Question

Broom Brothers produces and sells one product. The firm currently sells 10,000 units per year for $80 per unit. Total variable costs are $60 per unit and fixed costs are $150,000.

a) What is breakeven sales in units?

b) What is the margin of safety in units? What’s the margin of safety in dollars?

c) What is the degree of operating leverage?

d) If sales increase to 15,000 units per year, profits will increase by ____%.

e) How many units would the firm have to sell to earn profits of $100,000?

f) The firm is considering purchasing a machine to automate its production process, which would reduce variable costs by $20 per unit. At the current sales volume of 10,000 units, what is the most the firm should be willing to pay for this machine?

Answer 1

Solution a:

Selling price per unit = $80

Variable cost per unit = $60

Contribution per unit = $80 - $60 = $20

Fixed cost = $150,000

Brekeven sales unit = Fixed cost / contribution per unit = $150,000/20 = 7500 units

b. Current sales volume = 10000 units

Margin of safety in units = Current sales units - breakeven sales unit = 10000 - 7500 = 2500 units

Margin of safety in dollars = Margin of safety in units * Selling price per unit = 2500*$80 = $200,000

c. Contribution = 10000*20 = $200,000

Net income = Contribution - Fixed cost = $200,000 - $150,000 = $50,000

Operating leverage = contribution / EBIT = $200,000 / $50,000 = 4

d. If sales increased to 15000 units then revised profit = 15000*$20 - $150,000 = $150,000

Existing profit = $50,000

% increase in profit = ($150,000 - $50,000) / $50,000 = 200%

e. Target profit = $100,000

Target contribution = $100,000 + $150,000 = $250,000

Target sales units = Target contribution / Selling price = $250,000/20 = 12500 units

f. New machine will reduce variable cost by $20 per unit

At current sales volume of 10000 units, total reduction in variable cost will be = $20 * 10000 = $200,000

Hence firm can pay maximum $200,000 for new machine.