Break-Even Point in Sales Dollars ¼ Contribution Margin Ratio

6.2 Break-Even Point in Sales Dollars ¼ Contribution Margin Ratio

ðTotal Fixed Costs þ Target ProfitÞ

Target Profit in Sales Dollars

Contribution Margin Ratio

Solutions to Self-Study Problems 203

6. Explain the effect of taxes on financial modeling. To solve for after-tax target profit points, simply input the after-tax target profit amount and tax rate into the following equation. Note

that t is the tax rate. This will result in the before-tax target profit,

After-Tax Profit =

The resulting before-tax profit is used in the following formulas to find the target profit in units or the target profit in sales dollars.

ðTotal Fixed Costs þ Before-Tax Target ProfitÞ

Target Profit in Units

Unit Contribution Margin ðTotal Fixed Costs þ Before-Tax Target ProfitÞ

Target Profit in Sales Dollars ¼

Contribution Margin Ratio

7. Describe the use of financial modeling in a multiple-product setting. Multiple products make using financial models more complex. To deal with this, managers can (1) assume that all products have the same contribution margin, (2) assume that a particular product mix does not change, (3) assume a weighted-average contribution margin, or (4) treat each product line as a separate entity.

Ke y

Equation

Operating Profit ¼ ðContribution Margin for Product 1

þ ðContribution Margin for Product 2

8. Explain financial modeling with multiple cost drivers. Developing a financial model with multiple cost drivers is a more refined way of assessing how changes to the model’s variables

will impact other variables. Costs are analyzed using the five cost hierarchy categories: unit- level, batch-level, product-level, customer-level, and facility-level.

Key Terms and Concepts

Break-even point

Margin of safety

Contribution margin per unit

Operating leverage

Contribution margin ratio

Profit-volume graph

Cost structure

Relevant range

Cost-volume-profit (CVP) model

Sensitivity analysis

Financial model

S olutions to S elf-Study Problems

S U G G E S T E D S O L U T I O N T O P R O B L E M 6 . 1 F O R S E L F - S T U DY

a. Operating profit: Sales Revenue (20,000

Less Variable Costs (20,000

Contribution Margin .....................................................................................................................................

Less Fixed Costs .............................................................................................................................................

Operating Profit .............................................................................................................................................

204 Chapter 6 Financial Modeling for Short-Term Decision-Making

b. Break-even point:

Break-Even Units ¼ Fixed Costs=Contribution Margin per Unit

¼ 12,000 units

c. Target volume: Target Profit in Units ¼ ðFixed Costs þ Target ProfitÞ=Contribution Margin per Unit

¼ $66,000=$3 ¼ 22,000 units

SUGGESTEDSOLUTIONTOPROBLEM6.2FORSELF-STUDY

a. 0A ¼ (2) Fixed Cost per Period

b. IG ¼ (7) None of the Above

c. 0D ¼ (6) Break-Even Sales in Units

d. B0 ¼ (2) Fixed Cost per Period; also, Operating Loss When Sales Are Zero

f. B0/0D ¼ (4) Contribution Margin per Unit

g. HF þ HG ¼ (3) Revenue

h. True

i. False; if revenue is HE, the margin of safety is DH. j. False k. True l. False m. True

SUGGESTEDSOLUTIONTOPROBLEM6.3FORSELF-STUDY

a. To find the break-even point in units, first compute the weighted-average contribution margin:

Product Mix ...............................................................

Weighted-Average Contribution Margin .............

Then input the weighted-average contribution margin in the break-even formula: Break-Even Units ¼ Fixed Costs=Weighted-Average Contribution Margin per Unit

¼ $1,240,000=$3:10 ¼ 400,000 units

b. To find the break-even point in sales dollars, first compute the weighted-average con- tribution margin ratio:

Weighted-Average Contribution Margin Ratio ¼ Total Contribution Margin=Total Sales

¼ ð$200,000 þ $600,000 þ $750,000Þ=ð$500,000 þ $900,000 þ $1,750,000Þ ¼ $1,550,000=$3,150,000 ¼ 0:492ðroundedÞ

Questions, Exercises, Problems, and Cases 205

Then input the weighted-average contribution margin ratio in the break-even formula: Break-Even Sales Dollars ¼ Fixed Costs=Weighted-Average Contribution Margin Ratio

¼ $1,240,000=0:492 ¼ $2,520,000 ðroundedÞ

Que stions , Exercis e s , Problems , and Ca s e s

REVIEWQUESTIONS

1. Review the meaning of the terms or concepts given in Key Terms and Concepts.

2. Define the profit equation.

3. Define the term contribution margin.

4. Name three common assumptions of a linear cost-volume-profit analysis.

5. What effect could the following changes, occurring independently, have on (1) the break- even point, (2) the unit contribution margin, and (3) the expected total profit?

a. An increase in fixed costs.

b. A decrease in wage rates applicable to direct, strictly variable labor.

c. An increase in the selling price of the product.

d. An increase in production and sales volume.

e. An increase in building insurance rates. C R I T I C A L A N A LY S I S A N D D I S C U S S I O N Q U E S T I O N S

sold) differ from the gross margin often seen on companies’ financial statements?

