Techniques for Estimating Fixed and Variable Costs

Chapter 4

Learning Objectives

After studying this chapter, you will be able to:

Prepare a contribution margin statement.
Use the account classification method to identify fixed and variable costs.
Compute fixed and variable costs using the high-low method.
Perform regression analysis to estimate fixed and variable costs.
Construct segmented contribution margin statements.

Overview

Chapter 4 focuses on the value of contribution margin statements and the three techniques organizations use to separate fixed costs from variable costs: Account classification, the high-low method, and regression analysis. Chapter 4 is important because most organizations’ accounting systems are set up to comply with GAAP, as discussed in Chapter 3. Unfortunately, GAAP-based statements, with their emphasis on grouping costs by business function, frequently are not suitable for decision making. For example, costs related to property, plant, and equipment are fixed and non-controllable in the short-term. Yet, such costs are included in cost of goods sold, along with other variable and controllable manufacturing costs such as materials and labor. Likewise, selling, general, and administrative expenses include both fixed and variable components. This co-mingling of controllable and non-controllable costs makes it problematic to use gross margin or net income, the two summary metrics produced by GAAP-based statements, for decision making.

Moreover, variable costs typically are relevant and controllable for short-term decisions whereas fixed costs are not. Recognizing the need to modify GAAP-based statements to separate variable costs from fixed costs, Chapter 4 first shows the value of contribution margin statements, which separate variable costs from fixed costs, for decision making. This then leads to a natural question: How can we modify traditional income statements to get a contribution margin statement? We discuss the three common techniques organizations use to accomplish this objective: Accounting classification, the high-low method, and regression analysis. The mechanics of each method, along with the associated benefits and costs, are discussed in detail. Chapter 4 concludes with a discussion of segmented contribution margin statements, the natural extension of contribution margin statements to firms that offer multiple products and/or have multiple lines of business (regions, customers, etc.). Finally, we offer A glimpse of Chapter 5 and cost-volume-profit analysis, which follows directly from the contribution-margin statement studied in Chapter 4.

Learning Objective 1:

Prepare a contribution margin statement.

1.The contribution margin statement groups costs by their variability, reporting fixed costs and variable costs as separate line items. The contribution margin is the amount that remains after subtracting variable costs from revenues, contributing toward recovering fixed costs and earning a profit.

2.The contribution margin statement is particularly helpful for short-term decisions because variable costs are controllable for short-term decisions, whereas fixed costs are not.

3.Firms use three techniques to construct contribution margin statements:

a.Account-classification,

b.High-low method, and

c.Regression analysis.

Learning Objective 2:

Use the account classification method to identify fixed and variable costs.

1.The account classification method involves systematically classifying a company’s list of cost accounts into fixed and variable categories.

2.The account classification method is detailed and can provide very accurate estimates if done correctly. However, it is time consuming and subjective.

Learning Objective 3:

Compute fixed and variable costs using the high-low method.

1.The high-low method uses historical cost data to estimate total fixed and unit variable costs. The method uses two observations, the high activity level and the low activity level to estimate the cost equation.

2.The high-low method is straightforward to use. However, it assumes that the cost structure of a company does not vary over time and uses only two data points.

Learning Objective 4:

Perform regression analysis to estimate fixed and variable costs.

1.Regression analysis is a statistical method for estimating fixed and variable costs. The regression method uses all available data to come up with a line that best fits the data.

2.The major advantage of regression analysis is that it uses all available data to estimate the cost equation. It also provides a number of statistics to help evaluate the fitted equation.

3.A major drawback of using regression analysis is that the technique makes a number of assumptions about the structure of the data. Accounting data may not satisfy these assumptions, requiring users to make adjustments.

Learning Objective 5:

Construct segmented contribution margin statements.

1.Firms operating with many product lines and/or in many regions might construct a segmented contribution margin statement.

2.A segmented contribution margin statement reports the following:

a.Contribution margin, which equals revenues less all variable costs;

b.Segment margin, which equals the contribution margin less traceable fixed costs, and

c.Profit before taxes, which equals the segment margin less common fixed costs. This detail allows the firm to make decisions at the level of an individual product, segment, or the firm as a whole.

