2. [Exchange rateand optimal investment](20Points)

(a)Consider the exchange rate between US dollar and British pound.Let CPI be theconsumer price index, or equivalently the average price level in a country.

Assume the ratio CPI_UK/CPI_US=0.75.

According to the law of one price, what must be the exchange rate between US dollarand British pound (i.e. 1 pound equals to how many dollars)?

Suppose there arethreeinvestment projectsA, B and C.

Project A: You pay an investment cost of $1000 now and receive 900after one year.

Project B: You pay an investment cost of 600 now and receive $100after two years.

Project C: You pay an investment cost of $800 now and receive $1200after three years.

(b)Use your answer from part (a) to compute the yield-to-maturity(i.e. nominal interest rate) of A, B and C. Which project has the highest yield-to\-maturity?

(c) Find the range of exchange rate esuch that Project A has the highest yield-to-

maturity. Repeat the same calculation for B and C.

Let'sconsider the problem in part (a) and (b) again, except now we include the inflationratesin the calculation. Again assume CPI_UK/CPI_US=0.75this year.

Suppose the inflation rate in the US is 2% and that of UK is 0%.

(d)According to the law of one price, what must be the exchange rate between US dollar and British pound next year? What is the yield-to-maturity(i.e. nominal interest rate) of A,Band Cif we take the inflation rates into account?