7. Compare cost-volume-profit analysis with profit-volume analysis. How do they differ?

8. How do spreadsheets assist in financial modeling?

9. How does the profit equation change when the analyst uses the multiple-product financial model?

10. If companies that are operating below the break-even point cannot raise prices, what must they do to break even?

11. Fixed costs are often defined as ‘‘fixed over the short run.’’ Does this mean that they are not fixed over the long run? Why or why not?

12. Why do accountants use a linear representation of cost and revenue behavior in cost-volume- profit analysis? Justify this use.

13. Assume the linear cost relation of the cost-volume-profit model for a single-product firm, and use the following answer key: (1) more than double (2) double (3) increase, but less than double (4) remain the same (5) decrease Complete each of the following statements, assuming that all other things (such as quan- tities) remain constant.

a. If price doubles, revenue will ____________________________ . of units) will ____________________________ .

c. If price doubles, profit will ____________________________ .

d. If contribution margin per unit doubles, profit will ____________________________ .

e. If fixed costs double, the total contribution margin will ____________________________ .

f. If fixed costs double, profit will ____________________________ .

206 Chapter 6 Financial Modeling for Short-Term Decision-Making

g. If fixed costs double, the break-even point of units sold will ____________________________ .

h. If total sales of units double, profit will ____________________________ .

i. If total sales dollars double, the break-even point will ____________________________ . j. If the contribution margin per unit doubles, the break-even point will _________________ . k. If both variable costs per unit and selling price per unit double, profit will _________________ .

14. Is a company really breaking even if it produces and sells at the break-even point? What

costs may not be covered?

15. Why does multiple product cost-volume-profit analysis often assume a constant product mix?

16. When would the sum of the break-even quantities for each of a company’s products not be

the break-even point for the company as a whole?

17. A sporting goods retailer is running a monthly special, with snow skis and snowboards being priced to yield a negative contribution margin. What would motivate a retailer to do this?

EXERCISES Solutions to even-numbered exercises are at the end of the chapter.

18. Break-even and target profits. Analysis of the operations of Padillo Company shows the fixed costs to be $200,000 and the variable costs to be $8 per unit. Selling price is $16 per unit.

a. Derive the break-even point expressed in units.

b. How many units must the firm sell to earn a profit of $280,000?

c. What would profits be if revenue from sales were $2,000,000?

19. Cost-volume-profit; volume defined in sales dollars. An excerpt from the income state- ment of the Kelly Company follows. Estimated fixed costs in Year 1 are $660,000.

K E L LY C O M PA N Y IncomeStatement Ye a r E n d e d D e c e m b e r 3 1 , Ye a r 1

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

$3,000,000

Operating Expenses:

Cost of Goods Sold .....................................................................................

$1,425,000

Selling Costs ................................................................................................

450,000

Administrative Costs ..................................................................................

225,000

Total Operating Costs ............................................................................

a. What percentage of sales revenue is variable cost?

b. What is the break-even point in sales dollars for Kelly Company?

c. Prepare a cost-volume-profit graph for Kelly Company.

d. If sales revenue falls to $2,500,000, what will be the estimated amount of profit?

e. What amount of sales dollars produces a profit of $1,000,000?

20. Cost-volume-profit graph. Identify each item on the accompanying graph:

a. the total cost line

b. the total revenue line

c. total variable costs

d. variable cost per unit

e. the total fixed costs

f. the break-even point

g. the profit area (or volume)

h. the loss area (or volume)

208 Chapter 6 Financial Modeling for Short-Term Decision-Making

e. Assume an income-tax rate of 40 percent. What quantity of units is required for PJ Company to make an after-tax operating profit of $1,200,000 for the year?

