R1.6. Current liabilities are obligations that are due within the following year of the balance sheet date. Therefore, the portion of long-term liabilities that is due with twelve months of the balance sheet date must be listed as a current liability. The following accounts must be reported on a balance sheet aa current liabilities: •
Accounts Payable. These are the amounts that are due to vendors who have supplied goods or services, but they have not yet been paid.
R1.6. (continued) •
Unearned Revenues. This account reflects the amounts that customers have prepaid in advance for the goods or services to receive in near future.
•
Accrued Compensation (or Wages Payable). Includes payroll related items such as the amounts due to employees and the payroll taxes and health insurance.
•
Accrued Expenses. These include the amounts that the company owes for items not recorded in accounts payable or accrued compensation. Examples are the interests on loans that a firm has incurred (but has not yet paid), the utility and phone bills for the reporting year that firm has received in the following fiscal period, and repair services that took place but the firm had not paid the invoices in the reporting period.
•
Short-Term Notes Payable. These include the loans from banks that will be due within one year of the balance sheet date.
•
Current Portion of Long-Term Debt. The portion of principals of long-term loans that are due within one year of the balance sheet date. Note that the incurred interests on the long-term loans are included in Accrued Expenses account.
•
Taxes Payable. These include the accrued income taxes and deferred income taxes.
R1.7. The formula for calculating COGS is: Beginning Inventory + Net Purchases - Ending Inventory = Cost of Goods Sold. R1.8. For a merchandising firm, the COGS represents what the firm had paid for the inventory it has sold during a given fiscal period. It includes the purchasing costs, freight-in and storing costs of the goods that the firm sold during the period. For a manufacturing firm, the COGS is the manufacturing cost of products sold (the cost includes raw materials, including the purchasing cost, freight-in and storing cost the items, direct labor costs for workers who produce the products and factory overhead costs). R1.9. It includes things of value that a firm buys from another entities, or it has produced, and stored. Inventory includes materials and goods that a firm has stored to sell to its customers for some profit.
Chapter 1: Accounting and Cost Information Systems Problem Solutions P1.1 Solution a) John Smith Advertising Company General Journal Page 1 Date 20XX 2/01 02 02
03 03 04 05 06
12 13
14
Description Cash
Ref.
Dr.
Cr.
25,000
John Smith, Capital Prepaid Rent Cash Art Equipment Accounts Payable Purchase of art equipment from Zoran Art Supplies on credit Office Supplies Cash Prepaid Insurance Cash Accounts Payable Cash Accounts Receivable Fees Revenue Cash Unearned Fees Advance receipt from the car dealer John Smith, Withdrawals Cash Unearned Fees Accounts Receivable Fees Revenue Completion of service for the car dealer Salary Expense Cash TOTALS
P1.1: Part (b) Solution
25,000 2,000 2,000 6,000 6,000
300 300 650 650 1,000 1,000 900 900 500 500 300 300 500 700 1,200 500 500 38,350
38,350
Cash Dr. (1) (9)
John Smith, Capital Cr.
25,000 500
25,500 20,750
2,000 300 650 1,000 300 500 4,750
Dr. 25,000
Prepaid Rent Dr. (2)
Dr. (3)
2,000
1,000
6,000
1,000
6,000 5,000
(3)
Dr. (5)
Cr.
Cr. 300
Dr.
Cr.
650
900 1,200 2,100
500
500
500
500 0
(9)
Dr. (10)
Cr. 300
Salary Expense Cr.
900 700 1,600
(8) (11)
John Smith, Withdrawals Cr.
Accounts Receivable Dr. (8) (11)
6,000
Fees Revenue
Unearned Fees Dr. (11)
Cr.
Office Supplies Cr.
Prepaid Insurance Dr. (6)
(1)
Art Equipment Cr.
Accounts Payable Dr. (7)
Cr.
(2) (5) (6) (7) (10) (12)
Dr. (12)
Cr. 500
P1.2: Solution a) Bunyon Consulting Company Trial Balance As of June 30, 20XX Account Accounts Receivable Accounts Payable -Asset Accumulated Depreciation, Building -Asset Accumulated Depreciation, Equipment Asset Building Asset Cash Exp. Depreciation Expense, Building Exp. Depreciation Expense, Equipment Asset Equipment Asset Land Asset Marketable Secureties Liab Mortgage Payable Rev. Revenues Exp. Salary Expense Asset Supplies Exp. Supplies Expense Exp. Utilities Expense O.E. William Woody, Capital Asset Liab
Subtotals - O.E.
William Woody, Withdrawals TOTAL
Dr.
Cr.
$206,281 $145,895 171,200 162,702 856,000 350,150 34,240 40,675 406,750 222,000 256,734 545,000 765,435 210,653 12,789 8,662 3,238 892,940 $2,608,172
$2,683,172
$ 75,000 $2,683,172
$2,683,172
Note: The subtotals of the trial balance indicate that the debit (left) side is $75,000 less than the credit (right) side. This imbalance must be due the amount of Withdrawals.
P1.2 Solution (continued) b) Bunyon Consulting Company Income Statement For the six month period ended June 30, 20XX Revenues Less: Operating Expenses: Depreciation Expense, Building Depreciation Expense, Equipment
$765,435 $ 34,240 40,675
Salary Expense
210,653
Supplies Expense
8,662
Utilities Expense Total Operating Expenses
3,238 297,468
Net Income (Before Taxes)
$467,967
Less: Income Taxes (40%)
187,187
Net Income (After Taxes)
$280,780
P1.3 Solution a)
Adjusting Entries: Date Description 20XX 6/30 Office Supplies Used Office Supplies
Ref.
Debit
(1)
4,790
6/30 Insurance Expense Prepaid Insurance
(2)
6/30 Depreciation Expense, Equipment Accumulated Depreciation, Equip.
(3)
6/30 Depreciation Expense, Building Accumulated Depreciation, Building
(4)
6/30 Telephone Expense Accounts Payable
(5)
Credit
4,790 750 750 1,000 1,000 2,000 2,000 100 100
P.3 Solution (continued) Parts (b) & (c) Cash 21,742
Equipment 25,000
Accounts Receivable 15,986
Accumulated Depreciation, Equipment Building 1,000 60,000 1,000 (3) 2,000
Accounts Payable 1,200 100 (5) 1,300
Mortgage Payable 40,000
Revenues 250,000
Telephone Expense 450 (5) 100 550
Administrative Expenses 40,000
Prepaid Insurance 1,200 750 (2) 450
Interest Expense 20,000
Depreciation Expense, Depreciation Expense, Equipment Building (3) 1,000 (4) 2,000
Office Supplies 7,022 4,790 (1) 2,232 Accumulated Depreciation, Building 4,000 2,000 (4) 6,000
Ken Ramsey, Capital 35,000
Ken Ramsey, Withdrawals 36,900
Wages Expense 90,575
Utilities Expense 12,325
Office Supplies Used (Expense) (1) 4,790
Insurance Expense (2) 750
P1.3 Solution (continued) d) TBT Company Adjusted Trial Balance December 31, 20XX Account Debit Cash
Credit
$ 21,742
Accounts Receivable
15,986
Prepaid Insurance
450
Office Supplies
2,232
Equipment
25,000
Accumulated Depreciation, Equipment Building
$ 2,000 60,000
Accumulated Depreciation, Building
6,000
Accounts Payable
1,300
Mortgage Payable
40,000
Ken Ramsey, Capital
35,000
Ken Ramsey, Withdrawals
36,900
Revenue
250,000
Telephone Expense
550
Wage Expense
90,575
Utilities Expense
12,325
Administrative Expenses
40,000
Interest Expense
20,000
Office Supplies Used (Expense)
4,790
Insurance Expense
750
Depreciation Expense, Equipment
1,000
Depreciation Expense, Building
2,000
Totals
$334,300
$334,300
P1.3 Solution (continued) e) TBT Company Income Statement For the Year Ended December 31, 20XX Revenue Less: Operating Expenses:
$250,000
Telephone
$
Wages Expense
90,575
Utilities
12,325
Administrative Expenses
40,000
Office Supplies Used (Exp.)
4,790
Insurance Expense
550
750
Depreciation Expense, Equipment
1,000
Depreciation Expense, Building
2,000
Total Operating Expenses Operating Income
151,990 $ 98,010
Less: Non-operating Expenses: Interest Expense Net Income Before Tax
20,000 $ 78,010
Less: Income Taxes Net Income, After Tax
31,204 $ 46,806
P1.3 Solution (continued) f) TBT Company
Balance Sheet December 31, 20XX ASSETS Current Assets: Cash Accounts Receivable Prepaid Insurance Office Supplies Total Current Assets Fixed Assets: Equipment Less: Accumulated Depreciation Book Value of Equipment Building Less: Accumulated Depreciation Book Value of Building
$21,742 15,986 450 2,232 $40,410 $ 25,000 2,000 $23,000 $ 60,000 6,000 54,000
Net Fixed Assets
77,000
TOTAL ASSETS
$117,410
LIABILITIES Current Liabilities: Accounts Payable $ 1,300 Taxes Payable 31,204 Total Current Liabilities Long-Term Liabilities: Mortgage Payable Total Liabilities
$32,504
NET WORTH Ken Ramsey, Capital--Jan. 31, 1985 Add: Net Income $46,806 Less: Withdrawals 36,900 Excess of Net Income over Withdrawals Ken Ramsey, Capital, December 31, 20XX TOTAL LIABILITIES AND NET WORTH
40,000 $ 72,504 $35,000
9,906 44,906 $117,410
P1.4 Solution Satoosh Corporation
Income Statement For the Year ended December 31, 20XX Revenues Less: Operating Expenses: Office Supplies Used (Exp.) Selling & Administrative Exp. Power & Utilities Depreciation Exp., Equipment Depreciation Exp., Building Operating Income
$400,000 $ 7,000 232,800 38,500 12,500 4,500
Other (Non-operating) Expenses: Interest Expense
295,300 $104,700 18,000
Net Income before Taxes Less: Income Taxes (40%)
$ 86,700 34,680
Net Income (After Taxes)
$ 52,020
Note: The following calculation is not a part of the Income Statement. Retained Earnings: Beginning Balance $30,000 Undivided Net Income 52,020 Ending Balance $82,020 So, the Retained Earnings (in Balance Sheet) will be $82,020.
