1. Managerial Accounting
Balakrishnan | Sivaramakrishnan | Sprinkle | Carty | Ferraro
Chapter 5: Cost-Volume-Profit Analysis
Prepared by Debbie Musil, Kwantlen Polytechnic University

2. CVP Foundations
Classifies all revenue and cost into volume-related and non-volume related groups
Measure of volume depends on the business
Fixed cost stay the same
Revisit some definitions
LO1: Understand the Cost-Volume-Profit relation.

3. CVP Model Pre-tax profit As a formula: Profit = [( P – VC ) x Q] - FC
= Revenue – cost
= Revenue – variable cost – fixed cost
= Contribution margin – fixed cost
= Unit contribution margin × sales volume – fixed cost
As a formula: Profit = [( P – VC ) x Q] - FC
LO1: Understand the Cost-Volume-Profit relation.

4. Using the CVP Relation
LO1: Understand the Cost-Volume-Profit relation.

5. LO1: Understand the Cost-Volume-Profit relation.

6. CVP and Profit Planning
Profit planning: estimating profit at various levels of sales
What volume of business would provide a certain level of profit?
Breakeven volume: the sales volume at which profit is zero
The point where contribution margin covers fixed costs
LO2: Use the CVP relation to plan profit.

7. Cost-Volume-Profit (CVP) Model
LO2: Use the CVP relation to plan profit. 7

8. Profit Graph
LO2: Use the CVP relation to plan profit.

9. Test Your Knowledge!
Which one of the following correctly indicates how to calculate breakeven volume?
Variable costs divided by unit contribution margin
Profit divided by sales volume
Fixed costs divided by unit contribution margin
Variable costs divided by fixed costs
LO2: Use the CVP relation to plan profit.

10. Test Your Knowledge!
Which one of the following correctly indicates how to calculate breakeven volume?
Variable costs divided by unit contribution margin
Profit divided by sales volume
Fixed costs divided by unit contribution margin
Variable costs divided by fixed costs
Fixed costs divided by unit contribution margin indicates the breakeven volume where profit will be zero.
LO2: Use the CVP relation to plan profit.

11. $20
($50 - $30)
$75,000
($1,500,000/$20)
$3,750,000
($75,000 X $50)
0.40
($50 - $30)/$50
$3,750,000
($1,500,000/0.40)
$75,000
($3,750,000/$50)
LO2: Use the CVP relation to plan profit.

12. Target Profit Can calculate profit at any volume Breakeven analysis
Volume with zero profit
LO2: Use the CVP relation to plan profit.

13. Target Profit: Examples
Data Table
Sales Volume of Perlast in Kilograms
Profit before taxes
90,000
100,000
120,000
140,000
= ($15 x Sales volume in kg) – $1,200,000
$150,000
$300,000
$600,000
$900,000
Breakeven volume for Sierra
0 = breakeven volume × $15 – 1,200,000
Breakeven volume = 80,000 kilograms
LO2: Use the CVP relation to plan profit. 13

14. Alternate Formulation
Can work with revenues instead of units
Contribution margin ratio = Unit Contribution Margin / Price
This is the contribution per sales $
We have: Multiply & divide the first term by price to get…
Work with percent and $ directly
LO2: Use the CVP relation to plan profit.

15. Target Profit with CMR Can calculate profit at any volume
Breakeven analysis
Revenue for zero profit
LO2: Use the CVP relation to plan profit.

16. The Methods are Equivalent
Profit at sales of 100,000 units = $300,000
Contribution margin ratio = $15/$25 = 60%
Revenue at 100,000 units = $2,500,000
Profit = $2,500,000 × $1,200,000 = $300,000!
We also know breakeven = 80,000 kilograms
Associated revenue = $2,000,000
Profit = $2,000,000 × $1,200,000 = $0!
LO2: Use the CVP relation to plan profit.

17. Taxes Taxes are an unavoidable cost of doing business
Single tax rate on income
Profit after tax (PAT) = Profit before tax (PBT) – taxes paid
Taxes paid = tax rate  Profit before tax
Profit after tax =(1- tax rate)  Profit before tax
Profit after tax = (1- tax rate)  [Contribution margin – fixed cost]
LO2: Use the CVP relation to plan profit.

