CHAPTER 3



CHAPTER 3

Cost-Volume-Profit Analysis and Pricing Decisions

Learning Objectives

1. Calculate the breakeven point in units and sales dollars. (Unit 3.1)

2. Calculate the level of activity required to meet a target income. (Unit 3.2)

3. Determine the effects of changes in sales price, cost, and volume on operating income. (Unit 3.2)

4. Define operating leverage and explain the risks associated with the tradeoff between variable and fixed costs. (Unit 3.2)

5. Calculate the multi-product breakeven point and level of activity required to meet a target income. (Unit 3.3)

6. Define markup and explain cost-plus pricing. (Unit 3.4)

7. Explain target costing and calculate a target cost. (Unit 3.4)

Summary of End of Chapter Material by Learning Objective and Bloom’s Taxonomy

|Puzzle Clues | |

|$12x = |$150,000 |

|x = |12,500 hats to breakeven |

|12,500 hats ( $30 per hat = |$375,000 breakeven sales dollars |

b. Contribution margin ratio = [pic]

Variable cost ratio = $1 - .4 = .60

c. Managers could increase the selling price or purchase the hats from another distributor at a lower cost.

LO: 1, Bloom: AN, AP, Unit: 3-1, Difficulty: Easy, Min: 8, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-2

a. $.80 - $.45 = $.35

b. Contribution margin ratio = [pic]

c.

|$.80x – $.45x – $175,000 = |$0 |

|$.35x = |$175,000 |

|x = |500,000 bars to breakeven |

|500,000 bars ( $.80 per bar = |$400,000 to breakeven |

d. The breakeven point will increase to

[pic] bars ( $.80 = $560,000

LO: 1, Bloom: AP, Unit: 3-1, Difficulty: Moderate, Min: 10, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-3

a.

|$25x – $15x – $12,000 = |$30,000 |

|$10x = |$42,000 |

|x = |4,200 baskets |

b. Marissa can raise the selling price, reduce variable cost per basket, or reduce fixed expenses. Holding two of these inputs constant, we can solve for the third. Remember that sales volume of 4,000 units is known.

Raise the selling price (SP):

|(SP ( 4,000 units) – ($15 ( 4,000 units) - $12,000 = |$30,000 |

|(SP ( 4,000 units) = |$102,000 |

|SP = |$25.50 |

Reduce variable cost per basket (VC)

|($25 ( 4,000 units) – (VC ( 4,000 units) - $12,000 = |$30,000 |

|$58,000 = |(VC ( 4,000 units) |

|$14.50 = |VC |

Reduce fixed expenses (FC)

|($25 ( 4,000 units) – ($15 ( 4,000 units) - FC = |$30,000 |

|FC = |$10,000 |

Various combinations of these changes would also work.

Alternate Solution:

|CM/unit × 4,000 baskets = |$42,000 |

|CM/unit = |$10.50 |

The contribution margin on each basket needs to be $10.50, so Marissa could raise prices to $25.50 ($15.00 + $10.50) or reduce variable costs to $14.50 ($25.00 - $10.50). Alternatively, holding sales price and variable costs constant, fixed expenses could be reduced to $10,000: ($10 × 4,000 baskets) - $10,000 = $30,000.

LO: 2, Bloom: AP, Unit: 3-2, Difficulty: Difficult, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-4

|$12,000x – $8,200x – $6,840,000 = |[pic] |

|$3,800x = |$11,400,000 |

| x = |3,000 freezers |

LO: 2, Bloom: AP, Unit: 3-2, Difficulty: Easy, Min: 5, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-5

a.

|$12x – $3x – $432,000a = |$0 |

|$9x = |$432,000 |

|x = |48,000 frisbees to breakeven |

|48,000 frisbees ( $12 = |$576,000 to breakeven |

a$36,000 per month × 12 months per year

b.

|$9x = |$432,000 + $18,000 |

| x = |50,000 frisbees |

c.

[pic] = $27,000

d.

|$9x = |$432,000 + $27,000 |

| x = |51,000 frisbees |

LO: 1,2, Bloom: AP, Unit: 3-1,3-2, Difficulty: Moderate, Min: 10, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-6

a. Contribution margin ratio = [pic]

Variable cost ratio = 1 - .65 = .35

b. Margin of safety = Current sales – Breakeven sales

|Breakeven sales = |[pic] |

|= |$450,000 |

|Margin of safety = |$600,000 – $450,000 |

| = |$150,000 |

c. Net operating income would increase by the change in contribution margin: $100,000 ( .65 = $65,000

d.

|new variable cost = |$17.50 ( 1.16 |

|= |$20.30 |

|new price = |$50 ( 1.1 |

|= |$55 |

|current unit sales = |[pic] |

|= |12,000 |

| | |

|new unit sales = |12,000 ( .98 = 11,760 |

|operating income = |[($55.00 – $20.30) ( 11,760] – $292,500 |

|= |$115,572 |

LO: 3, Bloom: AP, Unit: 3-2, Difficulty: Difficult, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-7

a. Operating income would increase by the change in contribution margin:

|contribution margin ratio = |[pic] |

|= |.60 |

|change in operating income = |$39,000 ( .60 |

|= |$23,400 |

b.

|operating income last year = |(32,000 ( $18.00) - $360,000 |

|= |$216,000 |

|new price = |$30.00 ( .95 |

|= |$28.50 |

|new fixed expenses = |$360,000 + $50,000 |

|= |$410,000 |

|new unit sales = |32,000 ( 1.3 |

|= |41,600 units |

|projected income = |[($28.50 – $12.00) ( 41,600] – $410,000 |

|= |$276,400 |

Clarkson should implement the price reduction because the estimated operating income is larger than the current operating income.

