VALUATION OF

FINANCIAL ASSETS

Valuation
Is a process of determination of
worth of an asset.
Different concepts of Valuation
Book Value
Market Value
Going concern Value
Liquidating Value
Capitalizes value

Book value

In case of debentures, preference Shares the value shown in

the Balance sheet will be treated as historical value or book
value.
In case of equity shares Book Value = Net worth / No. of equity
Shares.

Market Value
The price at which the shares & debentures are sold. In case of
the financial assets which are listed in a recognized stock
exchange, the price prevailing at the stock exchange is the
market value.

Going Concern Value

It refers to the value of the business, as an operating, performing
and run by business unit. This is the value, which a prospective
buyer of a business may be ready to pay.

Liquidating value
L.V. represents to the net difference between the realizable
value of all assets and the sum total of external, liabilities.
This net difference belongs to the shareholders.

Capitalized Value
C.V. defined as the sum of present value of cash flows,
from an asset discounted at the required rate of return
(i.e.) to find out C.V. the future expected benefits are
discounted for time value of money.

BOND VALUATION
Bond is a long term financing used
by firms, which upon issuing,
promise to make some future cash
inflows interest/ repayment of the
bond.

Bond Terminology
Coupon Rate - This is the stated rate of interest
on the bond. It is fixed for the life of the bond.
Also, this rate time the face value determines the
annual interest payment amount.
Face Value - This is the principal amount
(nominally, the amount that was borrowed). This
is the amount that will be repaid at maturity
Maturity Date - This is the date after which the
bond no longer exists. It is also the date on
which the loan is repaid and the last interest
payment is made.

Valuation Base of Bond

Bond Risk
Bond Return
Bond Yield to Maturity

Bond Risk
Interest Rate Risks: The return expected from bond will
vary as per the variation in the interest rate in the market.
This is known as interest rate risk. Market Interest is inversely
related to the price of the bond.

Default Risks: Sometime the issuer fails to pay the

agreed value of debt Instrument in full/ on time or both, this
is default risk.

Marketability Risk: Sometimes there is a difficulty in

selling the bonds in the market at its face value without giving
any discount, this is marketability risk.

Call-ability Risk: Sometimes there is an inability of the

issues to call the bond at any time & this creates an
uncertainty in the return of investor, this is called as callability risk.

Bond Return
Holding Period Return

Current Yield

Price +Coupon Rate Payment

Annual Coupon Payment

Current Price

Purchase Price

Where,
Price = Selling Price Purchase
Price

Bond Yield to Maturity

Yield to maturity means
the expected rate of return,
which an investor can
expect to earn if the bond is
held till maturity.

Rv Bo
I
n
Ytm
Rv Bo
2

Yield to maturity is a
single discount factor that
makes the present value of
future cash flows from a
bond equals to the current
price of bond.

Ytm = Yield to Maturity

I

= coupon interest

Rv = Redemption value
Bo = Bond Price
n

= years to maturity

Value of Bond
n

Ii
Fv
VB

i
n
(1 r )
i 1 (1 r )

I = Interest
receivable per year
Rv = Redemption
Value
Fv = Face value

Value of Deep Discount payable at maturity

Bond/Zero Coupon Bond r = Required rate of

VDD B

Fv

n
(1 r )

return
n = No. of years

Decision

If Net Present Value of Bond

(Value of the Bond)
is greater than the
current market price,
then Investors can buy

If Net Present Value of Bond

(Value of the Bond)
is smaller than the
current market price
then investor should sell

Bond Value Theorems

Theorem 1- If the Market Price of bond
increases the yield will decreases and vice versa.
Based on Concept that if the required rate of
return and the coupon rate are equal then the
bond will be equal to the par value. So, if the
required rated return is greater then the coupon
rate, the bond value is less the par value.
Theorem 2- If the bond yields remain same over
its life, the discount premium depends on
maturity period.
Bond with a short term maturity sells at a lower
discount than the bond with long term maturity.

 Theorem 3- If a bonds yield remains constant

over its life , the discount or premium amount will
decreases at an increasing rates at its life gets
shorter.
Bond with shorter maturity has more present
value i.e. less discount.
Theorem 4 A raise in the bonds price for a
decline in the bonds yield is greater than the falls
in the bonds price for a raise in the yield.
The fall in the yield results in greater raise in
bond price than the raise in the yield results in
decrease in Bond price.

 Theorem 5 - The change in the price will be

lesser for a percentage change in bonds yield of
its coupon rate is higher.
When the yield to maturity changes by 1% then
the bond with higher coupon rate has a lower %
of change in price than bond with lower coupon
rate.