18. Taxes Change Slope of Profit Line
LO2: Use the CVP relation to plan profit.

19. Operational Planning In CVP model, profit is proportional to volume
Profit could be limited by:
Demand for product
Supply of product (capacity limitations)
Planning operations involves:
Making short term decisions that identify the factor limiting profit, and
Seeking to relax that constraint
LO3: Make short-term decisions using CVP analysis.

20. Evaluating Decisions Change the parameters to increase profit
If demand is the constraint
Increase prices - Expand product line
If capacity is the constraint
Change pricing - Rationalize product line
Add capacity (long-term decision considered later)
Manage risk
Change cost structure
Expand product portfolio
LO3: Make short-term decisions using CVP analysis.

21. Changing Prices Price per kilogram Demand (kilograms) UCM ($) Profit
$25
100,000
$15
$300,000
$23
120,000
$13
$360,000
$20
160,000
$10
$400,000
$18
184,000 $8
$272,000
$16
200,000 $6 $0
LO3: Make short-term decisions using CVP analysis. 21

22. Breakeven volume = $1,500,000 / $20 = 75,000
Breakeven revenues = $1,500,000 / 0.40 = $3,750,000
If sales were to increase by 20%, then the percent change in profit before taxes = 0.20 x (1/0.0625) = 3.20 or 320%
Because current profit before taxes = [($20 x 80,000) – $1,500,000] = $100,000
Profit would increase by $100,000 x 3.2 = $320,000
In turn, $100,000 + $320,000 = $420,000
LO3: Make short-term decisions using CVP analysis.

23. Evaluating Operating Risk
At a given volume, how much “cushion” does firm have before it starts making a loss?
Margin of safety formula:
Margin of safety is
Often expressed as a percentage
Can be calculated in units
Can be calculated using sales revenue
% change in profit = % change in sales × (1/ MOS)
LO4: Measure risk using the CVP relation.

24. Margin of Safety: Example
At sales of 100,000 kilograms
Profit Multiplier at 100K = (1 / MOS) = 5
Current profit 100K × $15 – 1.2MM = $300K
10% increase => sales = 110K kilograms
Profit = 110K × $15 – 1.2MM = $450K
50% increase = 10% × 5!
LO4: Measure risk using the CVP relation.

25. With the new technology… Without the new technology…
Total costs = $1,240,000 + ($9 x Sales volume in units)
Without the new technology…
Total costs = $1,200,000 + ($10 x Sales volume in units)
Setting the two equations equal to each other, we have:
$1,240,000 + ($9 x Sales volume in units) = $1,200,000 + ($10 x Sales volume in units)
Solving, we find Sales volume in units = 40,000 kilograms
LO4: Measure risk using the CVP relation.

26. Change Cost Structure Can change cost structure Operating Leverage
Automation substitutes FC for VC
Outsourcing substitutes VC for FC
Operating Leverage
Increasing the amount of fixed cost increases business risk, for given volume
Operating Leverage = Fixed Cost / Total Cost
LO4: Measure risk using the CVP relation.

27. Alternate Cost Structures
LO4: Measure risk using the CVP relation. 27

28. Points to note
As demand increases, OL decreases For given demand, decisions that increase FC and lower VC increase OL
Profit is more sensitive to volume changes when OL is high
At lower demand levels, a cost structure with lower OL is typically preferred to a cost structure with higher OL
LO4: Measure risk using the CVP relation.

29. (5/7 x $6) = (2/7 x $15) = $60/7 = $8.5714 (rounded)
175,000 kilograms 3
125, ,000 1
(5/7 x $6) = (2/7 x $15) = $60/7 = $ (rounded) 2
($1,275,000 + $225,000) / $ = 175,000 kilograms 3
175,000 kilograms x 5/7 = 125,000 kilograms of Economy;
175,000 x 2/7 = 50,000 kilograms of Standard
LO4: Measure risk using the CVP relation.

30. Multi-Product CVP Analysis
With two products, CVP model becomes
No appealing way to allocate joint cost and revenue
Multi-product CVP model is only valid for the specified mix.
Cannot determine “best” product mix
LO5: Perform CVP analysis with multiple products.

31. Mechanics: Multi-Product CVP
There are two equivalent approaches for applying the multi-product model
Weighted Unit Contribution Margin (“Weighted UCM”) Approach
CM per average unit
Weighted Contribution Margin (“Weighted CMR”) approach
Can use with aggregate financial data
LO5: Perform CVP analysis with multiple products.

