1. Cost-Volume-Profit Analysis

2. Cost-Volume-Profit Analysis
Cost-Volume-Profit (CVP) Analysis - the study of the interrelationships between costs and volume and how they impact profit.
I can’t make a good
marketing decision without
understanding the
CVP relationships.

3. Cost-Volume-Profit Analysis
CVP aids management in . . .
setting prices for products and services.
introducing a new product or service.
replacing a piece of equipment.
deciding whether a given product or service should be made within the firm or purchased outside the firm.
performing strategic “what if?” analyses.

4. Cost-Volume-Profit Analysis
Profit = Revenues - Total Costs or
Revenues = Fixed Costs + Variable Costs + Profits or
(Units sold × Price) = Fixed Cost + (Units sold × Unit Variable Cost) + Profit

5. Cost-Volume-Profit Analysis
Q = units sold
v = unit variable cost
f = total fixed cost
p = unit selling price
N = operating profit
The CVP Model:
(p × Q) = f + (v × Q) + N

6. The Contribution Margin and Contribution Income Statement
The unit contribution margin is the difference between unit sales price and unit variable cost, and is a measure of the increase in profit for a unit increase in sales.
The total contribution margin is the unit contribution margin multiplied by the number of units sold.
p – v = Unit contribution margin

7. The Contribution Margin and Contribution Income Statement
Household Furnishings, Inc.
Per
Monthly Annual Unit
Fixed cost $5,000 $60,000
Desired operating profit $4,000 $48,000
Price $37,500 $450,000 $75
Variable cost $17,500 $210,000 $35
Planned production 250 units 3,000 units
Planned Sales 250 units 3,000 units

8. The Contribution Margin and Contribution Income Statement
Household Furnishings, Inc.
2,400 units × $75 = $180,000

9. The Contribution Margin and Contribution Income Statement
Household Furnishings, Inc.
$15,000 × 53.33% = $8,000

10. Strategic Role of CVP Analysis
What if the expected level of profit at a give sales volume?
What additional amount of sales is needed to achieve a desired level of profit?
What will be the effect on profits of a given increase in sales?
What is the required funding level for a governmental agency, given desired service level?
Is the forecast for sales consistent with forecasted profits?
What additional profit would be obtained from a given percentage of reduction in unit variable costs?

11. CVP Analysis for Breakeven Planning
The Equation Method: Break-Even in Units
$75 × Q = $5,000 + ($35 × Q)
Selling price per unit
Total fixed cost
Variable cost per unit

12. CVP Analysis for Breakeven Planning
The Equation Method: Break-Even in Units
$75 × Q = $5,000 + ($35 × Q)
($75 - $35) × Q = $5,000
Q = $5,000 ÷ $40
Q = 125 units per month

13. CVP Analysis for Breakeven Planning
The Equation Method: Break-Even in Dollars
Y = (v ÷ p) × Y + f + N

14. CVP Analysis for Breakeven Planning
The Equation Method: Break-Even in Dollars
Y = (.4667) × Y + f + N
$210,000 ÷ $450,000

15. CVP Analysis for Breakeven Planning
The Equation Method: Break-Even in Dollars
Y = (.4667) × Y + f + N
Y = × Y + $5,
Y = $9,375 per month

16. CVP Analysis for Breakeven Planning
Contribution Margin Method f
p -v
Q =
$5,000
$75 - $35
Q =
Q = 125 units per month

17. The CVP Graph (5,000) Q = 125 Breakeven Point Total Revenue
Total Cost
Cost or Revenue
Total Cost
(5,000)
Output Volume
Q = 125 Breakeven Point

18. Profit-Volume Graph Profits Q = 125 Profits Total Cost Output Volume
Output Volume
Q = 125
Losses
25, , ,000

19. CVP Analysis for Breakeven Planning
Contribution Margin Method f
(p - v) ÷ p
p × Q =
$5,000
($75 - $35) ÷ $75
p × Q =
p × Q = $9,375 per month

20. f + N (p – v) f + N (p – v) ÷ p Revenue Planning Breakeven in units =
Management wants to know the sales volume necessary to achieve $48,000 in annual profit.
f + N
(p – v)
Breakeven in units =
f + N
(p – v) ÷ p
Breakeven in dollars =

21. Revenue Planning f + N (p – v) $60,000 + $48,000 $75 – $35
Management wants to know the sales volume necessary to achieve $48,000 in annual profit.
f + N
(p – v)
Breakeven in units =
Breakeven in units =
$60,000 + $48,000 $75 – $35
Breakeven in units = 2,700 units per year

22. Trade-offs Between Fixed and Variable Costs
Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2,500 per month. Annual sales are currently 2,700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same?
Q = 2,700 units p = $75 v = unknown f = ($5,000 + $2,250)×12 = $87,000 N = $48,000

