I = 3.65, PMT = 32.50, FV = 1,000; CPT PV = -943.91 The price decreased because the bond got riskier. c. The price change would be $943.91 − $1,037.19 = -$93.28 The change as a percentage would be -$93.28 / $1,037.19 = -8.99% d.In a firm buyout, the stockholders of the target firm generally earn a nice profit. However, the bond holders of the target firm can be unhappy if the new combined firm has a worse bond rating, like in this case.
Chapter 08 - Valuing Stocks
CHAPTER 8 – VALUING STOCKS Questions LG1
1. As owners, what rights and advantages do shareholders obtain? Shareholders are able to participate in the economic growth of publicly traded firms without having to manage business entities directly. They have the right to residual cash flows of corporate profits and often receive some of these cash flows through dividends. In addition, shareholders vote on the members of the board of directors and other proposals for the company. Shareholder capital losses are capped in that they can only lose their initial investment. Stocks are very liquid and investors can enjoy this liquidity in both their entrance into the stock market and their exit from it.
LG1
2. Describe how being a residual claimant can be very valuable. Residual claimants are able to delegate the operations of the firm to professional managers, enjoying the possibly vast gains in value that can be created by some firms over time.
LG2
3. Obtain a current quote of McDonald’s (MCD) from the Internet. Describe what has changed since the quote in Figure 8.1. The answer depends on the date the new quote is acquired. However, a discussion about changes in price, highs and lows, dividends, earnings, and volume would be appropriate.
LG2
4. Get the trading statistics for the three main U.S. stock exchanges. activity to that of Table 8.1.
Compare the trading
Again, this depends on the date the data is acquired. An important factor is whether the markets were up, down, or flat that day. LG3
5. Why might the Standard & Poor’s 500 Index be a better measure of stock market performance than the Dow Jones Industrial Average? Why is the DJIA more popular than the S&P 500? The S&P 500 is a broad market index that includes stocks of the 500 largest US firms from ten sectors of the economy. It captures 80 percent of the overall stock market capitalization and is a good proxy for what is occurring in the overall stock market. The DJIA has been used for a longer period, since the mid-1880’s, and represents the activity of the 30 largest corporations in the US, covering 30 percent of the stock market. Its popularity arises from it being the first index used by the media.
LG3
6. Explain how it is possible for the DJIA to increase one day while the Nasdaq Composite decreases during the same day.
Chapter 08 - Valuing Stocks
The components of the DJIA and the Nasdaq Composite index are mostly different companies. The DJIA includes the 30 industry leaders across all sectors of the economy. The Nasdaq is comprised of predominantly technology related firms and emits a noisy signal of technology performance on any given day. LG4
7. Which is higher, the ask quote or the bid quote? Why? The market maker’s ask price is the lowest price offered for stock sale and the bid price is the highest price a market maker will pay for stock purchase. Thus, the ask price is higher than the bid price. The difference is the bid-ask spread and it represents the gain a market maker achieves by taking the risk position and providing the needed liquidity for the stock in question.
LG4
8. Illustrate through examples how trading commission costs impact an investor’s return. Assume an investor wishes to purchase a stock at a strike price of $90. Two scenarios to consider, at their extremes, would be the purchase of 10 shares versus the purchase of 100 shares. The costs to purchase through a discount broker, assuming the broker charges $20 per trade would be $920 ($900 + $20) and $9020, respectively. The commission for the trades in percentages would be 2.22 percent and 0.22 percent, respectively. For the investor who owns only 10 shares, the price would have to rise by $2 per share to recoup the commission cost. It would only have to rise $0.20 for the investor who owns 100 shares. It is evident that the percentage of trading commissions is lower on larger volume trades and the effect would be even more pronounced if the trades had been placed through a retail broker.
LG4
9. Describe the difference in the timing of trade execution and the certainty of trade price between market orders and limit orders. Market makers fill market orders immediately at the current stock price. This provides the liquidity an investor needs to buy and sell stocks quickly. However, the price at which the stock will fill cannot be guaranteed. With limit orders, the market maker will only fill the order when the stated price is reached. This means that you can count on the execution only after your target buy or sell price is reached, but you cannot guarantee your trade will execute with a limit order.
LG5
10. What are the differences between common stock and preferred stock? Common stock dividends change over time, hopefully increasing in the long-term. Preferred stock pays a constant dividend. Preferred stockholders have higher precedence for payment in the event of firm liquidation from bankruptcy. However, preferred stockholders do not have voting rights that common stockholders enjoy. Preferred stock prices fluctuate with market interest rates and behave like corporate bond prices. Common stock price changes with the value of the company’s underlying business.
LG5
11. How important is growth to a stock’s value? Illustrate with examples.
Chapter 08 - Valuing Stocks
Consider two firms with a common next period dividend of $1, a common market discount rate of 8 percent, but differing growth rates of 3 percent and 5 percent, respectively. The implied current prices of these stocks are $20 [= $1 / (0.08 - 0.03)] and $33.33 [= $1 / (0.08 - 0.05)] respectively. The firm with higher growth prospects (5 percent) is valued more highly than the firm with lower growth rate prospects (3 percent). LG5
12. Under what conditions would the constant growth rate model not be appropriate? When the growth rate exceeds the discount rate, the constant growth rate model cannot be employed. It is also not appropriate when the growth rate cannot reasonably be expected to be constant into the future.
LG5
13. The expected return derived from the constant growth rate model relies on dividend yield and capital gain. Where do these two parts of the return come from? Rearranging the terms and solving for the i from the constant growth model yields the expected return model. The components are the dividend yield and the capital gain. The dividend yield reflects the percentage return from current firm operations. The capital gain captures the firm’s future growth prospects. Both components are important from an investor point of view, with dividends providing income to an investor over the stock holding period and the capital gain being realized at the time of stock sale.
LG6
14. Describe, in words, how to use the variable growth rate technique to value a stock. When the firm is growing at a very fast pace in its infancy, the expected growth rate will initially be very large. This rate should be used for the high growth period, but a terminal growth rate should be employed for valuation when the firm matures. Essentially, a firm cannot grow faster than the general economy indefinitely and must be capped in the long term by its mature growth rate.
LG6
15. Can the variable growth rate model be used to value a firm that has a negative growth rate in Stage 1 and a stable and positive growth rate in Stage 2? Explain. In this case, the firm would be contracting over a short period and then reaching a stable, positive growth rate. Insofar as the initial rate during contraction does not dominate the later mature growth rate, this is possible. It would suggest that a firm’s dividends in the short term decrease, followed by a positive growth dividend stream in the longer term.
LG7
16. Explain why using the P/E relative value approach may be useful for companies that do not pay dividends. Since dividends are non-existent, the forecast stock price is simply a function of current price and the discount rate. In isolation, it is hard to determine if the firm is under- or overvalued
Chapter 08 - Valuing Stocks
based on this information only. Using the P/E relative value approach, the trailing P/E can be calculated and compared to a firm’s competitors. LG7
17. How is a firm’s changing P/E ratio reflected in the stock price? Give examples. The P/E ratio multiplied by a firm’s earnings result in the stock price. For example, if a firm is experiencing high growth and all other factors are held constant, this will lead to a higher P/E ratio reflecting the growth prospects. Stock prices can change simply because the market changes the P/E ratio appropriate for that stock.
LG7
18. Differentiate the characteristics of growth stocks and value stocks? Taken in tandem, P/E ratios and growth rates illustrate the type of stock a firm is characterized as, growth or income. Firms with high P/E and high growth rates are growth stocks. A comparison across an industry of P/E ratios can be an aid to investors in selecting the best growth stock to purchase. By contrast, firms with low P/E ratios and low growth rates tend to be value stocks.
LG7
19. What’s the relationship between the P/E ratio and a firm’s growth rate? The price of a stock can be modeled with the constant growth rate equation. Note that the denominator is (i – g). So the price relative to earnings is impacted by the growth rate of the firm. A high growth rate will cause a high price and P/E. Thus, high growth firms should have high P/E ratios while low growth rate firms should have low P/E ratios.
LG7
20. Describe the process for using the P/E ratio to estimate a future stock price. Using current earnings and an expected growth rate for these earnings, the current P/E ratio can be multiplied by the estimate of future earnings to produce a price estimate for the future stock value. That is, the current P/E ratio acts as a guide for the stock’s future price. This approach should be employed cautiously by comparing the P/E ratios to similar firms to ensure that the firm you have selected has a reasonable P/E ratio.
Problems Basic Problems LG3
8-1 Stock Index Performance On March 5, 2013, the Dow Jones Industrial Average set a new high. The index closed at 14,253.77, which was up 125.95 that day. What was the return (in percent) of the stock market that day? FV = PV × (1 + i) 14,253.77 = (14,253.77 - 125.95) × (1 + i) i = (14,253.77 / 14,127.82) - 1 = 0.89% or
Chapter 08 - Valuing Stocks
N=1, PV=-14,127.82, PMT=0, FV=14,253.77, CPT I==0.8915LG3 8-2 Stock Index Performance On March 9, 2009, the Dow Jones Industrial Average reached a new low. The index closed at 6,547.05, which was down 79.89 that day. What was the return (in percent) of the stock market that day? FV = PV × (1 + i) 6,547.05 = (6,547.05 + 79.89) × (1 + i) i = (6,547.05 / 6,626.94) - 1 = -1.21% or N=1, PV=-6,626.94, PMT=0, FV=6,547.05, CPT I==-1.2055 LG4
8-3 Buying Stock with Commissions At your discount brokerage firm, it costs $7.95 per stock trade. How much money do you need to buy 200 shares of Pfizer, Inc. (PFE), which trades at $31.40? ($31.40/share × 200 shares) + $7.95 = $6,287.95
LG4 8-4 Buying Stock with Commissions At your discount brokerage firm, it costs $9.50 per stock trade. How much money do you need to buy 300 shares of Time Warner, Inc. (TWX), which trades at $22.62? ($22.62/share × 300 shares) + $9.50 = $6,795.50 LG4 8-5 Selling Stock with Commissions At your full-service brokerage firm, it costs $140 per stock trade. How much money do you receive after selling 200 shares of Nokia Corporation (NOK), which trades at $20.13? ($20.13/share × 200 shares) - $140 = $3,886.00 LG4 8-6 Selling Stock with Commissions At your full-service brokerage firm, it costs $135 per stock trade. How much money do you receive after selling 250 shares of International Business Machines (IBM), which trades at $96.17? ($96.17/share × 250 shares) - $135 = $23,907.50 LG4 8-7 Buying Stock with a Market Order You would like to buy shares of Sirius Satellite Radio (SIRI). The current ask and bid quotes are $3.96 and $3.93, respectively. You place a market buy-order for 500 shares that executes at these quoted prices. How much money did it cost to buy these shares? ($3.96/share × 500 shares) = $1,980.00 LG4 8-8 Buying Stock with a Market Order You would like to buy shares of Coldwater Creek, Inc. (CWTR). The current ask and bid quotes are $20.70 and $20.66, respectively. You place a
Chapter 08 - Valuing Stocks
market buy-order for 200 shares that executes at these quoted prices. How much money did it cost to buy these shares? ($20.70/share × 200 shares) = $4,140.00 LG4 8-9 Selling Stock with a Limit Order You would like to sell 200 shares of Xenith Bankshares (XBKS). The current ask and bid quotes are $4.66 and $4.62, respectively. You place a limit sell-order at $4.65. If the trade executes, how much money do you receive from the buyer? ($4.65/share × 200 shares) = $930.00 LG4 8-10 Selling Stock with a Limit Order You would like to sell 100 shares of Echo Global Logistics, Inc. (ECHO). The current ask and bid quotes are $15.33 and $15.28, respectively. You place a limit sell-order at $15.31. If the trade executes, how much money do you receive from the buyer? ($15.31/share ×100 shares) = $1,531.00 LG5 8-11 Value of a Preferred Stock A preferred stock from Duquesne Light Company (DQUPRA) pays $3.55 in annual dividends. If the required return on the preferred stock is 6.7 percent, what’s the value of the stock? Use equation 8-6, noting that for preferred stock, the growth rate g equals zero: Constant growth model = P = 0
LG5
D0 (1 + g ) i−g
= $3.55 = $52.99 0.067 − 0
8-12 Value of a Preferred Stock A preferred stock from Hecla Mining Co. (HLPRB) pays $3.50 in annual dividends. If the required return on the preferred stock is 6.8 percent, what is the value of the stock? Use equation 8-6, noting that for preferred stock, the growth rate g equals zero: Constant growth model = P = 0
LG7
D0 (1 + g ) i−g
= $3.50 = $51.47 0.068 − 0
8-13 P/E Ratio and Stock Price Ultra Petroleum (UPL) has earnings per share of $1.56 and a P/E ratio of 32.48. What’s the stock price? Use equation 8-10:
( )
Pn = P E En = 32.48 $1.56 = $50.67 n
LG7
8-14 P/E Ratio and Stock Price JP Morgan Chase Co. (JPM) has earnings per share of $3.53 and a P/E ratio of 13.81. What is the price of the stock?
Chapter 08 - Valuing Stocks
Use equation 8-10:
( )
Pn = P E En = 13.81 $3.53 = $48.75 n
intermediate problems LG5
8-15 Value of Dividends and Future Price A firm is expected to pay a dividend of $1.35 next year and $1.50 the following year. Financial analysts believe the stock will be at their price target of $68 in two years. Compute the value of this stock with a required return of 10 percent. Use equation 8-3:
P0 =
D1 D2 + P2 $1.35 $1.50 + $68.00 + = $58.67 + = 2 1+ i (1+ i) 1+ 0.10 (1+ 0.10)2
LG5 8-16 Value of Dividends and Future Price A firm is expected to pay a dividend of $2.05 next year and $2.35 the following year. Financial analysts believe the stock will be at their price target of $110 in two years. Compute the value of this stock with a required return of 12 percent. Use equation 8-3: LG5
P0 =
D1 D2 + P2 $2.05 $2.35 + $110.00 + = + = $91.40 1+ i (1+ i)2 1+ 0.12 (1+ 0.12)2
8-17 Dividend Growth Annual dividends of ATTA Corp grew from $0.96 in 2005 to $1.76 in 2017. What was the annual growth rate? Use equation 4-2: Future value in 12 years = $1.76 = $0.96 (1 + g ) g = 5.18% 12
or N=12, PV=-0.96, PMT=0, FV=1.76, CPT I==5.18 LG5
8-18 Dividend Growth Annual dividends of Generic Electrical grew from $0.66 in 2012 to $1.03 in 2017. What was the annual growth rate? Use equation 4-2: Future value in 5 years = $1.03 = $0.66 (1 + g ) g = 9.31% 5
or N=5, PV=-0.66, PMT=0, FV=1.03, CPT I==9.31 LG5 8-19 Value a Constant Growth Stock Financial analysts forecast Safeco Corp.’s (SAF) growth rate for the future to be 8 percent. Safeco’s recent dividend was $0.88. What is the value of Safeco stock when the required return is 12 percent? Use equation 8-6:
Chapter 08 - Valuing Stocks
Constant growth model = P =
D0 (1 + g )
0
i−g
=
$0.88(1 + 0.08)
= $23.76
0.12 − 0.08
LG5 8-20 Value a Constant Growth Stock Financial analysts forecast Limited Brands’ (LTD) growth rate for the future to be 12.5 percent. LTD’s recent dividend was $0.60. What is the value of Limited Brands’ stock when the required return is 14.5 percent? Use equation 8-6: Constant growth model = P0 =
D0 (1+ g ) $0.60(1+ 0.125) = = $33.75 i−g 0.145 − 0.125
LG5 8-21 Expected Return Ecolap, Inc. (ECL) recently paid a $0.46 dividend. The dividend is expected to grow at a 14.5 percent rate. At a current stock price of $44.12, what is the return shareholders are expecting? First convert D0 to D1: $0.46 × (1 + 0.145) = $0.5267. Then use equation 8-7: Expectedreturn = i =
D1
+ g = ($0.5267 / $44.12) + 0.145 = 15.69%
P0
LG5 8-22 Expected Return Paychex Inc. (PAYX) recently paid an $0.84 dividend. The dividend is expected to grow at a 15 percent rate. At a current stock price of $40.11, what is the return shareholders are expecting? First convert D0 to D1: $0.84 × (1 + 0.15) = $0.966. Then use equation 8-7: Expectedreturn = i =
D1
+ g = ($0.966 / $40.11) + 0.15 = 17.41%
P0
LG6
8-23 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its first dividend of $0.20 per share in three years. This dividend will grow at 11 percent indefinitely. Using a 12 percent discount rate, compute the value of this stock. First compute the year 2 value of the stock using equation 8-6 and then discount this back two years to get the present value of the stock price: Constant growth model = P = 2
P0 = ($20 /1.122 ) = $15.94
D3
= $0.20 /(0.12 − 0.11) = $20.00 i−g
Chapter 08 - Valuing Stocks
LG6
8-24 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay its first dividend of $0.25 per share in two years. This dividend will grow at 10 percent indefinitely. Using an 11.5 percent discount rate, compute the value of this stock. First compute the year 1 value of the stock using equation 8-6 and then discount this back one year to get the present value of the stock price: D2
Constant growth model = P = 1
= $0.25/(0.115 − 0.10) = $16.67
i−g
P0 = ($16.67 /1.115) = $14.95
LG7 8-25 P/E Ratio Model and Future Price Kellogg Co. (K) recently earned a profit of $2.52 per share and has a P/E ratio of 13.5. The dividend has been growing at a 5 percent rate over the past few years. If this growth rate continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio declined to 12 in five years? Under these two scenarios, the future price estimates using equation 8-10 are:
( ) E (1+ g ) = 13.5$2.52 (1+ 0.05) = $43.42
P= P
n
En
5
5
0
( ) E (1 + g ) = 12 $2.52 (1 + 0.05) = $38.59
P= P
En
5
LG7
n
5
0
8-26 P/E Ratio Model and Future Price New York Times Co. (NYT) recently earned a profit of $1.21 per share and has a P/E ratio of 19.59. The dividend has been growing at a 7.25 percent rate over the past six years. If this growth rate continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio increased to 22 in five years? Under these two scenarios, the future price estimates using equation 8-10 are:
( ) E (1 + g ) = 19.59 $1.21 (1 + 0.0725) = $33.64
P= P
n
En
5
5
0
( ) E (1 + g ) = 22 $1.21 (1 + 0.0725) = $37.77
P= P 5
n
En
5
0
advanced problems LG5
8-27 Value of Future Cash Flows A firm recently paid a $0.45 annual dividend. The dividend is expected to increase by 10 percent in each of the next four years. In the fourth year, the stock price is expected to be $80. If the required return for this stock is 13.5 percent, what is its current value? Find the dividends in the next four years: D1 = $0.45 × (1 + 0.10) = $0.495 D2 = $0.495 × (1 + 0.10) = $0.5445
Chapter 08 - Valuing Stocks
D3 = $0.5445 × (1 + 0.10) = $0.5990 D4 = $0.5990 × (1 + 0.10) = $0.6588 Then use equation 8-3 as: P0 =
D3 D2 D +P D1 + + + 4 44 2 3 1 + i (1 + i) (1 + i) (1 + i)
= $0.495 /1.135 + $0.5445 /1.1352 + $0.5990 /1.1353 + ($0.6588 + $80) /1.1354 = $49.87
LG5
8-28 Value of Future Cash Flows A firm recently paid a $0.60 annual dividend. The dividend is expected to increase by 12 percent in each of the next four years. In the fourth year, the stock price is expected to be $110. If the required return for this stock is 14.5 percent, what is its current value? Find the dividends in the next four years: D1 = $0.60 × (1 + 0.12) = $0.672 D2 = $0.672 × (1 + 0.12) = $0.7526 D3 = $0.7526 × (1 + 0.12) = $0.8430 D4 = $0.8430 × (1 + 0.12) = $0.9441 Now use equation 8-3: P0 =
D3 D2 D + P4 D1 + + + 4 2 1 + i (1 + i) (1 + i)3 (1 + i)4
= $0.672 /1.145 + $0.7526 /1.1452 + $0.8430 /1.1453 + ($0.9441+ $110) /1.1454 = $66.27
LG5 8-29 Constant Growth Stock Valuation Waller Co. paid a $0.137 dividend per share in 2006, which grew to $0.55 in 2012. This growth is expected to continue. What is the value of this stock at the beginning of 2013 when the required return is 13.7 percent? First calculate the growth rate from 2000 to 2012: FV = PV × (1 + g)12 $0.55 = $0.137 × (1 + g)12 g = ($0.55 / $0.137)1/12 - 1 = 0.1280 Now, use this growth rate in equation 8-6 to obtain the present value of the stock: Constant growth model = P = 0
LG5
D0 (1 + g )
= ($0.55 1.1228) /(0.137 − 0.1280) = $68.93
i−g
8-30 Constant Growth Stock Valuation Campbell Supper Co. paid a $0.632 dividend per share in 2013, which grew to $0.76 in 2016. This growth is expected to continue. What is the value of this stock at the beginning of 2017 when the required return is 8.7 percent? First calculate the growth rate from 2013 to 2016:
Chapter 08 - Valuing Stocks
FV = PV × (1 + g)3 $0.76 = $0.632 × (1 + g)3 g = ($0.76 / $0.632)1/3 - 1 = 0.0634 Now, use this growth rate in equation 8-6 to obtain the present value of the stock: Constant growth model = P = 0
D0 (1+ g )
= ($0.761.0634) /(0.087 − 0.0634) = $34.25
i−g
LG5 8-31 Changes in Growth and Stock Valuation Consider a firm that had been priced using a 10 percent growth rate and a 12 percent required return. The firm recently paid a $1.20 dividend. The firm has just announced that because of a new joint venture, it will likely grow at a 10.5 percent rate. How much should the stock price change (in dollars and percentage)? Use equation 8-6 to calculate the firm’s value prior to the venture: Constant growth model = P = 0
D0 (1+ g )
= ($1.201.10) /(0.12 − 0.10) = $66.00
i−g
If the firm’s growth rate changes to 10.5 percent, then the new stock price is: Constant growth model = P = 0
D0 (1+ g )
= ($1.201.105) /(0.12 − 0.105) = $88.40
i−g
The dollar amount of this change is $88.40 - $66.00 = $22.40 or 33.94 percent for the 0.5 percent increase in the growth rate. LG5
8-32 Changes in Growth and Stock Valuation Consider a firm that had been priced using an 11.5 percent growth rate and a 13.5 percent required return. The firm recently paid a $1.50 dividend. The firm has just announced that because of a new joint venture, it will likely grow at a 12 percent rate. How much should the stock price change (in dollars and percentage)? Use equation 8-6 to calculate the firm’s value prior to the venture: Constant growth model = P = 0
D0 (1+ g )
= ($1.501.115) /(0.135 − 0.115) = $83.625
i−g
If the firm’s growth rate changes to 12 percent, then the new stock price is: Constant growth model = P = 0
D0 (1+ g )
= ($1.501.12) /(0.135 − 0.12) = $112.00
i−g
The dollar amount of this change is $112.00 - $83.625 = $28.38 or 33.93 percent for the 0.5 percent increase in the growth rate.
Chapter 08 - Valuing Stocks
LG6 8-33 Variable Growth A fast growing firm recently paid a dividend of $0.35 per share. The dividend is expected to increase at a 20 percent rate for the next three years. Afterwards, a more stable 12 percent growth rate can be assumed. If a 13 percent discount rate is appropriate for this stock, what is its value? Use equation 8-8:
(
P = 0
P0 =
D0 1 + g 1
)
(
+
1+ i
D0 1 + g1
(1 + i)
1 + 0.13
)3
i − g2
(1 + i)
3
$0.35(1 + 0.20)
$0.35(1 + 0.20)
+
(1 + 0.13)2
+ $0.35(1 + 0.20) (1 + 0.12) 0.13 − 0.12 3
3
2
+
D0(1 + g1) (1 + g2 ) 3
D0 1 + g 1 + +
2
$0.35(1 + 0.20)
(
)2
(1 + 0.13)3
P0 = $0.372 + $0.395 + $47.36 = $48.13
LG6 8-34 Variable Growth A fastgrowing firm recently paid a dividend of $0.40 per share. The dividend is expected to increase at a 25 percent rate for the next four years. Afterwards, a more stable 11 percent growth rate can be assumed. If a 12.5 percent discount rate is appropriate for this stock, what is its value? Use equation 8-8:
(
P = 0
P0 =
D0 1 + g1 1+ i
)
(
+
D0 1 + g1
(1 + i)
2
$0.40(1 + 0.25) 1 + 0.125
)
(
2
+
D0 1 + g1
(1 + i)
3
$0.40(1.25)
2
+
(1.125)
2
(
)
D0 1 + g1
3
+
D0(1 + g 1) (1 + g 2 ) 4
+
(1 + i) ( )4
i − g2
4
$0.40(1.25)
3
+
)4
(1.125)3
+
$0.40(1.25) (1 + 0.11) $0.40 1.25 + 0.125 − 0.11 4
(1.125)4
= $0.444 + $0.494 + $0.549 + $45.725 = $47.21
LG5 8-35 P/E Model and Cash Flow Valuation Suppose that a firm’s recent earnings per LG7 share and dividend per share are $2.50 and $1.30, respectively. Both are expected to grow at 8 percent. However, the firm’s current P/E ratio of 22 seems high for this growth rate. The P/E ratio is expected to fall to 18 within five years. Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using a 10 percent required rate. Find the dividends in the next four years: D1 = $1.30 × (1 + 0.08) = $1.404 D2 = $1.404 × (1 + 0.08) = $1.516 D3 = $1.516 × (1 + 0.08) = $1.638 D4 = $1.638 × (1 + 0.08) = $1.769 D5 = $1.769 × (1 + 0.08) = $1.910
Chapter 08 - Valuing Stocks
Next, use equation 8-10 to calculate the stock price in year 5:
( E) E = (P E) E (1 + g ) = 18 $2.50 (1.08) = $66.12
P5 = P
5
5
5
5
5
0
Now find the present value of these cash flows using a 10 percent discount rate to get P0: P0 =
D2 D3 D4 D +P D1 + + + + 5 55 2 3 4 1 + i (1+ i) (1+ i) (1+ i) (1+ i)
= $1.404 /1.10 + $1.516 /1.102 + $1.638 /1.103 + $1.769 /1.104 + ($1.910 + $66.12) /1.105 = $47.21
LG5 8-36 P/E Model and Cash Flow Valuation Suppose that a firm’s recent earnings per LG7 share and dividend per share are $2.75 and $1.60, respectively. Both are expected to grow at 9 percent. However, the firm’s current P/E ratio of 23 seems high for this growth rate. The P/E ratio is expected to fall to 19 within five years. Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using an 11 percent required rate. Find the dividends in the next four years: D1 = $1.60 × (1 + 0.09) = $1.744 D2 = $1.744 × (1 + 0.09) = $1.901 D3 = $1.901 × (1 + 0.09) = $2.072 D4 = $2.072 × (1 + 0.09) = $2.258 D5 = $2.258 × (1 + 0.09) = $2.462 Next, use equation 8-10 to calculate the stock price in year 5:
( E) E = (P E) E (1 + g ) = 19 $2.75 (1.09) = $80.39
P5 = P
5
5
5
5
5
0
Now find the present value of these cash flows using an 11 percent discount rate to get P0: P0 =
D3 D + P5 D2 D4 D1 + + 5 + + 2 1 + i (1 + i) (1 + i)3 (1 + i)4 (1 + i)5
= $1.744 /1.11+ $1.901/1.112 + $2.072 /1.113 + $2.258 /1.114 + ($2.462 + $80.39) /1.115 = $55.29
8-37 Spreadsheet Problem Spreadsheets are especially useful for computing stock value under different assumptions. Consider a firm that is expected to pay the following dividends: Year 1 2 3 4 5 6 $1.20 $1.20 $1.50 $1.50 $1.75 $1.90 and grow at 5 percent thereafter A. Using an 11 percent discount rate, what would be the value of this stock? B. What is the value of the stock using a 10 percent discount rate? A 12 percent discount rate?
Chapter 08 - Valuing Stocks
C. What would the value be using a 6 percent growth rate after Year 6 instead of the 5 percent rate using each of these three discount rates? D. What do you conclude about stock valuation and its assumptions? SOLUTION:
Present Value
At 5 percent growth:
Year 1 2 3 4 5 6
Dividend $1.20 $1.20 $1.50 $1.50 $1.75 $1.90
6 @ 11% 6 @ 10% 6 @ 12%
Terminal Price $33.25 $39.90 $28.50 Sum =
11% Discount Rate $1.08 $0.97 $1.10 $0.99 $1.04 $1.02
Dividend $1.20 $1.20 $1.50 $1.50 $1.75 $1.90
6 @ 11% 6 @ 10% 6 @ 12%
Terminal Price $40.28 $50.35 $33.57 Sum =
12% Discount Rate $1.07 $0.96 $1.07 $0.95 $0.99 $0.96
$17.78 $22.52 $14.44 $23.97
$28.92
$20.44
Present Value
At 6 percent growth:
Year 1 2 3 4 5 6
10% Discount Rate $1.09 $0.99 $1.13 $1.02 $1.09 $1.07
11% Discount Rate $1.08 $0.97 $1.10 $0.99 $1.04 $1.02
10% Discount Rate $1.09 $0.99 $1.13 $1.02 $1.09 $1.07
12% Discount Rate $1.07 $0.96 $1.07 $0.95 $0.99 $0.96
$21.54 $28.42 $17.01 $27.73
$34.81
$23.01
Chapter 08 - Valuing Stocks
a. From the table calculated in Excel, the value of the stock based on an 11 percent discount rate would be $23.97. b. From the table, the value of the stock based on a 10 percent discount rate would be $28.92 and based on a 12 percent discount rate would be $20.44. c. From the table, the value of the stock that grows at 6 percent (rather than 5 percent) in year 7 and after causes a higher stock value than a future 5 percent growth. d. Assumptions are crucially important in stock valuation. Minor changes in either the discount rate or the growth assumption rate can have a big impact on stock valuation. 8-38 Spreadsheet Problem Design a spreadsheet similar to the one below to compute the value of a variable growth rate firm over a five-year horizon.
A. What is the value of the stock if the current dividend is $1.30, the first stage growth is 18%, the second stage growth is 9%, and the discount rate is 11%? B. What is the value of the stock if the current dividend is $1.30, the first stage growth is 2%, the second stage growth is 8%, and the discount rate is 9.5%? C. What is the value of the stock if the current dividend is $2.50, the first stage growth is 15%, the second stage growth is 7%, and the discount rate is 10%? SOLUTION A.
B.
Chapter 08 - Valuing Stocks
C.
Research It!: Stock Screener Investors can choose from many thousands of stocks. The large number to choose from can be quite daunting to new investors. Fortunately, some good stock screeners are available for free on the Internet that will find only the kinds of companies the investor is looking for. Looking for small value companies? A stock screen at Yahoo! Finance will show all the stocks that meet the three criteria of (1) market capitalization between $250 million and $1 billion, (2) P/E ratio less than or equal to 10, and (3) a quick ratio greater or equal to 1.0. In September of 2010, 127 firms met all three of these criteria. Yahoo! Finance provides 18 screens like this one to choose from. Pick one of these pre-set screens. Discuss the kinds of stocks the screen will find and report on those companies.(http://screener.finance.yahoo.com/presetscreens.html) SOLUTION: Consider the preset screen for Large Cap Value. The stock screener description is as follows: Stocks with market capitalizations greater than or equal to $5 billion with a price-earnings ratio less than or equal to 15 and a quick ratio of greater than or equal to 1.0. Selecting this prescreen yields many of the big, mature firms you would expect, such as ExxonMobil (XOM), Pfizer, Inc. (PFE), Goldman Sachs (GS) and Fedex Corp (FDX). These are mature firms in their industry that command very large capitalizations ($417 billion for XOM) and are favored investments for larger institutional investors. These firms tend to be leaders in their industry and offer an attractive stream of dividends for their investors.
Chapter 08 - Valuing Stocks
integrated minicase: Valuing Carnival Corporation Carnival Corp. (CCL) provides cruises to major vacation destinations. Carnival operates 99 cruise ships in North America, Europe, Australia, and Asia. The company also operates hotels, sightseeing motor coaches and rail cars, and luxury day boats. These activities generated earnings per share of $2.69 for 2015. The stock price at the end of 2015 was $54.48. The previous stock prices and dividends are shown in the following table.
Annual dividend Stock price at the end of the year
2008 2009 2010 2011 2012 2013 2014 2015 $ 1.20 $ 0.00 $ 0.40 $1.00 $1.00 $1.50 $1.00 $1.10 $20.77 $27.06 $39.81 $28.97 $34.07 $38.29 $44.31 $54.48
Carnival is a firm in the General Entertainment industry, which is in the Services sector. The following table shows some key statistics for Carnival, the industry, and the sector. Key Statistic P/E ratio Dividend yield Next 5-year growth
Carnival
Services Sector General Entertainment 20.26 19.75 18.60 2.67% 3.17% 1.57% 18.00% 17.65% 14.72%
Use the various valuation models and relative value measures to assess whether Carnival stock is correctly valued. Compute value estimates from multiple models. The appropriate required rate of return is 11 percent. It will be useful to calculate the stock price for the end of 2015 from various methods to compare to the actual value realized at the time, $54.48 per share. Note that the next 5 year expected growth rate is currently the higher than the discount rate, so the constant growth rate model cannot be used. (1) Determine the dividends to year 5 using the same growth rate at which the dividends had been growing the last 3 years and then use a terminal P/E ratio of 20.26 to compute the future price. Then find the PV of these cash flows. So first, determine the historical dividend growth rate: Future value in 3 years = 1.10 = 1.00 (1 + g ) g = 3.2% 3
Now use this 3.2 percent growth rate to find the next five dividends: D1 = $1.10 × (1 + 0.032) = $1.135 D2 = $1.135× (1 + 0.032) = $1.172 D3 = $1.172 × (1 + 0.032) = $1.209
Chapter 08 - Valuing Stocks
D4 = $1.209× (1 + 0.032) = $1.248 D5 = $1.248 × (1 + 0.032) = $1.288 Next, use equation 8-10 to calculate the stock price in year 5:
( ) E = (P ) E (1+ g ) = 20.26 $2.69 (1.032) = $63.80
P= P
5
E5
5
5
E5
5
0
Now find the present value, P0, of these cash flows: P0 =
D2 D3 D4 D +P D1 + + + + 5 55 2 4 3 1+ i (1+ i) (1+ i) (1+ i) (1+ i)
= $1.135 / 1.11+ $1.172 / 1.112 + $1.209 / 1.113 + $1.248 / 1.114 + ($1.288 + $63.80) / 1.115 = $42.30.
(2) Use the same procedure, but this time use the 18% expected growth rate. Now use this 18.0 percent growth rate to find the next five dividends: D1 = $1.10 × (1 + 0.18) = $1.298 D2 = $1.298 × (1 + 0.18) = $1.532 D3 = $1.532 × (1 + 0.18) = $1.807 D4 = $1.807 × (1 + 0.18) = $2.133 D5 = $2.133 × (1 + 0.18) = $2.517 Next, use equation 8-10 to calculate the stock price in year 5:
( ) E = (P ) E (1+ g ) = 20.26 $2.69 (1.18) = $124.680
P= P 5
5
E5
5
E5
5
0
Now find the present value, P0, of these cash flows: P0 =
D +P D2 D3 D4 D1 + 5 55 + + + 2 4 3 1+ i (1+ i) (1+ i) (1+ i) (1+ i)
= $1.298 / 1.11+ $1.532 / 1.112 + $1.807 / 1.113 + $2.133 / 1.114 + ($2.517 + $124.68) / 1.115 = $80.63
(3) Note that the expected return from equation 8-7 is: Expectedreturn = i =
D1
+ g = 2.02% + 18.0% = 20.02%
P0
This is higher than the proposed discount rate of 11 percent. This suggests that the stock is undervalued.
The results of (2) and (3) suggest that Carnival appears undervalued. However, (1) suggests that it is overvalued.
Chapter 08 - Valuing Stocks
Chapter 09 - Characterizing Risk and Return
CHAPTER 9 – CHARACTERIZING RISK AND RETURN Questions LG1
1. Why is the percentage return a more useful measure than the dollar return? The dollar return is most important relative to the amount invested. Thus, a $100 return is more impressive from a $1,000 investment than a $5,000 investment. The percentage return incorporates both the dollar return and the amount invested. Therefore, it is easier to compare percentage returns across different investments.
LG2
2. Characterize the historical return, risk, and risk-return relationship of the stock, bond and cash markets. Examining Table 9.2, it is clear that the stock market has earned about double the return since 1950 than bonds. Bonds have returned about 50 percent more than the cash markets. The risk in the stock market is also higher than the bond and cash markets according to the standard deviation measurement (Table 9.4). Another illustration of the high risk is that the stock market frequently loses money and sometimes does not earn more than the bond and cash markets over short periods of time (Table 9.2). The risk-return relationship tells us that we should expect higher returns on riskier investments.. In fact, we do see higher realized returns over the longterm on the higher-risk asset classes.
LG3
3. How do we define risk in this chapter and how do we measure it? Risk is defined as the volatility of an asset’s returns over time. Specifically, the standard deviation of returns is used to measure risk. This computation measures the deviation from the average return. The idea is to use standard deviation, a measure of volatility of past returns as a proxy for how variable returns are expected to be in the future.
LG3
4. What are the two components of total risk? Which component is part of the risk-return relationship? Why? Total risk includes firm-specific risk and market risk. The firm-specific risk portion can be eliminated through diversification by owning many different investments. The portion of total risk that is left after diversifying, market risk, is the risk that is expected to be rewarded. Thus, market risk in the risk of the risk-return relationship.
Chapter 09 - Characterizing Risk and Return
LG3
5. What’s the source of firm-specific risk? What’s the source of market risk? Firm-specific risk stems from the uncertainty arising from micro-events that primarily impact the firm or industry. Market risk comes from the macro events that impact all firms to some extent.
LG3
6. Which company is likely to have lower total risk, General Electric or Coca-Cola? Why? General Electric is a firm that has diversified business lines. It makes kitchen appliances, medical devices, and locomotives, owns the TV network NBC, and is involved in financial services. Thus, much of GE’s firm-specific risk is reduced. Coca-Cola does not have such business line diversification. So GE’s total risk is likely to be lower because its firm-specific risk is lower.
LG3
7. Can a company change its total risk level over time? How? A company can change its risk level over time by changing the mix of business lines it pursues. Some industries are riskier than others. For example, the airline industry has more risk while the utility industry has less risk. Companies can also change their risk level by changing the amount of money they have borrowed (more borrowing is riskier).
LG4
8. What does the coefficient of variation measure? Why is a lower value better for the investor? The coefficient of variation measures the amount of risk taken for each one percent of return achieved. It is computed by dividing the standard deviation of return by the total return. Investors would prefer to achieve a high return with little risk. In other words, they would like a high return with little standard deviation. This is realized in the coefficient of variation measure by a lower number.
LG4 9. You receive an investment newsletter advertisement in the mail. The letter claims that you should invest in a stock that has doubled the return of the S&P 500 Index over the last three months. It also claims that this stock is a surefire safe bet for the future. Explain how these two claims are inconsistent with finance theory. A stock that can earn a large return quickly versus the market is a very volatile stock. Thus, it is a high-risk stock. The stock’s price may indeed increase in the future. However, high risk means that it could also significantly decrease in price in the future. It is not a surefire safe bet. LG5
10. What does diversification do to the risk and return characteristics of a portfolio?
Chapter 09 - Characterizing Risk and Return
Diversifying does little for the return of the portfolio. The portfolio return is the weighted average of the investment returns in the portfolio. However, diversification can do much for reducing the total risk of the portfolio as measured by the standard deviation. By combining assets that perform differently in different economic environments, the overall level of the risk in the portfolio is reduced. In addition, diversifying reduces the firm- specific risk as illustrated in figure 9.1. LG5 11. Describe the diversification potential of two assets with a −0.8 correlation. What’s the potential if the correlation is +0.8? The diversification potential is very good with two assets that have a −0.8 correlation. Since these two assets tend to move in opposite directions, the combination will greatly reduce the risk or volatility an investor would experience with only one of the assets. There is not much diversification potential for two assets with a correlation close to one, like +0.8. LG5 12. You are a risk adverse investor with a low-risk portfolio of bonds. How is it possible that adding some stocks (which are riskier than bonds) to the portfolio can lower the total risk of the portfolio? Bonds and stocks have a low correlation (see Table 9.6). In some economic environments, stocks do well and bonds do not. During other times, bonds do better. Adding a small portion of stocks to a bond portfolio can actually decrease the volatility of the portfolio. LG5 13. You own only two stocks in your portfolio but want to add more. When you add a third stock, the total risk of your portfolio declines. When you add a tenth stock to the portfolio, the total risk declines. Adding which stock, the third or the tenth, likely reduced the total risk more? Why? A portfolio of two stocks most likely still has a lot of firm-specific risk. Assuming that the stocks are not highly correlated, a nine-stock portfolio should already have much of its firmspecific risk diversified away. Therefore, the third stock added has much more potential for reducing the risk of the portfolio than the tenth stock added. LG5 14. Many employees believe that their employer’s stock is less likely to lose half of its value than a well diversified portfolio of stocks. Explain why this belief is erroneous. A single firm has a lot of firm-specific risk. This means that it has more volatility in its returns than the overall stock market. Remember, high volatility means large price changes. Also consider that if a well diversified stock portfolio falls by half, this means large declines for the overall stock market and all firms, including the employer’s stock (known as market risk). But a large decline in the employer’s stock does not mean a large decline occurs in the overall market (firm-specific risk). LG6
15. Explain what we mean when we say that one portfolio dominates another portfolio?
Chapter 09 - Characterizing Risk and Return
A dominate portfolio has a better risk-return relationship. This means that it either has a high return for the level of risk taken or lower risk for the level of return achieved. Every investor should want a dominate portfolio. LG6
16. Explain what the efficient frontier is and why it is important to investors. The efficient frontier is the set of efficient, or dominating, portfolios. These portfolios have the highest return for each level of risk desired. Since all other portfolios are dominated by the efficient frontier portfolios, all investors should prefer these efficient portfolios.
LG6 17. If an investor’s desired risk level changes over time, should the investor change the composition of his or her portfolio? How? Yes, investors should modify their portfolios to be consistent with their level of risk. For example, many people want to reduce their level of risk as they approach their retirement years. One way to change the level of risk in a portfolio is to change the allocation of stocks and bonds. An increase in bonds would cause a decrease in the risk of the portfolio. LG7 18. Say you own 200 shares of Boeing and 100 shares of Bank of America. Would your portfolio return be different if you instead owned 100 shares of Boeing and 200 shares of Bank of America? Why? The portfolio return would be the weighted average of the Boeing and Bank of America stock returns. The weights are determined by the proportion of money invested in each firm. The portfolio’s return in these two cases would be different because the proportions of money invested in each stock would be different.
Problems basic problems LG1
9-1 Investment Return FedEx Corp stock ended the previous year at $103.39 per share. It paid a $0.35 per share dividend last year. It ended last year at $106.69. If you owned 200 shares of FedEx, what was your dollar return and percent return? Dollar Return = (Ending Value − Beginning Value) + Income = $106.69 200 - $103.39 200 + $0.35 200 = $700
Percentage Return = $700 / ($103.39 × 200) = 3.53% LG1 9-2 Investment Return Sprint Nextel Corp stock ended the previous year at $23.36 per share. It paid a $2.37 per share dividend last year. It ended last year at $18.89. If you owned 500 shares of Sprint, what was your dollar return and percent return?
Chapter 09 - Characterizing Risk and Return
Dollar Return = (Ending Value − Beginning Value)+ Income = $18.89 500 - $23.36 500 + $2.37 500 = −$1,050 Percentage Return = -$1,050 / ($23.36 × 500) = -8.99% LG2
9-3 Investment Return A corporate bond that you own at the beginning of the year is worth $975. During the year, it pays $35 in interest payments and ends the year valued at $965. What was your dollar return and percent return? Dollar Return = Capital gain + Income = $965 - $975 + $35 = $25 Percent return = $25 / $975 = 2.56%
LG2
9-4 Investment Return A Treasury bond that you own at the beginning of the year is worth $1,055. During the year, it pays $35 in interest payments and ends the year valued at $1,065. What was your dollar return and percent return? Dollar Return = Capital gain + Income = $1,065 - $1,055 + $35 = $45 Percent return = $45 / $1,055 = 4.27%
LG3 9-5 Total Risk Rank the following three stocks by their level of total risk, highest to lowest. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent; and of Poker-R-Us are 9 percent and 20 percent. Rank by standard deviation: Idol Staff, Rail Haul, and then Poker-R-Us LG3 9-6 Total Risk Rank the following three stocks by their total risk level, highest to lowest. Night Ryder has an average return of 12 percent and standard deviation of 32 percent. The average return and standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. Rank by standard deviation: Fruit Fly, Night Ryder, and then WholeMart LG4 9-7 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. Rail Haul has an average return of 12 percent and standard deviation of 25 percent. The average return and standard deviation of Idol Staff are 15 percent and 35 percent; and of PokerR-Us are 9 percent and 20 percent. Rank by coefficient of variation: Rail Haul CoV = 25 / 12 = 2.08, Poker-R-Us CoV = 20 / 9 = 2.22, and Idol Staff CoV = 35 / 15 = 2.33.
Chapter 09 - Characterizing Risk and Return
LG4 9-8 Risk versus Return Rank the following three stocks by their risk-return relationship, best to worst. Night Ryder has an average return of 12 percent and standard deviation of 32 percent. The average return and standard deviation of WholeMart are 11 percent and 25 percent; and of Fruit Fly are 16 percent and 40 percent. Rank by coefficient of variation: WholeMart CoV = 25 / 11 = 2.27, Fruit Fly CoV = 40 / 16 = 2.5,and Night Ryder CoV = 32 / 12 = 2.67 LG6 9-9 Dominant Portfolios Determine which one of these three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Blue has an expected return of 12 percent and risk of 18 percent. The expected return and risk of portfolio Yellow are 15 percent and 17 percent, and for the Purple portfolio are 14 percent and 21 percent. Portfolio Yellow dominates Portfolios Blue and Purple because it has both a higher expected return and a lower risk level. LG6 9-10 Dominant Portfolios Determine which one of the three portfolios dominates another. Name the dominated portfolio and the portfolio that dominates it. Portfolio Green has an expected return of 15 percent and risk of 21 percent. The expected return and risk of portfolio Red are 13 percent and 17 percent, and for the Orange portfolio are 13 percent and 16 percent. Portfolio Orange dominates Portfolio Red because it has the same expected return with a lower risk level. LG7 9-11 Portfolio Weights An investor owns $6,000 of Adobe Systems stock, $5,000 of Dow Chemical, and $5,000 of Office Depot. What are the portfolio weights of each stock? Total portfolio = $6,000 + $5,000 + $5,000 = $16,000 Adobe System weight = $6,000 / $16,000 = 0.3750 Dow Chemical weight = $5,000 / $16,000 = 0.3125 Office Depot weight = $5,000 / $16,000 = 0.3125 LG7 9-12 Portfolio Weights An investor owns $3,000 of Adobe Systems stock, $6,000 of Dow Chemical, and $7,000 of Office Depot. What are the portfolio weights of each stock? Total portfolio = $3,000 + $6,000 + $7,000 = $16,000 Adobe System weight = $3,000 / $16,000 = 0.1875 Dow Chemical weight = $6,000 / $16,000 = 0.375 Office Depot weight = $7,000 / $16,000 = 0.4375 LG7 9-13 Portfolio Return Year-to-date, Oracle had earned a −1.34 percent return. During the same time period, Valero Energy earned 7.96 percent and McDonalds earned 0.88 percent. If you have a portfolio made up of 30 percent Oracle, 25 percent Valero Energy, and 45 percent McDonalds, what is your portfolio return?
