Chapter 20
Cost-Volume-Profit Analysis
Review Questions
1. What is a variable cost? Give an example.
Variable costs are costs that increase or decrease in total in direct proportion to increases or
2. What is a fixed cost? Give an example.
Fixed costs are costs that do not change in total over wide ranges of volume. Fixed costs remain
3. What is a mixed cost? Give an example.
Mixed costs are costs that contain both a fixed and variable component. An example of a mixed cost
4. What is the purpose of using the high-low method?
5. Describe the three steps of the high-low method.
The three steps of the high-low method are:
6. What is the relevant range?
7. A chain of convenience stores has one manager per store who is paid a monthly salary. Relative to
Store #36 located in Atlanta, Georgia, is the manager’s salary fixed or variable? Why?
8. A chain of convenience stores has one manager per store who is paid a monthly salary. Relative to
the number of stores, is the manager’s salary fixed or variable? Why?
9. What is contribution margin?
10. What are the three ways contribution margin can be expressed?
The three ways that contribution margin can be expressed are:
11. How does a contribution margin income statement differ from a traditional income statement?
12. What is cost-volume-profit analysis?
13. What are the CVP assumptions?
The CVP assumptions are:
14. What is target profit?
15. What are the three approaches to calculating the sales required to achieve the target profit? Give the
formula for each one.
The three approaches to calculating the sales required to achieve target profit are:
a. The equation approach. The equation is:
16. Of the three approaches to calculate sales required to achieve target profit, which one(s) calculate the
required sales in units and which one(s) calculate the required sales in dollars?
17. What is the breakeven point?
18. Why is the calculation to determine the breakeven point considered a variation of the target profit
calculation?
The calculation to determine breakeven point is considered a variation of the target profit calculation
because the equations and methodology are the same as calculating target profit equal to zero.
19. On the CVP graph, where is the breakeven point shown? Why?
20. What is sensitivity analysis? How do managers use this tool?
Sensitivity analysis is a “what if” technique that estimates profit or loss results if selling price, costs,
21. What effect does an increase in sales price have on contribution margin? An increase in fixed costs?
An increase in variable costs?
22. What is the margin of safety? What are the three ways it can be expressed?
The margin of safety is the excess of expected sales over breakeven sales. The margin of safety can
be expressed in units, in dollars, or as a ratio.
23. What is a company’s cost structure? How can cost structure affect a company’s profits?
The cost structure of a company is the proportion of fixed costs to variable costs. The relationship
24. What is operating leverage? What does it mean if a company has a degree of operating leverage of
3?
Operating leverage predicts the effects that fixed costs have on changes in operating income when
25. How can CVP analysis be used by companies with multiple products?
CVP analysis can be used by companies with multiple products by using the same CVP formulas,
Short Exercises
S20-1 Identifying variable, fixed, and mixed costs
Learning Objective 1
Philadelphia Acoustics builds innovative speakers for music and home theater systems. Identify each
cost as variable (V), fixed (F), or mixed (M), relative to number of speakers produced and sold.
1. Units of production depreciation on routers used to cut wood enclosures.
2. Wood for speaker enclosures.
3. Patents on crossover relays.
4. Total compensation to salesperson who receives a salary plus a commission based on meeting sales
goals.
5. Crossover relays.
6. Straight-line depreciation on manufacturing plant.
7. Grill cloth.
8. Cell phone costs of salesperson.
9. Glue.
10. Quality inspector’s salary.
SOLUTION
1.
Units of production depreciation on routers used to cut wood enclosures.
V
2.
Wood for speaker enclosures.
V
3.
Patents on crossover relays.
6.
Straight-line depreciation on manufacturing plant.
7.
Grill cloth.
V
9.
Glue.
V
S20-2 Identifying variable, fixed, and mixed costs
Learning Objective 1
Holly’s Day Care has been in operation for several years. Identify each cost as variable (V), fixed (F), or
mixed (M), relative to number of students enrolled.
1. Building rent.
2. Toys.
3. Compensation of the office manager, who receives a salary plus a bonus based on number of
students enrolled.
4. Afternoon snacks.
5. Lawn service contract at $200 per month.
6. Holly’s salary.
7. Wages of afterschool employees.
8. Drawing paper for student artwork.
9. Straight-line depreciation on furniture and playground equipment.
10. Fee paid to security company for monthly service.
SOLUTION
1.
Building rent.
F
2.
Toys.
V
based on number of students enrolled.
4.
Afternoon snacks.
V
6.
F
7.
Wages of afterschool employees.
V
9.
Straight-line depreciation on furniture and playground equipment.