LO: 3, Bloom: AP, AN, Unit: 3-2, Difficulty: Difficult, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-8

a. B: $25,000 x 60% = $15,000

b. C

c. D:

|TC – VC = |FC |

|= |$170,000 – ($150,000 × .60) |

|= |$80,000 |

d. A: The additional 1,000 units × the $8 contribution margin per unit ($20 × .4) provide $8,000 in additional contribution margin, while the advertising campaign increases costs by $6,000. The net result is a $2,000 increase in operating income.

[($20 ( .4) ( 1,000] - $6,000 = $2,000

e. C: At breakeven, CM = FC. Using the contribution margin ratio to find the contribution margin per unit,

|[(.32 ( $50) ( x] = |$200,000 |

|x = |12,500 units |

LO: 1,3, Bloom: AP, Unit: 3-2, Difficulty: Difficult, Min: 20, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-9

a.

|annual fixed expenses = |$120,000 ( 12 months |

|= |$1,440,000 |

|contribution margin ratio = |1 – .4 |

|= |.60 |

|breakeven = |[pic] |

|= |$2,400,000 |

b. Operating income will increase by the increase in contribution margin

|Additional units sold = |100,000 ( .15 |

|= |15,000 |

| | |

|Additional contribution margin = |15,000 additional units ( ($40 ( .60) |

|= |$360,000 |

c. new variable cost: .45 ( $40 = $18 per unit

new fixed expenses: $1,440,000 + ($10,000 ( 12 months) = $1,560,000

new sales price: $40 ( 1.1 = $44 per unit

|Sales – VC – FC = |0 |

|$44x - $18x - $1,560,000 = |0 |

|$26x = |$1,560,000 |

|x = |60,000 blankets |

|60,000 blankets ( $44 = |$2,640,000 |

d. new variable cost: .45 ( $40 = $18 per unit

new fixed expenses: $1,440,000 + ($10,000 ( 12 months) = $1,560,000

new sales price: $40 ( 1.1 = $44 per unit

new contribution margin: $44 – $18 = $26 per blanket

new sales volume: 100,000 ( .95 = 95,000 blankets

|Sales – VC – FC = |Operating Income |

|($26 ( 95,000) – $1,560,000 = |$910,000 |

| | |

e. From part d, operating income = $910,000

With a sales price of $40 per blanket and sales volume of 100,000 blankets, operating income is:

[($40 – $18) ( 100,000] – $1,560,000 = $640,000

Matoaka is better off to raise the sales price to $44 and sell fewer blankets.

LO: 1,3, Bloom: AP, Unit: 3-1, 3-2, Difficulty: Difficult, Min: 20, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-10

a.

|($3.00 – $1.75)x – $25,000 = |$0 |

| $1.25x = |$25,000 |

|x = |20,000 hamburgers |

b.

|($3.00 – $1.75)x – $25,000 = |$6,000 |

|$1.25x = |$25,000 + $6,000 |

|x = |24,800 hamburgers |

c.

[pic]

d. It is unlikely that Wimpee’s can sell the 24,800 hamburgers required to earn the desired $6,000 in operating income. Instead, Wimpee could try to reduce variable costs per unit and/or fixed expenses. Alternatively, Wimpee could increase the selling price, but that might further reduce the number of hamburgers sold.

LO: 1,2,3, Bloom: AP, AN, Unit: 3-1, 3-2, Difficulty: Moderate, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-11

| | | | | |

|Sales | | |$50,000 | |

|Variable expenses | | | | |

| COGS | |$26,000 | | |

| Selling | |1,600 | | |

| Administrative | | 7,200 | | |

|Total variable expenses | | |34,800 | |

|Contribution margin | | |15,200 | |

|Fixed expenses | | | | |

| Selling | |6,400 | | |

| Administrative | | 4,800 | | |

|Total fixed expenses | | |11,200 | |

|Operating income | | |$ 4,000 | |

a.

|Operating leverage = |[pic] |

|= |[pic] |

|= |3.8 |

b. Increase in operating income = 3.8 x 10% = 38%, or $1,520

LO: 4, Bloom: AP, Unit: 3-2, Difficulty: Moderate, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-12

a. Warner’s breakeven point would decrease. Reducing fixed expenses lowers the breakeven point.

b. Warner’s margin of safety would increase. The margin of safety is current sales minus breakeven sales. When the breakeven point decreases, all other things equal, the margin of safety increases.

c. Warner’s degree of operating leverage would decrease because the level of fixed expenses relative to variable costs decreased.

