# Chapter 19 (4) Cost Behavior and Cost-Volume-Profit Analysis Study Guide Solutions Fill-in-the-Blank Equations

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1 Chapter 19 (4) Cost Behavior and Cost-Volume-Profit Analysis Study Guide Solutions Fill-in-the-Blank Equations 1. Variable cost per unit 2. Fixed cost 3. Variable costs 4. Contribution margin 5. Change in sales dollars 6. Unit contribution margin 7. Change in sales units 8. Break-even sales (units) 9. Contribution margin ratio 10. Fixed costs 11. Contribution margin ratio 12. Income from operations 13. Percent change in income from operations 14. Sales 15. Break-even sales (dollars) 16. Sales (units) 1

2 2 Chapter 19 (4) Exercises 1. Determine if each of the following would be considered a fixed cost, variable cost, or mixed cost. a. The company s lawyer charges a base fee of \$400 per month plus \$20 for each hour of legal service provided. Mixed cost b. The property taxes for the year are 5% of the value of the building. Fixed cost c. The direct materials used for packaging finished goods cost \$2 per finished good. Variable cost 2. Determine if each line plotted in the graph below, which represent total cost, is an example of a fixed cost, variable cost, or mixed cost Variable Mixed Fixed 3. Determine if each situation describes a variable cost, fixed cost, or mixed cost. a. As the number of units produced increases, the cost per unit remains the same. Variable cost b. Each month, the company pays \$1,200 for interest. Fixed cost c. The bank charges \$50 per month to maintain a checking account and an additional \$1.50 for each check if the company writes more than 60 checks. Mixed cost

3 Cost Behavior and Cost-Volume-Profit Analysis 3 Strategy: A variable cost is incurred for each activity, such as producing finished goods. Fixed costs are incurred regardless of the number of finished goods produced. Mixed costs have a base rate and an additional cost for each additional activity. 4. The total cost of production for the last four quarters for Moore s Mowers is shown below. Use the high-low method to determine the variable cost per unit and the fixed cost. Total Cost Units Produced Quarter 1 \$51,000 2,000 Quarter 2 56,400 2,300 Quarter 3 49,200 1,900 Quarter 4 53,700 2,150 Variable cost = \$18 per unit; (\$56,400 - \$49,200)/(2,300 1,900) Fixed cost = \$15,000; \$56,400 (\$18 2,300) 5. With the information for the first four months of production, determine the variable cost per unit and the fixed cost using the high-low method. Total Cost Units Produced January \$155,100 9,000 February 166,350 9,750 March 158,100 9,200 April 157,350 9,150 Variable cost = \$15 per unit; (\$166,350 - \$155,100) / (9,750 9,000) Fixed cost = \$20,100; \$155,100 (\$15 9,000) 6. Calculate the variable cost per unit and the fixed cost using the high-low method for the production information given. Total Cost Units Produced August \$46,800 5,600 September 58,200 7,500 October 42,600 4,900 November 53,880 6,780 Variable Cost = \$6 per unit; (\$58,200 - \$42,600)/(7,500 4,900) Fixed Cost = \$13,200; \$58,200 (\$6 7,500)

4 4 Chapter 19 (4) Strategy: First, identify the highest and lowest number of units produced. Next, find the difference between the total cost and units produced for the highest and lowest number of units produced. Divide the difference between the total costs by the difference of the number of units produced to calculate the variable cost since the total cost will increase for the variable costs incurred for each additional product. The difference between the total cost and the total variable cost is the fixed cost. 7. For 2015, Moore s Mowers had total sales of \$42,000, with each product selling for \$15 each. Each product had variable costs of \$8. Calculate the (a) contribution margin, (b) contribution margin ratio, and (c) unit contribution margin. Round contribution margin ratio to the nearest percent. Units sold = 2,800; \$42,000/\$15 per units a. \$19,600; \$42,000 (\$8 per unit 2,800 units) b. 47%; \$19,600/\$42,000 c. \$7 per unit; \$15 \$8 8. During 2015, Cards by Shannon sold 50,000 finished products with a contribution margin of 55%. The variable costs totaled \$40,500 for the year. Calculate the contribution margin and unit contribution margin. Sales \$90,000 (\$40,500/100% 55%) Sales price per unit \$1.80 Variable cost per unit 0.81 Contribution margin per unit \$0.99 Contribution margin \$49,500

