CHAPTER 5

COST-VOLUME-PROFIT

CHAPTER LEARNING OBJECTIVES

1. Explain variable, fixed, and mixed costs and the relevant range. Variable costs are costs that vary in total directly and proportionately with changes in the activity index. Fixed costs are costs that remain the same in total regardless of changes in the activity index.

The relevant range is the range of activity in which a company expects to operate during a year. It is important in CVP analysis because the behavior of costs is assumed to be linear throughout the relevant range.

Mixed costs change in total but not proportionately with changes in the activity level. For purposes of CVP analysis, mixed costs must be classified into their fixed and variable components.

2. Apply the high-low method to determine the components of mixed costs. Determine the variable costs per unit by dividing the change in total costs at the highest and lowest levels of activity by the difference in activity at those levels. Then, determine fixed costs by subtracting total variable costs from the amount of total costs at either the highest or lowest level of activity.

3. Prepare a CVP income statement to determine contribution margin. The five components of CVP analysis are (1) volume or level of activity, (2) unit selling prices, (3) variable costs per unit, (4) total fixed costs, and (5) sales mix. Contribution margin is the amount of revenue remaining after deducting variable costs. It is identified in a CVP income statement, which classifies costs as variable or fixed. It can be expressed as a total amount, as a per unit amount, or as a ratio.

4. Compute the break-even point using three approaches. The break-even point can be (a) computed from a mathematical equation, (b) computed by using a contribution margin technique, and (c) derived from a CVP graph.

5. Determine the sales required to earn target net income and determine margin of safety. The general equation for required sales is: Sales - Variable costs - Fixed costs = Target net income. Two other equations are (1) Sales in units = (Fixed costs + Target net income) ÷ Unit contribution margin, and (2) Sales in dollars = (Fixed costs + Target net income) ÷ Contribution margin ratio.

Margin of safety is the difference between actual or expected sales and sales at the break-even point. The equations for margin of safety are (1) Actual (expected) sales – Break-even sales = Margin of safety in dollars, and (2) Margin of safety in dollars ÷ Actual (expected) sales = Margin of safety ratio.

TRUE-FALSE STATEMENTS

1. An activity index identifies the activity that has a causal relationship with a particular cost.

2. Unit variable cost remains constant at various levels of activity.

3. Fixed costs remain constant in total and on a per unit basis at various levels of activity.

4. If the volume of activity increases, all costs will increase.

5. If the activity index decreases, total variable costs will decrease proportionately.

6. Changes in the level of activity will cause unit variable costs and unit fixed costs to change in opposite directions.

7. In CVP analysis, both variable and fixed costs are assumed to have a linear relationship within the relevant range of activity.

8. The relevant range of activity is the activity level where the firm will earn a net income.

9. Total costs do not change within the relevant range of activity.

10. The high-low method is used to classify mixed costs into variable and fixed components.

11. A mixed cost has both selling and administrative cost components.

12. The fixed cost component of a mixed cost is the cost of having a service available.

13. For planning purposes, mixed costs are generally grouped with fixed costs.

14. The difference between the costs at the high and low levels of activity represents the fixed cost component of a mixed cost.

15. When applying the high-low method, the unit variable cost of a mixed cost is calculated before the fixed cost component.

16. One assumption of CVP analysis is that all costs can be classified as either variable or fixed.

17. In CVP analysis, the term “cost” includes manufacturing costs as well as selling and administrative expenses.

18. The contribution margin is the amount of revenue remaining after deducting cost of goods sold.

19. The unit contribution margin is the amount that each unit sold contributes to the recovery of fixed costs and profit.

20. The contribution margin ratio is calculated by multiplying the unit contribution margin by the unit selling price.

21. Both variable and fixed costs are included in calculating the contribution margin.

22. A CVP income statement reports the contribution margin instead of gross profit.

23. Break-even point in sales dollars is the point at which total sales revenue equals total variable costs.

24. Break-even point in sales dollars is the point at which total sales revenue equals total fixed costs.

25. The break-even point in sales dollars is equal to the fixed costs plus net income.

26. If the unit contribution margin is $1 and sales are 10,000 units above the break-even point, then net income will be $10,000.

Ex. 182

Sandburg Manufacturing manufactures a single product. Annual production costs incurred in the manufacturing process are shown below for the production of 2,000 units. The company’s Utilities and Maintenance costs are mixed costs. The fixed portions of these costs are $300 and $200, respectively.

