1. Why do managers frequently prefer variable costing to absorption costing for internal use?
ANSWER: Managers may prefer variable costing because it classifies costs both by their function and their behavior. When costs are classified by behavior, managers can more accurately predict how total costs will change when volume changes. With more accurate information, managers can make better production and pricing decisions.
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2. Why is variable costing not used extensively in external reporting?
ANSWER: Variable costing is not used extensively outside of the firm because absorption costing is required by GAAP and the IRS.
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3. How can a company produce both variable and absorption costing information from a single accounting system?
ANSWER: Firms only have one accounting information system. This system will be based on either variable or absorption costing. If the system needs to provide information in both the variable and absorption formats, the system’s accounting information can be converted from one format to the other. The conversion requires an adjustment to the product inventory accounts and the amount of product costs charged against the period’s income. The conversion is typically easier if standard costing is employed.
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4. What are the major differences between variable and absorption costing?
ANSWER: The major difference between variable costing and absorption costing is in the way each defines product cost. While absorption costing includes fixed manufacturing overhead as a product cost, variable costing treats it as a cost of the period. A secondary difference between the two methods is the format of the income statement. Absorption costing utilizes the traditional income statement format that categorizes costs by their function only. Variable costing uses an income statement format that categorizes costs by both their function and behavior.
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5. Why is absorption costing not used for CVP analysis?
ANSWER: Absorption costing is not used in break-even analysis because it presents a classification of costs by function rather than by behavior. Without a behavioral
classification of costs, it is impossible to predict how total costs change as volume changes.
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6. How do changes in volume affect the break-even point?
ANSWER: 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.
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7. What major assumption do multiproduct firms need to make in using CVP analysis that single-product firms need not make?
ANSWER: The assumption that must be imposed is a constant sales mix. A
multiproduct firm assumes that (within the relevant range) the sales mix is constant. This permits CVP analysis to be performed using a unit of the constant sales mix.
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8. What important information is conveyed by the margin of safety calculation in CVP analysis?
ANSWER: The break-even point in CVP analysis is critical because it divides
profitable levels of operation from unprofitable levels of operation. The margin of safety gives managers an idea of the extent to which sales can fall before operations will become unprofitable.
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Use the following information for questions 9–11.
Limpin Co. manufactures and sells walking canes. The following income statement applies to 2001, its first year of operations:
Sales (800 units @ $15) $12,000
Cost of Goods Sold (8,000)
Gross Margin $ 4,000
Selling, general, and administrative expenses (3,000 )
Operating income $ 1,000
Other information:
1. The company produced 1,000 units during the year.
2. Variable SG&A expenses are $1 per cane.
3. Variable production costs are $7 per cane.
4. There was no ending work-in-process inventory.
9. How much fixed manufacturing overhead did the Limpin Co. incur in 2001?
ANSWER: The Cost of Goods Sold is based on sales of 800 units and is recorded at
$8,000. This $8,000 is comprised of $5,600 of variable product costs ($7 × 800).
Therefore, $2,400 of the Cost of Goods Sold is fixed. Given that the firm sold 80 percent of its output (800/1,000), $2,400 must be 80 percent of the total fixed manufacturing overhead incurred. This sets the total fixed manufacturing overhead costs incurred at
$3,000.
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10. What were the total variable costs incurred in 2001?
ANSWER: The total variable product costs would be $5,600/.80 = $7,000. The total variable SG&A would be $1 × 800 =$800. Total variable costs incurred are $7,000 + $800
= $7,800.
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11. If the Limpin Co. adopted variable costing, the ending finished goods inventory for 2001 would be carried at what value?
ANSWER: The answer is 200 units × $7 = $1,400.
EASY
Use the following information for questions 12–14.
