financial economics
Financial Economics (FS6061)
Net present value and capitalization
(valuation) models
Introduction
Valuation model is a
mechanism to convert a set of forecasts of, or to observe, a series of company
and economic variables into a forecast of market value for the company`s stock.
In this model we take input in terms of economic variables such as dividends,
futures earning, variability of earnings, interest rate etc. and the output is
in terms of expected market value or expected return from the stock variables.
Valuation model helps to describe the relationship that is assumed to exist
between a set of economic and corporate factors and the valuations of these
factors in market.
The use of valuation
models in investment decisions are based upon the perception that markets are
inefficient and assumption about how and when these inefficiencies will get
corrected. Nowadays every financial organization employs a valuation model and
with this model they make their financial decisions.
Valuation Models
1) Liquidation
value
1) Equity and firm
1) Option to delay
2) Replacement
Cost
2) Sector and market
2) Option to expand
3) Option to liquidate
1) Equity
valuation model(Dividend and free cash flow to firm)
2) Firm
valuation model (Cost of capital, AVP approach, and excess return model.)
Discounted cash flow
model (DCF)
According to discounted
cash flow approach the value of share of stock is equal to the present value of
the cash flow that shareholders are expected to receive from it. The concept of
DCF valuation is based on the principle that the value of a business is
inherently based on its ability to generate cash flows for the shareholders or
investors.
Key components of DCF
model
1)
Free cash flow (cash generated by the
assets of business available for shareholders)
2)
Terminal value (value at the end of the
free cash flow projection)
3)
Discount rate (the rate used to discount
the projected free cash flow and terminal value to their present values)
Let’s
see one example to be clear on above discussions:
According
to DCF approach value of shares is equal to the present value of its expected
cash flows.
Let
us assume if a stock is held for one period (t), then cash flows received from
stock are dividend (d) and the value of stock when sold is Pt+1,
then
(1+K) (1+K)
Where, Pt=
the price of share at time t/ current price of share
Dt+1=the dividend received at time t+1/
last year dividend
Pt+1=
the price at period t+1
K= the
appropriate discount rate
This
is the case for one period if we will hold stock more than a period suppose for
3 year, then
(1+K) (1+K) ² (1+K) ³
(1+K)³
The
DCF equation can be employed in three ways:
1)
Pt can be treated as an unknown
2)
K can be treated as an unknown
3)
Converted to a price earnings
ratio.
Dividend stream: This
model is typically the DCF using dividend forecasts over several stages. Under
this model it is necessary to forecast the growth rate in dividend each year. A
number of different assumptions about the growth rate patterns are made in this
model. In particular we examine three sets of growth assumption. They are:
a)
Zero growth (assume constant dividend).
b)
Constant growth in dividend
c)
Super normal growth (growth for a finite
number of years at a constant rate, followed by a period during which growth
declines to a steady and remains the same.)
Now, we will examine
these three DCF dividend model in brief.
Zero growth
In the case of zero
growth in dividend, the company pays a fix and constant amount of dividend
every year, there will be no change in dividend paid in 1st year and
2nd year or any year.
Let us assume the
constant dividend amount be $ D, then,
dividend paid last
year(Do)= $D
dividend expected at
the end of year 1(D1)= $D
dividend expected at
the end of 2nd year(D2)= $ D
Since the dividend is
always the same with cash flow equal to $D, therefore price of share is given
as:
Po= D/r
where, r= required rate
of return
D= constant dividend per year
Po= Price of share
Example, CASIO Company
has policy of paying $ 20 per share as dividend every year. If this policy is
to be continued indefinitely, what is the value of the share of the stock if
required rate of return of the investment is 18%.
Solution:
We are given that,
D=$ 20
r= 20% or (0.2)
Present value per share
(PO) = 20/0.2
= $ 100
Constant growth in
dividend
In the case of constant
growth rate the dividend for company always grow at a steady rate. Suppose the
dividend growth rate of company is g% then it will be the same rate for
indefinite future. The price of share in constant growth rate can be calculated
as:
PO= D1/r-g
We can write D1= DO (1+g)
D1=dividend at year 1
g= growth rate of dividend
DO= dividend paid at year 0 (just
paid dividend)
The above equation of
constant growth model can be interpret as, the price of share should be equal
to next year`s dividend divided by the difference between appropriate discount
rate for the stock and its expected long term growth rate.
Example, A company has
just paid dividend of $0.8 and is expected to exhibit of growth rate of 12%
into the indefinite future and expected rate of return on investment is 15%.
What is the value of stock?
Solution
We are given that,
DO= 0.8$
g= 12%
r= 15%
The present value of
share (PO) = D1/r-g
= DO (1+g)/r-g
=0.8(1+0.12)/0.15-0.12
=$29.867
Super normal growth
model (two- period growth)
In this case, it is
assumed that irregular amounts of dividend are paid during the first few years
and then followed by a constant growth rate. Assumption of growth to be constant
after some period of time is followed by the reasoning like after some period
of time the firms are not differentiate on the basis of growth. The firms with
higher growth will no longer have high growth and firm with less growth can
generate high growth in future. Thus after some years, it is sensible not to
differentiate between firms but simply to assume they all grow at same rate.
