Question

Outback Outfitters sells a small camp stove for $50 per unit. Variable expenses are $32 per unit, and fixed expenses total $108,000 per month.

Required:
What is the break-even point in unit sales and in dollar sales?
If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher or a lower break-even point? (Assume the fixed expenses remain unchanged.)
At present, the company is selling 8,000 stoves per month. The sales manager is convinced a 10% reduction in the selling price would result in a 25% increase in unit sales. Prepare two contribution format income statements, one under present operating conditions, and one as operations would appear after the proposed changes.
Refer to the data in Required 3. How many stoves would have to be sold at the new selling price to attain a target profit of $35,000 per month?

Answer 1

To calculate various financial metrics for Outback Outfitters, we will use the given data. Let's break down the question step by step.

### 1. Break-even point in unit sales and in dollar sales.

**Given data:**
- Selling price per unit (SP) = $50
- Variable expenses per unit (VE) = $32
- Fixed expenses (FE) = $108,000

**Step 1: Calculate Contribution Margin (CM) per unit:**
\[
CM = SP - VE = 50 - 32 = 18
\]

**Step 2: Calculate break-even point in units:**
\[
\text{Break-even point (units)} = \frac{FE}{CM} = \frac{108,000}{18} = 6,000 \text{ units}
\]

**Step 3: Calculate break-even point in dollar sales:**
\[
\text{Break-even sales (dollars)} = \text{Break-even point (units)} \times SP = 6,000 \times 50 = 300,000
\]

**Results:**
- Break-even point in unit sales: **6,000 units**
- Break-even point in dollar sales: **$300,000**

### 2. Effect of an increase in variable expenses as a percentage of the selling price.

If variable expenses increase as a percentage of the selling price, that means the Variable Expenses per unit will rise, which leads to a decrease in the Contribution Margin. Since the fixed expenses remain unchanged, a lower Contribution Margin would increase the break-even point in units and dollars.

Thus, the break-even point will be **higher**.

### 3. Contribution format income statements.

**Current conditions:**
- Selling price per unit = $50
- Variable expenses per unit = $32
- Units sold = 8,000

**Contribution Margin for Current Conditions:**
- Total Sales = \( 50 \times 8,000 = 400,000 \)
- Total Variable Expenses = \( 32 \times 8,000 = 256,000 \)
- Total Contribution Margin = \( 400,000 - 256,000 = 144,000 \)

**Current Income Statement:**
\[
\begin{array}{|l|r|}
\hline
\text{Sales} & 400,000 \\
\hline
\text{Variable Expenses} & 256,000 \\
\hline
\text{Contribution Margin} & 144,000 \\
\hline
\text{Fixed Expenses} & 108,000 \\
\hline
\text{Net Operating Income} & 36,000 \\
\hline
\end{array}
\]

**Proposed changes:**
- Selling price reduction: \( 50 \times 90\% = 45 \)
- Expected increase in unit sales: \( 8,000 \times 125\% = 10,000 \)
- New variable expense (unchanged for simplicity) = $32

**Contribution Margin for Proposed Changes:**
- Total Sales = \( 45 \times 10,000 = 450,000 \)
- Total Variable Expenses = \( 32 \times 10,000 = 320,000 \)
- Total Contribution Margin = \( 450,000 - 320,000 = 130,000 \)

**Proposed Income Statement:**
\[
\begin{array}{|l|r|}
\hline
\text{Sales} & 450,000 \\
\hline
\text{Variable Expenses} & 320,000 \\
\hline
\text{Contribution Margin} & 130,000 \\
\hline
\text{Fixed Expenses} & 108,000 \\
\hline
\text{Net Operating Income} & 22,000 \\
\hline
\end{array}
\]

### 4. Number of stoves to achieve a target profit of $35,000 at the new selling price.

- Current situation after price change and new sales:
- New contribution margin = Selling price - Variable expenses = \( 45 - 32 = 13 \)

**Step 1: New required contribution margin to achieve target profit:**
\[
\text{Total Required Contribution Margin} = \text{Fixed Expenses} + \text{Target Profit} = 108,000 + 35,000 = 143,000
\]

**Step 2: Calculate required unit sales:**
\[
\text{Required Units} = \frac{\text{Total Required Contribution Margin}}{\text{Contribution Margin per Unit}} = \frac{143,000}{13} \approx 11,000 \text{ units}
\]

### Final Results:
- Break-even point in units: **6,000 units**
- Break-even point in dollars: **$300,000**
- Higher break-even point with increased variable expenses.
- Current income statement shows a profit of **$36,000**.
- Proposed income statement shows a profit of **$22,000**.
- To achieve a target profit of **$35,000**, Outback Outfitters would need to sell **11,000 stoves** at the new selling price.