P1.4. Solution (continued) Satoosh Corporation
Balance Sheet December 31, 20XX ASSETS Current Assets: Cash Accounts Receivable Prepaid Insurance Office Supplies Total Current Assets
$125,500 115,000 1,200 2,000 $243,700
Fixed Assets: Equipment Less: Accumulated Depreciation, Equip. Equipment Book (Net) Value Building Less: Accumulated Depreciation, Build. Building Book (Net) Value
$125,000 _ 37,500 $ 87,500 $135,000 _ 18,000 117,000
Total Net Fixed Assets
204,500
TOTAL ASSETS $448,200 ______________________________________________________________________ LIABILITIES Current Liabilities: Accounts Payable Taxes Payable Total Current Liabilities
$121,500 34,680 $156,180
Long-Term Liabilities: Mortgage Payable Total Liabilities Common Stocks Outstanding Retained Earnings Total Owner's Equity
120,000 $276,180 OWNER'S EQUITY $ 90,000 82,020
TOTAL LIABILITIES AND OWNER'S EQUITY
172,020 $448,200
P1.5. (TADJ Company) a) Date 20XX 02-01
02-02
Description
Ref.
Debit
Cash Office Equipment Land Preferred Stocks
30,000 20,000 150,000
Cash
800,000
200,000 800,000
Common Stocks 02-04
02-05 02-06 02-07
02-10
Credit
Building Cash Mortgages
500,000
Prepaid Insurance Cash
24,000
Advertising Expense Cash
1,000
50,000 450,000 24,000 1,000
Construction Equipment Cash Notes Payable
500,000
Commission Expense Accounts Payable
16,000
50,000 450,000 16,000
b) Cash (1) $ 30,000 (4) $50,000 (2) 800,000 (5) 24,000 (6) 1,000 (7) 50,000 $705,000
Prepaid Insurance (5) $24,000
Land (1) $150,000
Building (4) $500,000
Office Equipment (1) $20,000
Construction Equipment (7) $500,000
Accounts Payable (10) 16,000
Notes Payable (7) 450,000
Common Stocks (2) 800,000
Preferred Stocks (1) 200,000
Commission Expenses (10) 16,000
P1.6 Solution
Mortgages (4) 450,000 Advertising Expenses (6) 1,000
a)
Roofing Company Income Statement For the Year Ending December 31, 20XX Revenue (Sales) Cost of Goods Sold Gross Profit Less: Operating Expenses: Selling Administrative Total Operating Expenses Operating Income Less: Other Expenses: Interest Net Income before Taxes Income Taxes (50%) Net Income after Taxes
b)
$930,000 400,000 $530,000 $140,000 110,000 250,000 $280,000 40,000 $240,000 120,000 $120,000
Roofing Company Income Statement For the Year Ending December 31, 20XX ASSETS Current Assets: Cash Accounts Receivable Office Supplies Inventories Total Current Assets Fixed Assets: Equipment Less: Accumulated Depreciation Net Book Value of Equipment Building Less: Accumulated Depreciation Net Book Value of Building
$160,000 220,000 20,000 250,000 $650,000 $300,000 60,000 $240,000 $500,000 100,000 400,000
Net Fixed Assets
640,000
Total Assets
$1,290,000 LIABILITIES
Current Liabilities: Accounts Payable Taxes Payable Dividends Payable Total Current Liabilities Long-Term Liabilities: Mortgage Payable Total Liabilities
$ 200,000 120,000 48,000 $368,000 400,000 $768,000 NET WORTH
Common Stocks Retained Earnings Net Worth
Total Liabilities and Net Worth
$300,000 222,000 522,000
$1,290,000
Chapter 2: Cost Analysis Fundamentals Answers to Review Questions R2.1. (Total variable cost, VC) = (Variable cost per unit, V) (Output quantity, Q) TC = V × Q R2.2. The total variable costs vary in direct proportion to the production levels changes, but remain fixed in per unit. Fixed costs remain constant regardless of production levels. Mixed costs are partially fixed and partially variable. R2.3. Prime cost is the sum of direct material and direct labor costs. Conversion cost is the sum of direct labor and overheads incurred to convert raw material into finished goods. R2.4. Manufacturing Unit Cost or Average Cost. R2.5. Conversion costs. R2.7. Book value of the old machine. R2.8. Product costs are the manufacturing costs of products and cannot be expensed in the period they incur. Otherwise, if the product is not sold in the period they are produced, then when they sold in a later period, there would not be any cost to deduct from the revenues they generate. Period costs are expenses a company incur to operate its business as a result of which they sell their products. The cost of goods sold is also a period cost and deducted from the revenues in the period the products are sold. R2.9. RMI → WIP → FGI → COGS. R2.10. The cost of goods manufactured the costs of all the units that a company completes and transfers to the finished goods inventory during an accounting period, and these costs are the value of the finished goods inventory (an asset), which appear on the balance sheet of the company. Whereas the cost of goods sold is the manufacturing cost the items sold during the fiscal period.
Chapter 2: Cost Analysis Fundamentals Problem Solutions P2.1 Solution Prime costs = direct materials + direct labor = 25,000 + 45,000 = $70,000 Conversion costs = direct labor + overheads = 45,000 + 30,000 + 2,500 + 22,000 = $99,500
P2.2 Solution (a) The last year’s total cost of manufacturing Qa = 50,000 computers is: TCa = TC(50,000) = VCa + FCa = ($1,550,000 + $1,200,000) + $2,000,000 = $4,750,000 The manufacturing unit cost is found as follows UCa = TCa/Qa = $4,750,000 / 50,000 units = $95 per computer (b) To compute next years estimated total cost of manufacturing Qb = 60,000 computers, we need to compute the cost components as follows: Expected direct material cost = ($1,550,000/50,000) × 60,000 = $1,860,000 Expected direct labor cost = 1.025($1,200,000/50,000) × 60,000 = $1,476,000 Expected fixed cost = $2,000,000 + $ 160,000 = $2,160,000 Then, the expected total cost for the next is found as TCb = TC(60,000) = VCb + FCb = ($1,860,000 + $1,476,000) + $2,160,000 = $5,496,000 The manufacturing unit cost is found as follows UCb = TCb/Qb = $5,496,000 / 60,000 units = $91.60 per computer
P2.3 Solution Current Production: Production: 16,000 units/per month Current total cost: $416,000 Unit cost (or average cost): $416,000 / $16,000 = $30 per unit Expanded Production: New total cost: $480,000 Production: 16,000(1.25) = 20,000 units/per month Average unit cost: $480,000 / $20,000 = $24 per unit The incremental cost to produce the additional units is: Total incremental cost (change in total cost) = $480,000 - $416,000 = $64,000 Number of additional units produced = 20,000 – 16,000 = 4,000 units Increment cost per unit: $64,000 / 4,000 = $16
Problem 2.4 Solution Total Cost of Manufacturing 10,000 computers = $1,000,000 Total Cost of Purchasing 10,000 computers = Purchasing Cost + Unavoidable Fixed Costs = $950,000 + (150,000 - $50,000) = $1,050,000 Additional Cost incurred by purchasing externally = $1,050,000 - $1,000,000 = $50,000
Problem 2.5 Solution Total Production Cost = $49,000 Total Outsource Cost = $3.10(10,000) = $31,000 Increase (or decrease) in net income = 49,000 – 31,000 - 14,600 + 4,600 = $8,000 increase
Problem 2.6 Solution Should further process if the increment in sales price exceeds the further processing costs Price Increment for Product A: $125 - $70 = $55 > $45 Price Increment for Product B: $220 - $85 = $135 < $160 Product A has an increment selling price that exceeds its further processing costs. Hence, Product A should be processed further, but not Product B
P2.7 Solution 1)
Cost of Goods Available for Sale: Beginning Inventory 17,000 units @ $6.00 = February 20,000 units @ $6.50 = $130,000 March 40,000 units @ $6.20 = $248,000 May 30,000 units @ $6.30 = $189,000 July 50,000 units @ $6.40 = $320,000 September 40,000 units @ $6.30 = $252,000 November 15,000 units @ $6.60 = $99,000 Cost of Goods Available for Sale (212,000 units)
$102,000
$1,340,000
2) (a) Average-Cost Method: Cost of Goods Sold = ($1,340,000/212,000 units) x 192,000 = $1,213,585 F&AT Company Income Statement For the Year Ending December 31, 20XX Sales (192,000 units @ $10.00) $1,920,000 Cost of Goods Sold 1,213,585 Gross Profit on Sales (Profit Margin) $706,415 Operating Expenses: Sales and Administrative Expenses 592,000 Operating Income $114,415 2) (b) FIFO Method: Cost of Goods Sold: From beginning inventory From February purchases From March purchases From May purchases From July purchases From September purchases Cost of Goods Sold
Sales
17,000 units @ $6.00 = $102,000 20,000 units @ $6.50 = $130,000 40,000 units @ $6.20 = $248,000 30,000 units @ $6.30 = $189,000 50,000 units @ $6.40 = $320,000 35,000 units @ $6.30 = $220,500 (192,000 units) $1,209,500
F&AT Company Income Statement For the Year Ending December 31, 20XX (192,000 units @ $10.00)
$1,920,000
Cost of Goods Sold
1,209,500
Gross Profit on Sales (Profit Margin)
$ 710,500
Operating Expenses: Sales and Administrative Expenses
592,000
Operating Income
$118,500
P2.7 Solution (Continued) 2) (c) LIFO Method: Cost of Goods Sold: From November purchases 15,000 units @ $6.60 = $ 99,000 From September purchases 40,000 units @ $6.30 = $252,000 From July purchases
50,000 units @ $6.40 = $320,000
From May purchases
30,000 units @ $6.30 = $189,000
From March purchases
40,000 units @ $6.20 = $248,000
From February purchases
17,000 units @ $6.50 = $110,500
Cost of Goods Sold 192,000 units $1,218,500 F&AT Company Income Statement For the Year Ending December 31, 20XX Sales (192,000 units @ $10.00)
$1,920,000
Cost of Goods Sold
1,218,500
Operating Expenses: Sales and Administrative Expenses
592,000
Operating Income
$109,500
P2.8 Solution January 1 (Beg. Inventory)
15,000 units @ 9.90 = $148,500
March purchase
18,000 units @ 13.00 =
234,000
May purchase
20,000 units @ 12.50 =
250,000
July purchase
40,000 units @ 11.50 =
460,000
August purchase
40,000 units @ 13.00 =
520,000
October purchases
15,000 units @ 13.50 =
202,500
December purchase
12,000 units @ 15.00 =
180,000
Total
160,000 units
$1,995,000
a) Average Cost Method: Average Cost per unit = 1,995,000 / 160,000 = $12.46875 Cost of Goods Sold = $12.46875 X 130,000 units = $1,620,937.50 b) FIFO Method: January 1 (Beg. Inventory) 15,000 units @ 9.90 = $148,500 March purchase
