1. Cost-Volume-Profit Analysis
Chapter 18
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Wild, Shaw, and Chiappetta
Financial & Managerial Accounting
6th Edition

2. 18-C1: Fixed Costs
2

3. Identifying Cost Behavior
Cost-volume-profit analysis is used to answer questions
such as:
– How much does income increase if we install a
new machine to reduce labor costs?
– What is the change in income if selling prices
decline and sales volume increases?
– How will income change if we change the sales
mix of our products or services?
– What sales volume is needed to earn a target
income?
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4. Fixed Costs
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5. Variable Costs
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6. Mixed Costs
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7. Step-Wise Costs
Total cost increases to a new higher cost for the next higher range of
activity, but remains constant within a range of activity.
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8. Curvilinear Costs
Costs that increase when activity
increases, but in a nonlinear manner.C 1
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9. NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls $0.50 per tennis ball Variable cost
Depreciation (straight-line method)
Electricity cost
Supervisory salaries
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
$0
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
0 2,000 4,000 6,000 8,000 10,000
TotalCost
Units Produced
$0.50 per tennis ball - Variable
C 1
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10. NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls $0.50 per ball Variable cost
Depreciation (straight-line method) $2,000 per month Fixed cost
Electricity cost
Supervisory salaries
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
$0
$500
$1,000
$1,500
$2,000
$2,500
0 2,000 4,000 6,000 8,000 10,000
TotalCost
Units Produced
$2,000 per month - Fixed
C 1
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11. NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls $0.50 per ball Variable cost
Depreciation (straight-line method) $2,000 per month Fixed cost
Electricity cost $500 + $0.10 per ball Mixed cost
Supervisory salaries
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
$0
$200
$400
$600
$800
$1,000
$1,200
$1,400
$1,600
0 2,000 4,000 6,000 8,000 10,000
TotalCost
Units Produced
$500 + $0.10 per unit- Mixed
C 1
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12. NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls $0.50 per ball Variable cost
Depreciation (straight-line method) $2,000 per month Fixed cost
Electricity cost $500 + $0.10 per ball Mixed cost
Supervisory salaries 4,000 units per shift $5,000 per mo. per supervisor Step-wise cost
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
0 2,000 4,000 6,000 8,000 10,000
Units Produced
$5,000 per supervisor per month - Step-wise
TotalCost
C 1
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13. NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls $0.50 per ball Variable cost
Depreciation (straight-line method) $2,000 per month Fixed cost
Electricity cost $500 + $0.10 per ball Mixed cost
Supervisory salaries 4,000 units per shift $5,000 per mo. per supervisor Step-wise cost
Curvilinear costA salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
$0
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000
Sales $
Sales Commissions - Curvilinear
TotalCost
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14. 18-P1: Measuring Cost Behavior
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15. Measuring Cost Behavior
The objective is to classify all costs as either fixed
or variable. We will look at three methods:
1. Scatter diagrams.
2. The high-low method.
3. Least–squares regression.
A scatter diagram is a plot of cost data points on a
graph. It is almost always helpful to plot cost data to
be able to observe a visual picture of the relationship
between cost and activity.
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16. Scatter Diagrams
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17. The High-Low Method
The following relationships between units
produced and total cost are observed:
Using these two levels of activity, compute:
 the variable cost per unit.
 the total fixed cost.P 1
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18. Units Cost
High activity level - October 67,500 29,000$
Low activity level - February 17,500 20,500
Change in activity 50,000 8,500$
The High-Low Method
Total cost = $17,525 + $0.17 per unit produced
P 1
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19. The objective of the cost
analysis remains the
same: determination of
total fixed cost and the
variable unit cost.
Least-Squares Regression
Least-squares regression is usually covered
in advanced cost accounting courses. It is
commonly used with spreadsheet programs
or calculators.
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20. Comparison of Cost Estimation
Methods
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21. NEED-TO-KNOW
Using the information below, use the high-low method to determine the cost equation
(total fixed costs plus variable costs per unit).
Activity
Level
Units
Produced
Total Cost
Lowest 1,600 $9,800
Highest 4,000 17,000
Variable Cost = $7,200
2,400
$3 per unit produced
Fixed Costs (at high point) Total cost = Fixed costs + $3 per unit
$17,000 = Fixed costs + ($3 x 4,000)
$5,000 = Fixed costs
Fixed Costs (at low point) Total cost = Fixed costs + $3 per unit
$9,800 = Fixed costs + ($3 x 1,600)
$5,000 = Fixed costs
Cost at high point - Cost at low point
Units at high point - Units at low point
($17,000 - $9,800)
(4,000 - 1,600)
Total costs = $5,000 + $3 per unit
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22. NEED-TO-KNOW
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
$16,000
$18,000
0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500
TotalCost
Units Produced
Total Cost
Slope = Variable Cost $3 per unit
y-intercept = Fixed Costs $5,000
(1,600 units, $9,800)
(4,000 units, $17,000)
(0 units, $5,000)
= $5,000 + $3 per unit
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23. 18-A1: Contribution Margin and
Its Measures
23