LO: 1,4, Bloom: C, Unit: 3-1, 3-2, Difficulty: Moderate, Min: 10, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-13

a. Abado’s sales mix is 60,000 math tests and 20,000 reading tests, or a sales mix of 3 to 1.

|Breakeven point = |[pic] |

|= |10,000 |

reading tests = x = 10,000; math tests = 3x = 30,000

|reading test sales: |10,000 tests × $36 per test = |$360,000 |

|math test sales: |30,000 tests × $20 per test = | 600,000 |

| |breakeven sales = |$960,000 |

b.

| |Math Testing | |Reading Testing | |Total Company |

| |Total |Per Unit | |Total |Per Unit | | |

|Sales |$1,200,000 |$20 | |$1,200,000 |$20 | |$2,400,000 |

|Variable costs | 840,000 | 14 | | 1,080,000 | 18 | | 1,920,000 |

|Contribution margin |$ 360,000 |$ 6 | |$ 120,000 |$ 2 | |480,000 |

|Fixed expenses | | | | | | | 360,000 |

|Operating income | | | | | | |$ 120,000 |

c. Abado’s sales mix is now 60,000 math tests and 60,000 reading tests, or a sales mix of 1 to 1.

|Breakeven point = |[pic] |

| | |

|= |45,000 |

reading tests = x = 45,000; math tests = x = 45,000

|reading test sales: |45,000 tests × $20 per test = |$ 900,000 |

|math test sales: |45,000 tests × $20 per test = | 900,000 |

| |breakeven sales = |$1,800,000 |

Since the breakeven sales revenue has increased and the expected operating income has decreased, Abado should not make the change.

LO: 1,5, Bloom: AP, C, Unit: 3-1,3-3, Difficulty: Difficult, Min: 20, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-14

a. Kitchenware’s sales mix is 14,000 plastic pitchers and 42,000 glass pitchers, or a sales mix of 1 to 3.

|($30 – $15)x + ($45 – $24)3x – $982,800 = |0 |

|$15x + $63x = |$982,800 |

|x = |12,600 |

plastic pitchers = x = 12,600; glass pitchers = 3x = 37,800

b.

|($30 – $13)x + ($45 – $24)3x – $982,800 = |0 |

|$17x + $63x = |$982,800 |

|x = |12,285 |

plastic pitchers = x = 12,285; glass pitchers = 3x = 36,855

LO: 1,5, Bloom: AP, Unit: 3-1,3-3, Difficulty: Moderate, Min: 10, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-15

a.

|Cost = |$249 × .75 |

|= |$186.75 |

b.

|Markup = |[pic] |

|= |50% |

c.

|.75(sales price) = |$166 |

|sales price = |$221.33 |

LO: 6, Bloom: AP, C, Unit: 3-4, Difficulty: Easy, Min: 8, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-16

a. [pic] = 67%

b. Total cost = $324,000 + $126,000 = $450,000

markup percentage = [pic] = 20%

c. [pic] = 40%

d. Use the gross margin percentage

|[pic] = |.4 |

|x -$42 = |.4x |

|.6x = |$42 |

|x = |$70 |

LO: 6, Bloom: AP, C, Unit: 3-4, Difficulty: Moderate, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-17

a.

|.6 = |[pic] |

|.6x = |$36 – x |

|1.6x = |$36 |

|x = |$22.50 |

b. Justin should try to value engineer the product to reduce the unit price by $1.50 to reach the target price of $22.50.

LO: 7, Bloom: AP, C, Unit: 3-4, Difficulty: Easy, Min: 8, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Exercise 3-18

a. cost of original pet bed = $45 – $15 = $30 per bed

markup percentage = [pic] = 50% markup on cost of goods sold

price of high-end bed = $58 × 1.5 = $87 per bed

b. current gross margin = [pic] = 1/3; cost of goods sold = 2/3

high-end bed target cost of goods sold = 2/3 × $78 = $52 per bed

c. Pet Designs could

• redesign the high-end bed to reduce the cost to produce the bed;

• accept a lower gross margin percentage; or,

• not make the bed

LO: 6, 7, Bloom: AP, C, Unit: 3-4, Difficulty: Moderate, Min: 8, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

SOLUTIONS TO PROBLEMS

Problem 3-19

a. Using the sales revenue of $10,000 and sales price of $5.00 per unit, determine that The Robinson Company sold 2,000 units ([pic]).

| | | | |Per Unit |

|Sales | | |$10,000 |$5.00 |

|Less variable expenses | | | | |

| Cost of goods sold | |$3,000 | |1.50 |

| Operating costs | | 1,000 | | 0.50 |

|Total variable expenses | | | 4,000 | 2.00 |

|Contribution margin | | |6,000 |$3.00 |

|Less fixed operating expenses | | | 1,500 | |

|Operating income | | |$ 4,500 | |

|contribution margin per unit = |[pic] |

|= |$3.00 per unit |

|breakeven point = |[pic] |

|= |500 units |

|breakeven sales = |500 units × $5.00 |

|= |$2,500 |

b.