18,000 units @ 13.00 = 234,000
May purchase
20,000 units @ 12.50 = 250,000
July purchase
40,000 units @ 11.50 = 460,000
August purchase
37,000 units @ 13.00 = 481,000
Cost of Goods Sold
$1,573,500
c. LIFO Method: December purchase
12,000 units @ 15.00 = $180,000
October purchase
15,000 units @ 13.50 = 202,500
August purchase
40,000 units @ 13.00 = 520,000
July purchase
40,000 units @ 11.50 = 460,000
May purchase
20,000 units @ 11.50 = 250,000
March purchase
3,000 units @ 13.00 =
Cost of Goods Sold
130,000 units
39,000
$1,651,500
P2.9 Solution Hee Haw Manufacturing Company Cost-of-Good-Sold Statement For the Year Ending December 31, 20XX Change in Materials Inventory: Beginning Inventory $50,000 Purchases During the Year 650,000 Total Materials Available For Use $700,000 Ending Inventory (12/31/20XX) 100,000 Cost of Materials Used Direct Labor Factory Overhead Total Factory Cost During the Year
$600,000 400,000 250,000 $1,250,000
Change in Work-in-Process Inventory: Beginning Inventory (1/1/20XX) Ending Inventory (12/31/20XX) Decrease in Work-in-Process Cost of Goods Manufactured
50,000 $1,300,000
Change in Finished Goods Inventory: Beginning Inventory (1/1/20XX) Ending Inventory (12/31/20XX) Increase in Finished Goods Inventory Cost of Goods Sold
P2.10 Solution (a) (b) (c) (d) (e) (f) (g) (h) (i)
12,000 10,000 32,000 50,000 35,000 30,000 27,000 141,000 127,000
(j) (k) (l) (m) (n) (o) (p) (q) (r)
42,000 91,000 26,000 91,000 85,000 112,000 111,000 81,000 26,000
$75,000 25,000
$100,000 150,000 (50,000) $1,250,000
P2.11 Solution BBY Manufacturing, Inc. Statement of Cost of Goods Sold For the Year Ended December 20XX Raw Materials Used: Raw Materials Inventory, January 1, 2006 Purchases, Raw Materials Cost Materials Available for Use Less: Raw Materials Inventory, December 31
$
505,000 4,752,000
$ 5,257,000 457,000
Cost of Raw Materials Used
$4,800,000
Direct Labor
2,210,000
Factory Overhead Costs: Supplies Used, Factory
$ 55,000
Depreciation, Machinery
60,000
Depreciation, Building (Factory)
20,000
Indirect Labor, Factory Services
842,000
Supervisory Salaries, Factory
280,000
Property Taxes, Factory
60,000
Factory Miscellaneous Expenses
23,000
Total Factory Overhead
1,340,000
Total Manufacturing Costs for the Year
$8,350,000
Change in Work-In-Process Inventory: Beginning Inventory, January 1
$1,565,000
Ending Inventory, December 31
2,035,000
Less: Increase in Work-In-Process Inventory
(470,000)
Cost of Goods Manufactured
$7,880,000
Change in Finished Goods Inventory: Beginning Inventory, January 1
$2,325,000
Ending Inventory, December 31
1,265,000
Add: Decrease in Finished Goods Inventory
Cost of Goods Sold
1,060,000 $8,940,000
Chapter 3: Product Costing Answers to Review Questions R3.1. The following equation applies to raw materials, work-in-process and finished goods inventories Beginning Balance + Transfers In - Transfers Out = Ending Balance Correct answer is D: all of the above. R3.2. Correct answer is D. The predetermined rate is used to apply overhead costs to work-in-process units. R3.3. Correct answer is D. The costs to be accounted for consist of: Costs in the beginning inventory and costs added during the period. R3.4. Correct answer is C: The detailed materials, labor, and overhead costs are needed when determining the cost per equivalent units. R3.5. The job-order costing system assign costs directly to the product or job by adding the direct materials and direct labor costs to the work-in-process (WIP) inventory. When the manufacturing process is continuous, it is difficult to establish how much of each material is used and exactly how much labor time is consumed to produce each unit of a product. Thus, under process costing, costs are accounted for by the production process or production department instead of by the product or the job. R3.6. The predetermined rate is calculated as shown below and is used to apply overhead costs to work-in-process: Predetermined Overhead Rate =
Budgeted (Estimated)Overhead Cost Budgetted (Estimated)Level of Activity (basis)
R3.7. Correct answer is B. When products or services are different from each other, joborder costing should be used. R3.8. Correct answer is D. Direct materials, direct labor and manufacturing costs are recorded on the job cost sheet. R3.9. Correct answer is B. Work in process debited & Materials credited for the issuance of direct materials to production.
R3.10. The relationship between machine-hours and applied overhead is a constant of $5 per machine-hour, which indicates a strong, projected cause-and-effect relationship between the two.
Chapter 3: Problems Solutions P3.1. Solution Material cost = ($12,000 + $32,800) / 20,000 = $2.24 per unit Conversion cost = ($13,000 + $50,000) / 18,000 = $3.50 per unit Manufacturing cost = $2.24 + $3.50 = $5.75 per unit P3.2. Solution WIP ending inventory = 5,350 + 650 – 5,330 = 670 P3.3. Solution Units in WIP ending inventory = 60,000 – 56,800 = 3,200 Equivalent Units for: Materials = 56,800 + 3,200(100%) = 60,000 equivalent units Conversion = 56,800 + 3,200(60%) = 58,720 equivalent units P3.4. Solution Units in WIP ending inventory = 2,200 + 60,000 – 56,800 = 5,400 Equivalent Units for: Materials = 56,800 + 5,400(100%) = 62,200 equivalent units Conversion = 56,800 + 5,400(50%) = 59,500 equivalent units P3.5: Solution Total units to account for = 1,200 + 11,000 = 12,200 units Units in ending WIP inventory = 13,000 – 11,500 = 1,500 units Equivalent Units for Materials = 11,500 + 1,500(100%) = 13,000 units Equivalent Units for Conversion = 11,500 + 1,500(60%) = 12,400 units P3.6. Solution a) Total units to be Account For = 1,200 + 10,000 = 11,200 Units in WIP ending inventory = 11,200 – 9,200 = 2,000 Equivalent Units in Ending WIP Inventory: For Material Cost = 2,000(80%) = 1,600 units For Conversion Costs (Labor and OH) = 2,000(60%) = 1,200 Total Equivalent Units: For Material Cost = 9,200 + 1,600 = 10,800 units For Conversion Costs (Labor and OH) = 9,200 + 1,200 = 10,400 Total Cost to be Account For: Material Cost = $6,600 + $53,880 = $60,480 Conversion Costs (Labor and OH) = $2,400 + ($18,800 + $23,000) = $44,200 Total Cost to be Account For = $60,480 + $44,200 = $104,680 Cost Per Equivalent Unit: For Material Cost = $60,480 / 10,800 = $5.60 per unit For Conversion Costs (Labor and OH) = $44,200 / 10,400 = $4.25 per unit Manufacturing Cost = $5.60 + $4.25 = $9.85 per equivalent (complete) unit b)
Cost of Units Transferred Out = $9.85(9,200 units) = $90,620
P3.6. Solution (continued) c) Cost of Ending WIP Inventory: For Material Cost = $5.60(1,600 units) = $8,960 For Conversion Costs (Labor and OH) = $4.25(1,200 units) = $5,100 Total of Ending WIP Inventory = $8,960 + $5,100 = $14,060 Total Cost Accounted For = $90,620 + $14,060 = $104,680 P3.7. The manufacturing overhead cost: Indirect materials Salary of production supervisor: Rent on factory equipment: Total Factory OH
$7,000 $33,000 $14,000 $54,000
Estimated direct labor hours 10,000 What will be the predetermined overhead rate if company applies to jobs on the basis of direct labor hours. Predetermined Overhead Rate =
$𝟓𝟒,𝟎𝟎𝟎 𝟏𝟎,𝟎𝟎𝟎
= $5.40 per labor hour
P3.8: Solution Predetermined overhead rate = $200,000 / 50,000 estimated labor hours = $4 per DL hour Applied overhead = (Predetermined OH Rate per DL hour) × (Actual DL hours) = $4(55,000 hours) = $220,000 Actual manufacturing overhead Applied manufacturing overhead ($4 × 55,000 hrs)
$208,000 220,000
Manufacturing overhead overapplied
($ 12,000)
Since applied manufacturing overhead exceeds actual manufacturing overhead, manufacturing overhead is overapplied P3.9: Solution
Sum of inventory balance = $5,000 + $8,000 + $37,000 = $50,000 The proportion of ending balances to total ending balance is: for WIP = $5,000 / $50,000) = 10% for FG = $8,000 / $50,000) = 16% for COGS = $37,000 / $50,000 = 74% The allocation is To WIP = $25,000(0.10) = $2,500 To FG = $25,000(0.16) = $4,000 To COGS = $25,000(0.74) = $18,500
Chapter 4: Manufacturing Cost Allocation Answers to Review Questions R4.1. Companies allocate costs to estimate or assess the costs of their cost objects (products, processes, divisions, etc.). The main issue in cost allocation is that estimated costs are assigned to the cost objects, which are subject to inaccuracies due to the use of the allocation bases are arbitrarily chosen.
R4.2. There are three commonly used methods to allocate support costs: 1) the direct method; 2) the sequential (or step) method; and 3) the reciprocal method. The direct method is the simplest method among all three, while the reciprocal method is the most complicated among all three. R4.3. Cost allocation is the process of distributing an overhead cost across multiple products, business units, or cost objects/centers. R4.4. Costs allocating serves three main purposes: 1) make decisions, 2) reduce non-value-added costs, and 3) determine pricing. R4.5. 1) Add up total overhead in groups of costs pools; 2) Compute the overhead allocation rate by dividing total overhead by the total measure of cost allocation basis (e.g., number of direct labor hours); 3) Apply overhead by multiplying the overhead rate by the measure of allocation basis for each product. R4.6. The three common methods used to allocate of costs support departments to operating/production departments are: (1) direct method. (2) sequential method, and. (3) reciprocal method. R4.7. A service department is a unit in a firm that is not involved directly in producing its goods or services. However, service departments provide services that enable the production departments to perform their functions. Production departments, on the other hand, are the units that are directly involved in producing goods and services. R4.8. The term reciprocal services refers to the situation in which two or more service departments provide services to each other.
