Question

Super Sales Company is the exclusive distributor for a high-quality knapsack. The product sells for $100 per unit and has a CM ratio of 30%. The company’s fixed expenses are $429,000 per year. The company plans to sell 16,000 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 $117,000?

c. What sales level in units is required to earn an annual after-tax profit of $117,000 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 $9 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 $117,000?

c. What sales level in units is required to earn an annual after-tax profit of $117,000 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 $9 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.)

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Answer 1

1) calculation of variable expenses per unit:

Contribution margin ratio = 30%

Selling price per unit = $100

Variable cost ratio = 1- contribution margin ratio

= 1-30%

= 70%

Variable cost per unit = $100 ×70%

= $70 per unit

2-a) calculation of break even point:

Break even point (in dollars)

= Fixed cost/ contribution margin ratio

= $429,000/30%

= $1,430,000

Break even point( in units)

= Fixed cost/ contribution margin per unit

Contribution margin per unit = selling price per unit - variable cost per unit

= $100 - $70

= $30 per unit

Break even point = $429,000/$30

= 14300 units

2-b) calculation of sales level in units and in dollars:

Sales ( in units)

= (Fixed cost + required profit)/contribution margin per unit

= ($429,000 + $117,000)/$30

= 18,200 units

Sales ( in dollars)

= (Fixed cost + Required profit)/contribution margin ratio

= ($429,000 + $117,000)/30%

= $1,820,000

2-c) calculation of sales in units and in dollars :

Profit after tax = $117,000

Tax rate = 20%

Profit before tax = $117000/80%

= $146,250

Sales (in units)

= (Fixed cost + required profit)/contribution margin per unit

= ($429,000 + $146,250)$30

= 19,175 units

Sales (in dollars)

= (Fixed cost + required profit)/contribution margin ratio

= ($429,000 + $146,250)/30%

= $1,917,500

2-d) calculation new break even point:

If variable cost is reduced by $9 per unit

New variable cost = $70-$9 = $61 per unit

Contribution margin per unit = selling price per unit - variable cost per unit

= $100 - $61

= $39

Contribution margin ratio = contribution margin/sales

= $39/$100

= 39%

Break even point ( in units) = Fixed cost/contribution margin per unit

= $429,000/$39

= 11,000 units

Break even point (in dollars)

= fixed cost/contribution margin ratio

= $429,000/39%

= $1,100,000