Chapter 09 - Characterizing Risk and Return
Portfolio Return = (0.30 × −1.34%) + (0.25 × 7.96%) + (0.45 × 0.88%) = 1.98% LG7 9-14 Portfolio Return Year to date, Yum Brands had earned a 3.80 percent return. During the same time period, Raytheon earned 4.26 percent and Coca-Cola earned −0.46 percent. If you have a portfolio made up of 30 percent Yum Brands, 30 percent Raytheon, and 40 percent CocaCola, what is your portfolio return? Portfolio Return = (0.3 × 3.80%) + (0.3 × 4.26%) + (0.4 × −0.46%) = 2.23% intermediate problems LG1
9-15 Average Return The past five monthly returns for Kohl’s are 4.11 percent, 3.62 percent, −1.68 percent, 9.25 percent, and −2.56 percent. What is the average monthly return? Average Return = (4.11% + 3.62% − 1.68% + 9.25% − 2.56%) / 5 = 2.548%
LG1
9-16 Average Return The past five monthly returns for PG&E are −3.17 percent, 3.88 percent, 3.77 percent, 6.47 percent, and 3.58 percent. What is the average monthly return? Average Return = (−3.17% + 3.88% + 3.77% + 6.47% + 3.58%) / 5 = 2.906%
LG3 9-17 Standard Deviation Compute the standard deviation of Kohls’ monthly returns shown in Problem 9-15. (4.11% − 2.548%)2 + (3.62% − 2.548%)2 + (−1.68% − 2.548%)2 + (9.25% − 2.548%)2 + (− 2.56% − 2.548%)2 5 −1
LG3
= 4.81%
9-18 Standard Deviation Compute the standard deviation of PG&E’s monthly returns shown in Problem 9-16. (− 3.17% − 2.906%)2 + (3.88% − 2.906%)2 + (3.77% − 2.906%)2 + (6.47% − 2.906%)2 + (3.58% − 2.906%)2 = 3.60% 5 −1
LG2&4 9-19 Risk versus Return in Bonds Assess the risk-return relationship of the bond market (see Tables 9.2 and 9.4) during each decade since 1950. Compute the coefficient of variation for each decade using the standard deviation and average return: Decade 1950s
CoV NA
Chapter 09 - Characterizing Risk and Return
1960s 1970s 1980s 1990s 2000s
3.88 1.19 1.12 1.35 1.29
The lower the coefficient of variation, the better the risk-return relationship. The early two decades, 1950s and 1960s, have a poor risk-return relationship for bonds. The 1950s coefficient of variation is not defined because the average return is zero. The poor relationship in the 1960s is caused by the very low return in that decade. The three full decades since 1970 have had a good risk-return relationship. LG2&4 9-20 Risk versus Return in T-bills Assess the risk-return relationship in T-bills (see Tables 9.2 and 9.4) during each decade since 1950. Compute the coefficient of variation for each decade using the standard deviation and average return: Decade 1950s 1960s 1970s 1980s 1990s 2000s
CoV 0.40 0.33 0.29 0.29 0.24 0.68
The lower the coefficient of variation, the better the risk-return relationship. All these CoVs are very low. While they appear to have great risk-return relationships, it is because the risk is very low. T-bills are very safe instruments. However, they offer very low returns. LG4&5 9-21 Diversifying Consider the characteristics of the following three stocks: Expected Standard Return Deviation Thumb 13% 23% Devices Air Comfort 10 19 Sport Garb 10 17 The correlation between Thumb Devices and Air Comfort is −0.12. The correlation between Thumb Devices and Sport Garb is −0.21. The correlation between Air Comfort and Sport Garb is 0.77. If you can pick only two stocks for your portfolio, which would you pick? Why?
Chapter 09 - Characterizing Risk and Return
Air Comfort and Sport Garb have similar expected returns and standard deviations. Since their correlation is very high, minimal risk reduction will occur by combining these two stocks.. Combining either stock with Thumb Devices has good potential for risk reduction as they have a low (negative) correlation. Since Sport Garb has both lower risk (standard deviation) and lower correlation with Thumb Devices than does Air Comfort, you should combine Sport Garb and Thumb Devices. LG4&5 9-22 Diversifying Consider the characteristics of the following three stocks: Expected Standard Return Deviation Pic Image 11% 19% Tax Help 9 19 Warm Wear 14 25 The correlation between Pic Image and Tax Help is 0.88. The correlation between Pic Image and Warm Wear is −0.21. The correlation between Tax Help and Warm Wear is −0.19. If you can pick only two stocks for your portfolio, which would you pick? Why? Pic Image and Tax Help have similar expected returns and standard deviations. Since their correlation is very high, minimal risk reduction will occur by combining these two stocks. Combining either stock with Warm Wear has good potential for risk reduction as they have a low (negative) correlation. Since Pic Image has both higher expected return and lower correlation with Warm Wear than does Tax Help, you should combine Pic Image and Warm Wear. LG7
9-23 Portfolio Weights If you own 200 shares of Alaska Air at $42.88, 350 shares of Best Buy at $51.32, and 250 shares of Ford Motor at $8.51, what are the portfolio weights of each stock? Total portfolio = (200 × $42.88) + (350 × $51.32) + (250 × $8.51) = $28,665.50 Alaska Air weight = (200 × $42.88) / $28,665.50 = 0.299 Best Buy weight = (350 × $51.32) / $28,665.50 = 0.627 Ford Motor weight = (250 × $8.51) / $28,665.50 = 0.074
LG7
9-24 Portfolio Weights If you own 400 shares of Xerox at $17.34, 500 shares of Qwest at $8.15, and 350 shares of Liz Claiborne at $44.73, what are the portfolio weights of each stock? Total portfolio = (400 × $17.34) + (500 × $8.15) + (350 × $44.73) = $26,666.50 Xerox weight = (400 × $17.34) / $26,666.50 = 0.260 Qwest weight = (500 × $8.15) / $26,666.50 = 0.153 Liz Claiborne weight = (350 × $44.73) / $26,666.50 = 0.587
Chapter 09 - Characterizing Risk and Return
LG7
9-25 Portfolio Return At the beginning of the month, you owned $5,500 of General Dynamics, $7,500 of Starbucks, and $8,000 of Nike. The monthly returns for General Dynamics, Starbucks, and Nike were 7.44 percent, −1.36 percent, and −0.54 percent. What is your portfolio return? Total portfolio = $5,500 + $7,500 + $8,000 = $21,000 General Dynamics weight = $5,500 / $21,000 = 0.2619 Starbucks weight = $7,500 / $21,000 = 0.3571 Nike weight = $8,000 / $21,000 = 0.3810 Portfolio return = (0.2619 × 7.44%) + (0.3571 × −1.36%) + (0.3810 × −0.54%) = 1.26%
LG7
9-26 Portfolio Return At the beginning of the month, you owned $6,000 of News Corp, $5,000 of First Data, and $8,500 of Whirlpool. The monthly returns for News Corp, First Data, and Whirlpool were 8.24 percent, −2.59 percent, and 10.13 percent. What’s your portfolio return? Total portfolio = $6,000 + $5,000 + $8,500 = $19,500 News Corp weight = $6,000 / $19,500 = 0.3077 First Data weight = $5,000 / $19,500 = 0.2564 Whirlpool weight = $8,500 / $19,500 = 0.4359 Portfolio return = (0.3077 × 8.24%) + (0.2564 × −2.59%) + (0.4359 × 10.13%) = 6.29% advanced problems
LG2&5 9-27 Asset Allocation You have a portfolio with an asset allocation of 50 percent stocks, 40 percent long-term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 to compute the return of the portfolio in the year 2010 and each year since. Then compute the average annual return and standard deviation of the portfolio and compare them with the risk and return profile of each individual asset class. These answers were computed using a spreadsheet. The portfolio return is computed as: (0.5 × 15.1%) + (0.4 × 9.4%) + (0.1 × 0.01%) = 11.3% 11.3% 13.0% 9.4% 11.1% 16.9% 0.2% 6.5% 14.4% 10.4%
2010 2011 2012 2013 2014 2015 2016 2017 = Ave
5.15
= St Dev
The portfolio has the second highest return with the second lowest level of risk. Combining these assets achieved some risk reduction as seen in the standard deviation.
Chapter 09 - Characterizing Risk and Return
LG2&5 9-28 Asset Allocation You have a portfolio with an asset allocation of 35 percent stocks, 55 percent long-term Treasury bonds, and 10 percent T-bills. Use these weights and the returns in Table 9.2 to compute the return of the portfolio in the year 2010 and each year since. Then compute the average annual return and standard deviation of the portfolio and compare them with the risk and return profile of each individual asset class. These answers were computed using a spreadsheet. The portfolio return is computed as: (0.35 × 15.1%) + (0.55 × 9.4%) + (0.1 × 0.01%) = 10.46% 10.5% 17.2% 7.6% 4.4% 18.6% -0.1% 4.9% 12.4% 9.4%
2010 2011 2012 2013 2014 2015 2016 2017 = Ave
6.5%
= St Dev
The portfolio has the second highest return with the second lowest level of risk. Combining these assets achieved some risk reduction. Compare these results to the results of problem 9-27 to see the effects caused by changing the portfolio weights. LG7
9-29 Portfolio Weights You have $15,000 to invest. You want to purchase shares of Alaska Air at $42.88, Best Buy at $51.32, and Ford Motor at $8.51. How many shares of each company should you purchase so that your portfolio consists of 30 percent Alaska Air, 40 percent Best Buy, and 30 percent Ford Motor? Report only whole stock shares. Alaska Air: 0.30 × $15,000 / $42.88 = 105 shares Best Buy: 0.40 × $15,000 / $51.32 = 117 shares Ford Motor: 0.30 × $15,000 / $8.51 = 529 shares Because of rounding up, this adds up to slightly more than $15,000. So, you might have to purchase a share or two less of a stock to allow for this overage and also to allow for any commission or trading costs.
LG7
9-30 Portfolio Weights You have $20,000 to invest. You want to purchase shares of Xerox at $17.34, Qwest at $8.15, and Liz Claiborne at $44.73. How many shares of each company should you purchase so that your portfolio consists of 25 percent Xerox, 40 percent Qwest, and 35 percent Liz Claiborne? Report only whole stock shares. Xerox: 0.25 × $20,000 / $17.34 = 288 shares Qwest: 0.40 × $20,000 / $8.15 = 982 shares Liz Claiborne: 0.35 × $20,000 / $44.73 = 156 shares Excluding commissions paid, you will still have a cash balance of $24.90.
Chapter 09 - Characterizing Risk and Return
LG7 9-31 Portfolio Return The table below shows your stock positions at the beginning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio dollar return and percentage return? Beginning Dividend End of Company Shares of Year per Year Price Share Price US Bank 300 $43.50 $2.06 $43.43 PepsiCo 200 59.08 1.16 62.55 JDS Uniphase 500 18.88 16.66 Duke Energy 250 27.45 1.26 33.21 Solution by spreadsheet: Company
Beginning Value
Portfolio Capital Weight Gain
Income Total Return
Percentage Return
US Bank PepsiCo JDS Uniphase Duke Energy Total =
$13,050.00 11,816.00 9,440.00 6,862.50 $41,168.50
0.3170 0.2870
($21.00) $618.00 694.00 232.00
0.2293 (1,110.00)
$0.00
0.1667
315.00
1,440.00
$597.00 926.00
4.57% 7.84
(1,110.00)
-11.76
1,755.00 25.57 $2,168.00 Portfolio Return = 5.27%
Chapter 09 - Characterizing Risk and Return
LG7 9-32 Portfolio Return The table below shows your stock positions at the beginning of the year, the dividends that each stock paid during the year, and the stock prices at the end of the year. What is your portfolio dollar return and percentage return?
Company
Shares
Johnson Controls Medtronic Direct TV Qualcomm
350 200 500 250
Beginning of Year Price $72.91 57.57 24.94 43.08
Dividend per Share $1.17 0.41 0.45
End of Year Price $85.92 53.51 24.39 38.92
Solution by spreadsheet:
Company Johnson Controls Medtronic Direct TV Qualcomm Total =
Beginning Value
Portfolio Capital Weight Gain
Income Total Return
$25,518.50
0.4234
$4,553.50 $409.50
$11,514.00 $12,470.00
0.1910 0.2069
(812.00) (275.00)
$10,770.00
0.1787 (1,040.00)
$60,272.50
Percent Return
$4,963.00
19.45%
82.00 0.00
(730.00)
-6.34
(275.00)
-2.21
112.50
(927.50)
-8.61
$3,030.50 Portfolio Return =
5.03%
LG3&4 9-33 Risk, Return, and Their Relationship Consider the following annual returns of Estee Lauder and Lowe’s Companies: Estee Lauder Year 1 Year 2 Year 3 Year 4 Year 5
23.4% −26.0 17.6 49.9 −16.8
Lowe’s Companies −6.0% 16.1 4.2 48.0 −19.0
Chapter 09 - Characterizing Risk and Return
Compute each stock’s average return, standard deviation, and coefficient of variation. Which stock appears better? Why? Solution by spreadsheet: Estee Lowe’s Lauder Companies Average = Std dev = CoV =
9.62%
8.66%
31.00% 3.22
25.51% 2.95
Estee Lauder has experienced a higher average return than Lowe’s but also has more risk (standard deviation). On a risk-return basis, Lowe’s appears to be the better stock as it has less risk per unit of return (coefficient of variation). LG3&4 9-34 Risk, Return, and Their Relationship Consider the following annual returns of Molson Coors and International Paper: Molson International Coors Paper Year 1 16.3% 4.5% Year 2 −9.7 −17.5 Year 3 36.5 −0.2 Year 4 −6.9 26.6 Year 5 16.2 −11.1 Compute each stock’s average return, standard deviation, and coefficient of variation. Which stock appears better? Why? Solution by spreadsheet: Molson International Coors Paper Average = Std dev = CoV =
10.48%
0.46%
19.06% 1.82
17.00% 36.96
Molson Coors has experienced a much higher average return than International Paper with slightly more risk (standard deviation). Thus, it is not a surprise that Molson Coors has a significantly better (lower) coefficient of variation. Molson Coors is superior on a risk-return basis.
Chapter 09 - Characterizing Risk and Return
9-35 Excel Problem Below are the monthly returns for March 2011 to February 2016 of three international stock indices; All Ordinaries of Australia, Nikkei 225 of Japan, and FTSE 100 of England. A. Compute and compare each indices’ monthly average return and standard deviation. B. Compute the correlation between i) All Ordinaries and Nikkei 225, ii) All Ordinaries and FTSE 100, and iii) Nikkei 225 and FTSE 100, and compare them. C. Form a portfolio consisting of one third of each of the indices and show the portfolio return each year, and the portfolio’s return and standard deviation. A. All Ordinaries Ave = Std. Dev. =
NIKKEI 225 FTSE
0.10% 3.63%
0.83% 5.37%
0.05% 3.36%
The NIKKEI 225 index had the highest monthly return with the highest risk. B. Correlations All Ordinaries All Ordinaries NIKKEI 225 FTSE
NIKKEI 225
FTSE
1 0.431 0.688
1 0.529
1
The correlations are quite high. Nikkei and the All Ordinaries are the least correlated. The All Ordinaries and the FTSE have the highest correlation. C. Date February-16 January-16 December-15 November-15 October-15 September-15 August-15 July-15 June-15 May-15 April-15 March-15 February-15 January-15
Portfolio -3.57% -5.30% -0.99% 0.69% 6.41% -4.69% -7.67% 2.88% -4.61% 1.90% 0.96% -0.31% 5.18% 2.37%
Chapter 09 - Characterizing Risk and Return
December-14 November-14 October-14 September-14 August-14 July-14 June-14 May-14 April-14 March-14 February-14 January-14 December-13 November-13 October-13 September-13 August-13 July-13 June-13 May-13 April-13 March-13 February-13 January-13 December-12 November-12 October-12 September-12 August-12 July-12 June-12 May-12 April-12 March-12 February-12 January-12 December-11 November-11 October-11 September-11 August-11 July-11 June-11 May-11 April-11 March-11
-0.22% 1.77% 1.42% -1.29% 0.03% 2.43% 0.16% 1.10% 0.16% -1.14% 2.71% -4.92% 2.08% 2.05% 2.39% 3.51% -1.14% 3.97% -3.04% -1.06% 5.29% 1.77% 3.20% 6.22% 4.61% 2.29% 1.43% 0.81% 1.39% 0.47% 3.39% -8.34% -1.68% 0.89% 5.08% 3.76% -0.10% -3.63% 6.18% -4.88% -6.35% -1.81% -0.72% -1.72% 1.03% -3.17%
Chapter 09 - Characterizing Risk and Return
Ave = Std. Dev. =
0.33% 3.43%
9-36 Spreadsheet Problem Create the spreadsheet below. The spreadsheet should use the returns for assets A and B to form a portfolio return using the weights for each asset shown in cells E1 and E2. The average portfolio return and standard deviation should compute at the bottom of the column of portfolio returns. When you change the weights, the portfolio returns, average, and standard deviation should recalculate. A -9.1% 11.9% -22.1% 28.7% 10.9% 4.9% 15.8% 3.5% -5.5%
32.39% 13.69%
B 20.11% 4.56% 7.17% 2.06% 7.70% -6.50% 1.85% 9.81% 22.7% 12.19% 9.38% 29.93% 3.56% 12.66% 15.07%
9.4% 14.41%
6.8% 12.04%
23.45% 15.06% 2.11% 16.00%
Weight A = Weight B = sum =
0.50 0.50 1
Portfolio 5.51% 8.23% -7.47% 15.38% 9.30% -0.80% 8.82% 6.66% 8.60% 5.63% 12.22% 16.02% 9.78% 9.87% 14.38%
= Average =StDev
Average = StDev =
8.1% 6.07%
A. Create the spreadsheet. B. Use the Solver function to find the weights that provide the highest return for a standard deviation of 6%, 7.5%, 9%, 10.5%, 12%, and 13.5%. Report the weights and the return for each of these portfolio standard deviations. The Solver function is found in the Data tab. (You may have to enable the function through the File tab, then Options, then Add-ins.) The solver image illustrates the maximizing of the average return for the specific constraints. The constraints are that the weights must be between 0 and 1, inclusive, and must sum to 1. Lastly, set the standard deviation constraint to the desired level.
Chapter 09 - Characterizing Risk and Return
A. Student should build the spreadsheet that looks like the one in the problem. B. Answers are: Standard Deviation Weight A Weight B Average Return 6% 0.48 0.52 8.1% 7.5 0.64 0.36 8.5 9 0.73 0.27 8.7 10.5 0.81 0.19 9.0 12 0.89 0.11 9.1 13.5 0.96 0.04 9.3
Research It!: Following a Portfolio Following stocks in a portfolio is easier than ever. Many financial Web sites have the capability to follow the stocks in your portfolio over time. Just enter your stocks, the number of shares, your purchase price, and your commission cost and you can see how your portfolio is doing. These portfolio managers will update your portfolio as stock prices change, minute to minute. Yahoo! Finance has a portfolio management tool. Go to the site and start a portfolio to watch (which requires free registration). Try entering symbols EBAY, T, LMT, DUK, and GSK. As a start, assume you own 200 shares of each. You can watch the value of the portfolio change and see how each stock is doing every day. (http://www.finance.yahoo.com/) The portfolio might look something like this:
Chapter 09 - Characterizing Risk and Return
Chapter 09 - Characterizing Risk and Return
integrated minicase: Diversifying with Other Asset Classes Many more types of investments are available besides stocks, bonds, and cash securities. Many people invest in real estate and in precious metals, primarily gold. What are the risk and return characteristics of these investments and do they provide diversification opportunities to the typical stock investor? You can invest in real estate in many ways. You can build properties, own rental units, and trade raw land. These activities take enormous time and expertise. One of the easiest ways to invest in real estate is through real estate investment trusts (REITs) that trade like stocks on the stock exchanges. A REIT represents ownership in a portfolio consisting of a pool of real estate assets. An index of all REITs is a good measure of the performance of the real estate market. The table below shows the annual returns for the All REITs Index alongside the returns of the S&P 500 Index.
1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
S&P 500 Index 37.2% 23.8% -7.2% 6.6% 18.4% 32.4% -4.9% 21.4% 22.5% 6.3% 32.2% 18.5% 5.2% 16.8% 31.5% -3.2% 30.6% 7.7% 10.0% 1.3% 37.4% 23.1% 33.4% 28.6% 21.0% -9.1% -11.9% -22.1% 28.7% 10.9% 4.9% 15.8%
All REITs Index 36.3% 49.0% 19.1% -1.6% 30.5% 28.0% 8.6% 31.6% 25.5% 14.8% 5.9% 19.2% -10.7% 11.4% -1.8% -17.3% 35.7% 12.2% 18.5% 0.8% 18.3% 35.8% 18.9% -18.8% -6.5% 25.9% 15.5% 5.2% 38.5% 30.4% 8.3% 34.4%
Gold Price -19.9% -4.1% 22.6% 37.0% 126.5% 15.2% -32.6% 14.9% -16.3% -19.2% 5.7% 21.3% 22.2% -15.3% -2.8% -1.5% -10.1% -5.7% 17.7% -2.2% 1.0% -4.6% -21.4% -0.8% 0.9% -5.4% 0.7% 25.6% 19.9% 4.6% 17.8% 24.0%
Chapter 09 - Characterizing Risk and Return
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
3.5% -35.5% 23.5% 15.1% 2.1% 16.0% 32.4% 13.7% 1.4% 12.0% 21.8%
-17.8% -40.0% 20.9% 22.8% 3.6% 15.5% 2.9% 28.0% 2.8% 8.6% 8.7%
31.1% 4.3% 25.0% 25.3% 8.9% 8.3% -27.3% 0.1% -11.9% 7.8% 12.7%
Gold has been a highly sought-after asset all over the world, and has retained at least some economic value over thousands of years. The United States has had a very chaotic history with gold. Americans have sought to “strike it rich” through gold rushes in North Carolina (early 1800s), California and Nevada (mid-1800s), and Alaska (late 1800s). Struggling in the Great Depression, President Franklin D. Roosevelt ordered U.S. citizens to hand in all the gold they possessed. The ban on U.S. citizens owning gold was not lifted until the end of 1974. The table also shows the return from gold prices. The returns for stocks, real estate, and gold are all volatile. However, during many years, the return of one asset is up while the others are down. This looks promising for diversification opportunities. a. Using a spreadsheet, compute the average return and standard deviation of each of the three asset classes. b. Compute the annual returns of a portfolio consisting of 50% stocks / 40% real estate / 10% gold. What is the average return and standard deviation of this portfolio? Also compute the average return and standard deviation of the following portfolios: 75%/20%/5% and 80%/5%/15%. How do these portfolios perform compared to owning just stocks? c. Plot the average return and standard deviation of the three assets and the three portfolios on a risk-return graph like Figure 9.3. SOLUTION: a.
Ave = Std. Dev.=
b.
S&P 500 Index 13.3%
All REITs Index 13.4%
16.2%
18.1%
Gold Price 7.0% 24.9%
Chapter 09 - Characterizing Risk and Return
Ave = Std. Dev.=
50/40/10 12.7%
75/20/5 13.0%
80/5/15 12.4%
13.3%
14.2%
13.6%
The portfolio is dominated by the first portfolio because it has lower return and higher risk. The second portfolio achieved a very slight higher return than the first, but need more risk to do it. c.
14.0% 13.0% 12.0% 50/40/10
Average Return
11.0%
75/20/5 80/5/15
10.0%
S&P 500 Index All REITs Index
9.0%
Gold Price
8.0% 7.0% 6.0% 10.0%
15.0%
20.0%
25.0%
Standard Deviation of Annual Returns
30.0%
Chapter 10 - Estimating Risk and Return
CHAPTER 10 – ESTIMATING RISK AND RETURN Questions LG1
1. Consider an asset that provides the same return no matter what economic state occurs. What would be the standard deviation (or risk) of this asset? Explain. Since this asset has no variation in its return, it will have no standard deviation. This could be shown mathematically by demonstrating that each economic state’s return is the same as its’ average. Therefore, all terms in the standard deviation summation equation are zero. This asset would be known as a risk-free asset.
LG1
2. Why is expected return considered “forward-looking”? practitioners to utilize expected return?
What are the challenges for
Expected return is “forward-looking” in the sense that it represents the return investors expect to receive in the future as compensation for the market risk taken. The challenge is that practitioners cannot precisely know what the future holds and thus what the expected return should be. Thus, we create methods to estimate the expected return. LG2
3. In 2000, the S&P 500 Index earned −9.1 percent while the T-bill yield was 5.9 percent. Does this mean the market risk premium was negative? Explain. The market risk premium is a forward-looking tool and should always be positive. Because the market has risk, it will periodically have a negative return or a small positive return that is smaller than the T-bill rate. Thus, realized returns over a short period of time will sometimes show what appears to be a negative risk premium. However, historical risk premiums should be measured over long periods of time.
LG2
4. How might the magnitude of the market risk premium impact people’s desire to buy stocks? Everybody has a different level of risk aversion. People who have a low level of risk aversion would be willing to buy stocks with high risk. However, people who have a high level of risk aversion would only be willing to buy stocks with low risk. Therefore, the magnitude of the risk premium does impact who wants to buy stocks and the type of stocks they prefer.
Chapter 10 - Estimating Risk and Return
LG3
5. Describe how adding a risk-free security to modern portfolio theory allows investors to do better than the efficient frontier. The best portfolios investors can hold with only risky assets are the efficient portfolios on the efficient frontier. If investors can borrow and lend at a risk-free rate, then they can do better. To improve over the efficient frontier, investors should allocate their portfolio between the risk-free rate and the market portfolio. With the right weights between the two, an investor can find a portfolio with the same level of risk as an efficient portfolio but with a higher expected return.
LG3
6. Show on a graph like Figure 10-2 where a stock with a beta of 1.3 would be located on the security market line. Then show where that stock would be located if it is undervalued. Figure shown: Required Return (%)
Security Market Line Undervalued stock with 1.3 Beta RStock Stock with 1.3 Beta
RM M
Rf
1
1.3
Beta
LG3 7. Consider that you have three stocks in your portfolio and wish to add a fourth. You want to know if the fourth stock will make the portfolio riskier or less risky. Compare and contrast how this would be assessed using standard deviation versus market risk (beta) as the measure of risk. Using standard deviation, you would need to determine how the fourth stock interacts with the three stocks already owned. To do this you would have to compute the correlation between the new stock and each of the three already held. Then, the portfolio standard deviation could be computed. If the new portfolio standard deviation is lower then the original portfolio
Chapter 10 - Estimating Risk and Return
standard deviation, then adding the new stock lowers the risk. Of course, the portions, or weights of all the stocks will matter. Determining whether adding a stock will increase or lower the risk of the portfolio is much easier using beta. If the beta of the fourth stock is higher than the beta of the portfolio, then it will increase the risk when added. LG3 8. Describe how different allocations between the risk-free security and the market portfolio can achieve any level of market risk desired. Give examples of a portfolio from a person who is very risk averse and a portfolio for someone who is not so averse to taking risk. An investor can allocate money between a risk-free security that has zero risk (β = 0), and the market portfolio that has market risk (β = 1). If 75 percent of the portfolio is invested in the market, then the portfolio will have a β = 0.75. If only 25 percent is invested in the market, then the portfolio will have a market risk of β = 0.25. The first example (β = 0.75) might be taken by a less risk averse investor while the second example (β = 0.25) illustrates the portfolio of a more risk averse investor. By allocating the investment money between 0 and 100 percent into the market portfolio, an investor can achieve any level of market risk desired. LG4 9. Cisco Systems has a beta of 1.25. Does this mean that you should expect Cisco to earn a return 25 percent higher than the S&P 500 Index return? Explain. Not quite. A beta of 1.25 means that Cisco’s risk premium is 25 percent higher then the market risk premium. In other words, we must account for the risk-free rate. This relationship is shown in the CAPM equation. LG4 10. Note from Table 10-2 that some technology-oriented firms (Apple) in the Dow Jones Industrial Average have high market risk while others (Intel and Verizon) have low market risk. How do you explain this? Not all technology industries have the same level of risk. Notice from this example that the manufacturing (hardware) tech companies have higher risk. The service and software tech companies have lower risk. This may be an indication of the type of assets needed by the firms and the amount of debt required. LG4 11. Find a beta estimate from three different sources for General Electric (GE). Compare these three values. Why might they be different? Yahoo! Finance beta is 0.59. MSN Money shows a beta of 0.76. Hoovers lists a beta of 0.8. The beta sources may use (i) different market portfolios, (ii) different time periods, or (iii) different time increments (annual returns versus months, weeks, etc.). LG4 12. If you were to compute beta yourself, what choices would you make regarding the market portfolio, the holding period for the returns (daily, weekly, etc.), and the number of returns? Justify your choices.
Chapter 10 - Estimating Risk and Return
It is common to use the S&P 500, monthly returns, and either three or five years of data. LG5
13. Explain how the concept of a positive risk-return relationship breaks down if you can systematically find stocks that are overvalued and undervalued. Consider two stocks: one stock has a beta of 0.9 and is undervalued, the other has a beta of 1 and is overvalued. If beta perfectly explained expected returns, then the higher beta stock would offer a higher expected return. However, if you believe the lower beta stock is undervalued, then you are saying it will achieve a return higher than expected by its beta. You also believe the overvalued stock will earn a return lower than expected by its beta. Thus, you might expect the undervalued stock to outperform the overvalued stock even though the risks of the two stocks suggest otherwise.
LG5
14. Determine what level of market efficiency each event is consistent with: a. Immediately after an earnings announcement the stock price jumps and then stays at the new level. b. The CEO buys 50,000 shares of his company and the stock price does not change. c. The stock price immediately jumps when a stock split is announced, but then retraces half of the gain over the next day. d. An investor analyzes company quarterly and annual balance sheets and income statements looking for undervalued stocks. The investor earns about the same return as the S&P 500 Index. a. b. c. d.
LG5
semi-strong form strong form not efficient semi-strong form
15. Why do most investment scams conducted over the Internet and e-mail involve penny stocks instead of S&P 500 Index stocks? There is tremendous liquidity in the large stocks. As such, these scams would not impact stock prices and thus not be effective. Penny stocks have very little liquidity. So if a few investors buy the stocks in the scam, they will push up the price and allow the scam promoters to sell at a profit.
LG5
16. Describe a stock market bubble. Can a bubble occur in a single stock? Bubbles are initially started with an increase in price that is typically justified by the economics and fundamentals. Then many people get irrationally exuberant about the asset(s) and push prices beyond those that are justified. Eventually, there are no more buyers for the overvalued asset and prices drop. As people begin to believe that the price is a bubble, the price free falls. No one buys the stock while it is plummeting. Yes, a bubble can occur in a single stock.
Chapter 10 - Estimating Risk and Return
LG6
17. If stock prices are not strong-form efficient, then what might be the price reaction to a firm announcing a stock buyback? Explain. Two different arguments could be made. First, the price could increase with the realization that this demand for stock will push up the stock price. Alternatively, the price could decline if investors believe that the company does not have any good product related investments and thus must buy back its stock.
LG7
18. Compare and contrast the assumptions that need to be made to compute a required return using CAPM and the constant growth rate model. When using the CAPM to compute required return, you need to make assumptions about what the expected market return will be, what the risk-free rate will be, and what the future beta of the firm will be. The future beta is commonly similar to the recent past beta. The risk-free rate is well estimated by T-bill rates and the yield curve. These two are reasonably estimated. However, the stock market is very volatile and the future market return is difficult to estimate. The constant growth rate model assumes that the growth of the firm will remain constant. The growth rate and the dividend must be assumed. Firms do not change their dividends very much, so that estimation is not difficult. However, the required rate is very sensitive to the estimated growth rate. Both models require difficult assumptions.
LG7
19. How should you handle a case where required return computations from CAPM and the constant growth rate model are very different? First, examine the assumptions of each model. If no mistakes have been made, then compute the required return for similar firms in the same industry. Use the CAPM or constant growth rate estimate that most resembles that of its competitors.
Problems basic problems LG1
10-1 Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns: Economic State Fast growth Slow growth Recession
Probability Return 0.3 0.4 0.3
40% 10 −25
Expected return = (0.3 × 40%) + (0.4 × 10%) + (0.3 × -25%) = 8.5%
Chapter 10 - Estimating Risk and Return
LG1 10-2 Expected Return Compute the expected return given these three economic states, their likelihoods, and the potential returns: Economic State Fast growth Slow growth Recession
Probability Return 0.2 0.6 0.2
35% 10 −30
Expected return = (0.2 × 35%) + (0.6 × 10%) + (0.2 × -30%) = 7% LG2
10-3 Required Return If the risk-free rate is 3 percent and the risk premium is 5 percent, what is the required return? Required return = 3% + 5% = 8%
LG2
10-4 Required Return If the risk-free rate is 4 percent and the risk premium is 6 percent, what is the required return? Required return = 4% + 6% = 10%
LG2
10-5 Risk Premium The average annual return on the S&P 500 Index from 1986 to 1995 was 15.8 percent. The average annual T-bill yield during the same period was 5.6 percent. What was the market risk premium during these ten years? Average market risk premium = 15.8% − 5.6% = 10.2%
LG2
10-6 Risk Premium The average annual return on the S&P 500 Index from 1996 to 2005 was 10.8 percent. The average annual T-bill yield during the same period was 3.6 percent. What was the market risk premium during these ten years? Average market risk premium = 10.8% − 3.6% = 7.2%
LG3
10-7 CAPM Required Return Hastings Entertainment has a beta of 0.65. If the market return is expected to be 11 percent and the risk-free rate is 4 percent, what is Hastings’ required return? Hastings’ required return = 4% + 0.65 × (11% − 4%) = 8.55%
LG3 10-8 CAPM Required Return Nanometrics, Inc. has a beta of 3.15. If the market return is expected to be 10 percent and the risk-free rate is 3.5 percent, what is Nanometrics’ required return? Nanometrics’ required return = 3.5% + 3.15 × (10% − 3.5%) = 23.98%
Chapter 10 - Estimating Risk and Return
LG3
10-9 Company Risk Premium Netflix, Inc. has a beta of 3.61. If the market return is expected to be 13 percent and the risk-free rate is 3 percent, what is Netflix’ risk premium? Netflicks’ risk premium = 3.61 × (13% − 3%) = 36.1%
LG3 10-10 Company Risk Premium Paycheck, Inc. has a beta of 0.94. If the market return is expected to be 11 percent and the risk-free rate is 3 percent, what is Paycheck’s risk premium? Paycheck’s risk premium = 0.94 × (11% − 3%) = 7.52% LG3 10-11 Portfolio Beta You have a portfolio with a beta of 1.35. What will be the new portfolio beta if you keep 85 percent of your money in the old portfolio and 5 percent in a stock with a beta of 0.78 New portfolio beta = (0.85 × 1.35) + (0.15 × 0.78) = 1.26 LG3 10-12 Portfolio Beta You have a portfolio with a beta of 1.1. What will be the new portfolio beta if you keep 85 percent of your money in the old portfolio and 15 percent in a stock with a beta of 0.5? New portfolio beta = (0.85 × 1.1) + (0.15 × 0.5) = 1.01 LG5 10-13 Stock Market Bubble The Nasdaq stock market bubble peaked at 4,816 in 2000. Two and a half years later it had fallen to 1,000. What was the percentage decline? Market decline = (1,000 − 4,816) / 4,816 = −79.24% LG5 10-14 Stock Market Bubble The Japanese stock market bubble peaked at 38,916 in 1989. Two and a half years later it had fallen to 15,900. What was the percentage decline? Market decline = (15,900 − 38,916) / 38,916 = −59.14% LG7 10-15 Required Return Paccar’s current stock price is $48.20 and it is likely to pay a $0.80 dividend next year. Since analysts estimate Paccar will have an 8.8% growth rate, what is its required return? Use equation 10.6: i =
LG7
D1
+ g = $0.80 + 0.088 = 10.46% $48.20 P0
10-16 Required Return Universal Forest’s current stock price is $57.50 and it is likely to pay a $0.26 dividend next year. Since analysts estimate Universal Forest will have a 9.5 percent growth rate, what is its required return?
Chapter 10 - Estimating Risk and Return
Use equation 10.6: i =
D1
+ g = $0.26 + 0.095 = 9.95% $57.50 P0
intermediate problems LG1
10-17 Expected Return Risk For the same economic state probability distribution in Problem 10-1, determine the standard deviation of the expected return.
Economic State Fast growth Slow growth Recession
Probability Return 0.3 0.4 0.3
40% 10% −25%
Use equation 10-2 and expected return from Problem 10-1 of 8.5%: Standard Deviation = 0.3 (40% − 8.5%) + 0.4 (10% − 8.5%) + 0.3 (−25% − 8.5%) 2 2
2
= 297.7 + 0.9 + 336.7 = 25.21%
LG1
10-18 Expected Return Risk For the same economic state probability distribution in Problem 10-2, determine the standard deviation of the expected return. Economic State Fast growth Slow growth Recession
Probability Return 0.2 0.6 0.2
35% 10% −30%
Use equation 10-2 and expected return from problem 10-2 of 7%: Standard Deviation = 0.2 (35% − 7%) + 0.6 (10% − 7%) + 0.2 (−30% − 7%)2 2
2
= 156.8 + 5.4 + 273.8 = 20.88%
LG3 10-19 Under-/Over Valued Stock A manager believes his firm will earn a 14 percent return next year. His firm has a beta of 1.5, the expected return on the market is 12 percent, and the risk-free rate is 4 percent. Compute the return the firm should earn given its level of risk and determine whether the manager is saying the firm is undervalued or overvalued.
Chapter 10 - Estimating Risk and Return
Use CAPM to determine the firm’s required return: 4% + 1.5 × (12% − 4%) = 16% Since the return required for the level of risk is 16% and the manager believes a 14% return will be achieved, the manager is saying the firm is overvalued. LG3 10-20 Under-/Over Valued Stock A manager believes his firm will earn a 14 percent return next year. His firm has a beta of 1.2, the expected return on the market is 11 percent, and the risk-free rate is 5 percent. Compute the return the firm should earn given its level of risk and determine whether the manager is saying the firm is undervalued or overvalued. Use CAPM to determine the firm’s required return:5% + 1.2 × (11% − 5%) = 12.2% Since the return required for the level of risk is 12.2% and the manager believes a 14% return will be achieved, the manager is saying the firm is undervalued. LG3 10-21 Portfolio Beta You own $10,000 of Olympic Steel stock that has a beta of 2.2. You also own $7,000 of Rent-a-Center (beta = 1.5) and $8,000 of Lincoln Educational (beta = 0.5). What is the beta of your portfolio? First determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = $10,000 + $7,000 + $8,000 = $25,000 Olympic Steel weight = $10,000 / $25,000 = 40% Rent-a-Center weight = $7,000 / $25,000 = 28% Lincoln Educational weight = $8,000 / $25,000 = 32% Now compute the portfolio beta: (0.40 × 2.2) + (0.28 × 1.5) + (0.32 × 0.5) = 1.46 LG3 10-22 Portfolio Beta You own $7,000 of Human Genome stock that has a beta of 3.5. You also own $8,000 of Frozen Food Express (beta = 1.6) and $10,000 of Molecular Devices (beta = 0.4). What is the beta of your portfolio? First determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = $7,000 + $8,000 + $10,000 = $25,000 Human Genome weight = $7,000 / $25,000 = 28% Frozen Food Express weight = $8,000 / $25,000 = 32% Molecular Devices weight = $10,000 / $25,000 = 40% Now compute the portfolio beta: (0.28 × 3.5) + (0.32 × 1.6) + (0.40 × 0.4) = 1.65
Chapter 10 - Estimating Risk and Return
advanced problems LG1
10-23 Expected Return and Risk Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns: Economic State Fast growth Slow growth Recession Depression
Probability Return 0.30 0.50 0.15
60% 13 −15
0.05
−45
Expected return = (0.3 × 60%) + (0.5 × 13%) + (0.15 × -15%) + (0.05 × -45%) = 20% Standard Deviation = 0.3(60% − 20%) + 0.5 (13% − 20%) + 0.15 (−15% − 20%) 2 + 0.05 (−45% − 20%) 2 2
2
= 480 + 24.5 +183.75 + 211.25 = 29.99%
LG1
10-24 Expected Return and Risk Compute the expected return and standard deviation given these four economic states, their likelihoods, and the potential returns: Economic State Fast growth Slow growth Recession Depression
Probability Return 0.25 0.55 0.15 0.05
50% 11 −15 −50
Expected return = (0.25 × 50%) + (0.55 × 11%) + (0.15 × -15%) + (0.05 × -50%) = 13.8% Standard Deviation = 0.25 (50% −13.8%) + 0.55 (11% −13.8%) + 0.15 (−15% −13.8%) 2 + 0.05 (−50% −13.8%) 2 2
= 327.6 + 4.3 +124.4 + 203.5 = 25.69%
2
Chapter 10 - Estimating Risk and Return
LG3 10-25 Risk Premiums You own $10,000 of Denny’s Corp stock that has a beta of 2.9. You also own $15,000 of Qwest Communications (beta = 1.5) and $5,000 of Southwest Airlines (beta = 0.7). Assume that the market return will be 11.5 percent and the risk-free rate is 4.5 percent. What is the market risk premium? What is the risk premium of each stock? What is the risk premium of the portfolio? Market risk premium = 11.5% − 4.5% = 7% Denny’s risk premium = 2.9 × (11.5% − 4.5%) = 20.30% Qwest’s risk premium = 1.5 × (11.5% − 4.5%) = 10.50% Southwest Airlines risk premium = 0.7 × (11.5% − 4.5%) = 4.9% For the portfolio, determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = $10,000 + $15,000 + $5,000 = $30,000 Denny’s weight = $10,000 / $30,000 = 33.33% Qwest’s weight = $15,000 / $30,000 = 50% Southwest Airlines weight = $5,000 / $30,000 = 16.67% Now compute the portfolio beta: (0.3333 × 2.9) + (0.5 × 1.5) + (0.1667 × 0.7) = 1.833 So, the portfolio’s risk premium = 1.833 × (11.5% − 4.5%) = 12.83% LG3 10-26 Risk Premiums You own $15,000 of Opsware, Inc. stock that has a beta of 3.8. You also own $10,000 of Lowe’s Companies (beta = 1.6) and $10,000 of New York Times (beta = 0.8). Assume that the market return will be 12 percent and the risk-free rate is 6 percent. What is the market risk premium? What is the risk premium of each stock? What is the risk premium of the portfolio? Market risk premium = 12% − 6% = 6% Opsware’s risk premium = 3.8 × (12% − 6%) = 22.8% Lowe’s risk premium = 1.6 × (12% − 6%) = 9.6% New York Times risk premium = 0.8 × (12% − 6%) = 4.8%
Chapter 10 - Estimating Risk and Return
For the portfolio, determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = $15,000 + $10,000 + $10,000 = $35,000 Opsware’s weight = $15,000 / $35,000 = 42.86% Lowe’s weight = $10,000 / $35,000 = 28.57% New York Times weight = $10,000 / $35,000 = 28.57% Now compute the portfolio beta: (0.4286 × 3.8) + (0.2857 × 1.6) + (0.2857 × 0.8) = 2.31 So, the portfolio’s risk premium = 2.31 × (12% − 6%) = 13.89% LG3
10-27 Portfolio Beta and Required Return You hold the positions in the table below. What is the beta of your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, what is the required return of the portfolio?
http://www.Amazon.com Family Dollar Stores McKesson Corp Schering-Plough Corp
Price $40.80 30.10 57.40 23.80
Shares 100 150 75 200
Beta 3.8 1.2 0.4 0.5
This problem can be solved two different and equivalent ways. Both ways require the weights of the stocks in the portfolio. In one method, compute the required return for each stock and then use the weights to form the portfolio required return. The other solution uses the weights to compute the portfolio beta. This portfolio beta is used to compute the portfolio required return. The solution below shows the portfolio beta approach. For the portfolio, determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = ($40.80 × 100) + ($30.10 × 150) + ($57.40 × 75) + ($23.80 × 200) = $17,660 http://www.Amazon.com weight = ($40.80 × 100) / $17,660 = 23.10% Family Dollar weight = ($30.10 × 150) / $17,660 = 25.57% McKesson weight = ($57.40 × 75) / $17,660 = 24.38% Schering-Plough weight = ($23.80 × 200) / $17,660 = 26.95% Now compute the portfolio beta: (0.2310 × 3.8) + (0.2557 × 1.2) + (0.2438 × 0.4) + (0.2695 × 0.5) = 1.42So, the portfolio’s required return = 3.5% + 1.42 × (12% − 3.5%) = 15.57% LG3
10-28 Portfolio Beta and Required Return You hold the positions in the table below. What is the beta of your portfolio? If you expect the market to earn 12 percent and the risk-free rate is 3.5 percent, what is the required return of the portfolio?