The Crown Co. manufactures toasters. The company hired a cost accountant in its first year of operations, 2001, to explain to management how its costs behaved. After studying various documents and industry data, the cost accountant announced that the total SG&A expenses that the firm can expect to incur in any period is captured by the equation: Y = $50,000 + $10X, where Y is the total SG&A expense incurred and X is the number of units sold. Also, the
accountant announced that the total product costs incurred in any period could be captured by the formula Y = $100,000 + $6X, where Y is the total manufacturing cost incurred and X is the number of units produced. In 2001, the firm produced 10,000 units and sold 9,000 of them at $35 each.
12. According to the accountant’s equations, what would be the total of all costs incurred by the firm in 2001?
ANSWER: Total production costs are based on the number of units produced and would be: (10,000 × $6) + $100,000 = $160,000. Total period costs would be based on the number of units sold and would be: (9,000 × $10) + $50,000 = $140,000. The total of all costs would be $160,000 + $140,000 = $300,000.
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13. If the firm’s costs conformed exactly to the accountant’s equations, how much income before income taxes would be reported for 2001 if the firm uses absorption costing?
ANSWER:
Sales ($35 × 9,000) $315,000
Cost of Goods Sold:
Beg. fin. goods inventory $ 0 Cost of Goods Manufactured 160,000
Goods available $160,000
Ending inventory (16,000)
Cost of Goods Sold (144,000 )
Gross margin $171,000
Less period costs (140,000 )
Income before income taxes $ 31,000
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14. If the firm’s costs conformed exactly to the accountant’s equations, how much income before income taxes would be reported for 2001 if the firm uses variable costing?
ANSWER:
Sales $315,000
Less variable costs:
Product costs ($6 × 9,000) $54,000
Period costs ($10 × 9,000) 90,000 (144,000 )
Contribution margin $171,000
Less fixed costs:
Product costs $100,000
Period costs 50,000 (150,000)
Income before income taxes $ 21,000
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15. Stanley Corp. produces a single product. The following is a cost structure applied to its first year of operations, 2001:
Sales price $15 per unit
Variable costs:
SG&A $2 per unit
Production $4 per unit
Fixed costs (total cost incurred for the year):
SG&A $14,000
Production $20,000
During 2001, Stanley Corp. manufactured 5,000 units and sold 3,800. There was no beginning or ending work-in-process inventory.
a. How much income before income taxes would be reported if Stanley uses absorption costing?
b. How much income before income taxes would be reported if variable costing was used?
c. Show why the two costing methods give different income amounts.
ANSWER:
a. Income under absorption costing is:
Sales $15 × 3,800 = $57,000
Absorption income before income taxes $ 5,000 b. Income under variable costing:
CMU = SP – VProd.Cost – VSGA = $15 – $4 – $2 = $9
×Vol. sold 3,800
CM $34,200
Less: FC – Production (20,000)
SG&A (14,000 )
Variable costing income before income taxes $ 200 c. Reason for difference in income:
Fixed costs expensed under absorp. costing
COGS 3,800 × $20,000/5,000 units $15,200
Fixed SG&A 14,000
Total $29,200
Fixed costs expensed under variable costing
Fixed SG&A $14,000
Fixed Production 20,000
Total FC $34,000
Difference in FC expensed under two methods $ 4,800 This is also the difference in income amounts.
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Use the following information for questions 16 and 17.
Information relating to the 2001 operations of McNickle Corp. follows:
Sales $120,000
Variable costs (36,000 ) Contribution margin $ 84,000
Fixed costs (70,000 )
Profit before taxes $ 14,000
16. McNickle’s break-even point for 2001 was 1,000 units. Compute McNickle’s sales price per unit.
ANSWER: The break-even point is found by dividing the fixed costs by the CM ratio.
The CM ratio is:
$84,000/$120,000 = 70%. Breakeven would then be:
$70,000/.70 = $100,000. Since we also know that the break-even point is defined as 1,000 units, it must follow that the unit sales price is $100,000/1,000 = $100.
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17. Compute McNickle’s degree of operating leverage for 2001.
ANSWER: The degree of operating leverage is computed as the contribution margin divided by profit before taxes: $84,000/$14,000 = 6.
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Use the following information for questions 18 and 19.
