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**FNCE 370v8 Assign 4**

1. Explain the interactions among market efficiency, capital budgeting, and the cost of capital.

2. (5 marks)

a. Give two examples of anomalies in the financial markets.

b. What does the existence of these anomalies say about financial market efficiency?

3. You bought one of BB Co.’s 9% coupon bonds one year ago for $1020. These bonds make annual payments and mature six years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 10%. If the inflation rate was 4.2% over the past year, what would be your total real return on investment? (5 marks)

You bought one of Great White Shark Repellant Co.’s 10 percent coupon bonds one year ago for $770. These bonds make annual payments and mature 13 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 13 percent. If the inflation rate was 3.3 percent over the past year, your total real return on this investment was percent ____?

4. The returns on XYZ Corp. over the last four years are 10%, 12%, 3%, and -9%. (5 marks)

a. What is the historical average return over the last four years?

b. What is the variance of the returns over the last four years?

c. What is the standard deviation of the returns over the last four years?

5. (10 marks)

a. Suppose we have two assets, A and B. What correlation levels between the two assets will yield diversification benefits in terms of portfolio risk reduction?

b. At what correlation level will there be no diversification benefits in terms of portfolio risk reduction?

c. Will there be any diversification benefits in terms of portfolio risk reduction in the case when the correlation between the two assets’ returns is -1?

6. (15 marks)

The expected returns, return variances, and the correlation between the returns of four securities are shown below.

Security Expected Return Variance of Returns Correlation

A B C D

A 0.17 0.0169 1 0.4 0.7 0.2

B 0.13 0.0361 1 0.6 0.5

C 0.09 0.0049 1 0.9

D 0.07 0.005 1

a. Determine the expected return and variance for a portfolio composed of 25% of security A and 75% of security B.

b. Determine the expected return and variance of a portfolio that contains 78% security A and 22% security B. Is this portfolio superior to that one in (a) above?

c. Calculate the expected return and variance of a portfolio that contains 60% security C and 40% security D.

d. If an investor were to select among the following three portfolios, which one would he or she prefer?

o An equally-weighted portfolio of securities A, B, and C.

o An equally-weighted portfolio of A, B, and D.

o An equally-weighted portfolio of B, C, and D.

e. If a risk-adverse investor desires to hold a portfolio of only two securities and expects a return of 11%, what would you advise the investor to do?

d. If an investor were to select among the following three portfolios, which one would he or she prefer?

o An equally-weighted portfolio of securities A, B, and C.

o An equally-weighted portfolio of A, B, and D.

o An equally-weighted portfolio of B, C, and D.

e. If a risk-adverse investor desires to hold a portfolio of only two securities and expects a return of 11%, what would you advise the investor to do?

7. Use the following information to answer the questions below. (10 marks)

Security Return Standard Deviation Beta

A 15% 8% 1.2

B 12% 14% 0.9

a. Which of A and B has the least total risk? The least systematic risk?

b. What is the value of systematic risk for a portfolio with 75% of the funds invested in A and 25% of the funds invested in B?

c. Calculate the risk free rate of return and the market risk premium (i.e., Rf and RM – Rf).

d. What is the portfolio expected return and the portfolio beta if you invest 30% in A, 30% in B, and 40% in the risk-free asset? (For questions (d) and (e), assume the risk free rate of return is 5%.)

e. What is the portfolio expected return with 125% invested in A and the remainder in the risk-free asset via borrowing at the risk-free interest rate?

f. What is the beta of the portfolio created in part (e)?

8. Consider the following information on three stocks. (10 marks)

Rate of Return if State Occurs State of economy Probability of state of economy Stock A Stock B Stock C

Boom 0.5 0.2 0.35 0.6

Normal 0.3 0.15 0.12 0.05

Bust 0.2 0.01 -0.25 -0.5

a. If your portfolio is invested 40% each in A and C, and 20% in B, what is the portfolio expected return?

b. What is the variance of this portfolio?

c. What is the standard deviation of this portfolio?

d. If the expected T-Bill rate is 5%, what is the expected risk premium on the portfolio?

e. If the expected inflation rate is 2.50%, what are the approximate and exact expected real returns on the portfolio?

f. If the expected T-Bill rate is 5% and the expected inflation rate is 2.50%, what are the approximate and exact expected real risk premiums on the portfolio?

9. Briefly discuss the advantages and disadvantages of using the dividend growth model to estimate the cost of equity. (5 marks)

a. What is the firm’s tax adjusted WACC?

b. Ignoring flotation costs, what is the NPV of the proposed project?

c. What is the weighted average flotation cost, fA, for the firm?

d. What is the dollar flotation cost of the proposed financing?

e. After considering flotation costs, what is the NPV of the proposed project?

11. Photosynthesis, Inc. is considering a project that will result in initial after-tax cash savings of $2 million at the end of the first year, and these savings will grow at a rate of 6% per year indefinitely. The firm has a target debt-equity ratio of 1.5, a cost of equity of 20%, and an after-tax cost of debt of 7%. The cost-saving proposal is somewhat riskier than the usual projects the firm undertakes; management uses the subjective approach and applies an adjustment factor of +10% to the cost of capital for such risky projects.

Under what circumstances should Photosynthesis take on the project? (10 marks)

12. ABC Co. has the following dividend payment history: (10 marks)

Year Dividend

2003 $1.00

2004 1.15

2005 1.25

2006 1.35

2007 1.45

a. How many periods of growth are there in the information given?

b. What is the compound growth rate of dividends?

c. Calculate the year-to-year growth rates in dividends.

d. What is the average year-to-year dividend growth rate?

e. Assume a retention ratio of 0.45 and a historical return on equity (ROE) of 0.18. Using these two additional pieces of information, calculate an alternative estimate of dividend growth rate, g.

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