Chapter 10 - Estimating Risk and Return
Advanced Devices FedEx Corp Microsoft Sara Lee Corp
Micro
Price $14.70
Shares 300
Beta 4.2
120.00 28.90 17.25
50 100 150
1.1 0.7 0.5
This problem can be solved two different and equivalent ways. Both ways require the weights of the stocks in the portfolio. In one method, compute the required return for each stock and then use the weights to form the portfolio required return. The other solution uses the weights to compute the portfolio beta. This portfolio beta is used to compute the portfolio required return. The solution below shows the portfolio beta approach. For the portfolio, determine the total value of the portfolio and the weights of each stock in the portfolio: Total value = ($14.70 × 300) + ($120.00 × 50) + ($28.90 × 100) + ($17.25 × 150) = $15,887.50 Advanced Micro Devices weight = ($14.70 ×300) / $15,887.50 = 27.76% FedEx Corp weight = ($120.00 × 50) / $15,887.50 = 37.77% Microsoft weight = ($28.90 × 100) / $15,887.50 = 18.19% Sara Lee Corp weight = ($17.25 × 150) / $15,887.50 = 16.29% Now compute the portfolio beta: (0.2776 × 4.2) + (0.3777 × 1.1) + (0.1819 × 0.7) + (0.1629 × 0.5) = 1.79 So, the portfolio’s required return = 3.5% + 1.79 × (12% − 3.5%) = 18.72% LG3&7 10-29 Required Return Using the information in the table, compute the required return for each company using both CAPM and the constant growth model. Compare and discuss the results. Assume that the market portfolio will earn 12 percent and the risk-free rate is 3.5 percent. Price US Bancorp
$36.55
Upcoming Dividend $1.60
Praxair Eastman Kodak
64.75 24.95
1.12 1.00
Growth
Beta
10.0%
1.8
11.0 4.5
2.4 0.5
First, use CAPM to determine each firm’s required return: US Bancorp required return = 3.5% + 1.8 × (12% − 3.5%) = 18.8% Praxair required return = 3.5% + 2.4 × (12% − 3.5%) = 23.9% Eastman Kodak required return = 3.5% + 0.5 × (12% − 3.5%) = 7.75%
Chapter 10 - Estimating Risk and Return
Now, compute the required return using the constant growth rate model: US Bancorp required return = $1.60 + 0.10 = 14.38%
$36.55 $1.12 Praxair required return = + 0.11 = 12.73% $64.75 $1.00 Eastman Kodak required return = + 0.045 = 8.51% $24.95
The US Bancorp CAPM estimate of 18.8 percent is too high compared to the 14.38 percent constant growth rate model estimate. The CAPM estimate for Praxair is far different than the constant growth rate model estimate. The CAPM estimate for Eastman Kodak is similar to that of the constant growth rate model. LG3&7 10-30 Required Return Using the information in the table, compute the required return for each company using both CAPM and the constant growth model. Compare and discuss the results. Assume that the market portfolio will earn 11 percent and the risk-free rate is 4 percent. Price Estee Lauder Kimco Realty Nordstrom
$47.40 52.10 5.25
Upcoming Dividend $0.60 1.54 0.50
Growth
Beta
11.7% 8.0 14.6
0.75 1.3 2.2
First, use CAPM to determine each firm’s required return: Estee Lauder required return = 4% + 0.75 × (11% − 4%) = 9.25% Kimco Realty required return = 4% + 1.3 × (11% − 4%) = 13.10% Nordstrom required return = 4% + 2.2 × (11% − 4%) = 19.40% Now, compute the required return using the constant growth rate model: $0.60 + 0.117 = 12.97% $47.40 Kimco Realty required return = $1.54 + 0.08 = 10.96% $52.10
Estee Lauder required return =
$0.50 Nordstrom required return =
+ 0.146 = 24.12%
$5.25
The Estee Lauder CAPM estimate of 9.25 percent is low compared to the 12.97 percent constant growth rate model estimate. The CAPM estimate for Kimco Realty is high compared to the constant growth rate model estimate. The CAPM estimate for Nordstrom is a little lower than that of the constant growth rate model.
Chapter 10 - Estimating Risk and Return
10-31 Spreadsheet Problem As discussed in the text, beta estimates for one firm will vary depending on various factors like such as the time over which the estimation is conducted, the market portfolio proxy, and the return intervals. You will demonstrate this variation using returns for Microsoft. a. Using all 45 monthly returns for Microsoft and the two stock market indices, compute Microsoft’s beta using the S&P 500 Index as the market proxy. Then compute the beta using the NASDAQ indices as the market portfolio proxy. Compare the two beta estimates. b. Now estimate the beta using only the most recent 30 monthly returns and the S&P 500 Index. Compare the beta estimate to the estimate in part (a) when using the S&P 500 Index and all 45 monthly returns. Date
MSFT
S&P500
Nasdaq
Date
MSFT
S&P500
Nasdaq
Date
MSFT
S&P500
Nasdaq
Apr 2018
2.47%
0.27%
0.04%
Jan 2017
4.04%
1.79%
3.13%
Oct 2015
18.93%
8.30%
9.38%
Mar 2018
-2.21%
-2.69%
-2.88%
Dec 2016
3.82%
1.82%
2.27%
Sep 2015
2.37%
-2.64%
-4.00%
Feb 2018
-1.31%
-3.89%
-1.87%
Nov 2016
0.57%
3.42%
2.59%
Aug 2015
-6.81%
-6.26%
-6.15%
Jan 2018
11.07%
5.62%
7.36%
Oct 2016
4.03%
-1.94%
-2.31%
Jul 2015
5.78%
1.97%
2.84%
Dec 2017
2.14%
0.98%
0.43%
Sep 2016
0.87%
-0.12%
1.89%
Jun 2015
-5.17%
-2.10%
-1.64%
Nov 2017
1.19%
2.81%
2.17%
Aug 2016
1.38%
-0.12%
0.99%
May 2015
-3.66%
1.05%
2.60%
Oct 2017
11.67%
2.22%
3.57%
Jul 2016
10.77%
3.56%
6.60%
Apr 2015
19.63%
0.85%
0.83%
Sep 2017
0.16%
1.93%
1.05%
Jun 2016
-2.78%
0.09%
-2.13%
Mar 2015
-6.61%
-1.74%
-1.26%
Aug 2017
2.85%
0.05%
1.27%
May 2016
6.28%
1.53%
3.62%
Feb 2015
8.54%
5.49%
7.08%
Jul 2017
5.47%
1.93%
3.38%
Apr 2016
-9.70%
0.27%
-1.94%
Jan 2015
-13.02%
-3.10%
-2.13%
Jun 2017
-0.74%
0.48%
-0.94%
Mar 2016
9.33%
6.60%
6.84%
Dec 2014
-2.23%
-0.42%
-1.16%
May 2017
2.02%
1.16%
2.50%
Feb 2016
-7.64%
-0.41%
-1.21%
Nov 2014
1.83%
2.45%
3.47%
Apr 2017
3.95%
0.91%
2.30%
Jan 2016
-0.70%
-5.07%
-7.86%
Oct 2014
1.27%
2.32%
3.06%
Mar 2017 Feb 2017
3.56% -1.04%
-0.04% 3.72%
1.48% 3.75%
Dec 2015 Nov 2015
2.77% 3.25%
-1.75% 0.05%
-1.98% 1.09%
Sep 2014 Aug 2014
2.68% 5.26%
-1.55% 3.77%
-1.90% 4.82%
c. Estimate Microsoft’s beta using the quarterly data returns below. Compare the estimate to the ones from parts (a) and (b). Date Q1 2018 Q4 2017 Q3 2017 Q2 2017 Q1 2017 Q4 2016 Q3 2016 Q2 2016 Q1 2016 Q4 2015 Q3 2015 Q2 2015 Q1 2015
MSFT 7.20% 15.41% 8.64% 5.26% 6.63% 8.61% 13.27% -6.70% 0.26% 26.20% 0.91% 9.29% -11.84%
S&P500 -0.25% 7.12% 2.48% 2.04% 7.50% 1.28% 3.53% 8.52% -7.12% 5.49% -5.11% 0.14% 1.79%
Chapter 10 - Estimating Risk and Return
Q4 2014
0.83%
3.20%
Answers: A. Beta estimates using different market proxies and 45 months. The estimate is from the Excel Slope function. 45 months
Beta =
S&P500 1.381
Nasdaq 1.186
Microsoft’s beta is more than 20% higher when using the S&P 500 versus the NASDAQ as the market proxies.
B. Beta estimate using 30 months. 30 months
Beta =
S&P500 0.988
Nasdaq 1.033
The beta estimate is larger using the most recent 30 months compared to the full 45 months. C. Beta estimate using quarterly returns. quarterly
Beta =
S&P500 0.493
Note that the assumptions used can make a large difference in the beta estimate. This makes beta difficult to use in practice. 10-32 Spreadsheet Problem Build a spreadsheet that automatically computes the expected market return and risk for different assumptions about the state of the economy. a. First, create the following spreadsheet and compute the expected return and standard deviation.
Chapter 10 - Estimating Risk and Return
b. Compute the expected return and risk for the following scenarios:
and
Answers: a. State of Economy Fast Growth Slow Growth No Growth Recession Depression Sum =
Probability of State 0.13 0.42 0.25 0.18 0.02
Expected Market Return 35% 17% 3% -15% -30%
1.00 Expected Return = Standard Deviation =
9.14% 16.06%
Probability of State 0.13 0.33 0.3 0.2 0.04
Expected Market Return 30% 15% 2% -18% -25%
1.00 Expected Return = Standard Deviation =
4.85% 16.09%
Probability of State
Expected Market Return
b. State of Economy Fast Growth Slow Growth No Growth Recession Depression Sum =
State of Economy
Chapter 10 - Estimating Risk and Return
Fast Growth Slow Growth No Growth Recession Depression Sum =
0.15 0.35 0.34 0.15 0.01
40% 18% 4% -20% -35%
1.00 Expected Return = Standard Deviation =
10.31% 18.02%
research it!: Find a Beta Using beta as a risk measure has been fully integrated into corporate finance and the investment industry. You can obtain a beta for most companies at many financial Web sites. Sites that list a beta include: MSN Money (in the Company Report section), Yahoo! Finance (in the Key Statistics section), and Zacks (follow the Detailed Quote link). Obtain the beta for your favorite company from several different Web sites. Are the values you obtain similar? If they are not, why might they be different? (moneycentral.msn.com, finance.yahoo.com, http://www.zacks.com) SOLUTION: For General Electric (GE), I found: Yahoo! Finance beta was 0.59. MSN Money shows a beta of 0.76. Zacks reports a beta of 0.83. The beta sources may use (i) different market portfolios, (ii) different time periods, or (iii) different time increments (annual returns versus months, weeks, etc.). integrated minicase: Disney’s Beta When you go on the Web to find a firm’s beta, you do not know how recently it was computed, what index was used as a proxy for the market portfolio, or which time series of returns the calculations used. Earlier in this chapter, it was shown that when we went on the Web to find a beta for Disney, we found the following: MSN Money (1.29), Yahoo! Finance (1.18). An alternative is to compute beta yourself. A common estimation procedure is to use 60 months of return data and to use the S&P 500 Index as the market portfolio. You can obtain price data for a company and for the S&P 500 Index for free from Web sites like Yahoo! Finance. Using monthly prices, you can compute the monthly returns, as (Pn − Pn-1) / Pn-1. Below are 60 monthly returns for Disney and the S&P 500 Index. You can use these returns to compute Disney’s beta. A spreadsheet, like Excel, can run a regression (go to Tool menu, select Data Analysis, and then Regression). Select Disney returns as the y variable and S&P 500 Index return as the x variable. The coefficient for the x variable is the beta estimate. The
Chapter 10 - Estimating Risk and Return
regression will provide all the statistical information you might like. However, if you only want beta, you can simply use the SLOPE function in Excel. Or, you may have learned to run a regression using statistical software. Date Apr-18 Mar-18 Feb-18 Jan-18 Dec-17 Nov-17 Oct-17 Sep-17 Aug-17 Jul-17 Jun-17 May-17 Apr-17 Mar-17 Feb-17 Jan-17 Dec-16 Nov-16 Oct-16 Sep-16
Disney -0.11% -2.64% -5.07% 1.89% 2.57% 7.17% -0.77% -2.60% -7.26% 3.46% -1.57% -6.63% 1.95% 3.00% -0.51% 6.99% 5.15% 6.94% -0.18% -1.69%
S&P500 Index 0.27% -2.69% -3.89% 5.62% 0.98% 2.81% 2.22% 1.93% 0.05% 1.93% 0.48% 1.16% 0.91% -0.04% 3.72% 1.79% 1.82% 3.42% -1.94% -0.12%
Date Aug 16 Jul 16 Jun 16 May 16 Apr 16 Mar 16 Feb 16 Jan 16 Dec 15 Nov 15 Oct 15 Sep 15 Aug 15 Jul 15 Jun 15 May 15 Apr 15 Mar 15 Feb 15 Jan 15
Disney -0.84% -1.91% -1.41% -3.91% 3.98% 3.97% -0.31% -8.23% -7.39% -0.24% 11.29% 0.31% -14.61% 5.13% 3.42% 1.52% 3.65% 0.78% 14.42% -2.20%
S&P500 Index -0.12% 3.56% 0.09% 1.53% 0.27% 6.60% -0.41% -5.07% -1.75% 0.05% 8.30% -2.64% -6.26% 1.97% -2.10% 1.05% 0.85% -1.74% 5.49% -3.10%
Date Dec 14 Nov 14 Oct 14 Sep 14 Aug 14 Jul 14 Jun 14 May 14 Apr 14 Mar 14 Feb 14 Jan 14 Dec 13 Nov 13 Oct 13 Sep 13 Aug 13 Jul 13 Jun 13 May 13
Disney 1.82% 1.24% 2.64% -0.95% 4.66% 0.16% 2.06% 5.89% -0.91% -0.92% 11.29% -3.79% 8.31% 2.84% 6.36% 6.02% -5.91% 2.38% 0.11% 0.38%
S&P500 Index -0.42% 2.45% 2.32% -1.55% 3.77% -1.51% 1.91% 2.10% 0.62% 0.69% 4.31% -3.56% 2.36% 2.80% 4.46% 2.97% -3.13% 4.95% -1.50% 2.08%
a. Compute Disney’s beta using the above returns. b. Compare your estimate with the ones found on the Web as listed above. c. How different are the required returns using these betas? Compute required return using each beta (assume that the risk free rate is 5 percent and the market return will be 13 percent). SOLUTION: a. Excel Regression output. Using SLOPE function, Beta = 1.26.
b. This beta is close to the MSN Money estimate. c. Required returns using these beta estimates: Excel estimate = 5% + 1.26 × (12% − 5%) = 13.82% MSN Money = 5% + 1.29 × (12% − 5%) = 14.03% Yahoo! Finance estimate = 5% + 1.18 × (12% − 5%) = 13.26%
Chapter 11 - Calculating the Cost of Capital
CHAPTER 11 – CALCULATING THE COST OF CAPITAL
Questions LG1
1.
How would you handle calculating the cost of capital if a firm were planning to issue two different classes of common stock? As the two different classes of common stock are likely to have different component costs, calculate the cost and weight for each separately.
LG2
2.
Expressing WACC in terms of iE, iP, and iD, what is the theoretical minimum for the WACC? The theoretical minimum WACC would be that for an all-debt firm: iD × (1–TC).
LG3
3.
Under what situations would you want to use the CAPM approach for estimating the component cost of equity? The constant-growth model? You would want to use the CAPM when you can estimate the firm’s beta with a good deal of certainty; you would only want to use the constant-growth model if the firm’s stock is expected to experience constant dividend growth.
LG3
4.
Could you calculate the component cost of equity for a stock with nonconstant expected growth rates in dividends if you didn’t have the information necessary to compute the component cost using the CAPM? Why or why not? You could try and adjust the constant-growth model for initial periods of nonconstant growth, but doing so would require estimating the growth rate for all of the nonconstant growth periods.
LG4
5.
Why do we use market-based weights instead of book-value-based weights when computing the WACC? We use market-based rather than book-value-based weights because we are interested in determining what the cost of financing the firm’s assets would be given today’s market situation and the component costs the firm currently faces, not what the historic prices would have been.
LG5
6.
Suppose your firm wanted to expand into a new line of business quickly, and that management anticipated that the new line of business would constitute over 80 percent of your firm’s operations within three years. If the expansion was going to be financed partially with debt, would it still make sense to use the firm’s existing cost of debt, or should you compute a new rate of return for debt based on the new line of business?
Chapter 11 - Calculating the Cost of Capital
Given that the new line of business will comprise so much of the firm’s operations, it probably isn’t appropriate to count on the current, existing operations to pay off the debt. Therefore, the firm should probably compute a new required rate of return for this debt. LG6
7.
Explain why the divisional cost of capital approach may cause problems if new projects are assigned to the wrong division. If projects are assigned to the wrong division, the risk of that division may be significantly different than the risk of the project, implying that the project will be evaluated with a divisional cost of capital that is much different from what a projectspecific cost of capital would be.
LG7
8.
When will the subjective approach to forming divisional WACCs be better than using the firmwide WACC to evaluate all projects? As long as the subjective approaches manages to use divisional costs of capital that are, on average, closer to what the project-specific costs of capital would be than the firmwide cost of capital is, the subjective approach will improve the firm’s accept/reject decisions.
LG8
9
Suppose a new project was going to be financed partially with retained earnings. What flotation costs should you use for retained earnings? Retained earnings do not carry any flotation cost, so you should use a cost of zero.
Problems LG3
11-1
Cost of Equity Diddy Corp. stock has a beta of 1.2, the current risk-free rate is 5 percent, and the expected return on the market is 13.5 percent. What is Diddy’s cost of equity? Using equation 11-2: iE = if + E E (iM ) − if = .05 +1.2.135 −.05 = 0.152, or 15.20%
LG3
11-2
Cost of Equity JaiLai Cos. stock has a beta of 0.9, the current risk-free rate is 6.2 percent, and the expected return on the market is 12 percent. What is JaiLai’s cost of equity? Using equation 11-2: iE = if + E E (iM ) − if
= .062 + 0.9.12 −.062 = 0.1142, or 11.42%
Chapter 11 - Calculating the Cost of Capital
LG3
11-3
Cost of Debt Oberon, Inc. has a $20 million (face value) 10-year bond issue selling for 97 percent of par that pays an annual coupon of 8.25 percent. What would be Oberon’s before-tax component cost of debt? Solving equation 11-5 for iD: 1− (1+ 1i 10 $1, 000 D) + (1+ i 10 for iD Solve $970 = $82.50 iD D)
Yields iD = 0.087115, or 8.71% LG3
11-4
Cost of Debt KatyDid Clothes has a $150 million (face value) 30-year bond issue selling for 104 percent of par that carries a coupon rate of 11 percent, paid semiannually. What would be Katydid’s before-tax component cost of debt? Solving equation 11-5 for iD: 1− 1+ 1i 60 $1, 000 ( D) + 1+ i ( Solve $1,040 = $55 60 for iD iD D)
iD = 0.052787, or 5.2787% on a semiannual basis. Since the cost of debt is normally quoted on a nominal annual basis, we should multiple this semiannual rate by two to get a quoted component cost of 5.2787% × 2 = 10.56% LG3
11-5
Tax Rate Suppose that LilyMac Photography expects EBIT to be approximately $200,000 per year for the foreseeable future, and that they have 1,000 10-year, 9 percent annual coupon bonds outstanding. What would the appropriate tax rate be for use in the calculation of the debt component of LilyMac’s WACC? The interest payments on the bonds would total 1,000 × $1,000 × 0.09 = $90,000, resulting in EBT of $200,000 – $90,000 = $110,000. Since, as taxable income falls from $200,000 to $110,000 the firm is entirely in the 39 percent tax bracket from Table 11.1, the average applicable tax rate would also be equal to 39 percent.
LG3
11-6
Tax Rate PDQ, Inc. expects EBIT to be approximately $11 million per year for the foreseeable future, and that they have 25,000 20-year, 8 percent annual coupon bonds outstanding. What would the appropriate tax rate be for use in the calculation of the debt component of PDQ’s WACC?
Chapter 11 - Calculating the Cost of Capital
The interest payments on the bonds would total 25,000 × $1,000 × 0.08 = $2m, resulting in EBT of $11m – $2m = $9m. Since, as taxable income falls from $11m to $9m the firm is in the 35 percent tax bracket from $11m down to $10m and in the 34 percent tax bracket from $10m down to $9m, the weighted average applicable tax rate will be equal to: $11m − $10m $10m −$9m TC = 35% + 34% $2m $2m = 0.345, or 34.50% LG3
11-7
Cost of Preferred Stock ILK has preferred stock selling for 97 percent of par that pays an 8 percent annual coupon. What would be ILK’s component cost of preferred stock? Using equation 11-4: D1 P0 $8 = $97 = 0.0825, or 8.25%
iP =
LG3
11-8
Cost of Preferred Stock Marme, Inc. has preferred stock selling for 96 percent of par that pays an 11 percent annual coupon. What would be Marme’s component cost of preferred stock? Using equation 11-4: D1 P0 $11 = $96 = 0.1146, or 11.46%
iP =
LG4
11-9
Weight of Equity FarCry Industries, a maker of telecommunications equipment, has two million shares of common stock outstanding, one million shares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $27 per share, the preferred shares are selling for $14.50 per share, and the bonds are selling for 98 percent of par, what would be the weight used for equity in the computation of FarCry’s WACC? Using the computation for equity weight given in example 11-5:
Chapter 11 - Calculating the Cost of Capital
2m$27 E = E + P + D 2m$27 +1m$14.50 +10, 000 .98$1, 000 $54m = $78.3m = 0.6897, or 68.97%
LG4
11-10 Weight of Equity OMG Inc. has four million shares of common stock outstanding, three million shares of preferred stock outstanding, and 5,000 bonds. If the common shares are selling for $17 per share, the preferred shares are selling for $26 per share, and the bonds are selling for 108 percent of par, what would be the weight used for equity in the computation of OMG’s WACC? Using the computation for equity weight given in example 11-5: 4m$17 E = 4m$17 + 3m$26 + 5, 000 1.08$1, 000 E+P+D $68m = $151.4m = 0.4491, or 44.91%
LG4
11-11 Weight of Debt FarCry Industries, a maker of telecommunications equipment, has two million shares of common stock outstanding, one million shares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $27 per share, the preferred shares are selling for $14.50 per share, and the bonds are selling for 98 percent of par, what weight should you use for debt in the computation of FarCry’s WACC? Using the computation for debt weight given in example 11-5: D 10, 000 .98$1, 000 = E + P + D 2m$27 +1m$14.50 +10, 000 .98$1, 000 $9.8m = $78.3m = 0.1252, or 12.52%
LG4
11-12 Weight of Debt OMG Inc. has four million shares of common stock outstanding, three million shares of preferred stock outstanding, and 5,000 bonds. If the common shares are selling for $27 per share, the preferred shares are selling for $26 per share, and the bonds are selling for 108 percent of par, what weight should you use for debt in the computation of OMG’s WACC? Using the computation for debt weight given in example 11-5:
Chapter 11 - Calculating the Cost of Capital
5, 000 1.08$1, 000 D = E + P + D 4m$27 + 3m$26 + 5, 000 1.08$1, 000 $5.4m = $191.4m = 0.0282, or 2.82%
LG4
11-13 Weight of Preferred Stock FarCry Industries, a maker of telecommunications equipment, has two million shares of common stock outstanding, one million shares of preferred stock outstanding, and 10,000 bonds. If the common shares sell for $27 per share, the preferred shares sell for $14.50 per share, and the bonds sell for 98 percent of par, what weight should you use for preferred stock in the computation of FarCry’s WACC? Using the computation for preferred weight given in equation 11-1: 2m$27 P = E + P + D 2m$27 +1m$14.50 +10, 000 .98$1, 000 $14.5m = $78.3m = 0.1852, or 18.52%
LG4
11-14 Weight of Preferred Stock OMG Inc. has four million shares of common stock outstanding, three million shares of preferred stock outstanding, and 5,000 bonds. If the common shares sell for $17 per share, the preferred shares sell for $16 per share, and the bonds sell for 108 percent of par, what weight should you use for preferred stock in the computation of OMG’s WACC? Using the computation for preferred weight given in equation 11-1: 3m$16 P = E + P + D 4m$17 + 3m$16 + 5, 000 1.08$1, 000 $48m = $121.4m = 0.3954, or 39.54%
intermediate problems LG2
11-15 WACC Suppose that TapDance, Inc.’s capital structure features 65 percent equity, 35 percent debt, and that its before-tax cost of debt is 8 percent, while its cost of equity is 13 percent. If the appropriate weighted average tax rate is 21 percent, what will be TapDance’s WACC? Using equation 11-1:
Chapter 11 - Calculating the Cost of Capital
WACC =
E
i +
P
i +
D
i (1− T )
E+P+D E+P+D E+P+D D = .6513% + 0 0% +.358% (1− .21) E
P
C
= 10.66% LG2
11-16 WACC Suppose that JB Cos. has a capital structure of 78 percent equity, 22 percent debt, and that its before-tax cost of debt is 11 percent while its cost of equity is 15 percent. If the appropriate weighted average tax rate is 21 percent, what will be JB’s WACC? Using equation 11-1: WACC =
E
i +
P
i +
D
i (1− T )
E+P+D E+P+D E+P+D D = .7815% + 0 0% +.2211% (1− .21) E
P
C
= 13.61% LG2
11-17 WACC Suppose that B2B, Inc. has a capital structure of 37 percent equity, 17 percent preferred stock, and 46 percent debt. If the before-tax component costs of equity, preferred stock and debt are 14.5 percent, 11 percent, and 9.5 percent, respectively, what is B2B’s WACC if the firm faces an average tax rate of 21 percent? Using equation 11-1: WACC =
E
i +
P
i +
D
i (1− T )
E+P+D E+P+D E+P+D D = .37 14.5% +.17 11% +.46 9.5% (1− .21) E
P
C
= 10.69% LG2
11-18 WACC Suppose that MNINK Industries’ capital structure features 63 percent equity, 7 percent preferred stock, and 30 percent debt. If the before-tax component costs of equity, preferred stock and debt are 11.60 percent, 9.5 percent, and 9 percent, respectively, what is MNINK’s WACC if the firm faces an average tax rate of 21 percent? Using equation 11-1: WACC =
E
i +
P
i +
D
i (1− T )
E+P+D E+P+D E+P+D D = .6311.60% +.07 9.5% +.30 9% (1− .21) E
= 10.11%
P
C
Chapter 11 - Calculating the Cost of Capital
LG3
11-19 WACC TAFKAP Industries has three million shares of stock outstanding selling at $17 per share and an issue of $20 million in 7.5 percent, annual coupon bonds with a maturity of 15 years, selling at 106 percent of par. If TAFKAP’s weighted average tax rate is 21 percent and its cost of equity is 14.5 percent, what is TAFKAP’s WACC? First, solve equation 11-5 for iD: 1− 1+ 1i ( D )N + FV (1+ i Solve PV = PMT N for iD iD D) 1− 1+ 1i ( D )15 + $1, 000 (1+ i Solve $1,060 = $75 15 for iD iD D) iD = 6.8476% Then, using equation 11-1: E D iE + iD (1− TC ) E+P+D E+P+D 3m $17 $20m 1.06 14.5% + 6.8476% (1−.21) = 3m $17 + $20m 1.06 3m $17 + $20m 1.06 = .7064 14.5% +.2936 6.8476% (1 −.21)
WACC =
= 11.83% LG3
11-20 WACC Johnny Cake Ltd. has ten million shares of stock outstanding selling at $23 per share and an issue of $50 million in 9 percent, annual coupon bonds with a maturity of 17 years, selling at 93.5 percent of par. If Johnny Cake’s weighted average tax rate is 21 percent, its next dividend is expected to be $3 per share, and all future dividends are expected to grow at 6 percent per year, indefinitely, what is its WACC? First, solve equation 11-5 for iD:
Chapter 11 - Calculating the Cost of Capital
1 − (1 + 1i )N PV + D 1 + i ( Solve PV = PMT for iD N iD D) 1 1 − (1 + i )17 + $1, 000 D (1 + i Solve $935 = $90 for iD 17 i D D) iD = 9.8003% Next, use equation 11-3 to solve for iE: D1 +g P0 $3.00 = +.06 $23 = .190435, or 19.0435%
iE =
Then, using equation 11-1, solve for WACC:
E
LG4
i +
D
i (1− T ) C E+P+D E E+P+D D 10m $23 $50m .935 19.0435% + 9.8003% (1−.21) = 10m $23 + $50m .935 10m $23 + $50m .935 = .831119.0435% +.1689 9.8003% (1 −.21) = 17.13%
WACC =
11-21 WACC Weights BetterPie Industries has three million shares of common stock outstanding, two million shares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $47 per share, the preferred shares are selling for $24.50 per share, and the bonds are selling for 99 percent of par, what would be the weights used in the calculation of BetterPie’s WACC? Using the computations for component weights given in equation 11-1:
Chapter 11 - Calculating the Cost of Capital
3m$47 E = E + P + D 3m$47 + 2m$24.50 +10, 000 0.99 $1, 000 $141m = $199.9m = 0.7054, or 70.54% 2m$24.50 P = 3m$47 + 2m$24.50 +10, 000 0.99 $1, 000 E+P+D $49m = $199.9m = 0.2451, or 24.51% D 10, 000 0.99 $1, 000 = E + P + D 3m$47 + 2m$24.50 +10, 000 0.99 $1, 000 $9.9m = $199.9m = 0.0495, or 4.95%
LG4
11-22 WACC Weights WhackAmOle has two million shares of common stock outstanding, 1.5 million shares of preferred stock outstanding, and 50,000 bonds. If the common shares are selling for $63 per share, the preferred shares are selling for $52 per share, and the bonds are selling for 103 percent of par, what would be the weights used in the calculation of WhackAmOle’s WACC? Using the computations for component weights given in equation 11-1: 2m$63 E = E + P + D 2m$63 +1.5m$52.00 + 50, 000 1.03$1, 000 $126m = $255.5m = 0.4932, or 49.32% P 2m$24.50 = E + P + D 2m$63 +1.5m$52.00 + 50, 000 1.03$1, 000 $78m = $255.5m = 0.3053, or 30.53% 50, 000 1.03$1, 000 D = E + P + D 2m$63 +1.5m$52.00 + 50, 000 1.03$1, 000 $51.5m = $255.5m = 0.2016, or 20.16%
Chapter 11 - Calculating the Cost of Capital
LG8
11-23 Flotation Cost Suppose that Brown-Murphies’ common shares sell for $19.50 per share, that the firm is expected to set their next annual dividend at $0.57 per share, and that all future dividends are expected to grow by 4 percent per year, indefinitely. If BrownMurphies faces a flotation cost of 13 percent on new equity issues, what will be the flotation-adjusted cost of equity? Using equation 11-8: iE = =
D1 +g P0 − F $0.57 + 0.04 $19.50 − (0.13$19.50)
= 0.0736, or 7.36% advanced problems LG2
11-24 Flotation Cost A firm is considering a project that will generate perpetual after-tax cash flows of $15,000 per year beginning next year. The project has the same risk as the firm's overall operations and must be financed externally. Equity flotation costs 14 percent and debt issues cost 4 percent on an after-tax basis. The firm's D/E ratio is 0.8. What is the most the firm can pay for the project and still earn its required return? If the D/E ratio is 0.8, then D/(D+E) will be 0.8 / 1.8 = 0.4444 and E/(D+E) will be 1.0 / 1.8 = 0.5556. Then, using equation 11-1, solve for WACC: WACC =
E
i +
D
i (1− T )
E+P+D E+P+D D = 0.555614% + 0.4444 4% = 9.56% E
C
Chapter 11 - Calculating the Cost of Capital
LG6
11-25 Firmwide vs. Project-Specific WACCs An all-equity firm is considering the projects shown as follows. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its current WACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly rejected? Project Expected Return Beta A 8.0% 0.5 B 19.0 1.2 C 13.0 1.4 D 17.0 1.6 Using the firm’s WACC of 12 percent as the IRR benchmark, project A would be rejected. Using equation 11-2, the project-specific benchmarks for each project should be: For Project A: iE = i f + E E (iM ) − i f = 4% + 0.5 7% = 7.5% For Project B: iE = i f + E E (iM ) − i f = 4% + 1.2 7% = 12.4% For Project C: iE = i f + E E (iM ) − i f = 4% + 1.4 7% = 13.8% For Project D: iE = i f + E E (iM ) − i f = 4% + 1.6 7% = 15.2% If Project A’s expected return of 8 percent had been compared to the project-specific required return of 7.5 percent, it would have been accepted. Therefore, Project A would have been incorrectly rejected if the firmwide WACC had been used as its benchmark.
LG6
11-26 Firmwide vs. Project-Specific WACCs An all-equity firm is considering the projects shown as follows. The T-bill rate is 4 percent and the market risk premium is 7 percent. If the firm uses its current WACC of 12 percent to evaluate these projects, which project(s), if any, will be incorrectly accepted? Project A
Expected Return 8.0%
Beta 0.5
Chapter 11 - Calculating the Cost of Capital
B C D
19.0 13.0 17.0
1.2 1.4 1.6
Using the firm’s WACC of 12 percent as the IRR benchmark, projects B, C, and D would be accepted. Using equation 11-2, the project-specific benchmarks for each project should be: For Project A: iE = i f + E E (iM ) − i f = 4% + 0.5 7% = 7.5% For Project B: iE = i f + E E (iM ) − i f = 4% + 1.2 7% = 12.4% For Project C: iE = i f + E E (iM ) − i f = 4% + 1.4 7% = 13.8% For Project D: iE = i f + E E (iM ) − i f = 4% + 1.6 7% = 15.2% If Project C’s expected return of 13 percent had been compared to the project-specific required return of 13.8 percent, it would have been rejected. Therefore, Project C would have been incorrectly accepted if the firmwide WACC had been used as its benchmark. LG7
11-27 Divisional WACCs Suppose your firm has decided to use a divisional WACC approach to analyze projects. The firm currently has four divisions, A through D, with average betas for each division of 0.6, 1.0, 1.3, and 1.6, respectively. If all current and future projects will be financed with half debt and half equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk-free rate of 7 percent) is 13 percent and the after-tax yield on the company’s bonds is 8 percent, what will the WACCs be for each division? Using equation 11-2, we can solve for the expected rate of return on the market:
Chapter 11 - Calculating the Cost of Capital
iE = if + E E (iM ) − i f 13% = 7% +1.0 E (iM ) − 7% 6% = E (iM ) − 7%
E (iM ) = 13%
Reusing equation 11-2, we can solve for the divisional costs of equity using the average divisional betas: For Division A: iE = i f + E E (iM ) − i f = 7% + 0.613% − 7% = 10.6% For Division B: iE = i f + E E (iM ) − i f = 7% +1.013% − 7% = 13.0% For Division C: iE = i f + E E (iM ) − i f = 7% +1.313% − 7% = 14.8% For Division D: iE = i f + E E (iM ) − i f = 7% +1.613% − 7% = 16.6%
Finally, we can solve for the divisional WACCs using equation 11-1: E
D i + i (1− TC ) = 0.510.6% + 0.58% = 9.3% E+P+D E E+P+D D E D For Division B: WACC = i + i (1− TC ) = 0.513.0% + 0.58% =10.5% E E+P+D E+P+D D E D For Division C: WACC = i + i D (1− TC ) = 0.514.8% + 0.58% =11.4% E E+P+D E+P+D E D For Division D: WACC = i + i (1− TC ) = 0.516.6% + 0.58% = 12.3% E+P+D E E+P+D D For Division A: WACC =
LG7
11-28 Divisional WACCs Suppose your firm has decided to use a divisional WACC approach to analyze projects. The firm currently has four divisions, A through D, with average betas for each division of 0.9, 1.1, 1.3, and 1.5, respectively. If all current and future projects will be financed with 25 percent debt and 75 percent equity, and if the current cost of equity (based on an average firm beta of 1.2 and a current risk-free rate of 4 percent) is 12 percent and the after-tax yield on the company’s bonds is 9 percent, what will the WACCs be for each division? Using equation 11-2, we can solve for the expected rate of return on the market:
Chapter 11 - Calculating the Cost of Capital
iE = if + E E (iM ) − if 12% = 4% +1.2 E (iM ) − 4% 8% = E (iM ) − 4% 1.2 E (iM ) = 10.67% Reusing equation 11-2, we can solve for the divisional costs of equity using the average divisional betas: For Division A: iE = i f + E E (iM ) − i f = 4% + 0.9 10.667% − 4% = 10.00% For Division B: iE = if + E E (iM ) − if = 4% +1.110.667% − 4% = 11.33% For Division C: iE = if + E E (iM ) − if = 4% +1.310.667% − 4% = 12.67% For Division D: iE = if + E E (iM ) − if = 4% +1.510.667% − 4% = 14.00%
Finally, we can solve for the divisional WACCs using equation 11-1: D 1− T ) = 0.7510% + 0.25 9% = 9.75% i + i ( C E+P+D E E+P+D D E D 1− T ) = 0.7511.33% + 0.25 9% = 10.75% For Division B: WACC = i + i ( C E+P+D E E+P+D D E D 1− T For Division C: WACC = i + ) = 0.7512.67% + 0.259% = 11.75% iD ( E C E+P+D E+P+D E D 1− T ) = 0.7514% + 0.25 9% = 12.75% For Division D: WACC = i + i ( C E+P+D E E+P+D D For Division A: WACC =
E
Research It! (Web-Exercises): Finding the Before-Tax Cost of Debt, iD For component debt costs, we’d like to use the yield to maturity on bonds that resembles the maturity of our potential debt if possible. Let’s assume that we want to find a bond issue with approximately 10 years until maturity (as of October 2018) for Amazon. Luckily, Amazon has quite a few outstanding bond issues to choose from, and we can access the information on these issues on the Morningstar Bond page. Go to http://finra-markets.morningstar.com/BondCenter/Screener.jsp and start by entering "Amazon" in the “Issuer Name” box and click on “Show Results.” You’ll be presented with an agreement that you have to acknowledge, then a list of Amazon's outstanding bonds sorted in order of increasing maturity. Click on the issue that is closest to the maturity you're looking for, then once the details come up click on the "Yield" tab and hover the mouse over the last part of the line in the graph to see what the latest YTM is.
Chapter 11 - Calculating the Cost of Capital
Your turn: Go to the Morningstar Bond website and find the YTM on the bond with a maturity that’s as close as possible to 10 years from today’s date.
Integrated Minicase: WACC for a New Project LilyMac Studios, a national chain of photography studios, is considering opening up a chain of coffee shop/art galleries. While the existing operations of the firm have a beta of 1.17, the new chain is expected to have a beta of 0.8. LilyMac currently has 500,000 shares of common stock outstanding, which are selling for $63.72 per share, and a $10 million dollar bond issue, selling at 104 percent of par. The expected market risk premium is 6 percent, and the current risk-free rate is 5.5%. The bonds pay an 8 percent semiannual coupon and mature in 20 years. LilyMac’s next expected dividend is $4.00 per share, and future dividends are expected to grow at 4% per year. The current operations of the firm produce EBIT of $18 million per year, and the chain’s operations are expected to add only $25 million per year to that. The new chain will be funded with 65% percent equity and 35% debt, and estimated flotation costs are expected to be 12 percent and 5 percent, respectively. What should be the WACC for the new chain of coffee shops? Solution:
Using the constant growth formula along with the flotation cost of equity, 12 percent of $63.72 will be $7.64, so the cost of equity will be equal to: D1 +g P0 − F $4.00 = + .04 $63.72 − $7.65 = .1113,or 11.13%
iE =
Notice that, without the flotation cost, this would be: D1 +g P0 $4.00 = +.04 $63.72 = .1028,or 10.28%
iE =
Which is an increase of 11.13% - 10.28% = .86% due to the flotation cost, so if we use the CAPM approach, the cost of equity will be equal to:
Chapter 11 - Calculating the Cost of Capital
iE = rf + E ,Pr oject E (rM ) − rf = .055 + 0.8.06 = .103, or 10.3% Which would be similarly adjusted to 10.3% + .86% = 11.16%. Taking an average of the two costs of equity, we will use (11.13% + 11.16%)/2 = 11.145%. The YTM on the new bonds issued to finance this project will be: 1− 1+ 1i ( D )40 + $1000 (1+ i Solve $1,040- (.05*$1,040) = $40 for iD 40 i D D) Which gives us an annual iD of 8.1224%.
Which gives us an after-tax cost of debt of 8.1224%×(1-.21)=6.4167% Using these component costs for equity and debt, and taking the capital structure of the new chain, we get a WACC of: .6511.145% + .35 6.417% = 9.490%
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
CHAPTER 12 – ESTIMATING CASH FLOWS ON CAPITAL BUDGETING PROJECTS
questions LG1
1.
How is the pro forma statement we used in this chapter for computing OCF different from an accountant’s income statement? The two major differences are (1) we do not count interest when computing OCF and (2) we add back depreciation at the end.
LG2
2.
Suppose you paid your old college finance professor to evaluate a project for you. If you would pay him regardless of your decision concerning whether to proceed with the project, should his fee for evaluating the project be included in the project’s incremental cash flows? No, because his fee would be a sunk cost.
LG3
3.
Why does a decrease in NWC result in a cash inflow to the firm? A decrease in NWC involves either a reduction in current assets, which generates cash (e.g., inventory is sold or accounts receivable are collected), or an increase in current liabilities, which involves someone giving the firm credit, thereby freeing up the shareholders’ cash for other things.
LG4
4.
Everything else held constant, would you rather depreciate a project with straight-line depreciation or with DDB? Depreciating quicker is better, so DDB would be preferred.
LG4
5.
Everything else held constant, would you rather depreciate a project with DDB depreciation or deduct it under a Section 179 deduction? Since a Section 179 deduction would allow you to expense the assets immediately rather than depreciating them over multiple periods, this would maximize the project’s NPV, and you would prefer it.
LG5
6.
In a replacement problem, would we ever see changes in NWC? It’s possible. If, for example, the new machine had less wastage of raw materials, then the firm might need less raw materials inventory.
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
LG5
7.
In a replacement problem, will incremental net depreciation always be less than the gross depreciation on the new piece of equipment? No. It would be equal if the old piece of equipment was already fully depreciated.
LG6
8.
In a cost-cutting proposal, what might cause you to sometimes have negative EBIT? Depreciation of the necessary new equipment might be larger than the cost savings during particular periods, especially at the beginning of a project if the assets are depreciated using DDB.
LG7
9.
How many TVM formulas do you use every time you calculate EAC for a project? You use the lump sum present value to find the NPV, and you solve for the payment of an annuity using the present value of an annuity formula, so you use at least two.
LG8
10.
Will an increase in flotation costs increase or decrease the initial cash flow for a project? It will cause the initial cash outflow to increase (i.e., become more negative).
problems basic problems LG3
12-1
After-tax Cash Flow from Sale of Assets Suppose you sell a fixed asset for $109,000 when its book value is $129,000. If your company’s marginal tax rate is 21 percent, what will be the effect on cash flows of this sale (i.e., what will be the after-tax cash flow of this sale)? Using equation 12-3, the after-tax cash inflow from the sale of the asset will be: ATCF = Book value + (Market value - Book value) (1-Tc ) = $129, 000 + ($109, 000 − $129, 000) (1− .21) = $113, 200
LG4
12-2
PV of Depreciation Tax Benefits Your company is considering a new project that will require $1 million of new equipment at the start of the project. The equipment will have a depreciable life of 10 years and will be depreciated to a book value of $150,000 using straight-line depreciation. The cost of capital is 13 percent, and the firm’s tax rate is 21 percent. Estimate the present value of the tax benefits from depreciation. Using equation 12-2, the depreciation per year will be:
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
Depreciable basis - Ending book value Life of asset $1m. − $150,000 = 10 years
Depreciation =
= $85,000 per year With a 21 percent tax rate, this depreciation will save you $85,000 × 0.21 = $28,900 in taxes each year. Across the entire project, these savings will constitute a 10-period annuity, which we can value using equation 5-4: 1 1− 1 1− (1+ i)N (1+ .13)10 PVAN = PMT = $17,850 .13 i = $96,858.45 LG7
12-3
EAC Approach You are trying to pick the least-expensive car for your new delivery service. You have two choices: the Scion xA, which will cost $14,000 to purchase and which will have OCF of -$1,200 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $20,000 to purchase and which will have OCF of -$650 annually throughout that vehicle’s expected four-year life. Both cars will be worthless at the end of their life. If you intend to replace whichever type of car you choose with the same thing when its life runs out, again and again out into the foreseeable future, and if your business has a cost of capital of 12 percent, which one should you choose? One iteration of each delivery car will consist of the following cash flows:
Year 0 1 2 3 4 Scion xA CFs -$14,000 -$1,200 -$1,200 -$1,200 Toyota Prius CFs -$20,000 -$650 -$650 -$650 -$650
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
The NPV of one Scion xA will be: 3
CF0
1 + i = 1+ i CFt
t =0
=
(
)
(
t
−$14, 000
(1.12)
0
+
+
)
0
CF1
+
(1 + i )
1
CF2
+
(1 +
CF
−$1, 200
(
= −$
Treating this as the present value of a three-period annuity, setting i to 12 percent, and solving for payment will yield a payment of -$7,028.89, which is the Scion’s EAC. The NPV of one Toyota Prius will be: 4
CF1
CF0
CF2
CF3
CF4
(1 + i ) = (1 + i ) + (1 + i ) + (1 + i ) + (1 + i ) + (1 + i ) CFt
t
t =0
=
0
−$20, 000
(1.12)
0
+
−$650
(1.12)
1
1
+
2
−$650
(1.12)
2
+
3
−$650
(1.12)
3
+
4
−$650
(1.12)
4
= −$21, 974.2771
Treating this as the present value of a four-period annuity, setting i to 12 percent, and solving for payment will yield a payment of -$7,234.69, which is the Toyota’s EAC. Based on the EACs, we should choose the Scion. LG8
12-4
EAC Approach You are evaluating two different cookie-baking ovens. The Pillsbury 707 costs $57,000, has a five-year life, and has an annual OCF (after tax) of -$10,000 per year. The Keebler CookieMunster costs $90,000, has a seven-year life, and has an annual OCF (after tax) of -$8,000 per year. If your discount rate is 12 percent, what is each machine’s EAC? One iteration of each oven will consist of the following cash flows:
Year 0 Pillsbury -$57,000 CFs Keebler -$90,000 CFs
1 -$10,000
2 -$10,000
3 -$10,000
4 5 -$10,000 -$10,000
-$8,000
-$8,000
-$8,000
-$8,000
The NPV of one Pillsbury 707 will be:
-$8,000
6
7
-$8,000
-$8,000
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
5
1+ i CFt
t =0
=
(
= t
)
−$57, 000
(1.12)
0
+
CF0
(1 + i)
+
0
CF1
(1 + i )
1
−$10, 000
(1.12)
1
+
+
CF2
+ 2
(1 + i )
CF3
+ 3
(1 + i )
CF4
(1
+
CF
−$10, 000
= −$93
Treating this as the present value of a five-period annuity, setting i to 12 percent, and solving for payment will yield a payment of -$25,812.35, which is the Pillsbury 707’s EAC. The NPV of one Keebler CookieMunster will be:
Treating this as the present value of a seven-period annuity, setting i to 12 percent, and solving for payment will yield a payment of -$27,720.60, which is the Keebler Cookie Munster’s EAC. Based on the EACs, we should choose the Pillsbury 707. LG8
12-5
EAC Approach You are considering the purchase of one of two machines used in your manufacturing plant. Machine A has a life of two years, costs $80 initially, and then $125 per year in maintenance costs. Machine B costs $150 initially, has a life of three years, and requires $100 in annual maintenance costs. Either machine must be replaced at the end of its life with an equivalent machine. Which is the better machine for the firm? The discount rate is 12 percent and the tax rate is zero. One iteration of each machine will consist of the following cash flows:
Year 0 1 2 3 Machine A CFs -$80 -$125 -$125 Machine B CFs -$150 -$100 -$100 -$100
The NPV of one Machine A will be:
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
2
1+ i
CFt
t =0
=
(
−$80
(1.12)
0
= t
)
+
CF0
+
(1 + i )
0
−$125
(1.12)
1
+
CF1
(1 + i )
1
+
CF2
(1 + i )
2
−$125
(1.12)
2
= −$291.2564
Treating this as the present value of a two-period annuity, setting i to 12 percent, and solving for payment will yield a payment of -$172.34, which is Machine A’s EAC. The NPV of one Machine B will be:
Treating this as the present value of a three-period annuity, setting i to 12 percent, and solving for payment will yield a payment of -$162.45, which is Machine B’s EAC. Based on the EACs, we should choose Machine B.
intermediate problems LG3
12-6
Project Cash Flows KADS, Inc. has spent $400,000 on research to develop a new computer game. The firm is planning to spend $200,000 on a machine to produce the new game. Shipping and installation costs of the machine will be capitalized and depreciated; they total $50,000. The machine has an expected life of three years, a $75,000 estimated resale value, and falls under the MACRS seven-year class life. Revenue from the new game is expected to be $600,000 per year, with costs of $250,000 per year. The firm has a tax rate of 21 percent, an opportunity cost of capital of 15 percent, and it expects net working capital to increase by $100,000 at the beginning of the project. What will the cash flows for this project be?
