Zhao Company has fixed costs of $354,000. Its single product sells for $175 per unit, and variable costs are $116 per unit. If the company expects sales of 10,000 units, compute its margin of safety

(a) in dollars and
(b) as a percent of expected sales.

To calculate the **margin of safety** for Zhao Company, we need to use the following formulas:

1. **Break-even point in units**:
   \[
   \text{Break-even point (in units)} = \frac{\text{Fixed costs}}{\text{Selling price per unit} - \text{Variable cost per unit}}
   \]
   
2. **Margin of safety in dollars**:
   \[
   \text{Margin of safety (in dollars)} = \text{Expected sales in dollars} - \text{Break-even sales in dollars}
   \]
   Where:
   \[
   \text{Expected sales in dollars} = \text{Expected units sold} \times \text{Selling price per unit}
   \]
   \[
   \text{Break-even sales in dollars} = \text{Break-even units} \times \text{Selling price per unit}
   \]

3. **Margin of safety as a percentage**:
   \[
   \text{Margin of safety (percentage)} = \frac{\text{Margin of safety (in dollars)}}{\text{Expected sales in dollars}} \times 100
   \]

### Step-by-step calculation:

#### Step 1: Calculate the break-even point in units
Given:
- Fixed costs = \$354,000
- Selling price per unit = \$175
- Variable cost per unit = \$116

\[
\text{Break-even point (in units)} = \frac{354,000}{175 - 116} = \frac{354,000}{59} \approx 6,000 \text{ units}
\]

#### Step 2: Calculate the margin of safety in dollars
- Expected units sold = 10,000 units
- Selling price per unit = \$175

\[
\text{Expected sales in dollars} = 10,000 \times 175 = 1,750,000 \text{ dollars}
\]
\[
\text{Break-even sales in dollars} = 6,000 \times 175 = 1,050,000 \text{ dollars}
\]
\[
\text{Margin of safety (in dollars)} = 1,750,000 - 1,050,000 = 700,000 \text{ dollars}
\]

#### Step 3: Calculate the margin of safety as a percentage
\[
\text{Margin of safety (percentage)} = \frac{700,000}{1,750,000} \times 100 \approx 40\%
\]

### Final answers:
(a) **Margin of safety in dollars** = \$700,000  
(b) **Margin of safety as a percent of expected sales** = 40%

---

Would you like more details or have any questions about this process?

Here are some related questions to explore further:
1. How is the break-even point affected if the variable cost changes?
2. What happens to the margin of safety if fixed costs increase by 10%?
3. How would the margin of safety change if the selling price per unit was increased by \$10?
4. How would the result differ if the company planned to sell 15,000 units instead of 10,000?
5. How is the margin of safety useful for managerial decision-making?

**Tip:** A higher margin of safety indicates lower risk of loss, giving the company more room for error or sales fluctuations.

Zhao Company has fixed costs of $354,000. Its single product sells for $175 per unit, and variable costs are $116 per unit. If the company expects sales of 10,000 units, compute its margin of safety (a) in dollars and (b) as a percent of expected sales.

Learn how to calculate the margin of safety for Zhao Company, which has fixed costs of $354,000 and sells a product for $175 per unit with variable costs of $116 per unit. Find out the margin of safety in dollars and as a percentage of expected sales (10,000 units). Suitable for business and accounting students.

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