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/$. The appropriate dollar cost of capital for this cash flow is r^ast$ = 5% and the

Question

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 [latex]r^{\ast }_{\$} [/latex] = 5% and the appropriate yen cost of capital for this cash flow is [latex]r^{\ast }_{¥} [/latex] = 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?

Accepted Answer

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:

Future CF = ¥10 million, one-year forward rate = ¥105.8095/$

[latex]r^{\ast }_{\$} [/latex]=0.05 spot rate = ¥110/$

[latex]r^{\ast }_{¥} [/latex] = 0.10

EXECUTE

For the Japanese investor, the dollar present value of the yen cash flow is:

[latex]\frac{ ext{Yen} ext{Cash} ext{Flows}}{(1 + ext{Yen Discount Rate})} imes ext{Spot Rate} = \frac{¥10,000,000}{1.01} imes(\$1/¥110) = \$90,009[/latex]

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:

[latex]\frac{ ext{Yen Cash Flows} imes ext{Forward Rate}}{(1 + ext{Dollar Discount Rate})}=\frac{¥10,000,000 imes (\$1/¥105.8095)}{1.05} =\$90,009[/latex]

EVALUATE

Because the U.S. and Japanese capital markets are internationally integrated, both methods produce the same result.

Question 23.4: You are a U.S. investor trying to calculate the present valu...

Related Answered Questions

Verified Answer:

Suppose that in December 2016, the spot exchange rate for the Japanese yen is ¥116/$. At the same time, the one-year interest rate in the United States is 4.85% and the one-year interest rate in Japan is 0.10%.Based on these rates, what forward exchange rate is consistent with no arbitrage? ...

Verified Answer:

Use the Law of One Price to infer the pound WACC from Ityesi’s dollar WACC. Verify that the NPV of Ityesi’s project is the same when its pound free cash flows are discounted at this WACC and converted at the spot rate. ...

Verified Answer:

Assume that in January 2009, banks were offering one-year currency forward contracts with a forward exchange rate of $1.29/€. Suppose that at that time, Manzini placed the order with Campagnolo with a price of 500,000 euros and simultaneously entered into a forward contract to purchase 500,000 ...

Verified Answer:

Verified Answer: