Chapter 7



Chapter 7

Problems and Solutions

1. Murphy Motors, Inc. has just set the company dividend policy at $0.50 per year. The company plans on being in business forever. What is the price of this stock if

a. An investor wants a 5% return?

b. An investor wants an 8% return?

c. An investor wants a 10% return?

d. An investor wants a 13% return?

e. An investor wants a 20% return?

SOLUTION: Use the constant dividend infinite dividend stream model:

Price = Dividend / r

a. Price = $0.50 / 0.05 = $10.00

b. Price = $0.50 / 0.08 = $6.25

c. Price = $0.50 / 0.10 = $5.00

d. Price = $0.50 / 0.13 = $3.85

e. Price = $0.50 / 0.20 = $2.50

2. Rice Electronics wants its shareholders to earn a 15% return on their investment in the company. At what price would the stock need to be priced today if Rice Electronics had the following cash dividend policy:

a. $0.25 constant annual dividend forever?

b. $1.00 constant annual dividend forever?

c. $1.75 constant annual dividend forever?

d. $2.50 constant annual dividend forever?

SOLUTION: Use the constant dividend infinite dividend stream model:

Price = Dividend / r

a. Price = $0.25 / 0.15 = $1.67

b. Price = $1.00 / 0.15 = $6.67

c. Price = $1.75 / 0.15 = $11.67

d. Price = $2.50 / 0.15 = $16.67

5. King Waterbeds has an annual cash dividend policy that raises the dividend each year by 4%. Last year’s dividend was $0.40 per share. What is the price of this stock if

a. An investor wants a 5% return?

b. An investor wants an 8% return?

c. An investor wants a 10% return?

d. An investor wants a 13% return?

e. An investor wants a 20% return?

SOLUTION: Use the constant growth dividend model with an infinite dividend stream:

Price = Last Dividend x (1 + g) / (r – g)

a. Price = $0.40 x (1.04) / (0.05 – 0.04) = $0.4160 / 0.01 = $41.60

b. Price = $0.40 x (1.04) / (0.08 – 0.04) = $0.4160 / 0.04 = $10.40

c. Price = $0.40 x (1.04) / (0.10 – 0.04) = $0.4160 / 0.06 = $6.93

d. Price = $0.40 x (1.04) / (0.13 – 0.04) = $0.4160 / 0.09 = $4.62

e. Price = $0.40 x (1.04) / (0.20 – 0.04) = $0.4160 / 0.16 = $2.60

6. Seitz Glassware is trying to determine its growth rate for it’s an annual cash dividend. Last year’s dividend was $0.25 per share. The target return rate for the stock is 10%. What is the price of this stock if

a. The annual growth rate is 1%?

b. The annual growth rate is 3%?

c. The annual growth rate is 5%?

d. The annual growth rate is 7%?

e. The annual growth rate is 9%?

SOLUTION: Use the constant growth dividend model with an infinite dividend stream:

Price = Last Dividend x (1 + g) / (r – g)

a. Price = $0.25 x (1.01) / (0.10 – 0.01) = $0.2525 / 0.09 = $2.81

b. Price = $0.25 x (1.03) / (0.10 – 0.03) = $0.2575 / 0.07 = $3.68

c. Price = $0.25 x (1.05) / (0.10 – 0.05) = $0.2625 / 0.05 = $5.25

d. Price = $0.25 x (1.07) / (0.10 – 0.07) = $0.2675 / 0.03 = $8.92

e. Price = $0.25 x (1.09) / (0.10 – 0.09) = $0.2725 / 0.01 = $27.25

9. Mulder Fashions expects the following dividend pattern over the next seven years:

|Year 1 |Year 2 |Year 3 |Year 4 |Year 5 |Year 6 |Year 7 |

|$1.00 |$1.10 |$1.21 |$1.33 |$1.46 |$1.61 |$1.77 |

Then the company will have a constant dividend of $2.00 forever. What is the price of this stock today if an investor wants to earn

a. 15%?

b. 20%?