Costs Incurred

Production in Units 2,000 4,000

Production Costs

a. Direct Materials $6,000 ?

b. Direct Labor 16,000 ?

c. Utilities 1,000 ?

d. Rent 3,000 ?

e. Indirect Labor 4,200 ?

f. Supervisory Salaries 1,500 ?

g. Maintenance 1,000 ?

h. Depreciation 2,500 ?

Instructions

Calculate the expected costs to be incurred when production is 4,000 units. Use your knowledge of cost behavior to determine which of the other costs are fixed or variable.

Ex. 183

Bill Braddock is considering opening a Fast ‘n Clean Car Service Center. He estimates that the following costs will be incurred during his first year of operations: Rent $9,200, Depreciation on equipment $7,000, Salaries $16,400, Motor oil $2.00 per quart. He estimates that each oil change will require 5 quarts of oil. Oil filters will cost $3.00 each. He must also pay The Fast ‘n Clean Corporation a franchise fee of $1.10 per oil change since he will operate the business as a franchise. In addition, utility costs are expected to vary with the quantity of oil changes as follows:

Quantity of Oil Changes Utility Costs

4,000 $6,000

6,000 7,300

9,000 9,600

12,000 12,600

14,000 15,000

Bill Braddock anticipates that he can provide the oil change service with a filter at $25 each.

Instructions

(a) Using the high-low method, determine the unit variable costs and total fixed costs.

(b) Determine the break-even point in quantity of oil changes and sales dollars.

(c) Without regard to your answers in parts (a) and (b), determine the oil changes required to earn a net income of $20,000, assuming fixed costs are $32,000 and the unit contribution margin is $8.

Ex. 184

Jane Botosan operates a bed and breakfast hotel in a resort area near Lake Michigan. Depreciation on the hotel is $60,000 per year. Jane employs a maintenance person at an annual salary of $41,000 and a cleaning person at an annual salary of $24,000. Real estate taxes are $10,000 per year. The rooms rent at an average price of $60 per person per night including breakfast. Other costs are laundry and cleaning service at a cost of $10 per person per night and the cost of food, which is $5 per person per night.

Instructions

(a) Determine the quantity of rentals and the sales revenue Jane needs to break even using the contribution margin technique.

(b) If the current level of rentals is 4,000, by what percentage can rentals decrease before Jane has to worry about having a net loss?

(c) Jane is considering upgrading the breakfast service to attract more business and increase prices. This will cost an additional $3 for food costs per person per night. She feels she can increase the room rate to $68 per person per night. Determine the quantity of rentals and the sales revenue Jane needs to break even if the changes are made.

Ex. 185

Corris Co. accumulates the following data concerning a mixed cost, using miles as the activity level.

Miles Driven Total Cost

January 10,000 $17,000

February 8,000 13,500

March 9,000 14,400

April 7,000 12,500

Instructions

Compute the unit variable costs and fixed costs using the high-low method for this mixed cost.

Ex. 186

Moresan Co. gathered the following information on power costs and factory machine usage for the last six months:

Month Power Cost Factory Machine Hours

January $24,400 13,900

February 30,400 17,600

March 29,000 16,800

April 22,340 13,200

May 19,900 11,600

June 16,900 8,600

Instructions

(a) What is the estimated unit variable costs per factory machine hour?

(b) What is the estimated fixed power cost each month?

(c) If it is estimated that 10,000 factory machine hours will be run in July, what is the expected total power cost for July?

Ex. 187

The Bradshaw Law Office has the following monthly telephone records and costs:

Calls Costs

2,000 $2,400

1,500 2,000

2,200 2,600

2,500 2,800

2,300 2,700

1,700 2,200

Instructions

Identify the unit variable cost and the fixed cost using the high-low method.

Ex. 188

Determine the missing amounts.

Unit Contribution Contribution

Unit Selling Price Unit Variable Costs  Margin  Margin Ratio

1. $300 $210 A B

2. $600 C $210 D

3. E F $360 30%

Ex. 189

Henderson Farms reports the following results for the month of November:

Sales (10,000 units) $600,000

Variable costs 420,000

Contribution margin 180,000

Fixed costs 110,000

Net income $ 70,000

Management is considering the following independent courses of action to increase net income.

1. Increase unit selling price by 5% with no change in total variable costs.

2. Reduce variable costs to 66% of sales.

3. Reduce fixed costs by $10,000.

Instructions

If maximizing net income is the objective, which is the best course of action?

