SZABIST
Financial Management
Lecture 4
Valuation of Stocks (a)
After examining the characteristics of bonds and their valuation,
we now turn our attention towards the more common financial
asset we all know as share or stock
Faizan Ahmed
1
SZABIST
Financial Management
Equity
A Source of Financing…
• Referring back to our very first lecture where we deliberated upon the
decisions that a financial manager has to take. Amongst them, one was to
identify the sources of financing.
• During the last two lectures, we focused on debt or leverage financing; now we
will turn our attention towards equity.
• Firms when in need to raise capital or raise money sometimes opt for equity
financing. In such a case, they either issue shares of common stock or issue
preferred shares.
• Regardless of the case, the need of capital is fulfilled by resorting to this source
of capital.
Faizan Ahmed
2
SZABIST
Financial Management
Equity
Common Terminologies Used…
• Primary Market
– These are the markets in which shares or securities are issued for the very first time
by corporations.
• Secondary Market
– These are the markets in which the subsequent trading of already issued securities
take place.
• Initial Public Offering (IPO)
– IPO is referred to as the very first offering of securities or shares to the general
public.
• Examples…
Faizan Ahmed
3
SZABIST
Financial Management
Equity
Common Stock Valuation…
• Common stock represents an ownership interest in a corporation, but to a
typical investor, a share of common stock is simply a piece of paper
characterized by two features:
– It entitles its owner to dividends, but only if the company has earnings out of which
dividends can be paid, and only if management chooses to pay dividends rather
than retaining and reinvesting all the earnings.
– Stocks can be sold at some future date, hopefully at a price greater than the
purchase price. If the stock is actually sold at a price above (below) its purchase
price, the investor will receive a capital gain (loss).
• Recall the definition of fair value of financial assets, it is the present value of all
the expected cash flows. In case of stocks, what do you think will be the future
cash flows?
Faizan Ahmed
4
SZABIST
Financial Management
Equity
Common Stock Valuation…
• Depending upon the investment horizon of the investor, an investor is
generally entitled to the following two cash flows in case of stocks:
– A regular cash stream in the form of dividends;
– The payment an investor receives when he sells the stock at some future date.
• In our discussion of bonds, we found the value of a bond as the present value
of interest payments over the life of the bond plus the present value of the
bond’s face value:
Interest Interest
Interest Face Value
Value Bond 

 ... 

1
2
n
(1  Kd) (1  Kd)
(1  Kd)
(1  Kd) n
• Stock prices are likewise determined as the present value of a stream of cash
flows and the basic stock valuation equation is similar to the bond valuation
equation.
Faizan Ahmed
5
SZABIST
Financial Management
Equity
Common Stock Valuation…
• Think of yourself as an investor who buys a stock with the intention of holding
it forever. In this case, what cash flows do you think you will receive?
• In such a case, you and your heirs will only receive a stream of dividend
payments and the value of the stock today will be calculated as the present
value of an infinite stream of dividends:
Value Share
(Dividend)1 (Dividend) 2
(Dividend) n
 P0 

 ... 
1
2
(1  Ks)
(1  Ks)
(1  Ks) n
Where,
Value Share = P0 = Fair value of the share or stock;
(Dividend)1 = Dividend received at the end of this year or year 1;
(Dividend)n = Dividend received at the end of year n;
Ks = The required rate of return demanded by investors.
Faizan Ahmed
6
SZABIST
Financial Management
Equity
Common Stock Valuation…
•
What about the more typical case, where you expect to hold the stock for a finite
period and then sell it – what will be the value of P0 in this case? Would the
approach be any different?
•
To see this, recognize that for any individual investor, the expected cash flows
consist of expected dividend plus the expected sale price of the stock.
•
However, the sale price the current investor receives will depend on the dividends
some other investor expects in the future.
•
In case if the investor has a two year investment horizon, then we will have:
Value Share
(Dividend)1 (Dividend) 2 (Price) 2
 P0 


1
2
(1  Ks)
(1  Ks)
(1  Ks) 2
Where,
(Price)2 = The fair value of the stock at the end of year 2, which is actually the
present value of all the future dividends that an investor expects to
receive after year 2
Faizan Ahmed
7
SZABIST
Financial Management
Finite Investment Horizon
Examples…
• IBF stock will pay a dividend this year of PKR 2.40 per share. It is expected that
the price of the stock at the end of this year will be PKR30. Given a 13%
required rate of return, what should be the fair value of the stock today?
Value Share
(Dividend)1 (Price)1
 P0 

