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VALUATION OFSECURITIES
1
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What is Value?
Value= Fundamental Value= Intrinsic Value
This is the value of an asset (stocks, bond, currency, gold
etc.) if all the information is know to all market disciplines
about it.
Fundamental or Intrinsic value in finance is based or
calculated as a Discounted Value.
Discounted value is the present discounted value of all
future cash flows.
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Definition of Intrinsic Value
It is the estimate of stock true value or investmentvalue based on accurate risks in other words basedon true risk and an accurate evaluation of returns.
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Need for Valuation of
Securities The objective of financial management being to
maximize the market value of equity shares,managers must know how equity shares are valued.
Understand how their investment and financingdecisions influence the value of equity shares.
Managers must also know how non equity claims arevalued.
Knowing the value of securities is also important for
investor to make decision of buy and sell.
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The Investment Decision
ProcessI. Determine the required rate of return
II. Evaluate the investment to determine if its market price is
consistent with your required rate of return
III. Estimate the value of the security based on its expected
cash flows and your required rate of return
IV. Compare this intrinsic value to the market price to decide
if you want to buy it
V. If Estimated Value > Market Price, Buy
VI. If Estimated Value < Market Price, Dont Buy
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Required Rate of Return is determined by,
1. Economys risk-free rate of return, plus2. Expected rate of inflation during the holding
period, plus
3. Risk premium determined by the uncertainty
of returns
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Two major approaches havebeen developed:
1. Discounted cash-flow valuation
Present value of some measure of cash flow, including
dividends, operating cash flow, free cash flow andresidual income
2. Relative valuation technique
Value estimated based on its current price relative to
significant variables, such as earnings, cash flow, book
value, or sales
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In this chapter
This chapter is focused on understanding the basic discounted
cash flow valuation model and its application to bond and equity
shares.
Also, it looks into non discounted cash flow approaches to
equity valuation.
Four sections:
Basic valuation model
Bond valuation
Equity valuation: dividend capitalization approach
Equity valuation: ratio approach
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Basic Valuation Model9
The value of any asset, real or financial, is equal to the present value of
the cash flows expected from it.
Using the present value technique, the value of an asset can be
expressed as,
V0= C1/(1+k)1 + C2/(1+k)
2+.+Cn/(1+k)n
V0- value of an asset at time zero
Ct- cash flow expected at the end of year t
k- discount rate applicable to the cash flows
n- life of an asset
Using the present value interest factor, PVIFk,n above equation can be
written as,
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Key Inputs10
The key inputs to the valuation process are,
1. Cash flows- Cash flow expected from any asset
may be constant or fluctuating or growing.
2. Timing- It is customary to specify the timing along
with the estimates of the cash flow.
3. Discount rate- The discount rate must be
commensurate with the risk characterizing the
cash flows.
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Bond Valuation11
Terminologies-par value, coupon rate, maturity period.
Basic Bond Valuation Model
Holder of bond receives a fixed annual interest payment for a certain
number of years and a fixed principal repayment at the time of
maturity. Hence value of a bond is,
V=n
t=1I/ (1+kd)
t + F/ (1+kd)n
V= I (PVIFAkd,n) + F (PVIFkd,n
)
V- value of bond
I- annual interest payable on the bond
F- principal amount of the bond repayable at he time of
maturity
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Example12
A Rs.100 par value bond, bearing a coupon
rate of 12%, will mature after 8 years. The
required rate of return on this bond is 15%.
What is the value of this bond?
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Bond value theorem13
Based on the bond valuation model several theorems have been
derived,
1. When the required rate of return equals the coupon rate, the
bond sells at its par value2. When the required rate of return exceeds the coupon rate, the
bond sells at a discount. However, the discount declines as
maturity approaches.
3. When the required rate of return is less than the coupon rate,
the bond sells at a premium. However premium declines as
maturity approaches.
4. The longer the maturity of a bond, the greater is its price
change in response to a given change in the required rate of
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Yield to Maturity (YTM)14
Suppose the market price of a Rs.1000 par
value bond, carrying a coupon rate of 9% and
maturing after 8years, is Rs.800. What rate of
return would an investor earn if he buys this
bond and holds it till its maturity? The rate of return that he is earns, called the
YTM is the value ofkd.
