WHAT ARE SOME OTHER WAYS CVP ANALYSIS CAN BE USED?
5. What are some other ways CVP analysis can be used?
■
■ Margin of safety
• The excess of expected sales over breakeven sales.
• In units: Expected sales in units - Breakeven sales in units.
• In dollars: Margin of safety in units * Sales price per unit.
• As a ratio: Margin of safety in units / Expected sales in units.
■
■ Operating leverage
• Effects that fixed costs have on changes in operating income when sales volume changes.
• Degree of operating leverage = Contribution margin / Operating income.
■
■ Sales mix
• Calculate the breakeven point with multiple products:
Step 1: Calculate the weighted-average contribution margin per unit.
Step 2: Calculate the breakeven point in units for the “package” of products.
Step 3: Calculate the breakeven point in units for each product. Multiply the
“ package” breakeven point in units by each product’s proportion of the sales mix.
> Check Your Understanding 20-1
Check your understanding of the chapter by completing this problem and then looking at the solution. Use this practice to help identify which sections of the chapter you need to study more.
The Sock Company buys hiking socks for $6 per pair and sells them for $10. Manage- ment budgets monthly fixed costs of $10,000 for sales volumes between 0 and 12,000 pairs of socks.
Requirements
1. Use both the equation approach and the contribution margin approach to compute the company’s monthly breakeven point in units. (See Learning Objective 3)
2. Use the contribution margin ratio approach to compute the breakeven point in sales dollars. (See Learning Objective 3)
3. Compute the monthly sales level (in units) required to earn a target operating income of $6,000. Use either the equation approach or the contribution margin approach. (See Learning Objective 3)
4. Prepare a graph of The Sock Company’s CVP relationships, similar to Exhibit 20-8.
Draw the sales revenue line, the fixed cost line, and the total cost line. Label the axes, the breakeven point, the operating income area, and the operating loss area. (See Learning Objective 3)
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Requirement 1 Equation approach:
> Solution
Net sales revenue − Variable costs − Fixed costs = Target profit (+10 per unit * Units sold) - (+6 per unit * Units sold) - +10,000 = + 6,000
[(+10 per unit - +6 per unit) * Units sold] - +10,000 = + 6,000 +4 per unit * Units sold = +16,000
Units sold = +16,000 / +4 per unit Units sold = 4,000 units
Required sales in units = Fixed costs + Target profit Contribution margin per unit
= +10,000 + +0 +10 per unit - +6 per unit
= 2,500 units
Contribution margin ratio = Contribution margin Sales price = +4
+10 = 40%
Required sales in dollars = Fixed costs + Target profit Contribution margin ratio
= +10,000 + +0 40%
= +25,000
Contribution margin approach:
Net sales revenue − Variable costs − Fixed costs = Target profit (+10 per unit * Units sold) - (+6 per unit * Units sold) - +10,000 = + 0
[(+10 per unit - +6 per unit) * Units sold] - +10,000 = + 0 +4 per unit * Units sold = +10,000
Units sold = +10,000 / +4 per unit Units sold = 2,500 units
Requirement 2
This can be confirmed by multiplying the breakeven point in units (as calculated in Require- ment 1) by the sales price:
2,500 pairs of socks * +10 per pair of socks = +25,000
Requirement 3 Equation approach:
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Breakeven Point (2,500 units, $25,000)
$40,000
Dollars
0
Units
$30,000
$25,000
$20,000
$10,000
$0 1,000 2,000 3,000 4,000 5,000
Sales Revenue
Operating Loss
Operating Income Total Costs
Fixed Costs Required sales in units = Fixed costs + Target profit
Contribution margin per unit
= +10,000 + +6,000 +4 per unit
= 4,000 units
Contribution margin approach:
Requirement 4
> Check Your Understanding 20-2
Check your understanding of the chapter by completing this problem and then looking at the solution. Use this practice to help identify which sections of the chapter you need to study more.
The Sock Company buys hiking socks for $6 per pair and sells them for $10.
Management budgets monthly fixed costs of $12,000 for sales volumes between 0 and 12,000 pairs.