5 Cost Behavior and Cost-Volume-Profit Analysis 5 9. If a manufacturing company had a contribution margin of \$65,700 for 2015 from selling 25,000 products at \$6 each, determine the variable cost per unit, contribution margin ratio, and unit contribution margin. Round unit answers to two decimal places and percentages to the nearest percent. Sales (dollars) \$150,000 Contribution margin 65,700 Total variable cost \$ 84,300 Variable cost per unit \$3.37 Unit contribution margin \$2.63 Contribution margin ratio 44% Strategy: The contribution margin is the sales less variable cost, which is the profit produced from the sale of goods to contribute to the payment of fixed costs. The unit contribution margin is the selling price per unit less the variable cost per unit. Contribution margin ratio is calculated by dividing the contribution margin by total sales or unit contribution margin by selling price per unit. 10. Use the following information to determine the change in income from operations for each situation if the company sells its products for \$4 each. a. Contribution margin ratio of 35% and a 10,000 increase in sales units. \$14,000 = 35% (10,000 units \$4 per unit) b. Unit contribution margin of \$2.10 and an increase of \$20,000 in sales. \$10,500 = \$2.10 (\$20,000/\$4 per unit) c. Contribution margin of ratio of 30% and an increase in sales of \$30,000. \$9,000 = 30% \$30, Determine the change in income from operations for each situation for a company that has an increase in total sales of \$52,000. a. Unit contribution margin of \$4.50 and each product selling for \$8. \$29,250 = \$4.50 (\$52,000/\$8 per unit) b. Contribution margin ratio of 24% and each product selling for \$10. \$12,480 = 24% \$52,000 c. Unit contribution margin of \$6, with total variable costs of \$25,000 at \$5 per unit. \$30,000 = \$6 5,000 units

6 6 Chapter 19 (4) 12. During 2015, Jackson Computer Supply produced income from operations of \$95,000 from sales of 80,000 units at \$2.50 each. The company s fixed costs totaled \$22,000. If the company has a 4,000 increase in sales units in the upcoming year, what will income from operations be for 2016? Assume that fixed costs and the selling price and variable cost per unit will remain the same Sales \$210,000 \$200,000 Variable costs 87,150 83,000 Contribution margin \$122,850 \$117,000 Fixed costs 22,000 22,000 Income from operations \$100,850 \$ 95, Contribution margin = \$95,000 + \$22, Variable costs = \$200,000 \$117,000 Change in income from operations = \$5,850 = (\$117,000/\$200,000) \$10,000 Strategy: The change in income from operations can be determined using the unit contribution margin or the contribution margin ratio. If fixed costs remain the same, the only difference in income from operations is the difference in sales and variable costs. The change in income from operations is calculated by the change in sales dollars multiplied by the contribution margin or the unit contribution margin multiplied by the change in unit sales. 13. A new manufacturing company would like to know the sales needed to break-even for the first year of operations. The expected total fixed costs will be \$27,000 for 15,000 units. The company expects to sell the units for \$10 each and incur variable cost of \$4 per unit. Determine the break-even sales point in dollars and units. Unit contribution margin = \$6 = \$10 \$4 Break-even point (units) = 4,500 units = \$27,000/\$6 Contribution margin ratio = 60% = \$90,000/\$150,000 or \$6/\$10 Break-even point (sales) = \$45,000 = \$27,000 / 60% or 4,500 units \$10 per unit