Convexity
Bond Price and YTM are inversely related
The rise in the price results in a fall in the yield
and vice versa.(Theorem-1)
This relationship is not linear. i.e., A raise in the
bonds price for a decline in the bonds yield is
greater than the falls in the bonds price for a
raise in the yield and vice versa.(Theorem-4)
This refers to Bond convexity.
Differs from bond to bond depending upon the
size of the bond, years to maturity and the
current market price.

Yield Curve
Term structure of Interest rate is the relationship
between the yield and time to maturity.
This is know as Yield Curve
The general perception is that the curve will be
upward moving up to a point and then becomes
flat.
This is explained through three theories
Expectation theory
Liquidity preference theory
Segmentation theory

Expectation theory
Based on Investors Expectation
A rising yield curve- investors
expectation of continuous rise in
interest rate.
A flat yield curve- investors expect
interest rate to remain constant.
A declining yield curve- investors
expectation of decline in interest rate

Liquidity preference theory

The investors prefer to invest in the
short term bonds than to long term
bonds because of the uncertainty of
the future and of greater liquidity in
short term.
So the investors have to be
motivated through premium to be
paid to them.

Segmentation theory
This theory is based on the supply and
demand of the funds segmented in sub
markets because of the preferred habits of
the individuals.
Insurance company prefers Long term
bonds, whereas the commercial banks and
corporates may prefer liquidity to meet
their short term requirements through
short term bonds.

Duration
Measures the time structure of a bond and
the bonds interest rate risk.
Measures the average time taken for all
interest coupons and the principal to be
recovered.
This is called Macaulays duration.
It is the weighted average of periods to
maturity, with the weights being present
values of the cash flow in each period.

Pv (Ct )
D
xt
Po
t 1
D Duration
C Cash flow
t number of years
Pv (Ct ) present value of the cash flow
Po sum of the present value of cash flows

General rule
Higher coupon rate, lower duration-less
volatile bond price
Longer term of maturity, longer durationmore volatile bond
Higher YTM, lower duration-more bond
volatility and vice versa.
In case of a zero coupon bond, the bonds
term to maturity and duration are the
same. It repays at the time of maturity the
principal and the interest at the same
time.

Immunization
The coupon rate risk and the price risk can
be made to offset each other.
Whenever there is a increase in the
market interest rate, the price of the bond
falls. At the same time, the newly issued
bonds offer higher interest rate. The
coupon can be reinvested in the bond
offering higher interest rate and losses
that occur due to fall in price of the bond
can be offset and the portfolio is
immunised.

 The bond manager can offset the

interest rate and price risks by
matching the outflow duration with
cash inflow duration from bond
investment.
Investment outflow = (X1 x duration
of bond 1) + (X2 x duration of bond 2)
Where X1 and X2 refers to proportions
of investment in bond 1 and bond 2

Bond Portfolio Management

Four strategies used to manage bond
portfolio:
Passive strategy
Quasi-passive strategy
Immunization or quasi-active
strategy
Active strategy

Passive strategy
Buy and hold
Buy the bonds and hold till the
maturity
Reinvestment of the coupons.

Quasi-passive strategy
Ladders-portfolio of individual bond
with various maturity dates.

Par Value Held ($ in Thousands)

Laddered Portfolio
(contd)

Years Until Maturity

29

Bullets
Staggered purchase of several bonds
that mature at the same time.
Maturity matching strategy

Barbell strategy
The barbell strategy differs from
the laddered strategy in that less
amount is invested in the middle
maturities

Par Value Held ($ in Thousands)

Barbell Portfolio (contd)

Years Until Maturity

32

Active Strategy
Valuation strategy- depends upon
the portfolio managers ability to
identify and purchase the
undervalued bonds and avoid the
overvalued bonds.
Bond swap startegies

Bond swap
In a bond swap, a portfolio manager
exchanges an existing bond or set of
bonds for a different issue
Bond swaps are intended to:
Increase current income
Increase yield to maturity
Improve the potential for price appreciation
with a decline in interest rates
Establish losses to offset capital gains or
taxable income

Substitution Swap
In a substitution swap, the investor
exchanges one bond for another of
similar risk and maturity to increase
the current yield
E.g., selling an 8% coupon for par and
buying an 8% coupon for Rs.980
increases the current yield.

