Question

Morris Industries manufactures and sells three products (AA, BB, and CC). The sales price and unit variable cost for the three products are as follows:

Product	Sales Price per Unit	Variable Cost per Unit
AA	$55	$25
BB	40	15
CC	30	10

Their sales mix is reflected as a ratio of 5:3:2. Annual fixed costs shared by the three products are $397,500 per year.

A. What are total variable costs for Morris with their current product mix?

Total variable costs $

B. Calculate the number of units of each product that will need to be sold in order for Morris to break even.

	Number of Units per Product
AA
BB
CC

C. What is their break-even point in sales dollars?

Break-even point in sales $

D. Using an income statement format, prove that this is the break-even point. If an amount is zero, enter "0".

Income Statement
Sales
Product AA	$
Product BB
Product CC
Total Sales	$
Variable Costs
Product AA	$
Product BB
Product CC
Total Variable Costs	$
Contribution Margin	$
Fixed Costs
Net Income	$

Answer 1

Answer

A Total variable cost

Variable cost per unit of AA = $25

Variable cost per unit of BB = $15

Variable cost per unit of CC = $10

Total variable cost = 25 + 15 + 10 = $50

Total variable cost is $50 of Morris industries.

B Break even point in unit of Morris

= fixed cost / weighted average contribution margin per unit

Weighted average contribution margin per unit = (contribution margin per unit of AA × sales mix of AA) + (Contribution margin per unit of BB × sales mix of BB) + (Contribution margin per unit of CC × sales mix of CC)

Sales mix of AA = 5 / 10 = .5

Sales mix of BB = 3 / 10 = .3

Sales mix of CC = 2 / 10 = .2

Contribution margin = selling price - variable cost

Contribution margin per unit of AA = 55 - 25 = $30

Contribution margin per unit of BB = 40 - 15 = $25

Contribution margin per unit of CC = 30 - 10 = $20

Weighted average contribution margin

= (30 × .5) + (25 × .3) + (20 × .2) = $26.5

Break even point in unit of Morris

= 397,500 / 26.5 = 15,000 units

Break even point in unit of product AA

= 15,000 × .5 = 7,500 units

Break even point in unit of product BB

= 15,000 × .3 = 4,500 units

Break even point in unit of product CC

= 15,000 × .2 = 3,000 units

C Break even point in dollar = Break even point in unit × selling price

Break even point in dollar of product AA

= 7,500 × 55 = $412,500

Break even point in dollar of product BB

= 4,500 × 40 = $180,000

Break even point in dollar of product CC

= 3,000 × 30 = $90,000

Break even point in dollar of Morris

= 412,500 + 180,000 + 90,000 = $682,500

D Income statement

	Product AA	Product BB	Product CC	Total
Sales	412,500	180,000	90,000	682,500
Less variable cost	187,500	67,500	30,000	285,000
Contribution margin	225,000	112,500	60,000	397,500
Fixed cost				397,500
Net income				0

Variable cost of product AA = 7,500 × 25 = $187,500

Variable cost of product BB = 4,500 × 15 = $67,500

Variable cost of product CC = 3,000 × 10 = $30,000

The above are the detailed calculations.

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