Question 23.4: You are a U.S. investor trying to calculate the present valu...
You are a U.S. investor trying to calculate the present value of a ¥10 million cash flow that will occur one year in the future. The spot exchange rate is ¥110/$ and the one-year forward rate is ¥105.8095/$. The appropriate dollar cost of capital for this cash flow is r^∗_\$ = 5% and the appropriate yen cost of capital for this cash flow is r^∗_¥ = 1% What is the dollar present value of the ¥10 million cash flow from the standpoint of a Japanese investor? What is the present value of the ¥10 million cash flow from the standpoint of a U.S. investor who first converts the ¥10 million into dollars and then applies the dollar discount rate?
PLAN
For the Japanese investor, we can compute the present value of the future yen cash flow at the yen discount rate and use the spot exchange rate to convert that amount to dollars.
For the U.S. investor, we can convert the future yen cash flow to dollars at the forward rate and compute the present value using the dollar discount rate.
We know:
EXECUTE
For the Japanese investor, the dollar present value of the yen cash flow is:
\frac{\text{Yen Cash Flows}}{(1+ \text{Dollar Discount Rate})} \times \text{Spot Rate} = \frac{¥10,000,000}{1.01} ($1/¥110) = $90,009
For a U.S. investor who first converts the ¥10 million into dollars using the forward rate and then applies the dollar cost of capital:
\frac{\text{Yen Cash Flows}\times \text{Foward Rate}}{(1+ \text{Dollar Discount Rate})} = \frac{¥10,000,000 \times (\$1/¥105.8095)}{1.05} = $90,009
EVALUATE
Because the U.S. and Japanese capital markets are internationally integrated, both methods produce the same result.