# Fixed costs. Contribution margin ratio

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1 SOLUTIONS TO EXERCISES EXERCISE 3-1 (20 minutes) 1. Fixed costs B E point in units = Contribution margin per unit \$180,000 \$180,000 = = = 7,500 units \$40 - \$16 \$24 B E point in sales dollars = Fixed costs Contribution margin ratio \$180,000 \$180,000 \$180,000 = = = CM Selling Price \$24 \$ = \$300,000

2 2. At the break-even point, CM = fixed costs. Accordingly, the total CM is \$180, Total CM = CM per unit x Units sold = \$24 x 12,000 units = \$288,000 Operating income = Total CM - Fixed costs = \$288,000 - \$180,000 = \$108,000 EXERCISE 3-1 (Continued) 4. Target sales in units = Fixed costs + Target income Contribution margin per unit = \$180,000 + \$60,000 \$24

3 = 10,000 units 5. Contribution Income Statement Sales (\$40 x 10,000 units) \$ 400, % Variable costs (\$16 x 10,000 units) 160,000 40% Contribution margin 240,000 60% Fixed costs ,000 Operating income.. \$60,000

4 EXERCISE 3-2 (10 minutes) 1. The decrease in the sales units mentioned here is called margin of safety (MS) in units. MS in units = Units sold - BE point in units = 12,000-7,500 = 4,500 units 2. MS in dollars = Total sales - BE point in dollars = \$480,000 - \$300,000 = \$180,000 MS in percentage = 4,500 units 12,000 units, or = \$180,000 \$480,000 = 37.5% 3. Yes. The sales decrease of \$150,000 is still less than the MS of \$180,000. Until the sales decreases by additional \$30,000 (\$180,000 - \$150,000), the company would still make a profit. 4. Yes. The sales decrease of 30% is still below the MS of 37.5%. Accordingly, the company would still make a profit until there is an additional sales decrease of 7.5% (37.5% - 30%).

5 EXERCISE 3-3 (20 minutes) 1. Degree of operating leverage = = Total CM Operating income \$288,000 \$108,000 = If sales increase 10% and the degree of operating leverage is , then the following effects will take place: % Increase in operating income = % Increase in sales x = 10% x = % New operating income = \$108,000 x ( ) = \$108,000 + \$28,800 = \$136, Contribution Income Statement Sales (\$40 x 12,000 x 1.1).. \$528, % Variable costs (\$16 x 13,200 units) 211,200 40% Contribution margin. 316,800 60% Fixed costs ,000 Operating income... \$136,800

6 EXERCISE 3-3 (Continued) 4. If sales decrease 20% and the degree of operating leverage is , then the following effects will take place: % Decrease in operating income = % Decrease in sales x = 20% x = % New operating income = \$108,000 x ( ) = \$108,000 - \$57,600 = \$50, Contribution Income Statement Sales (\$40 x 12,000 x 0.8).. \$384, % Variable costs (\$16 x 9,600 units) 153,000 40% Contribution margin. 230,000 60% Fixed costs ,000 Operating income... \$50,400

7 PROBLEM 3-11 (25 minutes) 1. a. Variable costs per unit: Selling price..... \$ 30 Variable cost ratio: 1 - CM ratio = 100% - 40% = 60% Variable costs per unit... \$ 18 b. Break-even point (Equation method): Sales = VC + FC \$30X = \$18X + \$120,000 \$30X - \$18X = \$120,000 \$12X = \$120,000 X = 10,000 units (BE point in units) \$30X = \$300,000 (BE point in sales dollars) c. Let X = Required volume in units. Sales = VC + FC + Target income \$30X = \$18X + \$120,000 + \$24,000 \$30X - \$18X = \$144,000 \$12X = \$144,000 X = \$144,000 ( \$12 = 12,000 units Required sales: \$30X = \$30 x 12,000 units = \$360,000

8 2. a. CM per unit: Selling price....\$12.00 Variable expenses: Manufacturing and selling.... \$ 8.00 Sales commissions (\$12 x 5% =) Contribution margin... \$3.40 b. Operating income for the year: Total CM (\$3.40 x 9,000 units).... \$ 30,600 Fixed costs ,000 Operating income..... \$6,600 0 = \$100,010

9 PROBLEM 3-11 (Continued) 3. First determine last quarter's income. Units sold ,000 Contribution margin per unit.... x \$3 Total contribution margin.... \$75,000 Fixed costs....60,000 Operating income..... \$15,000 Required sales volume this year (\$60,000 + \$30,000) + \$15,000 = = 35,000 units \$3

10 PROBLEM 3-13 (50 minutes) 1. Selling price per unit.... \$20 100% VC per unit % CM per unit... \$12 60% B E point in units = Fixed costs Contribution margin per unit \$69,000 = = 5,750 units \$12 B E point in sales dollars = Fixed costs Contribution margin ratio \$69,000 = = \$115, Total CM (\$12 x 9,000)....\$ 108,000 Fixed costs ,000 Operating income..... \$39,000

11 3.a. Selling price per unit... \$ % New VC per unit: Existing VC... \$8 Sales commission (\$20 x 5%) % CM per unit... \$11 55% New fixed costs per quarter: Rent... \$15,000 Salaries ,000 Advertising, etc ,000 Total fixed costs.... \$55,000 PROBLEM 3-13 (Continued) B E point in units = Fixed costs Contribution margin per unit \$55,000 = = 5,000 units \$11 b. We will determine whether the new policy generates an operating income of more than \$39,000, the operating income in (2).

12 Total CM (\$11 x 9,000)..... \$99,000 Fixed costs ,000 Operating income.... \$44,000 The new income, \$44,000, is higher than the original level of \$39,000. Therefore, the answer is yes. 4. a. At the required sales level (point of indifference), the profit under each policy would be equal. Sales - Total costs = Profit Sales would be the same under both policies. Accordingly, we must find the sales level at which the total costs under each policy would be equal. Let X = Required sales volume in units. Then, \$8X + \$69,000 = \$9X + \$55,000 \$69,000 - \$55,000 = \$9X - \$8X X = 14,000 units

13 PROBLEM 3-13 (Continued) b. If 14,000 units are sold, the company would make the same profit under each plan as shown below: Original policy: Total CM (\$12 x 14,000 units) \$168,000 Fixed costs ,000 Operating income \$ 99,000 Incentive policy: Total CM (\$11 x 14,000 units)... \$154,000 Fixed costs... 55,000 Operating income.... \$ 99,000 The company would be "indifferent" as to which policy is used. 5. Incremental approach: Profit Break-even sales... 5,000 units \$ 0 Excess over break-even sales.. 1,500 CM \$11 - Extra (\$20 x 5%) = x \$10 15,000

14 Total profit \$ 15,000 Note: CM = Profit (for sales in excess of BE point) Total approach: Sales (\$20 x 6,500 units).... \$ 130,000 Variable costs: \$9 x 5,000 units = \$ 45,000 \$10 x 1,500 units =.15,000 60,000 Contribution margin... 70,000 Fixed costs ,000 Operating income.... \$ 15,000

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