R4.9. Under the direct method of service department cost allocation, all service department costs are allocated directly to the production departments, and none of these costs are allocated to other service departments. Under the step-down method, a sequence is first established for allocation of service department costs. Then, the costs incurred in the first service department in the sequence are distributed among all other departments (production and other service departments) that use the services provided by that service department. The method proceeds in the same manner through the sequence of service departments. Under the reciprocal-services method, a system of simultaneous equations is established to reflect the reciprocal provision of services among service departments. Then, the costs of all of the service departments are allocated among all of the departments that use services provided by the various service departments. The reciprocal-services method of service department cost allocation is the only method that fully accounts for the reciprocal services among service departments. R4.10. Under the step-down method, the first department in the sequence is the service department that serves the largest number of other service departments. The second department in the sequence is the service department that serves the second-largest number of service departments, and so on. The sequence among tied service departments usually is an arbitrary choice. R4.11. - A single-stage cost allocation system uses a single, plantwide, rate to allocate costs. - A two-stage system first allocates costs to departments or activities and then allocates costs from the departments or activities to the products or services. R4.12. The plantwide allocation approach uses one cost pool to collect and apply overhead costs and, therefore, uses one predetermined overhead rate for the entire company. The department allocation approach uses several cost pools (one for each department) and therefore uses several predetermined overhead rates. R4.13. The essential difference is the allocation of costs among service departments. The direct method makes no inter-service-department allocation, the step-down method makes a partial inter-service-department allocation, while the reciprocal method fully recognizes interservice-department activities. All three methods allocate costs to the production departments based on the production department’s relative use of the services provided by the service departments. R4.14. Allocations usually begin from the service department that has provided the greatest proportion of its services to other service departments, or that services the largest number of other service departments. This criterion is used to minimize the unrecognized portion of reciprocal service department costs. Another criterion used is the amount of cost incurred by the service department. That is, the reallocation begins with the service department that has the greatest amount of cost.
Chapter 4: Problem Solutions Solution 4.1 (Waldoor Company) Waldoor Company Work-Sheet for Allocation of Factory Overhead For the Month of August, 20XX Overhead Cost Indirect Materials Indirect Labor Payroll Taxes Light and Power Repairs Depreciation, Machinery Fire Insurance Other Expenses TOTALS Reallocation of Service Department Costs: Storeroom TOTALS Building Service TOTALS
Allocation Basis Materials Used Labor Performed Wages K.W-h used Cost of Repairs Cost of Machine Floor Space No. of Employees
Total $21,425 27,000 810 3,500 2,740 7,500 1,300 1,800 $66,075
No.of Requisitions $66,075 Floor Space $66,075
Production Departments A B C $6,045 $5,400 $3,350 6,750 5,000 4,000 203 150 120 1,225 1,050 770 1,250 430 250 2,640 1,800 1,200 455 325 260 720 450 360 $19,288 $14,605 $10,310
Service Departments Building Storeroom $4,915 $1,715 3,750 7,500 112 225 315 140 635 175 1,860 --156 104 180 90 $11,923 $9,949
4,975
2,487
1,492
995
$24,263 5,652 $29,915
$17,092 4,037 $21,129
$11,802 3,329 $15,031
$12,918 (12,918)
(9,949)
P4.2. Solution (Delta Company) a) Cost allocation using the direct method. $90,000
Predetermined Maintenance Cost Allocation Rate = 30,000+50,000 = $1.125 per sq. ft. $48,000
Predetermined Warehouse Cost Allocation Rate = 10,000+15,000 = $1.92 per requisition
Costs Before Allocation Allocation of Maintenance Costs Allocation of Warehouse Costs Costs After Allocation
Service Dept. Maint Ware $90,000 $48,000 (90,000) (48,000) $0 $0
Operating Dept. A B $180,000 $250,000 33,750 56,250 19,200 28,800 $232,950 $335,050
b) Cost allocation using the step-down method. 20,000
Percentage of Maintenance Service to Warehouse = 20,000+30,000+50,000 = 20% 7,000
Percentage of Warehouse Service to Maintenance = 7,000+10,000+15,000 = 21.875%
Problem 4.2 Solution (continued) Warehouse has given more service to the Maintenance Department than vice versa. Thus, the Warehouse costs are allocated first. $48,000
Predetermined Warehouse Cost Allocation Rate = 7,000+10,000+15,000 = $1.50 per req.
Costs Before Allocation Allocation of Warehouse Costs Costs After Warehouse Allocation
Service Dept. Maint Ware $90,000 $48,000 10,500 (48,000) $100,500 $0
Operating Dept. A B $180,000 $250,000 15,000 22,500 $232,950 $335,050
$100,500
Predetermined Maintenance Cost Allocation Rate = 30,000+50,000 = $1.25625 / req.
Costs Before Allocation Allocation of Warehouse Costs Allocation of Maintenance Costs Costs After Allocation
Service Dept. Maint Ware $90,000 $48,000 10,500 (48,000) (100,500) --$0 $0
Operating Dept. A B $180,000 $250,000 15,000 22,500 37,688 62,812 $232,688 $335,312
c) Cost allocation using the reciprocal method. Under this method, some of the Maintenance costs are allocated to Warehouse and some Warehouse costs are allocated to Maintenance Department. Thus, we must determine the total cost being allocated to both the Maintenance Departments and Warehouse first, as follows (1) Total Maintenance cost = Maintenance Department cost + Cost allocated to Maintenance from Warehouse. (2) Total Warehouse cost = Warehouse Department cost + Cost allocated to Warehouse from Maintenance. Step 1: Determining allocation bases: Maintenance Dept. Floor % of Space Total Maintenance --Warehouse 20,000 20% Department A 30,000 30% Department B 50,000 50% Total 100,000 100%
Warehouse No. of % of Requisitions Total 7,000 7/32 ----10,000 10/32 15,000 15/32 32,000 100%
Problem 4.2 Solution (continued) Step 2: Setting up the equations: Cost allocated to Warehouse from Maintenance is 20% of total Maintenance cost (M). Cost allocated to Maintenance from Warehouse is 7/32 of total Warehouse cost (W). W = $48,000 + 0.2M M = $90,000 + (7/32)W W = $48,000 + 0.2[$90,000 + (7/32)W] W = $48,000 + $18,000 + 0.04375W 0.95625W = $66,000 W = Total Cost of Warehouse = $69,020 M = $90,000 + (7/32)($69,020) M = Total Cost of Maintenance Department = $105,098 Step 2: Allocation of the computed total cost of each service department in Step 2 to all other departments using the proportions (percentages) computed in Step 1: Allocation of Warehouse’s total cost: To Maintenance Department = (7/32)($69,020) = $15,098 To Department A = (10/32)($69,020) = $21,569 To Department B = (15/32)($69,020) = $32,353 Allocation of Maintenance Department’s total cost: To Warehouse Department = (20%)($105,098) = $21,020 To Department A = (30%)($105,098) = $31,529 To Department B = (50%)($105,098) = $52,549
Costs Before Allocation
Service Dept. Maint Ware $90,000 $48,000
Operating Dept. A B $180,000 $250,000
Allocation of Warehouse Costs
15,098
(69,020)
21,569
32,353
Allocation of Maintenance Costs
(105,098)
21,020
31,529
52,549
$0
$0
$233,098
$334,902
Costs After Allocation
P4.3. Solution (MKATZ Company) The costs of indirect materials, indirect labor and repairs are recoded in the work-sheet as they are given: Allocating payroll taxes, based the indirect labor cost: ($2,460/$12,300 = $0.20 per $) × (Indirect Labor Cost). Department Indirect Payroll Labor Taxes Production X $3,690 $737 Production Y 3,075 615 Production Z 1,845 370 Maintenance 2,460 492 Warehouse 1,230 246 Total $12,300 $2,460 The $1,134 fuel cost charged to the Maintenance department only. Allocation of light and power cost: $3,400/100,000 = $0.034 per kW-hr Distribution of light and power costs
Production X Production Y Production Z Maintenance Warehouse Total
kW-h used 38,000 26,000 20,000 11,000 5,000 100,000
Light & Power Cost $1,292 884 680 374 170 $3,400
Allocation of rent and fire Insurance costs ($6,000 and $1,200, respectively), based on floor space occupied: Floor Space Fire (sq. ft.) Ratio Rent Insurance Department X 3,200 40% $2,400 $ 480 Department Y 2,400 30% 1,800 360 Department Z 1,200 15% 900 180 Maintenance Department 800 10% 600 120 Warehouse 400 5% 300 60 Total 8,000 100% $6,000 $1,200
Problem 4.3 Solution (continued) Allocation of the sundry (miscellaneous) expenses of total $1,800 based on the number of employees: Number of Sundry Employees Ratio Costs Department X 40 40% $720 Department Y 20 20% 360 Department Z 20 20% 360 Maintenance Department 15 15% 270 Warehouse 5 5% 90 Total 100 100% $1,800
Department X Department Y Department Z Maintenance Department Warehouse Total
Number of Store Requisitions 1,000 750 500 250 --2,500
Depreciation of machinery are recorded as have been computed according the company’s depreciation schedules: All distributed costs are recorded as shown in the "work-sheet for allocation of factory overhead" below. Then, the finalized costs of the service departments are reallocated to the production departments using the step-down methods, starting with the Warehouse Department that has provided more services to the Maintenance Department than the services received from.
Problem 4.3 Solution (continued) MKATZ Company Work-Sheet for Allocation of Factory Overhead For the Month of July, 20XX Production Departments Overhead Cost item Indirect Materials Indirect Labor Repairs Payroll Taxes Fuel Light and Power Rent Depreciation, Machinery Fire Insurance Sundry Costs TOTALS Reallocation of Costs of: Warehouse
Allocation Basis Materials Used Labor Performed Cost of Repairs Wages To Maintenance kW-h used Floor Space Cost of Machine Floor Space No. of Employees
Maintenance Dept. Final Cost Distribution
Floor Space
X
Y
Z
$8,500 4,600 998 920
$6,500 4,200 670 840
$4,000 4,300 490 860
1,320 2,475 2,200 330 120 $21,462
984 1,890 1,800 252 100 $17,236
676 1,710 1,200 228 72 $13,536
Service Dept. MaintWareenance house $20,500 --30,500 12,800 357 325 6,100 2,560 3,600 128 92 900 2,025 1,000 500 120 270 20 8 $63,225 $18,600
4,650 $26,113 28,600
3,720 $20,956 21,840
$54,713
$42,796
3,255 $16,791 19,760 $35,551
6,975 (18,600) $70,200 --(70,200) -----
Total $39,500 56,400 2,860 11,280 3,600 3,200 9,000 6,700 1,200 320 $134,060
# of Requisitions
--$134,060 --$134,060
See the computations for reallocation of the service departments below: The $18,600 final costs of the Warehouse Department are reallocated according to the number of requisitions filled, as shown in the following table.