Year Sales – Fixed costs
0 $0.00 0
1 $600,000.00 250,000.00
2 $600,000.00 250,000.00
3 $600,000.00 250,000.00
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
– Depreciation EBIT – Taxes (@21%) Net income + Depreciation OCF – ΔNWC – ΔFA FCF
LG4
12-7
0 $0.00
35,725.00 $314,275.00
61,225.00 $288,775.00
43,725.00 $306,275.00
0
65,997.75
60,642.75
64,317.75
$0.00 0 $0.00 100,000.00 250,000.00 ($350,000.00)
$248,277.25 35,725.00 $284,002.25 0 0 $284,002.25
$228,132.25 61,225.00 $289,357.25 0 0 $289,357.25
$241,957.25 43,725.00 $285,682.25 -100,000.00 -87,013.75 $472,696.00
Depreciation Tax Shield Your firm needs a computerized machine tool lathe which costs $50,000, and requires $12,000 in maintenance for each year of its three-year life. After three years, this machine will be replaced. The machine falls into the MACRS three-year class life category. Assume a tax rate of 21 percent and a discount rate of 12 percent. Calculate the depreciation tax shield for this project in year 3. Depreciation in year 3 will be 14.81% × $50,000 = $7,405. This will save the firm $7,405 × 0.21 = $1,555.05 in taxes.
LG4
12-8
After-tax Cash Flow from Sale of Assets If the lathe in the previous problem can be sold for $5,000 at the end of year 3, what is the after-tax salvage value? The lathe will have a remaining book value of 7.41% × $50,000 = $3,705. Using equation 12-3, the after-tax cash flows from the sale of the lathe will be: ATCF = Book Value + (Market Value - Book Value) (1-TC ) = $3, 705 + ($5, 000 − $3, 705) (.79) = $4, 728.05
LG6
12-9
Project Cash Flows You have been asked by the president of your company to evaluate the proposed acquisition of a new special-purpose truck for $60,000. The truck falls into the MACRS three-year class, and it will be sold after three years for $20,000. Use of the truck will require an increase in NWC (spare parts inventory) of $2,000. The truck will have no effect on revenues, but it is expected to save the firm $20,000 per year in beforetax operating costs, mainly labor. The firm's marginal tax rate is 21 percent. What will the cash flows for this project be?
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
0
Year Sales
1
2
3
$0.00
$0.00
$0.00
$0.00
– Variable costs
0
0
0
0
– Fixed costs
0
-20,000.00
-20,000.00
-20,000.00
– Depreciation
0
19,998.00
26,670.00
8,886.00
$0.00
$2.00
($6,670.00)
$11,114.00
0
$0.42
($1,400.70)
$2,333.94
“Net income”
$0.00
$1.58
($5,269.30)
$8,780.06
+ Depreciation
0
19,998.00
26,670.00
8,886.00
$0.00
$19,999.58
$21,400.70
$17,666.06
– ΔNWC
2,000.00
0
0
-2,000.00
– ΔFA
60,000.00
0
0
-13,778.40
FCF
($62,000.00)
$19,999.58
$21,400.70
$33,444.46
EBIT – Taxes
OCF
advanced problems LG3
12-10 Changes in NWC You are evaluating a project for The Tiff-any golf club, guaranteed to correct that nasty slice. You estimate the sales price of The Tiff-any to be $400 per unit and sales volume to be 1,000 units in year 1; 1,500 units in year 2; and 1,325 units in year 3. The project has a three-year life. Variable costs amount to $225 per unit and fixed costs are $100,000 per year. The project requires an initial investment of $165,000 in assets, which will be depreciated straight-line to zero over the three-year project life. The actual market value of these assets at the end of year 3 is expected to be $35,000. NWC requirements at the beginning of each year will be approximately 20 percent of the projected sales during the coming year. The tax rate is 21 percent and the required return on the project is 10 percent. What change in NWC occurs at the end of year 1? Sales will go from $400,000 to $600,000 between years 1 and 2, so NWC will have to increase from $80,000 to $120,000, an increase of $40,000.
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
LG3
12-11 Operating Cash Flow Continuing the previous problem, what is the operating cash flow for the project in year 2?
2
Year Sales
$600,000
– Variable costs
337,500
– Fixed costs
100,000
– Depreciation
55,000
EBIT
$107,500
– Taxes
22,575
“Net income”
$84,925
+ Depreciation
55,000
OCF
LG3
$139,925
12-12 Project Cash Flows You are considering adding a new software title to those published by your highly successful software company. If you add the new product, it will use capacity on your disk duplicating machines that you had planned on using for your flagship product, “Battlin’ Bobby.” You had planned on using the unused capacity to start selling “BB” on the west coast in two years. You would eventually have had to purchase additional duplicating machines 10 years from today, but using the capacity for your new product will require moving this purchase up to two years from today. If the new machines will cost $100,000 and will be depreciated straight-line over a five-year period to a zero salvage value, your marginal tax rate is 21 percent, and your cost of capital is 12 percent, what is the opportunity cost associated with using the unused capacity for the new product? At the time of purchase, the purchase itself has a present value of -$100,000 + the present value of the depreciation tax shields received at times 1 through 6:
Time Depreciation ×Tax Rate Tax Shield from
1 $ $
2 10000 0.21 2100
$ $
20000 0.21 4200
$ $
3 20000 0.21 4200
$ $
20000 0.21 4200
$ $
20000 0.21 4200
$ $
20000 0.21 4200
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
Depreciation PV of Tax Shield Sum of PV of Tax Shields
$ 1875.00 $ 15392.91
$ 3348.21
$ 2989.48
$ 2669.18
$ 2383.19
$ 2127.85
Or –$100,000 + $15,392.91 = –$84,607.09. The opportunity cost is the difference in PV terms in having to pay this in two years versus 10 years: 1 1 = – $40, 207.04 –$84, 607.09 – $84, 607.09 1.1210 1.122 LG3
12-13 Project Cash Flows You are evaluating a project for The Ultimate recreational tennis racket, guaranteed to correct that wimpy backhand. You estimate the sales price of The Ultimate to be $400 per unit and sales volume to be 1,000 units in year 1; 1,250 units in year 2; and 1,325 units in year 3. The project has a three-year life. Variable costs amount to $225 per unit and fixed costs are $100,000 per year. The project requires an initial investment of $165,000 in assets, which will be depreciated straight-line to zero over the three-year project life. The actual market value of these assets at the end of year 3 is expected to be $35,000. NWC requirements at the beginning of each year will be approximately 20 percent of the projected sales during the coming year. The tax rate is 21 percent and the required return on the project is 10 percent. What will the cash flows for this project be?
Year Sales – Variable costs – Fixed costs – Depreciation EBIT – Taxes Net income + Depreciation OCF – ΔNWC – ΔFA Total cash flow
LG5
0
1
2
3
$0.00 0 0 0 $0.00 0 $0.00 0 $0.00 -80,000.00 -165,000.00 ($245,000.00)
$400,000.00 -225,000.00 -100,000.00 -27,505.50 $47,494.50 9,973.85 $37,520.66 27,505.50 $65,026.16 -20,000.00 0 $45,026.16
$500,000.00 -281,250.00 -100,000.00 -54,994.50 $63,755.50 13,388.66 $50,366.85 54,994.50 $105,361.35 -6,000.00 0 $99,361.35
$530,000.00 -298,125.00 -100,000.00 -54,994.50 $76,880.50 16,144.91 $60,735.60 54,994.50 $115,730.10 106,000.00 32,451.87 $254,181.97
12-14 Project Cash Flows Mom's Cookies, Inc. is considering the purchase of a new cookie oven. The original cost of the old oven was $30,000; it is now five years old, and it has a current market value of $13,333.33. The old oven is being depreciated over a 10-year life toward a zero estimated salvage value on a straight-line basis, resulting in a current book value of $15,000 and an annual depreciation expense of $3,000. The old oven can be used
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
for six more years but has no market value after its depreciable life is over. Management is contemplating the purchase of a new oven whose cost is $25,000 and whose estimated salvage value is zero. Expected before-tax cash savings from the new oven are $4,000 a year over its full MACRS depreciable life. Depreciation is computed using MACRS over a five-year life, and the cost of capital is 10 percent. Assume a 21 percent tax rate. What will the cash flows for this project be? Using equation 12-3, the after-tax cash inflows of the sale of the old oven today would be: ATCF = Book Value + (Market Value - Book Value) (1-TC ) = $15, 000 + ($13, 333 − $15, 000) (.79) = $13, 683.33 Which will be counted as a cash inflow at the beginning of the proposed replacement:
LG5
12-15 Project Cash Flows Your company is contemplating replacing their current fleet of delivery vehicles with Nissan NV vans. You will be replacing 5 fully-depreciated vans, which you think you can sell for $3,000 apiece and which you could probably use for another 2 years if you chose not to replace them. The NV vans will cost $29,850 each in the configuration you want them, and can be depreciated using MACRS over a 5-year life. Expected yearly before-tax cash savings due to acquiring the new vans amounts to about $3,700 each. If your cost of capital is 8 percent and your firm faces a 21 percent tax rate, what will the cash flows for this project be? The five vans can be sold today for $15,000 and have a book value of $0, so, using equation 12-3, the after-tax cash inflows of the sale of the old vans today would be:
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
ATCF = Book Value + (Market Value - Book Value) (1-TC ) = $0 + ($15, 000 − $0) (.79) = $11,850 Which will be counted as a cash inflow at the beginning of the proposed replacement, partially offsetting the sum of the cash outflows (5 × $29,850 = $149,250) for the new vans: Year
0
Net Incremental Sales Net Incremental Variable Costs Depreciation on New Vans Foregone Depreciation on Old Vans Less: Incremental Depreciation EBIT Less: Taxes Net Income Plus: Depreciation OCF ΔFA for New Vans ΔFA for Old Vans
1
2 $0 -$3,700
$29,850 $0 $0 $0 $0 $0 $0 $0
3 $0 -$3,700
$47,760 $0 $29,850 -$26,150 -$5,492 -$20,659 $29,850
4 $0 -$3,700
$28,656 $0 $47,760 -$44,060 -$9,253
5 $0 -$3,700
6 $0
$17,194 $0 $28,656
$149,250 -$11,85
ΔFA ΔNWC Less: Investmen FCF =
research it! What is the maximum Section 179 deduction for the current tax year? As of 2018, the maximum Section 179 deduction was $1,000,000. Integrated Minicase Your company, Dawgs “R” Us, is evaluating a new project involving the purchase of a new oven to bake your hotdog buns. If purchased, the new oven will replace your existing oven, which was purchased seven years ago for a total, installed price of $1,000,000. Depreciation on the old oven has been being computed on a straight-line basis over its expected life of 15 years to an ending book value of $250,000, even though you expect it to be worthless at the end of that 15-year period. The new oven will cost $2,000,000 and will fall into the MACRS 5-year class life for depreciation purposes. If you purchase it, it is expected to last for eight years, at the end of which you expect to be able to sell it for $100,000. (Note that both of the ovens, old and new, therefore have an effective remaining life of eight years at the time of your analysis.) If you do purchase the new oven, you estimate that you can sell the old one for its current book value at the same time. The advantages of the new oven are two-fold: not only do you expect it to reduce the before-tax costs on your current baking operations by $75,000 per year, but you will also be able to produce new types of buns. The sales of the new buns are expected to be $200,000 per year throughout the eight-year life of the new oven, while associated costs of the new buns are only expected to be $80,000 per year.
Chapter 12 - Estimating Cash Flows on Capital Budgeting Projects
Since the new oven will allow you to sell these new products, you anticipate that NWC will have to increase immediately by $20,000 upon purchase of the new oven. It will then remain at that increased level throughout the life of the new oven to sustain the new, higher level of operations. Your company uses a required rate of return of 12 percent for such projects, and your incremental tax rate is 21 percent. What will be the total cash flows for this project?
Year Net Incremental Sales Net Incremental Variable Costs Depreciation on New Oven Foregone Depreciation on Old Oven Less: Incremental Depreciation EBIT Less: Taxes Net Income Plus: Depreciation OCF ΔFA for New Oven ΔFA for Old Oven ΔFA ΔNWC Less: Investment in Operating Capital FCF = OCF - IOC
0
1
2 $200,000 $5,000
$400,000 -$50,000 $0 $0 $0 $0 $0 $0 $2,000,000 -$650,000 $1,350,000 $20,000
$640,000 -$50,000 $350,000 -$155,000 -$32,550 -$122,450 $350,000 $227,550
$0 $0 $1,370,000 -$1,370,000
3 $200,000 $5,000 $384,000 -$50,000
$590,000 -$395,000 -$82,950 -$312,050 $590,000 $277,950
$0 $0 $0 $227,550
4 $200,000 $5,000 $230,400 -$50,000
$334,000 -$139,000 -$29,190 -$109,810 $334,000 $224,190
$0 $0 $0 $277,950
5 $200,000 $5,000 $230,400 -$50,000 $180,400 $14,600 $3,066 $11,534 $180,400 $191,934
$0 $0 $0 $224,190
6 $200,000 $5,000 $115,200 -$50,000 $180,400 $14,600 $3,066 $11,534 $180,400 $191,934
$0 $0 $0 $191,934
7 $200,000 $5,000 $0 -$50,000 $65,200 $129,800 $27,258 $102,542 $65,200 $167,742
$0 $0 $191,934
8 $200,000 $5,000
-$50,000 $245,000 $51,450 $193,550 -$50,000 $143,550
$0 $0 $167,742
$200,000 $5,000 $0 -$50,000 -$50,000 $245,000 $51,450 $193,550 -$50,000 $143,550 -$66,000 $0 -$20,000
$0 $143,550
-$20,000 $229,550
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
CHAPTER 13 - WEIGHING NET PRESENT VALUE AND OTHER CAPITAL BUDGETING CRITERIA
questions LG1
1.
Is the set of cash flows depicted in the following table normal or non-normal? Explain. Time 0 1 2 3 4 5 Cash Flow -$100 -$50 -$80 $0 $100 $100
They are normal; there is only one change in cash flows from negative to positive. LG1
2.
Derive an accept/reject rule for IRR similar to equation 13-8 that would make the correct decision on cash flows that are non-normal, but that always have one large positive cash flow at time zero followed by a series of negative cash flows: Time 0 1 2 3 4 5 Cash Flow + - - - - -
With one positive at the beginning and all future cash flows negative, this type of project would be worth more if rates were higher, implying that the NPV profile would be upward-sloping. So the appropriate accept/reject decision rule would look like: Accept project if IRR ≤ Cost of capital Reject project if IRR > Cost of capital LG1
3.
Is it possible for a company to initiate two products that target the same market that are not mutually exclusive? Sure, as long as the market has room for both products and the company has sufficient resources to produce both simultaneously.
LG2
4.
Suppose that your company used “APV,” or “All-the-Present Value-Except-CF0”, to analyze capital budgeting projects. What would this rule’s benchmark value be? Accept project if APV ≥ -CF0 Reject project if APV < -CF0
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
LG3
5.
Under what circumstances could payback and discounted payback be equal? They would be equal if i = 0.
LG5
6.
Could a project’s MIRR ever exceed its IRR? MIRR would be greater than IRR if a project with normal cash flows had a negative NPV.
LG6
7.
If you had two mutually exclusive, normal-cash-flow projects whose NPV profiles crossed at all points, for which range of interest rates would IRR give the right accept/reject answer? At all rates, because we would be indifferent between the two projects at any rate.
LG7
8.
Suppose a company wanted to double their firm’s value with the next round of capital budgeting project decisions. To what would they set the PI benchmark to make this goal? They would set it equal to two.
LG5
9.
Suppose a company faced different borrowing and lending rates. How would this range change the way that you would compute the MIRR statistic? We would want to use the borrowing rate to move the negative cash flows to time 0, and the lending rate to move the positive cash flows to the end of the project.
problems basic problems LG2
13-1
NPV with Normal Cash Flows Compute the NPV for Project M and accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 8 percent. Project M Time 0 1 2 3 4 5 Cash Flow -$1,000 $350 $480 $520 $600 $100 Using equation 13-2:
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
NPV = −$1, 000 +
$350
+
(1.08)
1
$480
+
(1.08)
2
$520
+
(1.08)
3
$600
+
(1.08)
4
$100
(1.08)
5
= $657.47 The project should be accepted. LG2
13-2
NPV with Normal Cash Flows Compute the NPV statistic for Project Y and note whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 12 percent. Project Y Time 0 1 2 3 4 Cash Flow -$8,000 $3,350 $4,180 $1,520 $300
Using equation 13-2: NPV = −$8, 000 +
$3, 350
(1.12)
1
+
$4,180
(1.12)
2
+
$1, 520
(1.12)
3
+
$300
(1.12)
4
= −$404.10
The project should be rejected. LG2
13-3
NPV with Non-normal Cash Flows Compute the NPV statistic for Project U and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is ten percent. Project U Time 0 1 2 3 4 5 Cash Flow -$1,000 $350 $1,480 -$520 $300 -$100
Using equation 13-2: NPV = −$1, 000 +
$350
(1.10)
1
+
$1, 480
(1.10)
= $293.45
The project should be accepted.
2
+
−$520
(1.10)
3
+
$300
(1.10)
4
+
−$100
(1.10)
5
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
LG3
13-4
NPV with Non-normal Cash Flows Compute the NPV statistic for Project K and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is six percent. Project K Time 0 1 2 3 4 5 Cash Flow -$10,000 $5,000 $6,000 $6,000 $5,000 -$10,000
Using equation 13-2: NPV = −$10, 000 +
$5, 000
(1.06)
1
+
$6, 000
(1.06)
2
+
$6, 000
(1.06)
3
+
$5, 000
(1.06)
4
+
−$10, 000
(1.06)
5
= $1, 582.56
The project should be accepted.
LG3 13-5 Payback Compute the payback statistic for Project B and decide whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 12 percent and the maximum allowable payback is three years. Project B Time 0 1 2 3 4 5 Cash Flow -$11,000 $3,350 $4,180 $1,520 $0 $1,000 Solving equation 13-3 for N: Year Cash Flow Cumulative Cash Flow
0 -$11,000
1 $3,350
2 $4,180
3 $1,520
4 $0
5 $1,000
-$11,000
-$7,650
-$3,470
-$1,950
-$1,950
-$950
This project will never achieve payback, and should be rejected. LG3
13-6
Payback Compute the payback statistic for Project A and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 8 percent and the maximum allowable payback is four years.
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
Project A Time 0 1 2 3 4 5 Cash Flow -$1,000 $350 $480 $520 $300 $100
Solving equation 13-3 for N: Year Cash Flow Cumulative Cash Flow
0 -$1,000
1 $350
2 $480
3 $520
-$1,000
-$650
-$170
$350
4 $300
5 $100
This project will achieve payback at time 2 + $170/$520 = 2.33 years. LG3
13-7
Discounted Payback Compute the discounted payback statistic for Project C and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 8 percent and the maximum allowable discounted payback is three years. Project C Time 0 1 2 3 4 5 Cash Flow -$1,000 $480 $480 $520 $300 $100 Solving equation 13-5 for N, cumulative PV of cash flow will switch from negative and positive between years 2 and 3: Year Cash Flow Cash Flow PV Cum. Cash Flow PV
0 -$1,000 -$1,000 -$1,000
1 $480
2 $480
3 $520
$480
$480
$520
(1.08) = $444.44 1
-$555.56
(1.08)
(1.08)
= $411.52 -$144.04
= $412.79 $268.75
2
4 $300
3
Specifically, DPB = 2+$144.04/412.79 = 2.35 and this project should be accepted. LG3
13-8
Discounted Payback Compute the discounted payback statistic for Project D and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 12 percent and the maximum allowable discounted payback is four years.
5 $100
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
Project D Time 0 1 2 3 4 5 Cash Flow -$11,000 $3,350 $4,180 $1,520 $0 $1,000
The NPV for this project is negative, so discounted payback never occurs. LG5
13-9
IRR Compute the IRR statistic for Project E and note whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 8 percent. Project E Time 0 1 2 3 4 5 Cash Flow -$1,000 $350 $480 $520 $300 $100
The IRR for this project will be the solution to equation 13-7: 0=
−$1, 000
(1+ IRR)
0
+
$350
(1+ IRR)
1
+
$480
(1+ IRR)
2
+
$520
(1+ IRR)
3
+
$300
(1+ IRR)
4
+
$100
(1+ IRR)
5
IRR = 25.49%
Since IRR > i, this project should be accepted. LG5
13-10 IRR Compute the IRR statistic for project F and note whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 12 percent. Project F Time 0 1 2 3 4 Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000 The IRR for this project will be the solution to equation 13-7: 0=
−$11, 000
(1+ IRR)
0
+
$3, 350
(1+ IRR)
1
+
$4,180
(1+ IRR)
2
+
$1, 520
(1+ IRR)
IRR = 0.21%
Since IRR < i, this project should be rejected..
3
+
$2, 000
(1+ IRR)
4
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
LG5
13-11 MIRR Compute the MIRR statistic for Project I and tell whether to accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 12 percent. Project I Time 0 1 2 3 4 Cash Flow -$11,000 $5,330 $4,180 $1,520 $2,000
Cash flows will be moved as shown as follows: Year Cash Flow Future Value (If Positive) Sum of FV Modified CFs
0 -$11,000
1 $5,330
2 $4,180
3 $1,520
4 $2,000
$5, 330 (1.12)
$4,180 (1.12)
$1,520 (1.12)
= $7, 488.27
= $5, 243.39
= $1, 702.40
3
2
1
$2, 000
$16,434.06 -$11,000
$16,434.06
With this new set of modified cash flows, the MIRR is: 0=
−$11, 000
(1+ IRR)
0
+
$16, 434.06
(1+ IRR)
4
IRR = 10.56%
Since our MIRR decision statistic is less than the 12 percent cost of capital, we would reject the project under the MIRR method. LG5 13-12 MIRR Compute the MIRR statistic for Project J and advise whether to accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 10 percent. Project J Time 0 1 2 3 4 5 Cash Flow -$1,000 $350 $1,480 -$520 $300 -$100
Cash flows will be moved as shown as follows: Year Cash Flow
0 -$1,000
1 $350
2 $1,480
3 -$520
4 $300
5 -$100
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
Present Value (If Negative)
−$520
−$100
(1.10)
(1.10)
= −$390.68
= −$62.09
3
-$1,000
5
Sum of PV -$1,452.78 $1, 480 (1.10)
3
$350 (1.10)
Future Value (If Positive) Sum of FV Modified CFs -$1,452.78
4
$300 (1.10)
1
= $1, 969.88
= $512.44
= $330
$2,812.32 $2,812.32
With this new set of modified cash flows, the MIRR is: 0=
−$1, 452.78 $2,812.32 + 0 5 1+ IRR ( ) (1+ IRR)
IRR = 14.12%
Since our MIRR decision statistic is greater than the 10 percent cost of capital, we would accept the project under the MIRR method. LG5
13-13 PI Compute the PI statistic for Project Z for and advise the firm whether to accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 8 percent. Project Z Time 0 1 2 3 4 5 Cash Flow -$1,000 $350 $480 $650 $300 $100 Using equation 13-10: NPV = −$1, 000 +
$350
(1.08)
1
+
$480
(1.08)
= $540.15 PI =
$540.15 + $1, 000 = 1.54 $1, 000
2
+
$650
(1.08)
3
+
$300
(1.08)
4
+
$100
(1.08)
5
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
Since PI > 1, the project should be accepted. LG5
13-14 PI Compute the PI statistic for Project Q and tell whether you would accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 12 percent. Project Q Time 0 1 2 3 4 Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000
Using equation 13-10: NPV = −$11, 000 +
$3, 350
(1.12)
1
+
$4,180
(1.12)
2
+
$1, 520
(1.12)
3
+
$2, 000
(1.12)
4
= −$2, 323.72 PI =
−$2, 323.72 + $11, 000 = 0.79 $11, 000
Since PI < 1, the project should be rejected. LG1
13-15 Multiple IRRs How many possible IRRs could you find for the following set of cash flows? Time 0 1 2 3 4 Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000 Since there’s only one change in sign, there can only be one IRR.
LG1
13-16 Multiple IRRs How many possible IRRs could you find for the following set of cash flows? Time 0 1 2 3 4 Cash Flow -$211,000 -$39,350 $440,180 $217,520 -$2,000
Since there are two changes in sign, there could potentially be as many as two IRRs.
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
intermediate problems Use this information to answer the next six questions. If a particular decision method should not be used, indicate why. Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 8 percent, and that the maximum allowable payback and discounted payback statistics for the project are 3.5 and 4.5 years, respectively. Time Cash Flow LG3
0
1
2
3
4
5
6
-$5,000
$1,200
$2,400
$1,600
$1,600
$1,400
$1,200
13-17 Payback Use the payback decision rule to evaluate this project; should it be accepted or rejected? Cumulative cash flow will switch from negative to positive between years 2 and 3: Year Cash Flow Cumulative Cash Flow
0 -$5,000 -$5,000
Specifically, PB = 2 +
1 $1,200 -3,800
2 $2,400 -1,400
3 4 $1,600 $1,600 200
5 $1,400
6 $1,200
$1, 400
= 2.88 years , which is less than the maximum allowable $1, 600 payback, so this project should be accepted.
LG3
13-18 Discounted Payback Use the discounted payback decision rule to evaluate this project; should it be accepted or rejected? Cumulative PV of cash flow will switch from negative to positive between years 3 and 4: Year Cash Flow Cash Flow PV Cum. Cash Flow PV
0 -$5,000 -$5,000 -$5,000
1 $1,200 $1,111 -$3,889
2 $2,400 $2,058 -$1,831
3 $1,600 $1,270 -$561
4 $1,600 $1,176 $615
5 $1,400 $953 $710
6 $1,200 $756
$561 = 3.48 years , which is less than the maximum allowable $1,176 payback of 4.5 years, so this project should be accepted.
Specifically, DPB = 3 +
LG5
13-19 IRR Use the IRR decision rule to evaluate this project; should it be accepted or rejected? The IRR for this project will be the solution to:
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
IRR > than required rate of return this project should be accepted.
LG5
13-20 MIRR Use the MIRR decision rule to evaluate this project; should it be accepted or rejected? Cash flows will be moved asfollows:
Year 0 Cash Flow $5,000 Future Value (If Positive) Sum of FV Modified CFs $5,000
1
2
3
4
5
6
$1,200
$2,400
$1,600
$1,600
$1,400
$1,200
$1, 200 (1.08)
$2, 400 (1.08)
$1, 600 (1.08)
$1, 600 (1.08)
$1, 400 (1.08)
= $1, 763.19
= $3, 265.17
= $2, 015.54
= $1, 866.24
= $1, 512
5
4
3
2
1
$11,622.15 $11,622.15 With this new set of modified cash flows, the MIRR is: 0=
−$5, 000
(1+ IRR)
0
+
$11, 622.15
(1+ IRR)
6
IRR = 15.09%
Since our MIRR decision statistic is greater than the 8 percent cost of capital, we would accept the project under the MIRR method. LG2
$1, 200
13-21 NPV Use the NPV decision rule to evaluate this project; should it be accepted or rejected? NPV = −$5, 000 + = $2, 323.92
$1, 200 $2, 400 $1, 600 $1, 600 $1, 400 $1, 200 + + + + + 1 2 3 4 5 6 (1.08) (1.08) (1.08) (1.08) (1.08) (1.08)
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
The project should be accepted because the NPV is positive.
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
LG7
13-22 PI Use the PI decision rule to evaluate this project; should it be accepted or rejected? NPV = −$5, 000 +
$1, 200 $1, 400 $1, 600 $1, 600 $1, 400 $1, 200 + + + + + 1 1 1 1 1 1 1.08 1.08 1.08 1.08 1.08 ( ) ( ) ( ) ( ) ( ) (1.08)
= $2, 323.92 PI =
$2, 323.92 + $5, 000 = 1.46 $5, 000
Since PI > 1, the project should be accepted. Use this information to answer the next six questions. If you should not use a particular decision technique, indicate why. Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 11 percent, and that the maximum allowable payback and discounted payback statistics for your company are 3 and 3.5 years, respectively. Time 0 1 2 3 4 5 Cash Flow -$235,000 $65,800 $84,000 $141,000 $122,000 $81,200 LG3
13-23 Payback Use the payback decision rule to evaluate this project; should it be accepted or rejected? Cumulative cash flow will switch from negative a positive between years 2 and 3: Year Cash Flow Cumulative Cash Flow
0 -$235,000 -$235,000
Specifically, PB = 2 + LG3
1 $65,800 -$169,200
2 $84,000 -$85,200
3 $141,000 $55,800
4 $122,000 $177,800
5 $81,200 $259,000
$85, 200 = 2.60 years so this project should be accepted. $141, 000
13-24 Discounted Payback Use the discounted payback decision rule to evaluate this project; should it be accepted or rejected? Cumulative PV of cash flow will switch from negative and positive between years 3 and 4: Year Cash Flow
0 -$235,000
1 $65,800
2 $84,000
3 $141,000
4 $122,000
5 $81,200
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
Cash Flow PV
-$235,000
Cum. Cash Flow PV
-$235,000
$65, 800
$84, 000
$141, 000
$122, 000
(1.11)
(1.11)
(1.11)
(1.11)
= $59, 279.28
= $68,176.28
= $103, 097.98
= $80, 365.18
-$175,721
-$107,544
-$4,446
$75,919
1
2
3
4
$4, 446 = 3.05 years , which is less than the maximum $80, 365.18 allowable discounted payback, so project should be accepted.
Specifically, DPB = 3 +
LG5
13-25 IRR Use the IRR decision rule to evaluate this project; should it be accepted or rejected? The IRR for this project will be the solution to: −$235, 000 $65,800 $141, 000 $122, 000 $84, 000 $81, 200 0= + + + + + 2 0 1 3 4 (1+ IRR) (1+ IRR) (1+ IRR) (1+ IRR) (1+ IRR) (1+ IRR)5 IRR = 28.79% Since IRR > i, this project should be accepted.
LG5
13-26 MIRR Use the MIRR decision rule to evaluate this project; should it be accepted or rejected? Cash flows will be moved as follows:
Year Cash Flow Future Value (If Positive) Sum of FV Modified CFs
0
1
2
3
4
5
-$235,000
$65,800
$84,000
$141,000
$122,000
$81,200
$65, 800 (1.11)
4
= $99, 889.03
$84, 000 (1.11)
$141, 000 (1.11)
= $114, 881
= $173, 726.10
3
2
$122, 000 (1.11)
1
= $135, 420
$81, 200
$605,116.14 -$235,000 With this new set of modified cash flows, the MIRR is:
$605,116.14
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
0=
−$235, 000
(1+ IRR)
0
+
$605,116.14
(1+ IRR)
5
IRR = 20.82%
Since our MIRR decision statistic is greater than the 11 percent cost of capital, we would accept the project under the MIRR method. LG2
13-27 NPV Use the NPV decision rule to evaluate this project; should it be accepted or rejected? NPV = −$235, 000 +
$65, 800
(1.11)
1
+
$84, 000
(1.11)
2
+
$141, 000
(1.11)
3
+
$122, 000
(1.11)
4
+
$81, 200
(1.11)
5
= $124,106.98
Since NPV > 0, the project should be accepted. LG7
13-28 PI Use the PI decision rule to evaluate this project; should it be accepted or rejected? NPV = −$235, 000 +
$6, 580 $84, 000 $141, 000 $122, 000 $81, 200 + + + + 1 2 3 4 5 (1.11) (1.11) (1.11) (1.11) (1.11)
= $124,106.98 PI =
$124,106.98 + $235, 000 = 1.53 $235, 000
Since PI > 1, the project should be accepted.
advanced problems Use the project cash flows for the two mutually exclusive projects shown below to answer the following two questions.
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
LG6
13-29 NPV Profiles Graph the NPV profiles for both projects on a common chart, making sure that you identify all of the “crucial” points. Since the two NPV profiles shown below do not cross in the first quadrant, the only crucial points are the two projects’ IRRs: IRRA = 13 percent and IRRB = 14.29 percent NPV Profiles
$600.00 $500.00 $400.00
NPV
$300.00 $200.00 $100.00
r A
LG6
B
13-30 IRR Applicability For what range of possible interest rates would you want to use IRR to choose between these two projects? For what range of rates would you NOT want to use IRR? Since the two projects’ NPV profiles do not cross in the first quadrant, IRR would work for ALL possible ranges of rates.
LG6
13-31 Multiple IRRs Construct an NPV profile and determine EXACTLY how many nonnegative IRRs you can find for the following set of cash flows:
20.00%
19.00%
18.00%
17.00%
16.00%
15.00%
14.00%
13.00%
12.00%
11.00%
9.00%
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
10.00%
-$200.00
1.00%
-$100.00
0.00%
$-
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
As the following graph shows, there appears to be only one.
LG6
13-32 Multiple IRRs Construct an NPV profile and determine EXACTLY how many nonnegative IRRs you can find for the following set of cash flows:
As shown, there appears to be only one.
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
research it! Business Valuation The capital budgeting decision techniques that we’ve discussed all have strengths and weaknesses, but they do comprise the most popular rules for valuing projects. Valuing entire businesses, on the other hand, requires that some adjustments be made to various pieces of these methodologies. For example, one alternative to NPV used quite frequently for valuing firms is called Adjusted Present Value (APV). To explore these alternative decision rules, do a Web search for APV and answer the following questions: 1. What is APV, and how does it differ from NPV?
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
2. What other business valuation models seem to be popular? Solution:
The two main approaches to valuation used by practitioners are those involving discounted cash flows, which we’ve discussed here, and those involving the “multiples” method, which involves using a sample of ratios from comparable peer groups to estimate an appropriate price for a firm.
integrated mini-case Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 11 percent, and that the maximum allowable payback and discounted payback statistics for your company are 3 and 3.5 years, respectively. Time Cash Flow
0 -$175,000
1 -$65,800
2 $94,000
3 $41,000
4 $122,000
5 $81,200
Using every one of the capital budgeting decision methods discussed in this chapter, evaluate this project, indicating whether each decision rule would call for acceptance or rejection of the project.
Chapter 13 - Weighing Net Present Value and Other Capital Budgeting Criteria
Solution:
The decision statistics and the appropriate accept/reject decisions are shown as follows:
Chapter 14 - Working Capital Management and Policies
CHAPTER 14– Working Capital Management and Policies Questions LG 1 1. Is it possible for a firm to have negative net working capital? How? Certainly. All that is required is that current liabilities be larger than current assets. LG1
2. Would it be possible for a decision to deny credit to your customers be value How?
maximizing?
If your customers have an unusually high tendency to default, then denying them credit would turn away sales, but you would benefit in the long run by not having to worry about losses from bad credit. LG2
3. Which of the following will result in an increase in net working capital? a. An increase in cash. b. A decrease in accounts payable. c. An increase in notes payable. d. A decrease in accounts receivable. e. An increase in inventory. Options a, b, and e will result in an increase in net working capital.
LG3
4. Would it be possible for a firm to have a negative cash cycle? How? Yes, but the firm’s average payment period would have to be longer than its operating cycle.
Chapter 14 - Working Capital Management and Policies
LG3
5. If a firm’s inventory turnover ratio increases, what will happen to the firm’s operating cycle? It should decrease, as the days’ sales in inventory will decrease.
LG3
6. If a firm’s inventory turnover ratio increases, what will happen to the firm’s cash
cycle
It should decrease, as the days’ sales in inventory will decrease as will the operating cycle LG4
7. Everything else held constant, will an increase in the amount of inventory on hand increase or decrease the firm’s profitability? It should decrease the profitability if there’s no change in sales due to the change in inventory, as the carrying cost should be higher.
LG5
8. Would a firm ever use short-term debt to finance permanent current assets? Why or not?
why
Sure, if rates on short-term debt are significantly more favorable than those on long-term debt, or if the firm has trouble raising long-term debt. LG5
9. Suppose that short-term borrowing actually becomes more expensive than long-term borrowing. How would this affect the firm’s choice between a flexible financing policy and a restrictive policy? Firms would be expected to move toward a more flexible policy.
LG6
10. If asset-backed loans are cheaper than unsecured loans, what is the disadvantage to firm in using an asset-backed loan?
the
If they fail to make the payments on the loan, it is easier for the creditor to seize the assets backing such a loan. LG7
11. Is an increase in the cash account a source of funds or a use of funds? It is a use of funds; cash is an asset just like accounts receivable or inventory.
LG7
12. What will be the carrying cost associated with a compensating balance requirement? The opportunity cost of not being able to invest that balance elsewhere, where it could earn interest.
LG7
13. What will be the shortage cost associated with a compensating balance requirement? It will depend upon the terms of the associated loan, but will usually involve some sort of penalty for failing to maintain the balance.
Chapter 14 - Working Capital Management and Policies
LG7
14. What would be the shortage costs associated with a restaurant not having enough cash on hand to make change? They would lose sales.
LG8
15. If a firm needs to keep a minimum cash balance on hand and faces both cash inflows and outflows, which of the cash management models discussed in this chapter would be more appropriate for them to use? The Miller-Orr model will be more appropriate.
LG8
16. What effect will increasing the trading costs associated with selling marketable securities have on the optimal replenishment level in the Baumol model? Why? An increase in trading costs will increase the optimal replenishment level. As trading costs go up, it makes sense to incur less trades.
LG8
17. What effect will an increase in the standard deviation of daily cash flows have on the return point in the Miller-Orr model? Why? It will increase the optimal return point. As the volatility of cash flows increases, the model calls for holding more cash, on average, to handle higher expected volatility.
LG9
18. Could a firm ever have negative collection float? Why or why not? No. They would have to collect the payment before it was even mailed for that to be true.
LG9
19. Could a firm ever have negative disbursement float? Why or why not? Only if they withdrew the funds, sat on them for a few days, and then sent them to their supplier in cash. And they wouldn’t want to do that.
LG9
20. Would a draft have availability float? Why or why not? Yes, because the drafts are actually sent to the firm’s bank, who has to present them to the firm before disbursing the funds.
LG9
21. From our discussion of capital markets elsewhere in this book, why would you expect a firm to have a time delay between raising funds to finance a project and the expenditure of those funds on that project? There are several possible reasons, including reasons of market timing.
LG9
22. What purpose does a discount on credit terms serve? What is the cost of such a discount to the offering firm?
Chapter 14 - Working Capital Management and Policies
It gives customers incentive to pay earlier. The cost of the discount is the difference between the discounted price and the full price.
problems basic problems LG2
14-1 Net Working Capital Requirements JohnBoy Industries has a cash balance of $45,000, accounts payable of $125,000, inventory of $175,000, accounts receivable of $210,000, notes payable of $120,000, and accrued wages and taxes of $37,000. How much net working capital does the firm need to fund? NWC = CA – CL = ($45,000 + $210,000 + $175,000) – ($125,000 + $120,000 + $37,000) = $148,000.
LG2
14-2 Net Working Capital Requirements Dandee Lions, Inc., has a cash balance of $105,000, accounts payable of $220,000, inventory of $203,000, accounts receivable of $319,000, notes payable of $65,000, and accrued wages and taxes of $75,000. How much net working capital does the firm need to fund? NWC = CA – CL = ($105,000 + $203,000 + $319,000) – ($220,000 + $65,000 + $75,000) = $267,000.
LG3
14-3 Days’ Sales in Inventory Dabble, Inc., has sales of $980,000 and cost of goods sold of $640,000. The firm had a beginning inventory of $36,000 and an ending inventory of $46,000. What is the length of the days’ sales in inventory? Days’ sales in inventory = (Inventory × 365 days) / Cost of goods sold = ($46,000 × 365 days) / $640,000 = 26.23 days.
LG3
14-4 Days’ Sales in Inventory Sow Tire, Inc., has sales of $1,450,000 and cost of goods sold of $980,000. The firm had a beginning inventory of $97,000 and an ending inventory of $82,000. What is the length of the days’ sales in inventory? Days’s sales in inventory = (Inventory × 365 days) / Cost of goods sold = ($82,000 × 365 days) / $980,000 = 30.54 days.
LG3
14-5 Average Payment Period If a firm has a cash cycle of 67 days and an operating cycle of 104 days, what is its average payment period? Using equation 14-2: Cash Cycle = Operating Cycle - Average Payment Period
Operating Cycle - Cash Cycle = Average Payment Period 104 days − 67 days = 37 days
Chapter 14 - Working Capital Management and Policies
LG3
14-6 Average Payment Period If a firm has a cash cycle of 45 days and an operating cycle of 77 days, what is its average payment period? Using equation 14-2: Cash cycle = Operating cycle - Average payment period Operating cycle - Cash cycle = Average payment period 77 days − 45 days = 32 days
LG3
14-7 Payables Turnover If a firm has a cash cycle of 73 days and an operating cycle of 127 days, what is its payables turnover? Using equation 14-2: Cash cycle = Operating cycle - Average payment period Operating cycle - Cash cycle = Average payment period 127 days − 73 days = 54 days
Payables turnover will be 365 days / 54 days = 6.76 times LG3
14-8 Payables Turnover If a firm has a cash cycle of 54 days and an operating cycle of 77 days, what is its payables turnover? Using equation 14-2: Cash cycle = Operating cycle - Average payment period Operating cycle - Cash cycle = Average payment period 77 days − 54 days = 23 days
Payables turnover will be 365 days / 23 days = 15.87 times LG7
14-9 Compensating Balance Would it be worth it to incur a compensating balance of $10,000 in order to get a 1-percent-lower interest rate on a one-year, pure discount loan of $225,000? It depends upon whether $225,000 × (1 + i) or $235,000 × (1 + [i – 0.01]) is larger. The compensating balance for the lower loan rate will make sense if: $225, 000 (1+ i ) $235, 000 (1+ i −.01) $225, 000 (1+ i ) (1+ i −.01 ) $235, 000 .9574 +.9574i 1+ i −.01 −.0426i .0326 i −76.5%
Chapter 14 - Working Capital Management and Policies
In other words, only if the rate is less than -76.50 percent will it make sense to accept the lower rate. Since this is not likely to happen, the lower rate associated with the compensating balance isn’t worth it. LG7
14-10 Compensating Balance Would it be worth it to incur a compensating balance of $7,500 in order to get a 0.65-percent-lower interest rate on a two-year, pure discount loan of $150,000? It depends upon whether $150,000 × (1 + i) or $157,500 × (1 + [i – 0.0065]) is larger. The compensating balance for the lower loan rate will make sense if: $150, 000 (1+ i ) $157, 500(1+ i −.0065) $150, 000 (1+ i ) (1+ i −.0065 ) $157, 500 .9524 + .9524i 1+ i −.0065 −.0476i .0411 i −86.35%
In other words, only if the rate is less than -86.35 percent will it make sense to accept the lower rate. Since this is not likely to happen, the lower rate associated with the compensating balance isn’t worth it. LG9
14-11 Collection Float CM Enterprises estimates that it takes, on average, three days for their customers’ payments to reach them, one day for the payments to be processed and deposited by their bookkeeping department, and two more days for the check to clear once they are deposited. What is their collection float? Collection float = 3 days + 1 day + 2 days = 6 days
LG9
14-12 Collection Float Smelpank, Inc.,estimates that it takes, on average, four days for their customers’ payments to reach them, three days for the payments to be processed and deposited by their bookkeeping department, and three more days for the check to clear once they are deposited. What is their collection float? Collection float = 4 days + 3 days + 3 days = 10 days
intermediate problems LG3
14-13 Operating Cycle Suppose that Dunn Industries has annual sales of $2,300,000, cost of goods sold of $1,650,000, average inventories of $1,116,000, and average accounts receivable of $750,000. Assuming that all of Dunn’s sales are on credit, what will be the firm’s operating cycle? Using equation 14-1:
Chapter 14 - Working Capital Management and Policies
Operating cycle = Days' sales in inventory + Average collection period Inventory 365 days Accounts receivable365 days = + Cost of goods sold Credit sales $1,116, 000 365 days $750,000 365 days = + $1,650,000 $2,300,000 = 365.89 days
LG3
14-14 Operating Cycle Suppose that LilyMac Photography has annual sales of $230,000, cost of goods sold of $165,000, average inventories of $4,500, and average accounts receivable of $25,000. Assuming that all of LilyMac’s sales are on credit, what will be the firm’s operating cycle? Using equation 14-1: Operating cycle = Days' sales in inventory + Average collection period Inventory 365 days Accounts receivable365 days = + Cost of goods sold Credit sales $4, 500 365 days $25,000 365 days = + $165,000 $230,000 = 49.63 days
LG3
14-15 Cash Cycle Suppose that LilyMac Photography has annual sales of $230,000, cost of goods sold of $165,000, average inventories of $4,500, average accounts receivable of $25,000, and an average accounts payable balance of $7,000. Assuming that all of LilyMac’s sales are on credit, what will be the firm’s cash cycle? Using equation 14-1: Operating cycle = Days' sales in inventory + Average collection period Inventory 365 days Accounts receivable365 days = + Cost of goods sold Credit sales $4, 500 365 days $25,000 365 days = + $165,000 $230,000 = 49.6285 days
Using this, in turn, in equation 14-2:
Chapter 14 - Working Capital Management and Policies
Cash cycle = Operating cycle - Average payment period Accounts payable 365 days Cost of goods sold $7, 000 365 days = 49.6285 $165, 000 = 34.14 days
= Operating cycle -
LG3
14-16 Cash Cycle Suppose that the Ken-Z Art Gallery has annual sales of $870,000, cost of goods sold of $560,000, average inventories of $244,500, average accounts receivable of $265,000, and an average accounts payable balance of $79,000. Assuming that all of Ken-Z’s sales are on credit, what will be the firm’s cash cycle? Using equation 14-1: Operating cycle = Days' sales in inventory + Average collection period Inventory 365 days Accounts receivable365 days = + Cost of goods sold Credit sales $244, 500 365 days $265,000 365 days = + $560,000 $870,000 = 270.5398 days
Using this, in turn, in equation 14-2: Cash cycle = Operating cycle - Average payment period Accounts payable 365 days = Operating cycle Cost of goods sold $79, 000 365 days = 270.5398 days $560, 000 = 219.05 days
LG4
14-17 Compensating Balance Interest Rate Suppose your firm is seeking an eight-year, amortizing $800,000 loan with annual payments and your bank is offering you the choice between an $850,000 loan with a $50,000 compensating balance and an $800,000 loan without a compensating balance. If the interest rate on the $800,000 loan is 8.5 percent, how low would the interest rate on the loan with the compensating balance have to be in order for you to choose it? The payments on the $800,000 loan would be $141,864.52:
Chapter 14 - Working Capital Management and Policies
PMTN
i = PV 1 N 1− (1+ i )
.085 = $800, 000 1 8 1− (1+.085) .085 = $800, 000 1− 0.5207 = $141,864.52
Using this as the payment amount and $850,000 as the present value, we can solve for the interest rate, which tells us that the bank would have to offer 6.91 percent or lower on the loan with the compensating balance to make it worthwhile. LG4
14-17 Compensating Balance Interest Rate Suppose your firm is seeking a four-year, amortizing $200,000 loan with annual payments and your bank is offering you the choice between a $205,000 loan with a $5,000 compensating balance and a $200,000 loan without a compensating balance. If the interest rate on the $200,000 loan is 9.8 percent, how low would the interest rate on the loan with the compensating balance have to be in order for you to choose it? The payments on the $200,000 loan would be $62,821.21:
PMT
N
i = PV 1 1− (1+ i )N
.098 = $200, 000 1 4 1− (1+.098) = $200, 000
1− 0.6880 .098
= $62,821.21
Using this as the payment amount and $205,000 as the present value, we can solve for the interest rate, which tells us that the bank would have to offer 8.67 percent or lower on the loan with the compensating balance to make it worthwhile.
