Question

The Red Company makes two products. Cost data for these two products is as follows:

	Product A	Product B
Selling price	$10	$20
Variable costs	7	12

Total annual fixed costs are $840,000. The firm's experience has been that about 20 percent of unit sales come from product A, 80 percent from B.

The Red Company is taxed at 30%

Required:

a.	Determine the number of units to be sold at the break-even point.
b.	Determine the number of units to be sold if the company also wishes to make $120,000 profit before tax.

c.	Determine the number of units to be sold if the company also wishes to make $120,000 after tax profit.

Answer 1

break even units are sales at which there is no profit no loss.

total fixed cost = total contribution margin

contribution margin= sales- variable costs

suppose the total sales is X

product	selling price	variable cost	contribution margin	ratio of sale	weighted contribution margin
A	$10	$7	$3 [10-7]	0.2X	$0.6X[3*0.2X]
B	$20	$12	$8 [20-12]	0.8X	$6.4X

Fixed cost = contribution margin

$840,000 = 0.6X+6.4X

X=$840,000/7X

=120000units

(2) Determine the number of units to be sold if the company also wishes to make $120,000 profit before tax.

fixed cost + targeted profit before tax = contribution margin

$840,000+$120,000 = 0.6X+6.4X

x = 137,143 units

(3) Determine the number of units to be sold if the company also wishes to make $120,000 after tax profit.

tax rate = 30%

we will find before tax profit required

before tax profit = after tax profit / (1-tax rate)

=120000/0.7

=171,428$

fixed cost + before tax profit required = contribution margin

$840,000+$171,428 = 0.6X+6.4x

=144,490 units.