Department X Department Y Department Z Maintenance Department Total
Number of Requisitions 1,000 800 700 1,500 4,000
Ratio 25.0% 20.0% 17.5% 37.5% 100%
Warehouse Cost Reallocated $4,659 3,720 3,255 6,975 $3,340
The $70,200 final costs of the Maintenance Department are reallocated according to floor space occupied to the production departments (not to the Warehouse):
Department X Department Y Department Z Total
Floor Space (square feet) 3,200 2,400 1,200 6,800
Proportion 11/27 14/45 9/32 1.00
Maintenance Dept.’s Costs Allocated $28,600 21,840 19,760 $70,200
P4.4: Solution (Talesh Company) Allocation Bases Department S2 Sq. Ft Ratio ----20,000 1/10 100,000 5/10 80,000 4/10 200,000 1.00
Department S1 Employees Ratio 25 5/48 15 3/48 110 22/48 90 18/48 240 1.00
Department S2 Department S3 Department A Department B Totals
Service Departments Overhead Costs Allocation cost of: Department S1 Department S2 Department S3 Totals
Department S3 Hours Ratio --------15,000 1/3 30.000 2/3 45,000 1.00
Operating Departments
Dept. S1
Dept. S2
Dept. S3
Dept. A
Dept. B
Total
$84,000
$66,000
$40,000
$90,000
$97,000
$377,000
(84,000)
8,750 (74,750) ---
5,250 7,475 (52,725)
38,500 37,375 17,575
32,500 29,900 35,150
$
$
$183,450
$193,550
--$
0
0
0
$377,000
Chapter 5: Joint Cost Allocation Answers to Review Questions R5.1. A common cost is a cost associated with operating a production facility, or a business segment that is shared among two or more products, departments or activities. A common cost cannot be attributed to a specific single product, department or activity. R5.2. Common cost allocation is the process of equitably allocating shared or joint costs to joint products, processes, and activities, so that a company can accurately determine the cost of each product or activity, and set prices accordingly. ... They are shared costs because the trip benefited both product departments and cost objects. R5.3. After the split-off point, each product incurs separable (or independent) costs. Allocating joint costs using market value at the split-off may be the most effective method for planning and budgeting for the joint costs. R5.4 Joint cost allocations are usually made to assign a cost to a product after the split-off point. This is usually done for external reporting, tax, or rate-making purposes or to satisfy contract requirements. Because the joint costs are common to the outputs, it is not possible to find a direct way of relating the costs. Rather, the costs are related to economic benefits on the basis of some measure of relative outputs. R5.5 Because net realizable values of the output provide a measure of the economic benefit received from each output from the production process, this method is usually preferred when it can be implemented. Further, the physical quantities may be difficult to compare (e.g., weights versus volumes). R5.6 It could be preferable to use a physical quantities measure if it reflects the economic benefit ultimately obtainable from the production process, particularly if there is no objective selling price for joint products. Some examples include public utility rate setting, energy price regulation, new market setting, and new product price setting. In all of these cases, it is not possible to use the relative sales value method. Of course, the physical quantity measure used must make sense. Thus, ounces of lead should not be added to ounces of silver for joint cost allocation purposes. R5.7 For joint products, costs of the inputs up to the split-off point are allocated to each of the products. Costs prior to split-off are not allocated to by-products in the same way as to the main (joint) products. Either joint costs (costs incurred prior to split-off) equal to the sales value of the by-product are allocated to the by-product, reducing the costs allocated to the main products (Method 1 in the text) or no joint costs are allocated to the by-product and it is credited with its sales value (Method 2). R5.8. The joint costs of the product are irrelevant to this decision. Using the principle of
differential costs, the joint costs are not differential in this decision. They are sunk costs, because they must be incurred under either decision. R5.9.
A company should choose a method for joint cost allocation that is specifically appropriate the values its products and production requirements, and consistently use the selected method.
R5.10.
The process is a joint process.
R5.11.
The Sales-value (or market-value) method produces the same gross profit percentage for the joint products.
R5.12.
The net-realizable-value method be used to have comparable values of the joint products, then the company would be able to learn which is of negligible value to be considered as a by-product.
Chapter 5: Problem Solutions P5.1. Solution Average unit cost = Total joint cost/Total number of units produced Average unit cost = $150,000/1,000,000 units = $0.15 per pen Allocation of joint cost: Blue ink: 400,000 × $0.15 = $60,000 Black ink: 300,000 × $0.15 = $45,000 Green ink: 100,000 × $0.15 = $15,000 Red ink: 200,000 × $0.15 = $30,000 This cost allocation is for joint manufacturing costs of body of the pens at the split-off point, before the further processing for injecting them with the required ink colors. After passing through the further processing, the separable costs would be added to different pens for the inks.
P5.2. Solution a) Relative Market Value of Main Products And Net Realizable Value Of The By-Product: Sales Separable cost Price Volume $3.80/gallon $13 25,000 gallons Product A = 30,000 gallons
Joint cost = $195,500 Input = 50,000 gallons
$3.00/gallon Product B = 15,500 gallons
$11
12,500 gallons
$1.00/gallon By-Product = 4,500 gallons
$4
1,750 gallons
Net realizable value of the by-product = 4,500($4 - $1) = $13,500 which is subtracted from the total joint cost. Joint cost to be allocated to products A and B = $195,500-$13,500 = $182,000 Product
Approximate Market Value at Split-off Point
Relative Market Value
Proportion
Joint Cost to be Allocated
A
13-3.80 = $9.20
$9.20 x 30,000 = $276,000
276,000/400,000 = 69%
Share of Joint Cost $125,580
$182,000 B
11-3.00 = $8.00
$8.00 x 15,500 = $124,000
Total
124,000/400,000 = 31%
$ 56,420
$400,000
Product A B By-Product
Joint Cost Per gallon $4.186 3.640 3.000
$182,000
Separable Manufacturing Cost per gal. $3.80 3.00 1.00
Total Product Manufacturing Cost per gal. $7.986 6.640 4.000
b) Product-line income statement: HAROLD & SONS COMPANY Product-Line Income Statement For the Month of July 19XX Product A
Product B
By-Product
Total
Sales Revenue
$325,000
$137,500
$ 7,000
$469,500
Cost of Goods Sold
199,650
83,000
7,000
289,650
Gross Margin
$125,350
$ 54,500
-----
$179,850
Gross Margin %
38.57%
39.64%
-----
38.31%
P5.2. Solution (continued) c)
Physical measure of the main products and net realizable value of the by-product: As shown in part (A), joint cost to be allocated to the main products, A and B, is $182,000. The cost allocation under the physical measure method is as follows:
Product
Production Level (gal.)
Joint Cost to be Allocated
Proportion
A
30,000
30,000/45,500 = 60/91
Share of Joint Cost $120,000
$182,000 B
15,500
Total
45,500
15,500/45,500 = 31/91
62,000 $182,000
Product
Joint Cost per gallon
Separable Manufacturing Cost per gal.
Total Product Manufacturing Cost per gal.
A B By-Product
$4.00 4.00 3.00
$3.80 3.00 1.00
$7.80 7.00 4.00
P5.3. Solution Separable Cost
Product Sales Price
100 units @ $50 1000 units @ $30 Input Material
S.O.P.
250 units @ $25
$30,000
$5/unit
Sales Production Separabl Products Price units e Cost/unit A
$400
100
50
Relative Market Value at S.O.P
A
$400
B
$300
BP
$20
Joint Cost to Proportion be Allocated
(400-50)100 = $35,000
50% $30,000
B
165
250
25
(165-25)250 = 35,000
50%
Totals
70,000
100%
Product
Share of Joint Cost
Joint Cost per unit
Separable Cost/unit
Manufacturin g unit cost
A B C
$15,000 15,000 0
$150 60 0
$50 25 5
$200 85 5
P5.4. Solution
$30,000
a) Relative market value of the main products and zero cost to the by-product:
Joint cost = $450,000 Input = 100,000 gallons
Product A
Approximate Market Value at Split-off Point 15-3.75 = $11.25
Sales
Separable cost $3.75/gallon Product A = 45,000 gallons $2.20/gallon Product B = 37,500 gallons $1.00/gallon By-Product = 17,000 gallons $0.00/gallon Waste = 500 gallons
Price Volume $15.00 40,000 gallons $11.20 30,000 gallons $2.00
15,000 gallons
$0.00
XXXXXXXX Joint Cost to be Allocated
Relative Market Value
Proportion
$11.25x45,000 = $506,250
506,250/843,750 = 60%
Share of Joint Cost
$270,000 $450,000
B
11.20-2.20 = 9.00 $9.00 x 37,500 = $337,500
337,500/843,750 = 40%
$843,750
$180,000 $450,000 $450,000
Product
Joint Cost per gallon
Separable Manufacturing Cost per gal.
Total Product Manufacturing Cost per gal.