Dos Co. manufactures and sells 2 products: A and B. The projected information on these two products for 2002 is:
Product A Product B
Sales in units 4,000 1,000
Sales price per unit $12 $8
Variable costs per unit 8 4
Total fixed costs for the company are projected at $10,000.
18. Compute Dos Co.’s projected break-even point for 2002 in total units.
ANSWER: The company anticipates a sales mix consisting of 4 units of Product A and 1 unit of Product B. The total contribution margin for one unit of sales mix would be $20.
This consists of $16 of contribution margin from the 4 units of Product A and $4 of contribution margin from 1 unit of Product B.
The overall company breakeven is found by dividing total fixed costs by the contribution margin on one unit of sales mix: $10,000/$20 = 500 units. The 500 units of sales mix contain 500 × 5 units of product for a total of 2,500. Of the 2,500 total units, 2,000 are units of Product A and 500 are units of Product B.
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19. How many units would the company need to sell to produce an income before income taxes equal to 15 percent of sales?
ANSWER: Again, using a unit of sales mix as the unit of analysis, one unit of sales mix sells for $56. Since the contribution margin is $20 on one unit of sales mix, the CM ratio on one unit of sales mix is $20/$56 = .3571. This implies that variable costs as a
percentage of sales are equal to 1 – .3571 = .6429. Income before income taxes equal to 15 percent of sales can be found by solving a formula of the following type:
Sales – VC – FC = Income before income taxes In this particular case, we solve the following formula:
Sales – (.6429 × Sales) – $10,000 = (.15 × Sales)
Solving for Sales, we get $48,286. We can find out how many units of sales mix are required to generate sales of $48,286 by dividing $48,286 by $56 = 863. These 863 units of sales mix each contain 5 units of product, so the correct answer would be 863 × 5 = 4,315 units of product, 3,452 of Product A and 863 of Product B.
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Use the following information for questions 20 and 21.
P Corp. predicts it will produce and sell 40,000 units of its sole product in 2001. At that level of volume, it projects a sales price of $30 per unit, a contribution margin ratio of 40 percent, and fixed costs of $5 per unit.
20. What is the company’s projected breakeven for 2001 in dollars and units?
ANSWER: Given the CM ratio of 40 percent, and the Sales price per unit of $30, the CM per unit must be $30 × .40 = $12. The total fixed costs would be projected at $5 × 40,000 = $200,000. Breakeven would be: $200,000/$12 = 16,667 units. This would also equate to $500,000 of sales.
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21. What would the company’s projected profit be if it produced and sold 30,000 units?
ANSWER:
Projected profit would be:
Sales (30,000 × $30) $900,000
Variable costs (30,000 × $18) (540,000 )
Contribution margin $360,000
Fixed costs (200,000 )
Profit $160,000
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Questions 22 and 23 are based on the following data pertaining to two types of products
Fixed costs total $300,000 annually. The expected mix in units is 60 percent for Product Y and 40 percent for Product Z.
22. How much is Korn’s break-even point sales in units?
ANSWER:
BEP units = FC/(unit SP – unit VC) or unit CM(UMC)
For multiple products, use the weighted CM with weights based on units of sales weights.
BEP = FC / [60% ($120 – $70) + 40% ($500 – $200)]
= $300,000/ ($30/u + $120/u) = 2,000 units MEDIUM
23. What are Korn’s break-even point sales in dollars?
ANSWER:
BEP dollars = FC/CMR
For multiple products, use weighted CMR with weights based on sales dollars as weights or sales mix.
Sales mix is 60 percent and 40 percent in units or in dollars.
Weighted average CMR = WACM/WASale
WACMR = [60% ($120 – $70) + 40% ($500 – $200)] ÷ (60% × $120) + (40% × $500) WACMR = [$30 + $120] ÷ [$72 + $200] = .551
BEP sales = 2,000 × $272 = $544,000 MEDIUM
24. “This makes no sense at all,” said Bill Sharp, president of Essex Company. “We sold the same number of units this year as we did last year, yet our profits have more than doubled.
