Question

Lindon Company is the exclusive distributor for an automotive product that sells for $45 per unit and has a CM ratio of 20%. The company’s fixed expenses are $108,000 per year. The company plans to sell 14,000 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 $63,000?

c. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $9 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 $63,000?

c. Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $9 per unit. What is the company’s new break-even point in unit sales and in dollar sales?

Answer 1

Break even point is the sales at which there is no profit no loss.

equation method.

(1) variable cost per unit = sales cost per unit (1-contribution margin ratio)

=$45 (1-0.20)

=$36

(2a) Break even point

suppose break even units are X

Profit at break even = $0

CM per unit = Sales* CM ratio

$45*20%

=$9

Profit = Unit CM*X-fixed expenses

$0 = $9*X - $108,000

X=12,000 units

Break even dollars = 12,000 units*$45 sales price per unit

=$540,000

(2b)

profit=unit Cm*X-fixed expenses

$63,000 = $9*X- $108,000

9X = $171,000

X=19,000 units

Break even sales = 19,000 units*$45

=$855,000

(2c)new variable cost= $36-$9

=$27

Break even point

suppose break even units are X

Profit at break even = $0

CM per unit = Sales-variable cost

$45-$27

=$18

Profit = Unit CM*X-fixed expenses

$0 = $18*X - $108,000

X=6,000 units

Break even dollars = 6,000 units*$45 sales price per unit

=$270,000

(3A)

formula method

Break even point = fixed expenses /CM per unit

$108,000/$9

=12,000units

Break even sales = fixed expenses/CM ratio

$108,000/20%

=$540,000

3b)

Break even point = (targeted profit+fixed expenses)/contribution per unit

($63,000+$108,000)/$9

=19,000 units

sales in dollar = (targeted profit+fixed expense)/CM ratio

($63,000+$108,000)/0.20

=$855,000

3c)

new variable cost= $36-$9

=$27

New Contribution= ($45-$27) =$18

CM ratio = Contribution margin/sales=$18/$45

=40%

Break even point

Break even point = (targeted profit+fixed expenses)/contribution per unit

($108,000)/$18

=6,000 units

sales in dollar = (targeted profit+fixed expense)/CM ratio

($108,000)/0.40

=$270,000