2. Valuation of Bonds
Bond
A long-term debt instrument (a legal contract) in which a borrower agrees to make
payments of principal and interest, on specific dates, to the holders of the bond.
Types of Bonds
•
Bonds with Maturity
•
Pure Discount Bonds
•
Perpetual Bonds
Issuers of Bonds
1.
Central Government
2.
State Government
3.
Municipalities
4.
PSUs
5.
Private Sector Companies
•
Bond Yields
Coupon rate
Current yield
Yield to maturity
Yield to call
3. Terminology
Par Value
The Value Stated on the face of Bond is called as Face Value.
Coupon Rate
Bond carries a specific interest rate which is called the coupon rate.
Maturity Period
The maturity of a bond indicates the length of time until the bond issuer returns the par
value to the bond holder and terminates or redeems the bond.
Current Yield
The current yield on a bond refers to the ratio of the annual interest payment to the current
market price .
Bonds with Call Option
The bonds issued by some companies give the right to the company to redeem entire/part of
the bond issue prior to maturity are called as callable bond or bond with call option.
Yield to Maturity
This is the rate of return that investors earn if they buy the bond at a specific price and hold it
until maturity.
Yield to Call
This is the rate of return that investors earn if they buy the bond with a call option at a
specific price and hold it till the company exercises its call option.
4. Yield to Maturity:
The yield-to-maturity (YTM) is the annualized rate
of return on the investment that the investor expects
to earn from the date of investment to the date of
maturity. YTM is bond’s internal rate of return.
YTM = Lo + (m – p) /n
0.4(m) + 0.6(p)
Where, I = Annual Interest
m = Maturity Value
p = Price of Bond
n = Number of years to maturity
5. Valuation of Bonds Contd…
Current Yield
Current yield is the annual interest divided by the
bond’s current value.
It is calculated as:
Annual Pmt
CY =
Current Value
6. Valuation of Bonds Contd…
Yield to Call:
The yield to call is the average annual rate of return that a bondholder will earn
under the following assumptions:
The bond is held to maturity
The interest payments are reinvested at the YTM
YTC = FV + m – p
n
n1
0.4(m) + .0.6(p)
Where, FV = Face Value
m = Maturity Value
p = Price of Bond
n = Number of years to maturity
n1= Called Year
7. Valuation of Bonds Contd…
Pure Discount Bonds:
A pure discount bond makes a single payment at the
maturity date of the bond.
Value of pure discount bond = PV of the amount on
maturity
8. Valuation of Bonds Contd…
Perpetual Bonds:
A perpetual bond, is a bond with no maturity date.
Therefore, it may be treated as equity, not as debt.
PV = A
r
Where PV = Present Value of the Perpetuity, A = the
Amount of the periodic payment, and r = yield ,
discount rate or interest rate.
9. Valuation of Preference Share
Capital stock which provides a specific dividend that is paid before any
dividends are paid to common stock holders, and which takes
precedence over common stock in the event of a liquidation. Like
common stock, preference shares represent partial ownership in a
company, although preferred stock shareholders do not enjoy any of
the voting rights of common stockholders. Also unlike common stock,
preference shares pay a fixed dividend that does not fluctuate,
although the company does not have to pay this dividend if it lacks
the financial ability to do so. In general, there are four different types
of preferred stock: cumulative preferred, non-cumulative,
participating, and convertible. also called preferred stock.
Po = Preference
div
( PAVF
Kp, n
) + Pn (PVF
)
Kp, n
Where, Kp = Cost of Preference Share or expected rate of return.
Pn = Maturity value of Preference shares at the end of n
number of year.
10. Valuation of Equity
The valuation of ordinary or equity shares is
relatively more difficult.
The rate of dividend on equity shares is not known;
also, the payment of equity dividend is
discretionary.
The earnings and dividends on equity shares are
generally expected to grow, unlike the interest on
bonds and preference dividend.
11. Dividend Discount Models
A procedure for valuing the price of a stock by using
predicted dividends and discounting them back to
present value. The idea is that if the value obtained from
the DDM is higher than what the shares are currently
trading at, then the stock is undervalued.
∞
t
o
t
t =1
D
V =∑
(1 + k )
V0 = Value of Stock
Dt = Dividend
k = required return
12. No Growth Model
D
Vo =
k
D is the constant dividend
k is the required rate of return
Stocks that have dividends that are expected to
remain constant
13. Constant Growth Model
D0 (1 +g )
V0 =
k −g
Dividends are expected to grow at a constant
percent per period.
D0 is most recent dividend, D0(1+g) is next
dividend
g = constant perpetual growth rate
k = required rate of return
14. Estimating Dividend Growth Rates
g = ROE × b
g = growth rate in dividends
ROE = Return on Equity for the firm
b = plowback or retention percentage rate. The
proportion of the firm’s earnings that is reinvested
in the business.
= (1- dividend payout rate)
15. Multi-Period Dividend-Discount Model
D + D
V =
(1+ k ) (1+ k )
1
0
2
1
2
D +P
... +
(1+ k )
PN = expected sales price of stock at time N
N = number of years the stock is to be held
N
N
N
16. Multi-Period Earnings-Discount Model
(1 − b) E N + P N
(1 − b) E1 (1 − b) E 2
+
... +
V0=
(1 + k )1
(1 + k ) 2
(1 + k ) N
PN = expected sales price of stock at time N
N = number of years the stock is to be held
17. P/E Ratio and Growth Opportunities
D1
E 1(1 − b)
=
P0 =
k − g k − (b × ROE )
P0
1− b
=
E 1 k − (b × ROE )
b = retention ration
ROE = Return on Equity
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