# FIN 550 Week 1 Homework

5.During the past five years, you owned two stocks that had the following annual rates of return:

a.Compute the arithmetic mean annual rate of return for each stock. Which stock is most desirable by this measure?

b.Compute the standard deviation of the annual rate of return for each stock. (Use Chapter 1 Appendix if necessary.) By this measure, which is the preferable stock?

c.Compute the coefficient of variation for each stock. (Use the Chapter 1 Appendix if necessary.) By this relative measure of risk, which stock is preferable?

d.Compute the geometric mean rate of return for each stock. Discuss the difference between the arithmetic mean return and the geometric mean return for each stock. Discuss the differences in the mean returns relative to the standard deviation of the return for each stock.

7.A stockbroker calls you and suggests that you invest in the Lauren Computer Company. After analyzing the firm's annual report and other material, you believe that the distribution of expected rates of return is as follows:

LAUREN COMPUTER CO.

Possible Rate of Return

Probability

-0.60

0.05

-0.30

0.20

-0.10

0.10

0.20

0.30

0.40

0.20

0.80

0.15

Compute the expected return [E(Ri)] on Lauren Computer stock.

9.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 to 172 (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.

12.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?

her average tax rate for each of these income levels?

4.a. Someone in the 36 percent tax bracket can earn 9 percent annually on her investments in a tax-exempt IRA account. What will be the value of a one-time $10,000 investment in 5 years? 10 years? 20 years?

b.Suppose the preceding 9 percent return is taxable rather than tax-deferred and the taxes are paid annually. What will be the after-tax value of her $10,000 investment after 5, 10, and 20 years?

5.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?

6.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 4a and 5a.

a.Compute the arithmetic mean annual rate of return for each stock. Which stock is most desirable by this measure?

b.Compute the standard deviation of the annual rate of return for each stock. (Use Chapter 1 Appendix if necessary.) By this measure, which is the preferable stock?

c.Compute the coefficient of variation for each stock. (Use the Chapter 1 Appendix if necessary.) By this relative measure of risk, which stock is preferable?

d.Compute the geometric mean rate of return for each stock. Discuss the difference between the arithmetic mean return and the geometric mean return for each stock. Discuss the differences in the mean returns relative to the standard deviation of the return for each stock.

7.A stockbroker calls you and suggests that you invest in the Lauren Computer Company. After analyzing the firm's annual report and other material, you believe that the distribution of expected rates of return is as follows:

LAUREN COMPUTER CO.

Possible Rate of Return

Probability

-0.60

0.05

-0.30

0.20

-0.10

0.10

0.20

0.30

0.40

0.20

0.80

0.15

Compute the expected return [E(Ri)] on Lauren Computer stock.

9.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 to 172 (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.

12.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?

her average tax rate for each of these income levels?

4.a. Someone in the 36 percent tax bracket can earn 9 percent annually on her investments in a tax-exempt IRA account. What will be the value of a one-time $10,000 investment in 5 years? 10 years? 20 years?

b.Suppose the preceding 9 percent return is taxable rather than tax-deferred and the taxes are paid annually. What will be the after-tax value of her $10,000 investment after 5, 10, and 20 years?

5.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?

6.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 4a and 5a.

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