A B By-Product
$6.00 4.80 0.00
$3.75 2.20 1.00
$9.75 7.00 1.00
b) Product-line income statement is as follows: Barnow Manufacturing Company Production-Line Income Statement For the Month of July 19XX Sales Revenue Cost-of-Goods-Sold
Product A $ 600,000 390,000
Product B $ 336,000 210,000
By-Product $ 30,000 15,000
Total $ 966,000 615,000
Gross Margin Gross Margin%
$ 210,000 35 %
$ 126,000 37.5 %
$ 15,000 50 %
$ 351,000 36.3 %
P5.4. Solution (continued) c) Physical measure of the main products and zero cost to the by-product: As shown in part (A), the whole $450,000 joint cost is allocated to the main products A and B. The cost allocation under the physical measure method is as follows:
Product
Production Level (gallons)
Proportion
A
45,000
45,000/82,500 = 18/33
Joint Cost to be Allocated
Share of Joint Cost
Joint cost per gallon
Separable cost per gallon
Total cost per gallon
$245,455 $ 5.4545
$ 3.75
$ 9.2045
$204,545 $450,000
5.4545
$ 2.20
7.6545
0.0000
1.00
1.0000
$450,000 B B-P
37,500 82,500 N/A
37,500/82,500 = 15/33
P5.5. Solution PA = 50 - QA PB = 40 - 0.5QB Joint Cost = 35 + 25 = $60/unit Y units of raw material yield QA units of product A and QB units of product B, where QA ≤ Y and QB ≤ 3Y. TR = PAQA + PBQB = (50 - QA)QA + (40 - 0.5QB)QB TC = 60 Y Maximize: Z = 50QA – (QA)2 + 40QB - 0.5 (QB)2 - 60Y Subject to: QA ≤ Y QB ≤ 3Y QA, QB, Y ≥ 0 Select the Lagrangian multipliers A and B so that A(Y - QA) = 0 B(3Y - QB) = 0 with the following conditions hold: A > 0 if Y - QA = 0 A = 0 if Y - QA > 0 and B > 0 if 3Y - QB = 0 B = 0 if 3Y - QB > 0 The Lagrangian form of the objective function is as follows: Maximize: L(Q, Y, ) = 50QA - (QA)2 + 40QB - 0.5(QB)2 - 60Y + A(Y - QA) + B(3Y - QB) Subject to: QA, QB, Y, A, B ≥ 0
P5.5. Solution (continued) The partial derivatives are as follows: (1) L/QA = 50 - 2QA - A = 0 (2) ∂L/∂QB = 40 - QB - B = 0 (3) ∂L/∂Y = - 60 + A + 3B = 0 (4) ∂L/∂A = Y - QA = 0 =======> QA = Y (5) ∂L/∂B = 3Y - QB = 0 =======> QB = 3Y From (1): 50 - 2Y - A = 0 =====> A = 50 - 2Y From (2): 40 - 3Y - B = 0 =====> B = 40 - 3Y Substituting A by its equivalent, (50 - 2Y), and gives the following: -60 + 50 -2Y + 120 - 9Y = 0 110 - 11Y = 0
B by its equivalent, (40 - 3Y) in equation (3)
Y = 10 units of raw material QA = 10 units QB = 30 units A = $30 allocated to each unit of product A B = $10 allocated to each unit of product B PA = 50 - QA = 50 - 10 ========> PA = $40 PB = 40 - 0.5QB = 40 - 0.5(30) =======> PB = $25
P5.6. Solution Q1 = 47.5 - P1 =====> P1 = 47.5 - Q1 Q2 = 80 - 2P2 =====> P2 = 40 - 0.5 Q2 max: (47.5 - Q1) . Q1 + (40 - 0.5 Q2) . Q2 - 45Y s.t. : Q1 ≤ 2Y Q2 ≤ 3Y Q1, Q2, Y ≥ 0 Select the Lagrangian multipliers 1 and 2 such that 1(2Y - Q1) = 0 and 2(3Y - Q2) = 0 where:
if (2Y - Q1) = 0, 1 > 0 and if (2Y - Q1) > 0, 1 = 0 if (3Y - Q2) = 0, 2 > 0 and if (3Y - Q2) > 0, 2 = 0
The Lagrangian (L) form of the problem is : Maximize: L = 47.5Q1 – (Q1)2 + 40Q2 - 0.5(Q2)2 - 45Y + 1(2Y - Q1) + 2(3Y - Q2) Subject to: Q1, Q2, Y, 1, 2 > 0
P5.6. Solution (continued) First Order Conditions are: ∂L/∂Q1 = 47.5 - 2Q1 - 1 = 0 ===> 1 = 47.5 - 2Q1 ∂L/∂Q1 = 40 - Q2 - 2 = 0 ===> 2 = 40 - Q2 ∂L/∂Y = - 45 + 21 + 32 = 0 ∂L/∂1 = 2Y - Q1 = 0 ===> Q1 = 2Y ∂L/∂2 = 3Y - Q2 = 0 ===> Q2 = 3Y 1 = 47.5 - 4Y 2 = 40 - 3Y - 45 + 95 - 8Y = 120 - 9Y = 0 ===> Y = 10, Q1 = 20, Q2 = 30, 1 = 7.5, 2 = 10 P1 = 47.5 - Q1 ===> P1 = $27.50 P2 = 40 - 0.5Q2 ===> P2 = $25.00
P5.7. Solution Sales Level
Sales Price
Input Material
Q1 ≤ 0.2Y
P1 = 100 – 0.25Q1 ≤
Y units @ $50/unit
Q2 ≤ 0.1Y
P2 = 300 – 5Q2
Q3 ≤ 0.4Y
P3 = 50 – 0.25Q3 ≤
TR = P1Q1 + P2Q2 + P3Q3 = (100 - 0.25Q1)Q1 + (300 – 5Q2)Q2 + (50 - 0.25Q3)Q3 TC = 50Y max s.t.
Z(Q1, Q2, Q3) = 100Q1 - 0.25(Q1)2 + 300Q2 - 5 Q2)2 + 50Q3 - 0.25 Q3)2 - 50Y Q1 ≤ 0.2Y choose 1 so that =====> 1(0.2Y - Q1) = 0 Q2 ≤ 0.1Y choose 2 so that =====> 2(0.1Y - Q2) = 0 Q3 ≤ 0.4Y choose 3 so that =====> 3(0.4Y - Q3) = 0 Q1, Q2, Q3, Y ≥ 0
Lagrangian Form of the Problem: max L(Q1, Q2, Q3, Y, 1, 2, 3) = 100Q1 - 0.25(Q1)2 + 300Q2 - 5(Q2)2 + 50Q3 - 0.25(Q1)2 - 50Y + 1(0.2Y-Q1) + 2(0.1Y-Q2) + 3(0.4Y-Q33) s.t. Q1, Q2, Q3, Y, 1, 2, 3 ≥ 0
P5.7. Solution (continued) The first order partial derivatives are as follows: 1) L/Q1 = 100 - 0.5Q1 - 1 = 0 2) L/Q2 = 300 - 10Q2 - 2 = 0 3) L/Q3 = 50 - 0.5Q3 - 3 = 0 4) Z = -50 + 0.21+ 0.12 + 0.43 = 0 Y Z = 0.2Y - Q = 0 ==> Q = 0.2Y 5) 1 1 1 Z = 0.1Y - Q = 0 ==> Q = 0.1Y 6) 2 2 2 7) Z = 0.4Y - Q3 = 0 ==> Q3 = 0.4Y 3 100 - 0.1Y - 1 = 0 ==> 1 = 100 - 0.1Y 300 - Y - 2 = 0 ==> 2 = 300 - Y 50 - 0.2Y - 3 = 0 ==> 3 = 50 - 0.2Y -50 + 0.2(100 - 0.1Y) + 0.1(300 - Y) + 0.4(50 - 0.2Y) = 0 20-.2Y = 0 ==>Y = 100 units Y = 100 units of the input material 1 = 100 - 0.1(100) = $90 per units of Product 1 2 = 300 - (100) = $200 per units of Product 2 3 = 50 - 0.2(100) = $30 per units of Product 3 Q1 = 0.2(100) = 20 units Q2 = 0.1(100) = 10 units Q3 = 0.4(100) = 40 units P1 = 100 - 0.25(20) = $95 P1 = 300 - 0.25(10) = $250 P1 = 50 - 0.25(40) = $40
P5.8. Solution Q1 = 200 – 0.8P1,
======> P1 = 250 - 1.25Q1
Q2 = 40 – 0.4P2,
======> P2 = 100 - 2.5Q2
2 Q3 = 800 3 - 3 P3
======> P3 = 400 - 1.5Q3
C = 50 + 60 = $110 per unit of the input material. The followings are the total revenue (TR) and total cost (TC): TR = P1Q1 + P2Q2 + P3Q3 = (250 - 1.25Q1)Q1 + (100 - 2.5Q2)Q2 + (400 - 1.5Q3)Q3 TC = 110Y The problem is formulated as follows: max s.t.
Z(Q1, Q2, Q3) = 250Q1 - 1.25(Q1)2 + 100Q2 - 2.5(Q2)2 + 400Q3 - 1.55(Q3)2 - 110Y Q1 ≤ Y Q2 ≤ 0.5Y Q3 ≤ 1.5Y Q1, Q2, Q3, Y ≥ 0
Now, choose the Lagrabgian multipliers 1, 2 and 3 so that: 1(Y - Q1) = 0 2(0.5Y - Q2) = 0 3(1.5Y - Q3) = 0 The Lagrangian Form of the problem: Max s.t.
L(Q,Y, ) = 250Q1 - 1.25(Q1)2 + 100Q2 - 2.5(Q2)2 + 400Q3 - 1.5(Q3)2 - 110Y + 1(Y - Q1) + 2(0.5Y - Q2) + 3(1.5Y - Q3) Q1, Q2, Q3, Y, 1, 2, 3 ≥ 0
The followings are the first order partial derivatives: 1) 2) 3) 4) 5) 6) 7)
L/Q1 = 250 - 2.5Q1 - 1 = 0 L/Q2 = 100 - 5Q2 - 2 = 0 L/Q3 = 400 - 3Q3 - 3 = 0 L/Y = -110 + 1+ 0.52 + 1.53 = 0 L/1 = Y - Q1 = 0 ==> Q1 = Y L/2 = 0.5Y - Q2 = 0 ==> Q2 = 0.5Y L/3 = 1.5Y - Q3 = 0 ==> Q3 = 1.5Y
P5.8. Solution (continued) 250 - 2.5Y - 1 = 0 ==> 1 = 250 - 2.5Y 100 - 2.5Y - 2 = 0 ==> 2 = 100 - 2.5Y 400 - 4.5Y - 3 = 0 ==> 3 = 400 - 4.5Y - 110 + (250 - 2.5Y) + 0.5(100 - 2.5Y) + 1.5(400 - 4.5Y) = 0 790 - 10.5Y = 0 ==>Y = 75.238 units Y = 75.238 units 1 = 250 - 2.5(75.238) = 61.905 2 = 100 - 2.5(75.238) = -88.095 < 0 not acceptable (Product 2 is a by-product) 3 = 400 - 4.5(75.238) = 61.429 Since 2 = -88.095 < 0, we arbitrary set 2 = 0 and redo the calculations, as follows: 1) 2) 3) 4) 5) 6) 7)
L/Q1 = 250 - 2.5Q1 - 1 = 0 L/Q2 = 100 - 5Q2 = 0 ==========> Q2 = 20 units L/Q3 = 400 - 3Q3 - 3 = 0 L/Y = -110 + 1+ 0.52 + 1.53 = 0 L/1 = Y - Q1 = 0 ==> Q1 = Y Deleted L/3 = 1.5Y - Q3 = 0 ==> Q3 = 1.5Y
250 - 2.5Y - 1 = 0 ==> 1 = 250 - 2.5Y 400 - 4.5Y - 3 = 0 ==> 3 = 400 - 4.5Y - 110 + (250 - 2.5Y) + 1.5(400 - 4.5Y) = 0 740 - 9.25Y = 0 ==>Y = 80 units Optimal Amount of Input Material: Y = 80 units Shares of Joint Costs: 1 = 250 - 2.5(80) = $50 per unit of Product 1 2 = $0 per unit of Product 2 (Product 2 is a by-product) 3 = 400 - 4.5(80) = $40 per unit of Product 3 Sales Volumes: Q1 = Y = 80 units of Product 1 should sold Q2 = 20 units of Product 2 should sold (of 40 units produced), and the rest discarded. Q3 = 1.5Y = 120 units of Product 3 should sold Sales Prices: P1 = 250 - 1.25(80) = $150 P1 = 100 - 2.5(20) = $50 P1 = 400 - 1.5(120) = $220
P5.9. Solution No Joint Cost to the By-Product.
