A project requires an initial investment of $200,000 and expects to produce a cash flow before taxes of $120,000 per year for two years . The corporate tax rate is 21 percent. The assets will depreciate using the MACRS 3-year schedule: (t = 1, 33%); (t = 2: 45%); (t = 3: 15%); (t = 4: 7%). The company's tax situation is such that it can use all applicable tax shields. The opportunity cost of capital is 12 percent. Assume that the asset can sell for book value at the end of the project. Calculate the NPV of the project (approximately).
A)$22,463
B)$19,315
C)$22,735
D)$5,721

Question

Quizplus · Accepted Answer

First, we need to calculate the depreciation each year using the MACRS schedule:

- Year 1: Depreciation = $200,000 × 0.33 = $66,000
- Year 2: Depreciation = ($200,000 - $66,000) × 0.45 = $59,850
- Year 3: Depreciation = ($200,000 - $66,000 - $59,850) × 0.15 = $7,473.75
- Year 4: Depreciation = ($200,000 - $66,000 - $59,850 - $7,473.75) × 0.07 = $1,961.41

Next, we can calculate the taxable income each year:

- Year 1: $120,000 - $66,000 = $54,000
- Year 2: $120,000 - $59,850 = $60,150
- Year 3: $120,000 - $7,473.75 = $112,526.25
- Year 4: $120,000 - $1,961.41 = $118,038.59

We can then calculate the taxes owed each year:

- Year 1: $54,000 × 0.21 = $11,340
- Year 2: $60,150 × 0.21 = $12,632.50
- Year 3: $112,526.25 × 0.21 = $23,530.81
- Year 4: $118,038.59 × 0.21 = $24,788.70

After-tax cash flow for each year will be:

- Year 1: $120,000 - $11,340 - $66,000 = $42,660
- Year 2: $120,000 - $12,632.50 - $59,850 = $47,517.50
- Year 3: $120,000 - $23,530.81 - $7,473.75 = $88,995.44
- Year 4: $120,000 - $24,788.70 - $1,961.41 = $93,249.89

Now we can calculate the present value of each year's after-tax cash flow:

- Year 1: $42,660 ÷ (1 + 0.12) = $38,021.43
- Year 2: $47,517.50 ÷ (1 + 0.12)^2 = $38,352.73
- Year 3: $88,995.44 ÷ (1 + 0.12)^3 = $62,624.97
- Year 4: $93,249.89 ÷ (1 + 0.12)^4 = $59,735.06

The total present value of the after-tax cash flows is:

$38,021.43 + $38,352.73 + $62,624.97 + $59,735.06 = $198,734.19

Finally, we need to subtract the initial investment of $200,000 to find the net present value:

NPV = -$1,265.81 (rounded to nearest dollar)

Therefore, the NPV is approximately -$1,266, which means the project is not profitable and should not be pursued. Option C is the closest approximated answer.

A Project Requires an Initial Investment of $200,000 and Expects