KEY TERMS VOCABULARY QUIZ

We frequently use the key terms quiz to provide incentives for students to read the chapter prior to attending class. For this quiz, we provide students the glossary definitions, and ask them to “fill in the blank” by providing the key term being defined. Rather than having students completely rely on memory, instructors may wish to provide students a scrambled list of terms. We typically administer this quiz on the day we introduce the chapter material.

______1.A statistical method that uses all available observations to estimate fixed and variable costs.

______2.An income statement that groups costs by their variability, reporting variable costs and fixed costs as separate line items.

______3.The proportion of total costs that are fixed and variable.

______4.A cost estimation technique that uses two observations pertaining to the highest and lowest activity levels to estimate fixed and variable costs.

______5.Revenues less variable costs.

______6.A firm’s normal range of operations. Over this range, we expect a stable relationship between activity and cost.

______7.A cost estimation technique that involves systematically classifying a company’s list of cost accounts into fixed and variable categories.

______8.The contribution margin of a segment (e.g., product, customer, geographical region) less traceable fixed costs.

MULTIPLE CHOICE PRACTICE QUESTIONS

1.Over the course of one year, depreciation expense on plant equipment is likely to be:

Fixed and controllable.
Fixed and non-controllable.
Variable and controllable.
Variable and non-controllable.

2.During the current year, Britton’s Bread Bakery reported the following costs:

Building rent$60,000

Equipment depreciation$13,000

Supervisor’s salary$50,000

Bread ingredients, per loaf$0.89

Packaging, per loaf$0.07

Britton baked and sold 375,000 loaves of bread during the year.What was the total cost incurred for the year?

$360,000
$123,000
$483,000
$237,000

3.For the previous year, Renz Fast Lube performed 1,820 oil changes on automobiles and incurred the following total costs:

Garage rent$26,000

Service equipment depreciation$5,965

Supervisor’s salary$24,000

Parts and supplies$40,040

Employees’ wages$74,620

If Renz Fast Lube performs 2,100 oil changes in the current year, what will be the total cost?

$188,265
$132,300
$170,625
$196,875

4.During the current year, Pasternak Publishing incurred fixed costs of $384,000 and variable costs of $24.50 per book.Pasternak produced and sold 1,200,000 books.Each book was sold for $28.99.If Pasternak Publishing could sell an additional 80,000 books, by how much would profit before taxes increase?

$333,600
$2,319,200
$335,200
$359,200

5.During the current year, Hinton Handyman Services provided 2,300 service hours and incurred the following costs:

Office space rental$6,000

Service vehicle depreciation$2,400

Supervisor’s salary$10,000

Supplies, average per service hour$18.00

Employees wages, per hour$40.00

Hinton bills clients $75 per hour.If Hinton could provide an additional 200 service hours next year, by how much would profit before taxes increase?

$1,800
$15,000
$11,600
$3,400

6.During the current year, Young’s Lighting Company incurred fixed costs of $84,000 and variable costs of $34.50 per lamp.Young’s produced and sold 12,000 lamps.Each lamp was sold for $48.99.What was profit before taxes?

$89,880
$173,880
$414,000
$587,880

7.During the current year, Pasternak Publishing produced and sold 1,200,000 books and incurred the following costs:

Building rent$150,000

Printing press depreciation$45,000

Employee Salaries$189,000

Paper, average per book$20.50

Covers and binding materials, per book$4.00

Each book was sold for $28.99.What was profit before taxes?

$5,004,000
$5,388,000
$29,400,000
$34,788,000

8.During the current year, Hinton Handyman Services provided 2,300 service hours and incurred the following costs:

Office space rental$6,000

Service vehicle depreciation$2,400

Supervisor’s salary$10,000

Supplies, average per service hour$18.00

Employees wages, per hour$40.00

Hinton bills clients $75 per hour.What was Hinton’s contribution margin?

$20,700
$39,100
$133,400
$154,100

9.If revenue and fixed costs remain constant, but total variable cost increases, what happens to contribution margin?

Increases.
Decreases.
Doesn’t change.
Can’t be determined.

10.If revenue and fixed cost remain constant, but total variable cost decreases, what happens to contribution margin?

Increases.
Decreases.
Doesn’t change.
Can’t be determined.

11.Advantages of the account classification method used to identify variable and fixed costs include all of the following except:

Can provide very accurate estimates.
Can be used even if historical data does not exist.
Easy to implement if there are few accounts.
Classification is somewhat subjective.

