valuation of securities

Valuation of Securities
• Time value of money affects the valuation of
the securities
• We apply the TVM concept to find out the
value of different types of securities
• Different types of securities that will be
covered are
– Debentures(Bonds)
– Preference Shares
– Equity Shares

• What is a Security?
– A financial security is some type of financial
instrument that has a recognized financial worth
– Usually referred to simply as securities, the financial
security can take on several forms
– Generally, a financial security will have the potential
to generate some additional return above face value
in the future
– Thus we can say that the value of a security is the
“Present value of the future benefits” associated
with it

• Symbolically
– A= Future Annual cash flow
– PVIFA = Present Value Interest Factor for Annuity
– Value of Asset = A X PVIFA
– An Investor expects an annual return of Rs 1000
for the next 10 years, find the current value of the
asset ,with interest rate of 15 %
– Rs 5019

• Valuation of Debentures
– In corporate finance, the term is used for a
medium- to long-term debt instrument used by
large companies to borrow money. In some
countries the term is used interchangeably with
bond, loan stock or note.

• Important terms associated with Debentures
– Face Value: the amount on which the issuer pays interest,
and which, most commonly, has to be repaid at the end/
maturity. Generally it is RS 100 or RS 1000.
– Coupon :the interest rate that the issuer pays to the bond
holders. Usually this rate is fixed throughout the life of the
bond
– Maturity Date : the date on which the issuer has to repay the
FV.As long as all payments have been made, the issuer has
no more obligation to the bond holders after the maturity
date. The length of time until the maturity date is often
referred to as the term or tenor or maturity of a bond.

• Debentures Valuation Model
– An investor of debenture is entitled to get the following two
things
• Interest at a fixed rate till maturity
• Principal amount of the debenture on its maturity
– Vd= PV of all the future Interest inflows+ PV of the FV paid at the maturity
– Vd = PVIFA X Annual Interest Payment+ PVIF X Face Value

– A debenture of with FV = Rs 100 carrying an interest rate @
15 % will mature in 5 years. The required rate of return of
this debenture is 10%.Calculate the PV of the debenture.
– Annual interest inflow = Rs 15
– Face Value inflow at maturity = Rs 100
– PVIFA ( 5 years,10%) =3.791
– PVIF(5 years,10 %) =.621
– PV of the Debenture = 3.791*15+.621*100
– Rs 118.965

– Relation between the Interest Rate(Coupon Rate) and the
Required Rate of Interest( discount rate)
– Coupon Rate can be denoted by “c”
– RRI(Discount Rate) can be denoted by ‘k”
– Conditions
• Let Face Value of the Bond = Rs 1000
• Let k = c =15% , Recalculate the value of the debenture?
• Let k = 12 % and c = 15 % Recalculate the value of the
debenture?
debenture?

– Conditions
• Let k = c =15% , Recalculate the value of the debenture?
– Vd =1000 (k = c)
debenture?
– Vd =1108 ( k < c)
debenture?
– Vd = 900 ( k > c)

– Semi-Annual Interest Rate and Valuation of the bond
– This is the case when the interest is payable semi-annually (
twice in 1 year)
– To calculate the value of the Bond
• Divide the coupon rate (c )by 2
• Divide the required rate of return(k) by two
• Multiply the maturity period by 2
• Do the calculations as before for the annual compounding

– Mr. A holds the debenture with face value of Rs
1000 carrying an interest rate of 12 % pa. The
interest is payable semi-annually. The required rate
of return is 16% pa. The debenture is payable at a
premium of 10 % after 8 years. Calculate the value
of debenture

– Face Value= Rs 1000
– Coupon Rate = 6% (12/2)
– RR =8% (16/2)
– Maturity Period 16 years (8X2)
– PVIFA (16 years,6%)=10.106
– PVIF( 16 Years,4%) =.292
– Vd= 10.106 X 60 + .292 X1100
– Rs 927.56

– Valuation of perpetual debenture
• A debenture that never matures
• Rarely found in practice
• Vdp = Annual Interest Payment/Required rate of Return
• Example : A debenture holder is to receive an annual interest @10 %
for perpetuity. The face value of the debenture is Rs 1000.Calculte the
Value of the debenture if the required rate of return is:
1. 15%
1. Rs 667
2. 8%
1. RS 1250
3. 10%
1. RS 1000

– Yield To Maturity( YTM)
• That interest rate at which the Value of the debenture
become equal to its market price.
– Example:
– A company’s debenture has a face value( par value) of Rs 1000,
and carry an interest rate of 9% and matures in 8 years. If the
current price of the bond in the market is Rs 800 would you buy
the bond? Discount rate is 10 %.
– What is the YTM?
• What is YTM of this bond
800 = 8∑90 /(1+r)t + 1000/(1+r)8
t=1
• YTM is nothing but r which equates its value to its MV

