Prepare a contribution margin format income statement; answer what-if questions. Shown here is an income statement in the traditional format for a firm with a sales volume of 15,000 units: Problem 12.20 LO 7, 8, 9, 12 Revenues:
8,000 x
62,000 Gross profit:
1,500 x
13,500 – Administration (
0.50/unit):
18,000 a. Prepare an income statement in the contribution margin format. b. Calculate the contribution margin per unit and the contribution margin ratio. c. Calculate the firm’s operating income (or loss) if the volume changed from: 1. 15,000 units to 20,000 units. 2. 15,000 units to 10,000 units.
The Correct Answer and Explanation is:
To help you with the problem, let’s go step by step.
Given Information:
- Sales volume: 15,000 units
- Sales price per unit: $8,000 (Total revenue of $62,000 / 8,000 units)
- Cost of Goods Sold (COGS): $13,500 (Gross profit – Administration expense)
- Administration expenses: $18,000 (Fixed cost, as it’s given at $0.50 per unit)
a) Contribution Margin Format Income Statement:
The contribution margin format is designed to separate variable costs from fixed costs. In this case, the variable cost is the cost of goods sold (COGS) and administration (which is per unit), while the fixed costs will be the fixed portion of administration expenses.
- Sales: 15,000 units * $8,000 per unit = $120,000
- Variable Costs: We have variable costs for both COGS and administration.
- Variable COGS: $13,500 (Total for the volume of 15,000 units)
- Variable Administration: $18,000 (Fixed cost component)
Thus, the contribution margin income statement looks like:
Contribution Margin Income Statement (For 15,000 units):
| Revenues | $120,000 |
|---|---|
| Variable Costs: | |
| – Variable COGS | $13,500 |
| – Variable Administration | $18,000 |
| Total Variable Costs | $31,500 |
| Contribution Margin | $88,500 |
| Fixed Costs | $18,000 |
| Operating Income | $70,500 |
b) Contribution Margin per Unit and Ratio:
- Contribution Margin per Unit: Contribution Margin per Unit=Total Contribution MarginUnits Sold=88,50015,000=5.9\text{Contribution Margin per Unit} = \frac{\text{Total Contribution Margin}}{\text{Units Sold}} = \frac{88,500}{15,000} = 5.9Contribution Margin per Unit=Units SoldTotal Contribution Margin=15,00088,500=5.9 The contribution margin per unit is $5.90.
- Contribution Margin Ratio: Contribution Margin Ratio=Contribution MarginSales=88,500120,000=0.7375 or 73.75%\text{Contribution Margin Ratio} = \frac{\text{Contribution Margin}}{\text{Sales}} = \frac{88,500}{120,000} = 0.7375 \, \text{or} \, 73.75\%Contribution Margin Ratio=SalesContribution Margin=120,00088,500=0.7375or73.75%
c) Operating Income (or Loss) if Volume Changes:
- From 15,000 units to 20,000 units:
- Sales for 20,000 units = 20,000 * $8,000 = $160,000
- Variable costs = $31,500 (calculated for 15,000 units), so for 20,000 units, they will increase proportionally: New Variable Costs=31,50015,000×20,000=42,000\text{New Variable Costs} = \frac{31,500}{15,000} \times 20,000 = 42,000New Variable Costs=15,00031,500×20,000=42,000
- Contribution Margin = $160,000 – $42,000 = $118,000
- Operating Income = $118,000 – $18,000 (Fixed costs) = $100,000
- From 15,000 units to 10,000 units:
- Sales for 10,000 units = 10,000 * $8,000 = $80,000
- Variable costs for 10,000 units = $\frac{31,500}{15,000} \times 10,000 = 21,000$
- Contribution Margin = $80,000 – $21,000 = $59,000
- Operating Income = $59,000 – $18,000 (Fixed costs) = $41,000
Explanation:
- Contribution Margin is calculated as Sales minus Variable Costs. It tells you how much money is left to cover fixed costs and contribute to profits.
- Contribution Margin per Unit is the amount each unit contributes to covering fixed costs and generating profit.
- Contribution Margin Ratio shows the percentage of each dollar of sales that is available to cover fixed costs and contribute to profit.
- Operating Income varies with the level of sales volume because variable costs increase or decrease proportionally with changes in sales. When sales increase, operating income increases significantly due to the higher contribution margin, and when sales decrease, operating income decreases, but fixed costs remain the same.