23. Break-even and target profits; volume defined in sales dollars. The manager of Wong’s Food Express estimates operating costs for the year will total $300,000 for fixed costs.

a. Find the break-even point in sales dollars with a contribution margin ratio of 40 percent.

b. Find the break-even point in sales dollars with a contribution margin ratio of 25 percent.

c. Find the sales dollars required with a contribution margin ratio of 40 percent to generate

a profit of $100,000.

24. CVP—sensitivity analysis; spreadsheet recommended. Quality Cabinet Construction is considering introducing a new cabinet-production seminar with the following price and cost characteristics:

Tuition ..................................................................................................................................

$200 per Student

Variable Costs (wood, supplies, etc.) ...........................................................................

$120 per Student

Fixed Costs (advertising, instructor’s salary, insurance, etc.) ...............................

$400,000 per Year

a. What enrollment enables Quality Cabinet Construction to break even?

b. How many students will enable Quality Cabinet Construction to make an operating

profit of $200,000 for the year?

c. Assume that the projected enrollment for the year is 8,000 students for each of the

following situations: (1) What will be the operating profit for 8,000 students? (2) What would be the operating profit if the tuition per student (that is, sales price)

decreased by 10 percent? Increased by 20 percent? (3) What would be the operating profit if variable costs per student decreased by 10

percent? Increased by 20 percent? (4) Suppose that fixed costs for the year are 10 percent lower than projected, whereas variable costs per student are 10 percent higher than projected. What would be the operating profit for the year?

25. Multiple-product profit analysis. Cisco’s Sumptuous Burritos produces two burritos,

chicken and steak, with the following characteristics:

Chicken Steak

Selling Price per Unit .......................................................................................................

Variable Cost per Unit ......................................................................................................

Expected Sales (units) .....................................................................................................

The total fixed costs for the company are $200,000.

a. What is the anticipated level of profits for the expected sales volumes?

b. Assuming that the product mix would be 40 percent chicken and 60 percent steak at the

break-even point, compute the break-even volume.

c. If the product sales mix were to change to four chicken burritos for each steak burrito,

what would be the new break-even volume?

26. Multiple-product profit analysis. The Salinas Company produces and sells three products.

Operating data for the three products follow.

Selling Price

Variable Cost Fixed Cost

per Unit

per Unit per Month

Product P .......................................

Product Q ......................................

5 3 -----

Product R .......................................

8 5 -----

Entire Company ............................

Define a unit as the sum of one unit of product R sold, two units of product Q sold, and three units of product P sold.

Questions, Exercises, Problems, and Cases 209

a. Draw a cost-volume-profit graph for the Salinas Company.

b. At what number of units does the Salinas Company break even?

c. Change the facts. Suppose a ‘‘unit’’ now consists of two units of product P for every two units of product Q and one unit of product R. At what number of units does Salinas Company break even?

27. Solving for cost-based selling price. Whey Company follows a cost-based approach to pricing. Prices are 150 percent of variable manufacturing costs. The annual cost of pro- ducing one of its products follows:

Variable Manufacturing Costs ..........................................................................................................

$15 per Unit

Fixed Manufacturing Costs ...............................................................................................................

$50,000 per Year

Variable Selling and Administrative Costs ...................................................................................

$2 per Unit

Fixed Selling and Administrative Costs ........................................................................................

$75,000 per Year

a. Assume that Whey produces and sells 10,000 units. Calculate the selling price per unit.

b. Assume that Whey produces and sells 20,000 units. Calculate the selling price per unit.

c. Is Whey company profitable at either 10,000 or 20,000 units? PROBLEMS

28. Explaining sales and cost changes. You have acquired the following data for Years 1 and 2 for Harry’s Horseback Rides.

Revenue from Rides ................................................

Variable Costs of Operations .................................

Contribution Margin ...............................................

Price per Person per Hour .....................................

Write a short report to Harry’s uncle who loaned Harry the money to start this business. Explain the cause of the increase in total contribution margin between Year 1 and Year 2. Your report should consider the effect of each of the following: change in price per person per hour, change in volume, and change in operating costs per admission.

29. CVP analysis and financial modeling (adapted from CMA exam). Bronkowski is a retailer for high-tech recording disks. The projected operating profit for the current year is $200,000 based on a sales volume of 200,000 units. The company has been selling the disks for $16 each; variable costs consist of the $10 purchase price and a $2 handling cost. The company’s annual fixed costs are $600,000.