1
(1  Ks)
(1  Ks)1
2.40
30
Value Share  P0 

1
(1  0.13) (1  0.13)1
2.40
30
Value Share  P0 

1
(1.13) (1.13)1
Value Share  P0  28.67
Faizan Ahmed
8
SZABIST
Financial Management
Finite Investment Horizon
Examples…
• IBF has already paid a dividend of PKR2.40 last year. Based upon the historical
payout, investors expect that the stock will pay a dividend of PKR2.75 at the
end of this year and PKR3 at the end of the next year. It is also expected that
the price of the stock at the end of the next year will be PKR38. What do you
think should be its fair value today if the required rate of return is 13%?
(Dividend)1 (Dividend) 2 (Price) 2
Value Share  P0 


1
2
(1  Ks)
(1  Ks)
(1  Ks) 2
2.75
3
38
Value Share  P0 


1
2
(1  0.13) (1  0.13) (1  0.13) 2
Value Share  P0  34.54
Faizan Ahmed
9
SZABIST
Financial Management
Equity – Common Stock Valuation
The General Dividend Discount Model…
•
If we extend the holding period of an investor indefinitely then the fair value of the
stock simply becomes the present value of an infinite stream of dividends,
represented by John Burt William’s (1938) original DDM formula:
Value Share
(Dividend)1 (Dividend) 2
(Dividend) n
 P0 

 ... 
1
2
(1  Ks)
(1  Ks)
(1  Ks) n
•
While the above mentioned general dividend discount model is theoretically
correct, applying it in practice requires an accurate forecast of dividends for many
periods into the future, a task for which we rarely expect to have sufficient
information;
•
To simplify the almost impossible task of making accurate forecasts, we can use of
the following growth models:
–
–
–
–
Gordon Constant Growth Model;
Two-Stage Growth Model;
The H-Model;
Three-Stage Growth Model.
Faizan Ahmed
10
SZABIST
Financial Management
Equity – Common Stock Valuation
Gordon Constant Growth Model…
• The dividends disbursed by corporations can assume any pattern, in case of
the Gordon Constant Growth Model however, it is assumed that dividends
grow at a constant rate forever;
• In such a case, the general dividend discount model can be transformed into
the following equation:
Value Share
D0 (1  g) D0 (1  g) 2
D0 (1  g) n
 P0 

