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	$	16		$	13			–
Variety 2		17			15			–
Variety 3		22			15			–
Entire firm		–			–		$	48,600

The sales mix (in cases) is 40 percent Variety 1, 35 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 $51,090 after taxes assuming the same sales mix?

Answer 1

Solution:

a)

Unit selling price of overall product E:

=(16 *0.4)+($17*0.35)+($22*0.25)

=6.4+5.95+5.5

=$17.85

Unit variable cost of overall product :

=(13*0.4)+(15*0.35)+(15*0.25)

=5.2+5.25+3.75

=14.2

Unit contribution margin E = Unit selling price E - unit variable cost of E

=$17.8 - $14.2

=$3.6

Break even point = fixed cost/contribution margin per unit

=$48,600 / 3.6

=$13,500

Break even point of variety 1= 13500*0.4= 5,400 cases

Break even point of variety 2= 13500*0.35= 4,725 cases

Break even point of variety 3= 13500*0.25= 3,375 cases

calculate sales revenue per month required to break even

Variety 1 sale revenue = 5,400 * $16 =$86,400

Variety 2 sale revenue = 4,725 * $17 =$80,325

Variety 3 sale revenue = 3,375 * $22 =$74,250

Total sales revenue = $86,400+$80,325+$74,250 =$240,975

b)

Target volume = fixed cost +[Target profit /(l-i)]/ contribution margin per unit

=$48,600+[$51,090/(1-.35)/]3.6

=$22,724 cases

Calculate the sales volume in units for each individuals product in their sales mix ratio

Target volume (cases) of variety1= 22,724 cases *0.4 = 9,089

Target volume (cases) of variety2= 22,724 cases *0.35 =7,953

Target volume (cases) of variety3= 22,724 cases *0.25 = 5,681

Calculate the sales revenue per month required by the company to ear an after tax operating profit of 51,090

Variety 1 target sale revenue = 9,089 *16 = 145,424

Variety 2 target sale revenue = 7,953 *17 = 135,201

Variety 3 target sale revenue = 5,681 *22 = 124,982

Total target sales revenue = $145,424+$135,201+$124,982 = 405,607