Question

Blanchard Company manufactures a single product that sells for \(180 per unit and whose total variable costs are \)135 per unit. The company’s annual fixed costs are $562,500. Use this information to compute the company’s (a) contribution margin, (b) contribution margin ratio, (c) break-even point in units, and (d) break-even point in dollars of sales.

Short answer

1. The contribution margin per unit is $45
2. The contribution margin ratio is 25%
3. Break-even points in units are 12,500
4. Break-even points in dollars of sales are $2,250,000

Step-by-step solution

Meaning of Break-even Point

It is a stage of operation during which a business experiences revenues generated in balance with costs incurred. As a result, when a business hits its break-even point, it does not declare any profit or loss from the operation.

(1) Computing contribution margin

$\begin{array}{rcl}\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}& \mathbf{=}& \mathbf{Selling}\mathbf{}\mathbf{price}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}\mathbf{-}\mathbf{Variable}\mathbf{}\mathbf{cost}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}\\ & \mathbf{=}& \mathbf{\$}\mathbf{180}\mathbf{-}\mathbf{\$}\mathbf{135}\\ & \mathbf{=}& \mathbf{\$}\mathbf{45}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}\end{array}$

(2) Computing contribution margin ratio

$\begin{array}{rcl}\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{ratio}& \mathbf{=}& \frac{\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}}{\mathbf{Selling}\mathbf{}\mathbf{price}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{45}}{\mathbf{\$}\mathbf{180}}\\ & \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{25}\mathbf{}\mathbf{or}\mathbf{}\mathbf{25}\mathbf{\%}\end{array}$

(3) Break-even points in the unit

$\begin{array}{rcl}\mathbf{Break}\mathbf{-}\mathbf{even}\mathbf{}\mathbf{points}\mathbf{}\mathbf{in}\mathbf{}\mathbf{units}& \mathbf{=}& \frac{\mathbf{Total}\mathbf{}\mathbf{fixed}\mathbf{}\mathbf{costs}}{\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{per}\mathbf{}\mathbf{unit}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{562}\mathbf{,}\mathbf{500}}{\mathbf{\$}\mathbf{45}}\\ & \mathbf{=}& \mathbf{12}\mathbf{,}\mathbf{500}\mathbf{}\mathbf{units}\end{array}$

(4) Break-even point in dollars of sales

$\begin{array}{rcl}\mathbf{Break}\mathbf{-}\mathbf{even}\mathbf{}\mathbf{points}\mathbf{}\mathbf{in}\mathbf{}\mathbf{dollars}& \mathbf{=}& \frac{\mathbf{Total}\mathbf{}\mathbf{fixed}\mathbf{}\mathbf{costs}}{\mathbf{Contribution}\mathbf{}\mathbf{margin}\mathbf{}\mathbf{ratio}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{562}\mathbf{,}\mathbf{500}}{\mathbf{0}\mathbf{.}\mathbf{25}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{250}\mathbf{,}\mathbf{000}\end{array}$