Total joint cost (to be allocated to the main products) = $34.50/unit x 20,000 units = $690,000 Sales Products Price
Production units
Separable Cost/unit
Relative Market Value at S.O.P
Proportion
A
$200
5,000
$30
(200-30)5,000 = $850,000
42.5%
B
$110
11,500
$10
(110-10)11,500= $1,150,000
57.5%
Joint Cost to be Allocated
$690,000 Totals
$2,000,000
Product
Share of Joint Cost
Joint Cost per unit
Separable Cost/unit
Manufacturing unit cost
A B BP
$293,250 396,750 0
$58.65 34.50 0.00
$30.00 10.00 2.50
$88.65 44.50 2.50
100%
$690,000
Chapter 6: Estimating Cost Functions Answers to Review Questions R6.1. A: Estimation is prediction or forecast of resources (time, cost and materials) required to achieve or obtain an agreed upon scope of a project or a volume of a product. R6.2. A: It is an indication of the degree to which the final cost outcome for a given project will vary from the original estimate cost. R6.3. It is an amount added to an estimate to allow for items, conditions or events for which the state occurrence or effect is uncertain and that experience shows will likely result in additional costs. R6.4. It is an algorithm or formula that is used to perform the costing operation. CER’s relate (Cost, Time, and Quantity) with quantity scope, execution strategies or other defining elements. . R6.5. A regression line intercepts the Y-axis at the fixed level. R6.6
The account analysis approach requires that an experienced cost analyst to review the cost accounts and determine whether the costs in each account are fixed or variable. Then, the sum of all costs identified as fixed will be the estimate of total fixed costs. To determine the variable cost per unit, the sum of all costs identified as variable is divided by the measure of activity (e.g., number of units).
R6.7. The high-low method uses the historical data during several reporting periods; but, it uses only the data points corresponding to the highest and lowest levels of activity (output) to derive the algebraic equation for the total cost. The slope of the resulting equation is the variable cost and its y-intercept is the fixed cost. It ignores all other data points than the two extremes ones. R6.8. Account analysis method of cost estimation is used to classify cost accounts as fixed or variable with respect to specific output level. AR6.9. When the cost is constant (fixed) the slope coefficient of a cost function equal to zero.
Chapter 6: Problem Solutions P6.1: Solution a) F = $270,000 (total fixed cost) V = $810,000 / 7,500 unit = $108 per unit C = $270,000 + $108Q Total cost model, where Q is the production units. b) Using the equation in part (a), C = $270,000 + $108(8,000) = $1,134,000 (total production cost of 8,000 units)
P6.2: Solution a) Fixed cost = F = $162,000. Variable cost = V = $408,000 / 7,000 units = $58.29 per unit. The total cost equation: C = $162,000 + $58.29X. b) In the cost equation derived in part (a), substitute 8,000 units for Q, as follows: C = $162,000 + $58.29(8,000) = $628,320 Total production cost is estimated to be $628,320 in July.
P6.3: Solution Cost A is variable as it remains constant on per unit basis. TCB(10,000) = 10,000($12.00) = $120,000 TCB(20,000) = 20,000($8.50) = $170,000 Cost B is mixed cost per unit, as neither the per-unit cost nor the total is constant. TCC(10,000) = 10,000($15.00) = $150,000 TCC(20,000) = 20,000($7.50) = $150,000 Cost C is fixed cost per unit, as the total remains constant
P6.4: Solution V = (70,000 – 45,000) / (10,000 – 5,000) = $25,000 / 5,000 = $5 per unit Using either the high point or low point, total fixed cost is calculated next: F = TC(5,000 units) – VC(5,000 units) = $45,000 - $5(5,000) = $20,000 TC = $20,000 + $5Q
P6.5: Solution a) Variable cost per activity unit = (Change in cost)/(Change in Activity) V = (136,700 – 5109,700) / (15,500 – 10,500) = $5.40/unit Using either the high point or low point, total fixed cost is calculated next: F = 136,700 - $5.40(15,500) = $53,300 OR F = 109,700 - $5.40(10,500) = $53,300 TC = $53,300 + $5.40Q b) For the activity level of 15,000 units, the total cost is estimated to be: TC(15,000 = $53,300 + $5.40(15,000) = $134,300
P6.6: Solution a) Variable Cost Rate (Slope) = =
Change in Total Cost Change in Activity Level $13,550 − $11,100 $2,450 11,500 − 8,000
=
3,500
= $0.70 variable cost per unit
Using either the high point or low point, total fixed cost is calculated next: Fixed Cost = Total Cost – Total Variable Cost Fixed Cost (8,000) = $11,100 - $0.70(8,000) = $5,500 OR Fixed Cost (11,500) = $13,550 - $0.70 (11,500) = $5,500 The equation is: TC = $5,500 + $0.70Q or Y = $5,500 + $0.70X b) Total Cost = Fixed Cost + Total Variable Cost TC = $5,500 + $0.70(12,000) Total Cost = $5,500 + $8,4000 = $13,900
P6.7: Solution a) High-Low Method High Point: 4,900 machine hours Total Cost = $5,195 Low Point: 6,500 machine hours Total Cost = $6,075 Variable Cost Rate (Slope) =
Change in Total Cost Change in Activity Level $6,075 − $ 5,195
=
6,500− 4,900
= $0.55 per hour
Using either the high point or low point, total fixed cost is calculated next: Fixed Cost = Total Cost – Total Variable Cost Fixed Cost (6,500) = $6,075 - $0.55(6,500) = $2,500 The equation is: C = $52,500 + $0.55Q or Y = $2,500 + $0.55X
P6.7: Solution (continued) b) Regression Method Month January February March April May June Sum
X Hours 5,000 5,200 4,900 5,600 5,200 6,500 32,400
Y Cost $5,200 $5,335 $5,195 $5,595 $5,400 $6,075 32,800
X2 Hrs-Square $25,000,000 $27,040,000 $24,010,000 $31,360,000 $27,040,000 $42,250,000 176,700,000
XY Hrs × Cost
$26,000,000 $27,742,000 $25,455,500 $31,332,000 $28,080,000 $39,487,500 178,097,000
Plug the summation terms into the regression equations, as follows: b=
𝑛(∑ 𝑋𝑌) − (∑ 𝑋)(∑ 𝑌) 𝑛(∑ 𝑋 2 ) − (∑ 𝑋)2
=
6(178,097,000) − (32,400)(32,800) 6(176,700,000)− (32,400)2
= 0.56149
a = 𝑌̅ - b𝑋̅ = (32,800/6) - 0.56149 (46,700/12) = 2,423.5977 $2,425 The total cost estimating equation will then be: C = $2,425 + $0.5615Q
Chapter 7: Cost-Volume-Profit Analysis Review Questions: Answers R7.1 Answer 1) volume or level of activity, 2) unit selling prices, 3) variable cost per unit, 4) fixed costs. R7.2.
The CVP income statement classifies costs as variable or fixed.
R7.3. The contribution margin ratio is the difference between the sales price and the variable cost of product divided by the sales price and expressed in a percentage of sales. It is useful in planning business operations as it is a key component of the cost-volumeprofit analysis to examine the effects of changes in sales volumes, sales prices, and costs on the profit of a business. R7.4. The breakeven point can be calculated by. - Graphical method as the intersection of the revenue curve and the total cost curve; - Setting total revenue equal to total costs; - Setting the CVP equation equal to zero. R7.5. Breakeven Quantity = Fixed Costs / Contribution Margin Per Unit QBE = F / (P – V) R7.6. Breakeven Sales Dollars = Fixed Costs / Contribution Margin Ratio BE Sales $ = F / CMR R7.7
Required Sales = Variable Costs + Fixed Costs + Target Profit. Another formula is; Required Sales = (Fixed Costs + Target Profit) / (Contribution Margin Ratio)
R7.8
Margin of safety is the difference between actual (or expected) sales and sales at the breakeven point. The formulas for margin of safety are: - Margin of Safety in Dollars = Actual (Expected) Sales - Breakeven Sales and - Margin of Safety Ratio = (Margin of Safety in Dollars) / [Actual (Expected) Sales].
R7.9
The sales mix is the relative proportion in which each product is sold when a company sells two or more different products. For a multi-product company, breakeven sales in units is determined by using the weighted-average unit contribution margin of all the products.
R7.10. The contribution margin is the difference between the revenue and variable costs. The contribution margin is the portion of revenue available to cover the company's fixed costs. The contribution margin is an important factor to consider when determining a company's breakeven point. It is computed using the following formula:
Contribution Margin = Revenue − Variable Costs The margin of safety is the difference between the actual (estimated) sales and the breakeven sales. It is a measure of the extent to which the sales can drop before a firm incurs a loss. It is computed using the following formula:
Margin of Safety = Actual Sales − Breakeven Sales R7.11. Gross Profits = Sales Revenues Less Costs of Goods Sold. Gross Profits Less Operating Expenses (Selling, Administrative, Depreciation) = Operating Profits [Operating Profits] plus [Miscellaneous Income (royalties, interest income, capital gains)] less [Miscellaneous Expenses (interest expense) and Income Taxes] = Net Profit. Sales Revenue Less: Cost of Goods Sold Gross Profit Less: Operating Expenses Selling Expenses Administrative Expenses Depreciation Expense Total Operating Expenses Operating Income (Profit) Add: Misc. Income (Royalties, Capital Gains & Earned Interests and Dividends) Less: Interest Expense and Fees Net Income, Before Income Taxes Income Taxes Profit (Net Income)
xxx (xxx) xxx xxx xxx xxx (xxx) xxx xxx (xxx) xxx (xxx) xxx
R7.12. Within the relevant range, the break-even point does not change. This is due to the linearity assumptions that apply to total revenues, fixed costs, and variable costs.
R7.13. The margin of safety gives decision-makers an idea of the extent to which sales can fall before operations will become unprofitable.