The price of share in
super normal growth can be calculated as:
(1+r) (1+r)² (1+r)ⁿ (1+r) ⁿ
r-g
Example, A company is
expected to pay dividend $ 0.10 per share in 1st year, $0.20 in 2nd
year and $0.25 per share in third year. After third year the dividend will grow
at a constant rate of 5% per year. The required rate of return for your
investment is 10% per year. What is price of share now?
Solution,
From question we are
given that,
Dividend for 1st
year (D1) = $0.10
Dividend for 2nd
year (D2) = $0.20
Dividend for 3rd
year (D3) = $0.25
Required rate of
return(r) =10% (0.10)
Growth after third year
(g) = 5% (0.05)
First we calculate the
share price at third year,
(r-g)
(r-g) 0.10-0.05
Now calculating share
price,
(1+r) (1+r)² (1+r)³ (1+r³)
(1+0.10) (1+0.10)² (1+0.10)³ (1+0.10)³
= 0.09 +
0.17 + 0.19
+ 3.94
= $4.93
Model based on Price-
Earnings ratios
This model argues
common stocks are possible to analyze by applying price-earnings ratio to
either present or forecasted earnings. The major factor that separates this
model from DCF model is the selection of a terminal P/E ratio. Under this model
we have to compare the price and earnings per share for a company. By comparing
these two factors we can analyze the markets stock valuation of company and its
shares relative to the income company is generating. Stocks with higher or
certain forecasts earnings growth will usually have a higher P/E and those
expected to have lower or riskier earnings growth will usually have a lower
P/E. To use this model one should at least explore growth rate implicit in the
use of terminal P/E ratio.
Basically P/E ratio is
calculated as:
P/E= MPS/EPS
Or, MPS= EPS× P/E ratio
PO = EPS×
Multiplier (m)
Where, MPS= market
price of share
EPS=
Earnings per share
Under this model we examine two sets of growth
assumption. They are:
1)
Zero growth
2)
Constant growth
Zero growth: In zero
growth all earnings of firms are distributed as a dividend. Here,
Price of share (PO)=
EPS × m
Where m= multiplier and
calculated as
= dividend payout
ratio/ required rate of return
Example: A company has
a earning per share of $4 and required rate return is 16%. If company decided
to pay all earnings as a dividend then what is the price of share now?
Solution,
We are given that,
EPS= $4
r= 16% or 0.16
First calculating
multiplier,
m= DPR/r
=
1/0.10
=
6.25
(Since company have
decided to pay all earnings as a dividend, DPR=100% or 1)
PO= EPS× m
= 4× 6.25
= 25$
Constant growth: in
constant growth the company has a policy of constant retained earnings for
future investment. Here,
Price of share (PO) =
EPS × m
Where, m= multiplier= DPR
(1+g)/r-g
Example: A firm has
decided to pay 60% of their earnings as a dividend and remaining 40% is
retained for future investment. Earnings per share are $4 and required rate of
return is 16%. What is the price of share?
Solution,
We are given that
Dividend payout ratio
(DPR)= 60% or 0.60
Required rate of
return(r) = 16% or 0.16
Earnings per share
(EPS) = $4
Now, multiplier (m) =
DPR/ r
= 0.60/0.16
=3.75
Price of share (PO)
= EPS ×m
= 3.75× 4
` = $15
The theoretical Price
earnings ratio can be estimated by calculating an average historical value,
using an explanatory model assigning weights to certain factors by qualitative
reasoning and using regression analysis to estimate the weights.
In 1963 Whitbeck- Kisor
model was introduced which attempt to use multiple regressions to explain price
earnings ratios. According to this model,
Price earnings ratio= 8.2
+1.50(earnings growth rate) +0.067 (dividend payout rate) – 0.200 (standard
deviation in growth rate)
This equation
represents the estimate of stock at a point of time and the impact of three
variables, earnings growth rate, dividend payout and standard deviation on the
price earnings ratio. The numbers represent the weight that the market placed
on each variable at the point of time and the signs represent the direction of
impact of each variable on the price earnings ratio.
There are three reasons suggesting Whitbeck-
kisor model does not work. They are:
i)
Market tastes changes and with change in
tastes the weight on each variable also changes over time.
ii)
Inputs like dividend and growth in
earning changes over time
iii)
This model has failed to show the firm effects.
Capital
assets pricing model (CAPM)
Capital
assets pricing model is tool used to analyze the relationship between risk and
rates of return. CAPM model states that the relevant riskiness of an individual
stock is its contribution to the riskiness of a well diversified
portfolio. Beta coefficients are key
elements in this model, which measures the extent to which return of a given
stock move with the stock market.
Under
CAPM,
E (RA) = Rf
+ [E (RM) – RF] × BA
The
above equation is also known as Security market line (SML).
Where,
Rf = risk free rate
RM = market return
BA= Beta coefficients
DCF and the CAPM
Wells
Fargo stock valuation system attempts to implement stock valuation and
selection systems that incorporate the DCF approach and capital assets pricing
theory. There normally three steps in Wells Fargo stock valuation system,
Step1
·
Estimation of expected rate of return
implied by the market price.
·
Find the discount rate which equates the
present value of all future dividends with price.
Step2
·
Estimation of the beta of each security.
Step
3
·
Using the expected return and expected
beta from each of the stocks.
·
A graph is plotted and the straight line
which fits these points is used as an estimated SML
Result:
If the stock has return above the SML, given its risk, it should be a good buy
and if it has a lower return, it should not be bought.