24. Contribution Margin and Its
Measures
A 1
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25. 18-P2: Computing the Break-
Even Point
25

26. Using Break-Even Analysis
The break-even point (expressed in
units of product or dollars of sales) is the
unique sales level at which a company
earns neither a profit nor incurs a loss.
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27. Computing the Break-Even Point
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28. P 2
Computing the Margin of Safety
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29. NEED-TO-KNOW
A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,
and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next
year.
1. Compute the contribution margin per unit.
2. Compute the break-even point (in units).
3. Compute the margin of safety (in dollars).
Contribution margin per unit, or unit contribution margin, is the amount by which a
product’s unit selling price exceeds its total variable cost per unit.
Sales $170 per unit
Variable costs 150 per unit
Contribution margin $ 20 per unit
$20 per unit
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30. NEED-TO-KNOW
A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,
and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next
year.
1. Compute the contribution margin per unit.
2. Compute the break-even point (in units).
3. Compute the margin of safety (in dollars).
Break-even point in units = Fixed costs
Contribution margin per unit
$400,000
$20 per unit
20,000 units to break-even
Units per unit Total
Sales 20,000 $170 $3,400,000
Variable costs 20,000 $150 3,000,000
Contribution margin $20 400,000
Fixed costs 400,000
Net income $0
$20 per unit
20,000 units
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31. NEED-TO-KNOW
A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,
and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next
year.
1. Compute the contribution margin per unit.
2. Compute the break-even point (in units).
3. Compute the margin of safety (in dollars).
The excess of expected sales over the break-even sales
level is called a company’s margin of safety
$20 per unit
20,000 units
Units per unit Total
Expected sales 25,000 $170 $4,250,000
Break-even sales 20,000 $170 3,400,000
Margin of safety $850,000
$850,000
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32. 18-P3: Preparing a Cost-Volume-
Profit Chart
32

33. Preparing a CVP Chart
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34. Working with Changes
in Estimates
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35. 18-C2: Applying Cost-Volume-
Profit Analysis
35

