Question

Lindon Company is the exclusive distributor for an automotive product that sells for $35.00 per unit and has a CM ratio of 31%. The company’s fixed expenses are $249,550 per year. The company plans to sell 24,000 units this year.

Required:

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

      

2.	Use the equation method:

a.	What is the break-even point in unit sales and in dollar sales? (Do not round intermediate calculations.)

b.	What amount of unit sales and dollar sales is required to earn an annual profit of $54,250? (Do not round intermediate calculations.)

            

c.	Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $3.60 per unit. What is the company’s new break-even point in unit sales and in dollar sales? (Do not round intermediate calculations. Round up break even point answers to the nearest whole number.)

           

3.	Repeat (2) above using the formula method.

a.	What is the break-even point in unit sales and in dollar sales? (Do not round intermediate calculations.)

          

b.	What amount of unit sales and dollar sales is required to earn an annual profit of $54,250? (Do not round intermediate calculations.)

         

c.	Assume that by using a more efficient shipper, the company is able to reduce its variable expenses by $3.60 per unit. What is the company’s new break-even point in unit sales and in dollar sales? (Do not round intermediate calculations. Round up break even point answers to the nearest whole number.)

        

Answer 1

1. Selling price per unit = $35 per unit

Contribution margin ratio = 31%

Fixed expenses = $249,550

Since contribution margin ratio is 31%, hence variable expenses must be 69% of selling price.

Variable expenses = 35 x 69%

= $24.15 per unit

(2a)

At Break even point, there is no profit no loss. Hence, total sales revenue is equal to the sum of total variable expenses and total fixed expenses.

Let the number of units to be sold to break even = X units

Break even sales = Variable cost + Fixed cost

35X = 24.15X + 249,550

35X - 24.15X = 249,550

10.85X = 249,550

X = 249,550/10.85

= 23,000

Hence, break even point = 23,000 units

Break even point in dollars = 23,000 x 35

= $805,000

(2b) Sales to get a desired profit can be calculated as under:

Let the number of unts to be sold to get a profit of $54,250 = Y

Sales = Variable expenses + Fixed expenses + Profit

35Y = 24.15Y + 249,550 + 54,250

35Y - 24.15Y = 303,800

10.85Y = 303,800

Y = 303,800/10.85

= 28,000 units

Hence, when 28,000 units are sold, profit earned will be $54,250

Sales revenue to get $54,250 profit = 28,000 x 35

= $980,000

(2c) Reduction in variable cost = $3.60 per unit

Hence, new variable expenses per unit = 24.15 - 3.60

= $20.55

Let the number of units to be sold to break even = X units

Break even sales = Variable cost + Fixed cost

35X = 20.55X + 249,550

35X - 20.55X = 249,550

14.45X = 249,550

X = 249,550/14.45

= 17,270

Hence, break even point = 17,270 units

Break even point in dollars = 17,270 x 35

= $604,450