F
S20-3 Using the high-low method
Learning Objective 1
Mel owns a machine shop. In reviewing the shop’s utility bills for the past 12 months, he found that the
highest bill of $2,600 occurred in August when the machines worked 1,400 machine hours. The lowest
utility bill of $2,300 occurred in December when the machines worked 900 machine hours.
Requirements
1. Calculate the variable rate per machine hour and the total fixed utility cost.
2. Show the equation for determining the total utility cost for the machine shop.
3. If Mel anticipates using 1,000 machine hours in January, predict the shop’s total utility bill using the
equation from Requirement 2.
SOLUTION
Requirement 1
Variable cost per unit
=
Change in total cost
/
Change in volume of activity
=
(Highest volume – Lowest volume)
=
=
=
Total fixed cost
=
Total mixed cost
=
Total mixed cost
=
=
=
Requirement 2
Total utility cost
=
(Variable cost per unit × Number of units)
+
Total fixed cost
=
($0.60 per MHr × Number of machine hours)
+
$1,760
Total utility cost
=
(Variable cost per unit × Number of units)
+
Total fixed cost
=
+
$1,760
=
+
$1,760
=
S20-4 Calculating contribution margin
Learning Objective 2
Garson Company sells a product for $90 per unit. Variable costs are $60 per unit, and fixed costs are
$800 per month. The company expects to sell 540 units in September. Calculate the contribution margin
per unit, in total, and as a ratio.
SOLUTION
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$90 per unit
–
$60 per unit
=
$30 per unit
Total contribution margin
=
=
=
=
Contribution margin ratio
=
Contribution margin
Net sales revenue
=
=
Contribution margin ratio
=
Contribution margin
Net sales revenue
=
=
S20-5 Preparing a contribution margin income statement
Learning Objective 2
Gabrick Company sells a product for $30 per unit. Variable costs are $20 per unit, and fixed costs are
$2,500 per month. The company expects to sell 560 units in September. Prepare an income statement for
September using the contribution margin format.
SOLUTION
S20-6 Calculating required sales in units, contribution margin given
Learning Objective 3
Malden, Inc. sells a product with a contribution margin of $60 per unit. Fixed costs are $10,500 per
month. How many units must Malden sell to earn an operating income of $15,000?
SOLUTION
S20-7 Calculating required sales in units, contribution margin ratio given
Learning Objective 3
Summer Company sells a product with a contribution margin ratio of 60%. Fixed costs are $650 per
month. What amount of sales (in dollars) must Summer Company have to earn an operating income of
$7,000? If each unit sells for $30, how many units must be sold to achieve the desired operating income?
SOLUTION
Required sales in dollars
=
Fixed costs + Target profit
Contribution margin ratio
Required sales in dollars
=
Contribution margin per unit
=
S20-8 Computing contribution margin, units to achieve target profit, and breakeven point
Learning Objectives 2, 3
Compute the missing amounts for the following table.
SOLUTION
A
B
C
Number of units
870 units
25,000 units
2,800 units
Required units to achieve target profit
Use the following information to complete Short Exercises S20-9 through S20-14.
Playtime Park competes with Water World by providing a variety of rides. Playtime Park sells tickets at
$60 per person as a one-day entrance fee. Variable costs are $24 per person, and fixed costs are
$226,800 per month.
S20-9 Computing contribution margin per unit, breakeven point in sales units
Learning Objectives 2, 3
Compute the contribution margin per unit and the number of tickets Playtime Park must sell to break
even. Perform a numerical proof to show that your answer is correct.
SOLUTION
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$60 per ticket
–
$24 per ticket
=
$36 per ticket
Contribution margin per unit
–
–
Fixed costs
=
Target profit
–
–
=
–
–
=
breakeven point.
S20-10 Computing contribution margin ratio, breakeven point in sales dollars
Learning Objectives 2, 3
Compute Playtime Park’s contribution margin ratio. Carry your computation to two decimal places. Use
the contribution margin ratio approach to determine the sales revenue Playtime Park needs to break
even.
SOLUTION
Utilizing the contribution margin per unit calculated in S20-9:
Contribution margin ratio
S20-11 Applying sensitivity analysis of changing sales price and variable cost
Learning Objective 4
Using the Playtime Park information presented, do the following tasks.
Requirements
1. Suppose Playtime Park cuts its ticket price from $60 to $54 to increase the number of tickets sold.
Compute the new breakeven point in tickets and in sales dollars.
2. Ignore the information in Requirement 1. Instead, assume that Playtime Park in- creases the variable
cost from $24 to $30 per ticket. Compute the new breakeven point in tickets and in sales dollars.