Requirements
Consider each of the following questions separately by using the foregoing information each time.
1. Calculate the breakeven point in units. (See Learning Objective 3)
2. The Sock Company reduces its sales price from $10 per pair to $8 per pair. Calculate
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4. The Sock Company plans to advertise in hiking magazines. The advertising campaign will increase total fixed costs by $2,000 per month. Calculate the new breakeven point in units. (See Learning Objective 4)
5. In addition to selling hiking socks, The Sock Company would like to start selling sports socks. The Sock Company expects to sell one pair of hiking socks for every three pairs of sports socks. The Sock Company will buy the sports socks for $4 per pair and sell them for $8 per pair. Total fixed costs will stay at $12,000 per month. Calculate the breakeven point in units for both hiking socks and sports socks. (See Learning Objective 5)
> Solution
Requirement 1
Requirement 2
Requirement 3
Requirement 4
Required sales in units = Fixed costs + Target profit Contribution margin per unit
= +12,000 + +0 +8 per unit - +6 per unit
= 6,000 units
Required sales in units = Fixed costs + Target profit Contribution margin per unit
= +14,000 + +0 +10 per unit- +6 per unit
= 3,500 units
Required sales in units = Fixed costs + Target profit Contribution margin per unit
= +12,000 + +0 +10 per unit- +5 per unit
= 2,400 units
Required sales in units = Fixed costs + Target profit Contribution margin per unit
= +12,000 + +0 +10 per unit - +6 per unit
= 3,000 units
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Requirement 5
Step 1: Calculate the weighted-average contribution margin:
Step 2: Calculate the breakeven point for the “package” of products:
Step 3: Calculate the breakeven point for each product:
Sales price per unit $ 10
$ 4
$ 8
$ 12 $ 16
$ 4 Hiking Sports Total
6 4
4 4 Variable cost per unit
Contribution margin per unit
Sales mix in units 4 units
Contribution margin
Weighted-average contribution margin per unit ($16 per unit / 4 units)
× 1 × 3
Required sales in units = Fixed costs + Target profit Contribution margin per unit
= +12,000 + +0 +4 per unit
= 3,000 units
Breakeven sales of hiking socks (3,000 items * 1/4) = 750 pairs of hiking socks Breakeven sales of sport socks (3,000 items * 3/4) = 2,250 pairs of sport socks
> Key Terms
Breakeven Point (p. 1097) Contribution Margin (p. 1095) Contribution Margin Income
Statement (p. 1096)
Contribution Margin Ratio (p. 1096) Cost Stickiness (p. 1105)
Cost Structure (p. 1107)
Cost-Volume-Profit (CVP) Analysis (p. 1097)
Degree of Operating Leverage (p. 1108)
Fixed Cost (p. 1089)
High-Low Method (p. 1092) Margin of Safety (p. 1106)
Mixed Cost (p. 1091)
Operating Leverage (p. 1108) Relevant Range (p. 1094) Sales Mix (p. 1109)
Sensitivity Analysis (p. 1102) Target Profit (p. 1099) Variable Cost (p. 1088)
> Quick Check
1. For Frank’s Funky Sounds, straight-line depreciation on the trucks is a
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2. Assume Intervale Railway is considering hiring a reservations agency to handle pas- senger reservations. The agency would charge a flat fee of $13,000 per month, plus
$3 per passenger reservation. What is the total reservation cost if 200,000 passengers take the trip next month?
a. $613,000 b. $3.07 c. $600,000 d. $13,000
3. If Intervale Railway’s fixed costs total $90,000 per month, the variable cost per pas- senger is $45, and tickets sell for $75, what is the contribution margin per unit and contribution margin ratio?
a. $45 per passenger; 60%
b. $30 per passenger; 60%
c. $30 per passenger; 40%
d. $45 per passenger; 40%
4. If Intervale Railway’s fixed costs total $90,000 per month, the variable cost per pas- senger is $45, and tickets sell for $75, what is the breakeven point in units?
a. 1,200 passengers b. 2,000 passengers
c. 225,000 passengers d. 3,000 passengers
5. If Intervale Railway’s fixed costs total $90,000 per month, the variable cost per pas- senger is $45, and tickets sell for $75, how much revenue must the Railway generate to earn $120,000 in operating income per month?
a. $350,000 b. $210,000 c. $7,000 d. $525,000
6. On a CVP graph, the total cost line intersects the vertical (dollars) axis at a. the origin.
b. the level of the fixed costs.
c. the breakeven point.
d. the level of the variable costs.