32. Weighted UCM Approach Sales mix Breakeven volume
5/8 of sales from E, 3/8 from S
Weighted Unit Contribution Margin
(5/8 × $6) + (3/8 × $15) = $9.375 per average kilogram
Breakeven volume
= $1,275,000 / $9.375 = 136,000 kg
Applying sales mix, we have
85,000 E & 51,000 S
LO5: Perform CVP analysis with multiple products.

33. Weighted CMR Approach Revenue mix Breakeven revenue
50% from E and 50% from S
Weighted Contribution Margin Ratio
0.5 × 40% + .5 × 60% = 50%
Breakeven revenue
= $1,275,000 / = $2,550,000
Applying revenue mix, we have
$1.275 MM for E => 85,000 kg
$1.275 MM from S => 51,000 kg
LO5: Perform CVP analysis with multiple products.

34. $2,550,000 x 0.50 (Economy); $2,550,000 x 0.50 (Standard)1
$2,550,000 2
$1,275,000 $1,275,000 3 4
85, ,000 1
(0.50 x 0.40) + (0.50 x 0.60) 2
$1,275,000 / 0.50 3
$2,550,000 x 0.50 (Economy); $2,550,000 x 0.50 (Standard) 4
$1,275,000 / $15 (Economy); $1,275,000 x $25 (Standard)
LO5: Perform CVP analysis with multiple products.

35. Limitations of CVP Analysis
Linearity of revenue
Linearity of variable cost
Fixed costs cannot be changed
No uncertainty
Single period analysis
Valid only for given product mix
Profit maximization is not the criterion
Used to answer “what if” questions
Assumes that capacity is always available
LO6: List the assumptions underlying CVP analysis.

36. Test Your Knowledge!
Which of the following is not a key assumption using CVP analysis?
Capacity is available with no limitations on the supply of raw materials.
Selling prices, unit variable costs, and fixed costs are known with certainty.
Variable costs and revenue increase proportionately with sales volume.
CVP will always provide the best answer for short-term decisions.
LO6: List the assumptions underlying CVP analysis.

37. Test Your Knowledge!
Which of the following is not a key assumption using CVP analysis?
Capacity is available with no limitations on the supply of raw materials.
Selling prices, unit variable costs, and fixed costs are known with certainty.
Variable costs and revenue increase proportionately with sales volume.
CVP will always provide the best answer for short-term decisions.
CVP cannot predict the best decisions for all situations. For example, it is effective when revenues and variable costs increase proportionally with sales, sales prices and costs are known with certainty, and product mix stays the same.
LO6: List the assumptions underlying CVP analysis.

38. Exercise 5.30
CVP relation and profit planning, unit contribution margin approach (LO1, LO2).
Ajay Singh plans to offer gift-wrapping services at the local mall during the month of December. Ajay will wrap each package, regardless of size, in the customer’s choice of wrapping paper and bow for a price of $3. Ajay estimates that his variable costs will total $1 per package wrapped and that his fixed costs will total $600 for the month.
Required:
Express Ajay’s profit before taxes in terms of the number of packages sold.
How many packages does Ajay need to wrap to break even?
How many packages must Ajay wrap to earn a profit of $1,400?

39. Exercise 5.30 (Continued)
Express Ajay’s profit before taxes in terms of the number of packages sold.
Recall that:
Profit before taxes = (unit contribution margin x sales volume in units) – fixed costs.
Additionally,
Unit contribution margin = Unit selling price – Unit variable cost.
= $3.00 – $1.00 = $2.00 per package.
The problem also informs us that Ajay’s fixed costs for the month = $600.
Thus, Ajay’s profit is:
Profit before taxes = ($2.00 x number of packages sold) – $600.

40. Exercise 5.30 (Continued)
How many packages does Ajay need to wrap to break even?
Breaking even implies a profit of zero. Thus, we have:
$0 = ($2.00 x Breakeven volume) - $600
Or…

41. Exercise 5.30 (Concluded)
How many packages must Ajay wrap to earn a profit of $1,400?
Substituting Ajay’s target profit of $1,400 into the expression for profit we developed in part [a], we have:
$1,400 = ($2.00 x Required # of packages) - $600
Or…

42. Copyright
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