Question

The stores sell ten different styles of yoga pants with identical unit costs and selling prices. A unit is defined as one pair of yoga pants. Each store has a manager who is paid a fixed salary. Individual salespeople receive a fixed salary and a sales commission. The store is trying to determine the desirability of opening another store, which is expected to have the following revenue and cost relationships:

	Per Pair
Unit variable data:
Selling price	$60
Cost of pants	$29.50
Sales commissions	$4.50
Total variable costs	$34
Annual fixed costs:
Rent	$260,000
Salaries	$200,000
Advertising	$90,000
Other fixed costs	$70,000
Total fixed costs	$620,000

1. Refer to the original data. If the store manager were paid $1.30 per unit commission on each unit sold in excess of the breakeven point, what would be the store’s operating profit if 70,000 units were sold? (This is $1.30 is in addition to both the commission paid to the sales staff and the store manager’s fixed salary.) (The breakeven point is calculated to be 23,846 units or $1,430,760)
2. Calculate the number of units sold where the operating profit under (a)a fixed salary plan and (b) a lower fixed salary and commission plan (for salespeople only) would be equal. Above that number of units sold, one plan would be more profitable than the other; below that number of units sold, the reverse would occur.
3. Calculate the operating profit or loss under each plan in question 7 (above) at a sales level of (a) 50,000 units and (b) 60,000 units.
4. Suppose the target operating profit is $368,000. How many units must be sold to reach the target under (a) the fixed salary plan and (b) the lower fixed salary and commission plan?

Answer 1

Calculation of Contribution per unit and Breakeven Sales

Selling price per Unit	$60
Total Variable Cost per unit	$34
Contribution per unit	$26
Total Fixed Cost	$620,000
Break Even Sales ($620,000/$26)	23,846 Units

a. Operating Profit when 70,000 Units are sold

Units Sold	70,000
Break Even Sales	23,846
Difference	46,154
Commission @$1.30 per Unit (46,154 * $1.30)	$60,000
Contribution when 70,000 units sold (70,000*$26)	$1,820,000
Total Fixed Cost before sales commission	$620,000
Sales Commission	$60,000
Total Fixed Cost	$680,000
Operating Profit ($1,820,000 - $680,000)	$1,140,000

b.Calculate the number of units sold where the operating profit under (a)a fixed salary plan and (b) a lower fixed salary and commission plan (for salespeople only) would be equal.

Let the quantity sold be Q

For indifference, profits under both plans must be equal

Profits = Quantity x (Selling price - Unit variable cost) - Fixed costs

Q x $(60 - 34) - $620,000 = Q x $(60 - 29.5) - ($620,000 + $80,000)

Q* $ 26 - $620,000 = Q* $ 30.5 - $680,000

Q * $ 4.5 = $ 60,000

Q = $60,000 / $4.5 = 13,333 Units

C.Calculate the operating profit or loss under each plan in question 7 (above) at a sales level of (a) 50,000 units and (b) 60,000 units.

Operating Profit at 50,000 Units

Profits = Quantity x (Selling price - Unit variable cost) - Fixed costs

Let the quantity sold be Q

Profits = 50,000 X ($60 -$34) - $620,000

Profit = $1,300,000 - $620,000

Profit = $680,000

Operating Profit at 60,000 Units

Profits = Quantity x (Selling price - Unit variable cost) - Fixed costs

Let the quantity sold be Q

Profits = 60,000 X ($60 -$34) - $620,000

Profit = $1,560,000 - $620,000

Profit = $940,000

D.Suppose the target operating profit is $368,000. How many units must be sold to reach the target under (a) the fixed salary plan and (b) the lower fixed salary and commission plan?

a. Under Fixed Salary Plan

Profits = Quantity x (Selling price - Unit variable cost) - Fixed costs

Let the quantity sold be Q

$368,000 = Q*($60 - $34) - $620,000

Q*$26 = $988,000

Q = $988,000/$26 = 38,000 Units

b.The lower fixed salary and commission plan

Profits = Quantity x (Selling price - Unit variable cost) - (Fixed costs + Commission)

Let the quantity sold be Q

$368,000 = Q*($60 -$29.5) - ($620,000 + $60,000)

$368,000 = Q*$30.5 -$680,000

Q = $1,048,000/$ 30.5 = 34,361 Units