### Profitability Analysis

Module 15
Cost-Volume-Profit
Analysis and Planning
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
CVP Assumptions
1. All costs are classified as fixed or variable.
2. The total cost function is linear within the
relevant range.
3. The total revenue function is linear within the
relevant range.
4. The analysis is for a single product, or the sales
mix of multiple products is constant.
5. There is only one activity cost driver: unit or
dollar sales volume.
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
Manufacturing costs:
Direct materials
\$0.43
Direct labor
0.32
Manufacturing overhead
0.20
\$0.95
Selling and administrative
0.15
Total
\$1.10
Fixed Costs Per Month
Manufacturing overhead
\$1,200
Selling and administrative
580
Total
\$1,780
Required volume to earn \$1,000:
RV = (FC+DP)/(SP-VCU)
RV=(\$1,780+\$1,000)/(\$1.50-\$1.10)=6,950
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:
\$2,988
Direct materials (6,950 x \$0.43)
2,224
Direct labor (6,950 x \$0.32)
Variable manufacturing overhead (6,950 x \$0.20) 1,390
1,200 (7,802)
Fixed manufacturing overhead
Gross margin
2,623.
Less other expenses:
Variable selling and administrative (6,950 x \$0.15) 1,043
580 (1,623)
Fixed selling and administrative
Profit
\$ 1,000.
Contribution Income Statement
Chillin’ Time
Contribution Income Statement
For a Monthly Volume of 6,950 Ice Cream Bars
Sales (6,950 x \$1.50)
Less variable costs:
Direct materials (6,950 x \$0.43)
Direct labor (6,950 x \$0.32)
Manufacturing overhead (6,950 x \$0.20)
Selling and administrative (6,950 x \$0.15)
Contribution margin (6,950 x \$0.40)
Less fixed costs:
Manufacturing
Selling and administrative
Profit
\$10,425.
\$2,988
2,224
1,390
1,043
1,200
580
(7,645)
2,780.
(1,780)
\$ 1,000.
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
Contribution Margin Example
Chillin’ Time’s contribution income appears below:
Total
Sales (6,950 units)
Variable costs
Contribution margin
Fixed costs
Profit
Contribution margin per unit:
Contribution margin ratio:
\$ 10,425.
(7,645)
2,780.
(1,780)
\$ 1,000.
Per Unit
\$ 1.50
-1.10
\$ 0.40
\$1.50 – \$1.10 = \$0.40
[\$1.50 – \$1.10] ÷ \$1.50 = 0.2667
Sensitivity Analysis
EXAMPLE:
Total
Sales (6,950 units)
Variable costs
Contribution margin
Fixed costs
Profit
\$10,425.
(7,645)
2,780.
(1,780)
\$ 1,000.
Per Unit
Ratio to Sales
\$ 1.50
(1.10)
\$ 0.40
1.000
(0.733)
0.267
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 × 0.2667= \$280
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
\$1,780
Break-Even Unit =
\$1.50 – \$1.10
Sales Volume
= 4,450 units
When Chillin’ Time sells 4,450 ice cream bars
per month, it will break even.
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.
Before-tax profit = After-tax profit
(1 – tax rate)
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
Before-tax profit =
(1 – tax rate)
\$840
=
= \$1,200
(1 – 0.30)
Target unit
sales volume
\$1,780 + \$1,200
=
\$1.50 – \$1.10
= 7,450 ice cream bars
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
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 costvolume-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
Unit Sales Analysis
Chillin’ Time now has two products--ice cream bars and
popsicles, with the following information:
Ice Cream Bars
Unit sales
Selling price per unit
Variable cost per unit
Fixed costs per month
Sales revenue
Variable costs
Contribution margin
Contribution margin ratio
5,000
\$1.50
\$1.10
Popsicles
5,000
\$0.50
\$0.25
Total
10,000
\$ 1,780
\$7,500
5,500
\$ 2,000
0.2667
\$2,500
1,250
\$1,250
0.5000
\$10,000
6,750
\$ 3,250
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.
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
= 5,476.9 ≈ 5,477 units
=
\$0.325
Ice cream bars: 5,477 × 1/2 = 2,739*
and
Popsicles: 5,477 × 1/2 = 2,739*
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
\$1,780
= 4,811 units
=
\$0.37
Ice cream bars: 4,811 × 4/5 = 3,849
and
Popsicles: 4,811 × 1/5 = 962
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.
Dollar Multiproduct Break-Even
Example
Current sales mix in dollars is 10,000 to 4,000 or about 71% to
29%. How much is the break-even sales volume in dollars?
\$10,000*.2667+ \$4,000*.50= \$4,667
Average contribution margin ratio = \$4,667÷\$14,000 = 0.333*
[or 71%*.2667 + 29%*.500=0.334*] *rounding diff.
Dollar break-even point with new sales mix =
=
=
Fixed costs
Contribution margin per unit
\$1,780
0.333
= \$5,340
Ice cream bars:
\$5,340× 0.71 = \$3,792
and
Popsicles:
\$5,340 × 0.29 = \$1,549
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
Contribution margin
=
operating
Income before taxes
leverage
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
Sales
Variable costs
Contribution margin
Fixed costs
Before-tax profit
\$40,000
(22,000)
18,000
(8,000)
\$10,000.
Mexi Land
\$40,000.
(8,000)
32,000.
(22,000)
\$10,000.
If sales drop by 20% for both, which company suffers more?
Taco King
Degree of
operating leverage
Decrease
in profit
\$18,000
\$10,000
= 1.8
1.8 × 20% = 36%
Decline in Profit
Mexi Land
\$32,000
= 3.2
\$10,000
3.2 × 20% = 64%
Decline in Profit
Mexi Land’s higher operating leverage results in a larger profit decline.
Margin of Safety

Margin of Safety:


Revenues – Breakeven Revenues
Margin of Safety Ratio:

(Sales – BE Sales)/Sales
Margin of Safety
Taco King and Mexi Land are competitors and reported the same sales
revenue and before-tax profit during May:
Taco King
Sales
Variable costs
Contribution margin
Fixed costs
Before-tax profit
CM%
\$40,000
(22,000)
18,000
(8,000)
\$10,000.
\$18,000/40,000=45%
Taco King
Break-even sales
Margin of Safety
\$8,000/45%=\$17,778
\$40,000-\$17,778=22,222
Margin of Safety Ratio* \$22,222/\$40,000 = 55.6%
*Note that MSR = 1/OL
Mexi Land
\$40,000.
(8,000)
32,000.
(22,000)
\$10,000.
\$32,000/40,000=80%
Mexi Land
\$22,000/80%=\$27,500
\$40,000-\$27,500=\$12,500
\$12,500/\$40,000=31.3%