|Margin of safety = |2,000 units – 500 units |

|= |1,500 units |

|Margin of safety = |1,500 units × $5.00 |

|= |$7,500 |

LO: 1, Bloom: AP, Unit: 3-1, Difficulty: Moderate, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-20

a. current sales volume: [pic] = 50,000 units

new sales volume: 50,000 × .95 = 47,500 units

new sales price: $12.00 × 1.10 = $13.20

| |Total |Per unit |

|Sales |$627,000 |$13.20 |

|Less variable expenses | 332,500 | 7.00 |

|Contribution margin |294,500 |$ 6.20 |

|Less fixed expenses | 175,000 | |

|Operating income |$119,500 | |

b. new sales price: $12.00 × 1.10 = $13.20 per unit

new variable cost per unit: $7.00 × 1.05 = $7.35 per unit

| |Total |Per unit |

|Sales |$660,000 |$13.20 |

|Less variable expenses | 367,500 | 7.35 |

|Contribution margin |292,500 |$ 5.85 |

|Less fixed expenses | 175,000 | |

|Operating income |$117,500 | |

c. new sales price: $12.00 × .90 = $10.80

new sales volume: 50,000 × 1.20 = 60,000 units

| |Total |Per unit |

|Sales |$648,000 |$10.80 |

|Less variable expenses | 420,000 | 7.00 |

|Contribution margin |228,000 |$ 3.80 |

|Less fixed expenses | 175,000 | |

|Operating income |$ 53,000 | |

d. new fixed expenses: $175,000 + $20,000 = $195,000

| |Total |Per unit |

|Sales |$600,000 |$12.00 |

|Less variable expenses | 350,000 | 7.00 |

|Contribution margin |250,000 |$ 5.00 |

|Less fixed expenses | 195,000 | |

|Operating income |$ 55,000 | |

e. new sales price: $12.00 × 1.10 = $13.20

new variable cost per unit: $7.00 × 1.10 = $7.70

new fixed expenses: $175,000 + $25,000 = $200,000

new sales volume: 50,000 × .90 = 45,000 units

| |Total |Per unit |

|Sales |$594,000 |$13.20 |

|Less variable expenses | 346,500 | 7.70 |

|Contribution margin |247,500 |$ 5.50 |

|Less fixed expenses | 200,000 | |

|Operating income |$ 47,500 | |

LO: 3, Bloom: AP, Unit: 3-2, Difficulty: Difficult, Min: 20-25, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-21

a. Using the sales revenue of $2,000,000 and sales price of $20.00 per unit, determine that SND, Inc. sold 100,000 units ([pic]).

new sales volume: 100,000 × .90 = 90,000 units

| |Total |Per unit |

|Sales |$1,800,000 |$20.00 |

|Less variable expenses | 1,125,000 | 12.50 |

|Contribution margin |675,000 |$ 7.50 |

|Less fixed expenses | 400,000 | |

|Operating income |$ 275,000 | |

b. new sales price: $20.00 × 1.05 = 21.00

| |Total |Per unit |

|Sales |$2,100,000 |$21.00 |

|Less variable expenses | 1,250,000 | 12.50 |

|Contribution margin |850,000 |$ 8.50 |

|Less fixed expenses | 400,000 | |

|Operating income |$ 450,000 | |

c. new variable cost per unit: $12.50 + $1.50 = $14.00

| |Total |Per unit |

|Sales |$2,000,000 |$20.00 |

|Less variable expenses | 1,400,000 | 14.00 |

|Contribution margin |600,000 |$ 6.00 |

|Less fixed expenses | 400,000 | |

|Operating income |$ 200,000 | |

d. new sales volume: 100,000 + 5,000 = 105,000 units

new sales price: $18

| |Total |Per unit |

|Sales |$1,890,000 |$18.00 |

|Less variable expenses | 1,312,500 | 12.50 |

|Contribution margin |577,500 |$ 5.50 |

|Less fixed expenses | 400,000 | |

|Operating income |$ 177,500 | |

e. new sales volume: 100,000 × 1.15 = 115,000 units

new fixed expenses: $400,000 + $75,000 = $475,000

| |Total |Per unit |

|Sales |$2,300,000 |$20.00 |

|Less variable expenses | 1,437,500 | 12.50 |

|Contribution margin |862,500 |$ 7.50 |

|Less fixed expenses | 475,000 | |

|Operating income |$ 387,500 | |

f. new variable cost per unit: $12.50 + $2.00 = $14.50

new sales price: $20.00 + $1.50 = $21.50

new sales volume: 100,000 – 2,500 = 97,500 units

new fixed expenses: $400,000 + $20,000 = $420,000

| |Total |Per unit |

|Sales |$2,096,250 |$21.50 |

|Less variable expenses | 1,413,750 | 14.50 |

|Contribution margin |682,500 |$ 7.00 |

|Less fixed expenses | 420,000 | |

|Operating income |$ 262,500 | |

LO: 3, Bloom: AP, Unit: 3-2, Difficulty: Difficult, Min: 25-30, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-22

a. Using the sales revenue of $1,050,000 and sales price of $20.00 per unit from Exhibit 3-1, determine that Universal Sports Exchange sold 52,500 units ([pic]).

