Chapter 9 Valuation of Common Stock

1. Reading Stock Listings pp. 235 New York Stock Exchange Listing 52 Weeks

Hi Lo Stock Sym Div Yid% P/E Vol100s Hi Lo Close Net Chg -- -- -- -- -- -- -- -- - - -- --

-cont’

2. The Discounted Dividend Model (DDM) ☆A discounted dividend model (DDM) the model that computes the value of a share of stock as the

present value of its expected future CF. ☆ risk – adjusted discounted rate (market capitalization rate) the expected rate of return that investors require in order to b

e willing to invest in the stock. ☆ the expected rate of return that investors require, E(r):

kP

PPDrE

t

ttt

1

1)()(

--cont’ ☆-- A general valuation (pricing) model Based on above formula, we got:

1

33

221

0

2221

221

110

332

221

110

)1(

)1()1()1(1

)1(111

1

1

1

1

tt

t

nn

k

D

k

D

k

D

k

D

k

DP

k

PD

k

D

kkPD

D

k

PDP

k

PDP

k

PDP

k

PDP

--cont’

☆-- Zero Growth: g=0 As n→∞ ,

D1=D2=D3=······=D

P0=D / k

☆-- Constant Growth :g≠0D1=D0(1+g)

D2=D1(1+g)=D0(1+g)2

D3=D2(1+g)=D0(1+g)3 ······ ······ ······ ······

Dt=D1(1+g)t-1

--cont’

in general, we have: Pt=Dt+1 / (k-g)

☆ Question: XYZ stock is expected to pay a dividend of $2 per share a year from now, and its dividends are expected to grow by 6% per year thereafter. If its price is now $20 per share,what must be the market capitalization rate? 　 ( K= D1 / P0 + g )

gk

D

k

g

k

D

k

gD

k

DP

t

t

tt

t

tt

t

1

1

11

1

11

10

)1

)1(

)1(

)1(

)1(

)1(

--cont’ Valuing an Erratic-Growth Stock

Suppose: expected dividend growth varies for n periods but is constant at g forever after that. At time n, the next dividend is Dn+1=(1+g)Dn. Using above formula, the stock’s value at n is:

then we got P0 of stock:

gk

Dg

gk

DP nnn

)1(1

)()1(

)1(

)1()1()1(1

)1()1()1()1(1

33

221

33

221

0

gkk

Dg

k

D

k

D

k

D

k

D

k

P

k

D

k

D

k

D

k

DP

nn

nn

nn

nn

3. Earnings and Investment Opportunities

another approach to DCF valuation focuses on future earnings and investment opportunities. This helps to concentrate the analyst’s attention on the core business determinants of value. formula:

P0=E1/k + NPV of future investment opportunities

Example1 pp.239-241

1110 )1()1()1( t

tt

tt

t

tt

t

ttt

k

I

k

E

k

DP

NetIED

--cont’

Generalize E1 = earnings per shares without reinvestment

RI = rate of return on new investment

r = retention ratio g=Earnings retention rate×Rate of return on new investment

= r × RI

k= capital cost (market capitalization rate)

IRrk

rE

gk

rEP

)1()1( 11

0

--cont’

example 2 Quick check 9-2 pp.241, 250 E 1= $10 per shares RI = 18% r = 75% g = r × RI = 75% × 18% = 13.5% k= 15% without retention : P0=E1/ k =10 / 15% =$66.67 with retention : P0=D1/(k-g)=$10×25% / (15%-13.5%) =$166.67 NPV of future investment is the difference between th

e two values: $166.67- $66.67 = $100

4. Price/Earnings Multiple Approach

Growth stock stock’s future investments are expected to earn rates of return in excess

of the market capitalization rate. So it has relatively high P/E ratios. This stock are called Growth stock.

Why does stock’s price (P/E) much higher ? 　 → investors’ expectation (beliefs: investment opportunities better than

others) → market demand (also result from expectation)

P/E ratios tend to vary over time relatively small changes in expected growth rates of earnings o

r capitalization rates can result large changes in P/E ratios.

5. Dividend Policy

Dividend policy -- Company’s decision to payout a portion of its earnings to its s

hareholders in cash. -- A dividend policy involves a trade-off among cash dividend, c

apital budgeting, and capital structure. Whether does the dividend policy trade-off affect the value of the company?

-- irrelevant or relevant : dividend policy doesn’t matter in a perfect capital market environment. But dividend policy is relevant in imperfect capital market (in practice) .the empirical evidence shows consistent patterns of dividend policy,and shows significant average stock price reactions to dividend changes.

--cont’

Cash dividend and share repurchases -- cash dividend -- payout ratio: the ratio of cash dividend paid to earning

s -- ex-dividend ( 除息 ): P = P0 – dividend per share

-- share repurchases -- example1 pp.243-244 -- example2 Quick check 9-3, pp.243,250

--cont’

Stock dividend -- stock splits -- stock dividends (DR) -- example cash dividends vs. stock dividends pp. 245 - 246

endstockdivid

iceice before

after %1

PrPr

--cont’ MM theorem

-- In a frictionless financial market environment, in which there are no taxes, no costs of issuing new shares of stock or repurchasing existing shares, a firm’s dividend policy can have no effect on the wealth of its current shareholders.

-- some strict hypothesis Dividend policy in real world

income taxes, regulation, costs of external finance, informational content of dividends.