Practice Question
Your investment has a four-year life, and it costs $200,000 per year. It has an annual pre-tax operating income of $75,000 in the first year.
Operating incomes are expected to increase at a rate of 5% over the life of the investment. The depreciation cost is $10,000 each year.
Note that the corporate tax rate is 36% and your discount rate is 10%.
Assuming that there’s no salvage value for the investment, what is the NPV of this investment?
Step 1: Compute Annual Operating Income and Growth
Year 1 = 75,000
Year 2 = 75,000 × 1.05 = 78,750
Year 3 = 78,750 × 1.05 = 82,688
Year 4 = 82,688 × 1.05 = 86,822.81
Step 2: Calculate Taxable Income and Taxes
Taxable income = Operating income - Depreciation
Tax = 36% of taxable income
Step 3: Compute After-Tax Cash Flows
Cash Flow = (Operating Income - Depreciation) × (1 - Tax Rate) + Depreciation - Investment Cost
Compute year-by-year:
- Year 1: \((75,000 - 10,000) \times 0.64 + 10,000 - 200,000 = -144,000\)
- Year 2: \((78,750 - 10,000) \times 0.64 + 10,000 - 200,000 = -140,800\)
- Year 3: \((82,688 - 10,000) \times 0.64 + 10,000 - 200,000 = -137,282.58\)
- Year 4: \((86,822.81 - 10,000) \times 0.64 + 10,000 - 200,000 = -133,487\)
Step 4: Discount Cash Flows
\[ NPV = \frac{-144000}{(1.10)^1} + \frac{-140800}{(1.10)^2} + \frac{-137282.58}{(1.10)^3} + \frac{-133487}{(1.10)^4} \approx -25,587.32 \]
Conclusion: The net present value of this investment is -$25,587.32, indicating it destroys value at the given discount rate.