Problem 1) During the past year, you had a portfolio that contained U.S. government T-bills, long-term government bonds, and common stocks. The rates of return on each of them were as follows: U.S. government T-bills 5.50%, U.S. government long-term bonds 7.50%, U.S. common stocks 11.60%. During the year, the consumer price index, which measures the rate of inflation, went from 160 to172 (1982 - 1984 = 100). Compute the rate of inflation during this year. Compute the real rates of return on each of the investments in your portfolio based on the inflation rate.
Problem 2) Assume that the consensus required rate of return on common stocks is 14 percent. In addition, you read in Fortune that the expected rate of inflation is 5 percent and the estimated long-term real growth rate of the economy is 3 percent. What interest rate would you expect on U.S. government T-bills? What is the approximate risk premium for common stocks implied by these data?
Problem 3)
a) Someone in the 15 percent tax bracket can earn 10 percent on his investments in a tax exempt IRA account. What will be the value of a $10,000 investment in 5 years? 10 years? 20 years?
b) Suppose the preceding 10 percent return is taxable rather than tax-deferred. What will be the after tax value of his $10,000 investment after 5, 10, and 20 years?
Problem 4) Assume that the rate of inflation during all these periods was 3 percent a year. Compute the real value of the two tax-deferred portfolios in problems 3a and 3b.