12.Following is the GAAP income statement for Johnson and Jr., who makes a single product:

Revenue / $574,000
Cost of Goods Sold:
Direct Materials / $193,000
Direct Labor / 68,000
Production Supplies / 13,000
Building Rent / 80,000
Equipment Depreciation / 9,000
Total / 363,000
Gross Margin / $211,000
Management, Marketing and Administration:
Management Salaries / $115,000
Advertising / 29,000
Sales Commissions / 38,000
Office Rent / 17,000
Total / 199,000
Profit Before Taxes / $12,000

What is the total variable cost?

$312,000
$341,000
$274,000
$261,000

13.Following is the GAAP income statement for Kampmann Manufacturing, who makes a single product:

Revenue / $986,000
Cost of Goods Sold:
Direct Materials / $141,000
Direct Labor / 235,000
Engineering and Product Design / 38,000
Building Rent / 120,000
Equipment Lease / 37,000
Total / 571,000
Gross Margin / $415,000
Management, Marketing and Administration:
Administrative Salaries / $196,000
Office Supplies / 29,000
Delivery Vehicle Depreciation / 38,000
Product Delivery Wages / 78,000
Total / 341,000
Profit Before Taxes / $74,000

What is the total fixed cost?

$429,000
$391,000
$458,000
$507,000

14.Following is the GAAP income statement for Johnson and Jr., who makes a single product:

Johnson and Jr. sold 20,500 units.What is the variable cost per unit? Round your answer to the nearest penny.

$15.22
$16.63
$13.37
$12.73

15.Following is the GAAP income statement for Kampmann Manufacturing, who makes a single product:

What is the total variable cost?

$483,000
$521,000
$454,000
$520,000

16.Following is the GAAP income statement for Johnson and Jr., who makes a single product:

What is the total fixed cost?

$250,000
$221,000
$288,000
$301,000

17.Which of the equations below is used to find unit variable cost in the high-low method?

A.High Activity Level Total Cost – Low Activity Level Total Cost

High Activity Level – Low Activity Level

B.Low Activity Level Total Cost – High Activity Level Total Cost

Low Activity Level – High Activity Level

C.High Activity Level – Low Activity Level

High Activity Level Total Cost – Low Activity Level Total Cost

D.Low Activity Level – High Activity Level

Low Activity Level Total Cost – High Activity Level Total Cost

18.Which statement below is true about the estimated cost line developed using the high-low method?

The estimated cost line will usually overlap the true cost line.
The estimated cost line will usually pass through all observation points.
To use the high-low method you only need two observation points.
The high-low method doesn’t identify individual costs as fixed or variable.

19.GAAP income statements for Michelsen Inc. for the past six months are presented in the table below.

July / August / September
Sales Volume / 32,000 / 30,500 / 29,700
Revenues / $384,000 / $366,000 / $356,400
Cost of Goods Sold / 313,600 / 301,200 / 300,900
Gross Margin / $70,400 / $64,800 / $55,500
Marketing and Administration / 37,600 / 37,300 / 35,400
Profit Before Taxes / $32,800 / $27,500 / $20,100
October / November / December
Sales Volume / 29,200 / 33,400 / 36,800
Revenues / $350,400 / $400,800 / $441,600
Cost of Goods Sold / 297,000 / 327,300 / 348,800
Gross Margin / $53,400 / $73,500 / $92,800
Marketing and Administration / 34,100 / 38,900 / 42,800
Profit Before Taxes / $19,300 / $34,600 / $50,000

Use the high-low method to find the unit variable cost. Round your answer to the nearest penny.

$7.96
$0.13
$6.82
$0.15

20.GAAP income statements for Michelsen Inc. for the past six months are presented in the table below.

Use the high-low method to find the total variable cost at the low activity level. Round all calculations to the nearest penny.

$232,432
$3,796
$199,144
$4,380

21.GAAP income statements for Michelsen Inc. for the past six months are presented in the table below.

Use the high-low method to find the total fixed cost at the low activity level. Round your answer to the nearest thousand dollars.

$98,668
$331,100
$59,675
$34,100

22.The accountant for Reiser Rentals ran a regression analysis in Microsoft Excel to help estimate costs for the following year.The regression analysis results are below: