Question

Assume that Ocean King Products sells three varieties of canned seafood with the following prices and costs.

	Selling Price per Case			Variable Cost per Case			Fixed Cost per Month
Variety 1	$	4		$	3			–
Variety 2		6			4			–
Variety 3		11			7			–
Entire firm		–			–		$	46,400

The sales mix (in cases) is 50 percent Variety 1, 25 percent Variety 2, and 25 percent Variety 3.

Required:

a. At what sales revenue per month does the company break even?

b. Suppose the company is subject to a 35 percent tax rate on income. At what sales revenue per month will the company earn $41,795 after taxes assuming the same sales mix?

Answer 1

a.

working:

first let us know the amount of contribution per unit for each variety:

contribution per unit = selling price per unit - variable cost per unit

variety 1:

=>$4-$3

=>$1 per unit

variety 2:

=>$6- $4

=>$2.

variety 3:

=>$11-$7

=>$4.

weighted average contribution per unit:

sum of (weight * contribution per unit)

=> (0.50*$1) + (0.25*$2) + (0.25*$4)

=>0.50+0.50+1

=>$2.

break even point = fixed costs / weighted contribution per unit

=>$46,400 / $2

=>23,200 cases.

b.required after tax earnings

=>$41,795.

=> required before tax earnings = after tax earnings / (1- tax rate)

=>$41,795 / (1-0.35)

=>$64,300.

to get required before tax earnings we need to sell : (fixed cost + required before tax earnings) / weighted contribution per unit

=> (46,400+64,300) / $2

=>55,350 units.

number of units of variety 1 = 55,350 units * 50% weight =>27,675 units.

number of units of variety 2=55,350 units * 25% weight=>13,837.50 units.

number of units of variety 3 = 55,350 units*25% weight =>13,837.50 units.

sales revenue required:

variety 1 (27,675 units *$4)	$110,700
variety 2 (13,837.50*$6)	83,025
variety 3 (13,837.50*$11)	152,212.50
total sale revenue required	$345,937.50 (or) $345,938...(if rounded to nearest whole dollar)