Question

Wyatt Inc. expects to maintain the same inventories at the end of the year as at the beginning of the year. The estimated fixed costs for the year are $288,000, and the estimated variable costs per unit are $14. It is expected that 60,000 units will be sold at a price of $20 per unit. Maximum sales within the relevant range are 70,000 units.

1. What is (a) the contribution margin ratio and (b) the unit contribution margin?

2. Determine the break-even point in units.

3. What is the margin of safety?

 

Answer 1

 

1. (a) Contribution Margin Ratio: Contribution Margin Ratio = (Selling Price per Unit - Variable Cost per Unit) / Selling Price per Unit

Given: Variable cost per unit: $14 Selling price per unit: $20

(a) Contribution Margin Ratio = ($20 - $14) / $20 = $6 / $20 = 0.3 or 30%

Therefore, the contribution margin ratio is 30%.

(b) Unit Contribution Margin: Unit Contribution Margin = Selling Price per Unit - Variable Cost per Unit = $20 - $14 = $6

Therefore, the unit contribution margin is $6.

2. 2. Break-Even Point in Units: Break-Even Point (in units) = Fixed Costs / Unit Contribution Margin

Given: Fixed costs: $288,000

Break-Even Point (in units) = $288,000 / $6 = 48,000 units

Therefore, the break-even point in units is 48,000 units.

5. 3. Margin of Safety: Margin of Safety = (Actual Sales - Break-Even Sales) / Actual Sales

Given: Actual Sales = 60,000 units

Margin of Safety = (60,000 - 48,000) / 60,000 = 12,000 / 60,000 = 0.2

To express the margin of safety as a percentage, we multiply it by 100:

Margin of Safety (as a percentage) = 0.2 * 100 = 20%

Therefore, the margin of safety is 20%.

Therefore, the contribution margin ratio is 30%.

Therefore, the unit contribution margin is $6.

Therefore, the break-even point in units is 48,000 units.

Therefore, the margin of safety is 20%.