# ADMS 3530 Chapter Notes - Chapter 7: American Electric Power, Net Income, Efficient-Market Hypothesis

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Solutions to Chapter 7

1. No. The dividend discount model allows for the fact that firms may not currently

pay dividends. As the market matures, and Research in Motion’s growth

opportunities moderate, investors may justifiably believe that Research in Motion

will enjoy high future earnings and will pay dividends then. The stock price today

can still reflect the present value of the expected per share stream of dividends.

2. Dividend yield = Expected dividend/Price = DIV1/P0

So: P0 = DIV1/dividend yield

P0 = $2.4/.08 = $30

3. a. The typical preferred stock pays a level perpetuity of dividends. The expected

dividend next year is the same as this year’s dividend, $8. Thus the dividend

growth rate is zero and the price today is:

P0 = D1/r = 8/.12 = $66.67

b. The expected dividend in two years is this year’s dividend, $8.

P1= D2/r = 8/.12 = $66.67

c. Dividend yield = $8/$66.67 = .12 =12%

Expected capital gains = 0

Expected rate of return = 12%

4. r = DIV1/P0 + g = 8% + 5% = 13%

5. The value of a common stock equals the present value of dividends received out

to the investment horizon, plus the present value of the forecast stock price at the

horizon. But the stock price at the horizon date depends on expectations of

dividends from that date forward. So even if an investor plans to hold a stock for

only a year for two, the price ultimately received from another investor depends

on dividends to be paid after the date of purchase. Therefore, the stock’s present

value is the same for investors with different time horizons.

6. a. P0 = ⇒ r = + g

r = $3/$30+ .04 = .14 = 14%

b. P0 = 3.00/(.165 − .04) = $24

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7. The dividend yield is defined as the annual dividend (or the annualized current

dividend) divided by the current price. The current annual dividend is

($2 × 4) = $8 and the dividend yield is:

DIV1/P0 = .048 ⇒$8/ P0 = .048 ⇒ P0 = $8/.048 = $166.7

To work with the quarterly dividend, divide the dividend yield by 4 and repeat the

above steps:

Quarterly DIV/P0 = .048/4 = .012 ⇒ $2/ P0 = .012 ⇒ P0 = $2/.012 = $166.7

8. Weak, semi-strong, strong, fundamental, technical

9. True. The search for information and insightful analysis is what makes investor

assessments of stock values as reliable as possible. Since the rewards accrue to the

investors who uncover relevant information before it is reflected in stock prices,

competition among these investors means that there is always an active search on for

mispriced stocks.

10. Two such behavioral biases are alluded to in the text.

a.) Attitudes toward risk: Psychologists have observed the tendency of investors to be

particularly averse to the possibility of incurring losses. Consequently, when investors

sustain a loss they tend to exercise excessive conservatism in their subsequent

investment decisions to avoid worsening their deficit. Conversely, when investors have

secured a gain they are more eager to take on risky bets because they take comfort in

their cushion of profit. This behavioral bias has been implicated as a cause of stock

market “bubbles”: a phenomenon where market prices far exceed intrinsic firm values.

b.) Beliefs about probabilities: This bias is twofold. Firstly, investors tend to look at

previous periods and assume that future market fluctuations will follow suit. This is

incorrect since stock prices follow a random walk and ought to be independent of

previous market movements. To further compound their error, investors tend to be

myopic and place greater emphasis on recent market developments; as such, they

overlook valuable information from the distant past (i.e. market reactions to long-term

economic cycles). Secondly, investors tend to fall prey to overconfidence. When

investors profit in the market they wrongly attribute their success to skill rather than

mere luck. Such excessive optimism may cause prices to greatly deviate from intrinsic

share values.

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11. a. DIV1 = $1 × 1.04 = $1.04

DIV2 = $1 × 1.042 = $1.0816

DIV3 = $1 × 1.043 = $1.1249

b. P0 = DIV1/(r − g) = = $13

c. P3 = DIV4/(r − g) = = $14.6237

Note: the number of decimal places carried affects the solution. If you used this

formula the answer would be:

P3 = DIV4/(r − g) = = $14.623232, about $14.6232

d. Your payments are:

Year 1 Year 2 Year 3

DIV 1.04 1.0816 1.1249

Sales Price 14.6237

Total cash flow 1.04 1.0816 15.7486

PV of cash flow .9286 .8622 11.2095

Sum of PV = $13.00, the same as your answer to (b).

12. Dividend growth rate, g = return on equity × plowback ratio:

g = .15 × .40 = .06

r = + g = + .06 = .16 = 16%

13. a. P0 = = (3 x 1.05) / (0.15 - 0.05) = $31.50

b. P0 = (3 x 1.05) / (0.12 – 0.05) = $45

The lower discount rate makes the present value of future dividends higher,

raising the value of the stock.

c. P0 = (3 x (1 – .05) / (.15 – (-.05)) = $14.25

The price is the present value of the future dividends before they are eroded by

the negative growth rate.

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