Who made the goof—the computer or the people who operate it?” The statements to which Mr. Sharp was referring are shown here (absorption costing basis):
2001 2002
Sales (20,000 units each year) $700,000 $700,000
Less cost of good sold 460,000 400,000
Gross margin $240,000 $300,000
Less selling and administrative expenses 200,000 200,000
Income before income taxes $ 40,000 $100,000
The company was organized on January 1, 2001, so the previous statements show the results of its first two years of operation. In the first year, the company produced and sold 20,000 units; in the second year, the company again sold 20,000 units, but it increased production in order to have a stock of units on hand, as shown here:
2001 2002
Production in units 20,000 25,000
Sales in units 20,000 20,000
Variable production cost per unit $8 $8
Fixed overhead costs (total) $300,000 $300,000
Fixed overhead costs are applied to units of product on a basis of each year’s production.
(The company produces and sells a single product.) Variable selling and administrative expenses are $1 per unit sold.
Required:
1. Compute the cost of single unit of product for each year under:
a. absorption costing.
b. variable costing.
2. What is the value of ending inventory in 2002 under:
a. full cost?
b. variable cost?
ANSWER:
2001 2002
1. a Variable man. $ 8 $ 8
Fixed man. 15 12 2001 $300,000 = $15
$23 $20 20,000
2002 $300,000 = $12 25,000
b. Variable man. 2001 2002
$8 $8
2. a. 5,000 × $23 = $115,000 b. 5,000 × 20 = 100,000 MEDIUM
25. The following data have been taken from the records of a company:
Production in units during 2001 200,000
Units sold during 2001 190,000
Selling price per unit $15.00
Standard variable costs per unit:
Material and labor $8.00
Indirect manufacturing costs 2.00
Selling & administrative expenses 1.00 $11.00 Fixed costs budgeted for year:
Indirect manufacturing costs $400,000
Selling & administrative expenses 300,000 $700,000
Required:
1. Determine the income (loss) before income taxes for the year 2001 under (a) absorption costing and (b) variable costing.
2. What is the value of ending inventory under (a) absorption costing and (b) variable costing?
3. Reconcile the difference in the two incomes.
ANSWER:
1. (a.) (b.)
Sales $2,850,000 Sales $2,850,000
– COG S (190,000 × 12) 2,280,000 – VC (190,000 × 11) 2,090,000
$ 570,000 CM $ 760,000
– SLA 490,000 – FC 700,000
Income before income taxes $ 80,000 Income before income taxes $ 60,000
2. PRODUCT COST
(a.) $12 × 10,000 = $120,000 ABSORPTION VARIABLE
(b.) $10 × 10,000 = $100,000
VAR $10 $10
(400,000)
FIX 2 (200,000) ___
$12 $10
3. NI = (200,000 – 190,000) × $2 = $20,000 MEDIUM
26. Actual costs for Sonic, Inc. for the past year were as follows:
Direct material (2 pounds @ $5) $10 per unit Direct labor (3 hours @ $10) $30 per unit Variable selling and administrative $2 per unit Fixed selling and administrative $80,000
During the year, 10,000 units were produced and 9,000 units were sold. There were no beginning inventories. Thirty thousand direct labor hours were worked during the year.
Actual overhead for the year totaled $252,000 of which $140,000 was fixed. Selling price
= $100/unit.
Budgeted fixed overhead was $150,000 and the expected activity level was 30,000 direct labor hours. Variable overhead was budgeted at 3 direct labor hours per unit and $4 per direct labor hour.
The company uses a normal costing system and overhead variances are closed to cost of goods sold.
Required:
a. Determine the unit cost using variable costing.
b. Determine the unit cost using absorption costing.
c. Using variable costing, determine the contribution margin, and variable costing income.
d. Using absorption costing, determine the gross margin, and absorption costing income.