SOLUTION: This stock can be valued using a two-stage model. During the first stage, we must find the present value of the dividends individually.

In the second stage, we can use the Gordon growth model (constant growth model to find P7, which represents the cash flows in this stage. The first dividend in the second stage is D8 ($2).

a. The price today for this stock with a required rate of return of 15% is calculated in the following way:

In the second stage, dividends are $2 forever, therefore g = 0 and P7 is: [pic]

Therefore, the price today is:

[pic]

b. The price today for this stock with a required rate of return of 20% is calculated in the following way:

In the second stage, dividends are $2 forever, therefore g = 0 and P7 is: [pic]

Therefore, the price today is:

[pic]

11. Huber Athletic Club is going to offer preferred stock to its members with the following characteristics; par value is $100 and annual dividend rate of 6%. If a member wants the following returns, what price should he be willing to pay:

a. Brad wants a 10% return.

b. Mike wants a 12% return

c. Rick wants a 15% return

d. Julius wants a 18% return

SOLUTION: Use the constant dividend model with finite horizon

Price = Dividend / r

a. Brad’s Price = $100 x 0.06 / 0.10 = $60.00

b. Mike’s Price = $100 x 0.06 / 0.12 = $50.00

c. Rick’s Price = $100 x 0.06 / 0.15 = $40.00

d. Julius’s Price = $100 x 0.06 / 0.18 = $33.33

14. Find the annual growth rate of the dividends for each of the firms listed in the table below.

| |Dividend Payment per Year |

|Year |1999 |2000 |2001 |2002 |

|TJB |1.2 |15.10% |? |? |

|MAB |0.6 |10.55% |? |? |

|PMF |0.8 |9.40% |? |? |

|CNF |1.4 |14.45% |? |? |

|SJN |0.4 |5.70% |? |? |

|GFN |1.6 |18.80% |? |? |

|JE |1.0 |11.00% |? |? |

|PE |0.0 |3.0% |? |? |

SOLUTION: First find the expected return for the stocks if the betas are correct. Compare with the listed return. For stocks where the expected return is less than the listed return, the stock is underpriced. For stocks where the expected return is greater than the listed return, the stock is overpriced.

| |Company Beta |Listed Return |Expected |Underpriced or |

|Company | | |Return |Overpriced |

|TJB |1.2 |15.10% |2.5% + 1.2 (9.25%) = 13.6% |Underpriced |

|MAB |0.6 |9.55% |2.5% + 0.6 (9.25%) = 8.05% |Underpriced |

|PMF |0.8 |9.60% |2.5% + 0.8 (9.25%) = 9.90% |Overpriced |

|CNF |1.4 |14.45% |2.5% + 1.4 (9.25%) = 15.45% |Overpriced |

|SJN |0.4 |5.70% |2.5% + 0.4 (9.25%) = 6.20% |Overpriced |

|GFN |1.6 |18.80% |2.5% + 1.6 (9.25%) = 17.30% |Underpriced |

|JE |1.0 |11.00% |2.5% + 1.0 (9.25%) = 11.75% |Overpriced |

|PE |0.0 |3.0% |2.5% + 0.0 (9.25%) = 2.50% |Underpriced |

20. Challenge Problem: Royal Seattle Investment Club is thinking of buying 100 shares of Sun-Dollar Coffee Company. The stock is currently selling for $25.00 per share. The beta of Sun-Dollar Coffee is currently listed at 1.35 by almost every rating agency and model available. If the current risk-free rate is 2.75% (yield on the one-year U.S. Treasury bill) and the market risk-premium for the coming year is estimated at 8.25% by almost every financial service, what price should Royal Seattle Investment Club expect for Sun-Dollar Coffee at the end of the year?

SOLUTION: First find the expected return using the SML equation and then multiply the current price by one plus the return to find the expected year-end price.

Expected return of Sun-Dollar Company = 2.75% + 1.35 (8.25%) = 13.8875%

End of Year Price = $25.00 x 1.138875 = $28.47

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download