7. If a company increases its sales price per unit for Product A, the new breakeven point will
a. increase.
b. decrease.
c. remain the same.
d. More information is needed.
8. If a company increases its fixed costs for Product B, then the contribution margin per unit will
a. increase.
b. decrease.
c. remain the same.
d. More information needed.
9. The Best Appliances had the following revenue over the past five years:
2013 $ 600,000
2014 700,000
2015 900,000
2016 800,000
2017 1,000,000
To predict revenues for 2018, The Best Appliances uses the average for the past five years. The company’s breakeven revenue is $800,000 per year. What is The Best Appliances’s predicted margin of safety in dollars for 2018?
a. $800,000 b. $0 c. $200,000 d. $100,000
Learning Objective 1
Learning Objective 2
Learning Objective 3
Learning Objective 3
Learning Objective 3
Learning Objective 4
Learning Objective 4
Learning Objective 5
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10. Rocky Mountain Waterpark sells half of its tickets for the regular price of $75. The
other half go to senior citizens and children for the discounted price of $35. Vari- able cost per guest is $15 for both groups, and fixed costs total $60,000 per month.
What is Rocky Mountain’s breakeven point in total guests? Regular guests? Discount guests?
a. 2,000; 1,000; 1,000 b. 800; 400; 400
c. 750; 375; 375 d. 1,500; 750; 750 Check your answers at the end of the chapter.
Learning Objective 5
ASSESS YOUR PROGRESS
> Review Questions
1. What is a variable cost? Give an example.
2. What is a fixed cost? Give an example.
3. What is a mixed cost? Give an example.
4. What is the purpose of using the high-low method?
5. Describe the three steps of the high-low method.
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 sal- ary. 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?
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?
14. What is the breakeven point?
15. What are the three approaches to calculating the sales required to achieve the breakeven point? Give the formula for each one.
16. Of the three approaches to calculate sales required to achieve the breakeven point, which one(s) calculate the required sales in units and which one(s) calculate the required sales in dollars?
17. What is target profit?
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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 cost stickiness? Why do managers need to be aware of cost stickiness?
23. What is the margin of safety? What are the three ways it can be expressed?
24. What is a company’s cost structure? How can cost structure affect a company’s profits?
25. What is operating leverage? What does it mean if a company has a degree of operating leverage of 3?
26. How can CVP analysis be used by companies with multiple products?
> Short Exercises
S20-1 Identifying variable, fixed, and mixed costs
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 speak- ers 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. Insurance on the corporate office.
9. Glue.
10. Quality inspector’s salary.
S20-2 Identifying variable, fixed, and mixed costs
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 students’ artwork.
9. Straight-line depreciation on furniture and playground equipment.
10. Fee paid to security company for monthly service.
Learning Objective 1
Learning Objective 1
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S20-3 Using the high-low method
Mark 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 1,200 machine hours. The lowest utility bill of $2,300 occurred in December when the machines worked 600 machine hours.
Requirements
1. Use the high-low method to calculate the variable cost 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 Mark anticipates using 800 machine hours in January, predict the shop’s total utility bill using the equation from Requirement 2.
S20-4 Calculating contribution margin
Glenn Company sells a product for $80 per unit. Variable costs are $60 per unit, and fixed costs are $800 per month. The company expects to sell 560 units in September.
Calculate the contribution margin per unit, in total, and as a ratio.
S20-5 Preparing a contribution margin income statement
Gabelman Company sells a product for $95 per unit. Variable costs are $40 per unit, and fixed costs are $2,200 per month. The company expects to sell 570 units in Septem- ber. Prepare an income statement for September using the contribution margin format.