Management is planning for the coming year, when it expects that the unit purchase price of the disks will increase by 30 percent.

a. Calculate the company’s break-even point for the current year in units.

b. What will be the company’s operating profit for the current year if there is a 20 percent increase in projected unit sales volume?

c. What volume of dollar sales must be achieved in the coming year to maintain the current year’s operating profit if the selling price remains at $16?

d. Would the use of a financial model be helpful to the firm in addressing issues such as those raised in requirements b. and c.? Explain.

30. CVP—missing data. Ramanan, Inc., has performed cost studies and projected the following annual costs based on 200,000 units of production and sales:

Total Annual Costs (200,000 units)

Direct Material ......................................................................................

Direct Labor ...........................................................................................

Manufacturing Overhead .....................................................................

Selling, General, and Administrative ...............................................

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

210 Chapter 6 Financial Modeling for Short-Term Decision-Making

a. Compute Ramanan’s unit selling price that will yield a profit of $300,000, given sales of

200,000 units.

b. Assume management selects a selling price of $8 per unit. Compute Ramanan’s dollar sales that will yield a projected 20 percent profit on sales, assuming variable costs per unit are 60 percent of the selling price per unit and fixed costs are $420,000.

31. CVP analysis. A company is deciding which of two new thermostat systems to produce and sell. The Basic system has variable costs of $8.00 per unit, excluding sales commissions, and annual fixed costs of $520,000; the Deluxe system has variable costs of $6.40, excluding sales commissions, and fixed costs of $672,000. The company’s selling price is $32 per unit for the Basic model and $38 for the Deluxe model. The company pays a 10 percent sales commission.

a. Which of the two systems will be more profitable for the firm if sales for either system

are expected to average 150,000 units per year?

b. How many units must the company sell to break even if it selects the Deluxe system?

c. Suppose the Basic system requires the purchase of additional equipment that is not reflected in the preceding figures. The equipment will cost $224,000 and will be depreciated over a 10-year life by the straight-line method. How many units must the company sell to earn $40,000 of income, after considering depreciation, if the Basic system is selected?

d. Now, ignore the information presented in part c. Write a report that explains to man- agement the level of volume at which it should be indifferent between the Basic system and the Deluxe system.

32. CVP with taxes (adapted from CMA exam). Lighthouse Company, maker of quality flashlights, has experienced a steady growth in sales for the past five years. However, increased competition has led Mr. Das, the CEO, to believe that to maintain the company’s present growth requires an aggressive advertising campaign next year. To prepare the next year’s advertising campaign, the company’s accountant has prepared and presented to Mr. Das the following data for the current year, Year 1:

Cost Schedule Variable Costs:

Direct Labor ......................................................................................

$10.00 per Flashlight

Direct Materials ................................................................................

Variable Overhead ............................................................................

Total Variable Costs ....................................................................

$16.50 per Flashlight

Fixed Costs:

Total Fixed Costs .........................................................................

Selling Price, per Flashlight ..............................................................

Expected Sales, Year 1 (25,000 flashlights) ..................................

Tax Rate: 35 Percent

Mr. Das has set the sales target for Year 2 at a level of $1,120,000 (or 28,000 flashlights).

a. What is the projected after-tax operating profit for Year 1?

b. What is the after-tax break-even point in units for Year 1?

c. Mr. Das believes that to attain the sales target (28,000 flashlights) requires an additional selling expense of $40,000 for advertising in Year 2, with all other costs remaining constant. What will be the after-tax operating profit for Year 2 if the firm spends the additional $40,000?

d. What will be the after-tax break-even point in sales dollars for Year 2 if the firm spends

the additional $40,000 for advertising?

e. If the firm spends the additional $40,000 for advertising in Year 2, what is the sales level in dollars required to equal Year 1 after-tax operating profit?

f. At a sales level of 28,000 units, what is the maximum amount the firm can spend on

advertising to earn an after-tax operating profit of $75,000?

Questions, Exercises, Problems, and Cases 211

33. CVP—missing data; assumptions. You are analyzing the financial performance of Sonoma Winery based on limited data from a New York Times article. The article says that despite an increase in sales revenue from $4,704,000 in Year 8 to $4,725,000 in Year 9, Sonoma recently reported a decline in net income of $129,500 from Year 8 to an amount equal to

2 percent of sales revenue in Year 9. The average total cost per unit increased from $2.200 in Year 8 to $2.205 in Year 9.

a. Compute the changes, if any, in average selling price and sales in units from Year 8 to Year 9.

b. Can you compute the total fixed costs and variable cost per unit during Year 9? If so, do so. If not, illustrate why with a graph and discuss any important assumptions of the cost-volume-profit model that this application violates.

