Question

Question 4:

AB-25 is a top-selling electronic product. The company divides its customers into two groups: new customers and upgrade customers. Although the same physical product is provided to each customer group, sizeable differences exist in selling prices and variable marketing costs:

	New Customers	Upgrade Customers
Selling price Variable costs Manufacturing Marketing Contribution margin	$200                                 $25    50     75      $?	$150 $20 25      45       $?

The fixed costs of AB-25 are $16,000,000. The planned sales mix in units is 80% new customers and 20% upgrade customers.

Required:

1. What is the break-even point in units for AB-25, assuming that the planned 80%/20% sales mix is attained?
2. If the sales mix is attained, what is the profit when 150 000 units are sold?
3. Show how the break-even point in units changes with the following customer mixes (a and b):

a. new 30%/upgrade 70%                                                                               

b.    new 60%/upgrade 40%

c.    Comparing the break-even points in requirements a and b, is it always better for a company to choose the sales mix that yields the lower break-even point? Explain.

Answer 1

Contribution Margin per unit
New Customers = $200 - 75 = $125
Upgrade = $150 - 45 = $105 per unit

Weighted Average Contribution Margin per unit = $125 x 80% + $105 x 20% = $121 per unit

Break even units = Fixed Costs / Weighted Average Contribution Margin per unit
= $16000000 / 121 = 132231 units or 132232 units

Profit when 150000 units are sold
= 150000 x 80% x 125 + 150000 x 20% x 105 - 16000000 = $2,150,000

Break even point in units
a. new 30%/upgrade 70%
Weighted Average Contribution Margin per unit = $125 x 30% + $105 x 70% = $111 per unit

Break even units = Fixed Costs / Weighted Average Contribution Margin per unit
= $16000000 / 111 = 144144 units or 144145 units

b. new 60%/upgrade 40%
Weighted Average Contribution Margin per unit = $125 x 60% + $105 x 40% = $117 per unit

Break even units = Fixed Costs / Weighted Average Contribution Margin per unit
= $16000000 / 117 = 136752 units or 136753 units

c.
Yes, it is better for company to choose sales mix with lower break even point, since it will lead to higher weighted average contribution and hence higher profits