S20-6 Calculating breakeven point in units, contribution margin given Mackler, Inc. sells a product with a contribution margin of $50 per unit. Fixed costs are $8,000 per month. How many units must Mackler sell to break even?
S20-7 Calculating breakeven point in units, contribution margin ratio given Ocean Company sells a product with a contribution margin ratio of 80%. Fixed costs are $2,800 per month. What amount of sales (in dollars) must Ocean Company have to break even? If each unit sells for $30, how many units must be sold to break even?
S20-8 Computing contribution margin, units and required sales to break even, and units to achieve target profit
Compute the missing amounts for the following table.
A B C
Sales price per unit $ 200 $ 4,000 $ 5,220
Variable costs per unit 80 1,000 2,088
Total fixed costs 73,200 660,000 3,758,400
Target profit 266,760 3,000,000 3,132,000
Calculate:
Learning Objective 1
Learning Objective 2
Learning Objective 2
Learning Objective 3
Learning Objective 3
Learning Objectives 2, 3
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S20-9 Computing contribution margin, units and required sales to break even, units to achieve target profit
Compute the missing amounts for the following table:
A B C
Sales price per unit $ 1,400 $ (f) $ 2,500
Variable costs per unit (a) 2,940 1,250
Total fixed costs 273,000 1,097,600 (k)
Target profit 630,000 24,892,000 1,562,500
Contribution margin per unit 700 (g) (l)
Contribution margin ratio (b) 40% (m)
Required units to break even (c) (h) 325 units
Required sales dollars to break even (d) (i) (n)
Required units to achieve target profit (e) (j) (o)
Use the following information to complete Short Exercises S20-10 through S20-15.
Funday Park competes with Cool World by providing a variety of rides. Funday Park sells tickets at $70 per person as a one-day entrance fee. Variable costs are $42 per person, and fixed costs are $170,800 per month.
S20-10 Computing contribution margin per unit, breakeven point in sales units Compute the contribution margin per unit and the number of tickets Funday Park must sell to break even. Perform a numerical proof to show that your answer is correct.
S20-11 Computing contribution margin ratio, breakeven point in sales dollars Compute Funday Park’s contribution margin ratio. Carry your computation to two decimal places. Use the contribution margin ratio approach to determine the sales revenue Funday Park needs to break even.
S20-12 Applying sensitivity analysis of changing sales price and variable cost Using the Funday Park information presented, do the following tasks.
Requirements
1. Suppose Funday Park cuts its ticket price from $70 to $56 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 Funday Park increases the variable cost from $42 to $56 per ticket. Compute the new breakeven point in tickets and in sales dollars.
S20-13 Applying sensitivity analysis of changing fixed costs
Refer to the original information (ignoring the changes considered in Short Exercise S20-12). Suppose Funday Park increases fixed costs from $170,800 per month to $231,000 per month. Compute the new breakeven point in tickets and in sales dollars.
Learning Objectives 2, 3
Learning Objectives 2, 3
Learning Objectives 2, 3
Learning Objective 4
Learning Objective 4
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S20-14 Computing margin of safety
Refer to the original information (ignoring the changes considered in Short Exercises S20-12 and S20-13). If Funday Park expects to sell 8,100 tickets, compute the margin of safety in tickets and in sales dollars.
S20-15 Computing degree of operating leverage
Refer to the original information (ignoring the changes considered in Short Exercises S20-12 and S20-13). If Funday Park expects to sell 8,100 tickets, compute the degree of operating leverage (round to two decimal places). Estimate the operating income if sales increase by 15%.
Use the following information to complete Short Exercises S20-16 and S20-17.
Wild Waters Swim Park sells individual and family tickets. With a ticket, each person receives a meal, three beverages, and unlimited use of the swimming pools. Wild Waters has the following ticket prices and variable costs for 2018:
Individual Family
Sales price per ticket $ 50 $ 150
Variable cost per ticket 35 140
Wild Waters expects to sell one individual ticket for every four family tickets. Wild Waters’s total fixed costs are $27,500.