SOLUTION
Requirement 1
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$54 per ticket
–
$24 per ticket
=
$30 per ticket
Required sales in dollars
=
7,560 tickets × $54 per ticket
=
$408,240
Requirement 2
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$60 per tablet
–
$30 per tablet
=
$30 per tablet
Contribution margin ratio
=
Contribution margin
Net sales revenue
=
=
Fixed costs + Target profit
Contribution margin ratio
$226,800 + $0
Contribution margin per unit
S20-12 Applying sensitivity analysis of changing fixed costs
Learning Objective 4
Refer to the original information (ignoring the changes considered in Short Exercise S20-11). Suppose
Playtime Park reduces fixed costs from $226,800 per month to $208,800 per month. Compute the new
breakeven point in tickets and in sales dollars.
SOLUTION
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$60 per ticket
–
$24 per ticket
=
$36 per ticket
Contribution margin per unit
Required sales in dollars
Required sales in units
Sales price per unit
=
×
=
S20-13 Computing margin of safety
Learning Objective 5
Refer to the original information (ignoring the changes considered in Short Exercises S20-11 and S20-
12). If Playtime Park expects to sell 7,000 tickets, compute the margin of safety in tickets and in sales
dollars.
SOLUTION
Utilizing the breakeven sales in units from S20-9:
Expected sales
–
Breakeven sales
=
Margin of safety in units
–
=
Margin of safety in units
Sales price per unit
=
=
S20-14 Computing degree of operating leverage
Learning Objective 5
Refer to the original information (ignoring the changes considered in Short Exercises S20-11 and S20-
12). If Playtime Park expects to sell 7,000 tickets, compute the degree of operating leverage. Estimate
the operating income if sales increase by 15%.
SOLUTION
Net sales revenue
–
Variable costs
–
Fixed costs
=
Target profit
(7,000 tickets × $60/ticket)
–
(7,000 tickets × $24/ticket)
–
$226,800
=
$420,000
–
$168,000
–
$226,800
=
$25,200
$25,200
$25,200
Operating leverage
15%
Operating income
+
Increase in operating income
+
$37,800
Use the following information to complete Short Exercises S20-15 and S20-16.
SoakNFun Swim Park sells individual and family tickets. With a ticket, each person receives a meal,
three beverages, and unlimited use of the swimming pools. SoakNFun has the following ticket prices
and variable costs for 2016:
SoakNFun expects to sell one individual ticket for every four family tickets. SoakNFun’s total fixed
costs are $76,000.
S20-15 Calculating breakeven point for two products
Learning Objective 5
Using the SoakNFun Swim Park information presented, do the following tasks.
Requirements
1. Compute the weighted-average contribution margin per ticket.
2. Calculate the total number of tickets SoakNFun must sell to break even.
3. Calculate the number of individual tickets and the number of family tickets the company must sell to
break even.
SOLUTION
Requirement 1
Individual
Family
Total
Sales price per unit
Variable cost per unit
Contribution margin per unit
Sales mix in units
Contribution margin
Weighted-average contribution margin per unit
($95 / 5 units)
Requirement 2
=
Fixed costs + Target profit
Contribution margin per unit
=
4,000 tickets
Required sales of family tickets
=
4,000 tickets × 4/5
=
S20-16 Calculating breakeven point for two products
Learning Objective 5
For 2017, SoakNFun expects a sales mix of four individual tickets for every one family ticket.
Requirements
1. Compute the new weighted-average contribution margin per ticket.
2. Calculate the total number of tickets SoakNFun must sell to break even.
3. Calculate the number of individual tickets and the number of family tickets the company must sell to
break even.
SOLUTION
Requirement 1
Individual
Family
Total
Sales price per unit
$ 40
$ 120
Variable cost per unit
Contribution margin per unit
Sales mix in units
Contribution margin
$ 60
Weighted-average contribution margin per unit
($80 / 5 units)
Requirement 2
=
Fixed costs + Target profit
Contribution margin per unit
=
4,750 tickets
Required sales of family tickets
=
4,750 tickets × 1/5
=
950 tickets
Exercises
E20-17 Using terminology
Learning Objectives 1, 2, 3, 4, 5
Match the following terms with the correct definitions:
SOLUTION
1.
Costs that do not change in total over wide ranges of volume.
g.
Fixed costs
2.
Technique that estimates profit or loss results when conditions
change.
i.
Sensitivity
analysis
3.
The sales level at which operating income is zero.
Breakeven point
4.
Drop in sales a company can absorb without incurring an
operating loss.
d.
Margin of safety
5.
Combination of products that make up total sales.
Sales mix
6.
Net sales revenue minus variable costs.
b.
Contribution
margin
7.
Describes how a cost changes as volume changes.
Cost behavior
8.
Costs that change in total in direct proportion to changes in
volume.
h.
Variable costs