Question

Ritchie Manufacturing Company makes a product that it sells for $160 per unit. The company incurs variable manufacturing costs of $73 per unit. Variable selling expenses are $15 per unit, annual fixed manufacturing costs are $490,000, and fixed selling and administrative costs are $258,800 per year.

Required

Determine the break-even point in units and dollars using each of the following approaches:

Use the equation method.

Use the contribution margin per unit approach.

Use the contribution margin ratio approach.

Prepare a contribution margin income statement for the break-even sales volume.

Answer 1

Solution:

Equation method:

Let breakeven point in units = X

Contribution margin per unit = Selling price per unit - Variable cost per unit = $160 - ($73 + $15) = $72 per unit

At breakeven units, net income = 0

contribution margin - Fixed cost = Net income

= $72 X - ($490,000 + $258,800) = 0

$72 X = 748,800

X = 10400 units

Breakeven sales in dollar = Breakeven units * Selling price per unit = 10400 * $160 = $1,664,000

Contribution margin per unit approach:

Breakeven units = Fixed costs / Contribution margin per unit = ($490,000 + $258,800) / $72 = 10400 units

Breakeven sales in dollar = Breakeven units * Selling price per unit = 10400 * $160 = $1,664,000

Contribution margin ratio approach:

Contribution margin ratio = Contribution margin per unit / Selling price per unit = $72 / $160 = 45%

Breakeven sales in dollar = Fixed costs / Contribution margin ratio = ($490,000 + $258,800) / 45% = $1,664,000

Breakeven sales units = Breakeven sales in dollar / Selling price per unit = $1,664,000 / $160 = 10400 units

Contribution margin income statement
At breakeven sales volume
Particulars	Amount
Sales revenue (10400*$160)	$1,664,000.00
Variable costs:
Variable manufacturing costs	$759,200.00
Variable selling expenses	$156,000.00
Contribution margin	$748,800.00
Fixed Costs:
Fixed manufacturing costs	$490,000.00
Fixed selling and administrative expenses	$258,800.00
Net Income	$0.00