7 Cost Behavior and Cost-Volume-Profit Analysis The production manager at Athletix would like to know the break-even point for the company s goods in sales dollars and units. During the past year, the company earned an income from operations of \$69,600. The contribution margin for the year was \$120,000 after selling 50,000 units at \$4 each. Determine the sales and units sold needed at the break-even point. Sales \$200,000 Variable costs 80,000 Contribution margin \$120,000 Fixed costs 50,400 Income from operations \$ 69,600 Unit contribution margin = \$2.40 = \$120,000/50,000 units Break-even point (units) = 21,000 units = \$50,400/\$2.40 Contribution margin ratio = 60% = \$120,000/\$200,000 Break-even point (sales) = \$84,000 = \$50,400/60% or 21,000 \$4 per unit 15. After earning a loss of \$6,000 from operations in 2015, the production manager would like to know the break-even point in sales and units for the company. During 2015, the company sold 6,000 at \$3 each. Variable costs for the year totaled \$10,800. Determine the sales and units sold that were needed to break-even. Sales \$18,000 Variable costs 10,800 Contribution margin \$7,200 Fixed costs 13,200 Income from operations \$(6,000) Unit contribution margin = \$1.20 = \$7,200/6,000 units Break-even point (units) = 11,000 = \$13,200/\$1.20 Contribution margin ratio = 40% = \$7,200/\$18,000 Break-even point (sales) = \$33,000 = \$13,200/40% or 11,000 \$3 per unit Strategy: The break-even point is the point at which income from operations is zero, which means the company sold enough products to create a contribution margin to cover the fixed costs exactly. The break-even point in units can be calculated by dividing the fixed costs by the unit contribution margin. Break-even point in sales is calculated by the fixed costs divided by the contribution margin ratio.

8 8 Chapter 19 (4) 16. Would each of the following cause the break-even point to increase or decrease? a. Decrease in selling price of \$5 per unit. Increase b. Decrease in variable costs of \$1 per unit. Decrease c. Increase in fixed costs by \$12,000. Increase 17. A clothing manufacturer has a current break-even point of 3,200 units, which sell for \$8 each. The company s fixed cost total \$12,800. Determine the new units needed to break even in each situation. a. Increase in selling price to \$9 per unit. Decrease to 2,560 units = \$12,800/\$5 per unit b. Decrease fixed costs by 5%. Decrease to 3,040 units = (\$12,800 95%)/\$4 per unit c. Increase variable costs by \$2 per unit. Increase to 6,400 units = \$12,800/\$2 per unit

9 Cost Behavior and Cost-Volume-Profit Analysis In 2015, a paper manufacturer has the income from operations shown below for sales of 7,500 units. Determine the new break-even sales in each situation. Round answers to the nearest whole sales dollar. Sales \$60,000 Variable costs 24,000 Contribution margin \$36,000 Fixed costs 19,200 Income from operations \$16,800 Current break-even sales = \$32,000 = \$19,200/60% Sales price per unit = \$8.00 Variable cost per unit = \$3.20 a. Decrease in selling price per unit by 20%. Sales price per unit = \$6.40 Contribution margin ratio = \$3.20/\$6.40 Increase in break-even sales to \$38,400 = \$19,200/50% b. Increase in fixed costs by \$2,000. Increase in break-even sales to \$35,333 = \$21,200/60% c. Decrease in variable costs by \$1.20. Variable cost per unit = \$2.00 Contribution margin ratio = 25% Increase in break-even sales to \$76,800= \$19,200/25% Strategy: An increase in costs will cause the break-even point to increase because more units must be sold to cover the costs, while a decrease in cost will also decrease the break-even point. If the selling price increases, the break-even point will decrease because the increase will also cause the contribution margin to increase. If the selling price decreases, the break-even point will increase to reflect that more units will need to be sold to cover the fixed costs.

