Question

Hunter & Sons sells a single model of meat smoker for use in the home. The smokers have the following price and cost characteristics.

Sales price	$	85	per smoker
Variable costs		35	per smoker
Fixed costs		390,000	per month

Hunter & Sons is subject to an income tax rate of 40 percent.

a. How many smokers must Hunter & Sons sell every month to break even?

b. How many smokers must Hunter & Sons sell to earn a monthly operating profit of $87,000 after taxes?

a.	Break-even sales in units
b.	Number of units to be sold

Answer 1

a.

Break even sales in units = Fixed costs / Contribution margin per unit

Fixed costs = $390,000

Contribution margin per unit = Sales price - Variable costs

= $85 - $35

= $50

Break even sales in units = $390,000 / $50

= 7,800 units

b.

Tax rate = 40%

Operating profit after tax = $87,000

Operating profit before tax = Operating profit after tax / (1 - 0.40)

= $87,000 / 0.60

= $145,000

Number of units to be sold = (Operating profit before tax + Fixed costs) / Contribution margin per unit

= ($145,000 + $390,000) / $50

= 10,700 units