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%

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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.