Chapter 14 - Working Capital Management and Policies
LG8
14-18 Optimal Cash Replenishment Level Rose Axels faces a smooth annual demand for cash of $5,000,000, incurs transaction costs of $275 every time they sell marketable securities, and can earn 4.3 percent on their marketable securities. What will be their optimal cash replenishment level? The optimal cash replenishment level will be: C* = 2TF / i = 2($5, 000, 000)($275) / 0.043 = $252,890.27
LG8
14-19 Optimal Cash Replenishment Level Watkins Resources faces a smooth annual demand for cash of $1,500,000, incurs transaction costs of $75 every time they sell marketable securities, and can earn 3.7 percent on their marketable securities. What will be their optimal cash replenishment level? The optimal cash replenishment level will be: C* = 2TF / i = 2 ($1, 500, 000)($75) / 0.037 = $77, 981.29
LG8
14-20 Optimal Cash Return Point HotFoot Shoes would like to maintain their cash account at a minimum level of $25,000, but expect the standard deviation in net daily cash flows to be $4,000, the effective annual rate on marketable securities to be 6.5 percent per year, and the trading cost per sale or purchase of marketable securities to be $200 per transaction. What will be their optimal cash return point? The daily interest rate on marketable securities will be equal to: iday = 365 1.065 −1 = 0.000173 And the optimal cash return point will be equal to: 2 Z * = 3 3F / 4iday + L
= 3 3($200)($4, 000) / (4 0.000173) + $25, 000 2
= $ 49, 049.16
LG8
14-21 Optimal Cash Return Point Veggie Burgers, Inc., would like to maintain their cash account at a minimum level of $245,000, but expect the standard deviation in net daily cash flows to be $12,000, the effective annual rate on marketable securities to be 4.7 percent per
Chapter 14 - Working Capital Management and Policies
year, and the trading cost per sale or purchase of marketable securities to be $27.50 per transaction. What will be their optimal cash return point? The daily interest rate on marketable securities will be equal to: iday = 365 1.047 −1 = 0.000126 And the optimal cash return point will be equal to: 2 Z * = 3 3F / 4i day + L
= 3 3($27.50)($12, 000) / (4 0.000126) + $245, 000 2
= $ 273, 684.36
LG8
14-22 Optimal Upper Cash Limit Veggie Burgers, Inc., would like to maintain their cash account at a minimum level of $245,000, but expect the standard deviation in net daily cash flows to be $12,000, the effective annual rate on marketable securities to be 3.7 percent per year, and the trading cost per sale or purchase of marketable securities to be $27.50 per transaction. What will be their optimal upper cash limit? The daily interest rate on marketable securities will be equal to: iday = 365 1.037 −1 = 0.000100 And the optimal cash return point and upper limit will be equal to: Z * = 3 3F 2 / 4iday + L = 3 3($27.50)($12, 000) / (4 0.000100) + $245, 000 2
= $276, 015.57 H = 3($ 276, 015.57) − 2 ($245, 000) *
= $338, 046.71
LG8
14-23 Optimal Upper Cash Limit HotFoot Shoes would like to maintain their cash account at a minimum level of $25,000, but expect the standard deviation in net daily cash flows to be $2,000, the effective annual rate on marketable securities to be 3.5 percent per year, and the trading cost per sale or purchase of marketable securities to be $200 per transaction. What will be their optimal upper cash limit? The daily interest rate on marketable securities will be equal to: iday = 365 1.035 −1 = 0.000094
Chapter 14 - Working Capital Management and Policies
And the optimal cash return point and upper limit will be equal to: Z * = 3 3F 2 / 4iday + L = 3 3($200)($2, 000) / (4 0.000094) + $25, 000 2
= $43, 533.14 H = 3($43, 533.14) − 2 ($25, 000) *
= $80, 599.43
Appendix 14A LG1214A-1 Cumulative Net Cash Flow The net cash flow for a firm in January, February, and March are $-2.5 million, $-3.0 million, and $2.4 million. What is the cumulative net cash flow for March? -$3.1 million (Deficit) = -$2.5 million + (-$3.0 million) + $2.4 million LG1214A-2 Cumulative Net Cash Flow The Net Cash Flow for a firm in January, February, and March are $3.5 million, $-1.0 million, and $1.4 million. What is the Cumulative Net Cash Flow for March? $3.9 million (Surplus) = $3.5 million + (-$1.0 million) + $1.4 million LG1214A-3 Cash Disbursement The Hug’a’Bear company makes its teddy bears the month before they are sold. If sales of $2.5 million are expected in November and the firm pays 50 percent of sales in material costs, then what is the materials cash disbursement in October? $1.25 million = $2.5 million × 0.50 LG1214A-4 Cash Disbursement The Snow Adventures Company makes its snowboards the month before they are sold. If sales of $7.8 million are expected in November and the firm pays 65 percent of sales in material costs, then what is the materials cash disbursement in October? ( $5.07 million = $7.8 million × 0.65
Chapter 14 - Working Capital Management and Policies
LG1214A-5 Cash Collection Consider a company that has sales in May, June, and July of $10 million, $12 million, and $9 million, respectively. The firm is paid by 35 percent of its customers in the month of the sale, 40 percent in the following month, and 22 percent in the next month (3 percent are bad sales and never pay). What is the cash collected in July? $10.15 million = ($9 million × 0.35) + ($12 million × 0.40) + ($10 million × 0.22) = $2.2 + $4.80 +$3.15 LG1214A-6 Cash Collection Consider a company that has sales in May, June, and July of $11 million, $10 million, and $12 million, respectively. The firm is paid by 25 percent of its customers in the month of the sale, 50 percent in the following month, and 23 percent in the next month (2 percent are bad sales and never pay). What is the cash collected in July? $10.53 million = ($12 million × 0.25) + ($10 million × 0.50) + ($11 million × 0.23) = $3.0 + $5.0 + $2.53 LG1214A-7 Cash Surplus or Deficit A firm has estimated the following two month cash budget. What is the cash surplus or deficit for these two months? \ Mar
Apr
Sales
120
130
Cash collection
84.0
90.0
Total cash disbursement
90.0
85.0
Net cash flow
-6.0
5.0
Cumulative net cash flow
-15.0
?
Minimum cash balance
10.0
10.0
Cash surplus or deficit
?
?
April Cumulative Net Cash Flow = -10.0 = -15.0 + 5.0 March Cash Surplus or Deficit = -25.0 = -15.0 – 10.0
Chapter 14 - Working Capital Management and Policies
April Cash Surplus or Deficit = -20.0 = -10.0 – 10.0 LG12 14A-8 Cash Surplus or Deficit A firm has estimated the following two month cash budget. What is the cash surplus or deficit for these two months? Mar Apr Sales
75
68
Cash collection
63.0
65.0
Total cash disbursement
60.0
57.0
Net cash flow
3.0
8.0
Cumulative net cash flow
11.0
?
Minimum cash balance
3.0
3.0
Cash surplus or deficit
?
?
April cumulative net cash flow = 19.0 = 11.0 + 8.0 March cash surplus or deficit = 8.0 = 11.0 – 3 April cash surplus or deficit = 16.0 = 19.0 – 3
LG12 14A-9 Cash Budget Spreadsheet Problem The company from the text, Yellow Jacket, has decided to change its production strategy. Instead of a steady production throughout the year, they will produce the coats they estimate to sell in the month prior. This will impact the materials and wage disbursements of the cash budget. (For the December computation, assume that the following January sales with increase by 10 percent from the prior year.) Build this cash budget. How does this impact the cash surplus/deficit of the firm? Answer: ($ millions)
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Sales
10
10
5
2
1
1
1
5
20
30
25
15
Cash Collection
14.3
10.7
8.5
5.1
2.3
1.2
1.0
2.2
8.6
19.8
26.4
22.9
Disbursements Materials Wages, Salaries & Other Taxes Capital Projects
5.0 1.5 0 0
2.5 0.8 0 0
1.0 0.3 2.7 0
0.5 0.2 0 0
0.5 0.2 0 0
0.5 0.2 2.7 15.0
2.5 0.8 0 0
10.0 3.0 0 0
15.0 4.5 2.7 0
12.5 3.8 0 0
7.5 2.3 0 0
5.5 1.7 2.7 0
Chapter 14 - Working Capital Management and Policies
Long-term Financing (interest & dividends) Total Cash Disbursement
0
1.0
5.0
0
1.0
0
0
1.0
5.0
0
1.0
0
6.5
4.3
9.0
0.7
1.7
18.4
3.3
14.0
27.2
16.3
10.8
9.9
Net Cash Flow
7.8
6.4
-0.5
4.4
0.6
-17.2
-2.3
-11.8
-18.6
3.5
15.6
13.
Cumulative Net Cash Flow
7.8
14.2
13.7
18.1
18.7
1.5
-0.8
-12.6
-31.2
-27.7
-12.1
1.1
Minimum Cash Balance
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
Cash Surplus or Deficit
5.8
12.2
11.7
16.1
16.8
-0.5
-2.8
-14.6
-33.2
-29.7
-14.1
-0.9
While varying the production may greatly complicate managing the manufacturing aspect of the business, it improves the cash account of the Yellow Jacket. In this scenario, the firm doesn’t go into cash deficit until June (instead of May). In addition, the worst deficit here is $33.1 million (in September) whereas it was $45.3 in the other cash budget. Research It! (Web-Exercises): Looking Up Information on a Firm’s Cash Cycle Go to the SEC’s Edgar site at http://www.sec.gov/edgar.shtml and download the latest annual (“10-K”) report for the firm of your choice. Use the financial statements in the report to calculate the firm’s cash cycle.
Solution:
The company chosen was Diedrich Coffee, Inc. Selected financial statements for the fiscal years ended June 25, 2008, are shown below: As indicated, Inventories are $4,652,000, Accounts Receivable are $5,015,000, Cost of Goods Sold is $35,886,000, Credit Sales are $39,103,000, and Accounts Payable are $5,169,000, resulting in an operating cycle of: ($4,652,000 × 365)/ $35,886,000 + ($5,015,000 × 365)/ $39,103,000 = 94.1275 days And a cash cycle of: 102.78 days – ($5,169,000 × 365)/ $35,886,000 = 41.55 days.
Chapter 14 - Working Capital Management and Policies
Integrated Minicase: Line of Credit Your bank offers you a $140,000 line of credit with an interest rate of 2.30 percent per quarter. The loan agreement also requires that 7 percent of the unused portion of the credit line be deposited in a non-interest bearing account as a compensating balance. Your short-term investments are paying 1.55 percent per quarter. What is your effective annual interest rate if you borrow the whole $140,000 for the entire year? What will be the carrying cost in this problem? What will be the shortage cost in this problem? Solution:
The effective annual interest will be equal to (1+.023)4-1=.0952, or 9.52%.
Chapter 14 - Working Capital Management and Policies
The carrying costs in this problem will be those associated with keeping any compensating balance in the non-interest bearing account, assuming that you had no other reason for doing so (such to facilitate transactions, etc…). If you borrow the whole $140,000, there will be no compensating balance requirements, and therefore no carrying costs. However, if you do not use the entire line of credit, carrying costs would be equal to 7 percent of the amount not borrowed multiplied by the foregone potential interest rate for such funds, 1.55% per quarter. In the extreme case of not using any of the line of credit, this could total $151.90 per quarter. Shortage costs in this problem cannot be measured given the information provided, but would be a function of the opportunity costs associated with not having a compensating balance.
Chapter 15 - Financial Planning and Forecasting
CHAPTER 15 - FINANCIAL PLANNING AND FORECASTING Questions
LG1
1.
Compare and contrast the use of pro forma financial statements in corporate financial planning with their use in accounting. In corporate finance, pro forma statements are used to illustrate the expected financial situation of the firm under the most reasonable set of assumptions concerning relevant factors; in accounting, pro forma statements of the company's financial activities are those that exclude "unusual and nonrecurring transactions" when stating how much money the company actually made.
LG2
2.
Why might current liabilities be considered a spontaneous source of funding for a firm? When a firm makes more products or provides more services, it will use more raw materials from its suppliers and more labor from its employees. To the extent such a firm gets trade credit from its suppliers, current liabilities will tend to “automatically” increase; likewise, since employers tend to pay employees in a delayed manner (e.g., think about the local high school kid working at the burger joint down the road: if she works tonight, she will probably receive a paycheck for tonight’s work a week from this Friday), accrued wages and taxes will also automatically increase.
LG3
3.
What approach should be used to forecast sales if a firm believes that sales will be stable over time? The naïve approach.
LG3
41.
What approach should be used to forecast sales if a firm believes that sales will increase over time? The expected trend should be calculated using regression on past observations and then extrapolated into the future.
LG3
5.
What is the optimal length of time over which to take an average of historic sales when using the average approach? It basically depends upon how stable you think the sales figures have been and will be going forward in time: more observations are better if the sample is representative of the population, but, to the extent that sales may be expected to occasionally shift to a new level, historic sales figures from before the point in time where such a shift occurs may be “stale,” or not truly representative of the new level of sales. If we knew for sure that
Chapter 15 - Financial Planning and Forecasting
such a shift had not happened, then the best estimator for future expected sales would simply be an average of all available historic sales figures. LG3
6.
What is the theoretical minimum value for MAPE? If n is infinite, and if the forecast does a perfect job of predicting the actual values, then MAPE would be close to zero.
LG3 7.
If a firm needs to keep a minimum cash balance on hand and faces both cash inflows and outflows, which of the cash management models discussed in this chapter would be more appropriate for it to use? The use of pro forma statements to estimate additional funds needed would be most appropriate.
LG3 8.
Can the procedure described in this chapter for adjusting for seasonality apply to periods longer than a year? How? Yes, although it would require a great deal of historic observations. Rather than constructing a monthly or seasonal index as described here, you would need to construct a multi-year index, or something of the sort.
LG4
9.
Everything else held constant, which will be greater: AFN for a firm with excess fixedasset capacity, or AFN for a firm with no excess fixed-asset capacity? Why? AFN for a firm without excess capacity, as increasing sales will require increasing fixed assets immediately for such a firm.
LG4
10.
What does a negative value for AFN mean? That the projected spontaneous increase in liabilities and increase in retained earnings will provide more than enough money to finance the necessary increases in fixed assets during the period in question.
LG5
11.
Which specific item of a pro forma income statement should be most expected to vary proportionately with sales? Why? Variable costs, as they are defined as the expenses that change in proportion to the activity of a business.
LG5
12.
Explain why we need to use the iterative calculation approach described in the text to get a complete solution for AFN. If AFN will be raised at least partially by borrowing, then debt, and therefore interest, and therefore retained earnings, will all change as AFN changes. And, since AFN varies as retained earnings varies, it is a circular relationship.
Chapter 15 - Financial Planning and Forecasting
problems basic Problems LG3
15-1
Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using the naïve approach?
Year: Sales
2016 $1,500,000
2017 $1,750,000
2018 $1,400,000
2019 $2,000,000
2020 $1,600,000
The latest period observed is 2020, so the naïve estimate for 2017 would be $1,600,000. LG3
15-2
Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using the naïve approach?
Year: Sales
2016 $2,500,000
2017 $3,750,000
2018 $2,400,000
2019 $2,000,000
2020 $2,600,000
The latest period observed is 2020, so the naïve estimate for 2017 would be $2,600,000. LG3
15-3
Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using the average approach?
Year: Sales
2016 $1,500,000
2017 $1,750,000
2018 $1,400,000
2019 $2,000,000
2020 $1,600,000
The average over the historic observation is: $1,500,000 + $1,750,000 + $1,400,000 + $2,000,000 + $1,600,000 = $1,650,000 5 LG3
15-4
Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using the average approach?
Year: 2016 2017 2018 Sales $2,500,000 $3,750,000 $2,400,000 The average over the historic observation is:
2019 $2,000,000
$2,500,000 + $3,750,000 + $2,400,000 + $2,000,000 + $2,600,000 = $2,650,000 5
2020 $2,600,000
Chapter 15 - Financial Planning and Forecasting
LG4
15-5
Suppose that Gyp Sum Industries currently has the following balance sheet, and that sales for the year just ended were $10 million. The firm also has a profit margin of 25 percent, a retention ratio of 30 percent, and expects sales of $8 million next year. If all assets and current liabilities are expected to shrink with sales, what amount of additional funds will Gyp Sum need from external sources to fund the expected growth? Assets Current assets Fixed assets Total assets
$2,000,000 4,000,000
$6,000,000
Liabilities and Equity Current $1,500,000 liabilities Long-term 1,500,000 debt Equity 3,000,000 Total liabilities $6,000,000 and equity
The necessary increase in assets will be: A*
S S0 $6,000,000 = ($8,000,000 − $10,000,000) $10,000,000 = −$1,200,000
Necessaryincreasein assets =
The spontaneous increase in liabilities will be:
L*
S S0 $1,500, 000 = ($8, 000, 000 − $10, 000, 000) $10, 000, 000 = −$300, 000
Spontaneous increase in liabilities =
The projected increase in retained earnings will be:
Chapter 15 - Financial Planning and Forecasting
Projected increase in retained earnings = M S1 RR = 0.25$8, 000, 000 0.30 = $600, 000 So AFN will be = -$1,200,000 – (-$300,000) – $600,000 = -$1,500,000 LG4
15-6
Suppose that Wind Em Corp. currently has the following balance sheet, and that sales for the year just ended were $7 million. The firm also has a profit margin of 27 percent, a retention ratio of 20 percent, and expects sales of $8 million next year. If all assets and current liabilities are expected to grow with sales, what amount of additional funds will Wind Em need from external sources to fund the expected growth? Assets Current assets Fixed assets Total assets
$2,000,000 5,000,000
$7,000,000
Liabilities and Equity Current $2,500,000 liabilities Long-term 1,500,000 debt Equity 3,000,000 Total liabilities $7,000,000 and equity
The necessary increase in assets will be: Necessaryincreasein assets = =
A*
S S0 $7,000,000
($8,000,000 − $7,000,000)
$7,000,000 = $1,000,000
The spontaneous increase in liabilities will be: Spontaneous increase in liabilities = =
L*
S S0 $2, 500, 000
($8, 000, 000 − $7, 000, 000)
$7, 000, 000 = $357,143
The projected increase in retained earnings will be:
Chapter 15 - Financial Planning and Forecasting
Projected increase in retained earnings = M S1 RR = 0.27 $8, 000, 000 0.20 = $432, 000
Chapter 15 - Financial Planning and Forecasting
So AFN will be = $1,000,000 – $357,143 – $432,000 = $210,857 intermediate problems LG3 15-7 Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using regression to estimate a trend? Year: Sales
2016 $1,500,000
2017 $1,750,000
2018 $1,700,000
2019 $2,000,000
2020 $1,800,000
Since we are not instructed to deseasonalize the historic sales figures, all we need to do is run a regression and then use the intercept and slope to estimate sales for the next year. Using Excel, and treating the observation numbers shown as follows as our X variable and the sales figures as our Y variable, a linear regression yields an intercept of $1,495,000 and a slope of $85,000 as demonstrated.
Using these figures, the estimated sales figure for next year (i.e., observation 6) will be $1,495,000 + $85,000 × 6 = $2,005,000. LG3
15-8
Suppose a firm has had the historic sales figures shown as follows. What would be the forecast for next year’s sales using regression to estimate a trend?
Year:
2016
2017
2018
2019
2020
Chapter 15 - Financial Planning and Forecasting
Sales
$2,500,000
$3,750,000
$4,400,000
$5,000,000
$5,600,000
Since we are not instructed to deseasonalize the historic sales figures, all we need to do is run a regression and then use the intercept and slope to estimate sales for the next year. Using Excel, and treating the observation numbers shown as follows as our X variable and the sales figures as our Y variable, a linear regression yields an intercept of $2,015,000 and a slope of $745,000 as demonstrated.
Using these figures, the estimated sales figure for next year (i.e., observation 6) will be $2,015,000 + $745,000× 6 = $6,485,000. LG4
15-9
Suppose that Psy Ops Industries currently has the following balance sheet, and that sales for the year just ended were $5 million. The firm also has a profit margin of 25 percent, a retention ratio of 30 percent, and expects sales of $8 million next year. If fixed assets have enough capacity to cover the increase in sales and all other assets and current liabilities are expected to increase with sales, what amount of additional funds will Psy Ops need from external sources to fund the expected growth? Assets Current assets Fixed assets
$2,000,000 4,000,000
Liabilities and Equity Current $1,500,000 liabilities Long-term 1,500,000 debt Equity 3,000,000
Chapter 15 - Financial Planning and Forecasting
Total assets
Total liabilities and equity
$6,000,000
$6,000,000
In this case, the necessary increase in assets will be based on only CA: Necessaryincreasein assets = =
A*
S S0 $2,000,000
($8,000,000 − $5,000,000)
$5,000,000 = $1,200,000
The spontaneous increase in liabilities will be: Spontaneous increase in liabilities = =
L*
S S0 $1, 500, 000
($8, 000, 000 − $5, 000, 000)
$5, 000, 000 = $900, 000
The projected increase in retained earnings will be: Projected increase in retained earnings = M S1 RR = 0.25$8, 000, 000 0.30 = $600, 000 So AFN will be = $1,200,000 – $900,000 – $600,000 = -$300,000 LG4
15-10 Suppose that Wall-E Corp. currently has the following balance sheet, and that sales for the year just ended were $7 million. The firm also has a profit margin of 27 percent, a retention ratio of 20 percent, and expects sales of $9 million next year. Fixed assets are currently fully utilized, and the nature of Wall-E’s fixed assets is such that they must be added in $1 million increments. If current assets and current liabilities are expected to grow with sales, what amount of additional funds will Wall-E need from external sources to fund the expected growth?
Chapter 15 - Financial Planning and Forecasting
Assets Current assets Fixed assets Total assets
$2,000,000 5,000,000
$7,000,000
Liabilities and Equity Current $2,500,000 liabilities Long-term 1,500,000 debt Equity 3,000,000 Total liabilities $7,000,000 and equity
In this case, the necessary increase in assets will be: A*
Necessary increase in current assets = =
S S0 $2, 000, 000
($9, 000, 000 − $7, 000, 000)
$7, 000, 000 = $571, 429
Necessary increase in fixed assets = =
A* S S0 $5, 000, 000
($9, 000, 000 − $7, 000, 000)
$7, 000, 000 = $1, 428, 571
The necessary increase in fixed assets is $1,428,571. However, fixed assets must be added in $1 million increments. Thus, the asset need for fixed assets must be increased to $2 million. The spontaneous increase in liabilities will be: Spontaneous increase in liabilities = =
L*
S S0 $2, 500, 000
($9, 000, 000 − $7, 000, 000)
$7, 000, 000 = $714, 286
The projected increase in retained earnings will be:
Chapter 15 - Financial Planning and Forecasting
Projected increase in retained earnings = M S1 RR = 0.27 $9, 000, 000 0.20 = $486, 000 So AFN will be = $571,429 + $2,000,000 – $714,286 – $486,000 = $1,371,143
advanced problems LG3 15-11John’s Bait and Fish shop has had the monthly sales amounts listed as follows for the last four years. Assuming that there is both seasonality and a trend, estimate monthly sales for each month of the coming year. Year: January February March April May June July August September October November December
2017 $417,812 113,240 139,815 428,157 436,880 743,947 1,449,280 1,428,123 1,178,795 368,475 257,638 321,208
2018 $585,558 138,414 177,676 392,734 926,046 1,084,321 1,249,470 1,794,586 1,022,538 465,971 389,276 386,377
2019 $334,336 165,492 86,015 512,061 534,007 597,606 1,564,939 1,849,585 683,038 483,142 261,309 234,736
2020 $587,080 113,788 137,015 457,425 851,622 741,444 1,579,376 1,590,067 724,279 651,824 309,872 371,721
The steps to deseasonalize sales are as described in the book, with the addition of the need to calculate “Seas. Index” as the average of the “Seas-Irreg” values for the respective month. For example, the seasonal index for July, 2.19671256, is calculated as the average of 2.36063341, 1.76658549, and 2.526595268. These seasonal indices are then used to deseasonalize the monthly sales figures as described in the text.
Chapter 15 - Financial Planning and Forecasting
The deseasonalized monthly sales figures are then regressed against the observation numbers, with the results used to estimate expected (deseasonalized) sales figures for the coming year’s months, which are reseasonalized by multiplying them by the appropriate monthly index:
Chapter 15 - Financial Planning and Forecasting
LG3
15-12 Sara’s Ice Cream Shop is closed for six months out of the year, but has had the monthly sales amounts listed as follows for the last four years. Assuming that there is both seasonality and a trend, estimate monthly sales for each month of the coming year. Year: May June July August September October
2017 $436,880 743,947 1,449,280 1,428,123 1,178,795 368,475
2018 $926,046 1,084,321 1,249,470 1,794,586 1,022,538 465,971
2019 $534,007 597,606 1,564,939 1,849,585 683,038 483,142
2020 $851,622 741,444 1,579,376 1,590,067 724,279 651,824
Chapter 15 - Financial Planning and Forecasting
LG3
15-13 Suppose that the 2016 actual and 2017 projected financial statements for Comfy Corners Catbeds are initially shown as follows. In these tables, sales are projected to rise by 22 percent in the coming year, and the components of the income statement and balance sheet that are expected to increase at the same 22 percent rate as sales are indicated by green type. Assuming that Comfy Corners Catbeds wants to cover the AFN with half equity, 25 percent long-term debt, and the remainder from notes payable, what amount of additional funds will be needed if debt carries a 10 percent interest rate?
Chapter 15 - Financial Planning and Forecasting
Sales Costs Depreciation
$4,000,000 $2,600,000 $1,000,000
$4,880,000 $3,172,000 $1,220,000
EBIT Interest EBT Taxes (40%) Net Income
$400,000 $198,000 $202,000 $80,800 $121,200
$488,000 $235,449 $252,551 $101,021 $151,531
Dividends
$60,600
$60,600
Retained
$60,600
$90,931
Inc in Assets Inc in Liab RE change AFN
LG3
Cash A/R Inv Current Assets FA TA
$600,000 $137,000 $1,013,000
$732,000 $167,140 $1,235,860
$1,750,000 $5,000,000 $6,750,000
$2,135,000 $6,100,000 $8,235,000
A/P N/P Accruals Current Liab LTD Total Debt Common Sto RE Equity TD +E
$179,000 $980,000 $375,000
$218,380 $1,298,047 $457,500
$1,534,000 $1,000,000 $2,534,000
$1,973,927 $1,318,047 $3,291,975
$4,000,000 $216,000 $4,216,000 $6,750,000
$4,636,095 $306,931 $4,943,025 $8,235,000
$1,485,000.00 $121,880.00 $90,930.89 $1,272,189.11
15-14 Suppose that the 2016 actual and 2017 projected financial statements for AFS are initially shown as follows. In these tables, sales are projected to rise by 14 percent in the coming year, and the components of the income statement and balance sheet that are expected to increase at the same 14 percent rate as sales are indicated by green type. Assuming that AFS wants to cover the AFN with half equity and half long-term debt, what amount of additional funds will be needed if debt carries a 9 percent interest rate?
Chapter 15 - Financial Planning and Forecasting
Sales Costs Depreciation
$5,500,000 $3,000,000 $1,200,000
$6,270,000 $3,420,000 $1,368,000
EBIT Interest EBT Taxes (40%) Net Income
$1,300,000 $153,000 $1,147,000 $458,800 $688,200
$1,482,000 $170,658 $1,311,342 $524,537 $786,805
Dividends
$344,100
$344,100
Retained
$344,100
$442,705
Inc in Assets Inc in Liab RE change AFN AFN*
$936,600.00 $101,500.00 $442,705.34 $392,394.66 $196,197.33
Cash A/R Inv Current Assets FA TA A/P N/P Accruals Current Liab LTD Total Debt Common Sto RE Equity TD +E
$750,000 $140,000 $800,000
$855,000.00 $159,600.00 $912,000.00
$1,690,000 $5,000,000 $6,690,000
$1,926,600.00 $5,700,000.00 $7,626,600.00
$350,000 $500,000 $375,000
$399,000 $500,000 $427,500
$1,225,000 $1,200,000 $2,425,000
$1,326,500 $1,396,197 $2,722,697
$4,000,000 $265,000 $4,265,000 $6,690,000
$4,196,197 $707,705 $4,903,903 $7,626,600
Chapter 15 - Financial Planning and Forecasting
Integrated Mini-Case Effect of Capital Structure on AFN Suppose that the 2016 actual and 2017 projected financial statements for your firm are initially shown as follows. In these tables, sales are projected to rise by 18 percent in the coming year, and the components of the income statement and balance sheet that are expected to increase at the same 18 percent rate as sales are indicated by green type. Assuming that your firm has to pay 9 percent interest on debt, what would the AFN be if needed capital was to be raised entirely from equity? How would your answer change if the entire AFN was to be raised from long-term debt? And what does this imply about the relationship between the sources of funding and the amount needed? Income Statement
Balance Sheet
2016 Actual
2017 Forecast
Sales Costs except depreciation Depreciation EBIT Interest EBT Taxes (40%) Net income
$10,000,000 5,200,000 800,000 $ 4,000,000 181,530 $ 3,818,470 1,527,388 $ 2,291,082
$11,800,000 6,136,000 944,000 $ 4,720,000 181,530 $ 4,538,470 1,815,388 $ 2,723,082
Common dividends Addition to retained earnings
$2,000,000 $ 291,082
$2,000,000 $ 723,082
Spontaneous increase in assets Less: Spontaneous increase in liabilities Less: Projected increase in retained earnings Additional funds needed
2016 actual Assets Cash Accounts receivable Inventories Total current assets Net plant and equipment Total assets Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term debt Total debt Common stock Retained earnings Total common equity Total liabilities and equity
$1,879,200 316,260 723,082 $ 839,858
2017 Forecast
$
540,000 800,000 1,600,000 $ 2,940,000 7,500,000 $10,440,000
$
$
$
557,000 750,000 1,200,000 $ 2,507,000 2,017,000 $ 4,524,000 $ 5,250,000 666,000 $ 5,916,000 $10,440,000
637,200 944,000 1,888,000 $ 3,469,200 8,850,000 $12,319,200
657,260 750,000 1,416,000 $ 2,823,260 2,017,000 $ 4,840,260 $ 5,250,000 1,389,082 $ 6,639,082 $11,479,342
Chapter 15 - Financial Planning and Forecasting
If the ANF is funded entirely with equity, the financial statements will be: Income Statement
Balance Sheet
2016 Actual
2017 Forecast
Sales Costs except depreciation Depreciation EBIT Interest EBT Taxes (40%) Net income
$10,000,000 5,200,000 800,000 $ 4,000,000 181,530 $ 3,818,470 1,527,388 $ 2,291,082
$11,800,000 6,136,000 944,000 $ 4,720,000 181,530 $ 4,538,470 1,815,388 $ 2,723,082
Common dividends Addition to retained earnings
$2,000,000 $ 291,082
$2,000,000 $ 723,082
2016 Actual Assets Cash Accounts receivable Inventories Total current assets Net plant and equipment Total assets Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term debt Total debt Common stock Retained earnings Total common equity Total liabilities and equity
2017 Forecast
$
540,000 800,000 1,600,000 $ 2,940,000 7,500,000 $10,440,000
$
$
$
557,000 750,000 1,200,000 $ 2,507,000 2,017,000 $ 4,524,000 $ 5,250,000 666,000 $ 5,916,000 $10,440,000
637,200 944,000 1,888,000 $ 3,469,200 8,850,000 $12,319,200
657,260 750,000 1,416,000 $ 2,823,260 2,017,000 $ 4,840,260 $ 6,089,858 1,389,082 $ 7,478,940 $12,319,200
Common stock = $5,250,000 + $839,858 = $6,089,858
If the AFN is funded entirely with debt: Income Statement
Balance Sheet
2016 Actual
2017 Forecast
Sales Costs except depreciation Depreciation EBIT Interest EBT Taxes (40%) Net income
$10,000,000 5,200,000 800,000 $ 4,000,000 181,530 $ 3,818,470 1,527,388 $ 2,291,082
$11,800,000 6,136,000 944,000 $ 4,720,000 332,785 $ 4,458,568 1,783,427 $ 2,675,141
Common dividends Addition to retained earnings
$2,000,000 $ 291,082
$2,000,000 $ 632.329
2016 Actual Assets Cash Accounts receivable Inventories Total current assets Net plant and equipment Total assets Liabilities and Equity Accounts payable Notes payable Accruals Total current liabilities Long-term debt Total debt Common stock Retained earnings Total common equity Total liabilities and equity
2017 Forecast
$
540,000 800,000 1,600,000 $ 2,940,000 7,500,000 $10,440,000
$
$
$
557,000 750,000 1,200,000 $ 2,507,000 2,017,000 $ 4,524,000 $ 5,250,000 666,000 $ 5,916,000 $10,440,000
637,200 944,000 1,888,000 $ 3,469,200 8,850,000 $12,319,200
657,260 750,000 1,416,000 $ 2,823,260 2,947,611 $ 5.770,871 $ 5,250,000 1,298,329 $ 6,591,141 $12,319,200
Long-term debt = $2,017,000 + $887,799 = $2,904,799 Interest = 0.09 × $2,904,799 = $261,432
If the AFN is funded entirely with equity, the AFN is $839,858. However, if the AFN is funded with long-term debt, the AFN increases to $$930,611 due to the increase in the interest expense and the resulting decrease in the addition to retained earnings.
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
CHAPTER 16 – ASSESSING LONG-TERM DEBT, EQUITY, AND CAPITAL STRUCTURE Questions LG1
1.
How will passive and active capital structure changes differ? Active capital structure changes will be initiated immediately, regardless of whether the firm has any capital budgeting needs; passive capital structure changes will be accommodated in the course of financing future capital budgeting needs, with the firm raising money for such new projects in the form (debt or equity) they wish to increase in the capital structure.
LG2
2.
Why is debt often referred to as leverage in finance? Debt magnifies both the potential returns and the risk to equity holders.
LG3
3.
In M&M’s perfect world, will the debt holders ever bear any of the risk of the firm? No. If there is no chance of bankruptcy, there is no chance that the debt holders will not get paid back everything they are owed.
LG4
4.
Why does allowing for the existence of corporate taxation cause firms to prefer the maximum amount of debt possible? Since interest paid on corporate debt is tax-deductible, debt is “cheap” in the sense that the incremental cost to the firm is iD(1 – TC), so the firm will use as much debt as it feasibly can.
LG5
5.
If a firm increased the amount of debt in its capital structure, but a shareholder wanted to switch back to the mixture of expected return and risk she had before the switch, how would she go about doing so? She would “unleverage” by lending a portion of her wealth equivalent to the percentage of the firm’s capital structure that was shifted from equity to debt.
LG5
6.
If an investor wanted to reduce the risk of a levered stock in their portfolio, how could they go about doing so while still retaining shares in the company? They could sell some of their shares and use the proceeds to buy the firm’s bonds.
LG6 7.
Suppose you were the financial manager for a firm and were considering a proposed increase in the amount of debt in the firm’s capital structure. If you thought the firm was going to consistently earn a level of EBIT above its break-even level of EBIT
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
(based on the current and proposed new capital structures) would this cause you to prefer leveraging the firm up or staying at your current capital structure? Leveraging increases the EPS above the break-even level of EBIT, so you would prefer leveraging the firm up. LG7
8.
Explain why, in a world with both corporate taxes and the chance of bankruptcy, a small firm with volatile EBIT is unlikely to have much debt. In such a firm, debt would greatly increase both the chance of the firm going bankrupt and the expected associated costs of financial distress.
LG7
9.
If the U.S. government completely eliminated taxation at the corporate level, how would this influence the capital structures of firms in a world with bankruptcy? Since debt would no longer enjoy a tax advantage compared to equity, we would expect to see lower debt levels, everything else held constant.
LG8
10.
Would you expect a utility company to have high or low debt levels? Why? Most utility companies have high and stable earnings streams, which allow them to support a relatively large amount of debt.
problems basic problems LG3 16-1 Capital Structure Weights Suppose that Lil John Industries’ equity is currently selling for $37 per share and that there are 2 million shares outstanding. If the firm also has 30 thousand bonds outstanding, which are selling at 103 percent of par, what are the firm’s current capital structure weights? 2, 000, 000 $37 E = = 70.54% E + D 2, 000, 000 $37 + 30, 000 $1, 000 1.03 30, 000 $1, 000 1.03 D = = 29.46% 2, 000, 000 $37 + 30, 000 $1, 000 1.03 E+D
LG3
16-2 Capital Structure Weights Suppose that Papa Bell, Inc.’s, equity is currently selling for $55 per share, with 4 million shares outstanding. If the firm also has 17 thousand bonds outstanding, which are selling at 94 percent of par, what are the firm’s current capital structure weights?
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
4, 000, 000 $55 E = = 93.23% 4, 000, 000 $55 +17, 000 $1, 000 0.94 E+D 17, 000 $1, 000 0.94 D = = 6.77% E + D 4, 000, 000 $55 +17, 000 $1, 000 0.94
LG1
16-3 Restructuring Strategy Suppose that Lil John Industries’ equity is currently selling for $27 per share and that there are 2 million shares outstanding. The firm also has 50 thousand bonds outstanding, which are selling at 103 percent of par. If Lil John was considering an active change to their capital structure so that the firm would have a D/E of 1.4, which type of security (stocks or bonds) would they need to sell to accomplish this, and how much would they have to sell? Using the capital structure weights formulas from Chapter 11, the current capital weights are: 2, 000, 000 $27 E = = 0.5118 or 51.18% E + D 2, 000, 000 $27 + 50, 000 $1, 000 1.03 50, 000 $1, 000 1.03 D = = 0.4882 or 48.82% 2, 000, 000 $27 + 50, 000 $1, 000 1.03 E+D
The current D/E ratio is 0.4882 / 0.5118 = 0.9537, so Lil John would be contemplating increasing the D/E ratio. To do so, they would have to change their debt ratio to 1.4 / 2.4 = 0.5833, which would require issuing (0.5833 – 0.4882) × [($2,000,000 × $27) + (50,000 × $1,000 × 1.03)] = $$10,033,050 of new debt and using the proceeds to repurchase stock. Using these numbers: 0.5833–0.4822 = 0.0951 x D + E ($105,500,000) = $10,033,050 LG1
16-4 Capital Structure Weights Suppose that Papa Bell, Inc.’s, equity is currently selling for $45 per share, with 4 million shares outstanding. The firm also has seven thousand bonds outstanding, which are selling at 94 percent of par. If Papa Bell was considering an active change to their capital structure so as to have a D/E of 0.4, which type of security (stocks or bonds) would they need to sell to accomplish this, and how much would they have to sell? Using the capital structure weights formulas from Chapter 11, the current capital weights are: 4, 000, 000 $45 E = = 96.47% E + D 4, 000, 000 $45 + 7, 000 $1, 000 0.94 7, 000 $1, 000 0.94 D = = 3.53% E + D 4, 000, 000 $45 + 7, 000 $1, 000 0.94
The current D/E ratio is 0.0353 / 0.9647 = 0.0366, so Lil John would be contemplating increasing the D/E ratio. To do so, they would have to change their debt ratio to 0.4 / 1.4 =
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
0.2857, which would require issuing (0.2857 – 0.0353) × [($4,000,000 × $45) + (7,000 × $1,000 × 0.94)] = $46,719,632 of new debt and using the proceeds to repurchase stock. Using these numbers: 0.2857–0.0353=0.2504 x D + E ($186,580,000) =$46,719,632 intermediate problems LG3
16-5 Expected EPS after Leveraging Daddi Mac, Inc., doesn’t face any taxes and has $290 million in assets, currently financed entirely with equity. Equity is worth $37 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
RECESSION AVERAGE BOOM 0.25 0.55 0.20 $5 million $10 million $17 million
The firm is considering switching to a 20 percent debt capital structure, and has determined that they would have to pay an 8 percent yield on perpetual debt in either event. What will be the level of expected EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.08 × (0.20 × $290,000,000) = $4,640,000, and the number of shares outstanding will be equal to (0.80 × $290,000,000)/$37 = 6,270,270. The EPS in each state of nature will be as shown: STATE EBIT - Interest EBT - Taxes (@ 0%) Net Income EPS
$ $ $ $
EPS WITH 20% DEBT RECESSION AVERAGE 5,000,000 $ 10,000,000 $ 4,640,000 4,640,000 360,000 $ 5,360,000 $ 0 0 360,000 $ 5,360,000 $ 0.06 $ 0.85 $
BOOM 17,000,000 4,640,000 12,360,000 0 12,360,000 1.97
The expected EPS will be equal to (0.25 × $0.06) + (0.55 × $0.85) + (0.20 × $1.97) = $0.88 LG3
16-6 Expected EPS after Leveraging HiLo, Inc., doesn’t face any taxes and has $150 million in assets, currently financed entirely with equity. Equity is worth $7 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state
PESSIMISTIC OPTIMISTIC 0.45 0.55
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
Expected EBIT in state
$5 million
$19 million
The firm is considering switching to a 40 percent debt capital structure, and has determined that they would have to pay a 12 percent yield on perpetual debt in either event. What will be the level of expected EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.12 × (0.40 × $150,000,000) = $7,200,000, and the number of shares outstanding will be equal to (0.60 × $150,000,000)/$7 = 12,857,143. The EPS in each state of nature will be as shown: STATE EBIT - Interest EBT - Taxes (@ 0%) Net Income EPS
EPS WITH 40% DEBT PESSIMISTIC OPTIMISTIC $5,000,000 $19,000,000 7,200,000 7,200,000 -$2,200,000 $11,800,000 0.00 0.00 -$2,200,000 $11,800,000 -$0.17 $0.92
The expected EPS will be equal to (0.45 × -$0.17) + (0.55 × $0.92) = $0.43 LG3 16-7 Standard Deviation in EPS after Leveraging Daddi Mac, Inc., doesn’t face any taxes and has $350 million in assets, currently financed entirely with equity. Equity is worth $37 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT are dependent upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
RECESSION AVERAGE 0.25 0.55 $5 million
$10 million
BOOM 0.20 $17 million
The firm is considering switching to a 20 percent debt capital structure, and has determined that they would have to pay an 8 percent yield on perpetual debt regardless of whether they change their capital structure. What will be the standard deviation in EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.08 × (0.20 × $350,000,000) = $5,600,000, and the number of shares outstanding will be equal to (0.80 × $350,000,000)/$37 = 7,567,568.
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
The EPS in each state of nature will be as shown:
The expected EPS will be equal to (0.25 × -$0.08) + (0.55 ×$0.58) + (0.20 × $1.51) = $0.60, so the standard deviation in EPS will be equal to:
EPS = 0.25(−0.08 − 0.60) + 0.55(0.58 − 0.60) + 0.20 (1.51− 0.60) 2
2
2
= 52.90% LG3 16-8 Standard Deviation in EPS after Leveraging HiLo, Inc., doesn’t face any taxes and has $100 million in assets, currently financed entirely with equity. Equity is worth $7 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
PESSIMISTIC OPTIMISTIC 0.45 0.55 $5 million
$19 million
The firm is considering switching to a 40 percent debt capital structure, and has determined that they would have to pay a 12 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.12 × (0.40 × $100,000,000) = $4,800,000, and the number of shares outstanding will be equal to (0.60 × $100,000,000)/$7 = 8,571,429. The EPS in each state of nature will be as shown:
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
STATE EBIT - Interest EBT - Taxes (@ 0%) Net Income EPS
EPS WITH 40% DEBT PESSIMISTIC OPTIMISTIC $ 5,000,000 $ 19,000,000 4,800,000 4,800,000 $ 200,000 $ 14,200,000 0 0 $ 200,000 $ 14,200,000 $ 0.02 $ 1.66
The expected EPS will be equal to (0.45 × -$0.02) + (0.55 ×$1.66) = $0.92, so the standard deviation in EPS will be equal to:
EPS = 0.45(0.02 − 0.92) + 0.55(1.66 − 0.92) 2
2
= 81.59% advanced problems LG4 16-9 Expected EPS after Leveraging with Taxes NoNuns Cos. has a 21 percent tax rate and has $350 million in assets, currently financed entirely with equity. Equity is worth $37 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
RECESSION AVERAGE 0.25 0.55 $5 million
$10 million
BOOM 0.20 $17 million
The firm is considering switching to a 20 percent debt capital structure, and has determined that they would have to pay an 8 percent yield on perpetual debt in either event. What will be the level of expected EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.08 × (0.20 × $350,000,000) = $5,600,000, and the number of shares outstanding will be equal to (0.80 × $100,000,000)/$7 = 7,567,568. The EPS in each state of nature will be as shown:
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
EBIT - Interest EBT - Taxes (@21%) Net Income EPS Average EPS EPS S.D.