34. Alternatives to reduce break-even sales. Wolf Broadcasting operated at the break-even point of $2,250,000 during Year 1 while incurring fixed costs of $1,000,000. Management is considering two alternatives to reduce the break-even level. Alternative A trims fixed costs by $200,000 annually with no change in variable cost per unit; doing so, however, will reduce the quality of the product and result in a 10 percent decrease in selling price, but no change in the number of units sold. Alternative B substitutes automated equipment for certain operations now performed manually. Alternative B will result in an annual increase of $300,000 in fixed costs but a 5 percent decrease in variable costs per barrel produced, with no change in product quality, selling price, or sales volume.

a. What was the total contribution margin (contribution margin per unit times number of units sold) during Year 1?

b. What is the break-even point in sales dollars under alternative A?

c. What is the break-even point in sales dollars under alternative B?

d. What should the company do?

35. CVP analysis with semifixed (step) costs. Shout Company has one product: printing logos on sweatshirts for businesses. The sales price of $20 remains constant per unit regardless of volume, as does the variable cost of $12 per unit. The company is considering operating at one of the following three monthly levels of operations:

Increase in

Volume Range

Total

Fixed Costs from

(production and sales)

Fixed Costs

Previous Level

a. Calculate the break-even point(s) in units.

b. If the company can sell everything it makes, should it operate at level 1, level 2, or level 3? Support your answer.

36. CVP analysis with semifixed costs and changing unit variable costs. The Washington Company manufactures and sells crystal earrings. The sales price, $50 per unit, remains constant regardless of volume. Last year’s sales were 15,000 units, and operating profits were $200,000. Fixed costs depend on production levels, as the following table shows. Variable costs per unit are 40 percent higher for level 2 (two shifts) than for level 1 (day shift only). The additional labor costs result primarily from higher wages required to employ workers for the night shift.

Annual Production

Annual Total

Range (in units)

Fixed Costs

Level 1 (day shift) ....................................................................

0--20,000

Level 2 (day and night shifts) ...............................................

20,001--36,000

Washington expects last year’s cost structure and selling price not to change this year. Maximum plant capacity is 36,000. The company sells everything it produces.

a. Compute the contribution margin per unit for last year for each of the two production levels.

212 Chapter 6 Financial Modeling for Short-Term Decision-Making

b. Compute the break-even points in units for last year for each of the two production

levels.

c. Compute the volume in units that will maximize operating profits. Defend your choice.

37. CVP analysis with semifixed costs. Melissa Mooring, director and owner of the Kids Education Center, has a master’s degree in elementary education. In the seven years she has been running the Kids Education Center, her salary has ranged from nothing to $20,000 per year. ‘‘The second year,’’ she says, ‘‘I made 62 cents an hour.’’ (Her salary is what’s left over after meeting all other expenses.)

Could she run a more profitable center? She thinks perhaps she could if she increased the student–teacher ratio, which is currently five students to one teacher. (Government standards for a center such as this set a maximum of 10 students per teacher.) She refuses to increase the ratio to more than six-to-one. ‘‘If you increase the ratio to more than six-to-one, the children don’t get enough attention. In addition, the demands on the teacher are far too great.’’ She does not hire part-time teachers.

Mooring rents the space for her center in the basement of a church for $900 per month, including utilities. She estimates that supplies, snacks, and other nonpersonnel costs are $80 per student per month. She charges $380 per month per student. Teachers receive $1,200 per month, including fringe benefits. She has no other operating costs. At present, she cares for

30 students and employs six teachers.

a. What is the present operating profit per month of the Kids Education Center before

Ms. Mooring’s salary?

b. What is (are) the break-even point(s), before Ms. Mooring’s salary, assuming a student–

teacher ratio of 6:1?

c. What would be the break-even point(s), before Ms. Mooring’s salary, if the student–

teacher ratio increased to 10:1?

d. Ms. Mooring has an opportunity to increase the student body by six students. She must take all six or none. Should she accept the six students if she wants to maintain a maximum student–teacher ratio of 6:1?

e. (Continuation of part d.) Suppose that Ms. Mooring accepts the six children. Now she has the opportunity to accept one more, which requires hiring one more teacher. What would happen to profit, before her salary, if she accepts one more student?

38. Break-even analysis for management education. The dean of the Graduate School of Management at the University of California at Davis was considering whether to offer a particular seminar for executives. The tuition was $650 per person. Variable costs, which included meals, parking, and materials, were $80 per person. Certain costs of offering the seminar, including advertising the seminar, instructors’ fees, room rent, and audiovisual equipment rent, would not be affected by the number of people attending (within a ‘‘relevant range’’). Such costs, which could be thought of as step costs, amounted to $8,000 for the seminar.

