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Chapter 11 CVP Example - Cal Company

James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida

Chapter 11 | MAAW's Textbook Table of Contents

The Cal Company produces pocket size calculators that are sold for $10 per unit. The costs associated with each unit are as follows:

Direct material $3.00
Direct labor $0.25
Variable overhead $2.00
Variable selling and administrative cost $0.75
Fixed manufacturing costs $100,000
Fixed selling and administrative costs $20,000

The company’s tax rate is 40%.

In a recent meeting, the board of directors asked the following questions. How many calculators do we need to produce and sell to accomplish each of the following requirements?

1. Break-even.
2. Earn net income before taxes of $40,000.
3. Earn net income after taxes of $24,000.
4. Earn a 20% return on sales before taxes.
5. Earn a 12% return on sales after taxes.

To answer these questions, we start by calculating the contribution per unit as follows:

Contribution margin per unit = P - V = 10 - (3 + .25 + 2 + .75) = 10 - 6 = 4.

Then, the five questions are answered by using the equations from Exhibit 11-1.

1. Break-even.

4X = 120,000
X = $120,000 ÷ 4 = 30,000 units.

2. Earn net income before taxes of $40,000.

4X = 120,000 + 40,000
X = 160,000 ÷ 4 = 40,000 units.

3. Earn net income after taxes of $24,000.

4X = 120,000 + [24,000 ÷ (1-.4)]
4X = 120,000 + 40,000
X = 160,000 ÷ 4 = 40,000 unit.

4. Earn a 20% return on sales before taxes.

4X = 120,000 + .2(10X)
4X = 120,000 + 2X
2X = 120,000
X = 120,000 ÷ 2 = 60,000 units.

5. Earn a 12% return on sales after taxes.

4X = 120,000 + [.12(10X) ÷ (1-.4)]
4X = 120,000 + .2(10X)
4X = 120,000 + 2X
2X = 120,000
X = 120,000 ÷ 2 = 60,000 units.

A graphic solution to Example 11-1 is illustrated in Figure 11-18.

Graphic Analysis of Cost Volume Profit Example

Using The After Tax Equations As An Alternative

The equation for NIAT that appears in the graph is found by multiplying the equation for NIBT by (1-T) , i.e., (1-.4)(-120,000 + 4X) = -72,000 + 2.4X. Rearranging this equation we have 2.4X = 72,000 + NIAT. This revised equation indicates that the contribution margin after taxes ($2.4X) is equal to fixed costs after taxes ($72,000) plus the desired after tax income. It provides an alternative way to find the answers to questions 3 and 5 as illustrated below.

3. Earn net income after taxes of $24,000.

2.4X = 72,000 + NIAT desired
2.4X = 72,000 + 24,000
2.4X = 96,000
X = 96,000 ÷ 2.4 = 40,000 units.

5. Earn a 12% return on sales after taxes.

2.4X = 72,000 + NIAT desired
2.4X = 72,000 + .12(10X)
2.4X = 72,000 + 1.2X
1.2X = 72,000
X = 72,000 ÷ 1.2 = 60,000 units.

Checking the Solutions

The accuracy of linear cost-volume-profit calculations can be verified easily. For example, the answers to the questions above can be verified as follows:

1. Is 30,000 units the break-even point? Yes, since total contribution margin is equal to total fixed cost of 120,000, i.e., (4)(30,000) = $120,000.

2. Will 40,000 units generate a before tax profit of $40,000? Yes, because total contribution margin is (4)(40,000) = $160,000 and this amount is 160,000 - 120,000 = $40,000 above total fixed costs.

3. Will 40,000 units generate an after tax profit of $24,000? Yes, since (1-.4)($40,000 NIBT) = $24,000.

4. Will 60,000 units provide a 20% return on sales before taxes? Yes, since the NIBT is TCM - TFC or (4)(60,000) - 120,000 = $120,000. Sales equals PX or ($10)(60,000) = $600,000. R = 120,000 ÷ 600,000 = .20 or 20%.

5. Will 60,000 units provide a 12% return on sales after taxes. Yes, (1-.4)(.2) = .12 or 12%. For an alternative check (1-.4)(120,000) = $72,000 NIAT. Therefore, the after tax rate of return is 72,000 ÷ 600,000 = .12 or 12%.