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