10 10 Chapter 19 (4) 19. Assume the manufacturer in Exercise 18 would like to earn a target profit of \$36,000. Determine the sales in dollars and units needed to achieve the goal. Sales (units) = 11,500 units = (\$19,200 + \$36,000)/\$4.80 Sales (dollars) = \$92,000 = (\$19,200 + \$36,000)/60% or 11,500 units \$8 per unit 20. A tire manufacturer sells its finished goods for \$80 each. The variable cost to manufacture each product is \$20, while fixed costs equal \$20,700. In 2015, the company earned income from operations of \$32,100. In 2016, the CEO would like to increase income from operations by 5%. Determine the sales in dollars and units needed to achieve the CEO s goal. Round answers to the nearest whole number. Target profit = \$33,705 = \$32, Sales (units) = 907 units = (\$20,700 + \$33,705)/\$60 Sales (dollars) = \$72,540 = (\$20,700 + \$33,705)/75% or 907 units \$80 per unit *Due to rounding, the two methods will differ by \$20 in sales. 21. A paper manufacturer would like to earn an income from operations of \$55,006 in In 2015, the company had fixed costs of \$7,500, but expects this number to increase by 10%. Finished goods sell for \$10 each and have variable costs of \$2. Determine the sales in units and dollars in order to earn the target profit. Round answers to the nearest whole number. Fixed costs in 2016 = \$8,250 = \$7, Sales (units) = 7,907 units = (\$8,250 + \$55,006)/\$8 Sales (dollars) = \$79,070 = (\$8,250 + \$55,006)/80% or 7,907 units \$10 per unit Strategy: To earn a certain target income from operations, the company must sell a certain amount of goods over the break-even point. The company must earn enough income to cover the fixed costs and produce the target income. To determine the number of units needed to sell, divide the sum of the fixed costs and target profit by the unit contribution margin. To determine the sales needed in dollars, divide the sum of the fixed costs and target profit by the contribution margin ratio.

11 Cost Behavior and Cost-Volume-Profit Analysis Shooz manufactures finished goods for a variable cost of \$30 each and fixed costs of \$15,000. The company sells the goods for \$80 each. Prepare a cost-volume-profit chart for the company. Break-even point (units) = 300 units = \$15,000/\$50 Break-even point (sales) = \$24,000 = \$15,000/62.5% or 300 units \$80 per unit 40,000 35,000 30,000 25,000 20,000 15,000 10,000 5, Total Cost Total Sales 23. Use the information in Exercise 22 to prepare a profit-volume chart for Shooz, assuming that the maximum units of sales is 1,000 units. 40,000 30,000 20,000 10,000 - (10,000) (20,000) Profit Line Horizontal Zero

12 12 Chapter 19 (4) 24. Use the chart below to determine the following: a. Break-even point (units and sales) 200 units for \$4,000 b. Selling price per unit \$20 = \$4,000/200 units c. Variable cost per unit \$10 = (\$4,000 \$2,000)/200 units d. Income from operations for 600 units \$4,000 = \$12,000 \$8,000 or (\$10 per unit 600 units) \$2,000 14,000 12,000 10,000 8,000 6,000 4,000 Total Cost Total Sales 2,

13 Cost Behavior and Cost-Volume-Profit Analysis Assuming that the maximum unit of sales is 2,000 for the company in Exercise 24, prepare a profit-volume chart. Also determine the maximum profit and loss the company can earn. Maximum profit = \$18,000 = 2,000 units \$10 contribution margin per unit \$2,000 Maximum loss = \$2,000 20,000 15,000 10,000 5,000 Profit Horizontal Zero - (5,000) Prepare a cost-volume-profit chart for a company that has an 80% contribution margin for goods that it sells for \$150 each. The company s fixed costs total \$54,000. Also determine the break-even point in units and sales. Break-even point (units) = 450 units = \$54,000/\$120 per unit Break-even point (sales) = \$67,500 = \$54,000/80% or 450 units \$150 per unit 160, , , ,000 80,000 60,000 40,000 20, ,000 Total Costs Total Sales

14 14 Chapter 19 (4) Strategy: The cost-volume-profit chart plots two lines, total costs and total sales. The crossing point, which is when costs equal sales, is the break-even point. Any increase in goods will generate a profit, which would be the total sales less total costs. If the company sells less than the units needed at the breaking point, the company incurs an operating loss. 27. Use the information in Exercise 26 to prepare a profit-volume chart for the company if the maximum unit of sales is 5,000 units. What is the company s maximum profit and loss? Maximum profit = \$546,000 = (\$150 - \$30) 5,000 units - \$54,000 Maximum loss = \$54, , , , , ,000 Profit Horizontal Zero 100,000 - (100,000) - 2,000 4,000 6,000 Strategy: The profit-volume chart shows the largest loss and profits the company could generate. The largest possible loss is the y-intercept of profit, which represents zero sales. The largest possible profit represents the income when the company produces at maximum capacity.