$ $ $ $ $ $ $ $
Recession 5,000,000 $ 5,600,000 $ (600,000) $ (126,000) $ (474,000) $ (0.06) $ 0.47 0.42
Average 10,000,000 5,600,000 4,400,000 924,000 3,476,000 0.46
$ $ $ $ $ $
Boom 17,000,000 5,600,000 11,400,000 2,394,000 9,006,000 1.19
The expected EPS will be equal to (0.25 × -$0.06) + (0.55 ×$0.44) + (0.20 × $1.13) = $0.45 LG4 16-10 Expected EPS after Leveraging with Taxes GTB, Inc., has a 21 percent tax rate and has $100 million in assets, currently financed entirely with equity. Equity is worth $7 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
PESSIMISTIC OPTIMISTIC 0.45 0.55 $5 million
$19 million
The firm is considering switching to a 40 percent debt capital structure, and has determined that they would have to pay a 12 percent yield on perpetual debt in either event. What will be the level of expected EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.12 × (0.40 × $100,000,000) = $4,800,000, and the number of shares outstanding will be equal to (0.60 × $100,000,000)/$7 = 8,571,429. The EPS in each state of nature will be as shown:
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
EBIT - Interest EBT - Taxes (@21%) Net Income EPS Average EPS EPS S.D.
$ $ $ $ $ $ $ $
Recession 5,000,000 4,800,000 200,000 42,000 158,000 0.02 0.73 0.64
$ $ $ $ $ $
Boom 19,000,000 4,800,000 14,200,000 2,982,000 11,218,000 1.31
The expected EPS will be equal to (0.45 × $0.02) + (0.55 ×$1.31) = $0.73 LG4 16-11 Standard Deviation in EPS after Leveraging with Taxes NoNuns Cos. has a 21 percent tax rate and has $350 million in assets, currently financed entirely with equity. Equity is worth $37 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
RECESSION AVERAGE 0.25 0.55 $5 million
$10 million
BOOM 0.20 $17 million
The firm is considering switching to a 20 percent debt capital structure, and has determined that they would have to pay an 8 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.08 × (0.20 × $350,000,000) = $5,600,000, and the number of shares outstanding will be equal to (0.60 × $100,000,000)/$7 = 7,567,568. The EPS in each state of nature will be as shown:
EBIT - Interest EBT - Taxes (@21%) Net Income EPS
$ $ $ $ $ $
Recession 5,000,000 $ 5,600,000 $ (600,000) $ (126,000) $ (474,000) $ (0.06) $
Average 10,000,000 5,600,000 4,400,000 924,000 3,476,000 0.46
$ $ $ $ $ $
Boom 17,000,000 5,600,000 11,400,000 2,394,000 9,006,000 1.19
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
The expected EPS will be equal to (0.25 × -$0.06) + (0.55 ×$0.46) + (0.20 × $1.19) = $0.47, so the standard deviation in EPS will be equal to:
EPS = 0.25(−0.06 − 0.47) + 0.55(0.46 − 0.47) + 0.20 (1.19 − 0.47) 2
2
2
= 42% LG4 16-12 Standard Deviation in EPS after Leveraging with Taxes GTB, Inc., has a 21 percent tax rate and has $100 million in assets, currently financed entirely with equity. Equity is worth $7 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state
PESSIMISTIC OPTIMISTIC 0.45 0.55
Expected EBIT in state
$5 million
$19 million
The firm is considering switching to a 40 percent debt capital structure, and has determined that they would have to pay a 12 percent yield on perpetual debt in either event. What will be the standard deviation in EPS if they switch to the proposed capital structure? Interest in all states will be equal to 0.12 × (0.40 × $100,000,000) = $4,800,000, and the number of shares outstanding will be equal to (0.60 × $100,000,000)/$7 = 8,571,429. The EPS in each state of nature will be as shown:
EBIT - Interest EBT - Taxes (@21%) Net Income EPS Average EPS EPS S.D.
Pessimistic $ 5,000,000 $ 4,800,000 $ 200,000 $ 42,000 $ 158,000 $ 0.02 $ 0.73 $ 0.64
Optimistic $ 19,000,000 $ 4,800,000 $ 14,200,000 $ 2,982,000 $ 11,218,000 $ 1.31
The expected EPS will be equal to (0.45 × $0.02) + (0.55 ×$1.31) = $0.73, so the standard deviation in EPS will be equal to:
EPS = 0.45(0.02 − 0.61) + 0.55(1.09 − 0.61) 2
= 64.19%
2
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
LG6 16-13 Break-even EBIT with Taxes NoNuns Cos. has a 21 percent tax rate and has $350 million in assets, currently financed entirely with equity. Equity is worth $37 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
RECESSION AVERAGE 0.25 0.55 $5 million
$10 million
BOOM 0.20 $17 million
The firm is considering switching to a 20 percent debt capital structure, and has determined that they would have to pay an 8 percent yield on perpetual debt in either event. What will be the break-even level of EBIT? Interest in all states will be equal to 0.08 × (0.20 × $350,000,000) = $5,600,000, and the number of shares outstanding will be equal to (0.60 × $350,000,000)/$37 = 7,567,568 at the 20 percent debt capital structure, and the number of shares outstanding at the current capital structure is $350,000,000/$37 = 9,459,459. EPS20% Debt = EPSAll −equity
( EBIT − $5, 600, 000)(1−.21) = EBIT (1−.21)
7, 567, 568 9,459,459 .79EBIT − $4,424, 000 .79EBIT = 7, 567, 568 9,459,459 $7,472,973 EBIT − $41,848, 646, 616, 000 = 5, 978, 379 EBIT $1, 494, 594 EBIT = $41,848, 646, 616, 000 EBIT = $28,000, 010
LG6 16-14 Break-even EBIT with Taxes GTB, Inc., has a 21 percent tax rate and has $100 million in assets, currently financed entirely with equity. Equity is worth $7 per share, and book value of equity is equal to market value of equity. Also, let’s assume that the firm’s expected values for EBIT depend upon which state of the economy occurs this year, with the possible values of EBIT and their associated probabilities shown as follows: STATE Probability of state Expected EBIT in state
PESSIMISTIC OPTIMISTIC 0.45 0.55 $5 million
$19 million
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
The firm is considering switching to a 40 percent debt capital structure, and has determined that they would have to pay a 12 percent yield on perpetual debt in either event. What will be the break-even level of EBIT? Interest in all states will be equal to 0.12 × (0.40 × $100,000,000) = $4,800,000, and the number of shares outstanding will be equal to (0.60 × $100,000,000)/$7 = 8,571,429 at the 20 percent debt capital structure, and the number of shares outstanding at the current capital structure is $100,000,000/$7 = 14,285,714. EPS40% Debt = EPSAll −equity
(EBIT − $4,800, 000)(1−.21) = EBIT (1−.21)
8, 571, 429 14, 285, 714 .79 EBIT − $3,792,000 .79 EBIT = 8, 571, 429 14, 285, 714 $11, 285, 714 EBIT − $54,171, 427, 488, 000 = $6, 771, 429 EBIT 4, 514, 285 EBIT = $54,171, 427, 488, 000 EBIT = $12,000,002
Research It! (Web-Exercises): Investigating Firms’ Debt Ratios Go to the Yahoo! Industry Center at http://biz.yahoo.com/ic/, choose an industry from amongst the “Top Industries” listed in the left column, and choose three of the leading firms for that industry: What are these firms’ debt ratios? Investigate each firm’s background to try to determine whether the factors we discussed in this chapter are driving any differences in the amount of debt that they each have in their capital structures. Solution:
Choosing the “Semiconductor – Broad Line” industry, we see the following firms listed as the industry’s top performers and largest firms (by market capitalization):
Choosing Intel, Texas Instruments and Advanced Micro Devices (AMD), the easiest way to compare their debt ratios is to use the industry browser, linked to over on the right of the industry page: Using this, we see that the industry’s and firms’ debt ratios are: Description Semiconductor - Broad Line
Debt to Equity 0.3900
Debt/Assets 0.2806
Chapter 16 - Assessing Long-Term Debt, Equity, and Capital Structure
Advanced Micro Devices Inc. Intel Corporation Texas Instruments Inc.
3.6980 0.0610 0.0000
0.7871 0.0575 0.0000
As we can see, both Intel and Texas Instruments have debt ratios below that of the industry average, while AMD has a much higher debt level than is typical of the industry. The grossest explanation for AMD having such a large debt load is that they have been struggling (rather unsuccessfully) to compete with Intel for several years, with this being just one of the results. Integrated Minicase: Change in Equity Ownership The CEO of JJJ, Inc., owns 27 percent of his currently all-equity financed firm worth $100 million. He has proposed splitting off one of the divisions (worth $25 million) of his company to let it operate as an independent firm. Existing shareholders will not get shares in the new firm; instead, the new firm is expected to raise $25 million through an IPO, the proceeds from which are to be used to repurchase shares in JJJ. Assuming that the CEO does not participate in the stock buyback, what will his percentage ownership be after the division is split off? Solution:
Since his ownership will remain concentrated in the other 75% of the firm, we can calculate his post-split ownership percentage as 27%/75% = 36%.
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
CHAPTER 17 – SHARING FIRM WEALTH: DIVIDENDS, SHARE REPURCHASES, AND OTHER PAYOUTS questions LG1
1.
Why might a firm’s investors wish to delay receiving cash from the firm? They might wish to delay receiving cash if they expect to be in a lower tax bracket in the future.
LG2
2.
Why might the government actually want the capital gains tax rate to be lower than the dividend tax rate? The government might want to encourage firms to retain earnings for expansion.
LG2
3.
What condition would have to be necessary in order for the riskiness of the firm’s cash flows to investors to be affected by the firm’s dividend payout policy? This would be true if any of the assumptions of the dividend irrelevance theory did not hold. For example, if dividends and capital gains were subject to differential tax rates, if realizing capital gains subjected investors to transaction costs, or if markets weren’t perfectly efficient.
LG3
4.
Explain how an announced increase in a firm’s dividend payout might be perceived as either a good or a bad information signal. If investors think this is a signal that the firm expects to be more profitable in the future, it could be perceived as a good signal, but if investors think that the firm is paying out more in dividends because it is out of good money-making ideas, then it could be a bad signal.
LG3
5.
We talked about how a firm might attract a different clientele by switching dividend payout policies: Might a particular clientele change its preference for dividends versus capital gains through no action of the firm? Explain. Certainly. Think, for example, of people’s preferences for dividends versus capital gains changing when they retire.
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
LG4
6.
Suppose that federal banking regulators in the United States announced that they are going to allow banks to take on significant equity investments in firms to which they have lent. What would you expect, on average, to happen to those firms’ dividend payout ratios over time? We would expect a similar result to that which exists in Germany, where bank-controlled firms pay out lower dividends.
LG4
7.
If a firm follows the modified residual dividend model discussed in this chapter, are extraordinary dividends paid out of residual net income? Yes. Ordinary dividends may be paid out of a variety of sources, but extraordinary dividends will only be paid if the firm has an unusually large amount of residual net income.
LG4
8.
Suppose a firm announces a new dividend amount every year with the first quarterly dividend declaration, but never explicitly states that the dividend will be continued for the other three quarters of the year. However, in the past the firm has always continued the first quarter’s dividend into the other three quarters of the year. How much would you expect this firm’s share price to react when it announced the new, first-quarter dividend at the beginning of a new year? As investors begin to believe that this tendency to set all four quarters’ dividends at a constant amount is consistent, we would expect to see the price increase by the present value of all the expected quarterly dividend increases, not just by that of the one announced.
LG5
9.
Could the record date ever be before the ex-dividend date? Why or why not? No. The shares would need to stop trading with the dividend before the firm assessed ownership.
LG5
10.
Suppose a firm managed to consistently lower the length of time between the ex-dividend date and the payment date. On average, how would this affect the firm’s stock price? As this would move the payment date closer to the declaration date, we would see stock prices increase more when dividends are declared.
LG5
11.
If a firm announces a dividend decrease, would you expect the stock price to go down more or less than the present value of that decrease? Why? It would depend upon what investors thought was the reason for the decrease and how long they expected it to persist, but, in general, we would probably expect the price to decrease more than the present value of that decrease due to investors uncertainty concerning how long the decrease would persist and due to investors receiving what they perceived to be a pessimistic signal about the firm’s future prospects.
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
LG6
12.
How big of a stock dividend would a firm have to announce for the stock price to be affected as much as it would through a 3-for-1 stock split? The firm would have to announce a 200 percent stock dividend.
LG6
13.
Why might a firm announce a reverse stock split? A reverse stock split would cause the stock price to increase. If the firm desired this (due, perhaps, to listing requirements on the stock exchange they trade on), they might very well announce a reverse stock split.
LG6
14.
Would it be possible for a firm to announce a “reverse stock dividend”? No. This would require a negative percentage, and dividends can’t be negative.
LG7
15.
Why might firms prefer to conduct stock repurchases through open-market operations rather than through fixed-price tender offers? Open-market purchases might allow the firm to repurchase shares at a lower price, benefitting the shareholders who retained their shares.
problems basic problems LG2
17-1
Payout Ratio Suppose a firm pays total dividends of $500,000 out of net income of $2 million. What would the firm’s payout ratio be? Payout ratio = $500,000 / $2,000,000 = 0.25.
LG2
17-2
Payout Ratio Suppose a firm pays total dividends of $750,000 out of net income of $5 million. What would the firm’s payout ratio be? Payout ratio = $750,000 / $5,000,000 = 0.15.
LG2
17-3
Total Dividend Amount Suppose a firm has a retention ratio of 35 percent and net income of $5 million. How much does it pay out in dividends? If the firm retains 35 percent of net income, then it pays out: (1 – 0.35) × $5,000,000 = $3,250,000.
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
LG2
17-4
Total Dividend Amount Suppose a firm has a retention ratio of 56 percent and net income of $9 million. How much does it pay out in dividends? If the firm retains 56 percent of net income, then it pays out: (1 – 0.56) × $9,000,000 = $3,960,000.
LG2
17-5
Dividend per Share Suppose a firm has a retention ratio of 40 percent, net income of $17 million, and 10 million shares outstanding. What would be the dividend per share paid out on the firm’s stock? If the firm retains 40 percent of net income, then it pays out: (1 – 0.40) × $17,000,000 = $10,200,000. DPS = Common stock dividends paid / Number of shares of common stock outstanding = $10,200,000 / 10,000,000 = $1.02 per share.
LG2
17-6
Dividend per Share Suppose a firm has a retention ratio of 60 percent, net income of $35 million, and 140 million shares outstanding. What would be the dividend per share paid out on the firm’s stock? If the firm retains 60 percent of net income, then it pays out: (1 – 0.60) × $35,000,000 = $14,000,000. DPS = Common stock dividends paid / Number of shares of common stock outstanding = $14,000,000 / 140,000,000 = $0.10 per share.
LG6
17-7
Stock Dividend Effects If a firm has retained earnings of $3 million, a common shares account of $5 million, and additional paid-in-capital of $10 million, how would these accounts change in response to a 10 percent stock dividend? Assume market value of equity is equal to book value of equity.
Current value of outstanding shares: $18,000,000 x 10 percent = stock dividend = $1,800,000 Retained earnings decreased by $1,800,000 = $1,200,000 Common stock par value would increase by 10 percent = $5,500,000 Addition to paid in capital = $1,800,000 – $500,000 = $1,300,000 + $10,000,000 = $11,300,000 (Total paid in capital)
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
Total equity: $5,500,000 (Common stock) + $11,300,000 (Paid in capital) + $1,200,000 = $18,000,000.
LG6
17-8
Stock Dividend Effects If a firm has retained earnings of $23 million, a common shares account of $275 million, and additional paid-in-capital of $100 million, how would these accounts change in response to a 20 percent stock dividend? Assume market value of equity is equal to book value of equity. Since the current value of outstanding shares would be $275,000,000 + $100,000,000 + $23,000,000 = $398,000,000, the stock dividend would involve transferring 0.20 × $398,000,000 = $79,600,000 from the retained earnings account into the other two accounts. Since this is more than the amount of available retained earnings, the firm would be unable to complete the stock dividend as described.
intermediate problems LG4
17-9
Extraordinary Dividend JBK, Inc., normally pays an annual dividend. The last such dividend paid was $2.50, all future dividends are expected to grow at 5 percent, and the firm faces a required rate of return on equity of 11 percent. If the firm just announced that the next dividend will be an extraordinary dividend of $17 per share that is not expected to affect any other future dividends, what should the stock price be? Using equation 8-6, the price if only the ordinary dividend were paid would be: P0 =
D1 i−g
$2.50(1.05) 0.11 − 0.05 $2.625 = 0.11 − 0.05 = $43.75 =
However, the next dividend will be $17 – $2.625 = $14.375 higher than the model accounts for, so we would need to add the present value of this difference to get the actual stock price: P = $43.75 + 0
$14.375 1.11
= $56.70
LG4 17-10 Extraordinary Dividend MMK Cos. Normally pays an annual dividend. The last such dividend paid was $2.25, all future dividends are expected to grow at a rate of 7 percent per year, and the firm faces a required rate of return on equity of 13 percent. If the firm
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
just announced that the next dividend will be an extraordinary dividend of $25 per share that is not expected to affect any other future dividends, what should the stock price be? Using equation 8-6, the price if only the ordinary dividend were paid would be:
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
P0 =
D1 i−g
$2.25(1.07) 0.13 − 0.07 $2.4075 = 0.13 − 0.07 = $40.13 =
However, the next dividend will be $25 – $2.4075 = $22.5925 higher than the model accounts for, so we would need to add the present value of this difference to get the actual stock price: P = $40.13 +
$22.5925
0
1.13 = $60.12
LG5
17-11 Effects of Dividends on Stock Prices Gen Corp. is expected to pay a dividend of $3.50 per year indefinitely. If the appropriate rate of return on this stock is 11 percent per year, and the stock consistently goes ex-dividend 35 days before dividend payment date, what will be the expected minimum and maximum prices in light of the dividend payment logistics? The daily interest rate will be equal to: idaily = 365 1.11 −1 = 0.000286
So the maximum stock price, which will occur right before the stock goes ex-dividend, will be: P0 =
$3.50
(1 + 0.000286)36
+
$3.50 0.11
1
(1 + 0.000286)36
= $34.96
And the minimum stock price, which will occur right after the stock goes ex-dividend, will be: P0 =
LG5
$3.50 0.11
1
(1 + 0.000286)35
= $31.50
17-12 Effects of Dividends on Stock Prices Kenzie Cos. is expected to pay a dividend of $2.75 per year indefinitely. If the appropriate rate of return on this stock is 16 percent per year, and the stock consistently goes ex-dividend 40 days before dividend payment date, what
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
will be the expected minimum and maximum prices in light of the dividend payment logistics?
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
The daily interest rate will be equal to: idaily = 365 1.16 −1 = 0.000407
So the maximum stock price, which will occur right before the stock goes ex-dividend, will be: P0 =
$2.75
(1 + 0.000407)
+ 41
$2.75 1 = $19.61 0.16 (1 + 0.000407)41
And the minimum stock price, which will occur right after the stock goes ex-dividend, will be: P0 =
$2.75 0.16
1
(1 + 0.000407)40
= $16.91
advanced problems LG2
17-13 Dividends versus Capital Gains Show mathematically that, with a tax rate on both dividends and capital gains of 5 percent, it doesn’t matter whether earnings are paid out as dividends or kept in the firm to cause g to grow for a constant-dividend stock. This is basically a question of whether the tax rate is applied to the dividends or to the price when the stock is sold. Either way, the after-tax wealth of the shareholder will be equal to: P (1− t ) = 0
LG2
c
D1 (1− tc ) i
17-14 Dividends versus Capital Gains Show mathematically that, with a tax rate on both dividends and capital gains of 15 percent, it doesn’t matter whether earnings are paid out as dividends or kept in the firm to cause g to grow for a constant-dividend stock. This is basically a question of whether the tax rate is applied to the dividends or to the price when the stock is sold. Either way, the after-tax wealth of the shareholder will be equal to: P (1− t ) = 0
LG4
c
D1 (1− tc ) i
17-15 Dividends Set Annually Suppose that a firm always announces a yearly dividend at the end of the first quarter of the year, but then pays the dividend out as four equal quarterly
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
payments. If the next such “annual” dividend has been announced as $4, it is exactly one quarter until the first quarterly dividend from that $4, the effective annual required rate of return on the company’s stock is 13 percent, and all future “annual” dividends are expected to grow at 3 percent per year indefinitely, how much will this stock be worth? Since dividends come quarterly, we first need to convert the 13 percent EAR into an effective quarterly rate: iquarterly = 4 1.13 −1 = 0.0310
Using equation 5-4, the present value of the first year’s dividends will be the present value of a four-period annuity with payments of $1: 1 − 1 N (1 + i) PVAN = PMT i 1 1 − 4 (1 + 0.0310) = $1 0.0310 = $3.7080
Since each year’s dividends are expected to grow at 3 percent, the present value of each year’s dividends at the beginning of that year will also grow at 3 percent, so we can value the stock’s dividends as the present value of a growing perpetuity due: PV = $3.7080 +
$3.7080(1.03) 0.13 − 0.03
= $41.90
LG4
17-16 Dividends Set Annually Suppose that a firm always announces a yearly dividend at the end of the first quarter of the year, but then pays the dividend out as four equal quarterly payments. If the next such “annual” dividend has been announced as $6, it is exactly one quarter until the first quarterly dividend from that $6, the effective annual required rate of return on the company’s stock is 17 percent, and all future “annual” dividends are expected to grow at 6 percent per year indefinitely, how much will this stock be worth? Since dividends come quarterly, we first need to convert the 17 percent EAR into an effective quarterly rate: iquarterly = 4 1.17 −1 = 0.0400
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
Using equation 5-4, the present value of the first year’s dividends will be the present value of a four-period annuity with payments of $6 / 4 = $1.50: 1 − 1 N (1 + i ) PVAN = PMT i 1 1 − 4 (1 + 0.0400) = $1.50 0.0400 = $5.4444
Since each year’s dividends are expected to grow at 6 percent, the present value of each year’s dividends at the beginning of that year will also grow at 6 percent, so we can value the stock’s dividends as the present value of a growing perpetuity due: PV = $5.4444 +
$5.4444 (1.06) 0.17 − 0.06
= $57.91
LG5
17-17 Change in Lead Time of Dividend Announcement Everything else held constant, if a firm announces that it will double the length of time between its ex-dividend date and its payment date, what should be the effect on the stock price? If N is the previous number of days between the ex-dividend date and the payment date, the stock price should have a new maximum value of:
D
P0 =
(
D
+ 2 1 + idaily 1 + idaily 2 N iyearly 1
(
)
And a new minimum value of: D 1 P = 2 0 iyearly 1 + idaily
(
)
2N
1
)
2N
Chapter 17 - Sharing Firm Wealth: Dividends, Share Repurchases, and Other Payouts
LG5 17-18 Change in Lead Time of Dividend Announcement Everything else held constant, if a firm announces that it will halve the length of time between its ex-dividend date and its payment date, what should be the effect on the stock price? If N is the previous number of days between the ex-dividend date and the payment date, the stock price should have a new maximum value of:
D
P0 =
D
1
+ 2 N / 2 i 1+ idaily N / 2 1+ idaily yearly
(
1
(
)
And a new minimum value of: D 1 2 P = 0 N /2 iyearly 1+ idaily
(
)
)
Chapter 18 - Issuing Capital and the Investment Banking Process
CHAPTER 18 – ISSUING CAPITAL AND THE INVESTMENT BANKING PROCESS questions LG1
1. Describe the various sources of capital funding available to new and small firms. Most new and small firms finance their business assets by borrowing funds from private or public sources. Private capital fund suppliers fall into two basic categories: suppliers of debt financing and suppliers of equity financing. Debt financing includes capital funds borrowed from personal savings, friends or relatives, financial institutions such as commercial bank loans, or venture capitalists. Equity financing includes capital funds invested by venture capitalists. Public sources of capital include debt and equity financing provided by government agencies such as the U.S. Small Business Administration (SBA).
LG1
2. What process do banks use to evaluate bank loans to small versus midmarket business firms? Low profitability has caused many banks to build small-business scoring models similar to, but more sophisticated than, those used for mortgage loans and consumer credit. Small business loan models often combine computer-based financial analysis of borrower financial statements with behavioral analysis of the owner of the new and/or small business. Midmarket firms require credit analysis different from the kinds of analysis used for new or small businesses because, while still assessing the character of the firm’s management, the main focus is on the business itself. The credit process begins with a loan officer, the Bank, gathering information on the firm. Having gathered information about the firm, the loan officer will decide whether pursuing the new business is worthwhile, given the firm’s needs, the bank’s credit policies, the current economy, and the competitive lending environment. If loan officers decide that midmarket firms are worth the investment, they structure and price agreements as laid out in the bank’s credit-granting policy and then negotiate with the firm.
LG1
3. What is the difference between a spot loan and a loan commitment? Spot loans are loans in which the firm would receive the funds as soon as the bank approves the loan. These days, most business loans are made as firms “take down” (or borrow against) pre-negotiated lines of credit or loan commitments. Banks make loan commitment agreements–contractual commitments to loan the firm a certain maximum amount–at given interest rate terms. The loan commitment agreement also defines the length of time over which the borrower may take down this loan.
LG1
4. Why do banks charge up-front fees and back-end fees on loan commitments? In return for making the loan commitment, the bank may charge an up-front fee (or facility fee) based on the size of the commitment. The bank may also charge the borrower a back-end fee (or commitment fee) on any unused balances on the commitment line at the end of the period. The
Chapter 18 - Issuing Capital and the Investment Banking Process
fees are charged because the bank must stand ready to supply the full dollar amount at any time over the commitment period. LG1
5. What is the difference between a fixed-rate and a floating-rate loan? With fixed-rate loans, the firm makes fixed interest payments over the life of the loan. With floatingrate loans the loan’s interest rate (and thus the interest payments the firm must make) changes over the loan life. A floating rate is set at a fixed spread over a prevailing benchmark rate, such as a Treasury-bill rate, the federal funds rate, or a prime rate. If the benchmark rate rises during the loan period, so does the firm’s loan cost.
LG1
6. What types of programs does the Small Business Administration offer to new and small businesses? Under what conditions would a new or small firm use each program? For qualified new and small firms that cannot obtain long-term financing on reasonable terms from banks or other financial institutions, the SBA offers a basic loan guarantee program. Through this program, the SBA can guarantee up to $3,750,000 (representing 75 percent of the loan value) at an interest rate not to exceed 2.75 percent more than the prime lending rate. Maturities on these loans can extend up to 5-10 years for working capital and equipment loans, and 25 years for real estate loans. While the SBA’s primary function is to guarantee loans made to new and small businesses by private financial institutions (such as banks), the SBA offers direct loan programs as well. The SBA’s Certified Development Company Loan Program provides long-term, fixed-rate capital funding to small businesses that use the funds to purchase real estate, machinery, or equipment for expansion or modernization. Private, nonprofit corporations called certified development companies offer these loans to contribute to communities’ or regions’ economic development. The SBA funds the loans via a 100 percent SBA-guaranteed debenture and a bank generally secures the loans. SBA loans require an investment of at least 10 percent owner equity. The SBA’s Microloan Loan Program provides up to $50,000 in short-term loans to small businesses with repayment terms up to six years. Loan proceeds may be used to fund working-capital, inventory and supplies, furniture and fixtures, or machinery and equipment purchases. Through this program the SBA makes or guarantees a loan to a bank, which then makes the microloan to the firm. The bank also provides the fledgling firm with management and technical assistance.
LG2
7. What is venture capital? Venture capital is a professionally managed pool of money used to finance new and often highrisk firms. Venture capital is generally provided by investment institutions or private individuals willing to back an untried company and its managers in return for an equity investment in the firm. Venture capital firms do not make outright loans. Rather, they purchase equity interests in firms that give the venture capitalists the same rights and privileges associated with equity investments made by the firm’s other owners. As equity holders, venture capital firms are not generally passive investors. Rather, they provide valuable expertise to the firm’s managers and sometimes even help in recruiting senior managers for the firm. They also generally expect to be
Chapter 18 - Issuing Capital and the Investment Banking Process
kept fully informed about the firm’s operations, any problems, and whether all firm owners’ joint goals are being met. LG2
8. What are the different types of venture capital firms? How do institutional venture capital firms differ from angel venture capital firms? Many types of venture capital firms have sprung up since the 1980s. Institutional venture capital firms’ sole purpose is to find and fund the most promising new firms. Private-sector institutional venture capital firms include venture capital limited partnerships (that are established by professional venture capital firms, acting as general partners in the firm: organizing and managing the firm and eventually liquidating their equity investment), financial venture capital firms (subsidiaries of banks), and corporate venture capital firms (subsidiaries of nonfinancial corporations that generally specialize in making start-up investments in high-tech firms). Limited partner venture capital firms dominate the industry. In addition to private sector institutional venture capital firms, the federal government, through the SBA, operates Small Business Investment Companies (SBICs). SBICs are privately organized venture capital firms licensed by the SBA to make equity investments (as well as loans) to entrepreneurs for start-up activities and expansions. As federally sponsored entities, SBICs rely on their unique opportunity to obtain investment funds from the U.S. Treasury at very low rates relative to private-sector institutional venture capital firms. In contrast to institutional venture capital firms, angel venture capitalists (or angels) are wealthy individuals who make equity investments. Angel venture capitalists have invested much more in new and small firms than institutional venture capital firms have.
LG2
9. What are the advantages and disadvantages to a new or small firm of getting capital funding from a venture capital firm? Venture capital firms receive many unsolicited proposals of funding from new and small firms. The venture capital firms reject the majority of these requests. Venture capital firms look for two things in making their decisions to invest in a firm. The first is a high return. Venture capital firms are willing to invest in high-risk new and small firms. However, they require high levels of returns (sometimes as high as 700 percent within five to seven years) to take on these risks. The second is an easy exit. Venture capital firms realize a profit on their investments by eventually selling their firm interests. They want a quick and easy exit opportunity when it comes time to sell. Basically, venture capital firms provide equity funds to new, unproven, and young firms. This willingness separates venture capital firms from commercial banks and investment firms, which prefer to invest in existing, financially secure businesses.
LG1
10. As a new or small firm considers going public what must the owners consider? In making the decision to go from a private to a public firm, managers must consider the benefits versus the costs of doing so. A major benefit of going public is that the firm will have to a new, larger pool of equity capital than is available from any previous source (bank or venture capitalist). This new equity allows a firm to undertake new and profitable investment opportunities that it could not undertake as a private firm. The market provides a market value for the firm’s common stock, which is really a readily available measure of firm performance
Chapter 18 - Issuing Capital and the Investment Banking Process
(another advantage of going public). Such a transparent measure of firm performance can attract even more stockholders and can provide a tool that can be used to reward firm mangers (i.e., through stock or option payments as part of compensation packages). Finally, as private firms, managers generally must invest much of their personal wealth and human capital in the firm. From Chapters 9 and 10, we know that this results in a poorly diversified portfolio for the firm’s original owners. By going public, the original owners can reallocate their personal wealth away from the firm and into more diversified portfolios. However, some significant costs are attached to the decision to become a public firm. First and foremost is the direct financial cost of an IPO. Cash expenses associated with an IPO (e.g., legal services, printing) can sometimes total as much as $1 million. These expenses must be paid regardless of whether the IPO succeeds or not. Additionally, underwriters charge a discount (on average about 7 percent) to sell the stock and IPOs are typically underpriced (on average about 15 percent) to ensure a successful sale. Thus, a significant amount of the issue proceeds do not actually become available to the newly public firm. Add to these financial costs a substantial demand for time from the firm’s owners during the IPO process. That is, the firm’s owners and top managers must spend a significant amount of time with the investment bankers to discuss all aspects of the firm and with major potential stockholders before the IPO is completed. These time demands grow even more significantly as the offering date approaches. Further, throughout the IPO process, managers must disclose firm details that may be valuable to competitors. Further, as a public firm, shareholders have the right to a great deal of information about the firm. The release of this information to stockholders also releases it to competitors. Finally, the firm is exposed to reputational costs if the IPO is unsuccessful or is beset with problems. LG3
11. Describe the various sources of capital funding available to public firms. In contrast to small and new firms that can only get capital funding from mainly private sources, public firms raise the majority of their capital funds from public debt and equity markets. Public firms raise large amounts of short-term debt in the money market, primarily as commercial paper. Further, public firms raise long-term capital by issuing securities in the public debt and equity markets.
LG3
12. What is the difference between a direct and an indirect placement of commercial paper? Commercial paper is sold to investors either directly (about 12 percent of all issues in 2018), using the issuers’ own sales force (e.g., GMAC), or indirectly through brokers and dealers (about 88 percent of all issues in 2018), such as commercial banks and investment banks underwriting the issues. Commercial paper underwritten and issued through brokers and dealers is more expensive to the issuer, usually increasing the cost of the issue by one-tenth to one-eighth of a percent, reflecting an underwriting cost. In return, the dealer guarantees the sale of the whole issue.
LG3
13. Can a public firm with a lower-than-prime credit rating issue commercial paper? Commercial paper issuers with lower than prime credit ratings often back their commercial paper issues with lines of credit from commercial banks. In these cases, banks agree to make the
Chapter 18 - Issuing Capital and the Investment Banking Process
promised payment on the commercial paper if the issuer cannot pay off the debt at maturity. Thus, a letter of credit backing commercial paper effectively substitutes the credit rating of the issuing firm with the credit rating of the bank. This reduces the paper purchasers’ risk and results in a lower interest rate (and higher credit rating) on the commercial paper. LG4
14. How does a best efforts underwriting differ from a firm commitment underwriting? If a company issues stock for the first time, which type of underwriting would the firm prefer? Why might the firm still choose the alternative? Normally, the investment bank facilitates the sale of securities transaction using a firm commitment underwriting. The investment bank guarantees the firm a price for newly issued securities by buying the whole issue at a fixed price (the bid price) from the issuing firm at a discount from par. The investment bank then seeks to resell these securities to investors at a higher price (the offer price). As a result, the investment bank takes a risk that it may not be able to resell the securities to investors at a higher price. Some corporate securities are offered on a best efforts underwriting basis, in which the underwriter does not guarantee a firm price to the issuer (as with a firm commitment offering). Here, the underwriter acts more as a placing or distribution agent for a fee.
LG4
15. How does a competitive sale of corporate bonds differ from a negotiated sale? Which type of underwriting would a firm prefer? Why might a firm still choose the alternative? An investment bank can purchase bonds through competitive bidding against other investment bankers or by directly negotiating with the issuer. In a competitive sale, the bond-issuing firm invites bids from a number of underwriters. The investment bank that submits the highest bid to the bond issuer wins the bid. The underwriter may use a syndicate of other underwriters and investment banks to distribute (sell) the issue to the public. With a negotiated sale, a single investment bank obtains the exclusive right to originate, underwrite, and distribute the new bonds through a one-on-one negotiation process. With a negotiated sale, the investment bank provides the origination and advising services to the issuers.
LG4
16. How does a public offering of debt or equity securities issued by a public firm differ from a private placement? Most often, corporate bonds and stocks are offered publicly through investment banks acting as underwriters. In a public sale of debt or equity, once the issuing firm and the investment bank have agreed on the stock issue details, the investment bank must get SEC approval in accordance with the Securities and Exchange Act of 1934. Security registration can be a lengthy process. In a private placement, a public firm (sometimes with an investment bank’s help) seeks to find a large institutional buyer or group of buyers (usually less than ten) to purchase the whole issue. To protect smaller individual investors against a lack of disclosure, the Security and Exchange Act of 1934 requires publicly traded securities to be registered with the Securities and Exchange Commission (SEC). Private placements, on the other hand, can be unregistered and can only be resold to large, financially sophisticated investors. These large investors supposedly possess the resources and expertise to analyze a security’s risk.
Chapter 18 - Issuing Capital and the Investment Banking Process
LG4
17. What are the net proceeds, gross proceeds, and underwriter’s spread? How does each affect the funds received by a public firm when debt or equity securities are issued? In a firm commitment underwriting, the investment bank purchases stock from the issuing firm for a guaranteed price (called the net proceeds) and resells them to investors at a higher price (called the gross proceeds). The difference between the gross proceeds and the net proceeds on an issue (called the underwriter’s spread) is compensation for the expenses and risks incurred by the investment bank.
LG4
18. Why would an investment bank use a syndicate to assist in underwriting debt or equity securities? Once an issue is arranged and its terms set, each syndicate member is assigned a given number of shares in the issue for which it is responsible for selling. Shares of stock issued through a syndicate of investment banks spread the risk associated with the stock sale among several investment banks. A syndicate also results in a larger pool of potential outside investors, widening the scope of the investor base and increasing the probability of a successful sale.
LG4
19. What is the difference between a prospectus and a red herring prospectus? At the same time that the issuing firm and its investment bank prepare the registration statement to be filed with the SEC, they must also prepare a preliminary version of the public offering’s prospectus called the red herring prospectus. The red herring prospectus is similar to the registration statement, but is distributed to potential equity buyers. Once the SEC registers the issue, the red herring prospectus is replaced with the official or final prospectus.
LG4
20. What is a shelf registration? Why would a public firm want to issue securities using a shelf registration? To reduce registration time and costs, yet still protect the public by requiring issuers to disclose information about the firm and the security to be issued, the SEC passed a rule in 1982 allowing for “shelf registration.” A shelf registration allows firms that plan to offer multiple issues of stock over a three-year period to submit one registration statement as described above (called a master registration statement). The registration statement summarizes the firm’s financing plans for the three-year period. Thus, the securities are shelved for up to three years until the firm is ready to issue them. Once the issuer and its investment bank decide to issue shares during the three-year shelf registration period, they prepare and file a short form statement with the SEC. Upon SEC approval, the shares can be priced and offered to the public usually within one or two days of deciding to take the shares “off the shelf.” Thus, shelf registration allows a firm to get stocks into the market quickly (e.g., in one or two days) if the firm feels conditions (especially the price they can get for the new stock) are right, without the time lag generally associated with full SEC registration. problems
basic problems
Chapter 18 - Issuing Capital and the Investment Banking Process
LG1
18-1 Calculating Fees on a Loan Commitment You have approached your local bank for a start-up loan commitment for $250,000 needed to open a computer repair store. You have requested that the term of the loan be one year. Your bank has offered you the following terms: size of loan commitment = $250,000, term = one year, up-front fee = 50 basis points, back-end fee = 75 basis points. If you take down 80 percent of the total loan commitment, calculate the total fees you would pay on this loan commitment. Up-front fee = $250,000 × 0.0050 Back-end fee = $250,000 × 0.0075 x 0.20 Total fees
LG1
= $1,250 = 375 = $1,625
18-2 Calculating Fees on a Loan Commitment Calculate the total fees a firm would have to pay when its bank offers the firm the following loan commitment: A loan commitment of $4.25 million with an up-front fee of 75 basis points and a back-end fee of 25 basis points. The take down on the loan is 50 percent. Up-front fee = $4.25m. × 0.0075 = $31,875.00 Back-end fee = $4.25m. × 0.0025 x 0.50 = 5,312.50 Total fees = $37,187.50
LG4
18-3 Calculating Costs of Issuing Stock Husker’s Tuxedo’s, Inc. needs to raise $250 million to finance its plan for nationwide expansion. In discussions with its investment bank, Husker’s learns that the bankers recommend an offer price (or gross price) of $35 per share and they will charge an underwriter’s spread of $1.75 per share. Calculate the net proceeds to Husker’s from the sale of stock. How many shares of stock will Husker’s need to sell in order to receive the $250 million needed? Net proceeds = Gross proceeds – Underwriter’s spread = $35 per share – $1.75 per share = $33.25 per share
=> LG4
Funds needed = $250m. = $33.25 per share × Number of shares sold Number of shares sold = $250m. / $33.25 per share = 7,518,797 shares
18-4 Calculating Costs of Issuing Stock Don’s Captain Morgan, Inc. needs to raise $12.5 million to finance plant expansion. In discussions with its investment bank, Don’s learns that the bankers recommend an offer price (or gross proceeds) of $25.50 per share and Don’s will receive $23.75 per share. Calculate the underwriter’s spread on the issue. How many shares of stock will Don’s need to sell in order to receive the $12.5 million it needs? Underwriter’s spread = Gross proceeds - Net proceeds = $25.50 per share – $23.75 per share = $1.75 per share
=>
Funds needed = $12.5m. = $23.75 per share × Number of shares sold Number of shares sold = $12.5m. / $23.75 per share = 526,316 shares
Chapter 18 - Issuing Capital and the Investment Banking Process
LG4
18-5 Calculating Costs of Issuing Debt The Fitness Studio, Inc., with the help of its investment bank, recently issued $43.125 million of new debt. The offer price (and face value) on the debt was $1,000 per bond and the underwriter’s spread was 7 percent of the gross proceeds. Calculate the amount of capital funding The Fitness Studio raised through this debt offering. Underwriter’s fees = $43.125m. × 0.07 = $3,018,750 => Funds received by The Fitness Studio = $43.125m. - $3,018,750 = $40,106,250
LG4
18-6 Calculating Costs of Issuing Debt Harper’s Dog Pens, Inc., with the help of its investment bank, recently issued $191.5 million of new debt. The offer price on the debt was $1,000 per bond and the underwriter’s spread was 5 percent of the gross proceeds. Calculate the amount of capital funding Harper’s Dog Pens, Inc. raised through this bond issue. Underwriter’s fees = $191.5m. × 0.05 = $9.575m. => Funds received by Harper’s Dog Pens = $191.5m. - $9.575m. = $181.925m.
intermediate problems LG1 18-7 Calculating Fees on a Loan Commitment You have approached your local bank for a start-up loan commitment for $250,000 needed to open a computer repair store. You have requested that the term of the loan be one year. Your bank has offered you the following terms: size of loan commitment = $250,000, term = one year, up-front fee = 50 basis points, back-end fee = 75 basis points, and rate on the loan = 8 percent. If you immediately take down $150,000 and no more during the year, calculate the total interest and fees you will pay on this loan commitment. Up-front fee = $250,000 × 0.0050 Interest = $150,000 × 0.08 Back-end fee = $100,000 × 0.0075 Total interest and fees LG1
18-8 Calculating Fees on a Loan Commitment Casey’s One Stop has been approved for a $127,500 loan commitment from its local bank. The bank has offered the following terms: term = one year, up-front fee = 85 basis points, back-end fee = 35 basis points, and rate on the loan = 7.75 percent. Casey’s expects to immediately take down $119,000 and no more during the year unless there is some unforeseen need. Calculate the total interest and fees Casey’s One Stop can expect to pay on this loan commitment. Up-front fee = $127,500 × 0.0085 Interest = $119,000 × 0.0775 Back-end fee = $8,500 × 0.0035 Total interest and fees
LG4
= $ 1,250 = 12,000 = 750 = $14,000
=$ 1,083.75 = 9,222.50 = 29.75 =$10,336.00
18-9 Calculating Costs of Issuing Debt DiPitro’s Paint and Wallpaper, Inc., needs to raise $1 million to finance plant expansion. In discussions with its investment bank, DiPitro’s learns that the bankers recommend a debt issue with gross proceeds of $1,000 per bond and they will charge an
Chapter 18 - Issuing Capital and the Investment Banking Process
underwriter’s spread of 6.5 percent of the gross proceeds. How many bonds will DiPitro’s Paint and Wallpaper need to sell in order to receive the $1 million they need? Funds received by DiPitro’s = Issue size – (0.065 × Issue size) = $1m. = Issue size (1–0.065) => Issue size = $1m. / (1 - 0.065) = $1,069,519 => Number of bonds = $1,069,519 / $1,000 = 1,070 bonds LG4
18-10 Calculating Costs of Issuing Debt Renee’s Boutique, Inc., needs to raise $58 million to finance firm expansion. In discussions with its investment bank, Renee’s learns that the bankers recommend a debt issue with an offer price of $1,000 per bond and they will charge an underwriter’s spread of 5 percent of the gross price. Calculate the net proceeds to Renee’s from the sale of the debt. How many bonds will Renee’s Boutique need to sell in order to receive the $58 million they need? Funds received by Renee’s = Issue size – (0.05 × Issue size) = $58m. = Issue size (1 – 0.05) => Issue size = $58m. / (1 - 0.05) = $61,052,632 => Number of bonds = $61,052,632 / $1,000 = 61,053 bonds
LG4
18-11 Calculating Costs of Issuing Stock The Fitness Studio, Inc., with the help of its investment bank, recently issued 2.5 million shares of new stock. The offer price on the stock was $20.50 per share and The Fitness Studio received a total of $48,687,500 through this stock offering. Calculate the net proceeds and the underwriter’s spread on the stock offering. What percentage of the gross price is the investment bank charging The Fitness Studio for underwriting the stock issue? Net proceeds = $48,687,500 / 2.5m. shares = $19.475 per share Gross funds received = $20.50 per share× 2.5m. shares = $51.25m. Underwriter’s funds = $51.25m. - $48,687,500 = $2,562,500 => Underwriter’s spread = $2,562,500 / 2.5m. shares = $1.025 per share Investment bank’s percentage of gross = $1.025 per share / $20.50 per share = 5%
LG4
18-12 Calculating Costs of Issuing Stock Harper’s Dog Pens, Inc., with the help of its investment bank, recently issued 8.5 million shares of new stock. The offer price on the stock was $12.00 per share and Harper’s received a total of $97.75 million from the stock offering. Calculate the net proceeds and the underwriter’s spread charged by the underwriter to Harper’s Dog Pens, Inc. What percentage of the gross proceeds is the investment bank charging Harper’s Dog Pens for underwriting the stock issue? Net proceeds = $97.75m. / 8.5m. shares = $11.50 per share Gross funds received = $12.00 per share × 8.5m. shares = $102m. Underwriter’s funds = $102m. - $97.75m. = $4.25m. => Underwriter’s spread = $4.25m. / 8.5m. shares = $0.50 per share Investment bank’s percentage of gross = $0.50 per share / $12.00 per share = 4.17%
LG4
18-13 Calculating Costs of Issuing Stock Zimba Technology Corp. recently went public with an initial public offering of 2.5 million shares of stock. The underwriter used a firm commitment offering in which the net proceeds was $8.05 per share and the underwriter’s spread was 8 percent of
Chapter 18 - Issuing Capital and the Investment Banking Process
the gross proceeds. Zimba also paid legal and other administrative costs of $250,000 for the IPO. Calculate the gross proceeds and the total funds received by Zimba from the sale of the 2.5 million shares of stock. Total funds received by Zimba = (2.5m. shares × $8.05 per share) - $250,000 = $19.875m. Gross proceeds = Underwriter’s spread + Net proceeds => Gross proceeds = (0.08 × Gross proceeds) + $8.05 per share => Gross proceeds - (0.08 × Gross proceeds) = $8.05 per share => Gross proceeds = $8.05 per share / (1 - 0.08) = $8.75 per share LG4
18-14 Calculating Costs of Issuing Stock Howett Pockett, Inc. plans to issue 10 million new shares of its stock. In discussions with its investment bank, Howett Pocket learns that the bankers recommend a net proceed of $33.80 per share and they will charge an underwriter’s spread of 5.5 percent of the gross proceeds. In addition, Howett Pockett must pay $3.4 million in legal and other administrative expenses for the seasoned stock offering. Calculate the gross proceeds and the total funds received by Howett Pockett from the sale of the 10 million shares of stock. Total funds received by Howett Pockett = (10m. shares × $33.80 per share) - $3.4m. = $334.6m. Gross proceeds = Underwriter’s spread + Net proceeds => Gross proceeds = (0.055 × Gross proceeds) + $33.80 per share => Gross proceeds - (0.055 × Gross proceeds) = $33.80 per share => Gross proceeds = $33.80 per share / (1 - 0.055) = $35.77 per share
advanced problems LG1 18-15 Calculating Fees on a Loan Commitment During the last year, you have had a loan commitment from your bank to fund inventory purchases for your small business. The total line available was $500,000, of which you took down $400,000. It is now the end of the loan commitment period and your bank had you pay the back-end fees. You have misplaced the paperwork that listed the terms of the commitment, but you know you paid total fees (this does not include any interest paid to borrow the $400,000) of $3,250 on this loan commitment. You remember that the up-front fee was 50 basis points. Calculate the back-end fee on this loan commitment. Total fees Up-front fee Back-end fee
= $500,000 × 0.005 = $3,250 – $2,500
= $ 3,250 =- $ 2,500 = 750
=> Back-end fee = $750 / ($500,000 - $400,000) = 0.0075 = 75 basis points LG1
18-16 Calculating Fees on a Loan Commitment During the last year, you have had a loan commitment from your bank to fund working capital for your business. The total line available was $17 million, of which you took down $13 million. It is now the end of the loan commitment period and your bank had you pay the back-end fees. You have misplaced the paperwork that listed the terms of the commitment, but you know you paid total fees (this does not include any interest paid to
Chapter 18 - Issuing Capital and the Investment Banking Process
borrow the $13 million) of $72,500 on this loan commitment. You remember that the back-end fee was 75 basis points. Calculate the up-front fee on this loan commitment. Total fees Back-end fee Up-front fee
= $72,500 = ($17m. - $13m.) × 0.0075 = -30,000 = $72,500 - $30,000 = $42,500
=> Up-front fee = $42,500 / $17m. = 0.0025 = 25 basis points LG4
18-17 Calculating Costs of Issuing Stock DiPitro’s Paint and Wallpaper, Inc., needs to raise $1 million in common stock to finance plant expansion. In discussions with its investment bank, DiPitro’s learns that the bankers recommend a gross price of $25 per share and that 45,000 shares of stock be sold. If the net proceeds on the stock sale leaves DiPitro’s with $1 million, calculate the underwriter’s spread on the stock issue. Gross funds received from sale = $25 per share × 45,000 shares = $1.125m. Underwriter’s funds received = $1.125m. - $1m. = $125,000 => Underwriter’s spread in dollars = $125,000 / 45,000 shares = $2.778 per share => Underwriter’s spread in percentage = $2.778 per share / $25 per share = 11.11%
LG4
18-18 Calculating Costs of Issuing Stock Renee’s Boutique, Inc. needs to raise $58 million in common stock to finance firm expansion. In discussions with its investment bank, Renee’s learns that the bankers recommend an offer price of $33.75 per share and that 1.8 million shares of stock be sold. If the net proceeds on the stock sale leaves Renee’s with $58 million, calculate the underwriter’s spread on the stock issue. Gross funds received from sale = $33.75 per share × 1.8m. shares = $60.75m. Underwriter’s funds received = $60.75m. - $58m. = $2.75m. => Underwriter’s spread in dollars = $2.75m. / 1.8m. shares = $1.528 per share => Underwriter’s spread in percentage = $1.528 / $33.75 = 4.53%
LG4
18-19 Calculating Costs of Issuing Stock Hughes Technology Corp. recently went public with an initial public offering in which they received a total of $60 million in new capital funding. The underwriter used a firm commitment offering in which the offer price was $10 and the underwriter’s spread was $0.75. Hughes also paid legal and other administrative costs of $1.05 million for the IPO. Calculate the number of shares issued through this IPO. Net proceeds (not including legal and other administrative expenses) = $10 per share - $0.75 per share = $9.25 per share Funds received from sale plus legal and other administrative expenses = $61.05m. Shares sold = $61.05m. / $9.25 per share = 6.6m. shares
LG4
18-20 Calculating Costs of Issuing Stock Howett Pockett, Inc., needs to raise $12 million in new capital funding from a seasoned equity offering. In discussions with its investment bank, Howett Pocket learns that the bankers recommend a gross price of $13.50 per share and they will charge an
Chapter 18 - Issuing Capital and the Investment Banking Process
underwriter’s spread of $1.00 per share. In addition, Howett Pockett must pay $500,000 in legal and other administrative expenses for the seasoned stock offering. Calculate the number of shares of stock that Howett Pockett will need to sell to raise the $12 million. Net proceeds (not including legal and other administrative expenses) = $13.50 per share - $1.00 per share = $12.50 per share Funds received from sale plus legal and other administrative expenses = $12.5m. Shares sold = $12.5m. / $12.50 per share = 1m. shares
research it! Underwriters Go to the Thomson Financial—Investment Banking and Capital Markets Group Web site at http://dmi.thomsonreuters.com/DealsIntelligence/ and find the latest information available for debt and equity securities underwriting. Click on “QUARTERLY REVIEWS.” Click on the latest quarter’s “Global Equity Capital Markets.” This will download a file onto your computer that will contain the most recent information on top underwriters for equity securities. Go back and repeat the last step, clicking on “Global Debt Capital Markets.” What is the most recent dollar value of global debt and equity underwritten by investment banks? Who are the top underwriters of debt and equity? How have the top writers’ market shares changed in the last year? SOLUTION: The solution will vary with the date the Web site is accessed. However, most often, corporate securities are offered publicly through investment banks acting as underwriters. Normally, the investment banks facilitate these transactions.
