Question

Today the current EUR to USD exchange rate is 1 EUR = 1.19 USD. According to the Bloomberg consensus estimate, the EUR to USD exchange rate in four years is forecasted to be 1 EUR = 1.31 USD. You begin with 100 USD today and will invest in a European security that provides 10% annual returns (in EUR). Using this information, answer the following six (6) questions.

1) Is the USD forecasted to appreciate or depreciate relative to EUR? a) Appreciate b) Depreciate c)Neither appreciate nor depreciate d)Both appreciate and depreciate

2) To invest in the European security you must first convert USD to EUR. How many EUR will you have when exchange your 100 USD today for EUR?

3)Given that you will invest in a European security that earns 10% annually, how many euros will you have in 4 years? Assume that you reinvest all earnings (i.e., your investment simply compounds for 4 years).

4) You live in the US so you wish to exchange EUR for USD after 4 years. How many USD will you have in 4 years after exchanging your euros from the previous problem for USD?

5)What is your total return in USD? Use decimal notation, e.g., enter 0.2345 for 23.45%

6)What is your average annual return in USD? Use decimal notation, e.g., enter 0.2345 for 23.45%. [Hint: You can use your calculators built-in financial function ("fab five") to obtain this answer.]

Answer 1

1. b. Depreciate. Currently, you will have to pay $1.19 to get 1 EUR but 4 years from now you will have to pay $1.31 to get the same amount (1 EUR). So dollar depreciates relative to EUR.

2. Currently, 1.19 USD = 1 EUR, so 1 USD = 1/1.19 EUR => 100 USD = 1/1.19*100 = 84.03 EUR

3. With an annual return of 10%, in 4 years 84.03 EUR will become 84.03*1.1^4 = 123.03 EUR

4. 4 years later, expected exchange rate is 1 EUR = 1.31 USD, so 123.03 EUR = 161.17 USD

5. Total return = Final value/Initial investment - 1 = 123.03/100-1 = 61.17%

6. Average annual return = 61.17/4 = 15.29%

The average return is higher than the yearly return on EUR (10%) because we benefited from the depreciation in USD.