15 Cost Behavior and Cost-Volume-Profit Analysis Cold Weather Gear manufactures two products, Jackets and Hats. During the past year, the company incurred \$124,800 of fixed costs. Use the information shown below to calculate the break-even point in units of each product and total sales for the company. Use the sales mix to determine the mixed product. Jackets Hats Mixed Product Unit selling price \$55 \$15 \$45.40 Unit variable cost Unit contribution margin \$40 \$12 \$33.28 Units sold 95,000 30,000 Sales mix 76% 24% Mixed product unit selling price = (\$55 76%) + (\$15 24%) Mixed product unit variable cost = (\$15 76%) + (\$3 24%) Break-even point (units) for mixed product = 3,750 units = \$124,800/\$33.28 Unit sales of Jackets = 2,850 units = 3,750 76% Unit sales of Hats = 900 units = 3,750 24% Break-even point (sales) = \$170,250 = (2,850 units \$55 per unit) + (900 units \$15 per unit) or 3,750 units \$45.40 per unit

16 16 Chapter 19 (4) 29. A manufacturing company produces three products, as shown below. For 2015, the company incurred costs of \$102,500, but expects this number to remain the same in the upcoming year. Determine the break-even point in unit sales per product and total sales for Round percentages to the one decimal place and all others to three decimal places. Use the sales mix to determine the mixed product. Product A Product B Product C Mixed Product Unit selling price \$105 \$120 \$110 \$ Unit variable cost Unit contribution margin \$ 40 \$ 15 \$ 22 \$ Units sold 8,000 4,000 20,000 Sales mix 25.0% 12.5% 62.5% Mixed product unit selling price = (\$105 25%) + (\$ %) + (\$ %) Mixed product unit variable cost = (\$65 25%) + (\$ %) + (\$ %) Break-even point (units) for mixed product = 4,000 units = (\$102,500)/\$ Unit sales of Product A = 1,000 units = 4,000 25% Unit sales of Product B = 500 units = 4, % Unit sales of Product C = 2,500 units = 4, % Break-even point (sales) = \$440,000 = (1,000 units \$105 per unit) + (500 units \$120 per unit) + (2,500 units \$110 per unit) or 4,000 units \$110 per unit

17 Cost Behavior and Cost-Volume-Profit Analysis A manufacturing company produces Widgets and Gadgets. For 2015, the company s fixed costs totaled \$70,620 and expects this number to increase by 10% in the upcoming year. Determine the break-even point in unit sales per product and total sales for the upcoming year with the information below. Round unit sales to one decimal place. Use the sales mix to determine the mixed product. Widgets Gadgets Mixed Product Unit selling price \$30 \$28 \$29.46 Unit variable cost Unit contribution margin \$15 \$ 7 \$12.84 Contribution margin ratio 50% 25% Units sold 36,500 13,500 Sales mix 73% 27% Mixed product unit selling price = (\$30 73%) + (\$28 27%) Mixed product unit variable cost = (\$15 73%) + (\$21 27%) Break-even point (units) of mixed product = 6,050 units = (\$70, )/\$12.84 Unit sales of Widgets = 4,416.5 units = 6,050 units 73% Unit sales of Gadgets = 1,633.5 units = 6,050 units 27% Break-even point (sales) = \$178,233 = (4,416.5 units \$30 per unit) + (1,633.5 units \$28 per unit) or 6,050 units \$29.46 per unit Strategy: First, determine the sales mix by finding the percentage of total sales for each product. Next, determine the selling price, variable cost, and unit contribution margin of a mixed product, which represents both products as a single product according to the sales mix. To find the unit selling price, multiply the unit selling price of each product by its sales mix and sum the total of all products. The same is done for the unit variable price and contribution margin. The break-even point of the mixed product is calculated, which represents how many times the company needs to sell the products at the same sales mix.