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Formula for finding approximateYTM
15
YTM= [I + (F-P)/n]/ [0.4F + 0.6P]
YTM= yield to maturity
I= annual interest payment
F= par value of the bond
P= present price of bond
N= years to maturity
The price per bond of Zion limited is Rs.90. The
bond has a par value of Rs.100, a coupon rate of
14%, and a maturity period of 6years. What is the
yield to maturity?
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Bond Values with Semi-annualInterest
16
Most of the bonds pay interest semi-annually. This means that the
bond valuation has to be modified along the following lines:
i. The annual interest payment, I, must be divided by two to obtain the semi
annual interest payment.
ii. The number of years of maturity must be multiplied by two to get the number
of half-yearly periods.
iii. The discount rate has to be divided by two to get the discount rate applicable
to half-yearly periods.
V=2n
t=1
(I/2)/ (1+kd/2)t + F/ (1+kd/2)
2n
V= (I/2) * (PVIFAkd/2,2n) + F (PVIFkd/2,2n)
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Example17
A Rs.100 par value bond carries a coupon rate
of 12% and a maturity period of 8 years.
Interest is payable semi-annually. Compute the
value of the bond if the required rate of return
is 14%.
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Equity Valuation:
Dividend Capitalization Approach18
According to this approach, the value of an equity
share is equal to the present value of dividends
expected from its ownership plus the present
value of the sale price expected when the equity
share is sold.
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Single Period Valuation Model19
Investor expects to hold the equity share for one
year. The price share of the equity share will be,
P0= D1/(1 + ks) + P1/(1+ks) P0 = current price of equity share D1 = dividend expected a year hence
P1 = price of share expected a year hence
ks = rate of return required on the equity share
Prestiges equity share is expected to provide a dividend of
Rs.2.00 and fetch a price of Rs.18.00 a year hence. What
price would it sell for now if the investors required rate of
return is 12%?
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What happens if the price is expected to
grow at a rate of g% annually? (if the current
price,P0, it becomes P0(1+g) a year hence)
P0= D1/(1 +ks) + P0 (1+g)/(1+ks)
P0 = D1/ (ks-g)
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Expected rate of return21
Now we look at, What rate of return can beexpected, given the current market price andforecast values of dividend and share price?
It can be given by, ks= (D1/P0 )+g
The expected dividend per share of Vaibhav Limited is Rs.5. The
dividend is expected to grow at the rate of 6% per year. If the
price per share is now Rs.50, what is the expected rate of
return?
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Multi-Period Valuation Model22
Since equity share have no maturity period,
they may be expected to bring a dividend
stream of infinite duration. Hence the value of
an equity share may be put as,
P0= D1/(1+ks)1
+ D2/(1+ks)2
+.+D/(1+ks)
-A
P0 =
t=1Dt / (1+ks)
t
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The equation A is general enough to permit any
dividend pattern- rising, declining, constant or
randomly fluctuating.
For practical application we will simplify the
above equation and it can be done in two cases,
Constant dividends
Constant growth of dividends
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Valuation with ConstantDividends
24
If we assume that dividend per share remains
constant year after year at a value D, the
equation A becomes,
P0= D/(1+ks)1 + D/(1+ks)
2+.+D/(1+ks)
On simplification becomes,
P= D/ks
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Valuation with Constant Growth inDividends
25
If we assume that dividends grow at a constantrate we get,
Dt = D0 (1 + g)t
Dt - Dividend for year t D0 - Dividend for year 0 g - constant compound growth rate
Example- The current dividend for an equity shareis Rs.3.00. If the constant compound growth rate is
6% what will be the dividend 5years hence?
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When the dividend increases at a constant rate
the share valuation equation becomes,
P0= D1/(1+ks)1 + D1(1+g)/(1+ks)2 +D2 (1+g)2/(1+ks)3+
If simplified, P0= D1/ks - g
E it V l ti R ti
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Equity Valuation: RatioApproach
27
There are three main approaches viz.,
1. Book value approach
2. Liquidation value approach
3. Price / Earning Ratio (Earning
Capitalization Approach)
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Book Value Approach28
Book Value per share = Net worth ofcompany/Number of
outstanding equityshares
Book value can be established relatively easily.
