Question

Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondepreciation fixed costs are $2,800 per year, and variable costs are $40 per unit. The initial investment of $5,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 12%. a. What is the accounting break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.) b. What is the NPV break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.) c. What is the accounting break-even level of sales if the firm’s tax rate is 30%? (Do not round intermediate calculations. Round your answer to the nearest whole number.) d. What is the NPV break-even level of sales if the firm’s tax rate is 30%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

a. Answer: Accounting break-even level of sales = 95 units

Accounting break-even level of sales = Total Fixed Cost / Contribution Margin per Unit = $ ( 2800 + $ 1,000 ) / $ ( 80 - 40) = 95 units.

b. NPV break-even level of sales : 105 units

Annual depreciation = $ 5,000 / 5 = $ 1,000.

OCF = [( 80 - 40 ) Q - 2,800] x ( 1 - 0 ) + $ 1,000 x 0 = 40 Q - 2,800

NPV = ( 40 Q - 2,800) x [ { 1 - ( 1 / 1.12 ) ⁵ } / 0.12 ] = 5,000

or ( 40Q - 2,800 ) x 3.60478 = 5,000

or 144.1912 Q = 15,093.38

Q = 104.68 units

c. Accounting break-even level of sales : No change

d. NPV break-even level of sales : 109 units

OCF = [( 80 - 40 ) Q - 2,800] x ( 1 - 0.30 ) + 1,000 x 0.30 = 28 Q - 1,660

NPV = ( 28 Q - 1,660) x 3.60478 = 5,000

100.93 Q = 10,983.93

Q = 108.83 units