# Portfolio Expected Rate of Return and Beta and the Constant Dividend Growth Model

Monica Dubois, an ABC investment advisor, has a new client, Mr. Jack Klein. Mr. Klein is a conservative investor who is interested in a required rate of return of 10% on his stock investments while assuming lower market risk. You are asked to help Monica make a suitable portfolio recommendation backed by risk-return calculations. The 3 possible stock choices for Mr. Klein and their respective betas are as follows:

(see attached file for data)

Part I

Determine the expected returns and beta for a portfolio consisting of one third of Mr. Klein's funds in each stock.

Part II

Assume the following:

- Each ABC stock pays current dividends of $1.50 annually with 6% expected annual increases. The current market stock price for ABC is $30 per share.

- Each XYZ stock pays current dividends of $1.75 annually with 6% expected annual increases. The current market stock price for XYZ is $27 per share.

- Each WHY stock pays current dividends of $2.25 annually with 7% expected annual increases. Current market stock price for WHY is $35 per share.

Complete the following for this assignment:

- Using the constant dividend growth model, determine whether ABC and WHY are over- or undervalued.

- For what types of companies is the constant growth model an appropriate analysis tool?

- What are the limitations of the constant growth model?

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#### Solution Summary

The portfolio expected rate of return can be used to determine the best portfolio component stocks for an investor. The portfolio beta can be used to determine the beta for the portfolio of component stocks. The constant dividend growth model can be used to determine the value of a stock based on a constant dividend rate, dividend amount and investor's required rate of return.

Finance MCQ: market risk, portfolio beta, rate of return, growth rate, stock price

1. Which of the following statements is CORRECT?

a. An investor can eliminate virtually all market risk if he or she holds a very large and well diversified portfolio of stocks.

b. The higher the correlation between the stocks in a portfolio, the lower the risk inherent in the portfolio.

c. It is impossible to have a situation where the market risk of a single stock is less than that of a portfolio that includes the stock.

d. Once a portfolio has about 40 stocks, adding additional stocks will not reduce its risk by even a small amount.

e. An investor can eliminate virtually all diversifiable risk if he or she holds a very large, well diversified portfolio of stocks.

Answer: ____________________________

2. Currently, the risk-free rate is 6% and the market risk premium is 5%. Given this information, which of the following statements is CORRECT?

a. An index fund with beta = 1.0 should have a required return of 11%.

b. If a stock has a negative beta, its required return must also be negative.

c. An index fund with beta = 1.0 should have a required return less than 11%.

d. If a stock's beta doubles, its required return must also double.

e. An index fund with beta = 1.0 should have a required return greater than 11%.

Answer: ____________________________

3. Rick Kish has a $100,000 stock portfolio. $32,000 is invested in a stock with a beta of 0.75 and the remainder is invested in a stock with a beta of 1.38. These are the only two investments in his portfolio. What is his portfolio's beta?

a. 1.18

b. 1.24

c. 1.30

d. 1.36

e. 1.43

Answer: ____________________________

4. Rodriguez Roofing's stock has a beta of 1.23, its required return is 11.25%, and the risk-free rate is 4.30%. What is the required rate of return on the stock market?

a. 9.95%

b. 10.20%

c. 10.45%

d. 10.72%

e. 10.98%

Answer: ____________________________

5. Which of the following statements is CORRECT?

a. The constant growth model is often appropriate to evaluate start-up companies that do not have a stable history of growth but are expected to reach stable growth within the next year or so.

b. If a stock has a required rate of return rs = 12% and its dividend is expected to grow at a constant rate of 5%, this implies that the stock's dividend yield is 5%.

c. The stock valuation model, P0 = D1/(rs - g), can be used for firms that have expected negative, but constant, growth rates.

d. The price of a stock is the present value of all expected future dividends, discounted at the dividend growth rate.

e. The constant growth model cannot be used for a zero growth stock, where the dividend is expected to remain constant over time.

