Executive officers of Piedmont Company are assessing the profitability of a potential new product. They expect that the variable cost of making the product will be $60 per unit and fixed manufacturing cost will be $720,000. The executive officers plan to sell the product for $80 per unit.

Required

Determine the break-even point in units and dollars using each of the following approaches:

a. Contribution margin per unit.

b. Equation method.

c. Contribution margin ratio.

d. Prepare a break-even graph to illustrate the cost-volume-profit relationships.

a.         (Contribution margin per unit x N) = Fixed cost + Profit

N = (Fixed cost + Profit) ÷ Contribution margin per unit

N = ($720,000 + $0) ÷ ($80 − $60) = 36,000 units

         Break-even dollars = 36,000 units x $80 Selling price = $2,880,000

b.         N = Number of units to break-even

Sales − Variable cost − Fixed cost = Profit 

(Sales price x N) − (Variable cost per unit x N) = Fixed cost + Profit 

80N – 60N = 720,000

20N = 720,000

N = 36,000 units

            Break-even dollars = 36,000 units x $80 Selling price = $2,880,000

c.         Contribution margin ratio = Contribution margin/Unit ÷ Selling price

Contribution margin ratio = $20 ÷ $80 = 25%

Break-even dollars = Fixed costs ÷ Contribution margin ratio

Break-even dollars = $720,000 ÷ .25 = $2,880,000

Break-even units = $2,880,000 ÷ $80 per unit = 36,000 units