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.

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.
Instructions
1. What is (a) the contribution margin ratio and (b) the unit contribution margin?
2. Determine the break-even point in units.
3. Construct a cost-volume-profit chart, indicating the break-even point.
4. Construct a profit-volume chart, indicating the break-even point.
5. What is the margin of safety?

Accepted Answer

1. a. Contribution Margin Ratio = [latex]\frac{Sales – Variable Costs}{Sales}[/latex]

Contribution Margin Ratio = [latex]\frac{(60,000 units × \$20) – (60,000 units × \$14)}{(60,000 units × \$20)}[/latex]

Contribution Margin Ratio = [latex]\frac{\$1,200,000 – \$840,000}{ \$1,200,000} = \frac{\$360,000}{ \$1,200,000}[/latex]

Contribution Margin Ratio = 30%

b. Unit Contribution Margin = Unit Selling Price – Unit Variable Costs

Unit Contribution Margin = $20 – $14 = $6

2. Break-Even Sales (units) = [latex]\frac{Fixed Costs}{Unit Contribution Margin}[/latex]

Break-Even Sales (units) = [latex]\frac{\$ 288,000}{\$6}[/latex] = 48,000 units

5. Margin of safety:

Expected sales (60,000 units × $20) $1,200,000

Break-even point (48,000 units × $20) 960,000

Margin of safety [latex]\underline{\underline{\$ \ 240,000}}[/latex]

or

Margin of Safety (units) = [latex]\frac{ Margin of Safety (dollars)}{ Unit Selling Price}[/latex]

or

12,000 units ($240,000/$20)

or

Margin of Safety = [latex]\frac{ Sales – Sales at Break-Even Point}{Sales}[/latex]

Margin of Safety = [latex]\frac{\$ 240,000}{\$ 1,200,000}[/latex] = 20%

Question 19.IP.1: Wyatt Inc. expects to maintain the same inventories at the e...

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