S20-16 Calculating breakeven point for two products
Using the Wild Waters 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 Wild Waters 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.
S20-17 Calculating breakeven point for two products
For 2019, Wild Waters 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 Wild Waters 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.
Learning Objective 5
Learning Objective 5
Learning Objective 5
Learning Objective 5
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E20-18 Using terminology
Match the following terms with the correct definitions:
Learning Objectives 1, 2, 3, 4, 5
> Exercises
1. Costs that do not change in total over wide ranges of volume.
2. Technique that estimates profit or loss results when conditions change.
3. The sales level at which operating income is zero.
4. Drop in sales a company can absorb without incurring an operating loss.
5. Combination of products that make up total sales.
6. Net sales revenue minus variable costs.
7. Describes how a cost changes as volume changes.
8. Costs that change in total in direct proportion to changes in volume.
9. The band of volume where total fixed costs and variable cost per unit remain constant.
a. Breakeven point b. Contribution margin c. Cost behavior d. Margin of safety e. Relevant range f. Sales mix g. Fixed costs h. Variable costs i. Sensitivity analysis
E20-19 Determining cost behavior
Identify each cost below as variable (V), fixed (F), or mixed (M), relative to units sold.
Explain your reason.
Units Sold 25 50 75 100
a. Total phone cost $ 150 $ 200 $ 250 $ 300
b. Materials cost per unit 35 35 35 35
c. Manager’s salary 3,000 3,000 3,000 3,000
d. Depreciation cost per unit 60 30 20 15
e. Total utility cost 400 650 900 1,150
f. Total cost of goods sold 3,125 6,250 9,375 12,500
E20-20 Determining fixed cost per unit
For each total fixed cost listed below, determine the fixed cost per unit when sales are 50, 100, and 200 units.
Store rent $ 5,000
Manager’s salary 3,000
Equipment lease 500
Depreciation on fixtures 250
E20-21 Determining total variable cost
For each variable cost per unit listed below, determine the total variable cost when units produced and sold are 25, 50, and 100 units.
Direct materials $ 40
Direct labor 80
Variable overhead 9 Sales commission 12 Learning Objective 1
Learning Objective 1 100 units $87.50
Learning Objective 1 Total VC, 50 units $7,050
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E20-22 Determining total mixed cost
John Street Barber Shop pays $25 per month for water for the first 8,000 gallons and
$3.50 per thousand gallons above 8,000 gallons. Calculate the total water cost when the barber shop uses 7,000 gallons, 10,000 gallons, and 13,000 gallons.
E20-23 Determining mixed costs—the high-low method
The manager of Trusty Car Inspection reviewed the monthly operating costs for the past year. The costs ranged from $4,300 for 1,300 inspections to $3,900 for 900 inspections.
Requirements
1. Use the high-low method to calculate the variable cost per inspection.
2. Calculate the total fixed costs.
3. Write the equation and calculate the operating costs for 1,000 inspections.
4. Draw a graph illustrating the total cost under this plan. Label the axes, and show the costs at 900, 1,000, and 1,300 inspections.
E20-24 Calculating contribution margin ratio, preparing contribution margin income statements
For its top managers, Worldwide Travel formats its income statement as follows:
Learning Objective 1 10,000 gal. $32.00
Learning Objective 1 3. $4,000
Learning Objective 2 2. $253,000 sales level, VC
$108,790
Variable Costs
Net Sales Revenue $ 316,500
180,405 136,095 Fixed Costs
Contribution Margin
173,000
$ 7,405 Operating Income
WORLDWIDE TRAVEL
Contribution Margin Income Statement Three Months Ended March 31, 2018
Worldwide’s relevant range is between sales of $253,000 and $368,000.
Requirements
1. Calculate the contribution margin ratio.
2. Prepare two contribution margin income statements: one at the $253,000 sales level and one at the $368,000 sales level. (Hint: The proportion of each sales dollar that goes toward variable costs is constant within the relevant range.)