Question

CVP Analysis and Sales Mix (Multiple Products). Sierra Books Incorporated produces two different products with the following monthly data (this is the base case). Text Lecture Notes Total Selling price per unit $100 $12 Variable cost per unit $60 $3 Expected unit sales 21,000 14,000 35,000 Sales mix 60 percent 40 percent 100 percent Fixed costs $750,000 Assume the sales mix remains the same at all levels of sales except for requirement i. Required: Round to the nearest unit of product, hundredth of a percent, and nearest cent where appropriate. (An example for unit calculations is 3,231.15 = 3,231; an example for percentage calculations is 0.434532 = 0.4345 = 43.45 percent; an example for dollar calculations is $378.9787 = $378.98.) a. Calculate the weighted average contribution margin per unit. 1. How many units in total must be sold to earn a monthly profit of $100,000? 2. How many units of each product must be sold to earn a monthly profit of $100,000? d. Using the base case information, prepare a contribution margin income statement for the month similar to the one in . e. Calculate the weighted average contribution margin ratio. f. Find the break-even point in sales dollars. g. What amount of sales dollars is required to earn a monthly profit of $80,000? h. Assume the contribution margin income statement prepared in requirement d is the company’s base case. What is the margin of safety in sales dollars? i. If the sales mix shifts more toward the Text product than the Lecture Notes product, would the break-even point in units increase or decrease? Explain.

Answer 1

.a CALCULATION OF WEIGHTED AVERAGE CONTRIBUTION MATGIN PER UNIT

		Product A	Product B
X	Selling price per unit	$100	$12
Y	Variable cost per unit	$60	$3
Z=X-Y	Contribution unit per unit	$40	$9
	Sales mix	0.6	0.4

Contribution margin per unit=0.6*40+0.4*9=$27.60

.1 Units to be sold to earn profit of $100,000 per month:

Fixed cost:$750,000

Contribution required=(750000+100000)=$850,000

Contribution margin per unit=$27.60

Number of units to be sold in total=(850000/27.60)= 30797

.2 Units of each product need to be sold:

Product A to be sold=60% of 30797= 18478

Product B to be sold=40% of 30797= 12319

.d CONTRIBUTION MARGIN INCOME STATEMENT

	Product A	Product B	Total
Sales quantity in units	18478	12319	30797
Selling price per unit	$100	$12
Total sales in dollars	$1,847,800	$147,828	$        1,995,628
Variable cost per unit	$60	$3
Total variable costs in dollars	$1,108,680	$36,957	$        1,145,637
Contribution margin	$739,120	$110,871	$            849,991
Fixed cost			$750,000
Profit			$              99,991

e. Weighted average contribution margin ratio:

Weighted average contribution margin ratio=849991/1995628=0.425927

.f Break Even Sales in dollars:

Break even sales=Fixed cost/Contribution margin ratio=750000/0.425927= $ 1,760,866.88

.g Sales required to earn monthly profit of $80,000

Break even sales=$ 1,760,866.88

Contribution margin=0.425927

Sales required for profit of $80000=$ 1,760,866.88+(80000/0.425927)

Sales required for profit of $80000=$ 1,760,866.88+ $ 187,825.61 = $ 1,948,692.49

.h Margin of safety:

Breakeven sales=$ 1,760,866.88

Sales as per part d=$ 1,995,628

Margin of Safety=$ 1,995,628-$ 1,760,866.88= $ 234,761.12

.i Data on change in sales mix is required