|new cost of jersey = |$ 15.30 |

|current cost of jersey = |$ 14.80 |

|cost increase = |$ 0.50 |

|jerseys sold |× 52,500 |

|decrease in operating income = |$26,250 |

b. Alternative 1: new sales price: $20.00 + $0.50 = $20.50

new commission: $20.50 × .06 = $1.23 per jersey

new fixed expenses: $168,000 + $5,000 = $173,000

maintain current sales volume of 52,500 jerseys

| |Total |Per unit |

|Sales |$1,076,250 |$20.50 |

|Less variable expenses | | |

| Cost of goods sold |803,250 |15.30 |

| Commission | 64,575 | 1.23 |

|Contribution margin |208,425 |$ 3.97 |

|Less fixed expenses | 173,000 | |

|Operating income |$ 35,425 | |

Alternative 2: sales price remains $20.00 per jersey

new fixed expenses: $168,000 + $22,000= $190,000

new sales volume: 52,500 × 1.10 = 57,750 jerseys

new commission: $20.00 × .04 = $0.80 per jersey

| |Total |Per unit |

|Sales |$1,155,000 |$20.00 |

|Less variable expenses | | |

| Cost of goods sold |883,575 |15.30 |

| Commission | 46,200 | 0.80 |

|Contribution margin |225,225 |$ 3.90 |

|Less fixed expenses | 190,000 | |

|Operating income |$ 35,225 | |

c. Under this plan, the commission increased by $0.03 per jersey, or $1,575.

d. The two plans’ operating incomes differ by only $200, so there is not an overwhelming monetary advantage of one over the other. However, under plan 2, the company gains access to a large database of potential customers. The database could provide long-term benefits of additional sales in future periods.

If the sales team could be motivated to work hard enough to achieve the new sales volume with the smaller commission, Universal managers should seriously consider option 2.

LO: 3, Bloom: AP, C, Unit: 3-2, Difficulty: Difficult, Min: 20-25, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-23

a. Calculate total fixed expenses using the breakeven formula:

|[pic] = |20,000 |

| | |

|[pic] = |20,000 |

| | |

|Fixed Expenses = |20,000 × $12.60 |

|Fixed Expenses = |$252,000 |

Use the 40% tax rate and $15,120 net income given in the problem to calculate operating income of $25,200 ([pic]). Add this amount to the $252,000 fixed expenses to calculate contribution margin of $277,200.

| |Total |Per unit |

|Sales |$396,000 |$18.00 |

|Variable expenses | 118,800 | 5.40 |

|Contribution margin |277,200 |$ 12.60 |

|Less fixed expenses | 252,000 | |

|Operating income |25,200 | |

|Income tax (40%) | 10,080 | |

|Net income |$ 15,120 | |

b. new sales price: $21.00

new variable cost per unit: $5.40 + [pic] = $7.20

new fixed expenses: $252,000 + $30,900 = $282,900

|Breakeven point in units = |[pic] |

| | |

|[pic] = |20,500 T-shirts |

c. new sales price: $21.00

new variable cost per unit: $5.40 + [pic] = $7.20

new fixed expenses: $252,000 + $30,900 = $282,900

target operating income of $48,300 ([pic])

|Breakeven point in units = |[pic] |

| | |

|[pic] = |24,000 T-shirts |

LO: 1, 3, Bloom: AP, Unit: 3-1, 3-2, Difficulty: Difficult, Min: 20-25, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-24

a. At the breakeven point, contribution margin equals fixed expenses.

($18.00 - $13.00) × 15,000 hats = $75,000

b. $14,000 net income with a 30% tax rate yields $20,000 in operating income ([pic]). Using the profit equation:

|$18.00x - $13.00x - $75,000 = |$20,000 |

|$5.00x = |$95,000 |

|x = |19,000 hats |

Or approach the question as a target income question:

[pic] = 19,000 hats

c.

|Margin of Safety = |19,000 hats – 15,000 hats |

|= |4,000 hats |

|4,000 hats × $18.00 = |$72,000 |

d. $17,500 net income with a 30% tax rate yields $25,000 in operating income ([pic]). Using the profit equation:

|$18.00x - $13.00x - $75,000 = |$25,000 |

|$5.00x = |$100,000 |

|x = |20,000 hats |

Or:

[pic] = 20,000 hats

e. new variable cost = $14.00 per hat

new contribution margin = $4.00 per hat

|$18.00x – $14.00x – $75,000 = |0 |

|$4.00x = |$75,000 |

|x = |18,750 hats |

Or:

[pic] = 18,750 hats

f.

• seek a new supplier at a lower cost per hat

• raise prices to increase contribution margin

• do nothing and accept the lower level of income

g. new sales price: $20

new volume: 19,000 × .95 = 18,050 hats

Operating Income

[($20.00 - $14.00) × 18,050 hats] - $75,000 = $33,300

Net Income

$33,300 × .7 = $23,310

LO: 1,2,3, Bloom: AP, C, Unit: 3-1, 3-2, Difficulty: Moderate, Min: 30-40, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-25

a.

|$36.00x - $16.00x - $450,000 = |0 |

|$20.00x = |$450,000 |

|x = |22,500 units |

Or:

[pic] = 22,500 hats

b. Maximum operating income:

|($36.00 × 25,000) - ($16.00 × 25,000) - $450,000 = |$50,000 |

Maximum net income:

$50,000 × .06 = $30,000

c. $75,000 net income with a 40% tax rate yields $125,000 in operating income ([pic]). Using the profit equation:

|$36.00x - $16.00x - $450,000 = |$125,000 |

|$20.00x = |$575,000 |

|x = |28,750 units |

Or:

[pic] = 28,750 hats

d. $75,000 net income with a 40% tax rate yields $125,000 in operating income ([pic]). Using the profit equation:

|(SP × 25,000) - ($16.00 × 25,000) - $450,000 = |$125,000 |

|(SP × 25,000) - ($400,000) = |$575,000 |

|SP - $16.00 = |[pic] |

|SP - $16.00 = |$23.00 |

|SP = |$39.00 |

e. The project manager needs to look for ways to reduce the costs to produce the product or look for ways to expand capacity beyond the current limit of 25,000 units.