Chapter 18 - Issuing Capital and the Investment Banking Process
integrated mini-case: Capital Funding in a Public Firm Nuran Security Systems, Inc., needs to raise $150 million for asset expansion. As it raises the capital funding, Nuran wants to maintain its current debt ratio of 60 percent. Nuran has been approved for a loan commitment from its local bank. The bank has offered the following terms: term = one year, upfront fee = 60 basis points, back-end fee = 90 basis points. Nuran expects it will take down 90 percent of the loan commitment. Nuran’s will also issue new shares of stock to support this asset growth. Nuran’s investment bank will use a firm commitment offering in which the net proceeds are $23.875 per share and the underwriter’s spread is 7 percent of the gross proceeds. Nuran Security Systems will also pay legal and other administrative costs of $750,000 for the stock issue. Calculate the amount of debt and equity funding Nuran Security Systems will need to keep its current debt ratio constant and the number of shares of stock the firm must issue to raise the needed funds. What can Nuran Security Systems, Inc., expect to pay for fees on this loan commitment and stock issue? SOLUTION: Debt issued = $150m. × 0.6 = $90m. Equity issued = $150m. × 0.4 = $60m. Stock issue costs: Number of shares of stock issued = ($60m. + $750,000)/ $23.875 = 2,544,503 shares Gross price = $23.875 / (1 – 0.07) = $25.67 Total fees on stock issue = [($25.67 - $23.875) × 2,544,503 shares] + $750,000 = $5,317,383 Loan commitment fees: Loan commitment size: $90m. / 0.9 = $100m. Up-front fee Back-end fee Total fees
= $100m. × 0.006 = $ 600,000 = $100m. × (1 - 0.9) × 0.009 = 90,000 = $690,000
Chapter 19 - International Corporate Finance
Question and Problem Solutions CHAPTER 19 – International Corporate Finance Questions LG1
19-1 What do global organizations like the World Trade Organization and the International Monetary Fund do? These organizations attempt to facilitate international trade and help developing countries by creating international standards of business laws. They promote lower trade barriers, provide a platform for dispute resolution, and watch over the global financial system.
LG1
19-2 What is the purpose of trading zones? What are some of the most important zones for world trade? Trading zones reduce trade restrictions and tariffs to make trade easier between the countries in the zone. The most important trade zones are the European Union (EU), North American Free Trade Agreement (NAFTA), and the Central American Free Trade Agreement.
LG1
19-3 Explain how a country’s import trade limitations and tariffs influence MNC’s foreign direct investment. If a country has import limitations, some firms may choose to locate manufacturing facilities within the country in order to sell its products there. Thus, MNCs may increase their foreign direct investment in a country with import limitations. However, they need to be careful because governments that would impose these limitations on imports may also impose restrictions on foreign capital and operations within their country.
LG2
19-4 What are the risks of foreign direct investment into the United States? What does new FDI into the United States mean for firms already operating in that industry in the United States? One risk of FDI entering a country is that the capital may also flee the country at a later time. So while it is good for people to have the jobs that are created when FDI comes into a country, it also devastates those people if the capital were to leave. In addition, new investment by foreign firms creates more competition for the local firms already operating in that industry.
LG3&5 19-5 Describe the similarities and the differences of exchange rate/cross rate arbitrage and spot rate/forwardrate arbitrage. Both forms of arbitrage require the purchase of the cheaper rate and the sale of the expensive rate. The exchange/cross arbitrage does this by trading both directly with a foreign currency and through a third currency using the cross rate. The spot/forward arbitrage accomplishes a position by borrowing money in one country, converting the money through a spot currency exchange, and depositing the money in the other country. The return of the cash is locked in through a forward contract. If the exchange rates in either case are not properly aligned, an arbitrage profit is available.
Chapter 19 - International Corporate Finance
LG4
19-6 What is meant when it is said that the U.S. dollar is strengthening? How would it impact your vacation abroad and foreign visitors to the United States? A strengthening U.S. dollar means that the value of one U.S. dollar is changing so that it is worth more of the foreign currencies. An exchange rate of $1 = €0.6924 that changes to $1 = €0.7511 is an example of the dollar strengthening. Since you will get more of the foreign currency for your dollars, this will make the foreign vacation less expensive. Of course, it also makes the trip more expensive for foreign visitors coming to the United States.
LG4
19-7 Describe the difference between a forward rate selling at a discount and selling at a premium. If the spot rate between the U.S. dollar and the Brazilian real is $1 = 2.0875 real and the 3-month forward rate is $1 = 2.1025 real, is the forward real selling at a discount or a premium? The forward rate is said to be selling at a discount (premium) when the direct quote of the forward rate is for more (less) foreign currency to one dollar than is expressed by the spot rate. The Brazilian real forward rate is selling at a discount.
LG4
19-8 What is meant by hedging exchange rate risk and what are some ways it is done? Exchange rate risk is the risk that the currency exchange rate in the future may change, devaluing the conversion of cash flows in the future. This risk can be reduced or even mitigated through positions in the forward rate, futures contracts, options, and currency swaps. This process of “locking-in” future exchange rates is called hedging.
LG4&6 19-9 What are the advantages of borrowing money in the country you plan to invest it in? One advantage is that it reduces exchange rate risk. The money generated from the business operations within the firm can be used to pay the interest and principle on the loan. No currency exchange is needed. This also reduces the political risk of the government seizing the investment. If the investment is seized, the company can stop paying back the loan. LG5
19-10 If a Sony television costs $500 in the United States, what do you think it should cost in Japan? What are some reasons that your price might not be right? The law of one price suggests that it will cost the equivalent of $500 converted to yen. However, if the Sony TV is manufactured in Japan, then U.S. consumers would have the transportation costs included in the $500 price. Japanese consumers would not have to pay the cost of trans-Pacific transportation and thus it would be cheaper there.
LG5
18-11 What happens to a country’s currency over time when it has a high inflation rate? What will that mean for the country’s exports and imports? When a country experiences high inflation, then its currency devalues, or weakens, over time. This means that it will take more and more of its currency to buy one unit of foreign currency. The weakening currency makes exports of the firm less expensive in foreign countries. It also makes imported goods more expensive. So, the country should see more exports and fewer imports.
LG5
19-12 What forces are at work that cause the price of wheat per bushel to be the same in most every country of the world? Wheat is a commodity in that a bushel of wheat is the same everywhere. In addition, it is easy to transport. Therefore, the law of one price applies. If prices get too high in one country, then an arbitrage opportunity exists for someone to buy wheat cheap in another country and sell it in the high price country.
Chapter 19 - International Corporate Finance
LG5
19-13 If the spot exchange rate between the U.S. dollar and the Singapore dollar is $1 = SG$1.5266 and the 3-month expected exchange rate is $1 = SG$1.5305, then what is the expected inflation relationship between the two countries? First, change the quotes to direct quotes: Spot SG$1 = $0.6551 3-month SG$1 = $0.6534 The relative form of the PPP equation shows that
SG$1.5305 = SG$1.5266 (1 + Domestic inflation rate - Foreign inflation rate)
So, Domestic inflation − Foreign inflation = $0.6534 / $0.6551 − 1 = -0.0026 or -0.26%. The inflation rate in Singapore is expected to be slightly higher than the U.S. inflation rate. LG5 19-14 Over the past decade, China has acquired hundreds of billions of U.S. dollars because of the trade imbalance between the two countries. They have used many of these dollars to purchase U.S. Treasury bonds. What would likely happen to the dollar’s value, and interest rates and inflation in the United States, if China decided to suddenly sell the Treasury bonds and exchange the dollars for other currencies? A large selling of the bonds would drive down the price of the bonds, thus increasing interest rates (see Chapter 7 for a discussion about the inverse relationship between bond prices and interest rates). Selling the dollars for other currencies could push down the price of the U.S. dollar, causing it to weaken. The weakening dollar can also lead to higher inflation because it makes imports more expensive. LG6
19-15 Can a U.S. firm experience political risk problems in its overseas projects because of the U.S. government? Give examples. When governments have conflicts, the trade between the two countries often suffers. For example, if the U.S. is unhappy with another government, it might forbid U.S. defense contractors from selling weapons to that country. This can be expanded to all products. An example of that is the restriction on trade with Cuba. Lastly, a foreign country with a dispute with the U.S. government might seize U.S. business assets within the country to put additional pressure on the U.S. government.
LG7
19-16 Give some examples of the financial complications that occur when evaluating a capital budgeting project in a foreign country. The first complication is that multiple currencies might be involved. The capital to fund the project might come from the U.S. while the project might be in a foreign country. The production will occur in the foreign country, but the products might be sold throughout the world, which would involve cash flows in multiple currencies. Lastly, what discount rate should be used? The WACC is typically computed using the home country cost of capital. But this will have to be adjusted if the cash flows of another country are used in the capital budgeting analysis.
problems basic problems LG3
19-1 Exchange Rate Quote Convert each of the following direct quotes to dollar indirect quotes: a. 1 Danish krone = $0.170 b. 1 Indian rupee = $0.0184 c. 1 Israeli shekel = $0.2751 a. $1 = 1 krone /$ 0.170 = 5.882 krone b. $1 = 1 rupee / $0.0184 = 54.348 rupee c. $1 = 1 shekel / $0.2751 = 3.6350 shekel
Chapter 19 - International Corporate Finance
LG3
19-2 Exchange Rate Quote Convert each of the following direct quotes to dollar indirect quotes: a. 1 Korean won = $0.0009 b. 1 Malaysian ringgit = $0.3238 c. 1 Thai baht = $0.0331 a. $1 = 1 won / $0.0009 = 1,111.11 won b. $1 = 1 ringgit / $0.3238 = 3.088 ringget c. $1 = 1 baht / $0.0331 = 30.211 bhat
LG3
19-3 Exchange Rate Quote Convert each of the following indirect quotes to dollar direct quotes: a. $1 = 20,864 Vietnam dong b. $1 = 6.300 Venezuelan bolivar fuerte c. $1 = 9.175 South African rand a. 1 dong = $1 / 20,864 dong = $0.0000479 b. 1 bolivar fuerte = $1 / 6.300 bolivar fuerte = $0.1587 c. 1 rand = $1 / 9.175 rand = $0.1090
LG3
19-4 Exchange Rate Quote Convert each of the following indirect quotes to dollar direct quotes: a. $1 = 3.7497 Saudi Arabian riyal b. $1 = 44.15 Philippine peso c. $1 = 0.5409 Latvian lat a. 1 riyal = $1 / 3.7497 riyal = $0.2667 b. 1 peso = $1 / 44.15 peso = $0.0227 c. 1 lat = $1 / 0.5409 lat = $1.8488
LG3
19-5 Currency Exchange Compute the amount of each foreign currency that can be purchased for $500,000: a. 1 Danish krone = $0.170 b. 1 Indian rupee = $0.0184 c. 1 Israeli shekel = $0.2751 a. $500,000 = $500,000 / $0.170 per krone = 2,941,176.47 krone b. $500,000 = $500,000 / $0.0184 per rupee = 27,173,913.04 rupee c. $500,000 = $500,000 / $0.2751 per shekel = 1,817,520.90 shekel
LG3
19-6 Currency Exchange Compute the amount of each foreign currency that can be purchased for one million dollars: a. 1 Korean won = $0.0009 b. 1 Malaysian ringgit = $0.3238 c. 1 Thai baht = $0.0331 a. $1m = $1m / $0.0009 per won = 1,111,111,111 won b. $1m = $1m / $0.3238 per ringgit = 3,088,326 ringgit c. $1m = $1m / $0.0331 per baht = 30,211,480 baht
LG3
19-7 Currency Exchange Compute the number of dollars that can be bought with two million of each foreign currency units: a. $1 = 20,864 Vietnam dong b. $1 = 6.300 Venezuelan bolivar fuerte c. $1 = 9.175 South African rand
Chapter 19 - International Corporate Finance
a. 2m dong = 2m dong / 20,864 dong per $ = $95.86 b. 2m bolivar = 2m bolivar / 6.300 bolivar per $ = $317,460 c. 2m rand = 2m rand / 9.175 rand per $ = $217,984 LG3
19-8 Currency Exchange Compute the number of dollars that can be bought with one million of each foreign currency units: a. $1 = 3.7497 Saudi Arabian riyal b. $1 = 44.150 Philippine peso c. $1 = 0.5409 Latvian lat a. 1m riyal = 1m riyal / 3.7497 riyal per $ = $266,688 b. 1m peso = 1m peso / 44.150 peso per $ = $22,650 c. 1m lat = 1m lat / 0.5409 lat per $ = $1,848,771
LG5
19-9 Law of One Price If the price of silver in England is £15.23 per ounce, what is the expected price of silver in the United States if the spot exchange rate is $1 = £0.6535? £6.71 per ounce = £15.23 / £0.6535 per $ = $23.31 per ounce
LG5
19-10 Law of One Price If the price of copper in Europe is €2.12 per ounce, what is the expected price of copper in the United States if the spot exchange rate is $1 = €0.7623? €2.12 per ounce = €2.12 / €0.7623 per $ = $2.78 per ounce
LG7
19-11 Discount Rates A financial manager has determined that the appropriate discount rate for a foreign project is 12 percent. However, that discount rate applies in the United States using dollars. What discount rate should be used in the foreign country using the foreign currency? The inflation rate in the United States and in the foreign country is expected to be 3 percent and 6 percent, respectively. The discount rate in the foreign country should be 12% + (6% − 3%) = 15%
LG7
19-12 Discount Rates A financial manager has determined that the appropriate discount rate for a foreign project is 16 percent. However, that discount rate applies in the United States using dollars. What discount rate should the manager use in the foreign country using the foreign currency? The inflation rate in the United States and in the foreign country is expected to be 5 percent and 4 percent, respectively.
The discount rate in the foreign country should be 16% + (4%−5%) = 15%
intermediate problems LG3
19-13 Cross Rate Given these two exchange rates, $1 = 12.268 Mexican pesos and $1 = €0.7624, compute the cross rate between the Mexican peso and the euro. State this exchange rate in pesos and in euros. 1 peso = 1 peso × ($1 / 12.268 peso) × (€0.7624 / $1) = €0.0621 Also, €1 = €1 ÷ €0.0621 per peso = 16.0913 pesos
LG3
19-14 Cross Rate Given these two exchange rates, $1 = 0.9952 Australian dollars and $1 = £0.6476, compute the cross rate between the Australian dollars and the pound. State this exchange rate in Australian dollars and in pounds. A$1 = A$1 × ($1 / A$0.9952) × (£0.6476 / $1) = £0.6507 Also, £1 = £1 / £0.6507 per A$ = A$1.5368
Chapter 19 - International Corporate Finance
LG4 19-15 Exchange Rate Risk In 1997, many East Asian currencies suddenly and dramatically devalued. What is the percentage change in value of a $50 million investment in Indonesia when the exchange rate changes from $1 = 2,000 rupiah to $1 = 10,000 rupiah? The company invests $50 million at a value of $50m × (2,000 rupiah / $1) = 100,000 m rupiah Then the rupiah devalues and the value of the 100,000 million rupiah investment becomes: 100,000m rupiah × ($1 / 10,000 rupiah) = $10m This is a drop from $50 million to $10 million, or an 80 percent decline (= ($50m - $10m) / $50m) LG4
19-16 Exchange Rate Risk The Russian financial crisis of 1998 caused its currency to be dramatically devalued. What is the percentage change in value of a $100 million investment in Russia when the exchange rate changes from $1 = 6 rubles to $1 = 21 rubles? The company invests $100 million at a value of $100m × (6 ruples / $1) = 600m ruples Then the ruple devalues and the value of the 600 million ruple investment becomes: 600m ruples × ($1 / 21 ruples) = $28.57 million This is a drop from $100 million to $28.57 million, or an 71 percent decline {= ($100m -$28.57m ) / $100m}
LG5
19-17 Interest Rate Parity The spot rate between the U.S. dollar and the New Zealand dollar is $1 = NZD1.1867. If the interest rate in the United States is 5 percent and in New Zealand is four percent, then what should be the 3month forward exchange rate? Use equation 19-1. But the quote must be a direct quote and the interest rate must be for the same period as the forward rate. The spot direct quote is $1 / NZD1.1867= $0.8427 per NZD and the 3-month interest rates are 1.25 percent and 1 percent respectively.
Forward exchangerate = LG5
1 + 0.0125 1 + 0.01
$0.8427 per NZD = $0.8448 per NZD
19-18 Interest Rate Parity The spot rate between the U.S. dollar and the Taiwan dollar is $1 = TWD29.905. If the interest rate in the United States is five percent and in Taiwan is three percent, then what should be the 1-month forward exchange rate? Use equation 19-1. But the quote must be a direct quote and the interest rate must be for the same period as the forward rate. The spot direct quote is $1 / TWD29.905 = $0.0334 per TWD and the 1- month interest rates are 0.4167 percent and 0.25 percent respectively.
Forwardexchangerate =
1+ 0.004167
$0.0334 per TWD = $0.0335 per TWD
1+ 0.0025 LG6
19-19 Purchasing Power Parity The current spot rate between the U.S. dollar and the Swedish krona is $1 = 6.5228 krona. If the inflation rate in the United States is four percent and in Sweden is 2 percent, then what is the expected spot rate in one year? Use equation 19-3. But the quote must be a direct quote. The spot direct quote is $1 / 6.5228 krona = $0.1533 per krona.
Expected exchange rate = $0.1533 per krona (1+ 0.04 − 0.02) = $0.1564 per Krona
Chapter 19 - International Corporate Finance
LG6
19-20 Purchasing Power Parity The current spot rate between the U.S. dollar and the Netherland Antilles guilder is $1 = 1.7915 guilder. If the inflation rate in the United States is three percent and in the Netherland Antilles is seven percent, then what is the expected spot rate in one year? Use equation 19-3. But the quote must be a direct quote. The spot direct quote is $1 / 1.7915 guilder = $0.5582 per guilder.
Expected exchange rate = $0.5582 per guilder (1 + 0.03 − 0.07) = $0.5359 per guilder advanced problems LG4
19-21 Exchange Rate Risk A U.S. firm is expecting cash flows of 25 million Mexican pesos and 35 million Indian rupees. The current spot exchange rates are: $1 = 12.268 pesos and $1 = 45.204 rupees. If these cash flows are not received for one year and the expected spot rates at that time will be $1 = 11.118 pesos and $1 = 44.075 rupees, then what is the difference in dollars received that was caused by the delay? If the cash flows are received today, they would be: 25m pesos × ($1 / 12.268 pesos) + 35m rupees × ($1 / 45.204 rupees) = $2.81m If the cash flows come in one year, they would be: 25m pesos × ($1 / 11.118 pesos) + 35m rupees × ($1 / 44.075 rupees) = $3.04m The firm would get $0.23 million more in one year.
LG4
19-22 Exchange Rate Risk A U.S. firm is expecting to pay cash flows of 15 million Egyptian pounds and 25 million Qatar rials. The current spot exchange rates are: $1 = 5.725 pounds and $1 = 3.639 rials. If these cash flows are delayed one year and the expected spot rates at that time will be $1 = 5.892 pounds and $1 = 3.988 rials, then what is the difference in dollars paid that was caused by the delay? If the cash flows are received today, they would be: 15m pounds × ($1 / 5.725 pounds) + 25m rials × ($1 / 3.639 rials) = $9.49m If the cash flows come in one year, they would be: 15m pounds × ($1 / 5.892 pounds) + 25m rials × ($1 / 3.988 rials) = $8.81m The firm would get $0.68 million less in one year.
LG3
19-23 Triangular Arbitrage The U.S. dollar spot exchange rate with the Canadian dollar is $1 = CA$1.18. The U.S. dollar and Swiss franc exchange rate is $1 = 1.219 francs. If the cross rate between the franc and Canadian dollar is 1 franc = CA$0.9750 then show that an arbitrage is possible. What positions should be taken to profit from the mispricing? The inferred cross-rate is 1 franc = 1 franc × ($1 / 1.219 francs) × (CA$1.18 / $1) = CA$0.9680. Since this is not the same as the actual cross-rate, an arbitrage is possible. Starting with U.S. dollars, buy francs and convert them to Canadian dollars and then back to U.S. dollars.
LG3
19-24 Triangular Arbitrage The U.S. dollar spot exchange rate with the Australian dollar is $1 = AU$1.2697. The U.S. dollar and euro exchange rate is $1 = €0.7559. If the cross rate between the euro and Australian dollar is €1 = AU$1.598 then show that an arbitrage is possible. What positions should be taken to profit from the mispricing? The inferred cross-rate is €1 = €1 × ($1 / €0.7559) × (AU$1.2697 / $1) = AU$1.6797. Since this is not the same as the actual cross-rate, an arbitrage is possible. Starting with U.S. dollars, buy Australian dollars and convert them to euros and then back to U.S. dollars.
19-25 Spreadsheet Problem Below are the Consumer Price Index inflation rates each year for the United States and Japan. Also shown is the spot exchange rate for the beginning of each year.
Chapter 19 - International Corporate Finance
A. Using PPP (equation 19.3), compute what the 1-year forward exchange rate should be each year. B. Compare the forward rates computed in part (a) to the actual exchange rate at the beginning of the next year. How well does PPP predict the future exchange rate? Is it biased too high, too low, or about right?
Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016
Beginning of Year Exchange Rate 146.25 134.60 124.50 125.40 112.50 100.52 103.92 115.49 132.40 112.15 101.70 114.73 132.02 119.86 106.95 102.83 116.34 118.83 109.70 91.12 92.55 81.56 76.67 87.10 104.46 120.20 119.30
US CPI Inflation Rate 6.1 3.1 2.9 2.8 2.7 2.5 3.3 1.7 1.6 2.7 3.4 1.6 2.4 1.9 3.3 3.4 2.5 4.1 0 2.6 1.6 2.9 1.6 1.6 0.0 1.5
Spreadsheet solution:
1990 1991 1992 1993
Predicted Exchange Rate 143.0325 134.1962 122.01 123.0174
Difference with real 8.4325 9.6962 -3.39 10.5174
Japan CPI Inflation Rate 3.9 2.8 0.9 0.9 0.5 -0.4 0.5 1.8 0.6 -1.3 -0.3 -1.6 -0.3 -0.4 0.3 -0.4 0.4 0.9 0.4 -1.8 0.1 -0.2 -0.1 0.4 2.7 0.9
Chapter 19 - International Corporate Finance
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
110.025 97.60492 101.0102 115.6055 131.076 107.664 97.9371 111.0586 128.4555 117.1032 103.7415 98.92246 113.8969 115.0274 110.1388 87.11072 91.16175 79.03164 75.36661 86.0548 107.2804 119.4788
9.505 -6.31508 -14.4798 -16.7945 18.926 5.964 -16.7929 -20.9614 8.59546 10.15322 0.9115 -17.4175 -4.93314 5.32744 19.0188 -5.43928 9.60175 2.36164 -11.7334 -18.4052 -12.9196 0.1788 Average =
-1.16892
Note that roughly half of the predictions are too high and nearly half are too low. So there is no bias.
research it! Find Currency Exchange Rates Currency spot exchange rates are widely available on the Web. For example, at Yahoo! Finance (http://finance.yahoo.com/currency-converter) you can find the exchange rates between more than 150 currencies. The calculator the site provides computes the amount of one currency resulting from converting money in another currency. You can also see a graph of the desired exchange rate for a history of up to five years. Daily and monthly historical data for the dollar exchange rates are available at the Federal Reserve Web site (http://research.stlouisfed.org/fred2/). Many of the exchange rate data are available for more than 30 years. See how exchange rates have changed over the years.
SOLUTION: The answer will depend on which currencies the student uses and when the assignment is completed. An example may look like:
Chapter 19 - International Corporate Finance
integrated minicase: Assessing Exchange Rate Risk Imagine that you are a financial manager of a multinational corporation, like Starbucks Coffee, in charge of determining the impact of exchange rate changes on the firm. Changes in currency exchange affect both the balance sheet and the income statement. The balance sheet impact occurs when the value of international assets are translated to U.S. dollars. The values of those assets change as the exchange rate changes. The value of costs, revenue, and profit also are impacted on the income statement because of exchange rate risk. Consider that your firm has the following investments in coffee bean production and processing: COUNTRY Columbia Kenya
VALUE ($ MILLIONS) $75 100
Chapter 19 - International Corporate Finance
Papua New Guinea
80
The expense of all the labor, production, and beans will require the following exchanges to the foreign currency: COUNTRY CASH FLOW(MILLIONS) Columbia 78,180 pesos Kenya 3,200 shilling Papua New Guinea 100 kina Your firm has also invested in store facilities to sell the coffee products. The countries and the value of the investments are: COUNTRY VALUE ($ MILLIONS) Canada $200 Japan 100 United Kingdom 150 The net profit from these countries next year is projected to be: COUNTRY CASH FLOW (MILLONS) Canada CA$80 Japan ¥7,200 United Kingdom £30 Current spot exchange rates are:
$1 = 3,301.0 Colombian pesos $1 = 102.30 Kenyan shilling $1 = 3.010 Papua New Guinea kina $1 = 1.46 Canadian dollars $1 = 117.18 Japanese yen $1 = 0.7010 British pound Your task is to determine the following: a. What is the impact on the value of the international assets and the cash flow if the dollar were to devalue by ten percent against each currency (one at a time)? b. What is the overall impact of a ten percent dollar devaluation against every currency? c. What the impact on the value of the international assets and the cash flow if the dollar were to strengthen by ten percent against each currency (one at a time)? d. What is the overall impact of a ten percent strengthening against every currency? e. What can be done to hedge this risk? SOLUTION: (a) and (b). A devaluing dollar means that international assets will appear to be worth more in terms of the dollar. The shaded area below shows a ten percent increase in value for the assets of that country (or in all countries). Part B
Part A Country
Value, millions
Columbia
$75
$82.5
$75
$75
$75
$75
$75
$82.5
Kenya
$100
$100
$110
$100
$100
$100
$100
$110
Papua New Guinea
$80
$80
$80
$88
$80
$80
$80
$88
Chapter 19 - International Corporate Finance
Canada
$200
$200
$200
$200
$220
$200
$200
$220
Japan
$100
$100
$100
$100
$100
$110
$100
$110
United Kingdom
$150
$150
$150
$150
$150
$150
$165
$165
$705 percentage change=
$712.5
$715
$713
$725
$715
$720
$775.5
1.06%
1.42%
1.13%
2.84%
1.42%
2.13%
10.00%
Sum =
Note that a 10 percent increase in value of the Columbia assets results in a 1.06 percent increase in the value of the total international assets. A devaluing dollar makes foreign payments more expensive but also means that foreign profits will be more valuable. Country
Cash Flow, millions
millions
Columbia
-78,180 pesos
-$23.68
-$26.05
-$23.68
-$23.68
-$23.68
-$23.68
-$23.68
-$26.05
Kenya
-3,200 shilling
-$31.28
-$31.28
-$34.41
-$31.28
-$31.28
-$31.28
-$31.28
-$34.41
Papua New Guinea
-100 kina
-$33.22
-$33.22
-$33.22
-$36.54
-$33.22
-$33.22
-$33.22
-$36.54
$60.27
$54.79
$54.79
$60.27
Canada
CA$80
$54.79
$54.79
$54.79
Japan
¥7,200
$61.44
$61.44
$61.44
$61.44
$61.44
$67.59
$61.44
$67.59
United Kingdom
£30
$42.80
$42.80
$42.80
$42.80
$42.80
$42.80
$47.08
$47.08
$70.85
$68.48
$67.72
$67.53
$76.33
$76.99
$75.13
$77.93
Part C
$54.79
Sum=
(c) and (d).. A strengthening dollar decreases the value of foreign assets. COUNTRY Columbia Kenya Papua New Guinea Canada Japan United Kingdom Sum =
VALUE ($ MILLIONS) $75 100 80 200 100 150 $705 Percentage change =
(c). $67.5 100 80 200 100 150
(d) $75 90 80 200 100 150
$75 100 72 200 100 150
$75 100 80 180 100 150
$75 100 80 200 90 150
$75 100 80 200 100 135
$697.5
$695
$697
$685
$695
$690
$67.5 90.0 72.0 180.0 90.0 135.0 $634.5
-1.06%
-1.42%
-1.13%
-2.84%
-1.42%
-2.13%
-10.00%
Chapter 19 - International Corporate Finance
A strengthening dollar lowers the effective cost of foreign payments but also reduces the value of foreign profits.
Columbia Kenya Papua New Guinea
Cash Flow, millions -78,180 pesos -3,200 shilling -100 kina
Canada Japan United Kingdom
CA$80 ¥7,200 £30
Country
millions -$23.68 -$31.28 -$33.22
-$21.32 -$31.28 -$33.22
-$23.68 -$28.15 -$33.22
-$23.68 -$31.28 -$29.90
$54.79
Sum=
$61.52 $57.89 $86.02
$54.79 $61.52 $57.89 $88.39
$54.79 $61.52 $57.89 $89.15
$54.79 $61.52 $57.89 $89.34
-$23.68 -$31.28 -$33.22
-$23.68 -$31.28 -$33.22
-$23.68 -$31.28 -$33.22
$49.32
$54.79
$54.79
$61.52 $57.89 $80.54
$55.30 $57.89 $79.80
$61.52 $38.52 $66.64
-$31.92 -$41.45 -$29.81
$61.59 $55.37 $52.10 $65.88
Chapter 20 - Mergers and Acquisitions and Financial Distress
CHAPTER 20 –MERGERS AND ACQUISITIONS AND FINANCIAL DISTRESS questions LG1
1. Describe the difference between a merger and an acquisition. A merger is a transaction in which two firms combine to form a single firm. An acquisition is the purchase of one firm by another. Despite these two distinct definitions, the two terms, mergers and acquisitions, are often used interchangeably.
LG1
2. Describe the difference between a horizontal merger and a vertical merger. A horizontal merger combines two companies in the same industry, such as the merger between Heinz and Kraft. A vertical merger combines a firm with a supplier or distributor, such as the merger of Disney and Pixar. Pixar specialized in animation and Disney’s main aim was to create cartoon films using the animation. Disney bought Pixar who supplied animation to them. Vertical mergers occur between firms in different stages of production operation for many reasons such as avoidance of fixed costs, the elimination of costs of searching for prices, contracting, payment collection, communication, advertising and coordination, and better planning for inventory.
LG1
3. Classify each of the following as a horizontal merger, a vertical merger, a market extension merger, a conglomerate merger, or a product extension merger. a. Walmart acquires Kmart – horizontal merger b. Kroger grocery stores acquires Bunny Bread – vertical merger c. Schnucks grocery stores headquartered in St. Louis and operating in the Midwest acquires Food Land headquartered and operating in Hawaii – market extension merger d. Bank of America acquires Aflac – product extension merger e. Ford Motors buys the Los Angeles Rams – conglomerate merger
LG1
4. What is synergy and how does it apply to mergers? The main motivation for a merger or acquisition is synergy. That is, the value of the combined firms is greater than the sum of the value of the two firms individually. Thus, managers merge firms so as to maximize the value of the firms to the shareholders. The sources of value enhancing synergy in a merger come from four areas: revenue enhancement, cost reduction, tax considerations, and lower cost of capital. However, there are also some non-value-maximizing motives behind a merger. These include managers’ personal incentives that may destroy firm value and misallocation of capital.
LG1
5. Describe the three dimensions of revenue synergies that may be achieved in a merger. First, acquiring a firm in a growing market may enhance revenues. Second, the acquiring firm’s revenue stream may become more stable if the asset and liability portfolio of the target institution exhibits credit, interest rate, and liquidity risk characteristics that differ from those of the acquirer.
Chapter 20 - Mergers and Acquisitions and Financial Distress
Third, expanding into markets that are less than fully competitive offers an opportunity for revenue enhancement. That is, firms may be able to identify and expand geographically into those markets in which economic rents potentially exist, but in which regulators will not view such entry as potentially anticompetitive. LG1
6. What is the difference between economies of scope and economies of scale? Can two firms involved in a merger benefit from both economies of scale and economies of scope? As firms become larger through a merger, the increase in size allows for the reduction or elimination of overlapping resources. If these cuts lower the firm’s operating costs of production, merged firms may have an economy of scale advantage over smaller firms. Economies of scale imply that the unit or average cost of producing goods and services falls as the size of the firm expands. The simple economy of scale concept ignores the interrelationships among products and the “jointness” in the costs of producing them. In particular, merged firms’ abilities to generate synergistic cost savings through the joint use of inputs in producing multiple products are called economies of scope as opposed to economies of scale.
LG2
7. What is the Herfindahl-Hirschman Index? How is it calculated and interpreted? The Herfindahl-Hirschman Index (HHI) is a measure of market concentration whose value can be 0 to 10,000. The index is measured by adding the squares of the percentage market share of the individual firms in the market. An index value greater than 2,500 indicates a concentrated market, a value between 1,500 and 2,500 indicates a moderately concentrated market, and an unconcentrated market would have a value less than 1,500.
LG1
8. How can managers’ personal incentives result in value-destroying mergers and acquisitions? Managers expand through mergers to get personal benefits from building and managing large corporations. Academic research has documented this motive, finding that mergers are often positively related to sales and asset growth, and do not always result in increased stock prices. For example, in order to build corporate empires from which they get personal benefits, managers use free cash flows to acquire a firm that may have a negative net present value. This is particularly true for poorly monitored mangers who merge to maximize their corporation’s asset size because managers’ compensation is based on firm size. Likewise, unmonitored mangers can try to build corporate empires through the pursuit of negative NPV mergers to entrench themselves. That is, because of its greater size and the managers’ supposed expertise in managing the large company, management makes themselves indispensable to the firm. Finally, some managers overestimate their own managerial abilities and merge with the belief that they can better manage the takeover target than the target’s current management. Acquiring mangers then overbid for the target and fails to realize the gains expected from the merger in the postmerger period. Thus, the stock price and stockholders’ wealth fall.
LG2
9. Why is NPV valuation an appropriate tool to use in the evaluation of a merger target?
Chapter 20 - Mergers and Acquisitions and Financial Distress
The net present value (NPV) or discounted cash flow (DCF) method discussed in Chapter 13 is the most accurate and reliable tool used to evaluate whether a merger will be a profitable one. The NPV method allows bidder and target firm managers to predict pro forma cash flows of the
Chapter 20 - Mergers and Acquisitions and Financial Distress
merged firm. These forecasted cash flows are then discounted to a present value based on the merged firm’s weighted average cost of capital (WACC) to determine the merged firm’s present value. Finally, the present value of the merged firm is compared with the asking price of the target firm to determine whether the merger is profitable. LG3
10. What is the difference between business failure, economic failure, and technical insolvency? At the extreme, business failure is a type of financial distress in which a firm no longer stays in business. Economic failure is a type of financial distress in which the return on a firm’s assets is less than the firm’s cost of capital. Thus, the firm is not earning enough on its assets to pay the fund suppliers their promised payments. Technical insolvency is a type of financial distress in which a firm’s operating cash flows are not sufficient to pay its liabilities as they come due. In both cases, the firm can continue as a going concern and even eventually become a thriving firm.
LG3
11. A firm is experiencing a temporary period of financial distress as the result of a hurricane that has hit its local area. Because many of the firm’s customers have been severely hurt by the hurricane, they are unable to pay their debts to the firm. This stoppage of cash inflows has left the firm temporarily unable to pay its own bills. What options do the firm’s creditors have with respect to getting paid? When financial distress appears to be temporary, the firm’s creditors will generally work to restructure the firm to help it recover and reestablish itself as a viable entity. If, however, it is determined that the firm cannot recover from the financial distress, the firm and its creditors may agree to a liquidation of the firm’s assets.
LG3
12. What is the job of the trustee in an informal liquidation of a firm’s assets? The trustee or assignee liquidates the firm’s assets through a private sale or a public auction. The assignee then distributes any proceeds from the sale to the firms’ creditors and stockholders (if any funds are left after all creditors are paid). Once all assets are sold and creditors are paid the proceeds, the assignee has the creditors sign a release acknowledging the full settlement of the claim.
LG4
13. What is the difference between a Chapter 11 and a Chapter 7 bankruptcy? The goal of a Chapter 11 proceeding is to plan a reorganization of the corporation with some provision for repayment to the firm’s creditors. The Chapter 11 reorganization process allows a firm in temporary financial distress to continue operating while the creditors’ claims are settled using a collective procedure. Chapter 7 outlines the process to be followed for liquidating a failed firm. Chapter 7 is generally only used if it has been determined that reorganization under Chapter 11 is infeasible.
Chapter 20 - Mergers and Acquisitions and Financial Distress
LG4
14. Does a Chapter 7 bankruptcy increase the probability that creditors will be paid in full more so than a Chapter 11 bankruptcy? The goal of a Chapter 11 proceeding is to plan a reorganization of the corporation with some provision for repayment to the firm’s creditors. Chapter 7 outlines the process to be followed for liquidating a failed firm. Thus, Chapter 7 bankruptcy does not increase the probability that creditors will be paid in full more so than a Chapter 11 bankruptcy.
LG4
15. What is the order of payment to a firm’s creditors in a Chapter 7 bankruptcy? The distribution of the funds from asset liquidation occurs according to the following priority of claims: 1. Property taxes past due, 2. Claims of secured creditors, who receive the proceeds from the sale of specific collateral as stated in a lien or mortgage, 3. Administrative expenses associated with the bankruptcy proceedings, 4. Unpaid expenses incurred after the filing of the bankruptcy petition but before the trustee is appointed, 5. Wages due to employees in the 90 days immediately preceding the start of the bankruptcy proceedings (limited to $2,000 per employee), 6. Unpaid employee benefit plan contributions that should have been paid in the six months prior to the bankruptcy filing (limited to $2,000 per employee), 7. Unsecured customer claims (limited to $900 per customer), 8. Taxes due to federal, state, and other governmental agencies, 9. Unsecured creditor claims including any unsatisfied amounts of secured creditors’ claims, 10. Preferred stockholders (up to the par value of the preferred stock), and 11. Common stockholders receive any remaining funds.
LG4
16. To what extent are employees of a bankrupt firm paid their wages and benefits due? Employees are paid wages due in the 90 days immediately preceding the start of the bankruptcy proceedings (limited to $2,000 per employee).
LG5
17. What is a credit-scoring model? Credit-scoring models are quantitative models that use data on observed firm characteristics either to sort firms into different bankruptcy risk classes or to calculate the probability of bankruptcy. These models use past data, such as financial ratios, as inputs to explain repayment experiences on old debt. The relative importance of the factors used to explain past repayment performance then forecasts repayment performance on new debt.
LG5
18. What is the difference between a linear discriminant and a linear probability credit-scoring model? While linear discriminant models divide firms into high or low bankruptcy risk classes, linear probability (and logit models) produce a value for the expected probability of bankruptcy.
LG5
19. A firm has an Altman’s Z-score of 1.76. What does this mean? A Z-score of less than 1.81 indicates high risk of bankruptcy within the next year.
Chapter 20 - Mergers and Acquisitions and Financial Distress
Chapter 20 - Mergers and Acquisitions and Financial Distress
LG5
20. The Altman’s Z-score model has several weaknesses. What are they? The first problem is that this model usually discriminates only between two extreme cases of firm behavior: bankruptcy and no bankruptcy. In the real world various gradations of bankruptcy risk exist, from nonpayment or delay of interest payments (nonperforming assets) to outright default on all promised interest and principal payments. This problem suggests that a more accurate or finely calibrated sorting among firms may require defining more classes in the scoring model. The second problem is that there is no obvious economic reason to expect that the weights in the Z-score model—or, more generally, the weights in any credit-scoring model—will be constant over any but very short periods. The same concern also applies to the scoring model’s explanatory variables. Specifically, due to changing financial and market conditions, other firmspecific financial ratios may come to be increasingly relevant in explaining bankruptcy risk. The third problem is that these models ignore important, hard-to-quantify factors that may play a crucial role in the bankruptcy/no-bankruptcy decision. For example, the reputation of the firm and the managers’ backgrounds could be important firm-specific characteristics, as could macro factors such as the phase of the business cycle. Credit-scoring models often ignore these variables. Moreover, traditional credit-scoring models rarely use publicly available information, such as the prices of the outstanding public debt and equity of the borrower. A fourth problem relates to the availability of bankruptcy records. Currently, no centralized, publicly available database on defaulted loans or bankruptcies for proprietary or other reasons exists. Some task forces by consortiums of commercial banks and consulting firms are currently seeking to construct such databases, but it may well be many years before they are fully developed. This constrains the ability of many creditors to use credit-scoring models for larger business loans.
LG5
21. A linear probability model you have developed finds that a firm has a PD of 0.16. What does this mean? The firm’s expected probability of default, or bankruptcy, is estimated as 16 percent.
basic problems problems LG2 20-1 Calculation of Average Costs with Economies of Scope Peter’s TV Supplies is considering a merger with Jan’s Radio Supply Stores. Peter’s total operating costs of producing services are $250,000 for a sales volume (SP) of $4.5 million. Jan’s total operating costs of producing services are $50,000 for a sales volume (SJ) of $550,000. a. Calculate the average cost of production for the two firms. $250,000 ACPeter = ------------- = 0.0556 = 5.56%
$50,000 ACJan = ------------ = 0.0909 = 9.09%
Chapter 20 - Mergers and Acquisitions and Financial Distress
$4.5m.
