# CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS

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1 3-16 (10 min.) CVP computations. CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS Variable Fixed Total Operating Contribution Contribution Revenues Costs Costs Costs Income Margin Margin % a. \$2,000 \$ 500 \$300 \$ 800 \$1,200 \$1, % b. 2,000 1, , % c. 1, , % d. 1, , % 3-1

2 3-17 (10 15 min.) CVP computations. 1a. Sales (\$30 per unit 200,000 units) \$6,000,000 Variable costs (\$25 per unit 200,000 units) 5,000,000 Contribution margin \$1,000,000 1b. Contribution margin (from above) \$1,000,000 Fixed costs 800,000 Operating income \$ 200,000 2a. Sales (from above) \$6,000,000 Variable costs (\$16 per unit 200,000 units) 3,200,000 Contribution margin \$2,800,000 2b. Contribution margin \$2,800,000 Fixed costs 2,400,000 Operating income \$ 400, Operating income is expected to increase by \$200,000 if Ms. Schoenen s proposal is accepted. The management would consider other factors before making the final decision. It is likely that product quality would improve as a result of using state of the art equipment. Due to increased automation, probably many workers will have to be laid off. Patel s management will have to consider the impact of such an action on employee morale. In addition, the proposal increases the company s fixed costs dramatically. This will increase the company s operating leverage and risk. 3-2

3 3-22 (20 25 min.) CVP analysis, income taxes. 1. Variable cost percentage is \$3.20 \$8.00 = 40% Let R = Revenues needed to obtain target net income \$105,000 R 0.40R \$450,000 = R = \$450,000 + \$150,000 R = \$600, R = \$1,000,000 or, Target net income \$105,000 \$450, Tax rate Breakeven revenues = = = \$1,000,000 Contribution margin percentage 0.60 Proof: Revenues \$1,000,000 Variable costs (at 40%) 400,000 Contribution margin 600,000 Fixed costs 450,000 Operating income 150,000 Income taxes (at 30%) 45,000 Net income \$ 105,000 2.a. Customers needed to earn net income of \$105,000: Total revenues Sales check per customer \$1,000,000 \$8 = 125,000 customers b. Customers needed to break even: Contribution margin per customer = \$8.00 \$3.20 = \$4.80 Breakeven number of customers = Fixed costs Contribution margin per customer = \$450,000 \$4.80 per customer = 93,750 customers 3. Using the shortcut approach: Change in Unit Change in net income = number of customers contribution (1 Tax rate) margin = (150, ,000) \$4.80 (1 0.30) = \$120, = \$84,000 New net income = \$84,000 + \$105,000 = \$189,000 The alternative approach is: Revenues, 150,000 \$8.00 \$1,200,000 Variable costs at 40% 480,000 Contribution margin 720,000 Fixed costs 450,000 Operating income 270,000 Income tax at 30% 81,000 Net income \$ 189,

4 3-24 (10 min.) CVP analysis, margin of safety. Fixed costs 1. Breakeven point revenues = Contribution margin percentage \$600,000 Contribution margin percentage = = 0.40 or 40% \$1,500,000 Selling price Variable cost per unit 2. Contribution margin percentage = Selling price SP \$ = SP 0.40 SP = SP \$ SP = \$15 SP = \$25 3. Breakeven sales in units = Revenues Selling price = \$1,500,000 \$25 = 60,000 units Margin of safety in units = sales in units Breakeven sales in units = 80,000 60,000 = 20,000 units Revenues, 80,000 units \$25 \$2,000,000 Breakeven revenues 1,500,000 Margin of safety \$ 500,

5 3-25 (25 min.) Operating leverage. 1a. Let Q denote the quantity of carpets sold Breakeven point under Option 1 \$500Q \$350Q = \$5,000 \$150Q = \$5,000 Q = \$5,000 \$150 = 34 carpets (rounded up) 1b. Breakeven point under Option 2 \$500Q \$350Q (0.10 \$500Q) = 0 100Q = 0 Q = 0 2. Operating income under Option 1 = \$150Q \$5,000 Operating income under Option 2 = \$100Q Find Q such that \$150Q \$5,000 = \$100Q \$50Q = \$5,000 Q = \$5,000 \$50 = 100 carpets Revenues = \$ carpets = \$50,000 For Q = 100 carpets, operating income under both Option 1 and Option 2 = \$10,000 For Q > 100, say, 101 carpets, Option 1 gives operating income = (\$ ) \$5,000 = \$10,150 Option 2 gives operating income = \$ = \$10,100 So Color Rugs will prefer Option 1. For Q < 100, say, 99 carpets, Option 1 gives operating income = (\$150 99) \$5,000 = \$9,850 Option 2 gives operating income = \$ = \$9,900 So Color Rugs will prefer Option 2. Contribution margin 3. Degree of operating leverage = Operating income \$ Under Option 1, degree of operating leverage = \$10,000 \$ Under Option 2, degree of operating leverage = \$10,000 = 1.5 = The calculations in requirement 3 indicate that when sales are 100 units, a percentage change in sales and contribution margin will result in 1.5 times that percentage change in operating income for Option 1, but the same percentage change in operating income for Option 2. The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes. 3-5

