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%. a) 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? b) 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

1. Present value in pound=$23,752,969

Dollar equivalent=$46,073,634

2.Dollar equivalent for U.S investors=$48,952,500

Present value in pound=$46,072,918

Step-by-step explanation:

1a.Calculation for present value of the £25 million cash flow

Using this formula

Present value in pound =cash flow*(1/1+Cash flow cost of capital)^ One year in the future

Let plug in the formula

Present value in pound=$25,000,000*(1/1+0.0525)^1

Present value in pound=$25,000,000*(1/1.0525)^1

Present value in pound=$25,000,000*0.950119

Present value in pound=$23,752,969

1b.Calculation for the dollar equivalent of this amount

Using this formula

Dollar equivalent=Present value in pound*Spot exchange rate

Let plug in the formula

Dollar equivalent=$23,752,969*$1.9397

Dollar equivalent=$46,073,634

2a. Calculation for the Dollar equivalent for U.S investors

Using this formula

Dollar equivalent for U.S investors=Cash flow*one-year forward rate

Let plug in the formula

Dollar equivalent for U.S investors=$25,000,000*$1.9581

Dollar equivalent for U.S investors=$48,952,500

2b. Calculation for the present value of the £25 million cash flow from the standpoint of a U.S. investor .

Using this formula

Present value in pound =Cash flow*(1/1+Cash flow cost of capital)^ One year in the future

Let plug in the formula

Present value in pound=$48,952,500*(1/1.0625)^1

Present value in pound=$48,952,500*0.941176

Present value in pound=$46,072,918

Therefore the Present value in pound for question 1 is $23,752,969 while the Dollar equivalent is $46,073,634.

The Dollar equivalent for U.S investors in question 2 is $48,952,500 while the Present value in pound is $46,072,918