$550,000
b. If the two firms merge, calculate the total average cost (TAC) for the merged firm assuming no synergies. $300,000 TACPeterJan =-------------- = 0.0594 = 5.94% $5.05m. c. Suppose, instead, that synergies in the production process result in a cost of production for the merged firms totaling $270,000 for a sales volume of $5,050,000. Calculate the total average cost (ACPeterJan) for the merged firm. $270,000 ACPeterJan =---------------- = 0.0535 = 5.35% $5.05m. LG2
20-2 Calculation of Average Costs with Economies of Scope Cindy’s Computer Corp. is considering a merger with Bobby’s Hard Drive, Inc. Cindy’s total operating costs of producing services are $3.4 million for a sales volume (SC) of $16 million. Bobby’s total operating costs of producing services are $2.5 million for a sales volume (SB) of $8 million. a. Calculate the average cost of production for the two firms. $3.4m. ACCindy = ---------- = 0.2125 = 21.25% $16m.
$2.5m. ACBobby = ----------- = 0.3125 = 31.25% $8m.
b. If the two firms merge, calculate the total average cost (TAC) for the merged firm assuming no synergies. $5.9m. TACCindyBobby = ---------- = 0.2458 = 24.58% $24m. c. Suppose, instead, that synergies in the production process result in a cost of production for the merged firms totaling $5.3 million for a sales volume of $24 million. Calculate the total average cost (ACCindyBobby) for the merged firm $5.3m. ACCindyBobby = ----------- = 0.2208 = 22.08% $24m. LG2
20-3 Calculation of Change in the HHI Associated with a Merger Consider a market that has three firms with the following market shares:
Chapter 20 - Mergers and Acquisitions and Financial Distress
Firm A = 35% Firm B = 41% Firm C = 24% Suppose firm B wants to acquire firm C so that the post-acquisition market would exhibit the following shares: B + C = 65% A = 35% Calculate the pre- and postmerger HHI and the change in the HHI resulting from the merger. According to Department of Justice guidelines, is this merger likely to be challenged? The premerger HHI for the market is: HHI = (35)2 + (41)2 + (24)2 = 1,225 + 1,681 + 576 = 3,482 Thus, the market is highly concentrated according to the Department of Justice guidelines. The postmerger HHI would be: HHI = (65)2 + (35)2 = 4,225 + 1,225 = 5,450 Thus, the increase or change in the HHI (ΔHHI) postmerger is: ΔHHI = 5,450 – 3,482 = 1,968 Since the increase is 1,968 points, which is more than the 200-point benchmark defined in the Department of Justice guidelines, the market is heavily concentrated and the merger could be challenged. LG2
20-4 Calculation of Change in the HHI Associated with a Merger Consider a market that has three firms with the following market shares: Firm A = 35% Firm B = 41% Firm C = 24% Suppose firm A wants to acquire firm B so that the post-acquisition market would exhibit the following shares: A + B = 76% C = 24%
Chapter 20 - Mergers and Acquisitions and Financial Distress
Calculate the pre- and postmerger HHI, and the change in the HHI resulting from the merger. According to Department of Justice guidelines, is this merger likely to be challenged?
The premerger HHI for the market is: HHI = (35)2 + (41)2 + (24)2 = 1,225 + 1,681 + 576 = 3,482 Thus, the market is highly concentrated according to the Department of Justice guidelines. The postmerger HHI would be: HHI = (76)2 + (24)2 = 5,776 + 576 = 6,352 Thus, the increase or change in the HHI (ΔHHI) postmerger is: ΔHHI = 6,352 – 3,482 = 2,870 Since the increase is 2,870 points, which is more than the 200-point benchmark defined in the Department of Justice guidelines, the market is heavily concentrated and the merger could be challenged. LG5
20-5 Calculation of Altman’s Z-Score Suppose that the financial ratios of a potential borrowing firm take the following values: X1 = Net working capital/Total assets = 0.10, X2 = Retained earnings/Total assets = 0.20, X3 = Earnings before interest and taxes/Total assets = 0.22, X4 = Market value of equity/Book value of long-term debt = 0.60, X5 = Sales/Total assets ratio = 0.90. Calculate and interpret the Altman’s Z-score for this firm Z = 1.2(0.10) + 1.4(0.20) + 3.3(0.22) + 0.6(0.60) + 1.0(0.90) = 2.39 According to the Altman’s Z-score, this firm should be placed in the indeterminate bankruptcy risk class.
LG5
20-6 Calculation of Altman’s Z-Score Suppose that the financial ratios of a potential borrowing firm take the following values: X1 = Net working capital/Total assets = 0.27, X2 = Retained earnings/Total assets = 0.37, X3 = Earnings before interest and taxes/Total assets = 0.44, X4 = Market value of equity/Book value of long-term debt = 1.25, X5 = Sales/Total assets ratio = 2.75. Calculate and interpret the Altman’s Z-score for this firm Z = 1.2(0.27) + 1.4(0.37) + 3.3(0.44) + 0.6(1.25) + 1.0(2.75) = 5.79 According to the Altman’s Z-score, this firm should be placed in the low bankruptcy risk class.
LG5
20-7 Calculation of Bankruptcy Probability Suppose a linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the debt
Chapter 20 - Mergers and Acquisitions and Financial Distress
ratio and the profit margin. Based on past bankruptcy experience, the linear probability model is estimated as: PDi = 0.15 (Debt ratio) - 0.10 (Profit margin) A firm you are thinking of lending to has a debt ratio of 45 percent and a profit margin of 6 percent. Calculate the firm’s expected probability of default, or bankruptcy. PDi = 0.15 (0.45) - 0.10 (0.06) = 0.0615 or 6.15% LG5
20-8 Calculation of Bankruptcy Probability A linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the equity multiplier and the total asset turnover ratio. Based on past bankruptcy experience, the linear probability model is estimated as: PDi = 0.02 (Equity multiplier) - 0.01 (Total asset turnover) A firm you are thinking of lending to has an equity multiplier of 2.75 times and a total asset turnover ratio of 1.8. Calculate the firm’s expected probability of default, or bankruptcy.
intermediate PDi = 0.02 (2.75) - 0.01 (1.8) = 0.0370 or 3.70% problems LG2 20-9 Calculation of Average Costs with Economies of Scope George’s Dry Cleaning is considering a merger with Weezzie’s Laundry Supply Stores. George’s total operating costs of producing services are $550,000 for sales volume (SG) of $4.5 million. Weezzie’s total operating costs of producing services are $185,000 for a sales volume (SW) of $2 million. a. Calculate the average cost of production for the two firms. $550,000 ACGeorge = -------------- = 0.1222 = 12.22% $4.5m.
$185,000 ACWeezzie = --------------- = 0.0925 = 9.25% $2m.
b. For a sales volume of $6.5 million, calculate the reduction in production costs the merged firms need to experience such that the total average cost (ACGeorgeWeezie) for the merged firms is equal to 10 percent. TCI ACGeorgeWeezzie = --------- = 0.10 = 10% => TCI = 0.1 ($6.5m.) = $650,000 $6.5m. Thus, the reduction in production costs needs to be ($550,000 + $185,000) - $650,000 = $85,000 LG2
20-10 Calculation of Average Costs with Economies of Scope Jenny’s Day Care is considering a merger with Lionel’s Diaper Manufacturers. Jenny’s total operating costs of producing services are $595,000 for sales volume (SJ) of $2.4 million. Lionel’s total operating costs of producing services are $340,000 for a sales volume (SL) of $1,400,000.
Chapter 20 - Mergers and Acquisitions and Financial Distress
a. Calculate the average cost of production for the two firms. $595,000 ACJenny = -------------- = 0.2479 = 24.79% $2.4m.
$340,000 ACLionel = --------------- = 0.2429 = 24.29% $1.4m.
b. For a sales volume of $3.8 million, calculate the reduction in production costs the merged firms need to experience such that the total average cost (ACJennyLionel) for the merged firms is equal to 20 percent. TCI ACJennyLionel = ----------- = 0.20 = 20% => TCI = 0.2 ($3.8m.) = $760,000 $3.8m. Thus, the reduction in production costs needs to be ($595,000 + $340,000) - $760,000 = $175,000 LG2
20-11 Calculation of Change in the HHI Associated with a Merger The Justice Department has been asked to review a merger request for a market with the following four firms. Firm A B C D
Assets $12 million 25 million 102 million 3 million
a. What is the HHI for the existing market? Firm A B C D
Assets $12 m 25 m 102 m 3m
Market Share 8.45% 17.61 71.83 2.11 100.00%
The HHI = (8.45)2 + (17.61)2 + (71.83)2 + (2.11)2 = 5,546 b. If Firm A acquires Firm D, what will be the impact on the market's level of concentration? Firm A B C
Assets $15 m 25 m 102 m
Market Share 10.56% 17.61 71.83 100.00
Chapter 20 - Mergers and Acquisitions and Financial Distress
The HHI = (10.56)2 + (17.61)2 + (71.83)2 = 5,581 Thus, the increase or change in the HHI (ΔHHI) postmerger is: ΔHHI = 5,581 – 5,546 = 35 c. If Firm C acquires Firm D, what will be the impact on the market's level of concentration? Frim A B C
Assets $12 m 25 m 105 m
Market Share 8.45% 17.61 73.94 100.00
The HHI = (8.45)2 + (17.61)2 + (73.94)2 = 5,849 Thus, the increase or change in the HHI (ΔHHI) postmerger is: ΔHHI = 5,849 – 5,546 = 303 d. What is likely to be the Justice Department's response to the two merger applications? The Justice Department may challenge Firm C’s application to acquire Firm D since it significantly increases market concentration (∆HHI = 5,849 – 5,546 = 303). On the other hand, the Justice Department would most likely approve Firm A's application since the merger causes only a small increase in market concentration (∆HHI = 5,581 – 5,546 = 35). LG2
20-12 Calculation of Change in the HHI Associated with a Merger The Justice Department has been asked to review a merger request for a market with the following four firms. Firm A B C D
Assets $156 million 130 million 45 million 100 million
a. What is the HHI for the existing market? Firm A B C D
Assets $156 m 130 m 45 m 100 m
Market Share 36.19% 30.16 10.44 23.20 100.00%
Chapter 20 - Mergers and Acquisitions and Financial Distress
The HHI = (36.19)2 + (30.16)2 + (10.44)2 + (23.20)2 = 2,867 b. If Firm B acquires Firm D, what will be the impact on the market's level of concentration? Firm A B C
Assets $156 m 230 m 45 m
Market Share 36.19% 53.36 10.44 100.00
The HHI = (36.19)2 + (53.36)2 + (10.44)2 = 4,267 Thus, the increase or change in the HHI (ΔHHI) postmerger is: ΔHHI = 4,267 – 2,867 = 1,400 c. If Firm C acquires Firm D, what will be the impact on the market's level of concentration? Firm A B C
Assets $156 m 130 m 145 m
Market Share 36.19% 30.16 33.64 100.00
The HHI = (36.19)2 + (30.16)2 + (33.64)2 = 3,351 Thus, the increase or change in the HHI (ΔHHI) postmerger is: ΔHHI = 3,351 – 2,867 = 484 d. What is likely to be the Justice Department's response to the two merger applications? The Justice Department may challenge Firm B’s application to acquire Firm D since it significantly increases market concentration (∆HHI = 4,267 – 2,867 = 1,400). The Justice Department would also most likely challenge Firm C's application since the merger causes a significant increase in market concentration (∆HHI = 3,351 – 2,867 = 484). LG2
20-13 Valuation of a Merger Stubborn Motors, Inc., is asking a price of $75 million to be purchased by Rubber Tire Motor Corp. Stubborn Motors currently has total cash flows of $2 million that are expected to grow by 1 percent annually for the next 4 years. Managers estimate that because of synergies the merged firm’s cash flows will increase by $4 million the first year after the merger and these cash flows will grow by an additional 4 percent in years 2 through 4 following the merger. After the first four years, cash flows will grow at a rate of 1 percent annually indefinitely. The WACC for the merged firms is 10 percent. Calculate the NPV of the merger. Should Rubber Tire Motor Corporation agree to acquire Stubborn Motors for the asking price of $75 million?
Chapter 20 - Mergers and Acquisitions and Financial Distress
The incremental cash flows for the first four years after the merger are: Year after merger
1
2
3
4
Cash flow from Stubborn Motors
$2.0m.(1.01) = $2.02m.
$2.0m.(1.01)2 = $2.04m.
$2.0m.(1.01)3 = $2.06m.
$2.0m.(1.01)4 = $2.08m.
= $4.00m.
$4.0m.(1.04) = $4.16m.
$4.0m.(1.04)2 = $4.33m.
$4.0m.(1.04)3 = $4.50m.
$6.02m.
$6.20m.
$6.39m.
$6.58m.
Cash flow from synergies Incremental cash flow from merger
The value of incremental cash flows after year 4 is: Incremental cash flow in year 5 $6.58m.(1 + 0.01) Value of incremental cash flows received = ------------------------------ = ------------------------ = $73.85m. after year 4 at end of year 4 WACC – (Growth rate (0.10 - 0.01) in cash flows after year 4)
To find the present value of the total incremental cash flows, managers next discount the projected cash flows by the WACC as follows: $6.02m. $6.20m. $6.39m. $6.58m. $73.85m. Present value of cash flows = ----------- + ----------- + ----------- + ----------- + -------------- = $70.33m. from the merger (1.10)1 (1.10)2 (1.10)3 (1.10)4 (1.10)4
Finally, the NPV of the merger is calculated by subtracting the price of the target firm from the present value of the cash flows from the merger. NPV = $70.33m. - $75m. = -$4.67m.
This merger would not be beneficial for the stockholders of the bidder firm. Their wealth would decrease by $4.67 million as a result of the merger. LG2
20-14 Valuation of a Merger You own stock in Make-UP-Artists, Inc., which has just made a bid of $30 million to purchase MHM Corporation. MHM Corp. currently has total cash flows of $2.5 million that are expected to grow by 2 percent annually for the next 5 years. Managers estimate that because of synergies the merged firm’s cash flows will increase by $500,000 in the first year after the merger and these cash flows will grow by an additional 4 percent in years 2 through 5 following the merger. After the first five years, cash flows will grow at a rate of 2 percent annually indefinitely. The merged firms are expected to have a beta = 1.2, the risk-free rate is 4.5 percent, and the market risk premium is currently 5.5 percent. Calculate the NPV of the merger. Will you vote in favor of the merger? The incremental cash flows for the first five years after the merger are: Year after merger
1
2
3
4
5
Chapter 20 - Mergers and Acquisitions and Financial Distress
Cash flow from MHM Corp Cash flow from synergies
Incremental cash flow from merger
= $0.50m.
$2.5m.(1.02)2 = $2.60m. $0.50m.(1.04)1 = $0.52m.
$2.5m.(1.02)3 = $2.65m. $0.50m.(1.04)2 = $0.54m.
$2.5m.(1.02)4 = $2.71m. $0.50m.(1.04)3 = $0.56m.
$2.5m.(1.02)5 = $2.76m. $0.50m.(1.04)4 = $0.58m.
$3.05m.
$3.12m.
$3.19m.
$3.27m.
$3.35m.
$2.5m.(1.02) = $2.55m.
Required return = 4.5% + 1.2(5.5%) = 11.10% => the value of incremental cash flows after year 5 is: Incremental cash flow in year 6 $3.35m.(1 + 0.02) Value of incremental cash flows received = ------------------------------ = ------------------------ = $37.49m. after year 5 at end of year 5 Required – (Growth rate (0.1110 - 0.02) return in cash flows after year 5)
To find the present value of the total incremental cash flows, managers next discount the projected cash flows by the required return as follows: $3.05m. $3.12m. $3.19m. $3.27m. $3.35m. $37.49m. Present value of cash flows = + + + + + from the merger (1.1110)1 (1.1110)2 (1.1110)3 (1.1110)4 (1.1110)5 (1.1110)5 = $33.88m.
Finally, the NPV of the merger is calculated by subtracting the price of the target firm from the present value of the cash flows from the merger. NPV = $33.88m. - $30m. = $3.88m.
This merger would be beneficial for the stockholders of the bidder firm. The value of the firm would increase by $3.88 million as a result of the merger. LG4
20-15 Calculating Creditor and Stockholder Payoffs in a Chapter 7 Bankruptcy: You own $25,000 in subordinated debt of Local Crossings, Inc. which declared bankruptcy on May 15, 2020 through a Chapter 7 filing. Local Crossings’ balance sheet at the time of the bankruptcy filing is listed below. Local Crossings, Inc. Balance Sheet as of May 15, 2020 (in millions of dollars) Liabilities and Equity
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and
$ 406 978 1,038 $2,422
Current liabilities: Accrued wages (10,500 employees) Unpaid employee benefits Unsecured customer deposits Accrued taxes Accounts payable Notes payable to banks Total
$
20 15 50 375 841 1,518 $2,819
Chapter 20 - Mergers and Acquisitions and Financial Distress
equipment Less: Depreciation Net plant and equipment
Total assets
$7,253 1,050 $6,203
Long-term debt: First mortgage Subordinate debentures Total
$8,625
Stockholders’ equity: Preferred stock (100 million shares) Common stock and paid-in surplus (200 million shares) Retained earnings Total Total liabilities and equity
$1,200 2,018 $3,218
$ 100 1,500 988 $2,588 $8,625
The accrued wages were earned within the last 90 days prior to filing for bankruptcy. The unpaid employee benefits were due in the six months prior to the filing for bankruptcy. The unsecured customer deposits are for less than $900 each. Local Crossings, Inc., has no property taxes past due. The first mortgage is secured against the fixed assets of the firm. The debentures are subordinate to the notes payable to banks. The liquidation of the firm’s current assets produced $1,298 million and of the firm’s fixed assets produced $3,552 million for a total of only $4,850 million in funds to distribute to the creditors and stockholders of the firm. The administrative expenses associated with the bankruptcy totaled $15 million and unpaid expenses incurred after the filing of the bankruptcy petition but before the trustee was appointed totaled $10 million. Show how the trustee will distribute the $4,850 million of funds among the Local Crossings’ creditors and stockholders. How much of the $25,000 debt you own will you recover? The distribution of the $4,850 million of funds is as follows: Proceeds from liquidation of assets: Administrative expenses associated with the bankruptcy proceedings Unpaid expenses incurred after the filing of the bankruptcy petition but before the trustee is appointed Wages due to employees Unpaid employee benefit plan contributions Unsecured customer claims Taxes due to federal, state, and other governmental agencies Funds available for secured creditors: First mortgage Funds available for unsecured creditors:
$4,850m. 15m. 10m. 20m. 15m. 50m. 375m. $4,365m. 1,200m. $3,165m.
The remaining $3,165 million is distributed to the unsecured creditors on a pro rata basis, with senior creditors paid in full before subordinate creditors. Thus, Unsecured Creditors
Amount
Settlement at 72.31%a
Distribution after subordinate adjustment
Percent of claim received
Accounts payable Notes payable to banks
$ 841m. 1,518m.
$608.13m. 1,097.66m.
$608.13m 1,518.00m.b
72.31% 100.00
Chapter 20 - Mergers and Acquisitions and Financial Distress
Subordinate debentures Total
2,018m. $4,377m.
1,459.21m. $3,165.00m.
1,038.87m.b $3,165.00m.
51.48
a
$3,165 million is available to pay $4,377 million in unsecured creditors. Thus, the pro rata settlement rate is $3,165m. / $4,377m. = 72.31%. b Notes payable to banks must be paid in full before subordinate debenture holders can be paid anything. Thus, $420.34 million ($1,518m. - $1,097.66m.) of the original settlement amount is moved from subordinate debentures to notes payable to banks; subordinate debenture holders receive only $1,038.87 million ($1,459.21m. – $420.34m.) or 51.48 percent of the amount owed to them.
LG4
Thus, you will recover $25,000 x 0.5148 = $12,870 of your $25,000 investment in Local Crossings, Inc. 20-16 Calculating Creditor and Stockholder Payoffs in a Chapter 7 Bankruptcy: WorldGone, Inc., declared bankruptcy on September 25, 2020 through a Chapter 7 filing. WorldGone’s balance sheet at the time of the bankruptcy filing is listed below. WorldGone, Inc. Balance Sheet as of September 25, 2020 (in millions of dollars) Liabilities and Equity
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment
Total assets
$ 263 1,428 2,100 $3,791
$7,752 1,248
Current liabilities: Accrued wages (10,000 employees) Unpaid employee benefits Unsecured customer deposits Accrued taxes Accounts payable Notes payable to banks Total
$6,504
Long-term debt: First mortgage Subordinate debentures Total
$10,295
Stockholders’ equity: Preferred stock (100 million shares) Common stock and paid-in surplus (200 million shares) Retained earnings Total Total liabilities and equity
$
18 15 69 252 711 1,975 $3,040
$1,232 2,214 $3,446
$
100 2,500
1,209 $ 3,809 $10,295
The accrued wages were earned within the last 90 days prior to filing for bankruptcy. The unpaid employee benefits were due in the six months prior to the filing for bankruptcy. The unsecured customer deposits are for less than $900 each. WorldGone, Inc. has no property taxes past due. The first mortgage is secured against the fixed assets of the firm. The debentures are subordinate to the notes payable to banks. The liquidation of the firm’s current assets produced $2,263
Chapter 20 - Mergers and Acquisitions and Financial Distress
million and of the firm’s fixed assets produced $3,722 million for a total of only $5,985 million in funds to distribute to the creditors and stockholders of the firm. The administrative expenses associated with the bankruptcy totaled $25 million and unpaid expenses incurred after the filing of the bankruptcy petition but before the trustee was appointed totaled $10 million. Show how the trustee will distribute the $5,985 million of funds among the WorldGone’s creditors and stockholders. The distribution of the $5,985 million of funds is as follows: Proceeds from liquidation of assets: Administrative expenses associated with the bankruptcy proceedings Unpaid expenses incurred after the filing of the bankruptcy petition but before the trustee is appointed Wages due to employees Unpaid employee benefit plan contributions Unsecured customer claims Taxes due to federal, state, and other governmental agencies Funds available for secured creditors: First mortgage Funds available for unsecured creditors:
$5,985m. 25m. 10m. 18m. 15m. 69m. 252m. $5,596m. 1,232m. $4,364m.
The remaining $4,364 million is distributed to the unsecured creditors on a pro rata basis, with senior creditors paid in full before subordinate creditors. Thus, Unsecured Creditors
Amount
Settlement at 89.06%a
Distribution after subordinate adjustment
Percent of claim received
Accounts payable Notes payable to banks Subordinate debentures Total
$ 711m. 1,975m. 2,214m. $4,900m.
$633.22m. 1,758.96m. 1,971.82m. $4,364.00m.
$633.220m 1,975.00m.b 1,755.78m.b $4,364.00m.
89.06% 100.00 79.30
a
$4,364 million is available to pay $4,900 million in unsecured creditors. Thus, the pro rata settlement rate is $4,364m. / $4,900m. = 89.06%. b Notes payable to banks must be paid in full before subordinate debenture holders can be paid anything. Thus, $216.04 million ($1,975m. - $1,758.96m.) of the original settlement amount is moved from subordinate debentures to notes payable to banks; subordinate debenture holders receive only $1,755.78 million ($1,971.82m. – $216.04m.) or 79.30 percent of the amount owed to them. LG5
20-17 Calculation of Altman’s Z-Score: Use the following financial statements for Lake of Egypt Marina to calculate and interpret the Altman’s Z-score for this firm as of 2020.
Assets Current assets: Cash and marketable
Lake of Egypt Marina, Inc. Balance Sheet as of December 31, 2020 and 2019 (in millions of dollars) 2020 2019 Liabilities and Equity 2020 Current liabilities Accrued wages and
:
2019
Chapter 20 - Mergers and Acquisitions and Financial Distress
securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment Other long-term assets Total
$
75 115 200 $ 390
$
65 110 190 $ 365
$ 470 $ 371 50 49 $ 520 $ 420
Total assets
$ 910 $ 785
$ 580 $ 471 100 110
taxes Accounts payable Notes payable Total Long-term debt:
$
Stockholders’ equity: Preferred stock (5 million shares) Common stock and paid-in surplus (65 million shares) Retained earnings Total Total liabilities and equity
40 90 80 $ 210 $ 300
$
43 80 70 $ 193 $ 280
$
$
5
5
65
65
330 $ 400 $ 910
242 $ 312 $ 785
Lake of Egypt Marina, Inc. Income Statement for Years Ending December 31, 2020 and 2019 (in millions of dollars) 2020 2019 Net sales (all credit) $ 515 $ 432 Less: Cost of goods sold 292 233 Gross profits $ 223 $ 199 Less: Depreciation and other operating expenses 22 20 Earnings before interest and taxes (EBIT) $ 201 $ 179 Less: Interest 33 30 Earnings before taxes (EBT) $ 168 $ 149 Less: Taxes 25 22 Net income $ 143 $ 127 Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
$ 5 $ 138 50 $ 88
$ 5 $ 122 50 $ 72
Per (common) share data: Earnings per share (EPS) Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
$2.123 $0.769 $6.077 $14.750
$1.877 $0.769 $4.723 $12.550
X1 = Net working capital/Total assets = ($390m. – $210m.) / $910m. = 0.1978 X2 = Retained earnings/Total assets = $330m. / $910m. = 0.3626 X3 = Earnings before interest and taxes/Total assets = $201m. / $910m. = 0.2209 X4 = Market value of equity/Book value of long-term debt = ($14.75 × 65m.) / $300m. = 3.1958 X5 = Sales/Total assets ratio = $515m. / $910m. = 0.5659
Chapter 20 - Mergers and Acquisitions and Financial Distress
=> Z = 1.2(0.1978) + 1.4(0.3626) + 3.3(0.2209) + 0.6(3.1958) + 1.0(0.5659) = 3.96 According to the Altman’s Z-score, this firm should be placed in the low bankruptcy risk class. LG5
20-18 Calculation of Altman’s Z-Score: Use the following financial statements for Garners’ Platoon Mental Health Care, Inc., to calculate and interpret the Altman’s Z-score for this firm.
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total
Garners’ Platoon Mental Health Care, Inc. Balance Sheet as of December 31, 2020 (in millions of dollars) Liabilities and Equity
$ 247 652 1,035 $1,934
Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment Other long-term assets Total
$2,925 525 $3,450
Total assets
$5,384
$3,419 494
Current liabilities : Accrued wages and taxes Accounts payable Notes payable Total
$ 186 510 513 $1,209
Long-term debt:
$1,818
Stockholders’ equity: Preferred stock (35 million shares) $ 35 Common stock and paid-in surplus 375 (375 million shares) Retained earnings 1,947 Total $2,357 Total liabilities and equity
Garners’ Platoon Mental Health Care, Inc. Income Statement for Year Ending December 31, 2020 (in millions of dollars) Net sales (all credit) Less: Cost of goods sold Gross profits Less: Depreciation and other operating expenses Earnings before interest and taxes (EBIT) Less: Interest Earnings before taxes (EBT) Less: Taxes Net income
$2,964 1,738 $1,226 120 $1,106 187 $ 919 138 $ 781
Less: Preferred stock dividends Net income available to common stockholders Less: Common stock dividends Addition to retained earnings
$ 35 $ 746 $ 375 $ 371
Per (common) share data: Earnings per share (EPS)
$1.989
$5,384
Chapter 20 - Mergers and Acquisitions and Financial Distress
Dividends per share (DPS) Book value per share (BVPS) Market value (price) per share (MVPS)
$1.000 $6.192 $8.420
X1 = Net working capital/Total assets = ($1,934m. – $1,209m.) / $5,384m. = 0.1347 X2 = Retained earnings/Total assets = $1,947m. / $5,384m. = 0.3616 X3 = Earnings before interest and taxes/Total assets = $1,106m. / $5,384m. = 0.2054 X4 = Market value of equity/Book value of long-term debt = ($8.42 x 375m.) / $1,818m. = 1.7368 X5 = Sales/Total assets ratio = $2,964m. / $5,384m. = 0.5505 => Z = 1.2(0.1347) + 1.4(0.3616) + 3.3(0.2054) + 0.6(1.7368) + 1.0(0.5505) = 2.94 According to the Altman’s Z-score, this firm should be placed in the low bankruptcy risk class. LG5
20-19 Calculation of Bankruptcy Probability Suppose a linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the debt ratio and the profit margin. Based on past bankruptcy experience, the linear probability model is estimated as: PDi = 0.15 (Debt ratio) - 0.5 (Profit margin) You know a particular firm has a debt ratio of 55 percent and a probability of default of 5 percent. Calculate the firm’s profit margin. 0.05 = 0.15 (0.55) - 0.5 (Profit margin) => Profit margin = (0.05 - 0.15(0.55)) / (-0.5) = 0.065 = 6.5%
LG5
20-20 Calculation of Bankruptcy Probability A linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the equity multiplier and the total asset turnover ratio. Based on past bankruptcy experience, the linear probability model is estimated as: PDi = 0.02 (Equity multiplier) - 0.01 (Total asset turnover) A firm has an equity multiplier of 1.8 times and a probability of default of 2.2 percent. Calculate the firm’s total asset turnover ratio. 0.022 = 0.02 (1.8) - 0.01 (Total asset turnover) => Total asset turnover = (0.022 - 0.02(1.8)) / (-0.01) = 1.4 times
advanced problems LG1 20-21 Economies of Scope A survey of a local market has provided the following average cost data:
Chapter 20 - Mergers and Acquisitions and Financial Distress
Johnson Construction Corp. (JCC) has assets of $3 million and an average cost of 20 percent, Anderson Architects (AA) has assets of $4 million and an average cost of 30 percent, and Cole Home Builders (CHB) has assets of $4 million and an average cost of 25 percent. For each firm, average costs are measured as a proportion of assets. JCC is planning to acquire AA and CHB with the expectation of reducing overall average costs by eliminating the duplication of services. a. What should the average cost after the acquisition be for JCC to justify this merger? Average cost: Johnson Construction Anderson Architects Cole Home Builders Total costs
= 0.20 x $3m. = 0.30 x $4m. = 0.25 x $4m.
= $0.6m. = 1.2m. = 1.0m. $2.8m.
The average cost after merger = $2.8m. / $11m. = 25.45%. If Johnson Construction can lower its average costs to less than 25.45 percent, it should go ahead with the merger. b. If JCC plans to reduce operating costs by $500,000 after the merger, what will the average cost be for the new firm? Average cost: Johnson Construction Anderson Architects Cole Home Builders Total costs
$0.6m. - $0.5m. = 0.30 x $4m. = 0.25 x $4m.
= $0.1m. = 1.2m. = 1.0m. $2.3m.
The average cost after merger = $2.3m. / $11m. = 20.91% LG1
20-22 Economies of Scope A survey of a national market has provided the following average cost data: Jackson County Construction (JCC) has assets of $2.55 million and an average cost of 30 percent, Arkansas Architects (AA) has assets of $1.7 million and an average cost of 25 percent, and Colorado Home Builders (CHB) has assets of $1 million and an average cost of 15 percent. For each firm, average costs are measured as a proportion of assets. JCC is planning to acquire AA and CHB with the expectation of reducing overall average costs by eliminating the duplication of services. a. What should the average cost after the acquisition be for JCC to justify this merger? Average cost: Jackson County Construction Arkansas Architects Colorado Home Builders Total costs
= 0.30 x $2.55m. = 0.25 x $1.7m. = 0.15 x $1m.
= $ 0.765m. = 0.425m. = 0.150m. $1.340m.
The average cost after merger = $1.340m. / $5.250m. = 25.52%. If Johnson Construction can lower its average costs to less than 25.52 percent, it should go ahead with the merger.
Chapter 20 - Mergers and Acquisitions and Financial Distress
b. If JCC plans to reduce operating costs by $425,000 after the merger, what will the average cost be for the new firm? Average cost: Jackson County Construction Arkansas Architects Colorado Home Builders Total costs
$0.765m. - $0.425m. = $0.340m. = 0.25 x $1.7m. = 0.425m. = 0.15 x $1m. = 0.150m. $0.915m.
The average cost after merger = $0.915m. / $5.250m. = 17.43% LG2
20-23 Calculation of Change in the HHI Associated with a Merger Cakes Corp. currently has a 60 percent market share in baking services, followed by Cookies, Inc., with 20 percent and Dippen Dough with 20 percent. a. What is the concentration ratio as measured by the Herfindahl-Hirschman Index (HHI)? HHI = (60)2 + (20)2 + (20)2 = 4,400 b. If Cakes, Corp. acquires Cookies, Inc., what will be the new HHI? HHI = (80)2 + (20)2 = 6,800 c. Assume the Justice department will allow mergers as long as the changes in HHI do not exceed 1,400. What is the minimum amount of assets that Cakes, Corp will have to divest after it merges with Cookies, Inc.? For Cakes, Corp. to complete the merger, its maximum HHI should be such that when it disposes of part of its assets, the HHI will be (X + Y)2 + Z2 = 5,800. Since Z = 20 percent and Z2 = 400, we need to solve the following: (X + Y)2 = 5,400; that is, 5,800 less the share of Z2 which is 202 or 400. If the merger stands with no adjustment, then X = 80 and Y = 0. But some portion of X must be liquidated. Therefore, we need to solve the equation (80 – Q)2 = 5,400 where Q is the amount of disinvestment. Solving for Q, we get Q = 80 - (5,400)1/2 = 6.5153, which means Cakes, Corp. has to dispose of 6.5153 percent of total industry assets. To verify, we can check the total relationship: (80 - 6.5153)2 + (20)2 = 5,800.
LG2
20-24 Calculation of Change in the HHI Associated with a Merger Tractor Supply Corp. currently has a 50 percent market share in farming services, followed by Farm Equipment, Inc., with 30 percent and Plow Mart, Inc., with 20 percent. a. What is the concentration ratio as measured by the Herfindahl-Hirschman Index (HHI)?
Chapter 20 - Mergers and Acquisitions and Financial Distress
HHI = (50)2 + (30)2 + (20)2 = 3,800 b. If Tractor Supply Corp. acquires Plow Mart, Inc., what will be the new HHI? HHI = (70)2 + (30)2 = 5,800 c. Assume the Justice department will allow mergers as long as the changes in HHI do not exceed 1,500. What is the minimum amount of assets that Tractor Supply Corp. will have to divest after it merges with Plow Mart, Inc.? For Tractor Supply Corp. to complete the merger, its maximum HHI should be such that when it disposes of part of its assets, the HHI will be (X + Z)2 + Y2 = 5,300. Since Y = 30 percent and Y2 = 900, we need to solve the following: (X + Z)2 = 4,400; that is, 5,300 less the share of Y2 which is 302 or 900. If the merger stands with no adjustment, then X = 70 and Z = 0. But some portion of X must be liquidated. Therefore, we need to solve the equation Q = 70 - (4,400)1/2 = 3.6675; that is, 4,400 less the share of Y2 which is 302 or 900, which means Tractor Supply Corp. has to dispose of 3.6675 percent of total industry assets. To verify, we can check the total relationship: (70 3.6675)2 + (30)2 = 5,300. LG3
20-25 Valuation of a Merger The managers of BSW, Inc., have approached KCMP Corp. about a possible merger. KCMP Corp. is asking a price of $72 million to be purchased by BSW, Inc. KCMP Corp. currently has total cash flows of $6 million that are expected to grow at 2 percent annually for the next two years. Managers are uncertain of the growth in KCMP Corp.’s cash flows in year 3. Managers estimate that, because of synergies, the merged firm’s cash flows will increase by an additional $1 million in the first year after the merger and these cash flows will grow by 3 percent in years 2 and 3 following the merger. Managers have estimated that the present value of any incremental cash flows received after year three is $54.09 million. The WACC for the merged firms is ten percent. Calculate KCMP Corp.’s minimum incremental cash flow needed in year three after the merger such that BSW, Inc. would see this merger as a positive NPV project. The incremental cash flows for the first three years after the merger are: Year after merger Cash flow KCMP Corp.
1
2
$6m.(1.02) = $6.12m.
$6m.(1.02)2 = $6.24m.
?
= $1.00m.
$1m.(1.03) = $1.03m.
$1m.(1.03)2 = $1.06m.
$7.12m.
$7.27m.
?
Cash flow from synergies Incremental cash flow from merger
3
The present value of incremental cash flows after year 3 is $54.09 million.
To find the present value of the total incremental cash flows, managers next discount the projected cash flows by the WACC as follows:
Chapter 20 - Mergers and Acquisitions and Financial Distress
$7.12m. $7.27m. ? Present value of cash flows = ---------- + ------------ + -------------- + $54.09m. = $72m. from the merger (1.10)1 (1.10)2 (1.10)3 = $6.4727m. + $6.0102m. + (?/(1.10)3) + $54.09m = $72m. => ? = ($72m. - $6.4727m. - $6.0102m. - $54.09m) x (1.10)3 = $7.22m. = Incremental cash flows in year 3 => Cash flows from KCMP Corp. = $7.22m - $1.06m. = $6.16m.
This merger would be beneficial for the stockholders of BSW, Inc., if, in year three after the merger, KCMP Corp.’s incremental cash flows were $6.16 million. LG3
20-26 Valuation of a Merger The managers of State Bank have been approached by City Bank about a possible merger. State Bank is asking a price of $205 million to be purchased by City Bank. State Bank currently has total cash flows of $15 million that are expected to grow at 1 percent annually for the next two years. Managers are uncertain of the growth in State Bank’s cash flows in year three. Managers estimate that because of synergies the merged firm’s cash flows will increase by an additional $1.5 million in the first year after the merger and these cash flows will grow by 5 percent in years 2 and 3 following the merger. Managers have estimated that the present value of any incremental cash flows received after year 3 is $158.75 million. The WACC for the merged firms is 8 percent. Calculate State Bank’s minimum incremental cash flow needed in year 3 after the merger such that City Bank would see this merger as a positive NPV project. The incremental cash flows for the first 3 years after the merger are: Year after merger Cash flow from State Bank
1
2
3
$15m.(1.01) = $15.15m.
$15m.(1.01)2 = $15.30m.
?
= $1.5m.
$1.5m.(1.05)1 = $1.58m.
$1.5m.(1.05)2 = $1.65m.
$16.65m.
$16.88m.
?
Cash flow from synergies Incremental cash flow from merger
The present value of incremental cash flows after year 3 is $158.75 million: To find the present value of the total incremental cash flows, managers next discount the projected cash flows by the WACC as follows: $16.65m. $16.88m. ? Present value of cash flows = ---------- + ------------ + -------------- + $158.75m. = $205m. from the merger (1.08)1 (1.08)2 (1.08)3 = $15.42m. + $14.47m. + (?/(1.08)3) + $158.75m. = $205m. => ? = ($205m. - $15.42m. - $14.47m. - $158.75m.) x (1.08)3 = $20.61m. = Incremental cash flows in year 3
Chapter 20 - Mergers and Acquisitions and Financial Distress
=> Cash flows from State Bank = $20.61m - $1.65m. = $18.96m.
This merger would be beneficial for the stockholders of the bidder firm if, in year three after the merger, State Bank’s incremental cash flows in year 3 were $18.96 million. LG5
20-27 Calculating the Probability of Bankruptcy A linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the debtto-equity ratio and the sales-to-total assets ratio. Based on past bankruptcy experience, the linear probability model is estimated as PDi = 0.5 (Debt/Equity) - 0.01 (Sales/Total assets) A firm you are thinking of lending to has a sales-to-asset ratio of 2.0 and its expected probability of default, or bankruptcy, is estimated to be 8 percent. Calculate the firm’s debt ratio. 0.08 = 0.5 (Debt/Equity) - 0.01 (2.0) => Debt/Equity = (0.08 + 0.01(2.0))/0.5 = 0.20 times => Debt/Equity = (Total assets – Equity)/Equity = (Total assets/Equity) – 1 = 0.20 =>Total assets/Equity = 1.20 => Equity/Total assets = 1 / 1.20 = 0.8333 => Debt/Total assets = 1 - 0.8333 = 0.1667 = 16.67%
LG5
20-28 Calculating the Probability of Bankruptcy A linear probability model you have developed finds there are two factors influencing the past bankruptcy behavior of firms: the debtto-equity ratio and the profit margin. Based on past bankruptcy experience, the linear probability model is estimated as PDi = 0.1 (Debt/Equity) - 1.5 (Profit margin) A firm you are thinking of lending to has a debt-to-equity ratio of 110 percent and its expected probability of default, or bankruptcy, is estimated to be 5 percent. If sales are $1.5 million, calculate the firm’s net income. 0.05 = 0.1 (1.10) - 1.5 (Profit margin) => Profit margin = (0.05 - 0.1(1.10))/(-1.5) = 0.04 => Profit margin = 0.04 = Net income/Sales = Net income/ $1.5m. => Net income = 0.04 x $1.5m. = $60,000
research it! Mergers and Acquisitions Go to the Thomson Financial—Investment Banking and Capital Markets Group Web site at http://dmi.thomsonreuters.com/DealsIntelligence and find the latest information available for the dollar value of mergers and acquisition activity using the following steps. Click on “QUARTERLY REVIEWS.” Under “MERGERS & ACQUISITIONS,” click on “Global M&A Financial Advisory,” the most recent quarter. This will download a file on to your computer that will contain the most recent information on merger and acquisition activity. What is the most recent dollar value of global merger and acquisition activity undertaken? Who are the top
Chapter 20 - Mergers and Acquisitions and Financial Distress
advisors on these merger and acquisition deals? How has the top advisor market share changed in the last year? SOLUTION: The solution will vary with the date the Web site is accessed.
integrated minicase: Financial Distress Disaster Airlines is a firm in severe financial distress. The firm can no longer pay its bills on time and it is far behind on payments to its banks and long-term debt holders. The firm has decided to either be purchased by another air carrier or liquidate its assets and close. The managers have approached Altruistic Airlines about being acquired. After examining Disaster’s financial statements, looking at the routes owned by Disaster, and looking at the condition of the fixed assets, Altruistic Airlines has offered to pay the stockholders of Disaster Airlines $8 million to be acquired. Disaster Airlines covers flights to both areas in which Altruistic already flies, but also has routes in areas into which Altruistic is interested in expanding. As part of the analysis, Altruistic determined that the additional cash flows resulting from the acquisition would total $500,000 this year and would grow at a rate of 4 percent for the next three years. After this time the cash flows would grow at a rate of 2 percent annually. The WACC of Altruistic Airlines would be 8 percent after the merger. If, instead, Disaster Airlines decides to liquidate its assets, it will pay off its debt and give any remaining funds to the firm’s stockholders. Disaster Airlines’ balance sheet is listed below. Disaster Airlines, Inc. Balance Sheet as of June 25, 2020 (in millions of dollars) Liabilities and Equity
Assets Current assets: Cash and marketable securities Accounts receivable Inventory Total Fixed assets: Gross plant and equipment Less: Depreciation Net plant and equipment
$ 63 28 100 $ 191
$1,152 248 $ 904
Current liabilities: Accrued wages (2,500 employees) Unpaid employee benefits Unsecured customer deposits Accrued taxes Accounts payable Notes payable to banks Total Long-term Debt: First mortgage Subordinate debentures Total Stockholders’ equity: Common stock and paid-in surplus (100 million shares) Retained earnings Total
$
4 3 6 22 157 211 $ 403
$ 160 412 $ 572
$ 100 20 $ 120
Chapter 20 - Mergers and Acquisitions and Financial Distress
Total assets
$1,095
Total liabilities and equity
$1,095
The accrued wages were earned within the last 90 days prior to filing for bankruptcy. The unpaid employee benefits were due in the six months prior to the filing for bankruptcy. The unsecured customer deposits are for less than $900 each. Disaster Airlines has no property taxes past due. The first mortgage is secured against the fixed assets of the firm. The debentures are subordinate to the notes payable to banks. The liquidation of the firm’s current assets would produce $186 million and of the firm’s fixed assets would produce $800 million for a total of only $986 million in funds to distribute to the creditors and stockholders of the firm. The administrative expenses associated with the bankruptcy would be $1 million and unpaid expenses incurred after the filing of the bankruptcy petition but before the trustee was appointed are estimated to be $5 million. Show which method of dissolution, an acquisition by Altruistic Airlines or a liquidation of assets, is more beneficial for the creditors and stockholders of Disaster Airlines and the stockholders of Altruistic Airlines. SOLUTION: The distribution of the $986 million of funds is as follows: Proceeds from liquidation of assets: $986m. Administrative expenses associated with the bankruptcy proceedings 1m. Unpaid expenses incurred after the filing of the bankruptcy petition but before the trustee is appointed 5m. Wages due to employees (2,500 employees) 4m. Unpaid employee benefit plan contributions 3m. Unsecured customer claims 6m. Taxes due to federal, state, and other governmental agencies 22m. Funds available for secured creditors: $945m. First mortgage 160m. Funds available for unsecured creditors: $785m. The remaining $785 million is distributed to the unsecured creditors on a pro rata basis, with senior creditors paid in full before subordinate creditors. Thus, Unsecured Creditors
Amount
Settlement at 100%a
Percent of claim received
Accounts payable $157m. $157m. 100% Notes payable to banks 211m. 211m. 100 Subordinate debentures 412m. 412m. 100 Total $780m. $780m. a $785 million is available to pay $780 million in unsecured creditors. Thus, the pro rata settlement rate is $780m./$780m. = 100%.
The remaining $5 million ($785m. - $780m.) goes to the firm’s common stockholders.
Chapter 20 - Mergers and Acquisitions and Financial Distress
Altruistic Airlines has offered the shareholders of Disaster Airlines $8 million to be acquired. Thus, the shareholders of Disaster Airlines would be better to take this offer to be acquired rather than liquidate the firm’s assets. The shareholders of Disaster would receive an additional $3 million ($8m. - $5m.) with the acquisition compared to the liquidation of assets. The incremental cash flows for the first three years after the merger are: Year after merger Cash flows acquisition
1
2
3
= $0.50m.
$0.50m.(1.04)1 = $0.52m.
$0.50m.(1.04)2 = $0.541m.
The value of incremental cash flows after year three is: Incremental cash flow in year 4 $0.541m.(1 + 0.02) Value of incremental cash flows received = ------------------------------ = ------------------------ = $9.194m. after year 4 at end of year 4 WACC – (Growth rate (0.08 - 0.02) in cash flows after year 3)
To find the present value of the total incremental cash flows, managers next discount the projected cash flows by the WACC as follows: $0.50m. $0.52m. $0.541m. $9.194m. Present value of cash flows = ----------- + ----------- + ------------- + ------------ = $8.64m. from the merger (1.08)1 (1.08)2 (1.08)3 (1.08)3
Finally, the NPV of the acquisition is calculated by subtracting the price paid for Disaster Airlines from the present value of the cash flows from the acquisition. NPV = $8.64m. - $8m. = $0.64m.
This merger would be beneficial for the stockholders of Altruistic Airlines. Their wealth would increase by $0.63 million as a result of the merger. However, Disaster Airlines’ stockholders would receive $5 million through the liquidation of assets. Thus, stockholders would choose to liquidate the firm rather than sell it to Altruistic Airlines