E20-18 Determining cost behavior
Learning Objective 1
Identify each cost below as variable (V), fixed (F), or mixed (M), relative to units sold. Explain your
reason.
SOLUTION
a. Mixed
Total phone cost has the characteristics of both a fixed cost and a variable cost
making it a mixed cost. The total cost changes as volume changes, but not in
direct proportion. For example, $150 / 25 units = $6 per unit; $200 / 50 units =
$4 per unit.
Material cost per unit is directly proportional to the number units produced
making it a variable cost.
Depreciation cost per unit is inversely proportional to the number of units
produced while total cost remains constant making it a fixed cost. For example,
$60 per unit × 25 units = $1,500; $30 per unit × 50 units = $1,500.
e. Mixed
Total utility cost has the characteristics of both a fixed cost and a variable cost
making it a mixed cost. The total cost changes as volume changes, but not in
direct proportion. For example, $400 / 25 units = $16 per unit; $650 / 50 units =
$13 per unit.
Total cost of goods sold is directly proportional to the number units produced
making it a variable cost. The total cost changes as volume changes and in
direct proportion. For example, $3,125 / 25 units = $125 per unit; $6,250 / 50
units = $125 per unit.
E20-19 Determining fixed cost per unit
Learning Objective 1
For each total fixed cost listed below, determine the fixed cost per unit when sales are 45, 90, and 180
units.
SOLUTION
Units sold:
45 Units
90 Units
180 Units
$ 1,800
$ 40.00
$ 20.00
$ 10.00
E20-20 Determining total variable cost
Learning Objective 1
Total VC, 80 units $9,600
For each variable cost per unit listed below, determine the total variable cost when units produced and
sold are 40, 80, and 160 units.
SOLUTION
Units sold:
40 Units
80 Units
160 Units
$ 35
$ 1,400
$ 2,800
$ 5,600
$ 9,600
$ 19,200
E20-21 Determining total mixed cost
Learning Objective 1
17,000 gal. $42.25
Robert Street Barber Shop pays $30 per month for water for the first 10,000 gallons and $1.75 per
thousand gallons above 10,000 gallons. Calculate the total water cost when the barber shop uses 6,000
gallons, 12,000 gallons, and 17,000 gallons.
SOLUTION
($1.75 per 1,000 gal. × Water usage above 10,000 gal. ) + $30
=
Total Water Cost
($1.75 per 1,000 gal. × 0 ) + $30
=
($1.75 per 1,000 gal. × 7,000 gal. ) + $30
=
E20-22 Determining mixed costs—the high-low method
Learning Objective 1
3. $4,300
The manager of Quick Car Inspection reviewed the monthly operating costs for the past year. The costs
ranged from $4,400 for 1,400 inspections to $4,200 for 1,000 inspections.
Requirements
1. Calculate the variable cost per inspection.
2. Calculate the total fixed costs.
3. Write the equation and calculate the operating costs for 1,200 inspections.
4. Draw a graph illustrating the total cost under this plan. Label the axes, and show the costs at 1,000,
1,200, and 1,400 inspections.
SOLUTION
Requirement 1
Variable cost per unit
=
Change in total cost
/
Change in volume of activity
=
(Highest cost – Lowest cost)
/
(Highest volume – Lowest volume)
=
/
(1,400 inspections – 1,000 inspections)
=
$200
/
400 inspections
=
Requirement 2
Total fixed cost
=
Total mixed cost
–
Total variable cost
=
Total mixed cost
–
(Variable cost per unit × Number of units)
=
–
=
–
=
Requirement 3
Total mixed cost
=
(Variable cost per unit × Number of units)
+
Total fixed cost
=
($0.50 per inspection × Number of inspections)
+
$3,700
(for 1,200 units)
=
+
$3,700
=
+
$3,700
=
E20–22, cont.
Requirement 4
E20-23 Calculating contribution margin ratio, preparing contribution margin income statements
Learning Objective 2
2. $250,000 sales level, VC $87,500
For its top managers, Global Travel formats its income statement as follows:
Global’s relevant range is between sales of $250,000 and $360,000.
Requirements
1. Calculate the contribution margin ratio.
2. Prepare two contribution margin income statements: one at the $250,000 sales level and one at the
$360,000 sales level. (Hint: The proportion of each sales dollar that goes toward variable costs is
constant within the relevant range.)
$4,100
$4,200
$4,300
$4,400
Total Mixed Costs
SOLUTION
Requirement 1
Contribution margin ratio
=
Contribution margin
/
Net sales revenue
=
/
=
Requirement 2
If the contribution margin ratio is 65% (that is, contribution margin is 65% of sales), then
variable costs must be 35% of sales.
