Modern Artifacts can produce keepsakes that will be sold for $70 each. Nondeprec

Question

Modern Artifacts can produce keepsakes that will be sold for $70 each. Nondepreciation fixed costs are $1,600 per year, and variable costs are $35 per unit. The initial investment of $6,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 14%. 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.) 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.) What is the accounting break even level of sales if the firm's tax rate is 40%? (Do not round intermediate calculations. Round your answer to the nearest whole number.) What is the NPV break-even level of sales if the firm's tax rate is 40%? (Do not round intermediate calculations. Round your answer to the nearest whole number)

Explanation / Answer

A&b) Variable cost (per $ sale) = 50% of revenue ($35/$70).
Additional profit per $1 of additional sales is therefore $0.50

Depreciation per year = $6000/5 = $1,200

Accounting Break-even sales level = (Fixed costs + depreciation) / (1-var. cost per $1 of sales)
=> ($1,600 + $1,200)/(1-0.50) = $5,600

This sales level corresponds to a production level of $5,600/$70 per unit = 80 units

To find NPV break-even sales, first calculate cash flow. With no taxes,

CFop = Revenues – Cash Expenses

= 0.50 × Sales – 1600

The 14%, 5-year annuity factor is 3.4331. Therefore, if project NPV equals zero:

PV(cash flows) – Investment = 0

3.4331 × (0.50 × Sales – 1600) – 6000 = 0

1.71655Sales – 5492.96 – 6000 = 0
Sales = 11,492.96/1.71665 = $6,695.38

This sales level corresponds to a production level of $5,095.38/$70, almost 73 units. (Note: you can also deal with this problem another way, solving for units

C&D) Now taxes are 40% of profits. Accounting break-even is unchanged since taxes are not applicable for 0 profit.

NPV Break-even:

Cash Flow = [(1-Tax rate) x (revenue – cash expense)] + (Tax rate x Depreciation)
=> 0.60 x [(0.50 x sales) - $1,600] + (0.40 x $1,200)
=> (0.30 x sales) - $480

The annuity factor is 3.4331, so the NPV:

3.4331 x [(0.30 x sales) - $480] - $6,000 = 0

1.02993Sales - $1647.888 – $6,000 = 0
Sales = $7,647.888/1.02993 = $7,425.63 or $7,426

This corresponds to production of $7,426/$70 = 106 Units

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