6 3-20 (20 min.) CVP exercises. 1a. [Units sold (Selling price Variable costs)] Fixed costs = Operating income [5,000,000 (\$0.50 \$0.30)] \$900,000 = \$100,000 1b. Fixed costs Contribution margin per unit = Breakeven units \$900,000 [(\$0.50 \$0.30)] = 4,500,000 units Breakeven units Selling price = Breakeven revenues 4,500,000 units \$0.50 per unit = \$2,250,000 or, Selling price -Variable costs Contribution margin ratio = Selling price \$ \$0.30 = = 0.40 \$0.50 Fixed costs Contribution margin ratio = Breakeven revenues \$900, = \$2,250, ,000,000 (\$0.50 \$0.34) \$900,000 = \$ (100,000) 3. [5,000,000 (1.1) (\$0.50 \$0.30)] [\$900,000 (1.1)] = \$ 110, [5,000,000 (1.4) (\$0.40 \$0.27)] [\$900,000 (0.8)] = \$ 190, \$900,000 (1.1) (\$0.50 \$0.30) = 4,950,000 units 6. (\$900,000 + \$20,000) (\$0.55 \$0.30) = 3,680,000 units 3-6

7 3-23 (30 min.) CVP analysis, sensitivity analysis. 1. SP = \$30.00 ( margin to bookstore) = \$ = \$21.00 VCU = \$ 4.00 variable production and marketing cost 3.15 variable author royalty cost (0.15 \$21.00) \$ 7.15 CMU = \$21.00 \$7.15 = \$13.85 per copy FC = \$ 500,000 fixed production and marketing cost 3,000,000 up-front payment to Washington \$3,500,000 Solution Exhibit 3-23A shows the PV graph. SOLUTION EXHIBIT 3-23A PV Graph for Media Publishers \$4,000 FC = \$3,500,000 CMU = \$13.85 per book sold 3,000 2,000 Operating income (000 s) 1,000 0 Units sold 100, , , , ,000-1, ,708 units -2,000-3,000 \$3.5 million -4,

8 2a. Breakeven number of units FC = CMU \$3,500,000 = \$13.85 = 252,708 copies sold (rounded up) 2b. Target OI = FC+OI CMU \$3,500,000 + \$2,000,000 = \$13.85 \$5,500,000 = \$13.85 = 397,112 copies sold (rounded up) 3a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of \$30 has the following effects: SP = \$30.00 (1 0.20) = \$ = \$24.00 VCU = \$ 4.00 variable production and marketing cost variable author royalty cost (0.15 \$24.00) \$ 7.60 CMU = \$24.00 \$7.60 = \$16.40 per copy Breakeven number of units = FC CMU \$3,500,000 = \$16.40 = 213,415 copies sold (rounded up) The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies. 3b. Increasing the listed bookstore price to \$40 while keeping the bookstore margin at 30% has the following effects: SP = \$40.00 (1 0.30) = \$ = \$28.00 VCU = \$ 4.00 variable production and marketing cost variable author royalty cost (0.15 \$28.00) \$ 8.20 CMU= \$28.00 \$8.20 = \$19.80 per copy 3-8

9 Breakeven number of units = \$3,500,000 \$19.80 = 176,768 copies sold (rounded up) The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 copies. 3c. The answers to requirements 3a and 3b decrease the breakeven point relative to that in requirement 2 because in each case fixed costs remain the same at \$3,500,000 while the contribution margin per unit increases. 3-9