Sales Revenue
Variable Costs (35% of sales)
Contribution Margin (65% of sales)
Fixed Costs
Operating Income (Loss)
Sales Revenue
$ 360,000
Variable Costs (35 % of sales)
126,000
Contribution Margin (65% of sales)
234,000
Fixed Costs
175,000
Operating Income
$ 59,000
E20-24 Computing contribution margin in total, per unit, and as a ratio
Learning Objective 2
C. CMR 40%
Complete the table below for contribution margin per unit, total contribution margin, and contribution
margin ratio:
SOLUTION
A
B
C
Number of units
1,800 units
9,790 units
1,410 units
Sales price per unit
$ 1,900
Variable costs per unit
Contribution margin per unit
Total contribution margin
Contribution margin ratio
E20-25 Computing breakeven sales
Learning Objectives 2, 3
2. $150,000
Ten Toes Co. produces sports socks. The company has fixed costs of $75,000 and variable costs of
$0.75 per package. Each package sells for $1.50.
Requirements
1. Compute the contribution margin per package and the contribution margin ratio. (Round your
answers to two decimal places.)
2. Find the breakeven point in units and in dollars using the contribution margin approach.
SOLUTION
Requirement 1
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
–
=
Contribution margin ratio
=
Contribution margin
=
$1.50 per package
=
Requirement 2
Required sales in units
=
Fixed costs + Target Profit
Contribution margin per unit
=
Required sales in dollars
=
Fixed costs + Target Profit
=
Required sales in dollars
=
Required sales in units
×
Sales price per unit
=
×
$1.50 per unit
E20-26 Computing a change in breakeven sales
Learning Objectives 2, 3
1. $6,000
Owner Shan Lo is considering franchising her Noodles by Lo restaurant concept. She believes people
will pay $6.50 for a large bowl of noodles. Variable costs are $3.25 per bowl. Lo estimates monthly
fixed costs for a franchise at $3,000.
Requirements
1. Use the contribution margin ratio approach to find a franchise’s breakeven sales in dollars.
2. Lo believes most locations could generate $34,500 in monthly sales. Is franchising a good idea for
Lo if franchisees want a minimum monthly operating income of $13,500?
SOLUTION
Requirement 1
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$6.50 per bowl
–
$3.25 per bowl
=
$3.25 per bowl
Contribution margin ratio
=
=
=
Required sales in dollars
=
Fixed costs + Target profit
Contribution margin ratio
=
Required sales in dollars
=
Fixed costs + Target profit
Contribution margin ratio
=
$3,000 + $13,500
E20-27 Computing breakeven sales and operating income or loss under different conditions
Learning Objectives 2, 3
2. $1,010,000 sales level VC $202,000
Graham’s Steel Parts produces parts for the automobile industry. The company has monthly fixed costs
of $630,000 and a contribution margin of 80% of revenues.
Requirements
1. Compute Graham’s monthly breakeven sales in dollars. Use the contribution margin ratio approach.
2. Use contribution margin income statements to compute Graham’s monthly operating income or
operating loss if revenues are $550,000 and if they are $1,010,000.
3. Do the results in Requirement 2 make sense given the breakeven sales you computed in Requirement
1? Explain.
SOLUTION
Requirement 1
Requirement 2
If the contribution margin ratio is 80% (that is, contribution margin is 80% of sales), then
variable costs must be 20% of sales.
Sales Revenue
$ 550,000
Variable Costs (20% of sales)
110,000
Contribution Margin (80% of sales)
440,000
Fixed Costs
630,000
Operating Income (Loss)
$ (190,000)
Sales Revenue
$ 1,010,000
Variable Costs (20% of sales)
202,000
Contribution Margin (80% of sales)
808,000
Fixed Costs
630,000
Operating Income
$ 178,000
Requirement 3
The results in Requirement 2 do make sense given the breakeven sales computed in Requirement
1. For sales revenue of $550,000, Graham’s Steel Parts shows an operating loss of $190,000.
For sales revenue of $1,010,000, Graham’s Steel Parts shows operating income of $178,000. The
E20-28 Analyzing a cost-volume-profit graph
Learning Objective 3
3. $40,000
John Kyler is considering starting a Web-based educational business, e-Prep MBA. He plans to offer a
short-course review of accounting for students entering MBA programs. The materials would be
available on a password-protected Web site; students would complete the course through self-study.
Kyler would have to grade the course assignments, but most of the work would be in developing the
course materials, setting up the site, and marketing. Unfortunately, Kyler’s hard drive crashed before he
finished his financial analysis. However, he did recover the following partial CVP chart:
Requirements
1. Label each axis, the sales revenue line, the total costs line, the fixed costs line, the operating income
area, and the breakeven point.
