ANALISIS SAHAM BIASA
(COMMON STOCK ANALYSIS)
PERTEMUAN 11-12
Topics Covered
Stocks
and their valuation

zero dividend growth

constant dividend growth

non-constant dividend growth

earning and sales based valuation methods
Stocks
Shares, securities or equities – an ownership in part of a company
 You are entitled to a portion of company’s profits and any voting rights attached to stock
 A company
 issues the stocks –shares the profits with stock holders
 sells some ownership in company (in form of stocks) to raise money (equity
financing) to use for upgrading equipment, marketing, expansion…
Profits are paid out in dividends – the more shares you own, the larger profits you own
 Common Stock

yields higher return than other forms of investment securities
 ownership in a company & a portion of profits (variable dividends)
 voting rights
 in case of bankrupt, shareholders receive no money until rest of stockholders is paid

Preferred Stock
 some degree of ownership in a company
 no voting rights
 guaranteed a fixed dividend forever
 may be callable – company has an option to purchase shares from shareholders at anytime for a
premium
 paid off before common shareholders
Stock Prices
 The
price of a stock shows what investors feel the company is worth.

Stock prices change everyday by the market – risky + many factors

Buyers and sellers cause prices to change because of supply and demand

If more people want to

buy a stock than sell it, then price moves up

sell a stock, there would be more supply than demand, price would start to fall

Many factors drive stock prices – earnings (profit) of a company

For securities issued by the company, there is uncertainty and also


no maturity date,

no dividend rate,

need to estimate expected selling price to calculate current price
Discounted Dividend Model
Stock
price is PV (future cash flows to be received by investor)
Valuation of Stocks

If investor buys a stock, he is entitled to receive all future dividends and can sell the
stock in the future
 The cash flow of common stock consists of dividends plus a future sale price
 The stock discount rate re is the rate of return that investors expect to earn on securities
with similar risk
Time
0
Cash-Flow
They
The
At
1
2 … T
…
D1
D2 … DT
…
buy stock for P0 and sell for P1 after one year and receive dividend D1, P0 
next buyer also sells after one year
time period T,
PT 1 
DT  PT
1  re
P1 
D2  P2
D
D P
 P0  1  2 22
1  re
1  re (1  re )
D1  P1
1  re
Valuation of Stocks
Using
recursive substitution, the current price of the stock is
D1
D2
D3
Dt
P0 




2
3
t
1  re (1  re ) (1  re )
(1  re )

Dt
t
(
1

r
)
t 1
e

Expression for
expected price can be neglected for a large time horizon
The
current value of the stock is the present value of all future cash flows:
dividends and expected selling price

the value of T is determined by the investor

dividends are uncertain

need to estimate the expected selling price
Required Returns
The
return on equity is sum of dividend yield and expected capital gain
D 1  P1

P0 
1  re
D1


re
P0
dividend yield
D1

P1  P0
P0
capital
gain
is not known since it is an expected value about future dividend
dividend yield –percentage return for the dividend –annual dividend per share is
divided by price per share
historic
or trailing dividend yield
prospective
dividend yield
D0
P0
D1
P0
Stock’s Value Estimation
The Zero Dividend Growth Model
If
the dividend is expected to stay constant over time,
shares
are valued like perpetual bonds
expected
return on equity is equal to dividend yield.
Assume that
D1  D2    Dn  D
P0 
Do
D
D
 re 
re
P0
not reflect reality because of constancy of dividends
Constant Dividend Growth Model

an amount grows at a constant rate forever is called a growing perpetuity

stock with a constant dividend growth is a growing perpetuity

let g be a constant dividend growth rate
D2  D1 (1  g )
D3  D2 (1  g )  D1 (1  g ) 2
D4  D3 (1  g )  D1 (1  g )3

DT  DT 1 (1  g )  D1 (1  g )T 1
current stock price
D1
D1 (1  g ) D1 (1  g ) 2
D1 (1  g )T 1
P0 




2
3
T
1  re (1  re )
(1  re )
(1  re )
Constant Dividend Growth Model

If g  re , then
The
P0 
growth rate is g 
D1
D
 re  1  g
re  g
P0
P1  P0
 P1  (1  g ) P0
P0
If
the company in steady state where dividends are expected to grow at a constant
rate g, the stock price grows at the same constant rate.
Example: Next year dividends per share for Company X is expected to be £0.95.
The dividends are expected to grow at 14% per year in the future. What should be the
current price if the required rate of return is 16% per year?
0.95
0.95(1  0.14) 0.95(1  0.14) 2
P0 


  growing perpetuity
2
3
1  0.16
(1  0.16)
(1  0.16)
0.95

 47.5
0.16  0.14
Non-constant Dividend Growth Model
If
the company is not a steady state, not possible to use the previous model
Define
sub periods with different growth rates
Estimate
the value of stock by considering each sub period with their
discounting
PV
of non-constant growth dividends at each period
n
Dk ( NC )
PV ( NCD)  
k
(
1

r
)
k 1
e
PV
of constant growth dividends PV(Pt)
Dt 1
Pt 
re  g

Value of the stock is
P0  PV ( NCD)  PV ( Pt )
Example
The next three years dividends for Company Y are expected to be £0.50, £1.00, £1.50.
Then the dividends are expected to grow at a constant 5% forever. If the required return
is 10%, then what is the value of the stock?
Non-constant dividend growth
Constant dividend growth
based on 3rd dividend
3
Dk ( NC )
k
k 1 (1  re )
PV ( NCD)  
0.50
1.00
1.50



(1  0.10) (1  0.10) 2 (1  0.10)3
 0.454  0.826  1.127  2.407
 The current price of the stock
P0  PV ( NCD)  PV ( P3 )
 2.407  23.67  26.07
P3 
D3 (1  g )
re  g
1.5(1  0.05)
 31.50
0.10  0.05
P3
PV ( P3 ) 
(1  re )3


31.50
 23.67
1.331
Example
Consider a company pays a dividend of £0.75 per share. Demand for this company’s
product is growing at 2% per year and inflation averages 2.5% per year. The company
expects its profits and dividends to grow at about 4.55% per year (1.02X1.025= 1.0455).
Stockholders require a 10% rate of return. What is the market price of this company’s
stock?
The
dividend next period is
0.75  1.0455  0.0784
Using the formula for a growing perpetuity
D1
P
re  g
0.75  1.0455
P
 14.39
0.10  0.0455
Price-Earnings (P/E) Ratio

used to price equities: a fair value of stock can be determined with the P/E multiple
 the earning yield = E1 / P0 where E1 is the earnings per share.
dividends and earnings are related via the company’s pay out policy;
explained by the pay out ratio p
D1
p
 D1  pE1
E1

required return on equity is related to earnings yield
P0
D1
E1
p
re   g  re   p  g  
P0
P0
E1 re  g

If companies have the same pay out ratio, discount rate, growth rate, they have the
same P/E ratio
Price-Earnings (P/E) Ratio
 Analysts often report historical price earning ratio P0 /E0
P0 P0
1
E1  E0 (1  g ) 

E1 E0 (1  g )
When
dividends and earnings grow at the same constant rate g from now on,
E1  E0 (1  g ),
The
D1  D0 (1  g )
required return and P / E ratio are
re 
D
D1
 g  re  (1  g ) 0  g
P0
P0
P0
P0
P0
p (1  g )
p
 (1  g )

(using

)
E0
E1
re  g
E1 re  g