In addition to these costs, a number of staff, including the dean of the school, worked on the program. Although the salaries paid to these staff were not affected by offering the seminar, working on the seminar took these people away from other duties, thus creating an opportunity cost estimated at $7,000 for this seminar.

Given this information, the school estimated the break-even point to be ($8,000 þ $7,000)/($650 – $80) ¼ 26.3 students. If the school wanted to at least break even on this program, it should offer the program only if it expected at least 27 students to attend.

Write a report to the dean that evaluates the quality of this analysis. In particular, focus on concerns about the accuracy of the data and the limitations of cost-volume-profit analysis.

39. Cost cutting to break even. Cost-volume-profit analysis showed how much Auto, Inc. had to improve just to break even in Year 1. In that year, the break-even point was 2.2 million units, but the company was selling considerably fewer than 2 million units. Faced with a severe recession in the industry, Auto, Inc. had virtually no chance to increase sales enough to break even. Meanwhile, the company had received loan guarantees from the U.S. gov- ernment, which evoked considerable criticism that the federal government was supporting a ‘‘failing’’ company.

By Year 4, Auto, Inc. reduced its break-even point to 1.1 million units, and the company reported a profit for the first time in several years. The turnaround came despite continued low sales in the industry; it resulted primarily from severe cost cutting, which reduced fixed

216 Chapter 6 Financial Modeling for Short-Term Decision-Making

S ug ge ste d S olutions to Even -Numb ere d Exercis e s

18. Break-even and target profits.

a. Break-Even Units ¼ Fixed Costs=Unit Contribution Margin

b. Target Profit Units ¼ ðFixed Costs þ Target ProfitÞ=Unit Contribution Margin

c. Contribution Margin Ratio ¼

Unit Selling Price

Profit ¼ $800,000

20. Cost-volume-profit graph.

Profit

Total Revenue

Area g

Line

Break-Even Point

Slope = Variable Cost

Total Cost

per Unit d

Line

Loss

h Total Variable Costs Area

Area

Total Fixed Costs Area

Loss

Profit

h Volume

g Volume

Break-Even Point

22. Cost-volume-profit analysis.

a. $5,000,000/1,000,000 Units ¼ $5 per Unit.

b. $3,000,000/1,000,000 Units ¼ $3 per Unit.

c. $5 – $3 ¼ $2 per Unit.

d. Operating Profit

Unit Sales ¼

¼ 500,000 units

Suggested Solutions to Even-Numbered Exercises 217

e. After-Tax Profit = $1,200,000 = $2,000,000 ¼ Before-Tax Profit

Then, go back to the equation shown in d. above and set operating profit to $2,000,000 as follows:

Unit Sales ¼

¼ 1,500,000 units

24. Sensitivity analysis.

a. Fixed Costs Break-Even Point in Units ¼

Unit Contribution Margin $400 ; 000

¼ $400,000 ¼ 5,000 students $80

b. Fixed Costs Target Profit in Units

þ Target Profit

¼ Unit Contribution Margin

$200 ¼ $600,000 ¼ 7,500 students $80

c. (1) Profit ¼ $ 240; 000

(2) 10% price decrease. Now price ¼ $180

Profit ¼ $ 80; 000

Profit decreases by $160,000 (67%). 20% price increase. Now price ¼ $240

Profit ¼ $ 560; 000

Profit increases by $320,000 (133%). (3) 10% variable cost decrease. Now variable cost ¼ $108

Profit ¼ $ 336; 000

Profit increases by $96,000 (40%). 20% variable cost increase. Now variable cost ¼ $144

Profit ¼ $ 48, 000

Profit decreases by $192,000 (80%). (4)

Profit

Profit decreases by $56,000 (23%).

218 Chapter 6 Financial Modeling for Short-Term Decision-Making

26. Multiple-product profit analysis.

a. A unit ¼ production of three product Ps, two product Qs, and one product R.

Variable Cost per Unit Revenue per Unit

b. 0

$10X ¼ $48,000 X ¼ 4,800 Units:

$ TR = $27X Slope = $27

TC = $48,000 + $17X

Slope = $17 48,000

Units

Not Required: Total Revenue at Break-Even Level

c. A Unit ¼ two product Ps, two product Qs, and one product R.

Variable Cost per Unit Revenue per Unit

$9X ¼ $48,000 X ¼ 5,333:3 Units: