Question

Reid Company is considering the production of a new product. The expected variable cost is $27 per unit. Annual fixed costs are expected to be $810,000. The anticipated sales price is $72 each.

Determine the break-even point in units and dollars using each of the following:

a. Use the equation method.

b. Use the contribution margin per unit approach.

c. Use the contribution margin ratio approach. (Do not round intermediate calculations. Round "Contribution margin ratio" to 1 decimal place. (i.e., .234 should be entered as 23.4))

Use the equation method.

Answer 1

Answer of Part a:

Let the Unit be X to achieve Break Even Point

At Break Even Point, Profit is Zero.

Profit = (Selling price * X) – (Variable cost * X) – Fixed costs
0 = ($72 * X) – ($27 * X) - $810,000
0 = $72 X - $27 X - $810,000
$810,000 = $45 X
X = $810,000 / 45
X = 18,000 units

Break Even Point in Dollars = Break Even Units * selling price
Break Even Point in Dollars = 18,000 * $72
Break Even Point in Dollars = $1,296,000

Answer of Part b:

Contribution Margin per Unit = Selling Price – Variable Costs
Contribution Margin per unit = $72 - $27
Contribution Margin per Unit = $45

Break Even Point in Units = Fixed Costs / Contribution Margin per unit
Break Even Point in units = $810,000 / $45
Break Even Point in Units =18,000 units

Break Even Point in Dollars = Break Even Units * Selling price
Break Even Point in Dollars = 18,000 * $72
Break Even Point in Dollars = $1,296,000

Answer of Part c:            

Contribution Margin Ratio = Contribution Margin per unit / Selling price *100
Contribution Margin Ratio = $45 / $72 *100
Contribution Margin Ratio = 62.5

Break Even Point in Dollars = Fixed Costs / Contribution Margin Ratio
Break Even Point in Dollars = $810,000 / 0.625
Break Even Point in Dollars = $1,296,000

Break Even Point in Units = Break Even Point in Dollars / Selling Price per Unit
Break Even Point in Units = 1,296,000 / 72
Break Even Point in Units = 18,000 Units