CHAPTER 4
DEBT SECURITIES BOND VALUATION
Financial Theory
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Examples:
Debt securities issued by
Government
-
Treasury bill
Treasury note
Treasury bond
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Debt securities issued by
Companies (Corporate bonds)
-
-
-
Secured bonds
Debentures
Subordinated bonds
Convertible bonds
Zero-coupon bonds
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Bonds/ Debt Securities have 3 main characteristics:
- Maturity/ lifespan
- Interest Rate/ Coupon Rate (assume it is fixed)
- Nominal Payment/ final Repayment made at
maturity date/ Nominal Value/ Principal Value
Coupon (interest) payment
= coupon rate * nominal value
E.g. coupon rate = 5%; nominal value = Rs1000
Coupon = 5%*1000 = Rs50 (e.g. each year up until
maturity a coupon of Rs50 is paid)
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Example: Bond has a coupon rate of 5% and
nominal value Rs1000 and maturity 5 years
Fixed coupon bond
50
50
50
50
t=0
50
1000
Variable coupon bond
40
60
80
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70
50
1000
5
 Buyer’s Perspective
 Intrinsic/ Theoretical bond value > Market price
of bond
Underpriced/undervalued in bond market/ Buys
 Intrinsic bond value < Market price of bond
Overpriced/overvalued in the market. Does not
buy
 Intrinsic Bond value = Market price of bond
Fairly priced/ Normally buys
The investment decision will be different from a
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seller’s perspective.
Intrinsic value of bond (estimated
by investors) =
C/ (1 + k) + C/ (1 + k)
2
+ C/
(1 + k) 3+ … + C/ (1 + k)
N/ (1 + k)
T
+
T
C = coupon payment; N = nominal
value; k = required rate of return;
T = maturity date
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 Example:
Bond has fixed coupon rate of
5%, nominal value of Rs1000
and maturity of 5 years.
Required rate of return (k) = 6%
Calculate the value of the bond.
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Future cash flows associated with
bond:
Coupon = (5%*Rs1000) = Rs50
YEAR
1
2
3
4
5
Rs
50
50
50
50
50 + 1000
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Bond Value = 50/ 1.06 + 50/
1.06
4
2
+ 50/ 1.06
+ 1050/ 1.06
5
3
+ 50/ 1.06
= Rs957.88
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France Telecom 6,625% 10/11/10
Date
26/11/2004
Price/ €
115.10
Market Interest
rate/ %
3.743
03/12/2004
115.31
3.699
10/12/2004
115.74
3.616
21/12/2004
115.90
3.577
23/12/2004
115.91
3.571
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Yield to maturity > required rate
of return
Buys
Yield to maturity < required rate
of return
Does not buy
Yield to maturity = required rate
of return
Normally Buys
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Current market price of bond
(available from bond market)
= C/ (1 + YTM) + C/ (1 +
YTM)
2
+ C/ (1 + YTM)
C/ (1 + YTM)
T
3
+…+
+ N/ (1 + YTM)
YTM : Yield to maturity
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T
 Example:
A bond has the following
characteristics:
Coupon rate 5%, nominal value
Rs1000 and maturity 2 years.
If the market price of the bond is
equal to Rs960, calculate the
yield to maturity of the bond.
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960 = 50/ (1 + YTM) + 50/ (1 +
YTM)
2
+ 1000/ (1 + YTM)
2
Multiply both sides by 1/ (1 + YTM)
and simplify:
960 (1 + YTM)
– 1050 = 0
2
- 50 (1 + YTM)
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2
Assume (1 + YTM) = A
960 A
2
– 50 A – 1050 = 0
Use quadratic equation formula to
solve
YTM = 7.2191%
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Maturity:
01/05/11
Last
coupon
E.g.
01/05/08
Purchas
e date
E.g. 01/
09/ 08
Financial Theory
Next
coupon
E.g.
01/05/09
17
Assume fixed coupon payments = C
Nominal value = N
Bond price at purchase date = PV of
future cash flows (discounted at
YTM)
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Fractional period =
Number of (days/months)
between purchase date and next
coupon payment date divided by
total number of (days/ months)
over coupon period
E.g. 01/ 09/ 08 to 01/ 05/ 09 = 8
months
Fractional period = 8/ 12
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Fractional
period
= 8/ 12
Last
coupon
E.g.
01/05/08
Purchas
e date
E.g. 01/
09/ 08
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Next
coupon
E.g.
01/05/09
20
PV coupon at 01/ 05/ 09 = C/ (1
+ YTM)
8/12
PV coupon at 01/ 05/ 10 = C/ (1
+ YTM)
1 + 8/12
PV coupon and nominal at 01/05/11
= [C + N]/ (1 + YTM)
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2 + 8/12
21
Bond Price (Dirty Price)=
C/ (1 + YTM)
+ YTM)
YTM)
8/12
1 + 8/12
+ C/ (1
+ [C + N]/ (1 +
2 + 8/12
Dirty price: price at which buyer
purchases bond.
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Interest
earned
by Seller
Interest
earned
by Buyer
Purchase
date
E.g. 01/
Last coupon 09/ 08
E.g.
01/05/08
Financial Theory
Next coupon
E.g.
01/05/09
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Interest earned by seller = accrued
interest
Accrued interest = Coupon paid
from 01/ 05/ 08 to 01/ 09/ 08
= 4/ 12*C
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Dirty Price = Clean Price +
Accrued Interest
Clean price = Dirty price – Accrued
interest
Clean price: price at which bond is
selling in bond market at purchase
date (01/ 09/ 08)
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