LO: 1,2,3, Bloom: AP, C, Unit: 3-1, 3-2, Difficulty: Moderate, Min: 25-30, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-26

a. new variable cost of goods sold: $12.00 × 1.15 = $13.80 per unit

new total variable costs: $13.80 + $10.60 + $3.00 = $27.40 per unit

new contribution margin: $40.00 - $27.40 = $12.60 per unit

new fixed expenses: $7,800,000 + $1,550,000 + $3,250,000 +

$150,000 = $12,750,000

$1,800,000 net income with a 40% tax rate yields $3,000,000 in operating income ([pic]). Using the profit equation:

|$40.00x – $27.40x – $12,750,000 = |$3,000,000 |

|$12.60x = |$15,750,000 |

|x = |1,250,000 units |

Or:

[pic] = 1,250,000 hats

sales revenue required = 1,250,000 hats × $40.00 = $50,000,000

b.

|current contribution margin ratio = |[pic] = 36% |

|new contribution margin ratio = |[pic] = 36% |

|SP - $27.40 = |.36SP |

|.64SP = |$27.40 |

|SP = |$42.8125, rounded to $42.82 |

LO: 2, 3, Bloom: AP, Unit: 3-2, Difficulty: Moderate, Min: 15, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-27

a.

|Degree of operating leverage = |[pic] |

| | |

|= |[pic] |

|= |2 |

b. 5% sales increase × 2 degree of operating leverage =10% increase

new operating income = $2,000,000 × 1.10 = $2,200,000

c. Moving employees from a fixed salary to a commission based on sales will increase variable costs and decrease contribution margin. This will cause the degree of operating leverage to decrease.

LO: 4, Bloom: AP, AN, Unit: 3-2, Difficulty: Easy, Min: 12, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-28

a. When the sales mix changes, the effect on the breakeven point and operating income depends on the contribution margin ratios of the product lines involved. If coffee-making equipment has a higher contribution margin ratio than whole coffee beans, all other things equal, the breakeven point will decrease and operating income will increase as a result of the new sales mix. If whole coffee beans have the higher contribution margin of the two, the opposite will be true.

b. Yes, this is a desirable change in the sales mix. A higher percentage of a dollar from equipment sales than a dollar from whole coffee bean sales will be retained to cover fixed expenses and provide operating income.

c. No. There are a variety of products within the equipment and accessories line, and they all probably have different contribution margin ratios. For example, the contribution margin ratio on a high-end expresso machine is likely different from the contribution margin ratio of an insulated coffee mug.

LO: 5, Bloom: AN, C, Unit: 3-3, Difficulty: Moderate, Min: 20-25, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-29

a. molded briefcase contribution margin: $40.00 - $27.40 = $12.60

leather briefcase contribution margin: $90.00 - $36.00 = $54.00

fixed expenses: $12,750,000 + $300,000 = $13,050,000

Let x = number of leather briefcases sold

|$54.00x + $12.60(4x) - $13,050,000 = |0 |

|$104.40x = |$13,050,000 |

|x = |125,000 leather briefcases |

|4x = |500,000 molded briefcases |

b. new leather sales price: $66.00

new leather contribution margin: $66.00 - $36.00 = $30.00

new fixed expenses: $12,750,000 + $177,600 = $12,927,600

new sales mix: 1 molded briefcase for every 3 leather briefcases

Let x = number of molded briefcases sold

|$12.60x + $30.00(3x) - $12,927,600 = |0 |

|$102.6x = |$12,927,600 |

|x = |126,000 molded briefcases |

|3x = |378,000 leather briefcases |

c. The biggest risk of introducing the leather briefcase is the potential cannibalization of molded briefcase sales. While we have calculated breakeven points, managers also need to consider expected operating income under various scenarios.

LO: 1,4, Bloom: AP, C, Unit: 3-1, 3-2, Difficulty: Difficult, Min: 20-25, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-30

a. sales mix: 4:6 or 1:1.5

Let x = number of XL-709s sold

|($10.00 - $6.00)x + ($25.00 - $17.00)(1.5x) - $200,000 = |0 |

|$4.00x + $8.00(1.5x) = |$200,000 |

|16x = |$200,000 |

|x = |12,500 XL-709s |

|1.5x = |18,750 CD-918s |

b. new XL-709 contribution margin: $14.00 - $6.00 = $8.00

Let x = number of XL-709s sold

|($14.00 - $6.00)x + ($25.00 - $17.00)(1.5x) - $200,000 = |0 |

|$8.00x + $8.00(1.5x) = |$200,000 |

|20x = |$200,000 |

|x = |10,000 XL-709s |

|1.5x = |15,000 CD-918s |

c. new sales mix: 4:8 or 1:2

new fixed expense = $200,000 + $60,000 = $260,000

Let x = number of XL-709s sold

|($10.00 - $6.00)x + ($25.00 - $17.00)(2x) - $260,000 = |0 |

|$4.00x + $8.00(2x) = |$260,000 |

|20x = |$260,000 |

|x = |13,000 XL-709s |

|2x = |26,000 CD-918s |

d. Operating income if the company advertises XL-709:

[($14 - $6) × 50,000)] + [($25 - $17) × 60,000)] - $260,000 = $620,000

Operating income if the company advertises CD-918:

[($10 - $6) × 40,000)] + [($25 - $17) × 80,000)] - $260,000 = $540,000

The company should advertise product XL-709 since it expects to earn $80,000 more in operating income than if it advertised CD-918.

