The Fashion Shoe Company operates a chain of women’s shoe shops that carry many styles of shoes that are all sold at the same price. Sales personnel in the shops are paid a substantial commission on each pair of shoes sold (in addition to a small base salary) in order to encourage them to be aggressive in their sales efforts.

The Fashion Shoe Company operates a chain of women’s shoe shops that carry many styles of shoes that are all sold at the same price. Sales personnel in the shops are paid a substantial commission on each pair of shoes sold (in addition to a small base salary) in order to encourage them to be aggressive in their sales efforts.

The following worksheet contains cost and revenue data for Shop 48 and is typical of the company’s many outlets:

	Per Pair of Shoes
Selling price	$	20.00
Variable expenses:
Invoice cost	$	7.00
Sales commission		3.00
Total variable expenses	$	10.00
		Annual
Fixed expenses:
Advertising	$	32,000
Rent		21,000
Salaries		105,000
Total fixed expenses	$	158,000

Required:

1.

Calculate the annual break-even point in unit sales and in dollar sales for Shop 48. Explanation: 1. Profit  = Unit CM × Q − Fixed expenses $0  = ($20 − $10) × Q − $158,000 $0  = ($10) × Q − $158,000 $10Q  = $158,000 Q  = $158,000 ÷ $10 Q  = 15,800 pairs Alternative solution: Unit sales to break even   = Fixed expenses Unit CM           = $158,000  = 15,800 pairs   $10.00 Dollar sales to break even   = Fixed expenses CM ratio           = $158,000  = $316,000 in sales   0.5 15,800 pairs × $20 per pair = $316,000 in sales 3. The simplest approach is:         Break-even sales 15,800   pairs   Actual sales 15,200   pairs     Sales short of break-even 600   pairs   600 pairs × $10 contribution margin per pair = $6,000 loss Alternative solution:       Sales (15,200 pairs × $20.00 per pair) $304,000     Variable expenses (15,200 pairs × $10.00 per pair) 152,000       Contribution margin 152,000     Fixed expenses 158,000       Net operating loss $  (6,000)     4. The variable expenses will now be $10.70 ($10.00 + $0.70) per pair, and the contribution margin will be $9.30 ($20.00 − $10.70) per pair. Profit  = Unit CM × Q − Fixed expenses $0  = ($20.00 − $10.70) × Q − $158,000 $0  = ($9.30) × Q − $158,000 $9.30Q  = $158,000 Q  = $158,000 ÷ $9.30 Q  = 16,989 pairs (rounded) 16,989 pairs × $20.00 per pair = $339,785 in sales Alternative solution: Unit sales to break even   = Fixed expenses CM per unit           = $158,000  = 16,989 pairs   $9.30 Dollar sales to break even   = Fixed expenses CM ratio           = $158,000  = $339,785 in sales   0.465 5. The simplest approach is:         Actual sales 18,400    pairs   Break-even sales 15,800    pairs     Excess over break-even sales 2,600    pairs   2,600 pairs × $9.55 per pair* = $24,830 profit *$10.00 present contribution margin − $0.45 commission = $9.55 Alternative solution:       Sales (18,400 pairs × $20 per pair) $368,000     Variable expenses (15,800 pairs × $10.00 per pair +    2,600 pairs × $10.45 per pair) 185,170       Contribution margin 182,830     Fixed expenses 158,000       Net operating income $  24,830     6. The new variable expenses will be $7.00 per pair. Profit  = Unit CM × Q − Fixed expenses $0  = ($20.00 − $7.00) × Q − $188,500 $0  = ($13.00) × Q − $188,500 $13.00Q  = $188,500 Q  = $188,500 ÷ $13.00 Q  = 14,500 pairs 14,500 pairs × $20 per pair = $290,000 in sales Although the change will lower the break-even point from 15,800 pairs to 14,500 pairs, the company must consider whether this reduction in the break-even point is more than offset by the possible loss in sales arising from having the sales staff on a salaried basis. Under a salary arrangement, the sales staff has less incentive to sell than under the present commission arrangement, resulting in a potential loss of sales and a reduction of profits. Although it is generally desirable to lower the break-even point, management must consider the other effects of a change in the cost structure. The break-even point could be reduced dramatically by doubling the selling price but it does not necessarily follow that this would improve the company’s profit.