The chapter covers bond valuation in detail.

1. Bond Return
and
Valuation

2. Concept of Bond
 It is a contract between a borrower and a lender in
which the borrower is required to pay a certain
amount of interest income to the lender.
 In general, bonds carry a fixed payment of interest
till the maturity date.
 The rate of interest is also known as coupon rate.

3. Bond Risk
 Bonds are considered to be quite safe but they also
carry a certain amount of risk.
 Types of bond risk:
 Interest rate risk: The value of bonds changes due to
variability of the market interest rates.
 Default risk: The borrower fails to pay the agreed value of
debt instrument on time.
 Marketability risk: There is difficulty in liquidating the
bonds in the market.
 Callability risk: There is an uncertainty created in the returns
of the investor by the issuer’s right to call the bond any time.

4. Bond Return
There are several ways of describing a rate of return on
bond. Some of them are:
 Holding period return
 The current yield
 Yield to maturity

5. Holding Period Return
 It is a return in which an investor buys a bond and
liquidates it in the market after holding it for a
definite period of time.
 The formula for calculating holding period of return
is as follows:
 It can be calculated on a daily, monthly or annual
basis.
Price gain + Coupon payment
Purchase price

6.  An investor X purchased a bond at a price of Rs.900
with Rs.100 as coupon payment and sold it at
Rs.1000. What is his holding period return?
HPR =
= (100+100)/900 = 200/900 = .222
= 22.22%
 If the bond is sold for Rs.750 after receiving Rs.100
as coupon payment, then what is the holding period
return?
HPR = (-150 + 100)/ 900 = -50/900 = -.0555
= -5.5%
Price gain + Coupon payment
Purchase price

7. The Current Yield
 It is a measure through which the investors can easily
figure out the rate of cash flow on the investments
made by them every year.
 It is calculated as:
 If the coupon payment is 8% for Rs.100 bond with the same
market price, the current yield is same 8%. If the current
market price is Rs.80 then the current yield would be 10%.
Annual Coupon Payment
Current Market Price

8. Yield to Maturity
 It is the single discount factor that makes the present
value of future cash flows from a bond equivalent to
the current price of the bond.
 The following assumptions are used to calculate yield
to maturity:
 There should not be any default.
 The interest payments are reinvested at yield to maturity.
 The investor has to hold the bond till its maturity.
 It is calculated as:
1 2 n
1 2 n
Coupon Coupon (Coupon + Face value)
Present value = + +....+
(1+y) (1+y) (1+y)
0
( or /years to maturity)
( )/2
C P D
P F


Yield to Maturity =

9. Find out the yield to maturity on a 8 per cent
5 year bond selling at Rs 105?
Yield to Maturity =
=
= × 100
YTM = 6.82.
0
( or /years to maturity)
( )/2
C P D
P F


100 105
8
5 100
100 105
2
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8 ( 1)
102.5
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10. A Rs.100 par value bond bearing a coupon of
11% matures after 5 years. The expected yield
to maturity is 15 %. The present market price
is Rs.82. Can the investor buy it?
NPV = 11*3.3522 + 100* 0.4972
= 86.59

11. Bond Value Theorems
 These are evolved on the basis of three factors:
(i) coupon rate (ii) years to maturity (iii) expected rate of return.
 The five bond value theorems are as follows:
 Theorem 1: If the bond’s market price increases then its yield declines
and vice versa.
 Theorem 2: If the bond’s yield remains constant over its life, then the
discount or premium depends on the maturity period.
 Theorem 3: If the yield remains constant over its life, the discount and
premium on bonds will decline at an increasing rate as its life gets
shorter.
 Theorem 4: A raise in the bond’s price for a decline in the bond’s yield
is greater than the fall in the bond’s price for a raise in the yield.
 Theorem 5: The percentage change in the bond’s price owing to
change in its yield will be small if the coupon rate is high.

12. Duration
 It measures the time structure and interest rate risk of
the bond.
 The formula for calculating the duration is as follows:
where D = Duration
C = Cash flow
R = Current yield to maturity
T = Number of years
Pv (Ct) = Present value of the cash flow
P0 = Sum of the present value of cash flow
T
v t
t =1 0
P (C )
D = × t
P
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