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Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepreciation fixed costs are...

Modern Artifacts can produce keepsakes that will be sold for $100 each. Nondepreciation fixed costs are $1,800 per year, and variable costs are $45 per unit. The initial investment of $2,000 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 20%? (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 20%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Solutions

Expert Solution

a. accounting break-even level of sales if the firm pays no taxes

Depreciation = 2000 / 5 = 400

accounting break-even level of sales = Non depreciation fixed costs + Depreciation / (Selling price - Variable cost)

= 1800 + 400 / (100 - 45) = 2200 / 55 = 40 * 100 = $4000

accounting break-even level of sales if the firm pays no taxes = $4,000

b. NPV break-even level of sales if the firm pays no taxes

Variable cost = 0.45 sales

Fixed cost + depericiation = 2200

Pretax profit = 0.45 sales + 2200

Present value of NPV break even = (0.45sales + 2200) * 4.329

If NPV = 0

0 = (0.45 sales + 2200) * 4.329

0 = 1.94805 sales + 9523.8

Sales = 9523.8 / 1.94805 = $4888.88

NPV break-even level of sales if the firm pays no taxes = $4,888.88

c. accounting break-even level of sales if the firm’s tax rate is 20%

For this, the result calculated in question A will be tax adjusted.

= 4000 (1 - 0.2) = $3200

accounting break-even level of sales if the firm’s tax rate is 20% = $3200

d. NPV break-even level of sales if the firm’s tax rate is 20%

For this, the result calculated in question B will be tax adjusted and depreciation to be added back.

Present value of NPV break even = [(1 - 0.2)(0.45sales + 2200)] * 4.329

= [0.8 * (0.45 sales + 2200)] * 4.329

= [0.36 sales + 1760] * 4.329

= 1.55844 Sales + 7619.04

If NPV = 0

0 = 1.55844 Sales + 7619.04+Depreciation

0 = 1.55844 Sales + 7619.04+ 400

Sales = 8019.04 / 1.55844

= $5145.55

NPV break-even level of sales if the firm’s tax rate is 20% = $5,145.55

jeff jeffy answered 1 year ago

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