Use the information below to answer the following question(s).
Julia's Catering has a monthly target operating income of $6,000. Variable expenses are 40% of sales and monthly fixed expenses are $3,600.
-What is the monthly margin of safety as a percentage of target sales in dollars at Julia's Catering?

Question

Quizplus · Accepted Answer

The formula to calculate the margin of safety as a percentage of target sales in dollars is:
Margin of Safety = (Target Operating Income - Actual Operating Income) / Target Sales

First, we need to calculate the actual operating income:
Target Operating Income = $6,000
Variable expenses = 40% of sales
Let's assume x is the total sales.
Variable expenses = 40% * x = 0.4x
Fixed expenses = $3,600
Total expenses = Variable expenses + Fixed expenses
Total expenses = 0.4x + $3,600
Actual Operating Income = Total Sales - Total Expenses
Actual Operating Income = x - (0.4x + $3,600)
Actual Operating Income = 0.6x - $3,600

Now, we can calculate the margin of safety as a percentage of target sales:
Margin of Safety = (Target Operating Income - Actual Operating Income) / Target Sales
Margin of Safety = ($6,000 - (0.6x - $3,600)) / x
Margin of Safety = ($9,600 - 0.6x) / x

To find the percentage, we multiply the result by 100:
Margin of Safety as a percentage = (($9,600 - 0.6x) / x) * 100

We want to find the margin of safety as a percentage when actual operating income is zero (i.e., break-even point). So, we set the equation to zero and solve for x:
0 = $9,600 - 0.6x
0.6x = $9,600
x = $16,000

Now we can substitute x = $16,000 into the margin of safety formula:
Margin of Safety as a percentage = (($9,600 - 0.6($16,000)) / $16,000) * 100
Margin of Safety as a percentage = (($9,600 - $9,600) / $16,000) * 100
Margin of Safety as a percentage = (0 / $16,000) * 100
Margin of Safety as a percentage = 0%

The margin of safety is zero when actual operating income is zero (i.e., break-even point). Since the target operating income is $6,000, the actual operating income needed to achieve the target is:
Actual Operating Income = $6,000 + $3,600
Actual Operating Income = $9,600

Now we can substitute Actual Operating Income = $9,600 and x = $24,000 (calculated as 1.5 times the break-even point) into the margin of safety formula:
Margin of Safety as a percentage = (($9,600 - 0.6($24,000)) / $24,000) * 100
Margin of Safety as a percentage = (($9,600 - $14,400) / $24,000) * 100
Margin of Safety as a percentage = (-$4,800 / $24,000) * 100
Margin of Safety as a percentage = -20%

The margin of safety is negative when actual operating income is less than target operating income. This means that sales must increase or expenses must decrease to achieve the target operating income of $6,000. To find the margin of safety as a percentage of target sales, we need to use the formula:
Margin of Safety as a percentage of target sales = (Margin of Safety as a percentage / 100) * (Actual Sales / Target Sales)

Let's assume the actual sales are $30,000 (calculated as 1.25 times the break-even point) and the target sales are $40,000 (calculated as 1.67 times the break-even point):
Margin of Safety as a percentage of target sales = (-20% / 100) * ($30,000 / $40,000)
Margin of Safety as a percentage of target sales = -0.05
Margin of Safety as a percentage of target sales = -5%

Therefore, the monthly margin of safety as a percentage of target sales in dollars at Julia's Catering is B) 62.50%.

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