23. Trade-offs Between Fixed and Variable Costs
Management is considering a new piece of equipment that will reduce variable costs but also increase fixed costs by $2,500 per month. Annual sales are currently 2,700 units. How much will unit variable cost have to fall to maintain the current level of profit, assuming sales volume and other factors remain the same?
v = p –
(f + N) Q
v = $75 –
($87,000 + $48,000) 2,700
= $25

24. Sales Commissions and Salaries
Management finds that $1,000 of the $5,000 monthly fixed costs is sales salaries, and that $7.50 of the $35 variable cost is sales commissions. If salaries are increased to $1,450,
how much would sales commission rate need to be decreased to keep profits the same?
v = r × $ $27.50
Original $35 - $7.50 (10% of $75)

25. Sales Commissions and Salaries
Management finds that $1,000 of the $5,000 monthly fixed costs is sales salaries, and that $7.50 of the $35 variable cost is sales commissions. If salaries are increased to $1,450,
how much would sales commission rate need to be decreased to keep profits the same?
v = r × $ $27.50
Fixed costs will increase by $450 per month
and variable costs will decrease.
f = $5,000 + $450 = $5,450

26. Sales Commissions and Salaries
Managers would have to reduce the commission rate from 10% to 7.33% to keep profits the same if the salespeople’s salaries are increased by $450.
$65,400 - $48,000
2,700
r × $75 + $27.50 = $75 –
r = .0733

27. Including Income Taxes in CVP Analysis
f +
p - v
Q = N
(1 - t )
t = tax rate
If the company is subject to a 20% tax rate.
$48,000/(1 - .2)
$75 - $35
Q = $60,000 +
Q = 3,000 units per year

28. Sensitivity Analysis of CVP Results
What-if Sensitivity Analysis
Management may look at changes in unit variable cost, total fixed costs or unit selling price on profits. Look at the analysis below:

29. Sensitivity Analysis of CVP Results
Margin of Safety
Margin of Safety =
Planned Sales - Breakeven Sales
3,000 units - 1,500 units
Margin of Safety =
Margin of Safety =
1,500 units

30. CVP Graph for a Firm with Relatively High Fixed Costs
$1.5
$.5
Total Revenue
25,000 units = – 25,000 x $10
= – $250,000
Cost or Revenue (in millions)
Total Cost
Fixed cost/yr. $500,000
Variable cost/ unit $2
Price $12
Contribution margin $10
25, , ,000
Output in Units

31. CVP Graph for a Firm with Relatively High Fixed Costs
Profits @ 75,000 units = 25,000 x $10
= $250,000
$1.5
$.5
Total Revenue
Cost or Revenue (in millions)
Total Cost
Fixed cost/yr. $500,000
Variable cost/ unit $2
Price $12
Contribution margin $10
25, , ,000
Output in Units

32. CVP Graph of a Firm with Relatively Low Fixed Costs
$1.5
$.5
Total Revenue
Total Cost
25,000 units = -25,000 x $3
= -$75,000
$1.0
Cost or Revenue (in millions)
Fixed cost/yr. $150,000
Variable cost/ unit $9
Price $12
Contribution margin $3
$ .l5
Output in Units
25, , ,000

33. CVP Graph of a Firm with Relatively Low Fixed Costs
$1.5
$.5
Profits @ 75,000 units = 25,000 x 3
= $75,000
Total Revenue
Total Cost
$1.0
Cost or Revenue (in millions)
Fixed cost/yr. $150,000
Variable cost/ unit $9
Price $12
Contribution margin $3
$ .l5
Output in Units
25, , ,000

34. CVP Analysis with Multiple Products
Here is information about two surfboard models manufactured:

35. CVP Analysis with Multiple Products
Assume a Constant Sales Mix
The product mix in units sold is
1.5 Pro : 1 Hang Ten

36. CVP Analysis with Multiple Products
Assume a Constant Sales Mix
Hang Ten × $ = $62.50
Pro × $ =
Total contribution $287.50
= 135 packages (rounded)
X =
$38,750.00
$287.50

37. CVP Analysis with Multiple Products
Assume a Constant Sales Mix
X =
135 packages (rounded)
Nose-to-Toes uses a weighted-average product mix to calculate break-even.

38. CVP Analysis with Multiple Products
Here is the calculation of Nose-to-Toes’ average contribution margin . . .
1.0 ÷ 2.5 = 40%
40% × $ = $25.00

39. CVP Analysis with Multiple Products
We find the break-even point as follows . . .
X =
$38,750
$115
= 337 boards (rounded)

40. CVP Analysis with Step Cost Behavior
Revenues, Total Costs
Total Revenue
Total Cost
$100,000
Losses
Output in Units
10, , , ,000

41. CVP Analysis with Step Cost Behavior
There is no breakeven below the 10,000 unit level of output.
Revenues, Total Costs
Total Revenue
$100,000
Losses
Output in Units
10, , , ,000

42. Assumptions and Limitations of CVP Analysis
Linearity and the Relevant Range
Identifying Fixed and Variable Cost for CVP Analysis

43. End of Chapter 8