You are analyzing a project with an initial cost of £50,000. The project is expected to return £12,000 the first year, £36,000 the second year, and £40,000 the third and final year. There is no salvage value. Assume the current spot rate is £.6346. The nominal return relevant to the project is 12 percent in the U.S. The nominal risk-free rate in the U.S. is 3.4 percent while it is 4.1 percent in the U.K. Assume that uncovered interest rate parity exists. What is the net present value of this project in U.S. dollars?

Question

Quizplus · Accepted Answer

1. Convert the cash flows into USD using the current spot rate of £.6346:
Year 1: £12,000 / .6346 = $18,886.65
Year 2: £36,000 / .6346 = $56,659.94 
Year 3: £40,000 / .6346 = $62,958.82

2. Calculate the nominal return in the U.S. using the formula: 
Nominal Return = Real Return + Inflation
12% = Real Return + 3.6% (12% - 3.4%) 
Real Return = 8.4%

3. Calculate the present value of each cash flow in USD using the formula:
PV = CF / (1+r)^n
Year 1: $18,886.65 / (1+0.084)^1 = $17,427.10
Year 2: $56,659.94 / (1+0.084)^2 = $47,807.79
Year 3: $62,958.82 / (1+0.084)^3 = $49,999.25

4. Calculate the net present value (NPV) of the project:
NPV = PV of cash inflows - Initial cost
NPV = ($17,427.10 + $47,807.79 + $49,999.25) - £50,000 / .6346 = $79,125.42 - $78,527.80 = $597.62

Therefore, the net present value of this project in USD is $26,509.

You Are Analyzing a Project with an Initial Cost of £50,000