Ex. 190

Marvin Co. had a net loss of $150,000 in 2021 when the unit selling price was $20, the unit variable costs were $15, and the fixed costs were $600,000. Management expects per unit data and total fixed costs to be the same in 2022. Management has set a goal of earning a net income of $75,000 in 2022.

Instructions

(a) Compute the units sold in 2021.

(b) Compute the quantity of units that would have to be sold in 2022 to reach management's desired net income level.

(c) Assume that Marvin sells the same quantity of units in 2022 as it did in 2021. What would the unit selling price have to be in order to reach the target net income? Use the mathematical equation.

Ex. 191

In September, Matlock Industries sold 800 units of product. The average unit selling price was $30. During the month, fixed costs were $6,300 and variable costs were 70% of sales.

Instructions

(a) Determine the contribution margin in dollars, per unit, and as a ratio.

(b) Using the contribution margin technique, compute break-even point in sales dollars and sales units.

Ex. 192

In 2021, Stallman Co. had a break-even point in sales dollars of $800,000 based on a unit selling price of $10 and fixed costs of $200,000. In 2022, the unit selling price and unit variable costs did not change, but the break-even point in sales dollars increased to $840,000.

Instructions

(a) Compute the unit variable cost and the contribution margin ratio for 2021.

(b) Using the contribution margin ratio, compute the increase in fixed costs for 2022.

Ex. 193

The CVP income statement for Bradford Machine Company for 2021 appears below.

BRADFORD MACHINE COMPANY

Income Statement

For the Year Ended December 31, 2021

——————————————————————————————————————————

Sales (40,000 units) $1,000,000

Variable expenses 700,000

Contribution margin 300,000

Fixed expenses 360,000

Net income (loss) $ (60,000)

Instructions

1. What was the company's break-even point in sales dollars in 2021?

2. How many additional units would the company have had to sell in 2022 to earn a net income of $45,000?

3. If the company reduces variable costs by $2.50 per unit in 2022 while other costs and unit revenues remain unchanged, how many units will the company have to sell to earn a net income of $45,000?

Ex. 194

Webber, Inc. developed the following information for its product:

Per Unit

Sales price $90

Variable cost 63

Contribution margin $27

Total fixed costs $1,215,000

Instructions

1. How many units must be sold to break even?

2. What is the total sales that must be generated for the company to earn a profit of $60,000?

3. If the company is presently selling 50,000 units, but plans to spend an additional $108,000 on an advertising program, how many additional units must the company sell to earn the same net income it is now making?

4. Using the original data in the problem, compute the new break-even point in sales units if the unit selling price is increased by 20%, unit variable cost is increased by 10%, and total fixed costs are increased by $236,250.

Ex. 195

Werth & Garza Manufacturing's sales slumped badly in 2022 due to so many people purchasing gifts online. The company's income statement showed the following results from selling 500,000 units of product: net sales $2,125,000; total costs and expenses $2,500,000; and net loss $375,000. Costs and expenses consisted of the following:

Total Variable Fixed

Cost of goods sold $2,000,000 $1,300,000 $700,000

Selling expenses 200,000 50,000 150,000

Administrative expenses 300,000 150,000 150,000

$2,500,000 $1,500,000 $1,000,000

Management is considering modifications to the cost structure for 2023. The plan includes purchasing new automated equipment that will result in the following:

An increase in total fixed costs of $375,000.

A reduction in unit variable costs of $0.75.

Unit selling price would not change from 2022.

Instructions

(a) Compute the break-even point in sales dollars for 2022.

(b) Compute the break-even point in sales dollars under the alternative course of action.

Ex. 196

Henning Co. estimates that variable costs will be 70% of sales and fixed costs will total $2,160,000. The unit selling price of the product is $10, and 750,000 units will be sold.

Instructions

Using the mathematical equation,

(a) Compute the break-even point in units and sales dollars.

(b) Compute the margin of safety in dollars and as a ratio.

(c) Compute net income.

Ex. 197

Newport News Manufacturing, Inc. has the following information available for September 2022.

Unit selling price of navigational equipment $ 400

Unit variable costs $ 280

Total fixed costs $48,000

Units sold 500

Instructions

(a) Prepare a CVP income statement that shows both total and per unit amounts.

(b) Compute Newport News break-even point in units.

