Question

Super Sales Company is the exclusive distributor for a high-quality knapsack. The product sells for $80 per unit and has a CM ratio of 40%. The company’s fixed expenses are $720,000 per year. The company plans to sell 23,000 knapsacks this year.

Required:

1. What are the variable expenses per unit?

2. Use the equation method for the following:

a. What is the break-even point in units and in sales dollars?

b. What sales level in units and in sales dollars is required to earn an annual profit of $80,000?

c. What sales level in units is required to earn an annual after-tax profit of $80,000 if the tax rate is 20%?

d. Assume that through negotiation with the manufacturer, Super Sales Company is able to reduce its variable expenses by $4 per unit. What is the company’s new break-even point in units and in sales dollars? (Do not round intermediate calculations. Round your final answers to the nearest whole number.)

3. Use the formula method for the following:

a. What is the break-even point in units and in sales dollars?

b. What sales level in units and in sales dollars is required to earn an annual profit of $80,000?

c. What sales level in units is required to earn an annual after-tax profit of $80,000 if the tax rate is 20%?

d. Assume that through negotiation with the manufacturer, Super Sales Company is able to reduce its variable expenses by $4 per unit. What is the company’s new break-even point in units and in sales dollars? (Do not round intermediate calculations. Round your final answers to the nearest whole number.)

Answer 1

Answer :

(1)

Contribution margin ratio = Sales - variable cost/ Sales *100

Contribution Margin = Sales - Variable cost

Let variable cost is X

Sales per unit = $80

(80-X)/80 = 0.40

80-X = 80*0.4

80-X = 32

X = 48

Variable cost per unit = $48

(2)

(a)

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

Break even point (Sales) = Fixed cost / profit volume ratio

Profit volume ratio = Contribution/Sales *100

Contribution = Sales - Variable cost

= $80 - $48

= 32

Profit volume ratio = 32/80*100

= 40%

Fixed cost = $720,000

Break even point (units) = 720,000/32

= 22,500 units

Break even point (sales) = 720,000/0.4

= $1,800,000

(b)

Desired profit = $80,000

Required sales (units) = (Desired profit + Fixed cost)/Contribution per unit

= (80,000+720,000)/32

= 25,000 units

Required sales (value) = (80,000+720,000)/0.4

= 2,000,000

(c) Desired after tax profit = $80,000

Tax rate = 20%

Required sales (units) = [Fixed cost +(Target Income/1-tax rate)]/ Contribution margin per unit

= [720,000+(80,000/1-0.20)]/32

= [720,000+100,000]/32

= 25,625 units

Let's check the answer

Sales revenue (25,625*$80)	$2,050,000
Less: variable cost (25,625*$48)	1,230,000
Contribution margin	820,000
Less: fixed cost	720,000
Profit before tax	100,000
Tax @ 20%	20,000
Profit after tax	80,000

(d)

Variable cost per unit is reduced by $4 per unit

Hence, now variable cost per unit = $48 - $4

= $44

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

Break even point (Sales) = Fixed cost / profit volume ratio

Contribution margin per unit = $80 -$44

= $36

Profit volume ratio = 36/80*100

= 45%

Fixed cost = $720,000

Break even point (units) = 720,000/36

= 20.000 units

Break even point (sales) = 720,000/0.45

= $1,600,000

(3)

Equation method

(a)

Px= vx+FC+profit

P is the price per unit

X is the number of units

V is the variable cost per unit

80x = 48x + 720,000 + 0

80x - 48x = 720,000

32x = 720,000

x = 720,000/32

x= 22,500 units

Break even point in dollars = price per unit *Break even sales unit

= $80*22,500 units

= $1,800,000

(b)

Desired profit = $80,000

P= $80,000

Px = vx + FC + profit

80x = 48x + 720,000 + 80,000

80x - 48x = 800,000

32x = 800,000

X = 800,000/32

X = 25,000

Required sales level in units= 25,000 units

Required sales level in sales dollar = $80 * 25,000 units = $2,000,000

(c) Profit ater tax = $80,000

Profit before tax = 80,000/(1 - 0.20)

= $100,000

Profit before tax= $100,000

Px = vx + FC + profit

80x = 48x + 720,000 + 100,000

80x - 48x = 820,000

32x = 820,000

X = 820,000/32

X = 25,625

Required sales level in units to earn an annual after tax profit of $ 80,000 = 25,625 units

(d) Now variable cost = $ 48 - $4

= $44

Px= vx+FC+profit

P is the price per unitx

X is the number of units

V is the variable cost per unit

80x = 44x + 720,000 + 0

80x - 44x = 720,000

36x = 720,000

x = 720,000/36

x= 20,000 units

Break even point in dollars = price per unit *Break even sales unit

= $80*20,000 units

= $1,600,000

Thank you:)