Answer: ____________________________

6. Stock A has a required return of 10% and a price of $25, and its dividend is expected to grow at a constant rate of 7% per year. Stock B has a required return of 12% and a price of $40, and its dividend is expected to grow at a constant rate of 9% per year. Which of the following statements is CORRECT?

a. If the stock market were efficient, these two stocks would have the same price.

b. The two stocks have the same dividend yield.

c. If the stock market were efficient, these two stocks would have the same expected return.

d. The two stocks have the same expected capital gains yield.

e. The two stocks have the same expected year-end dividend.

Answer: ____________________________

7. Which of the following statements is CORRECT?

a. If a stock's beta increased but its growth rate remained the same, then the new equilibrium price of the stock will be higher (assuming dividends continue to grow at the constant growth rate).

b. Market efficiency says that the actual realized returns on all stocks will be equal to the expected rates of return.

c. Weak-form efficiency suggests that tape watchers and chartists can earn profits by discovering patterns as to when stock prices rise or fall.

d. An implication of the semi-strong form of the efficient markets hypothesis is that you cannot consistently benefit from trading on information reported in The Wall Street Journal.

e. None of the statements above is correct.

Answer: _________ ___________________

8. A stock is expected to pay a dividend of $0.75 next year. The required rate of return is rs = 12.5%, and the expected constant growth rate is g = 8.5%. What is the current stock price?

a. $17.82

b. $18.28

c. $18.75

d. $19.22

e. $19.70

Answer: _________ ___________________

9. If D1 = $1.25, g (which is constant) = 5.5%, and P0 = $44, what is the stock's expected total return for the coming year?

a. 7.54%

b. 7.73%

c. 7.93%

d. 8.13%

e. 8.34%

Answer: ____________________________

10. Gary Wells Inc. plans to issue perpetual preferred stock with an annual dividend of $6.50 per share. If the required return on this preferred stock is 6.5%, at what price should the stock sell?

a. $90.37

b. $92.69

c. $95.06

d. $97.50

e. $100.00

Answer: __________ __________________

11. The Isberg Company just paid a dividend of $0.80 per share, and that dividend is expected to grow at a constant rate of 6.00% per year in the future. The company's beta is 1.25, the market risk premium is 5.00%, and the risk-free rate is 4.00%. What is the company's current stock price?

a. $19.95

b. $20.45

c. $20.96

d. $21.49

e. $22.02

Answer: ____________ ________________

12. The Nikko Company's last dividend was $1.50. The dividend growth rate is expected to be constant at 15% for 3 years, after which dividends are expected to grow at a rate of 6% forever. If Nikko's required return (rs) is 11%, what is the company's current stock price?

a. $36.69

b. $37.82

c. $38.99

d. $40.20

e. $41.40

Answer: ____________________________

13. Which of the following is NOT a capital component when calculating the weighted average cost of capital (WACC)?

a. Long-term debt.

b. Accounts payable.

c. Retained earnings.

d. Common stock.

e. Preferred stock.

Answer: ____________ ________________

14. For a typical firm, which of the following sequences is CORRECT? All rates are after taxes, and assume the firm operates at its target capital structure.

a. re > rs > WACC > rd.

b. rs > re > rd > WACC.

c. WACC > re > rs > rd.

d. rd > re > rs > WACC.

e. WACC > rd > rs > re.

Answer: __________ __________________

15. You were hired as a consultant to Kroncke Company, whose target capital structure is 40% debt, 10% preferred, and 50% common equity. The after-tax cost of debt is 6.00%, the cost of preferred is 7.50%, and the cost of retained earnings is 13.25%. The firm will not be issuing any new stock. What is its WACC?

a. 9.48%

b. 9.78%

c. 10.07%

d. 10.37%

e. 10.68%

Answer: _________ ___________________

16. Schadler Systems is expected to pay a $3.50 dividend at year end (D1 = $3.50), the dividend is expected to grow at a constant rate of 6.50% a year, and the common stock currently sells for $62.50 a share. The before-tax cost of debt is 7.50%, and the tax rate is 40%. The target capital structure consists of 40% debt and 60% common equity. What is the company's WACC if all equity is from retained earnings?

a. 8.35%

b. 8.70%

c. 9.06%

d. 9.42%

e. 9.80%

Answer: _________ ___________________

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