# AFM 273 Chapter 7: C7 Valuing Stocks

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4 Nov 2016
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Chapter 7 1
C7: Valuing Stocks
7.1 The Dividend Discount Model
Law of one price implies that to value any security, we must determine the expected cash
flows an investor will receive from owning it
Dividend discount model: how to value a stock
Consider the cash flows for an investor in a 1 year stock
Time line for Investment
Future dividend payment and stock price in the timeline above are not known with certainty (Based
on investor's expectations at the time the stock is purchased)
The investor will be willing to pay a price today up to the point that this transaction has a 0
NPV (current price = PV of expected future dividend and sale price)
Since cash flows are risky, cannot discount them using the risk-free interest rate, use equity
cost of capital rE
Equity cost of capital rE: expected return of other investments available in the market with
equivalent risk to the firm's shares
If the current stock price were less than this amount, positive NPV investment opportunity
(investors rush in buy it, drive up price)
If stock price exceeded this amount, selling it would have a positive NPV and stock price
would fall
Dividend Yields, Capital Gains, Total Returns
Investor who buys this prototypical stock receives returns in the form of dividends and capital
gains
Dividend yield: expected annual dividend/current price, % return investors expects to earn
from the dividend paid by the stock
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Chapter 7 2
Capital gain: investor will earn on the stock, difference between expected sale price and
purchase price for the stock, P1-P0
Capital gain rate: capital gain/current stock price, % return of capital gain
Total return: dividend yield + capital gain rate, expected return that the investor will earn
for a one-year investment in the stock
Expected total return of the stock should equal the expected return of other
investments available in the market with equivalent risk
o Firm must pay shareholders a return commensurate with the return they can earn
elsewhere while taking the same risk
If the stock offered a higher return than other securities with the same risk,
investors would sell those other investments and buy the stock instead, to drive
up the stock's current price, lower dividend yield and capital gain rate
If stock offered a lower expected return, investors would sell the stock and drive
down its price
Ex. suppose you expect ABC stock to have Div1 = \$1.80 and P1 = \$63. Investments with
similar risk to ABC have an expected return of 8%. What is the most you would pay today
for ABC stock? What dividend yield and capital gain rate would you expect?
P = (1.80 + 63)/ 1.08 = \$60.0 (most you would pay)
Dividend yield = 1.80 /60 = 3%
Capital gain = 63 - 60 = \$3
Capital gain rate = 3/60 = 5%
Longer Horizons: A multiyear Investor
Receive dividends in both year 1 and year 2 before selling the stock
For an arbitrary horizon n, the dividend discount model for today's stock price is:
Formula above applies to an n-year investor (who receives dividends for n years and then
sells), or to investors who hold for shorter periods before selling
Formula holds for any horizon n, so all investors with the same beliefs attach the same value
to the stock, regardless of their investment horizons
7.2 Applying the Dividend-Discount Model
Constant Dividend Growth
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Chapter 7 3
Implies that the stock price today is the PV of all the expected future dividends it will pay
A common approximation used to estimate future dividends is to assume a long run constant
growth G
this implies that the firm’s share price increases with its current dividend Div1 and its long
run growth rate g
however, there is a trade off: investment is needed to pay for growth, but money spent on
investment cannot be used to pay current dividends
Dividend payout rate: fraction of its earnings paid out as dividends
3 ways to increase dividends per share:
1. Increase earnings
2. Increase dividend payout rate
3. Reduce number of shares outstanding
Assume for now that the firm keeps its number of shares outstanding constant. for simplicity,
suppose that the firm will maintain its current level of earnings if it makes no investments and that
all increases in future earnings are due to investments made with
retained earnings. Firm can do 1 of 2 things with its earnings
1. Pay them out to investors
2. Retain and reinvest: increase its future dividends
Changes in earnings = new investment * return on new investment
New investment = earnings * retention rate (fraction of current earnings that the firm
retains)
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