It is based on accounting convections and policies which
characterized by great deal of subjectivity and
arbitrariness.
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Price/ Book value Ratio29
It is specified as,
Widely used to indicate how aggressively the stock is being
priced.
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Liquidation Value Approach30
The liquidation value per share is equal to,
Value realized
from liquidatingall the assets ofthe firm
Amount to be paid to
all the creditors andpreferenceshareholders
Number of all outstanding equity shares
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Earning Capitalization Approach31
This is also known as Price/Earning Ratio
The steps involved in identifying the intrinsic
value using this approach is as follows,
1. Estimate the earning per share
2. Establish an appropriate price earningmultiple
3. Develop a value anchor and value range
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Forecasting earning per share of the current
year on the basis of:
1. Published information about the company
2. The impression gathered from plant visits
3. Interview with management
1. Estimate the earning per share
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Growth prospects and risk exposure (through its
impact on the discount rate) are the key
determinants of the price earning multiple.
Other factors like, share holder friendliness of
management and liquidity of the stock.
2. Establish an appropriate price - earning
multiple
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The value anchor is obtained as follows:
Projected earnings per share x Appropriate
price
earnings multiple
3. Develop a value anchor and value range
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Assessment35
Advantages
Since the price earning ratio reflects the price per
rupee of earnings, it provides a convenient measure
for comparing the prices of share having different
levels of earnings per share.
The estimates required for using the price- earning
ratio approach are fewer in comparison to the
estimates required for dividend capitalization
approach.But it does not have a sound conceptual basis and P-E Ratio
found doesnt have a firm theoretical underpinning
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Price/ Earning ratio36
The returns investors are entitled to receive are the
firms net earnings.
One way investors can estimate value is bydetermining how many dollars they are willing to pay
per dollar of expected earnings.
For example, if investors are willing to pay 10 timesexpected ornormal earnings, a stock they expect toearn $2 per share during the following year would bevalued at $20.
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The P/E ratio is computed as,
This indicates the prevailing attitude of investors toward astocks value.
Investors must decide if they agree with the prevailing P/E
ratio (i.e., is the earnings multiplier too high or too low?)
D idi h th ili P/E
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Deciding on whether prevailing P/Eratio is too high or too low
38
The spread between k and g is the maindeterminant of the size of the P/E ratio.
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Example39
A stock has an expected dividend payout of
50%, a required return of 12%, and an
expected dividend growth rate of 8%, identify
the stocks P/E ratio.
1. Multiply this P/E ratio with the expected earning
of the next year to get the estimated value of the
stock.
Wh t h if t k i h ld f 2
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What happens if stock is held for 2years and then sold?
40
P0= D1/(1 + ks) + D2/(1 + ks)2 + Pj2/(1+ks)
2
P0 = current price of equity share
D1 = dividend expected a year hence
Pj2 = price of share expected a 2 year hence
ks = rate of return required on the equity share
Expected selling price (Pj2) of stock j is
simply the present value of all remaining
dividend payments.
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Key Points41
Expected Rate of return =
Nominal risk free rate of return + Risk
premium
For example, for the long run, you expect a
nominal risk-free rate of about 8% and a riskpremium for this stock of 3%.Therefore, you
set your long-run required return on this stock
at 11%.
Ass mption in Di idend
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Assumption in DividendCapitalization Approach
42
Dividends grow at a constant rate and this rate
will continue for an infinite period.
The required return (k) is greater than the
infinite growth rate (g). If it is not, the model
gives meaningless results because thedenominator becomes negative.
Valuation with Temporary Super
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Valuation with Temporary SuperNormal Growth
43
Some firms experience periods of abnormally high rate
of growth for some finite period.
The infinite period Dividend Capitalization Approachcannot be used to value these true growth.
The Wood Company has a current dividend (D0) of $2 per share.The following are the expected annual growth rates for dividends.
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When the dividend increases at a constant rate the
share valuation equation becomes,
P0= D1/(1+ks)1 + D1(1+g)/(1+ks)
2 +D2
(1+g)2/(1+ks)3+
Where D1 - Dividend expected a year hence
Now if D0 is given what happens to the above equati
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