1. Valuation of
Bonds and
Shares
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2. Features of a Bond
• Face Value
• Interest Rate—fixed or floating
• Maturity
• Redemption value
• Market Value
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3. Bond with Maturity
Bond value = Present value of interest +
Present value of maturity value:
n
INTt Bn
B0 = ∑ +
t =1 (1 + kd ) (1 + kd )
t n
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4. Yield to Maturity
• The yield-to-maturity (YTM) is the
measure of a bond’s rate of return that
considers both the interest income and
any capital gain or loss. YTM is bond’s
internal rate of return.
• A perpetual bond’s yield-to-maturity:
n =∞
INT INT
B0 = ∑ =
t = (1 + k d )
t
1 kd
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5. Bond Value and Amortisation
of Principal
• A bond (debenture) may be amortised
every year, i.e., repayment of principal
every year rather at maturity.
• The formula for determining the value of a
bond or debenture that is amortised every
year, can be written as follows:
n
CFt
B0 = ∑
t =1 (1 + k d )
t
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6. Pure Discount Bonds
Pure discount bond do not carry an explicit
rate of interest. It provides for the payment of a
lump sum amount at a future date in exchange
for the current price of the bond
Value of a pure discount bond = PV of the amount
on maturity:
Mn
B0 =
( 1 +k d )
n
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7. Bond Duration and Interest
Rate Sensitivity
The bond’s price sensitivity can be more
accurately estimated by its duration.
A bond’s duration is measured as the weighted
average of times to each cash flow (interest
payment or repayment of principal).
(1+y/y) – [{(1+y) + T (c-y)}]/ [c {(1+y)T - 1}+
y]
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8. Volatility
The volatility or the interest rate
sensitivity of a bond is given by its
duration and YTM. A bond’s volatility,
referred to as its modified duration, is
given as follows:
Duration
Volatility of a bond =
(1 + YTM)
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9. Valuation of Shares
• A company may issue two types of
shares:
– ordinary shares and
– preference shares
• Features of Preference and Ordinary
Shares
– Claims
– Dividend
– Redemption
– Conversion
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10. Valuation of Preference
Shares
• The value of the preference share
would be the sum of the present values
of dividends and the redemption value.
• A formula similar to the valuation of
bond can be used to value preference
shares with a maturity period:
n
PDIV1 Pn
P0 = ∑ +
t =1 (1 + k p ) (1 + k p ) n
t
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11. Valuation of Ordinary Shares
• Single Period Valuation:
– If the share price is expected to grow at g per
cent, then P1:
– We obtain a simple formula for the share
valuation as follows:
DIV1
P =
0
ke − g
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12. Multi-period Valuation
If the final period is n, we can write the
general formula for share value as
follows:
n
DIVt Pn
P0 = ∑ +
t =1 (1 + ke ) (1 + ke )
t n
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13. Multi-period Valuation
• Growth in Dividends
Growth = Retention ratio × Return on equity
g = b × ROE
– Normal Growth
DIV
P =
0
1
ke −g
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14. Multi-period Valuation
In the case of super normal growth for a
particular period and normal growth for the
remaining period
Share value = PV of dividends during finite super-normal growth period
+ PV of dividends during indefinite normal growth period
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15. H - MODEL
In this there is super normal in the beginning
which linearly declines to a stable rate in a
particular time say 2H years.
The value of the shares is as follows
.
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16. Price-Earnings (P/E) Ratio
P/E ratio is calculated as the price of a
share divided by earning per share
Using PE ratio the price of the share can
be calculated as follows
Price = PE ratio * EPS.
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