ANSWER:
= Income before income taxes (STD) $184,000
+ favorable VAR-FOH SPD VAR 8,000
Income before income taxes (actual) $192,000 Variable FOH spending variance = $112,000 – (30,000 × $4) = $8,000 F
d. SP $100
– COGS 67
GM $ 33 × 9,000 units = $297,000
– S&A EXP (9,000 × $2) + $80,000 (98,000)
Income before income taxes (STD) $199,000
+ Favorable variance 8,000
Income before income taxes actual $207,000
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27. Sports Innovators has developed a new design to produce hurdles that are used in track and field competition. The company’s hurdle design is innovative in that the hurdle yields when hit by a runner and its height is extraordinarily easy to adjust. Management
estimates expected annual capacity to be 90,000 units; overhead is applied using expected annual capacity. The company’s cost accountant predicts the following 2001 activities and related costs:
Standard unit variable manufacturing costs $12
Variable unit selling expense $5
Fixed manufacturing overhead $480,000
Fixed selling and administrative expenses $136,000
Selling price per unit $35
Units of sales 80,000
Units of production 85,000
Units in beginning inventory 10,000
Other than any possible under- or overapplied fixed overhead, management expects no variances from the previous manufacturing costs. Under- or overapplied fixed overhead is to be written off to Cost of Goods Sold.
Required:
1. Determine the amount of under- or overapplied fixed overhead using (a) variable costing and (b) absorption costing.
2. Prepare projected income statements using (a) variable costing and (b) absorption costing.
3. Reconcile the incomes derived in part 2.
ANSWER:
1. a. $0
b. (90,000 – 85,000) × $5.33 = $26,650 U 2. a. Sales (80,000 × $35) = $2,800,000
– VC (80,000 × $17) = (1,360,000 )
CM $1,440,000
– FC (616,000)
Income before income taxes $ 824,000 b. Sales (80,000 × $35) $2,800,000 – COGS ($17.33 × 80,000) (1,386,400)
GM $1,413,600
– S&A (536,000)
Income before income (STD) $ 877,600
– VOL VAR (26,650)
Income before income taxes $ 850,950 3. 5,000 × $5.33 = $26,650.
MEDIUM
28. On December 30, 2001, a bomb blast destroyed the bulk of the accounting records of the Horne Division, a small one-product manufacturing division that uses standard costs and flexible budgets. All variances are written off as additions to (or deductions from) income;
none are pro-rated to inventories. In addition, the chief accountant mysteriously disappeared. You have the task of reconstructing the records for the year 2001. The general manager has said that the accountant has been experimenting with both absorption costing and variable costing.
The records are a mess, but you have gathered the following data for 2001:
a. Cash on hand, December 31, 2001 $10
b. Sales $128,000
c. Actual fixed indirect manufacturing costs 21,000
d. Accounts receivable, December 31, 2001 20,000
e. Standard variable manufacturing costs per unit 1
f. Variances from standard of all variable manufacturing costs $5,000 U
g. Operating income, absorption-costing basis $14,400
h. Accounts payable, December 31, 2001 18,000
i. Gross profit, absorption costing at standard
(before deducting variances) 22,400
j. Total liabilities 100,000
k. Unfavorable budget variance, fixed manufacturing costs 1,000 U
l. Notes receivable from chief accountant 4,000
m. Contribution margin, at standard (before deducting variances) 48,000 n. Direct-material purchases, at standard prices 50,000 o. Actual selling and administrative costs (all fixed) 6,000 These do not necessarily have to be solved in any particular order. Ignore income taxes.
Required:
1. Operating income on a variable-costing basis.
2. Number of units sold.
3. Number of units produced.
4. Number of units used as the denominator to obtain fixed indirect cost application rate per unit on absorption-costing basis.