 ... 
1
2
(1  Ks)
(1  Ks)
(1  Ks) n
D0 (1  g)
Value Share  P0 
Ks - g
D1
Value Share  P0 
Ks - g
Faizan Ahmed
11
SZABIST
Financial Management
Equity – Common Stock Valuation
Gordon Constant Growth Model…
• The equation that we just arrive d at is known as the Constant Growth Model
or the Gorden Growth Model:
Value Share
D1
 P0 
Ks - g
Here,
P0 = Fair value or intrinsic value of the stock today;
D1 = D0(1+g) = Dividend expected at the end of year 1 or this year;
Ks = Investor’s required rate of return;
g = Sustainable dividend growth rate of the firm.
• The Gorden Growth Model assumes that:
– The firm expects to pay a dividend, D1, in one year;
– Dividends grow indefinitely at a constant rate, g (Which may be less than zero);
– The growth rate, g, is less than the investor’s required rate of return.
Faizan Ahmed
12
SZABIST
Financial Management
Equity – Common Stock Valuation
Gordon Constant Growth Model…
• ABC Food Products just paid a dividend of PKR1.15. Its stock has a required
rate of return of 13.4%, and investors expect the company to grow at a
constant 8% in the future. What do you think should be the price of its stock
today?
• DEF Potato Chips paid a PKR1 per share dividend yesterday. You expect the
dividend to grow steadily at a rate of 4 percent per year.
–
–
–
–
What is the expected dividend in each of the next 3 years?
If the discount rate is 12 percent, at what price will the stock sell?
What is the expected price of the stock 3 years from now?
If you buy the stock and plan to hold it for 3 years, what payments will you receive?
What is the present value of those payments?
Faizan Ahmed
13
SZABIST
Financial Management
Equity – Common Stock Valuation
Multi-Stage Growth Models…
•
For most companies, the underlying assumption of the Gordon Growth Model that
dividends are expected to grow at a constant rate forever is unrealistic;
•
Owing to the competitive advantages they have developed or patents/trademarks
they hold, corporations experience substantially higher growth rates for shorter
periods. Subsequently as the market forces catches up, the growth rate of the firm
decreases and stabilizes at a sustainable level. This illustration emphasizes upon
two periods of different growth rates clearly deviating from the assumption laid
down by the Gorden Growth Model;
•
Similarly, we can develop multistage growth models depending upon the stages of
growth we expect the firm to experience. However, it should be kept in mind that
the appropriate model is the one which closely resembles the company’s expected
pattern of growth;
•
Regardless of the stages we have included in our model, keep in mind that we are
still forecasting dividends into the future and discounting them back to gauge the
fair value of the share.
Faizan Ahmed
14
SZABIST
Financial Management
Equity – Common Stock Valuation
The Two-Stage Dividend Discount Model…
• The most basic multistage model is a two-stage dividend discount model which
assumes that the company grows at a higher rate for a relatively short period
(The first stage) and then reverts back to a sustainable perpetual growth rate
(The second stage);
• An illustration in which the two-stage model would apply is a situation in which
a company has a patent that will expire after a certain number of years. For
example, suppose a firm is expected to grow at 15% until the expiry of its
patents in another 4 years then the firm is expected to revert to a long-term
growth rate of 3% in perpetuity. The stock of this company should be modeled
by a two-stage model with dividends growing at 15% until the expiry of patents
and then at 3% forever (See pictorial in the next slide).
Faizan Ahmed
15
SZABIST
Financial Management
Equity – Common Stock Valuation
15%
3%
Dividend Growth Rate (g)
The Two-Stage Dividend Discount Model…
Stage 1
Stage 2
Time
Faizan Ahmed
16
SZABIST
Financial Management
Equity – Common Stock Valuation
The Two-Stage Dividend Discount Model…
• Under the two-stage dividend discount model, the formula to calculate the fair
value of the share is:
Value Share
Here,
P0
D0
Ks
t
gs
gL
Faizan Ahmed
D0 (1  gS )1
D0 (1  g S ) t D0 (1  g S ) t (1  g L )
 P0 
 ... 

1
t
(1  K S )
(1  K S )
(1  K S ) t (K S  g L )
= Fair value or intrinsic value of the stock today;
= Last dividend paid by the company;
= Investor’s required rate of return;
= Length of the high growth period (In years);
= Short-term dividend growth rate;
= Long-term dividend growth rate.
17
SZABIST
Financial Management
Equity – Common Stock Valuation
The Two-Stage Dividend Discount Model…
• GHI Recreation just paid a dividend of PKR 1 per share. An analyst forecasts
that because of being the first entrant in the market, the company is currently
experiencing a growth rate of 20% which is expected to continue for another 5
years. However as competition mounts, the growth rate of the company is
expected to fall down to a sustainable level of 8%. If investor demands a return
of 18%, what do you think is the fair value of the stock today?
• JKL Distributors is a startup firm and currently pays no dividends. The company
recently reported earnings of PKR 1.50 per share which are expected to grow
at a rate of 15% for the next four years. It is in year 5 however, JKL is expected
to distribute 20% of its earnings in the form of dividends. The dividends are
then expected to grow at a constant rate of 5% forever. Calculate the fair value
of the stock if the required rate of return is 15%.
Faizan Ahmed
18
SZABIST
Financial Management
Equity – Common Stock Valuation
The H-Model…
• The problem with the basic two-stage dividend discount model is that it is
usually unrealistic to assume that a stock will experience high growth for a
short period and then the growth rate immediately falls to a sustainable level;
• The H-Model overcomes the drawback and uses a more realistic phenomenon.
In this model, the growth rate starts out high and then linearly declines over
the high-growth stage until it reaches the sustainable level;
• For example, consider a firm that generates high profit margins because of the
little competition it faces in the industry and is experiencing a growth rate of
18%. However, it is expected that as competitors enter the market the growth
rate of the firm will decline by 3% every year until it reaches 6% at the end of
the fourth year when the industry matures and growth rate stabilizes (See
pictorial in the next slide).
Faizan Ahmed
19
SZABIST
Financial Management
Equity – Common Stock Valuation
18%
6%
Dividend Growth Rate (g)
The H-Model…
Stage 1
Stage 2
Time
Faizan Ahmed
20
SZABIST
Financial Management
Equity – Common Stock Valuation
The H-Model…
• Under the H-Model, the general dividend discount model transforms into the
following equation:
Value Share
Here,
P0
D0
Ks
H
gs
gL
Faizan Ahmed
D0 (1  g L ) D0 H (gS  g L )
 P0 

