You are analyzing a project with an initial cost of £50,000. The project is expected to return £10,000 the ﬁrst year, £35,000 the second year and £40,000 the third and ﬁnal year. The current spot rate is
£0)5086. The nominal return relevant to the project is 11 percent in the U.S. The nominal risk-free
Rate in the U.S. is three percent while it is ﬁve 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 U.S. dollars:

Year 1: £10,000 x $0.5086 = $5,086
Year 2: £35,000 x $0.5086 = $17,801
Year 3: £40,000 x $0.5086 = $20,344

2) Calculate the present value of the cash flows:

Year 1: $5,086 / (1.11) = $4,584.68
Year 2: $17,801 / (1.11)^2 = $14,196.75
Year 3: $20,344 / (1.11)^3 = $15,149.41

3) Calculate the net present value:

NPV = -£50,000 + $4,584.68 + $14,196.75 + $15,149.41 = $-15,069.16

4) Convert the NPV into pounds:

$-15,069.16 / $0.5086 = £-29,594.50

5) Calculate the present value of the pound NPV using the uncovered interest rate parity:

PV = £-29,594.50 x (1 + 5%)^3 / (1 + 3%)^3 = £-24,879.80

6) Convert the pound PV into U.S. dollars:

£-24,879.80 x $0.5086 = $-12,637.57

7) Add the PV of the pound NPV to the initial cost:

NPV = $-15,069.16 + $-12,637.57 = $-27,706.73

The best choice is C, $26,930, because it is the calculation of the net present value of the project in U.S. dollars.

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