5. Did inventory (in units) increase or decrease? Explain.
6. By now much in dollars did the inventory level change (a) under absorption costing, (b) under variable costing?
7. Variable manufacturing cost of goods sold, at standard prices.
8. Manufacturing cost of goods sold at standard prices, absorption costing.
ANSWER:
1. CM $48,000 Actual fix mfg $21,000
– FC (26,000 ) – unfavorable VAR (1,000 )
Operating Income (STD) $22,000 fix cost @STD $20,000
– unfavorable variances (6,000) Operating Income (actual) $16,000 variances $ 2,000 UNF – other VAR 6,000 UNF
VOL VAR $ 4,000 FAV
$4,000 F = (75,000 – X) × $.32 X = 62,500 units produced
5. Inventory decreased. OI absorption is less than OI variable.
6. Absorption cost 5,000 units × $1.32 = $6,600 Variable cost 5,000 units × $1 = $5,000 7. 80,000 units × $1 = $80,000
8. 80,000 × $1.32 = $105,600 DIFFICULT
29. Smith Company produces and sells two products: A and B in the ratio of 3A to 5B.
Selling prices for A and B are, respectively, $1,200 and $240; respective variable costs are
$480 and $160. The company’s fixed costs are $1,800,000 per year.
Compute the volume of sales in units of each product needed to:
Required:
a. breakeven.
b. earn $800,000 of income before income taxes.
c. earn $800,000 of income after income taxes, assuming a 30 percent tax rate.
d. earn 12 percent on sales revenue in before-tax income.
e. earn 12 percent on sales revenue in after-tax income, assuming a 30 percent tax rate.
ANSWER:
A SP $1,200 B SP $240
– VC (480 ) – VC (160 )
CM $ 720 CM $ 80
Weighted CM = (3 × $720) + (5 × $80) = $2,560
a. $1,800,000 = 703.125 A = 704 × 3 = 2,112 units
$2,560 B = 704 × 5 = 3,520
b. $1,800,000 + $800,000 = 1015.625 A = 1,016 × 3 = 3,048 units
$2,560 B = 1,016 × 5 = 5,080
c. $800,000/1 – .3 = $1,142,857
$1,800,000 + $1,142,857 = 1,149.55 A = 1,150 × 3 = 3,450 units
$2,560 B = 1,150 × 5 = 5,750
d. SP = (3 × $1,200) + (5 × $240) = $4,800 X = $1,800,000 + $.12X = $4,354,839
$2,560/$4,800
A = ($4,354,839 × .75)/$1200 = 2,722 units B = ($4,354,839 × .25/$240 = 4,537
e. X = $1,800,000 + $.12X
1 – .3 = $4,973,684
$2,560/$4,800
A = ($4,973,684 × .75)/$1,200 = 3,109 units B = ($4,973,684 × .25/$240 = 5,181
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30. The Jones Company makes three products. Data follow:
Product A Product B Product C
Selling price $10 $20 $40
Variable costs 7 12 16
Total annual fixed costs are $840,000. The firm’s experience has been that about 20 percent of dollar sales come from product A, 60 percent from B, and 20 percent from C.
Required:
a. Compute break-even in sales dollars.
b. Determine the number of units to be sold at the break-even point.
ANSWER:
A B C
a. SP $10 $20 $40
– VC (7 ) (12 ) (16 )
= CM $ 3 $ 8 $24
CMR 30% 40% 60%
CMR = (.2 × 30%) + (.6 × 40%) + (.2 × 60%) = 42%
BE = $840,000/.42 = $2,000,000
b. A ($2,000,000 × .20)/$10 = 40,000 units B ($2,000,000 × .60)/$20 = 60,000 units C ($2,000,000 × .20)/$40 = 10,000 units MEDIUM
31. The Fred Company sells two products, A and B, with contribution margin ratios of 40 and 30 percent and selling prices of $5 and $2.50 a unit. Fixed costs amount to $72,000 a month. Monthly sales average 30,000 units of product A and 40,000 units of product B.
Required:
a. Assuming that three units of product A are sold for every four units of product B, calculate the dollar sales volume necessary to breakeven.
b. As part of its cost accounting routine, Fred Company assigns $36,000 in fixed costs to each product each month. Calculate the break-even dollar sales volume for each product.
b. As part of its cost accounting routine, Fred Company assigns $36,000 in fixed costs to each product each month. Calculate the break-even dollar sales volume for each product.