Question

Molly Company sells 37,000 units at $29 per unit. Variable costs are $17.40 per unit, and fixed costs are $167,400.

Determine (a) the contribution margin ratio, (b) the unit contribution margin, and (c) operating income.

Line Item Description Answer
a. Contribution margin ratio (Enter as a whole number.) fill in the blank 1
%
b. Unit contribution margin (Round to the nearest cent.) $fill in the blank 2
per unit
c. Operating income

Answer 1

To solve for each of the requested items, we can use the following formulas:

1. **Contribution Margin Ratio (CM Ratio)**:
\[
\text{CM Ratio} = \frac{\text{Contribution Margin}}{\text{Sales}} \times 100
\]
where:
\[
\text{Contribution Margin} = \text{Sales} - \text{Variable Costs}
\]

2. **Unit Contribution Margin**:
\[
\text{Unit CM} = \text{Selling Price per Unit} - \text{Variable Cost per Unit}
\]

3. **Operating Income**:
\[
\text{Operating Income} = \text{Contribution Margin} - \text{Fixed Costs}
\]

Now plug in the given values:

### Step 1: Calculate Sales and Variable Costs
- **Sales**:
\[
\text{Sales} = \text{Units Sold} \times \text{Selling Price per Unit} = 37,000 \times 29 = 1,073,000
\]

- **Variable Costs**:
\[
\text{Total Variable Costs} = \text{Units Sold} \times \text{Variable Cost per Unit} = 37,000 \times 17.40 = 645,800
\]

### Step 2: Calculate Contribution Margin
- **Contribution Margin**:
\[
\text{Contribution Margin} = \text{Sales} - \text{Total Variable Costs} = 1,073,000 - 645,800 = 427,200
\]

### Step 3: Calculate Contribution Margin Ratio (a)
- **CM Ratio**:
\[
\text{CM Ratio} = \frac{427,200}{1,073,000} \times 100 \approx 39.8\% \text{ (round to whole number 40\%)}
\]

### Step 4: Calculate Unit Contribution Margin (b)
- **Unit Contribution Margin**:
\[
\text{Unit CM} = 29 - 17.40 = 11.60
\]

### Step 5: Calculate Operating Income (c)
- **Operating Income**:
\[
\text{Operating Income} = \text{Contribution Margin} - \text{Fixed Costs} = 427,200 - 167,400 = 259,800
\]

### Summary of Results
1. **Contribution Margin Ratio**: 40%
2. **Unit Contribution Margin**: $11.60
3. **Operating Income**: $259,800

### Final Answer
- a. Contribution margin ratio: **40%**
- b. Unit contribution margin: **$11.60**
- c. Operating income: **$259,800**