Bewick Company and Stout, Incorporated, both earn annual operating profits of $40 million on revenues of $150 million. Bewick Company has an operating leverage of 2.4 and Stout, Incorporated, has an operating leverage of 1.5.

**Required:**

Calculate the break-even point in sales dollars for Bewick Company.

Calculate the break-even point in sales dollars for Stout, Incorporated. 

**Note: Round your answers to 1 decimal place. Enter your answers in millions.**





To calculate the break-even point in sales dollars, we need to use the concept of **operating leverage** and the **contribution margin ratio**.

The formula for the **degree of operating leverage (DOL)** is:

\[
DOL = \frac{Sales - Variable Costs}{Sales - Variable Costs - Fixed Costs}
\]

However, a simpler approach can be used when we have the operating leverage and profits:

\[
\text{DOL} = \frac{\text{Sales} - \text{Variable Costs}}{\text{Operating Profit}}
\]

Rearranging this formula, we get:

\[
\text{Sales} - \text{Variable Costs} = \text{DOL} \times \text{Operating Profit}
\]

From this, we can find the **contribution margin** (Sales - Variable Costs) as follows:

\[
\text{Contribution Margin} = DOL \times \text{Operating Profit}
\]

The break-even point in sales dollars (BE) is the point where the contribution margin exactly covers fixed costs. The formula for the break-even point in sales is:

\[
BE = \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}}
\]

Now, let's calculate:

1. **Contribution margin for Bewick Company**:
\[
\text{Contribution Margin} = DOL \times \text{Operating Profit} = 2.4 \times 40 = 96 \text{ million}
\]

2. **Fixed Costs for Bewick Company**:
The fixed costs can be determined using the formula:
\[
\text{Fixed Costs} = \text{Contribution Margin} - \text{Operating Profit} = 96 - 40 = 56 \text{ million}
\]

3. **Contribution Margin Ratio for Bewick Company**:
The contribution margin ratio is:
\[
\frac{\text{Contribution Margin}}{\text{Sales}} = \frac{96}{150} = 0.64
\]

4. **Break-even point for Bewick Company**:
\[
BE = \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}} = \frac{56}{0.64} = 87.5 \text{ million}
\]

Now let's calculate the same for Stout, Incorporated:

1. **Contribution margin for Stout, Incorporated**:
\[
\text{Contribution Margin} = DOL \times \text{Operating Profit} = 1.5 \times 40 = 60 \text{ million}
\]

2. **Fixed Costs for Stout, Incorporated**:
\[
\text{Fixed Costs} = \text{Contribution Margin} - \text{Operating Profit} = 60 - 40 = 20 \text{ million}
\]

3. **Contribution Margin Ratio for Stout, Incorporated**:
\[
\frac{\text{Contribution Margin}}{\text{Sales}} = \frac{60}{150} = 0.4
\]

4. **Break-even point for Stout, Incorporated**:
\[
BE = \frac{\text{Fixed Costs}}{\text{Contribution Margin Ratio}} = \frac{20}{0.4} = 50 \text{ million}
\]

### Final Answers:
- **Break-even point for Bewick Company**: **$87.5 million**
- **Break-even point for Stout, Incorporated**: **$50 million**

Would you like further explanation on any of the steps?

---

Here are 5 follow-up questions for deeper understanding:
1. How does a higher degree of operating leverage affect the break-even point?
2. What happens to the break-even point if fixed costs increase?
3. How can variable costs impact the contribution margin and operating leverage?
4. Why is operating leverage important for companies with high fixed costs?
5. How would a change in sales price per unit affect the break-even point?

**Tip:** Operating leverage magnifies the effect of sales changes on profits, so a higher operating leverage means greater risk and reward!

Bewick Company and Stout, Incorporated, both earn annual operating profits of $40 million on revenues of $150 million. Bewick Company has an operating leverage of 2.4 and Stout, Incorporated, has an operating leverage of 1.5. Calculate the break-even point in sales dollars for Bewick Company. Calculate the break-even point in sales dollars for Stout, Incorporated. Note: Round your answers to 1 decimal place. Enter your answers in millions.

Discover how to calculate the break-even points for Bewick Company and Stout, Incorporated. Using operating leverage, contribution margin, and fixed costs, this step-by-step solution walks you through finding the break-even sales dollars. Suitable for business students and professionals.

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