A project requires an initial investment of $200,000 and expects to produce a ca

Question

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 (i.e., cash flows will occur at t = 1 and t = 2). The corporate tax rate is 30%. 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%. Assume that the asset can sell for book value at the end of the project. Calculate the NPV of the project (approximately)

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Explanation / Answer

CF0 = -200,000

CF1= [120,000 - (200,000 x 0.33)] x 0.70 + [200,000 x 0.33]
CF1= [120,000 - 66000 ] x 0.70 + 66000
CF1= [54000] x 0.7 + 66000
CF1= 37800 + 66000
CF1= $103,800

CF2= [120,000 - (200,000 x 0.45)] x 0.70 + [200,000 x 0.45]
CF2= [120,000 - 90000 ] x 0.70 + 90000
CF2= [30,000] x 0.7 + 90000
CF2= 21000 + 90000
CF2= $111,000

CF2 = $111,000 + [200,000 x 0.22]
CF2 = $111,000 + $44,000
CF2 = $155,000

Free Cash Flows
-200000 +103800 +155000

NPV Calculation at 12%

Discounted Net Cash Flows
DCF1 = 103800/(1+0.12)^1 = 103800/1.12 = 92678.57
DCF2 = 155000/(1+0.12)^2 = 155000/1.2544 = 123565.05

NPV Calculation
NPV = 92678.57 + 123565.05 -200000
NPV = 216243.62 -200000
NPV = 16,243.62

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