35

Substitution Swap
(contd)
Profitable substitution swaps are
inconsistent with market efficiency
Obvious opportunities for
substitution swaps are rare

36

Intermarket or
Yield Spread Swap
The intermarket or yield spread swap
involves bonds that trade in different
markets
E.g., government versus corporate bonds

Small differences in different markets

can cause similar bonds to behave
differently in response to changing
market conditions
37

Intermarket or
Yield Spread Swap (contd)
In a flight to quality, investors
become less willing to hold risky
bonds
As investors buy safe bonds and sell
more risky bonds, the spread between
their yields widens

Flight to quality can be measured

using the confidence index
The ratio of the yield on AAA bonds to
the yield on BBB bonds

38

Bond-Rating Swap
A bond-rating swap is really a form
of intermarket swap
If an investor anticipates a change in
the yield spread, he can swap bonds
with different ratings to produce a
capital gain with a minimal increase
in risk
39

Rate Anticipation Swap

In a rate anticipation swap, the
investor swaps bonds with different
interest rate risks in anticipation of
interest rate changes
Interest rate decline: swap long-term
premium bonds for discount bonds
Interest rate increase: swap discount
bonds for premium bonds or long-term
bonds for short-term bonds
40

Valuation of Convertible
Debentures (CD)
In case of CD, the debenture holder get interest
at a specified rate for a specified period, after
which a part of / full value of the CD is converted
into specific number of equity shares.
Again in case of partial conversion, the nonconvertible portion continues to earn interest for
the remaining period, after which it is redeemed.
The cash flows associated with this transaction are:
Periodic interest receivable from the company.
Expected market price of the shares received on
conversion.
Redemption amount if any.

VCD

Ii
Rv
MxPt

i
n
t
(1 Kd ) (1 Ke)
i 1 (1 Kd )
Vcd = Value of CD
I = Interest receivable per year
Kd = Rate of discount
Ke = Required rate of return on equity
M = No. of shares received on conversion
Rv = Redemption value of debenture
N= Life of debenture
Pt = Share price at the time of conversion
t= n + 1 year

Valuation of preference
shares
Returns / Benefits of preference
share investment are:
A dividend at a fixed rate.
Redemption amount at the time of

redemption of preference shares (this

happens in case of redeemable
preference share only).

Redeemable Preference Share

n

Di
Rv
Po

i
n
(1 Kp )
i 1 (1 Kp )
Irredeemable Preference Share

Po

i 1

Di
D

i
(1 Kp )
kp

Po = Value of Preference Share

Di = Dividend
Kp = Required rate of return
Rv = Redemption Value
n = Life of Preference Share

Valuation of Equity Share

Valuation of equity share is most
typical because of its residual
ownership character. The equity
shareholders receive, the residual
profits and also the residual assets in
case of liquidation.

Valuation Approaches
Valuation of equity shares based on
accounting intermediaries.
Valuation of equity share based on
dividend.
Valuation of equity shares based on
earnings.

Valuation of equity shares as

per Dividend discount model
Two basis factors
Expected growth pattern of future
dividend
Appropriate discount rate / required rate
of return.

As far as growth in dividend is

concerned, growth may be as:
No growth
Constant growth
Varied growth.

ZERO GROWTH MODEL

(Perpetuity case)
The dividend per share remains constant year after year

Ve

i 1

Di
D

i
(1 Ke )
ke

CONSTANT GROWTH MODEL

The dividend per share grows at a constant rate.

Ve

i 1

D0 (1 g )
i
(1 Ke)

D1

ke g

D0 = Dividend of Ist year, D1 = Next year Dividend

g = Growth rate, Ke = Required rate of return
n = No. of years

VARRIED STAGE OF GROWTH MODEL

The extraordinary growth continues for a
finite no. of years and there after
normal growth rate will prevail infinitely.

D0 (1 g1 ) i NextyearDividend
1
Ve

x
i
n
(
1

Ke
)
Ke

g
(
1

Ke
)
i 1
2
n

D0 (1 g1 ) i D0 (1 g1 ) n (1 g 2 )
1

x
i
n
(
1

Ke
)
Ke

g
(
1

Ke
)
i 1
2
n

D0 = Dividend of previous period, g1 = Normal Growth

rate, g2 = Above normal growth rate
Ke = Required rate of return, n = Period of Normal
growth

Decision
Calculated Rate of Return > Required
Rate of Return Buy
Calculated Rate of Return < Required
Rate of Return Sell

Valuation based on P/E Ratio

E0 xd / e(1 g1 ) i E0 xP / E (1 g ) n
Ve

i
n
(
1

Ke
)
(
1

Ke
)
i 1
E0 EPS
n

d / e dividend payout
g growth rate
P/E Price earning ratio
Ke required rate of return
n expected holding period of the investor

Valuation based on P/E ratio

Graham-Dodd model
Whitbeck- Kisor model

Graham-Dodd model
P/E= 8.5 + (2 x Growth%)
Price = EPS (8.5 + (2 x Growth%))
If the calculated price is more than the
current price, then the stock is
considered to be underpriced and
placed in the buy list.
Model suggested to consider a stock if
the actual price was 80% or less than
the calculated price to reduce the risk

Whitbeck- Kisor model

P/E = 8.2 + 1.5g + 0.067 D/E - 0.2

g= growth rate %
D/E =dividend payout
=standard deviation in growth rate
Decision
Theoretical P/E > actual P/E Sell
Theoretical P/E < actual P/E - Buy