18 18 Chapter 19 (4) 31. Given the information below, calculate the operating leverage for 2015 and 2016, rounding to two decimal places. Determine which year a 5% increase in sales would have a larger impact on income from operations Sales \$425,000 \$300,000 Variable costs 145, ,000 Contribution margin \$280,000 \$195,000 Fixed costs 105,000 75,000 Income from operations \$175,000 \$120,000 Operating leverage \$280,000/\$175,000 \$195,000/\$120, Percent change in income from operations = 8.15% = 5% Percent change in income from operations = 8.00% = 5% 1.60 A 5% change in sales would cause a larger change in income from operations in 2015 (8.15%) than in With the information shown below, calculate the operating leverage for the company, rounding to two decimal places. Also determine the income from operations if there was a 10% increase in sales. Sales \$300,000 Variable costs 112,000 Contribution margin \$188,000 Fixed costs 79,000 Income from operations \$109,000 Operating leverage 1.72 \$188,000/\$109,000 Percent change in income from operations = 17.2% = 10% 1.72 Income from operations = \$127,748 = \$109,000 ( %)

19 Cost Behavior and Cost-Volume-Profit Analysis Use the information shown below to calculate the operating leverage for the two companies. Round answers to two decimal places. Also determine which company would have a higher income from operations if sales decreased by 2%. ABC Corp. XYZ Corp. Sales \$490,000 \$975,300 Variable costs 105, ,000 Contribution margin \$384,650 \$660,300 Fixed costs 99, ,500 Income from operations \$284,900 \$452,800 Operating leverage \$384,650/\$284,900 \$660,300/\$452,800 Percent change in income from operations 2.70% 2.92% 2% % 1.46 ABC Corp. would have a higher income from operations if a 2% decrease in sales occurred. The income from operations would decrease by 2.70%, while XYZ Corp. income from operations would decrease by 2.92%. Strategy: Operating leverage is calculated by dividing the contribution margin by income from operations. Operating leverage represents if a company incurs a large or small amount of fixed costs. If a company has a high operating leverage, it will be more sensitive to changes in sales since most of the costs incurred are fixed. If a company has a low operating leverage, it incurs mostly variable costs rather than fixed, so it is less sensitive to a change in sales. 34. ABC Corporation has a break-even point of 2,000 units, which sell for \$5 each. The company made total sales of \$75,000 each. Calculate the company s margin of safety in dollars, units, and percent of current sales, rounding to one decimal place. Margin of safety (dollars) = \$65,000 = \$75,000 \$10,000 Margin of safety (units) = 13,000 units = 15,000 2,000 Margin of safety (percent of current sales) = 86.7% = (\$75,000 \$10,000)/\$75,000

20 20 Chapter 19 (4) 35. Determine the margin of safety in dollars, units, and percent of current sales for a manufacturer that incurs \$20,000 of fixed cost to produce 5,000 finished goods that have a 25% contribution margin. The finished goods sell for \$40 each. Break-even point (sales) = \$80,000 = \$20,000/25% Break-even point (units) = 2,000 units = \$80,000/\$40 per unit Margin of safety (dollars) = \$120,000 = \$200,000 \$80,000 Margin of safety (units) = 3,000 units = 5,000 2,000 Margin of safety (percent of current sales) = 60% = (\$200,000 \$80,000)/\$200, Use the information below to calculate the margin of safety in dollars, units, and as a percentage of sales for the upcoming year if the company expects for sales to increase by 5%. Each finished good sells for \$100. Round percentages to one decimal place and units to the nearest whole unit. Sales \$250,700 Variable costs 105,294 Contribution margin \$145,406 Fixed costs 85,840 Income from operations \$ 59,566 Break-even point (sales) = \$148,000 = \$85,840/58% Break-even point (units) = 1,480 units = \$148,000/\$100 Sales in upcoming year = \$263,235 = \$250, Margin of safety (dollars) = \$115,235 = \$263,235 \$148,000 Margin of safety (units) = 1,152 units = \$263,235/\$100 per unit 1,480 units Margin of safety (percent of current sales) = 43.8% = (\$263,235 \$148,000)/\$263,235 Strategy: The margin of safety is how much income over the break-even point the company generates and how much extra costs the company can generate before reaching a zero income from operations. The margin of safety in units is found by subtracting the break-even point unit sales from the unit sales. The margin of safety in dollars is found by subtracting the sales in dollars less the break-even point sales. The margin of safety as a percent of current sales is found by the dividing the margin of safety in sales by the total sales.

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