– How to calculate( YTM)
• YTM = Annual Interest Payment + (F-P)/n
(F+P)/2
• F = Face Value
• P= Present Value of Debenture(Market Value)
• n = Maturity period of debenture
YTM = 90+ (1000-800)/8
(1000+800)/2
= 115/900 = 12.70 % > Required Rate of Return
– Simply put the annualized return an investor would get by
holding a fixed income instrument until maturity

– Example: Current Market Price of a a perpetual bond Rs
95(Face value is Rs 100).Coupon Rate is 13.5%.The Required
Rate of Return is 15 %.Calculate its intrinsic value. Should it
be bought?
– What is it YTM?
– Solution
• Intrinsic Value( Fair Value) =13.5/.15 =RS 90
• YTM for a perpetual bond =(Annual Interest Inflow/Market Price )X100
• YTM= 14.2% <Required Rate of Return

– Preference Shares
• Carry a fixed dividend and thus their valuation can be
done on the same basis as the bonds
• Two types of preference shares
• Redeemable
– Both annual dividend and a maturity amount is payable
• Irredeemable
– Only annual interest is payable

– Valuation of Redeemable Preference Shares
• Two Components
– Annual dividend Cash inflow
– Amount at maturity
– Vd = PVIFA X Annual dividend Payment+ PVIF X Amount
payable at maturity
– Example: Face value of Preference Share= Rs 100,Dividend
rate = @ 10%,Current Market Interest Rate =15%,Maturity =
15 Years
– PVIFA =5.019, PVIF = .247,
– VPS = Rs 74.89

– A pref share of RS 1000 carries a dividend rate of 10 %.The
current market interest rate is 15%.The preference share
becomes due for redemption in 10 years. Find the value of
the pref share.
• Rs 748.90

– Valuation of Irredeemable Preference Shares
• Single Component
– Annual dividend Cash inflow
– Value = annual dividend cash inflow/Current Yield
– Example :Face value of Preference Share= Rs 100.Dividend
rate = @ 10%.Current Yield on the preference share =15%
– VPS = 10/.15 = Rs 67
– Yield on the preference share can be calculated on the same
patterns as calculated for the Debentures
– Example: Current market price of a irredeemable pref share is Rs 80. Annual
dividend flow is Rs 10. Calculate the yield.
• Fair value = Annual Dividend/k
• Market Values = Annual Dividend/Yield
• 12.5%

– Equity Shares
– The valuation of securities is difficult as compared to
valuation of debentures and Preference shares. Why?
• There is no fixed dividend associated with the equity
• The dividends are expected to grow at a steady rate unlike in the case
of debenture and preference shares
– Two approaches to valuation of equity shares
• Dividend capitalization Approach
• Earning Capitalization Approach

Approaches to valuation of equity shares
Dividend Capitalization
Approach
Earning Capitalization
Approach
Growth in
Dividends
No Growth in
Dividends
Single Period Multiple PeriodMultiple Period
Constant Growth Variable Growth

– Dividend capitalization Approach
• Capitalize the future dividend flow
• Discount all the future cash inflows
– DCA approached is based on the following
assumptions
• Dividends are paid annually
• The dividend is received after the expiry of a year of the
purchase of the equity share

– DCA approached again divided in to following two
categories
• No growth in Dividends
– Single period approach
– Multiple Period approach
• Growth in Dividends
» Constant growth on year to year basis
» Variable growth in dividends On year to year basis

• DCA Approach (No growth in Dividends)
– Single period approach
• The investor is presumed to hold the share for 1 year only
• In such cash the cash inflow for the investor are
– Dividend that will come after 1 year
– The Price of the share that he/she may get after 1 year
– Fair value of the share
• PV of the Dividend + PV of the market Price of share after 1 year
• P= D1 + P1
(1+k)1 (1+k)1

• Example
– Mr. A holds an equity share giving him an annual
dividend of Rs 20.He is expected to sell the share at
Rs 180 after 1 year. Calculate the value of share at
present .The required rate of return(discount rate) is
12 %
• P= D1 + P1
(1+k)1 (1+k)1
• P= 20 + 180
(1+.12)1 (1+.12)1
• Rs 178.57

– Multiple period approach
• The investor is presumed to hold the share beyond 1 year
for an unspecified no of years
• Equity shares don’t have any maturity period
• One can expect the dividend cash inflow for infinite
period
• This kind of cash flow is similar to the cash flow of a
Perpetual Debenture( one with no Maturity)
• So valuation can be done in the similar way