Ex. 198

In June, Avante Salon gave 2,500 haircuts, shampoos, and permanents at an average unit selling price of $40. During the month, fixed costs were $20,000 and variable costs were 75% of sales.

Instructions

(a) Determine the contribution margin in dollars, per unit, and as a ratio.

(b) Using the contribution margin technique, compute the break-even point in dollars and units.

(c) Compute the margin of safety in dollars and as a ratio.

Ex. 199

Taveras Industries developed the following information for the product it sells:

Sales price $50 per unit

Variable cost of goods sold $28 per unit

Fixed cost of goods sold $650,000

Variable selling expense 10% of sales price

Variable administrative expense $2.00 per unit

Fixed selling expense $400,000

Fixed administrative expense $300,000

For the year ended December 31, 2022, Taveras produced and sold 100,000 units of product.

Ex. 199 (Cont.)

Instructions

(a) Prepare a CVP income statement using the contribution margin format for Taveras Industries for 2022.

(b) What was the company's break-even point in units in 2022? Use the contribution margin technique.

(c) What was the company's margin of safety in dollars in 2022?

Ex. 200

Gordon Manufacturing earned net income of $100,000 during 2021. The company wants to earn net income of $40,000 more during 2022. The company's fixed costs are expected to be $147,000, and variable costs are expected to be 30% of sales

Instructions

(a) Determine the required sales to meet the target net income during 2022.

Ex. 201

Ferris, Inc. has a unit selling price of $500, unit variable cost of $300, and total fixed costs of $260,000.

Instructions

Compute the break-even point in units and sales dollars.

Ex. 202

Erickson, Inc. makes computer bags that sell for $20 each. For the coming year, management expects fixed costs to be $225,000. Variable costs are $14 per unit.

Instructions

(a) Compute the break-even point in sales dollars using the mathematical equation.

(b) Compute the break-even point in sales dollars using the contribution margin ratio technique.

(c) Compute margin of safety ratio assuming actual sales are $937,500.

(d) Compute the sales required to earn a net income of $150,000, using the mathematical equation.

Ex. 203

Melody Manufacturing produces a computer microphone that is sold for $20 per unit. The contribution margin ratio is 40%. Fixed expenses total $9,200.

Instructions

(a) Compute the unit variable cost.

(b) Compute how many microphones Melody Manufacturing will have to sell to break even.

(c) Compute how many microphones Melody Manufacturing will have to sell to earn a target net income of $16,200.

Ex. 204

Usher, Inc. has prepared the following cost-volume-profit graph:

Ex. 204 (Cont.)

Instructions

For the items listed below, enter to the left of the item, the letter in the graph which best corresponds to the item.

____ 1. Activity base

____ 2. Break-even point

____ 3. Dollars

____ 4. Fixed costs

____ 5. Loss

____ 6. Profit (Net income)

____ 7. Revenues

____ 8. Total costs

____ 9. Variable costs

Ex. 205

Holder Manufacturing had $125,000 of net income in 2021 when the unit selling price was $100, the unit variable costs were $70, and the fixed costs totaled $475,000. Management expects per unit data and total fixed costs to remain the same in 2022. The president of Holder Manufacturing is under pressure from stockholders to increase net income by $60,000 in 2022.

Instructions

(a) Compute the quantity of units sold in 2021.

(b) Compute the quantity of units that would have to be sold in 2022 to reach the stockholders' desired profit level.

(c) Assume that Holder Manufacturing sells the same quantity of units in 2022 as it did in 2021. What would the unit selling price have to be to reach the stockholders' desired profit level?

Ex. 206

Englehart, Inc. reports the following operating results for August: Sales $450,000 (units 5,000); variable costs $280,000; and fixed costs $115,000. Management is considering the following independent courses of action to increase net income.

1. Increase the unit selling price by 10%.

2. Reduce variable costs to 60% of sales.

3. Reduce fixed costs by $15,000.

Instructions

Compute the net income to be earned under each alternative. Which course of action will produce the highest net income?

Ex. 207

Keeter, Inc. earned a net income of $300,000 last year. This year it wants to earn a net income of $450,000. The company's fixed costs are expected to be $300,000, and variable costs are expected to be 70% of sales.

Instructions

(a) Determine the required sales to meet the target net income of $450,000 using the mathematical equation.

Ex. 208

Cunningham Industries reported actual sales of $2,000,000 and fixed costs of $540,000. The contribution margin ratio is 30%.

Instructions

Compute the margin of safety in dollars and the margin of safety ratio.