978-0134730417 Chapter 7 Part 2

206 Brooks ◼ Financial Management: Core Concepts, 4e

4. Stock price. Pfender Guitars has a current annual cash dividend policy of $4.00. The price of

the stock is set to yield an 8% return. What is the price of this stock if the dividend will be

paid

a. for 10 years and then a liquidating or final dividend of $25.00?

b. for 15 years and then a liquidating or final dividend of $25.00?

c. for 40 years and then a liquidating or final dividend of $25.00?

d. for 60 years and then a liquidating or final dividend of $25.00?

e. for 100 years and then a liquidating or final dividend of $25.00?

f. forever with no repurchase of the stock?

ANSWER

Use the finite constant dividend model liquidating dividend except with f (use infinite constant

dividend model)

5. Stock price. 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 an

investor wants

a. a 5% return?

b. an 8% return?

c. a 10% return?

d. a 13% return?

e. a 20% return?

ANSWER

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

Chapter 7 ◼ Stocks and Stock Valuation 207

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

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

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

6. Stock price. Seitz Glassware is trying to determine its growth rate for an annual cash

dividend. Last year’s dividend was $0.25 per share. The stock’s target return rate is 10%.

What is the stock’s price if the annual growth rate is

a. 1%?

b. 3%?

c. 5%?

d. 7%?

e. 9%?

ANSWER

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

7. Stock price. Miles Hardware has an annual cash dividend policy that raises the dividend each

year by 3%. Last year’s dividend was $1.00 per share. Investors want a 15% return on this

stock. What is the stock’s price if the company will be in business

a. for five years and not have a liquidating dividend?

b. for fifteen years and not have a liquidating dividend?

c. for twenty-five years and not have a liquidating dividend?

d. for thirty-five years and not have a liquidating dividend?

e. for seventy-five years and not have a liquidating dividend?

f. forever?

ANSWER

Use the constant growth dividend model with a finite dividend stream:

208 Brooks ◼ Financial Management: Core Concepts, 4e

c. Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))25]

= $1.03 / 0.12 × [1 – 0.0636] = $8.58 × [0.9364] = $8.03

d. Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))35]

= $1.03 / 0.12 × [1 – 0.0211] = $8.58 × [0.9789] = $8.40

e. Price = $1.00 × (1.03) / (0.15 – 0.03) × [1 – ((1.03) / (1.15))75]

= $1.03 / 0.12 × [1 – 0.0003] = $8.58 × [0.9997] = $8.58

f. Price = $1.00 × (1.03) / (0.15 – 0.03) = $1.03 / 0.12 = $8.58

210 Brooks ◼ Financial Management: Core Concepts, 4e

g = ($1.77 / $1.00)1/6 – 1 = 1.771/6 – 1 = 10%

Next, use the finite dividend growth model

Price = Dividend × (1 + g) / (r – g) × [1 – ((1 + g) / (1 + r))n]

Chapter 7 ◼ Stocks and Stock Valuation 211

Part two: Use the constant dividend (infinite period) model and then discount the price at

period 7 back to the present

10. Stock price. Staton-Smith Software is a new up-start company and will not pay dividends for

the first five years of operation. It will then institute an annual cash dividend policy of $2.50

with a constant growth rate of 5% with the first dividend at the end of year six. The

company will be in business for 25 years total. What is the price of this stock if an investor

wants

a. a 10% return?

b. a 15% return?

c. a 20% return?

d. a 40% return?

ANSWER

Calculate the price at the beginning of the sixth year (end of the fifth year) with the finite

214 Brooks ◼ Financial Management: Core Concepts, 4e

Morse g = ($0.59 / $1.00)0.20 – 1 = –0.10 = negative 10%

Huddleston g = ($2.00 / $1.00)0.20 – 1 = 0.1487 = 14.87%

Meyer g = can only measure for the years 2014 to 2017, ($1.00 / $0.25)1/3 – 1 = 0.5874 = 58.74%

216 Brooks ◼ Financial Management: Core Concepts, 4e

This looks like a reasonable required return for a stock.

218 Brooks ◼ Financial Management: Core Concepts, 4e

2001

$0.72

Average Change 10.46%

18. Dividend growth rate. Using Yahoo! Finance, update the dividends for Johnson & Johnson

for the last ten years. Find both the arithmetic growth rate and the geometric growth rate of

the dividends. (Note: We used 2001–10 for this solution)

ANSWER

Year

Dividend

Change (percent)

2010

$2.11

$2.11 – $1.90 = $0.21 ($0.21/$1.90 = 11.05%)

2009

$1.90

$1.90 – $1.795 = $0.105 ($0.105/$1.795 = 5.85%)

2008

$1.795

$1.795 – $1.62 = $0.175 ($0.175/$1.62 = 10.80%)

2007

$1.62

$1.62 – $1.455 = $0.165 ($0.165 / $1.455 = 11.34%)

2006

$1.455

$1.455 – $1.275 = $0.18 ($0.18 / $1.275 = 14.12%)

2005

$1.275

$1.275 – $1.095 = $0.18 ($0.18 / $1.095 = 16.44%)

2004

$1.095

$1.095 – $0.925 = $0.17 ($0.17 / $0.925 = 18.38%)

2003

$0.925

$0.925 – $0.80 = $0.125 ($0.125 / $0.80 = 15.63%)

2002

$0.80

$0.80 – $0.70 = $0.10 ($0.10 / $0.70 = 14.29%)

2001

$0.70

Average Change 13.1% (Arithmetic Growth Rate)

Chapter 7 ◼ Stocks and Stock Valuation 219

INPUT 9 ? –0.55 0 1.795

KEYS N I/Y PV PMT FV

COMPUTE 13.04

19. Divided growth rate. Using Yahoo! Finance, update the dividends of Walmart for the last

ten years. Find the arithmetic growth rate and the geometric growth rate of the dividends.

(Note: We used 2001–10 for this solution)

ANSWER

Year

Dividend

Change (percent)

2010

$1.212

$1.212 – $1.092 = $0.12 ($0.12/$1.092 = 10.99%)

2009

$1.092

$1.092 – $0.952 = $0.14 ($0.14/$0.952 = 14.71%)

2008

$0.952

$0.952 – $0.88 = $0.072 ($0.072/$0.88 = 8.18%)

2007

$0.88

$0.88 – $0.672 = $0.208 ($0.208 / $0.672 = 30.95%)

2006

$0.672

$0.672 – $0.60 = $0.072 ($0.072 / $0.60 = 12.00%)

2005

$0.60

$0.60 – $0.52 = $0.08 ($0.08 / $0.52 = 15.38%)

2004

$0.52

$0.52 – $0.36 = $0.16 ($0.16 / $0.36 = 44.44%)

2003

$0.36

$0.36 – $0.30 = $0.06 ($0.06 / $0.30 = 20.00%)

2002

$0.30

$0.30 – $0.28 = $0.02 ($0.02 / $0.28 = 7.14%)

2001

$0.28

Average Change 19%