Question

Lindon Company is the exclusive distributor for an automotive product that sells for $38.00 per unit and has a CM ratio of 30%. The company’s fixed expenses are $228,000 per year. The company plans to sell 23,000 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 $114,000 per year?

4. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $3.80 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 $114,000?

Answer 1

1. Calculation of variable expenses per unit is as follows:

As we know, Sales - variable cost = Contribution margin

Thus,

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

= $ 38.00 - $ 11.40

= $ 26.60

Thus, Variable expenses per unit is $ 26.60

Working note:

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

= $ 38.00 * 30%

= $ 11.40

Alternative,

Variable expenses per unit = Selling price per unit * ( 1 - Contribution margin ratio )

= $ 38.00 * ( 1 - 30% )

= $ 26.60

2. Calculation of break-even point in unit sales and in dollar sales is as follows:

Break even sales is recovery of fixed cost, at break even point no profit no loss.

Break even point in units = Fixed Cost / Contribution margin per unit

= $ 2,28,000 / $ 11.40

= 20,000 units

Thus, Break even point is 20,000 units

Break even point in dollars = Fixed Cost / Contribution Margin ratio

= $ 2,28,000 / 30%

= $ 7,60,000

Thus, Break even poimt (in dollar) is $ 7,60,000

Alternative,

Break even point in dollars = Break even point in units * Selling price per unit

= 20,000 * $ 38.00

= $ 7,60,000

3. Calculation of unit sales and dollar sales is required to attain a target profit of $114,000 per year is as follows:

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

= ( $ 2,28,000 + $ 1,14,000 ) / $ 11.40

= 3,42,000 / $ 11.40

= 30,000 units

Thus, 30,000 units required to sale in order to earn profit of $ 1,14,000

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

= ( $ 2,28,000 + $ 1,14,000 ) / 30%

= 3,42,000 / 30%

= $ 11,40,000

Thus, Sales of $ 11,40,000 required to earn profit of $ 1,14,000

Alternative,

Sales (in dollar) for target profit = Sales (in units) for target profit * Selling price per unit

= 30,000 * $ 38

= $ 11,40,000

4. Calculation of new breakeven point unit sales , dollar sales & DollarSales to earn target profit of $ 114,000 is as follows:

Company is able to reduce its variable expenses by $3.80 per unit.

Revised variable expenses per unit = $ 26.60 - $ 3.80

   = $ 22.80

Revised Contribution margin per unit = Selling price per unit - Revised variable expenses per unit

= $ 38.00 - $ 22.80

= $ 15.20

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

= ( $ 15.20 / $ 38.00 ) * 100

= 40 %

Calculation of break-even point in unit sales and in dollar sales is as follows:

Break even point in units = Fixed Cost / Revised Contribution margin per unit

= $ 2,28,000 / $ 15.20

= 15,000 units

Thus, Break even point is 15,000 units

Break even point in dollars = Fixed Cost / Revised Contribution Margin ratio

= $ 2,28,000 / 40%

= $ 5,70,000

Thus, Break even poimt (in dollar) is $ 5,70,000

Alternative,

Break even point in dollars = Break even point in units * Selling price per unit

= 15,000 * $ 38.00

= $ 5,70,000

Calculation of dollar sales is required to attain a target profit of $114,000 per year is as follows:

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

= ( $ 2,28,000 + $ 1,14,000 ) / 40%

= 3,42,000 / 40%

= $ 8,55,000

Thus, Sales of $ 8,55,000 required to earn profit of $ 1,14,000