CVP, alternative cost structures

SuperShades operates a kiosk at the local mall, selling sunglasses for $20 each. SuperShades currently pays $800 a month to rent the space and pays two full-time employees to each work 160 hours a month at $10 per hour. The store shares a manager with a neighboring mall and pays 50% of the manager's annual salary of $40,000 and benefits equal to 20% of salary. The wholesale cost of the sunglasses to the company is $5 a pair.

Required:
1. How many sunglasses does SuperShades need to sell each month to break even?
2. If SuperShades wants to earn an operating income of $4,500 per month, how many sunglasses does the store need to sell?
3. If the store's hourly employees agreed to a 15% sales-commission-only pay structure, instead of their hourly pay, how many sunglasses would SuperShades need to sell to earn an operating income of $4,500?
4. Assume SuperShades pays its employees hourly under the original pay structure, but is able to pay the mall 8% of its monthly revenue instead of monthly rent. At what sales levels would SuperShades prefer to pay a fixed amount of monthly rent, and at what sales levels would it prefer to pay 8% of its monthly revenue as rent?

1. Variable cost per unit = $5
Contribution margin per unit = Selling price –Variable cost per unit
= $20 – $5 = $15
Fixed Costs:
Manager's salary ($40,000 × 1.20 × 0.5) ÷12 $2,000 per month
Rent 800 per month
Hourly employee wages (2 × 160 hours × $10) 3,200 per month
Total fixed costs $6,000 per month

Breakeven point = Fixed costs ÷ Contribution margin per unit
= $6,000 ÷ $15 = 400 sunglasses (per month)

2. Target number of sunglasses =

=

3. Contribution margin per unit = Selling price – Variable cost per computer
= $20 – 0.15 × $20 – $5 = $12
Fixed costs = Manager's salary + Rent = $2,000 + $800 = $2,800

Target number of sunglasses =
= (rounded up)

4. Let be the number of sunglasses for which SuperShades is indifferent between paying a monthly rental fee for the retail space and paying an 8% commission on sales. SuperShades will be indifferent when the operating income under the two alternatives are equal.

$20 − $5 – $6,000 = $20 – $5 − $20 (0.08) − $5,200
$15 – $6,000 = $13.40 − $5,200
$1.60 = $800
= 500 sunglasses

For sales between 0 and 500 sunglasses, SuperShades prefers to pay the 8% commission because in this range, $13.40 − $5,200 > $15 – $6,000. For sales greater than 500 sunglasses, the company prefers to pay the monthly fixed rent of $800 because $15 – $6,000 > $13.40 − $5,200.