36. Computing Income
from Sales and Costs
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37. Computing Sales
for a Target Income
C 2
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38. Computing Sales
for a Target Income
C 2
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39. Computing Sales
for a Target Income
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40. NEED-TO-KNOW
A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,
and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.
1. Compute the contribution margin ratio.
2. Compute the dollar sales needed to yield the target income.
3. Compute the unit sales needed to yield the target income.
The contribution margin ratio is the percent of a unit’s selling price that exceeds total
unit variable cost.
Contribution margin ratio = Contribution margin per unit
Selling price per unit
$180 - $126 $54
$180 $180
30%
30%
per unit Ratio
Sales $180 100%
Variable costs 126 70%
Contribution margin $54 30%
C 2
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41. NEED-TO-KNOW
Dollar sales to achieve target income = Fixed costs + Pretax Income
Contribution margin ratio
$502,000 + $200,000
.30
$2,340,000
A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,
and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.
1. Compute the contribution margin ratio.
2. Compute the dollar sales needed to yield the target income.
3. Compute the unit sales needed to yield the target income.
30%
per unit Ratio Total
Sales $180 100% $2,340,000
Variable costs $126 70% 1,638,000
Contribution margin $54 30% 702,000
Fixed costs 502,000
Net income $200,000
$2,340,000
C 2
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42. NEED-TO-KNOW
Break-even point in units = Fixed costs
Contribution margin per unit
A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,
and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.
1. Compute the contribution margin ratio.
2. Compute the dollar sales needed to yield the target income.
3. Compute the unit sales needed to yield the target income.
30%
$2,340,000
Units to yield target income = Fixed costs + target (pretax) income
Contribution margin per unit
$502,000 + $200,000 $702,000
$180 - $126 $54
13,000 units
Units per unit Total
Sales 13,000 $180 $2,340,000
Variable costs 13,000 $126 1,638,000
Contribution margin $54 702,000
Fixed costs 502,000
Net income $200,000
13,000 units (or $2,340,000 / $180)
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43. Using Sensitivity Analysis
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44. 18-P4: Computing a
Multiproduct Break-Even Point
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45. Computing a Multiproduct
Break-Even Point
The CVP formulas can be modified for use
when a company sells more than one product.
 The unit contribution margin is replaced with the
contribution margin for a composite unit.
 A composite unit is composed of specific numbers
of each product in proportion to the product sales
mix.
 Sales mix is the ratio of the volumes of the various
products.
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46. Computing a Multiproduct
Break-Even Point
The resulting break-even formula
for composite unit sales is:
Break-even point
in composite units
Fixed costs
Contribution margin
per composite unit
=
Continue
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47. Haircuts
Basic Ultra Budget
Selling Price 20.00$ 32.00$ 16.00$
Variable Cost 13.00 18.00 8.00
Unit Contribution 7.00$ 14.00$ 8.00$
Sales Mix Ratio 4 2 1
Hair-Today offers three cuts as shown below. Annual fixed
costs are $192,000. Compute the break-even point in
composite units and in number of units for each haircut at the
given sales mix.
Computing a Multiproduct
Break-Even Point
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48. Computing a Multiproduct
Break-Even Point
P 4
Haircuts
Basic Ultra Budget
Selling Price 20.00$ 32.00$ 16.00$
Sales Mix Ratio 4.00 2.00 1.00
Selling Price/cut 80.00$ 64.00$ 16.00$
Total Selling Price/Composite Unit 160.00$
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49. Computing a Multiproduct
Break-Even Point
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Haircuts
Basic Ultra Budget
Variable Costs 13.00$ 18.00$ 8.00$
Sales Mix Ratio 4.00 2.00 1.00
Selling Price/cut 52.00$ 36.00$ 8.00$
Total Variable Cost/Composite Unit 96.00$
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50. Break-even point
in composite units
Fixed costs
Contribution margin
per composite unit
=
Break-even point
in composite units
$192,000
$64.00 per
composite unit
=
Break-even point
in composite units
= 3,000 composite units
Computing a Multiproduct
Break-Even Point
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51. Sales Composite
Product Mix Cuts Haircuts
Basic 4 × 3,000 = 12,000
Ultra 2 × 3,000 = 6,000
Budget 1 × 3,000 = 3,000
Total 21,000
Computing a Multiproduct
Break-Even Point
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52. Multiproduct Break-Even
Income Statement
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53. NEED-TO-KNOW
The sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both products
are $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.
1. What is the contribution margin per composite unit?
2. What is the break-even point in composite units?
3. How many units of X and how many units of Y will be sold at the break-even point?
Selling price per composite unit Units per unit Total
Product X 2 $5 $10
Product Y 1 $4 4
Total 3 $14
Variable cost per composite unit Units per unit Total
Product X 2 $2 $4
Product Y 1 $2 2
Total 3 $6
Contribution margin per composite unit ($14 - $6) $8
$8
P 4
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54. NEED-TO-KNOW
The sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both products
are $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.
1. What is the contribution margin per composite unit?
2. What is the break-even point in composite units?
3. How many units of X and how many units of Y will be sold at the break-even point?
$8
Break-even point in composite units = Fixed costs
Contribution margin per composite unit
$640,000
$8 per composite unit
80,000 composite units to break even
80,000 composite units
P 4
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55. NEED-TO-KNOW
The sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both products
are $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.
1. What is the contribution margin per composite unit?
2. What is the break-even point in composite units?
3. How many units of X and how many units of Y will be sold at the break-even point?
$8
80,000 composite units
Units of each product at break-even Total
Product X 80,000 composite units x 2 units per composite unit 160,000
Product Y 80,000 composite units x 1 unit per composite unit 80,000
240,000
Total Sales Units per unit Total
Product X 160,000 $5 $800,000
Product Y 80,000 $4 320,000
Total 240,000 $1,120,000
Total Variable Costs Units per unit Total
Product X 160,000 $2 $320,000
Product Y 80,000 $2 160,000
Total 240,000 $480,000
Composite units per unit Total
Sales $14 $1,120,000
Variable costs $6 480,000
Contribution margin $8 640,000
Fixed costs 640,000
Net income $0
80,000
80,000
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56. Global View
Over 90 percent of German companies
surveyed report their cost accounting systems
focus on contribution margin. This focus helps
German companies like Volkswagen control
costs and plan their production levels.
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57. 18-A2: Degree of Operating
Leverage
57

58. Degree of Operating Leverage
A measure of the extent to which fixed costs
are being used in an organization.
A measure of how a percentage change in
sales will affect profits.
A 2
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59. Rydell Company
Sales (1,200 units) 120,000$
Less: variable expenses 84,000
Contribution margin 36,000
Less: fixed expenses 24,000
Pretax income 12,000$
If Rydell increases sales by 10 percent, what will the
percentage increase in income be?
Operating Leverage
A 2
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60. Appendix 18A: Using Excel to
Estimate Least-Squares Regression
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61. End of Chapter 18
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