Question

Lindon Company is the exclusive distributor for an automotive product that sells for $54.00 per unit and has a CM ratio of 30%. The company’s fixed expenses are $388,800 per year. The company plans to sell 28,600 units this year.

Required:

1. What are the variable expenses per unit? (Round your "per unit" answer to 2 decimal places.)

2. What is the break-even point in unit sales and in dollar sales?

3. What amount of unit sales and dollar sales is required to attain a target profit of $226,800 per year?

4. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $5.40 per unit. What is the company’s new break-even point in unit sales and in dollar sales? What dollar sales is required to attain a target profit of $226,800?

1.	Variable expense per unit
2.	Break-even point in units
	Break-even point in dollar sales
3.	Unit sales needed to attain target profit
	Dollar sales needed to attain target profit
4.	New break-even point in unit sales
	New break-even point in dollar sales
	Dollar sales needed to attain target profit

Answer 1

1. Calculation of variable expenses per unit:

Variable expenses per unit

$

37.80

Variable expense per unit = Selling price per unit * Variable expense ratio

= $ 54.00 * 70%

= $ 37.80

Variable expense ratio = 1 - Contribution margin ratio

= 1 - 30%

= 70%

Alternative,

As we know, Contribution margin per unit = Selling price per unit - variable expense per unit

Variable expense per unit = - Selling price per unit - Contribution margin per unit

= $ 54.00 - $ 16.20

= $ 37.80

Working note:

Contribution margin per unit = Selling price per unit * Contribution margin ratio

= $ 54.00 * 30%

= $ 16.20

2. Break even point:

Break-even point in units	24,000	units
Break-even point in dollar	$	12,96,000

Calculation of Break-even point in units :

Break-even point (units) = Fixed cost / Contribution margin per unit

= $ 388,800 / $ 16.20

= 24,000 units

Calculation of Break-even point in dollar :

Break-even point (in dollar) = Fixed cost / Contribution margin ratio

= $ 388,800 / 30 %

= $ 1,296,000

Alternative:

Break-even point (dollar) = Break-even point (units) * Selling price per unit

= 24,000 units * $ 54.00

= $ 1,296,000

3.

Sales required in units	38,000	Units
Sales required in dollar	$	20,52,000

Calculation of unit sales to attain a target profit of $ 226,800 is as follows:

Sales in units for target profit = ( Fixed Cost + Target Profit ) / Contribution Margin per unit

= ( $ 388,800 + $ 226,800 ) / $ 16.20

= $ 615,600 / $ 16.20

= 38,000 units

Calculation of Sales (in dollar) at target profit of $ 226,800 is as follows:

Sales (in dollar) for target profit = ( Fixed Cost + Target Profit ) / Contribution Margin Ratio

= ( $ 388,800 + $ 226,800 ) / 30%

= $ 615,600 / 30%

= $ 2,052,000

4.

Company is able to reduce its variable expenses by $5.40 per unit. Thus, revised variable expenses per unit is $ 32.40 ($ 37.80 - $ 5.40)

Thus, Contribution margin per unit will increase by $ 5.40 result in $ 21.60

Contribution margin per unit = Selling price per unit - Variable expenses per unit

= $ 54.00 - $ 32.40

= $ 21.60

Thus, Contribution margin ratio will also change due to change in variable expenses per unit

Contribution margin ratio = ( Contribution margin per unit / Selling price per unit) * 100

= ( $ 21.60 / $ 54.00 ) * 100

= 40%

Break-even point in units	18,000	units
Break-even point in dollar	$	9,72,000
Sales required in dollar	$	15,39,000

Calculation of Break-even point in units :

Break-even point (units) = Fixed cost / Contribution margin per unit

= $ 388,800 / $ 21.60

= 18,000 units

Calculation of Break-even point in dollar :

Break-even point (in dollar) = Fixed cost / Contribution margin ratio

= $ 388,800 / 40 %

= $ 972,000

Alternative:

Break-even point (dollar) = Break-even point (units) * Selling price per unit

= 18,000 units * $ 54.00

= $ 972,000

Calculation of Sales (in dollar) at target profit of $ 226,800 is as follows:

Sales (in dollar) for target profit = ( Fixed Cost + Target Profit ) / Contribution Margin Ratio

= ( $ 388,800 + $ 226,800 ) / 40%

= $ 615,600 / 40%

= $ 1,539,000