17 Feb 2015
School
Department
Course
Professor
Chapter 9: Valuing Stocks
Dividend Discount Model:
•Cash flows are risky, we discount them at the equity cost of capital
•
P0=
(
Div1+P1
1+ℜ
)
oIf current stock price less than this amount, investors buy and drives up
stock price
oIf stock price exceeded this amount, investors sell and stock price falls
Dividend Yields, Capital Gains, and Total Returns:
•rE =
¿+P1
P0 −1=Div1
P0 +P1−P0
P0
Dividend Yield + Capital Gain Rate
oTotal Return = Dividend Yield + Capital Gain Rate
oExpected total return of stock should equal expected return of other
investments available in market with equivalent risk
Multi-Year Investor:
•P0 =
Div1
1+ℜ +Div2
(1+ℜ)2+…+DivN
(
1+ℜ
)
N+PN
(1+ℜ)N
oThis is the Dividend Discount Model
Applying Dividend Discount Model:
•Constant dividend growth – simple forecast for the firm’s future dividends states
that they will grow at a constant rate, g.
•Constant dividend growth model
oP0 =
¿
ℜ−g
orE =
Div1
P0 +g
•Value of the firm depends on current dividend level, cost of equity, and growth
rate
Simple Model of Growth:
•Dividend payout ratio – the fraction of earnings paid as dividends each year
oDiv1 =
Earnings
SharesOutstanding × Dividend Payout Rate
•Assuming number of shares outstanding is constant, firms can do three things to
increase its dividend
oIncrease earnings (net income)
oIncrease dividend payout rate
oDecrease shares outstanding
•Firm can do one of two things with earnings
oPay them out to investors
oRetain and reinvest them
•Change in Earnings = New Investment x Return on New Investment
•New Investment = Earnings x Retention Rate
oRetention rate is the fraction of current earnings that the firm retains
•Earnings growth rate = Change in earnings / earnings = Retention Rate x Return
on new investment
•g = Retention Rate x Return on New Investment
oIf firm keeps retention rate constant, then growth rate in dividends will
equal growth rate of earnings
Profitable Growth:
•If firm wants to increase share price, it could cut its dividend and invest more or
cut investment and increase dividends
•The answer depends on profitability of firm’s investments
•Cutting firm’s dividend to increase investment will raise stock price only if new
investments have positive NPV
Changing Growth Rates:
•We cannot use constant dividend growth model to value a stock if growth rate is
not constant
•Young firms often have high initial earnings growth rates. During this period of
high growth, they often retain 100% of their earnings to exploit profitable
investment opportunities. As they mature, their growth slows. At some point, their
earnings exceed investment needs and they begin to pay dividends
•We cannot use constant dividend growth model directly when growth is not
constant, we can use general form of model to value a firm by applying constant
growth model to calculate future share price of the stock once expected growth
rate stabilizes
•PN = DivN+1 / rE – g
•Dividend-discount model with constant long-term growth
o
1
1 2
02
E E E E E
1
1 (1 ) (1 ) (1 )
+
= + + + + ÷
+ + + + −
LN N
N N
Div Div
Div Div
Pr r r r r g
Limitations of Dividend-Discount Model:
•There is uncertainty associated with forecasting firm’s dividend growth rate and
future dividends
•Small changes in dividend growth rate can lead to large changes in estimated
stock price
Total Payout and Free Cash Flow Valuation Models
•Share repurchases is when the firm uses excess cash to buy back its own stock
•Implications for dividend-discount model