2. If Kyler attracts 300 students to take the course, will the venture be profitable?
3. What are the breakeven sales in students and dollars?
SOLUTION
Requirement 1
$70,000
$80,000
Breakeven Point
Operating
Income
E20-28, cont.
Requirement 2
If Kyler attracts 300 students to take the course, the venture will not be profitable. The graph
Requirement 3
E20-29 Using sensitivity analysis
Learning Objective 4
1b. 1,400 students
Intersection Driving School charges $500 per student to prepare and administer writ- ten and driving
tests. Variable costs of $150 per student include trainers’ wages, study materials, and gasoline. Annual
fixed costs of $140,000 include the training facility and fleet of cars.
Requirements
1. For each of the following independent situations, calculate the contribution margin per unit and the
breakeven point in units by first referring to the original data provided:
SOLUTION
Requirement 1a
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$500 per student
–
$150 per student
=
$350 per student
Contribution margin per unit
Requirement 1b
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$250 per student
–
$150 per student
=
$100 per student
Contribution margin per unit
Requirement 1c
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$500 per student
–
$100 per student
=
$400 per student
Contribution margin per unit
E20-29, cont.
Requirement 1d
Unit contribution margin
=
Net sales revenue per unit
–
Variable costs per unit
=
$500 per student
–
$150 per student
=
$350 per student
Contribution margin per unit
not change when the fixed costs decrease.
fixed costs decrease.
E20-30 Computing margin of safety
Learning Objective 5
1. $42,500
Ricky’s Repair Shop has a monthly target profit of $17,000. Variable costs are 60% of sales, and
monthly fixed costs are $8,000.
Requirements
1. Compute the monthly margin of safety in dollars if the shop achieves its income goal.
2. Express Ricky’s margin of safety as a percentage of target sales.
SOLUTION
Requirement 1
If variable costs are 60% of sales, then the contribution margin ratio must be 40% of sales.
Fixed costs + Target profit
$8,000 + $0
Fixed costs + Target profit
Expected sales
–
Breakeven sales
=
Margin of safety in dollars
$62,500
–
$20,000
=
$42,500
Requirement 2
/
=
Margin of safety ratio
/
=
E20-31 Computing degree of operating leverage
Learning Objective 5
2. 40.2750%
Following is the income statement for Marsden Mufflers for the month of June 2016:
Requirements
1. Calculate the degree of operating leverage. (Round to four decimal places.)
2. Use the degree of operating leverage calculated in Requirement 1 to estimate the change in operating
income if total sales increase by 30% (assuming no change in sales price per unit). (Round interim
calculations to four decimal places and final answer to the nearest dollar.)
3. Verify your answer in Requirement 2 by preparing a contribution margin income statement with the
total sales increase of 30%.
SOLUTION
Requirement 1
Contribution margin
Requirement 2
Percent change in
sales revenue
×
Degree of
operating leverage
=
Percent change in
operating income
30%
×
1.3425
=
40.2750%
operating income
operating income
40.2750%
=
Requirement 3
30% increase in sales: 280 units × 1.30 = 364 units
MARSDEN MUFFLERS
Contribution Margin Income Statement
Month Ended June 30, 2016
Sales Revenue
$ 118,300
Variable Costs
Contribution Margin
Fixed Costs
Operating Income
$ 51,200
E20-32 Calculating breakeven point for two products
Learning Objective 5
2. 340 standards
Stewart’s Scooters plans to sell a standard scooter for $120 and a chrome scooter for $160. Stewart’s
purchases the standard scooter for $30 and the chrome scooter for $40. Stewart’s expects to sell one
standard scooter for every three chrome scooters. Stewart’s monthly fixed costs are $85,500.
Requirements
1. How many of each type of scooter must Stewart’s Scooters sell each month to break even?
2. How many of each type of scooter must Stewart’s Scooters sell each month to earn $67,500?
SOLUTION
Requirement 1
Standard
Scooter
Chrome
Scooter
Total
Sales price per unit
$ 120
$ 160
Variable cost per unit
30
40
Contribution margin per unit
90
Sales mix in units
× 1
4 units
Contribution margin
$ 360
$ 112.50
$112.50 per unit
Required sales of Standard Scooter
=
760 units × 1/4
=
190 standard scooters
Required sales of Chrome Scooter
=
760 units × 3/4
=
570 chrome scooters
Requirement 2
$112.50 per unit
Required sales of Standard Scooter
=
1,360 units × 1/4
=
340 standard scooters
Required sales of Chrome Scooter
=
1,360 units × 3/4
=
1,020 chrome scooters