– Multiple period approach
• Po= Expected annual dividend
Discount Rate
• Po= D
K
– Example: A company is paying an annual dividend of Rs 40 per share.
The company is expected not to deviate from this dividend amount in the
future. Current discount rate is 15 %.Calculate the Present value of the
share
• Po= D = 40/.15= Rs 267
K

• DCA Approach ( Growth in Dividends)
• The assumption of constant dividend without any growth is unrealistic as
companies grow over time
• So growth in dividends needs to be incorporated
• The model changes if the growth in the dividend is also taken care of

• DCA Approach (Constant Growth in Dividends)
• P0 = D1
(k-g)
D1= Dividend at the end of second year
k = discount rate
g = growth rate of dividends( in %)
The above formula can also be written as
• P0 = Do(1+g)
(k-g)

• Example:
ABC limited is expected to pay a dividend of Rs 40 per share. The dividends
are expected to grow at a rate of 10%.The capitalization rate is 15%.Find the
value of the share.
– D1 = Rs 40
– g = 10%=.10
– K = 15% = .15
– P0 = D1
k – g
= Rs 800

• More Example
– A share has current price of Rs 10 and is expected to earn a dividend of
Rs 2.The share will be sold at Rs 18 after 1 year. Find out the value of the
share if the capitalization rate(discount rate) is 12%
– Which Model
• No growth Model Single Time period
• P = .893X 2+.893X 18= Rs 17.86
– XYZ is paying a dividend of Rs 4 per equity share. This same rate of
dividend is going to continue for the coming years. T he discount rate is
12 %.Find out the value of the share?
– Which Model
• no growth Model Multiple Time period
• P = D/k = 4/.12= Rs 33.34

• More Examples
– A share is expected to earn a dividend of Rs 50.Dividend are expected to
grow perpetually at a constant growth rate of 8%.You are required to find
out the value of the share if the capitalization rate(discount rate) is 15%.
– Which Model
• constant growth Model Multiple Time period
• P0 = D1
(k-g)
– 50/(.15-.08)
– Rs 714.28

• Variable Growth -Multiple time Period
– The Dividends on the company share may not grow
at a constant rate
– Two Stage Dividend growth model
• Companies have years of super-normal growth where the
dividends grow at a very high rate
• After this super-normal growth period the dividends grow
at a lower rate
• 1 -5 year--- g=10%
• 6th year onwards--g = 6%

Two Stage Model
Time
g
10 %
6 %

• Using Two Stage Growth Model
– A company is expected to pay a dividend of Rs 4 per
share after a year. Its dividends are expected to
grow at a rate of 15 % for the next 5 years and then
at a rate of 8% indefinitely. Find out the present
value of the share if the capitalization rate is 12 %

37
Timeline for Supernormal Growth
3.87
3.08
1 2 3 4
g = 15% g = 15%
4.00 4.60 5.29 6.08 7.00 8.04
Total = Rs 21.93
3.67
3.77
PV
PV
PV
PV4
5
g = 15% g = 15%
6
g = 15%
0
3.57
PV
3.97
g = 8%

• Computation after 6th Year( Period of stable
growth
– What is the dividend after 6th year
• 8.04
– Dividend after 7th Year
• 8.04(1.08)= Rs 8.694
– Lets assume I go in to future and I am at the
beginning of the 6th Year. What is the value of the
share at the starting at 6th Year?
• D7/ k-g
• = Rs 8.694/(.12-.08) = Rs 217.35

• What is the Present value of P6 today
– 217.35 X PV factor( 6 years,12%)
– 217.35X .507 = Rs 110.20
– Present value of the share
• Rs 110.20+ Rs 21.93
• Rs 132.13
• Can not apply Gordon model for first 6 years
– g > k
– g changes after 6th year

• Example
– A ltd is expected to pay dividend of Rs 2 after the
end of the year. Dividends are expected to grow at a
rate of 20% for the next 4 years. After wards
dividends will grow only at 5%.The discount rate of
return is 12 %.Find the Present value of the share
– Rs 49.07

Earning capitalization Approach
•
– Po = E1/k
– E1= earnings of the company after 1 year
– Example
– Calculate the price of the equity share as per the
ECA
• Earnings per share(EPS) = Rs 10
• K= 12%
• Retained Earnings =0
• P0 = 10/.12 = Rs 50

Earning capitalization Approach
•
– Calculate the price of the equity share as per the
DCA
• Earnings per share(EPS) = Rs 10
• K= 12%
• Retained Earnings =0
– When the company is not retaining any earnings it
means that everything is distributed as dividends
• So D1= Rs 10, k = 12%, g=0,
• P0 = D1/k
• P0 = 10/.12 = Rs 50

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