(K S  g L )
(K S  g L )
= Fair value or intrinsic value of the stock today;
= Last dividend paid by the company;
= Investor’s required rate of return;
= (T/2) = Half-life (In years) of the high growth period;
= Short-term growth rate;
= Long-term growth rate.
21
SZABIST
Financial Management
Equity – Common Stock Valuation
The H-Model…
• MNO Foods just paid a dividend of PKR 2 per share. The growth rate of the
firm, which is currently 20%, is expected to decline linearly over the next 10
years to a stable growth rate of 5%. If the required rate of return is 19%, what
is the fair value of the stock?
• PQR Consultants paid of dividend of PKR 1.50 per share last year. Because of
the patent it owns, the company is currently experiencing a growth rate of 25%
which is expected to decline linearly over a period of 5 years to the long-term
growth rate of 5%. Calculate the fair value of the stock if the required rate of
return is 15%.
Faizan Ahmed
22
SZABIST
Financial Management
Equity
The Sustainable Growth Rate…
• The sustainable growth rate of the firm repeatedly mentioned in various
valuation models is primarily dependent upon the following two factors:
– The amount of earning the company retains and reinvests;
– The rate of return the company earns on its equity (ROE).
• So, mathematically the sustainable growth rate is:
g  Return on Equity  Retention Rate
 Net Income   Retained Earnings 
g



Total
Equity
Net
Income



 Net Income  
Dividends 
g
 1 


Total
Equity
Net
Income


 
Faizan Ahmed
23
SZABIST
Financial Management
Equity
Valuation of Preferred Stock…
• A preferred stock is a hybrid, that is, it possesses certain characteristics of a
bond and certain characteristics of a common stock.
• Like bonds, preferred stock has a par value and a fixed amount of dividends
that must be paid before dividends can be paid on the common stock.
• As noted above, a preferred stock entitles its owners to regular, fixed dividend
payments which lasts forever. So, preferred stock in essence is nothing but an
example of a perpetuity where the value of the preferred stock today is:
Value Share  P0 
Dp
Kp
Where,
Dp = Dividends paid by the preferred stock
Kp = The required rate of return on the preferred stock
Faizan Ahmed
24
SZABIST
Financial Management
Equity
Components of Total Expected Return…
• In case of common stock, an investor expects to generate return in the
following two forms:
– Periodic payments that the investor receives;
– Capital gain that the investor expects to book upon selling the stock.
• Based upon the two sources of return, the total return of the stock can be
represented as:
Total Return  Dividend Yield  Capital Gains Yield
 Dividends   Capital Gains 
Total Return  



Begining
Price
Beginning
Price

 

Faizan Ahmed
25
SZABIST
Financial Management
Stock Valuation
A Few Examples…
•
How can we say that price equals the present value of all future dividends when
many actual investors may be seeking capital gains and planning to hold their
shares for only a year or two? Explain.
•
FM Products has issued preferred stock with an annual dividend of PKR8 that will
last forever.
– If the discount rate is 12%, at what price should the preferred stock sell?
– At what price should the stock sell 1 year from now?
•
FM Cosmetics will pay a year-end dividend of PKR3 per share. Investors expect the
dividend to grow at a rate of 4 percent indefinitely.
– If the stock currently sells for PKR30 per share, what is the required rate of return on the
stock?
– If the expected rate of return on the stock is 16.5%, what is the stock price?
•
FM Industries pays a dividend of PKR2 per quarter. The dividend yield on its stock is
reported at 4.8 percent. What price is the stock selling at?
Faizan Ahmed
26