R7.14. Since there is no variable cost (only fixed costs), the marginal cost (MC) will be zero (MC = 0). Then, to maximize profit, set MR = MC, i.e., 1,200 – 0.4Q* = 0 → Q* = 1,200/0.4 = 3,000 units. Q = 6000 - 5P → P = 1,200 – 0.2Q → P* = 1,200 – 0.2(3,000) = $$600
Chapter 7 Problem Solutions P7.1: Solution a) 0 = $48QBE - $48,000 QBE = $48,000/$48 = 1,000 units b)
Z = ($90,000 + $48,000) = $48Q* - $48,000 Q* = $138,000/$48 = 2,875 units
P7.2: Solution a) Computing the breakeven point in sales dollars: Contribution Margin Ratio (CMR) = (P – V) / P = ($40 - $15) / $40 = 0.625 = 62.5% Breakeven in Sales Dollars = (Fixed Cost)/(Contribution Margin Ratio) Breakeven Point in dollars = F/CMR BE $ = $125,000 / 0.625 = $200,000 b) Finding expected margin of safety: Margin of Safety = Expected Sales - Breakeven Sales Expected Sales = $40(8,000) = $320,000 Breakeven Sales Dollars = $200,000 Margin of Safety (MOS) = $320,000 - $200,000 = $120,000 MOS % = $120,000 / $320,000 = 0.375 = 37.5% c) Computing the operating leverage: Operating Leverage = (Contribution Margin) / (Contribution Margin – Fixed Costs)
OL = $25(8,000) / [$25(8,000) - $125,000] = 2.67 = 267% d) Q* = (Fixed Costs + Target Profit) / (Contribution Margin Per Unit) Q* = ($100,000 + $125,000) / $25 = 9,000
P7.3: Solution a) Finding the breakeven sales dollars: Contribution Margin Ratio (CMR) = (P - V) / P Contribution Margin Ratio (CMR) = ($80 - $48) / $80 = 0.4 = 40% Breakeven in Sales Dollars = (Fixed Cost)/(Contribution Margin Ratio) Breakeven in Sales Dollars = $240,000 / 0.40 = $600,000 b)
Find current margin of safety: Expected Sales Income = $80(10,000) = $800,000 Margin of Safety = Expected Sales – Breakeven Sales Margin of Safety = $800,000 – $600,000 = $200,000 Margin of Safety % = $200,000 / $800,000 = 0.25 = 25%
c)
Computing number of units needed to produce to achieve $144,000 target profit: Q* = (Fixed Costs + Target Profit) / (Contribution Margin Per Unit) Q* = (240,000 + $144,000) / $32 = 12,000 units
P7.4: Solution TR = P.Q (Total Revenue) P = 300 - 3Q TR(Q) = (300 - 3Q).Q = 300Q - 3Q2 a) To maximize revenue set MR(Q) = 0, that is, TR'(Q) = MR(Q) = 300 - 6Q = 0 ====> Q = 50 units So maximum revenue is: TR(50) = 300(50) - 3(50)2 = $7,500 b) To maximize profit set the marginal revenue equal to marginal cost; that is, MR(Q) = MC(Q). MC(Q) = TC'(Q) = 60 - 6Q + 0.6Q2 300 - 6Q = 60 - 6Q + 0.6Q2 ========> Q = 20 units Then, the maximum profit is found as follows Z(20) = TR(20) - TC(20) = [300(20) -3(20)2] - [200+ 60(20)- 3(20)2 +0.2(20)3] = $3,000 c) P = 300 - 3(20) = $240
P7.5: Solution Contribution Margin per unit per unit per Pi - Vi hour machine time $9 $ 2.25 15 (b) 2.50 12 3.00 (a)
Product (i) Product 1 Product 2 Product 3
a) Product 3 is most profitable because it has the highest contribution margin per machine hour. b) Product 2 is most profitable because it has the highest contribution margin per unit. c) Formulating the problem for linear programming to maximize the profit: Maximize: Z =
9Q1 + 15Q2 + 12Q3
Subject to:
4Q1 + 6Q2 + 4Q3 ≤ 40,000 Q1 + 3Q2 + 2Q3 ≤ 24,000 Q1, Q2, Q3 ≥ 0.
P7.6: Solution Sales price and variable cost per unit Product A Product B Sales price $ 15.75 $ 21.00 Materials cost / unit $ 3.40 $ 4.25 Direct labor / unit 2.20 3.30 Variable overhead / unit 1.50 2.50 Total variable cost per unit $ 7.10 $ 10.05 Contribution margin per unit $ 8.65 $ 10.95 Fixed Costs: Product A Product B Total $ 150,000 + $ 200, 000 = $ 350,000 325,000 50,000 $ 725,000
Fixed Overhead Fixed Selling & Administrative + Increase in Advertising Total Fixed Cost Product
Pi
Vi
A
$ 15.75
$ 7.10
B
21.00
10.05
Total Fixed Cost $ 725,000
In 1985: QA = 750,000 / 15 = 50,000 units QB = 2,250,000 / 22.50 = 100,000 units
P7.6: Solution (continued)
(a)
So, the sales mix is QB = 2QA Z = (15.75 - 7.10)QA + (21 - 10.05)QB - 725,000 = 8.65QA + 10.95(2QA) - 725,000 = 30.55QA - 725,000 To break even , we set Z = 0. Then, we find the following break-even quantities: QA,BE = 23,731.6 units QB,BE = 47,463.2 units
(b)
Net income before taxes is Z* = 900,000 = 30.55QA - 725,000 if solved for QA, it gives 𝑄A∗ = 53,191.5 units Then, 𝑄B∗ = 2𝑄A∗ = 106,383 units
(c)
Z* = 300,000/0.3 = 1,000,000 = 30.55QA - 725,000 We find 𝑄A∗ = 56,464.8 units, and 𝑄B∗ = 2(56,464.8) = 112,929.6 units.
P7.7: Solution Palmon Company Budgeted Income Statement (CM Format) For the Year 20XX Per Unit
Total
Sales (180,000 units)
$ 5.00
$900,000
Variable Costs: Direct Materials Direct Labor Factory Overhead (Variable) Sales Commission (10% of Sales) Shipping Administrative Expenses Total Variable Cost & Expenses
$ 1.50 1.25 0.20 0.50 0.05 0.09 $ 3.59
$270,000 225,000 36,000 90,000 9,000 16,200 $646,200
Contribution Margin
$ 1.41
$253,800
Fixed Costs & Expenses: Factory Overhead (Fixed) Advertising, Salaries, etc. Administrative (Fixed) Total Fixed Costs
$ 95,000 120,000 26,000 $241,000
Net Income Before Taxes
$ 12,800
The CVP model will be Z = $1.41Q - $241,000.
P7.8: Solution Contribution margin is a key input for decision making about which product to produce, how much to produce, how to allocate limited resources. Total machine hours available per year = 2(7)(5)(50) = 3,500 hours. That is, the company’s production is limited by the available 3,500 machine-hours. Therefore. company should decide on how to use the limited machine-hours to maximize its total contribution margin. This means the product that generates a higher contribution margin per machine hour would have a higher priority to be produced first. Computation of contribution per machine hour: Selling price (per unit) Variable cost (per unit) Contribution margin per unit Units that can be produced per machine hour on the same production line Estimated demand (units) Contribution margin per machine hour (a) $30(10) = $300 per machine hour (b) $25(6) = $150 per machine hour
Product A $60 $30 $30
Product B $35 $10 $25
10 15,000 $300(a)
6 22,000 $200(b)
Machine hours consumed in producing Product A = 15,000 / 10 = 1,500 hours Machine hours remained for producing Product B = 3,500 – 1,500 = 2,000 hours Machine hours needed to producing 22,000 units of Product B = 22,000 / 6 = 3,667 hours Thus, the company can devote only 2,000 machine hours for producing Product B, by which it can produce 2,000(6 units/hour) = 12,000 units of Product B.
P7.9: Solution a) Developing the CVP Model. Q = 375 – 0.05P → P = -$20Q + $7,500 TR = PQ = (-20Q + 7,500)Q = - 20Q2 + 7,500Q (total revenue equation) TC = $240Q + $169,000 (total cost equation) Z = - $20Q2 + $7,260Q - $169,000 (the CVP model)
P7.9: Solution (continued) b) Computing the breakeven quantity(ies). To break even, set Z = 0 and solve the CVP equation for QBE as follows: Z = - $20(QBE)2 + $7,260QBE - $169,000 = 0 QBE =
−7,260 ± √(7,260)2 −4(−20)(−169,000) 2(−20)
QBE = 181.5 ± 156.5 QBE1 = 25 units and QBE2 =338 units c) Determining the selling price that maximizes the company’s monthly profit. To maximize profit set the derivative of profit (CVP) function equal to zero: Z’ = -40Q + 7,260 = 0 → Q* = 181.5 units P* = -$20(181.5) + $7,500 = $3,870 d) Computing the company’s monthly maximum profit. Z* = - $20(181.5)2 + $7,260(181.5) - $169,000 = $489,845
P7.10: Solution a) Fixed Cost = $15,000 + $18,000 = $33,000 Variable Cost = $3 + $4 = $7 per unit Z = (P – V)Q – F $45,000 = (P - $7)(15,000) - $33,000 (P - $7) = ($45,000 + $33,000)/15,000 = $5.20 P = $12.20 Sales Price per unit b) Sales Dollars = $12.50(16,000) = $200,000 TC = $7(16,000) + $33,000 = $145,000 BE Sales = Total Cost = $145,000 Margin of Safety = Sales – Breakeven Sales = $200,000 - $145,000 = $55,000 MOS % = $55,000/$200,000 = 0.275 = 27.5% CM = ($12.50 - $7)(16,000) = $88,000 Operating Income = CM – F = $88,000 – $33,000 = $55,000 Degree of Operating Leverage = CM/OI = $88,000/$55,000 = 1.6 = 160%
P7.11: Solution Before Tax Income: $90,000 / (1 - 0.25) Fixed Costs: Contribution Margin: Projected Sales: $10(125,000) less: Contribution Margin Variable Costs
$120,000 $500,000 $620,000 $1,250,000 620,000 $630,000
Variable Cost = $630,000 / 150,000 units = $4.20 per unit
P7.12 (a): Solution Contribution Margin: P – V = $15 - $6 = $9 per unit $9Q* - $335,000 = $250,000 $9Q* = $585,000 Q* = 65,000 units P7.12 (b): Solution Contribution Margin (CM) = ($15 - $6)(65,000 units) = $585,000 Operating Income (OI) = $585,000 - $335,000 = $250,000 Degree of Operating Leverage (DOL) = CM/OI = ($585,000/250,000) = 2.34 = 234%