10 3-27 (30 min.) Sales mix, new and upgrade customers. 1. SP VCU CMU New Customers \$ Upgrade Customers \$ The 60%/40% sales mix implies that, in each bundle, 3 units are sold to new customers and 2 units are sold to upgrade customers. Contribution margin of the bundle = 3 \$ \$80 = \$360 + \$160 = \$520 Breakeven point in bundles = \$14,000,000 = 26,923 bundles \$520 Breakeven point in units is: Sales to new customers: 26,923 bundles 3 units per bundle 80,769 units Sales to upgrade customers: 26,923 bundles 2 units per bundle 53,846 units Total number of units to breakeven (rounded) 134,615 units Alternatively, Let S = Number of units sold to upgrade customers 1.5S = Number of units sold to new customers Revenues Variable costs Fixed costs = Operating income [\$210 (1.5S) + \$120S] [\$90 (1.5S) + \$40S] \$14,000,000 = OI \$435S \$175S \$14,000,000 = OI Breakeven point is 134,616 units when OI = 0 because \$260S = \$14,000,000 S = 53,846 units sold to upgrade customers (rounded) 1.5S = 80,770 units sold to new customers (rounded) BEP = 134,616 units Check Revenues (\$210 80,770) + (\$120 53,846) \$23,423,220 Variable costs (\$90 80,770) + (\$40 53,846) 9,423,140 Contribution margin 14,000,080 Fixed costs 14,000,000 Operating income (caused by rounding) \$

11 2. When 200,000 units are sold, mix is: Units sold to new customers (60% 200,000) 120,000 Units sold to upgrade customers (40% 200,000) 80,000 Revenues (\$ ,000) + (\$120 80,000) \$34,800,000 Variable costs (\$90 120,000) + (\$40 80,000) 14,000,000 Contribution margin 20,800,000 Fixed costs 14,000,000 Operating income \$ 6,800,000 3a. At New 50%/Upgrade 50% mix, each bundle contains 1 unit sold to new customer and 1 unit sold to upgrade customer. Contribution margin of the bundle = 1 \$ \$80 = \$120 + \$80 = \$200 Breakeven point in bundles = \$14,000,000 = 70,000 bundles \$200 Breakeven point in units is: Sales to new customers: 70,000 bundles 1 unit per bundle 70,000 units Sales to upgrade customers: 70,000 bundles 1 unit per bundle 70,000 units Total number of units to breakeven 140,000 units Alternatively, Let S = Number of units sold to upgrade customers then S = Number of units sold to new customers [\$210S + \$120S] [\$90S + \$40S] \$14,000,000 = OI 330S 130S = \$14,000, S = \$14,000,000 S = 70,000 units sold to upgrade customers S = 70,000 units sold to new customers BEP = 140,000 units Check Revenues (\$210 70,000) + (\$120 70,000) \$23,100,000 Variable costs (\$90 70,000) + (\$40 70,000) 9,100,000 Contribution margin 14,000,000 Fixed costs 14,000,000 Operating income \$ 0 3b. At New 90%/ Upgrade 10% mix, each bundle contains 9 units sold to new customers and 1 unit sold to upgrade customers. Contribution margin of the bundle = 9 \$ \$80 = \$1,080 + \$80 = \$1,160 Breakeven point in bundles = \$14,000,000 = 12,069 bundles (rounded) \$1,160 Breakeven point in units is: Sales to new customers: 12,069 bundles 9 units per bundle 108,621 units Sales to upgrade customers: 12,069 bundles 1 unit per bundle 12,069 units Total number of units to breakeven 120,690 units 3-11

12 Alternatively, Let S = Number of units sold to upgrade customers then 9S = Number of units sold to new customers [\$210 (9S) + \$120S] [\$90 (9S) + \$40S] \$14,000,000 = OI 2,010S 850S = \$14,000,000 1,160S = \$14,000,000 S = 12,069 units sold to upgrade customers (rounded up) 9S = 108,621 units sold to new customers (rounded up) 120,690 units Check Revenues (\$ ,621) + (\$120 12,069) \$24,258,690 Variable costs (\$90 108,621) + (\$40 12,069) 10,258,650 Contribution margin 14,000,040 Fixed costs 14,000,000 Operating income (caused by rounding) \$ 40 3c. As Zapo increases its percentage of new customers, which have a higher contribution margin per unit than upgrade customers, the number of units required to break even decreases: Requirement 3(a) Requirement 1 Requirement 3(b) New Customers 50% Upgrade Customers 50% Breakeven Point 140, , ,