LO: 1,5, Bloom: AP, C, Unit: 3-1, 3-3, Difficulty: Difficult, Min: 25-30, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-31

a.

|Price |Demand |Sales |Variable |Fixed expense |Operating |

| | |Revenue |Cost | |Income |

|$200 | 40,657 | $ 8,131,400 | $2,439,420 | $350,000 | $5,341,980 |

| $190 | 44,486 | $ 8,452,340 | $2,669,160 | $350,000 | $5,433,180 |

| $180 | 48,675 | $ 8,761,500 | $2,920,500 | $350,000 | $5,491,000 |

| $170 | 53,259 | $ 9,054,030 | $3,195,540 | $350,000 | $5,508,490 |

| $160 | 58,275 | $ 9,324,000 | $3,496,500 | $350,000 | $5,477,500 |

| $150 | 63,763 | $ 9,564,450 | $3,825,780 | $350,000 | $5,388,670 |

| $140 | 69,768 | $ 9,767,520 | $4,186,080 | $350,000 | $5,231,440 |

| $130 | 76,338 | $ 9,923,940 | $4,580,280 | $350,000 | $4,993,660 |

| $120 | 83,527 | $10,023,240 | $5,011,620 | $350,000 | $4,661,620 |

| $110 | 91,393 | $10,053,230 | $5,483,580 | $350,000 | $4,219,650 |

| $100 | 100,000 | $10,000,000 | $6,000,000 | $350,000 | $3,650,000 |

A price of $170 generates the highest operating income.

b. [pic] = 183.33%

c. at $200: [pic] = 233.33%

at $100: [pic] = 66.67%

d. Cost-plus pricing does not take demand schedules into consideration when setting prices. Management must combine their knowledge of demand with desired markups to determine the best price to set.

LO: 6, Bloom: AP, E, Unit: 3-4, Difficulty: Moderate, Min: 20-25, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Problem 3-32

a. The minimum price Gail should quote is $30.00 per plate plus any other variable costs of serving the meal.

b. $30.00 × 1.6 = $48 per plate

c. [pic] = 50%

d. If Gail met the lower price of $45.00 per plate and won the bid, she would cover her variable costs and generate contribution margin to cover her fixed expenses and provide operating profit. She would also receive “free” advertising and have the potential for generating future sales that she would not have otherwise made.

On the downside, if the mayor chooses to use Gail again, he may expect the same level of markup concession. Future customers may also expect this same menu at $45.00 per plate.

LO: 6, 7, Bloom: AP, C, Unit: 3-4, Difficulty: Easy, Min: 15-20, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

SOLUTIONS TO CASES

Case 3-33

a. Tiffany’s fixed expenses are a much higher percentage of sales than Blue Nile. It has relatively more fixed expenses associated with building occupancy and salaries than Blue Nile.

b. While Blue Nile’s gross margin percentage is 37.2 points below Tiffany’s, its operating expense percentage is 29.5 points lower as well. Therefore the difference in operating income is 7.7 points. Blue Nile would hope to make up the difference in sales volume.

c. Tiffany, because it is likely to have higher fixed expenses relative variable costs due primarily to building space.

d. A move toward lower-margin products will decrease the contribution margin.

e. ’s cost structure is most like Blue Nile. Both are online retailers with little investment in buildings.

LO: 4, Bloom: AN, Unit: 3-2, Difficulty: Moderate, Min: 20-25, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Case 3-34

a. Operating income includes fixed expenses which do not change with changes in volume. By using operating income per mascot, Blake is treating these fixed expenses as variable costs. For decision making, Blake needs to use contribution margin per unit.

b. Use the high-low method to calculate the cost formula for each cost. Then use the cost formulas to create the contribution format income statement.

|Cost |Behavior |Cost formula |

|Cost of goods sold |Variable |y = $10x |

|Rent |Fixed |y = $1,500 |

|Wages |Mixed |y = $500 + $3x |

|Shipping |Variable |y = $1.25x |

|Utilities |Fixed |y = $750 |

|Advertising |Mixed |y = $500 + .25x |

|Insurance |Fixed |y = $400 |

| |Total |Per unit |

|Sales |$37,500 |$25.00 |

|Less variable costs | | |

| Cost of goods sold |15,000 |10.00 |

| Wages |4,500 |3.00 |

| Shipping |1,875 |1.25 |

| Advertising | 375 | 0.25 |

|Total variable costs | 21,750 | 14.50 |

|Contribution margin |15,750 |$10.50 |

|Less fixed expenses | | |

| Rent |1,500 | |

| Wages |500 | |

| Utilities |750 | |

| Advertising |500 | |

| Insurance | 400 | |

|Total fixed expenses | 3,650 | |

|Operating income |$12,100 | |

c.

