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?
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
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