Question

International Printer Machines (IPM) builds three computer printer models: Alpha,  Beta, Gamma. Information for these three products is as follows:

Alpha Beta Gamma Total

Selling price per unit $250    $400 $1500

Variable cost per unit $80 $200 $800

Expected unit sales (annual) 12,000 6,000 2,000 20,000

Sales mix 50 percent 40 percent 10 percent 100 percent

Total annual fixed costs are $5,000,000. Assume the sales mix remains the same at all levels of sales.

Required:

a) Calculate the weighted average unit contribution margin, assuming a constant sales mix.

b) How many units of each printer must be sold to break even?

c) i) Explain what is margin of safety

ii) Calculate in sales units the margin of safety for IPM, assuming projected sales are 25,000 units?

Answer 1

SOLUTION

A.

	Alpha	Beta	Gamma
Sales mix (a)	50%	40%	10%
Selling price per unit (b)	250	400	1,500
Variable cost per unit (c)	80	200	800
Contribution margin per unit (d = b-c)	170	200	700
Weights assigned to each product (a*d)	85	80	70

Weighted average contribution margin per unit = 85 + 80 + 70 = 235

B. Break even sales in units = Total fixed cost / Average contribution margin

= $5,000,000 / 235 = 21,277 units

Break even point for each printer-

Alpha = 21,277 * 50% = 10,638 units

Beta = 21,277 * 40% = 8,511 units

Gamma = 21,277 * 10% = 2,128 units

C1. Margin of safety is difference between the amount of expected profitability and the break even point

Margin of safety = Current sales - Break even point.

C2. Projected sales = 25,000 units

Break even point sales = 21,277 units

Margin of safety = 25,000 - 21,277 = 3,723 units