|Sales revenue – Variable costs – Fixed expenses = |Operating profit |

|($25.00 × 500) - ($14.50 × 500) - $3,650 = |$1,600 |

d.

|$25.00x - $14.50x -$3,650 = |$3,700 |

|$10.50x = |$7,350 |

|x = |700 mascots |

Or

[pic] = 700 mascots

To break even:

|$25.00x - $14.50x -$3,650 = |$0 |

|$10.50x = |$3,650 |

|x = |347.6 mascots, rounded to 348 |

Or

[pic] = 347.6 mascots, rounded to 348

e. Option 1

new fixed expenses: $3,650 + $1,200 = $4,850

new sales volume: 960 mascots

|($25.00 × 960) - ($14.50 × 960) - $4,850 = |Operating income |

|$24,000 - $13,920 - $4,850 = |$5,230 |

Option 2

new sales price: $25.00 × .90 = $22.50

new sales volume: 1,000 mascots

|($22.50 × 1,000) - ($14.50× 1,000) - $3,650 = |Operating income |

|$22,500 - $14,500 - $3,650 = |$4,350 |

Blake should implement option 1 to earn the highest operating income.

Blake would be indifferent between the two plans at the point where they generate the same operating income.

|($25.00 - $14.50)x - $4,850 = |($22.50 - $14.50)x - $3,650 |

|$10.50x - $4,850 = |$8.00x - $3,650 |

|$2.50x = |$1,200 |

|x = |480 mascots |

f. new variable cost of goods sold: $10.00 × 1.2 = $12.00

new variable cost per unit: $12.00 + $3.00 + $1.25 + $0.25 = $16.50

new sales price: $25.00 + [pic] = $26.00

new contribution margin: $26.00 - $16.50 = $9.50

new sales volume: 1,200 × .95 = 1,140

new projection with price increase

|[($26.00 - $16.50) × 1,140] - $3,650 = |$7,180 |

new projection without price increase

|[($25.00 - $16.50) × 1,200] - $3,650 = |$6,550 |

Blake is better off increasing the price by $1.00 even though it reduces the sale volume.

g. new sales mix: 1 blanket for every 3 mascots

blanket variable cost: $32.00 + $3.00 + $1.25 + $0.25 = $36.50

blanket contribution margin: $55.00 - $36.50 = $18.50

new fixed expenses = $3,650 + $350 = $4,000

Let x = number of blankets sold

|($55.00 - $36.50)x + ($25.00 - $14.50)(3x) - $4,000 = |0 |

|$18.50x + $10.50(3x) = |$4,000 |

|$50.00x = |$4,000 |

|x = |80 blankets |

|3x = |240 mascots |

LO: 1,2,3,5, Bloom: AN, AP, Unit: 3-1, 3-2, 3-3, Difficulty: Difficult, Min: 35-40, AACSB: Analytic, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

Case 3-35

a. Among the ethical issues in the case are:

• Jeff presented a long-term contract proposal that apparently was not within normal operating guidelines, since it required special approval.

• Jeff withheld critical information about the contract and the quality of the cartons.

• Jeff created a conflict of interest by entering into a contract with his brother.

• Jeff was influenced by the promise of attending the Super Bowl with his brother if he signed the contract.

• Jeff knowingly purchased lower-quality cartons to get a lower cost so that managers would look favorably on his performance and reward him with a promotion.

• The company has collected damages from freight carriers under the pretense that the carrier caused the damage when it was due to the lower-quality cartons.

• Jeff continued to withhold information when confronted by Dan about the lower-quality cartons.

b. Jeff and Dan have several possible action steps at this point.

• Jeff should inform Dan of his actions in obtaining the contract, including the conflict of interest with his brother and the fact that he knowingly purchased lower-quality cartons to inflate his performance evaluation.

• Dan should contact the carriers and offer to reimburse the claims that have been paid to date.

• Dan should stop using the lower-quality cartons immediately to prevent future damage claims by customers.

• Dan should investigate cancelling the remaining portion of the long-term contract.

• Dan should purchase cartons of the correct quality.

c. In this situation, the costs of ethical decision making include:

• The cost of damage claims

• The cost of inferior cartons if they can’t be returned or if the contract cannot be voided

In this situation, the benefits of ethical decision making include:

• Repairing the company’s reputation

• Building trust with freight carriers, customers, and employees

• Building relationships with stakeholders

• Demonstrating to employees that ethical decision making is valued

The costs of not making the appropriate decision include:

• Continued damage to company reputation from damaged goods

• Implicit approval of unethical behavior

• Increased unethical behavior, as conflicts of interest are viewed by employees as a normal part of doing business

• Increased unethical behavior as employees see that managers do not address unethical behavior

LO: 3, Bloom: AN, Unit: 3-2, Difficulty: Moderate, Min: 20-25, AACSB: Ethics, AICPA FN: Decision Modeling, AICPA PC: Problem Solving and Decision Making, IMA: Decision Analysis

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