Question

Lindon Company is the exclusive distributor for an automotive product that sells for $40 per unit and has a CM ratio of 40%. The company’s fixed expenses are $264,000 per year. The company plans to sell 17,000 units this year. Required: 1. What are the variable expenses per unit? 2. Use the equation method: a. What is the break-even point in unit sales and in dollar sales? b. What amount of unit sales and dollar sales is required to earn an annual profit of $70,000? c. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $4 per unit. What is the company’s new break-even point in unit sales and in dollar sales? . 3. Repeat (2) above using the formula method. a. What is the break-even point in unit sales and in dollar sales? b. What amount of unit sales and dollar sales is required to earn an annual profit of $70,000? c. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $4 per unit. What is the company’s new break-even point in unit sales and in dollar sales?

Answer 1

SOLUTION

1. Variable expense = Sales price - Contribution per unit

= $40 - ($40 * 40%)

= $40 - $16 = $24

2a. Break even point in units-

= (Unit contribution margin * Quantity) - Fixed expense

= $16 Q - $264,000

16 Q = $264,000

Q = 264,000/16 = 16,500

Break even point in units = 16,500

Break even point in dollars-

Sales = Variable expenses + Fixed expenses

Q = 0.6 Q + 264,000

Q - 0.6 Q = 264,000

Q = 264,000 / 0.40

= $660,000

Break even point in dollars $ 660,000

2b. Sales required to earn a profit of $70,000

= Units contribution margin * Q - Fixed costs + Profit

= 16 Q - 264,000+ 70,000

16 Q = 334,000

Q = 334,000 / 16 = 20,875

Target sales to earn profit of 70,000 in dollars-

Sales = Variable expenses + Fixed expense + profit

Q = 0.6 Q +264,000+ 70,000

0.4 Q = 334,000

Q = 334,000 / 0.4 = $835,000

2c. Break even point in units-

= (Unit contribution margin * Quantity) - Fixed expense

= $20 Q - $264,000

20Q = $264,000

Q = 264,000/20= 13,200

Break even point in units = 13,200

Break even point in dollars-

Sales = Variable expenses + Fixed expenses

Q = 0.5Q+ 264,000

Q - 0.5 Q = 264,000

Q = 264,000 / 0.50

= $528,000

Break even point in dollars $528,000

3a. Breakeven point in units = Fixed expenses / Contribution margin per unit

= $264,000 / $16 = 16,500

Breakeven point in sales dollar = Fixed expenses / Contribution margin ratio

= $264,000 / 40 % = $660,000

3b. Sales required to earn profit $70,000-

in units = (Fixed expenses + Profit)/Contribution margin per unit

= (264,000+70,000) / $16

= 334,000 / 16 = 20,875

in dollars = (Fixed expenses + Profit)/Contribution margin per unit

= (264,000+70,000) / 40%

= 334,000 / 40% = 835,000

3c. Breakeven point in units = Fixed expenses / Contribution margin per unit

= $264,000 / $20= 13,200

Breakeven point in sales dollar = Fixed expenses / Contribution margin ratio

= $264,000 / 50 % = $528,000