1. Cost-Volume-Profit Analysis and Planning
Module 15
Cost-Volume-Profit Analysis and Planning

2. Profitability Analysis
Involves examining the relationships among revenues, costs, and profits
Widely used in the economic evaluation of existing or proposed products or services
Performed before decisions are finalized
What you need to understand to perform profitability analysis
Selling prices
Behavior of activity cost drivers

3. CVP Assumptions All costs are classified as fixed or variable.
The total cost function is linear within the relevant range.
The total revenue function is linear within the relevant range.
The analysis is for a single product, or the sales mix of multiple products is constant.
There is only one activity cost driver: unit or dollar sales volume.

4. Example Using the Profit Equation
Chillin’ Time produces and sells one product, ice cream bars, for $1.50 each. To ensure top quality, no inventories are maintained.
Estimated costs are:
Variable Costs Per Ice Cream Bar
Fixed Costs Per Month
Manufacturing costs:
Manufacturing overhead
$1,200
Direct materials
$0.43
Selling and administrative
580
Direct labor
0.32
Total
$1,780
0.20
$0.95
0.15
$1.10
Required volume to earn $1,000:
RV = (FC+DP)/(SP-VCU)
RV=($1,780+$1,000)/($1.50-$1.10)=6,950

5. Functional Income Statement Example
Chillin’ Time
Functional Income Statement
For a Monthly Volume of 6,950 Ice Cream Bars
Sales (6,950 x $1.50)
$10,425.
Less cost of goods sold:
Direct materials (6,950 x $0.43)
$2,988
Direct labor (6,950 x $0.32)
2,224
Variable manufacturing overhead (6,950 x $0.20)
1,390
Fixed manufacturing overhead
1,200
(7,802)
Gross margin
2,623.
Less other expenses:
Variable selling and administrative (6,950 x $0.15)
1,043
Fixed selling and administrative
580
(1,623)
Profit
$ 1,000.

6. Contribution Income Statement
Chillin’ Time
Contribution Income Statement
For a Monthly Volume of 6,950 Ice Cream Bars
Sales (6,950 x $1.50)
$10,425.
Less variable costs:
Direct materials (6,950 x $0.43)
$2,988
Direct labor (6,950 x $0.32)
2,224
Manufacturing overhead (6,950 x $0.20)
1,390
Selling and administrative (6,950 x $0.15)
1,043
(7,645)
Contribution margin (6,950 x $0.40)
2,780.
Less fixed costs:
Manufacturing
1,200
Selling and administrative
580
(1,780)
Profit
$ 1,000.

7. Analysis Using Contribution Margin Ratio
Unit contribution margin
Indicates how sensitive an income model is to a change in unit sales
Contribution margin ratio
The portion of every sales dollar contributed toward covering fixed costs and earning a profit

8. Contribution Margin Example
Chillin’ Time’s contribution income appears below:
Total
Per Unit
Sales (6,950 units)
$ 10,425.
$ 1.50
Variable costs
(7,645)
-1.10
Contribution margin
2,780.
$ 0.40
Fixed costs
(1,780)
Profit
$ 1,000.
Contribution margin per unit:
$1.50 – $1.10 = $0.40
Contribution margin ratio:
[$1.50 – $1.10] ÷ $1.50 =

9. Sensitivity Analysis EXAMPLE:
Total
Per Unit
Ratio to Sales
Sales (6,950 units)
$10,425.
$ 1.50
1.000
Variable costs
(7,645)
(1.10)
(0.733)
Contribution margin
2,780.
$ 0.40
0.267
Fixed costs
(1,780)
Profit
$ 1,000.
If sales increase by 100 ice cream bars per month, by how much will net income increase?
100 × $0.40 = $40
If sales increase by $1,050 per month, by how much will net income increase?
$1,050 × = $280

10. Break-Even Point Example
Chillin’ Time sells ice cream bars with a
$1.10 unit variable cost for $1.50 each.
How many bars must it sell to break even? =
Fixed costs
Contribution margin per unit
Chillin’ Time’s Break-Even Unit = Sales Volume
$1,780
$1.50 – $1.10
= 4,450 units
When Chillin’ Time sells 4,450 ice cream bars per month, it will break even.

11. Impact of Income Taxes
Determining the unit sales volume required to earn a desired after-tax profit:
Step 1:
Determine the required before-tax profit.
Step 2:
Substitute the required before-tax profit into the profit formula.
Step 3:
Solve for the required unit sales volume.
After-tax profit
(1 – tax rate)
Before-tax profit =

12. Impact of Income Taxes Example
Chillin’ Time sells ice cream bars with a $1.10 unit variable cost for $1.50 each. It is subject to a 30 percent income tax rate. How many ice cream bars must Chillin’ Time sell to earn a desired monthly after-tax profit of $840?
After-tax profit
(1 – tax rate)
Before-tax profit =
$840
(1 – 0.30) =
= $1,200
Target unit
sales volume =
$1,780 + $1,200
$1.50 – $1.10
= 7,450 ice cream bars

