Question

As an American investor, you are trying to calculate the present value of a £25 million cash flow that will occur one year in the future. You know that the spot exchange rate is S= $1.9397/ £ and one-year forward rate is F= $1.9581/ £. You also know that the appropriate dollar cost of capital for this cash flow is 6.25% and that the appropriate pound cost of capital for this cash flow is 5.25%.

1. What is the present value of the £25 million cash flow from the standpoint of a British investor, and what is the dollar equivalent of this amount?
2. What is the present value of the £25 million cash flow from the standpoint of a U.S. investor who first converts the £25 million into dollars and then applies the dollar discount rate?

Answer 1

Calculation for both the parts are shown below

In first case we would calculate present value in pounds and then its dollar equivalent using spot rate

In second case we would convert first into dollar equivalent using forward rate and then calculate its present value.

a. Calculation of present value from British investor's point of view is shown below Present value in pounds 25 million*(1/(1.052541) Present value in pounds 25 million*0.950119 Present value in pounds 23,752,969 Dollar equivalent of amount Dollar equivalent of amount 23752969*1.9397 $46,073,634 b. Calculation of present value from US investor's point of view is shown below Dollar equivalent for U.S investor 25 million*1.9581 Dollar equivalent for US investor 48,952,500 PV in US dollars PV in US dollars PV in US dollars 48952500*(1/(1.062541)) 48952500*0.941176 $46,072,941 The difference in the two amount is due to rounding off