The actual relationship between a nominal rate R a real rate

The actual relationship between a nominal rate, R, a real rate, r, and an inflation rate, h, can be written as:

Your company has a project in France. The project\'s cost is 2 million and the cash flows are .9 million per year for the next three years. The dollar required return is 10% and the current exchange rate is 0.500. The risk-free rate on euros is 7% per year. It is 5% per year on the dollar. The NPV for the project using the exact forms for UIP and the international Fisher effect is $. (Do not include the dollar sign ($). Input your answer in dollars, not in millions, e.g, $1,234,567.89. Round your answer to 2 decimal places. (e.g., 32.16))

The actual relationship between a nominal rate, R, a real rate, r, and an inflation rate, h, can be written as:

Solution

This question contains two concepts which are enumerated below:

1. UIP - Uncovered Interest Rate Parity which says that the future exchange rate wont change based on the interest rate differences of the different countries.

2. Interenational Fisher Effect which says that if the interest rate of a country is higher than the other country the former country\'s currency will depreciate in future.

Therefore if the NPV in this question is to be calculated using above concepts than:

1. In case of UIP NPV will be given as below:

Year

Amount (Euros)

Present Value of 1 Euro at 7%

Present Value

1

                 900,000

0.934579439

       841,121.50

2

                 900,000

0.873438728

       786,094.86

3

                 900,000

0.816297877

       734,668.09

Total

    2,361,884.44

Total Present Value of Cash Inflow = 2,361,884.44 euros

Total NPV = 361.884.44 euros

Total NPV in dollar = $ 723,768.90

2. Using the international fisher effect

Future Exchange Rate will be based on the exchange rates, since the euro rate of return is higher than the dollar rate of return, therefore the euro will depreaciate in respect to dollar by 2% (7%-5%). Therefore future exchange rate = 0.5*102% = 0.51 euros for each dollar in the first year. For second year = 0.52 and for third year = 0.53

Year

Amount (Euros)

Amount (Dollar)

Present Value of $ 1 at 10%

Present Value

1

                 900,000

             1,764,706

0.909090909

    1,604,278.07

2

                 900,000

             1,730,769

0.826446281

    1,430,387.79

3

                 900,000

             1,698,113

0.751314801

    1,275,817.59

Total

    4,310,483.46

Total Cash inflow = $ 4,310,483,.46

Total Cash Outflow = $ 4,000,000

NPV = $ 310.483.46

Year	Amount (Euros)	Present Value of 1 Euro at 7%	Present Value
1	900,000	0.934579439	841,121.50
2	900,000	0.873438728	786,094.86
3	900,000	0.816297877	734,668.09
		Total	2,361,884.44