13. Multiple Product Break-Even Point
Applicable when unit information is not available or when a company sells more than one product.
Dollar break-even point =
Fixed costs
Contribution margin ratio
Target dollar sales volume =
Fixed costs + Desired profit
Contribution margin ratio

14. Sales Mix Analysis Sales mix
The relative portion of unit or dollar sales that are derived from each product
When sales mix is constant, the basic cost-volume-profit model can be used effectively
When sales mix is not constant, must determine average unit contribution margin or average contribution margin ratio for each alternative mix

15. Unit Sales Analysis
Chillin’ Time now has two products--ice cream bars and popsicles, with the following information:
Ice Cream Bars
Popsicles
Total
Unit sales
5,000
10,000
Selling price per unit
$1.50
$0.50
Variable cost per unit
$1.10
$0.25
Fixed costs per month
$ 1,780
Sales revenue
$7,500
$2,500
$10,000
Variable costs
5,500
1,250
6,750
Contribution margin
$ 2,000
$1,250
$ 3,250
Contribution margin ratio
0.267
0.500
0.325
Current sales mix based on units: 5,000 to 5,000 or 1 to 1. Chillin’ Time sells 1 ice cream bar for every popsicle.

16. Unit Multiproduct Break-Even Example
Average contribution margin per unit = [($0.40 × 1) + ($0.25 × 1)] ÷ 2 units= $0.325
Unit break-even point =
Fixed costs
Contribution margin per unit
$1,780
$0.325 =
= 5,476.9 ≈ 5,477 units
Ice cream bars: 5,477 × 1/2 = 2,739*
and
Popsicles: 5,477 × 1/2 = 2,739*

17. Unit Multiproduct Break-Even Example
If the sales mix changes to 4:1, how much will the unit break-even sales volume be?
Average contribution margin per unit =
[($0.40 × 4) + ($0.25 × 1)] ÷ 5 units = $0.37
Unit break-even point with new sales mix =
Fixed costs
Contribution margin per unit
Ice cream bars: 4,811 × 4/5 = 3,849
and
Popsicles: 4,811 × 1/5 = 962
$1,780
$0.37 =
= 4,811 units

18. Comparing Break-Even Example
Break-even units
Sales mix
1 to 1
Ice cream bars: 5,477 × 1/2 = 2,739*
and
Popsicles: 5,477 × 1/2 = 2739*
Sales mix
4 to 1
Ice cream bars: 4,811 × 4/5 = 3,849
and
Popsicles: 4,811 × 1/5 = 962
The change in sales mix causes the total number of units needed to break even to change because of the different contribution margins for the two products.

19. Dollar Multiproduct Break-Even Example
Current sales mix in dollars is 7,500 to 2,500 or 75% to 25%. How much is the break-even sales volume in dollars?
Average contribution margin ratio = $3,250 ÷ $10,000 = 0.325
Dollar break-even point with new sales mix = =
Fixed costs
Contribution margin per unit
Ice cream bars:
$5,477 × 0.75 = $4,108
and
Popsicles:
$5,477 × 0.25 = $1,369
$1,780
0.325
= $5,477 =

20. Degree of operating leverage
What is operating leverage?
Extent to which income will change with a change in sales
High degree of operating leverage
Signals the existence of a high portion of fixed costs
Degree of operating leverage
Contribution margin
Income before taxes =

21. Measuring Expected Change in Profit
Taco King and Mexi Land are competitors and reported the same sales revenue and before-tax profit during May:
Taco King
Mexi Land
Sales
$40,000
$40,000.
Variable costs
(22,000)
(8,000)
Contribution margin
18,000
32,000.
Fixed costs
Before-tax profit
$10,000.
If sales drop by 20% for both, which company suffers more?
Taco King
Mexi Land
Degree of operating leverage
$18,000
$10,000
= 1.8
$32,000
$10,000
= 3.2
Decrease in profit
1.8 × 20% = 36%
Decline in Profit
3.2 × 20% = 64%
Decline in Profit
Mexi Land’s higher operating leverage results in a larger profit decline.

22. Margin of Safety Margin of Safety: Margin of Safety Ratio:
Revenues – Breakeven Revenues
Margin of Safety Ratio:
(Sales – BE Sales)/Sales

23. Margin of Safety
Taco King and Mexi Land are competitors and reported the same sales revenue and before-tax profit during May:
Taco King
Mexi Land
Sales
$40,000
$40,000.
Variable costs
(22,000)
(8,000)
Contribution margin
18,000
32,000.
Fixed costs
Before-tax profit
$10,000.
CM% $18,000/40,000=45% $32,000/40,000=80%
Taco King
Mexi Land
Break-even sales $8,000/45%=$17, $22,000/80%=$27,500
Margin of Safety $40,000-$17,778=22, $40,000-$27,500=$12,500
Margin of Safety Ratio* $22,222/$40,000 = 55.6% $12,500/$40,000=31.3%
*Note that MSR = 1/OL