Final answer:
To compute the monthly margin of safety, start by calculating the break-even point using the formula Break-even point = Fixed costs / Contribution margin ratio. Then, subtract the break-even point from the actual sales to find the margin of safety. In this case, the margin of safety would be $71,500.
Step-by-step explanation:
To compute the monthly margin of safety, we first need to calculate the break-even point. The break-even point is the level of sales at which total revenue equals total cost, resulting in zero profit. The formula to calculate the break-even point is:
Break-even point (in dollars) = Fixed costs / Contribution margin ratio
The contribution margin ratio is calculated by subtracting variable costs from sales and dividing by sales:
Contribution margin ratio = (Sales - Variable costs) / Sales
In this case, the monthly fixed costs are $13,000 and variable costs are 75% of sales. So, the contribution margin ratio is:
Contribution margin ratio = (1 - 0.75) = 0.25
Now, we can calculate the break-even point:
Break-even point (in dollars) = $13,000 / 0.25 = $52,000
The margin of safety is the difference between actual sales and the break-even point. In this case, the monthly target profit is $19,500. So, if the shop achieves its income goal:
Margin of safety (in dollars) = Actual sales - Break-even point = $19,500 + $52,000 = $71,500