PROBLEM 4 Suppose a company has 3 products. Product A has a contribution margin

Question

PROBLEM 4 Suppose a company has 3 products. Product A has a contribution margin per unit of $15, product B has a contribution margin per unit of $25, and product C has a contribution margin per unit of $32. For every 3 units sold of product A the company sells 2 units of product B and 5 units of product C. The company has fixed costs of S835 ,000. Suppose that the company wants to make an after-tax profit of $2,450,000 and has a tax rate of 30%, how many units of each product must the company sell to achieve this goal?

Explanation / Answer

Solution:

Target after tax income = $2,450,000

Target pre tax income = $2,450,000 / (1-0.30) = $3,500,000

Fixed cost = $835,000

Target contribution = Pre tax Profit + Fixed cost

= $3,500,000 + $835,000 = $4,335,000

Total nos of units to be sold to achieve desired income = Target contribution / Weighted average contribution margin per unit

= $4,335,000 / $25.50 = 170000 units

Desired units of product A = 170000*3/10 = 51000 units

Desired units of product B = 170000*2/10 = 34000 units

Desired units of product C = 170000*5/10 = 85000 units

Computation of weighted average contribution margin per unit Particulars Product A Product B Product C Total Contribution margin per unit $15.00 $25.00 $32.00 Sales Mix 30% 20% 50% Weighted average contribution per unit $4.50 $5.00 $16.00 $25.50

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