Question

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

Alpha Beta Gamma Total

Selling price per unit $250 $400 $1 500

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 a margin of safety (1 mark)

ii) Calculate in sales units the margin of safety for IPM, assuming projected sales are 25,000 units? (1 mark)

Answer 1

a)

	Alpha	Beta	Gamma
Sales mix (a)	50%	40%	10%
Selling price per unit (b)	250	400	1500
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

c)

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

Margin of safety = Current sales - Break even point.

ii. Projected sales = 25,000 units

Break even point sales = 21,277 units

Margin of safety = 25,000 - 21,277

Margin of safety for IPM = 3,723 units