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.

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     $     40.00    
     
Variable expenses:                
     Invoice cost     $     19.50    
     Sales commission           4.50    
     


  Total variable expenses     $     24.00    
     


    Annual    
  Fixed expenses:                
     Advertising     $     38,000    
     Rent           28,000    
     Salaries           140,000    
     

 Total fixed expenses     $     206,000    
     


   Required:
1.     Calculate the annual break-even point in unit sales and in dollar sales for Shop 48.

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Explanation:

1.

Profit	= Unit CM × Q − Fixed expenses
$0	= ($40 − $24) × Q − $206,000
$0	= ($16) × Q − $206,000
$16Q	= $206,000
Q	= $206,000 ÷ $16
Q	= 12,875 pairs

Alternative solution:

Unit sales to break even	=	Fixed expenses
		Unit CM
	=	$206,000	= 12,875 pairs
		$16.00

Dollar sales to break even	=	Fixed expenses
		CM ratio
	=	$206,000	= $515,000 in sales
		0.4

12,875 pairs × $40 per pair = $515,000 in sales

2.

The simplest approach is:

Break-even sales	12,875	pairs
Actual sales	12,175	pairs
Sales short of break-even	700	pairs

700 pairs × $16 contribution margin per pair = $11,200 loss

Alternative solution:

Sales (12,175 pairs × $40.00 per pair)	$487,000
Variable expenses (12,175 pairs × $24.00 per pair)	292,200
Contribution margin	194,800
Fixed expenses	206,000
Net operating loss	$  (11,200)

3.

The variable expenses will now be $24.80 ($24.00 + $0.80) per pair, and the contribution margin will be $15.20 ($40.00 − $24.80) per pair.

Profit	= Unit CM × Q − Fixed expenses
$0	= ($40.00 − $24.80) × Q − $206,000
$0	= ($15.20) × Q − $206,000
$15.20Q	= $206,000
Q	= $206,000 ÷ $15.20
Q	= 13,553 pairs (rounded)

13,553 pairs × $40.00 per pair = $542,105 in sales

Alternative solution:

Unit sales to break even	=	Fixed expenses
		CM per unit
	=	$206,000	= 13,553 pairs
		$15.20

Dollar sales to break even	=	Fixed expenses
		CM ratio
	=	$206,000	= $542,105 in sales
		0.380

4.

The new variable expenses will be $19.50 per pair.

Profit	= Unit CM × Q − Fixed expenses
$0	= ($40.00 − $19.50) × Q − $237,800
$0	= ($20.50) × Q − $237,800
$20.50Q	= $237,800
Q	= $237,800 ÷ $20.50
Q	= 11,600 pairs

11,600 pairs × $40 per pair = $464,000 in sales

Although the change will lower the break-even point from 12,875 pairs to 11,600 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.