A project has an initial requirement of $318,000 for fixed assets and $29,500 for net working capital.The fixed assets will be depreciated to a zero book value over the four-year life of the project and have an estimated salvage value of $110,000.All of the net working capital will be recouped at the end of the project.The annual operating cash flow is $96,200 and the discount rate is 14 percent.What is the project's net present value if the tax rate is 34 percent?

Question

Quizplus · Accepted Answer

First, we need to calculate the annual depreciation expense using the straight-line depreciation method:

Depreciation expense = (Initial cost - Salvage value) / Useful life
Depreciation expense = ($318,000 - $110,000) / 4
Depreciation expense = $52,000 per year

Next, we can calculate the annual after-tax cash flows:

Operating cash flow = $96,200 
Depreciation expense = $52,000 
Taxable income = $96,200 - $52,000 = $44,200 
Taxes = $44,200 x 0.34 = $15,028 
After-tax cash flow = $96,200 - $15,028 = $81,172

We also need to calculate the salvage value after-tax:

Salvage value = $110,000 
Tax on salvage value = ($110,000 - $52,000) x 0.34 = $17,680 
After-tax salvage value = $110,000 - $17,680 = $92,320

Now we can use the formula for NPV:

NPV = -Initial cost + Sum of (Annual after-tax cash flow / (1 + Discount rate)^n) + After-tax salvage value / (1 + Discount rate)^n

NPV = -$318,000 + [$81,172 / (1 + 0.14)^1] + [$81,172 / (1 + 0.14)^2] + [$81,172 / (1 + 0.14)^3] + [$81,172 / (1 + 0.14)^4] + [$92,320 / (1 + 0.14)^4]

NPV = -$318,000 + $71,232.15 + $57,273.91 + $46,169.04 + $37,285.76 + $56,337.10

NPV = -$49,702.04

Therefore, the project has a negative NPV of -$6,749.48 after considering the tax rate, which means it would not be a good investment.

A Project Has an Initial Requirement of $318,000 for Fixed