13 3-38 (20 30 min.) CVP analysis, shoe stores. 1. CMU (SP VCU = \$30 \$21) \$ 9.00 a. Breakeven units (FC CMU = \$360,000 \$9 per unit) 40,000 b. Breakeven revenues (Breakeven units SP = 40,000 units \$30 per unit) \$1,200, Pairs sold 35,000 Revenues, 35,000 \$30 \$1,050,000 Total cost of shoes, 35,000 \$ ,500 Total sales commissions, 35,000 \$ ,500 Total variable costs 735,000 Contribution margin 315,000 Fixed costs 360,000 Operating income (loss) \$ (45,000) 3. Unit variable data (per pair of shoes) Selling price \$ Cost of shoes Sales commissions 0 Variable cost per unit \$ Annual fixed costs Rent \$ 60,000 Salaries, \$200,000 + \$81, ,000 Advertising 80,000 Other fixed costs 20,000 Total fixed costs \$ 441,000 CMU, \$30 \$19.50 \$ a. Breakeven units, \$441,000 \$10.50 per unit 42,000 b. Breakeven revenues, 42,000 units \$30 per unit \$1,260, Unit variable data (per pair of shoes) Selling price \$ Cost of shoes Sales commissions 1.80 Variable cost per unit \$ Total fixed costs \$ 360,000 CMU, \$30 \$21.30 \$ 8.70 a. Break even units = \$360,000 \$8.70 per unit 41,380 (rounded up) b. Break even revenues = 41,380 units \$30 per unit \$1,241, Pairs sold 50,000 Revenues (50,000 pairs \$30 per pair) \$1,500,000 Total cost of shoes (50,000 pairs \$19.50 per pair) \$ 975,000 Sales commissions on first 40,000 pairs (40,000 pairs \$1.50 per pair) 60,000 Sales commissions on additional 10,000 pairs 3-13

14 [10,000 pairs (\$ \$0.30 per pair)] 18,000 Total variable costs \$1,053,000 Contribution margin \$ 447,000 Fixed costs 360,000 Operating income \$ 87,000 Alternative approach: Breakeven point in units = 40,000 pairs Store manager receives commission of \$0.30 on 10,000 (50,000 40,000) pairs. Contribution margin per pair beyond breakeven point of 10,000 pairs = \$8.70 (\$30 \$21 \$0.30) per pair. Operating income = 10,000 pairs \$8.70 contribution margin per pair = \$87,

15 3-39 (30 min.) CVP analysis, shoe stores (continuation of 3-38). No. of units sold CM per Unit CM Salaries + Commission Plan Higher Fixed Salaries Only Fixed Costs Operating Income CM per Unit CM Fixed Costs Operating Income Difference in favor of higher-fixedsalary-only (1) (2) (3)=(1) (2) (4) (5)=(3) (4) (6) (7)=(1) (6) (8) (9)=(7) (8) (10)=(9) (5) 40,000 \$9.00 \$360,000 \$360,000 0 \$10.50 \$420,000 \$441,000 \$ (21,000) \$(21,000) 42, , ,000 18, , ,000 0 (18,000) 44, , ,000 36, , ,000 21,000 (15,000) 46, , ,000 54, , ,000 42,000 (12,000) 48, , ,000 72, , ,000 63,000 (9,000) 50, , ,000 90, , ,000 84,000 (6,000) 52, , , , , , ,000 (3,000) 54, , , , , , , , , , , , , ,000 3,000 58, , , , , , ,000 6,000 60, , , , , , ,000 9,000 62, , , , , , ,000 12,000 64, , , , , , ,000 15,000 66, , , , , , ,000 18,

16 1. See preceding table. The new store will have the same operating income under either compensation plan when the volume of sales is 54,000 pairs of shoes. This can also be calculated as the unit sales level at which both compensation plans result in the same total costs: Let Q = unit sales level at which total costs are same for both plans \$19.50Q + \$360,000 + \$ \$81,000 = \$21Q + \$360,000 \$1.50 Q = \$81,000 Q = 54,000 pairs 2. When sales volume is above 54,000 pairs, the higher-fixed-salaries plan results in lower costs and higher operating incomes than the salary-plus-commission plan. So, for an expected volume of 55,000 pairs, the owner would be inclined to choose the higher-fixed-salaries-only plan. But it is likely that sales volume itself is determined by the nature of the compensation plan. The salary-plus-commission plan provides a greater motivation to the salespeople, and it may well be that for the same amount of money paid to salespeople, the salary-plus-commission plan generates a higher volume of sales than the fixed-salary plan. 3. Let TQ = Target number of units For the salary-only plan, \$30.00TQ \$19.50TQ \$441,000 = \$168,000 \$10.50TQ = \$609,000 TQ = \$609,000 \$10.50 TQ = 58,000 units For the salary-plus-commission plan, \$30.00TQ \$21.00TQ \$360,000 = \$168,000 \$9.00TQ = \$528,000 TQ = \$528,000 \$9.00 TQ = 58,667 units (rounded up) The decision regarding the salary plan depends heavily on predictions of demand. For instance, the salary plan offers the same operating income at 58,000 units as the commission plan offers at 58,667 units. 4. WalkRite Shoe Company Operating Income Statement, 2008 Revenues (48,000 pairs \$30) + (2,000 pairs \$18) \$1,476,000 Cost of shoes, 50,000 pairs \$ ,000 Commissions = Revenues 5% = \$1,476, ,800 Contribution margin 427,200 Fixed costs 360,000 Operating income \$ 67,

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