1. Chapter 5
Bonds and Their Valuation

2. Definition of a Bond
Bond-
A bond is a long-term promissory note that
promises to pay the bondholder a
predetermined fixed amount of interest each
year until maturity. At maturity the principle
will be paid to the bondholder.

3. Types of Bonds
• Treasury Bond: also known as government bonds, issued by the U.S. federal
government. Three types: bills, notes, and bonds.
• Corporate Bonds: Issued by corporations, which unlike government bonds
has default risk.
• Municipal Bonds: Issued by state or local government. Advantage no
federal tax on the interest.
• Foreign Bonds: Issued by foreign government or corporations.
• Debentures: unsecured long-term debt
• Subordinated debentures: bonds that have a lower claim on assets in the
event of liquidation than do other senior debt holders
• Mortgage bonds: bonds secured by a lien on specific assets of the firm, such
as real estate
• Eurobonds: bonds issued in a country different from the one in whose
currency the bond is denominated; for instance, a bond issued in Europe or
Asia that pays interest and principal in U.S. dollars
• Zero and low coupon bonds: allow the issuing firm to issue bonds at a
substantial discount from their $1,000 face value with a zero or very low
coupon
• Junk bonds: bonds rated BB or below

4. Terminology
A.A bond’s par value is the amount that will be repaid by the firm when the
bond matures, usually $1,000
B. The contractual agreement of the bond specifies a coupon interest rate
that is expressed either as a percent of the par value or as a flat amount of
interest which the borrowing firm promises to pay the bond holder each
year. For example: A $1,000 par value bond specifying a coupon interest
rate of 9% is equivalent to an annual interest payment of $90
C. The bond has a maturity date, at which time the borrowing firm is
committed to repay the loan principal.
D.An indenture (or trust deed) is the legal agreement between the firm
issuing the bonds and the bond trustee who represents the bondholders. It
provides the specific terms of the bond agreement such as the rights and
responsibilities of both parties.

5. Terminology (Cont.)
E. Bond ratings:
1. Bond ratings are simply judgements about the future risk potential of the
bond in question. Bond ratings are extremely important in that a firm’s
bond rating tells much about the cost of funds and the firm’s access to
the debt market
2. Three primary rating agencies exist-Moody’s, Standard & Poor’s, and
Fitch Investor Services
3. The different ratings and their implications are described
Recently the bond rating agencies have been criticize for not upgrading or downgrading quick
enough.

6. Definition of Value
A.Book value is the value of an asset shown on a firm’s balance sheet,
which is, determined by its historical cost, rather than its current
worth.
B.Liquidation value is the amount that could be realized if an asset is
sold individually and not as part of going concern
C.Market value is the observed value of an asset in the marketplace
where buyers and sellers negotiate an acceptable price for the asset
D.Intrinsic value is the value based upon the expected cash flows from
the investment, the riskiness of the asset, and the investor’s
required rate of return. It is the value in the eyes of the investor and
is the same as the present value of expected future cash flows to be
received from investment

7. The value of a bond is a function of three
elements.
1. The amount and timing of the asset’s expected cash flow
2. The riskiness of these cash flows
3. The investor’s required rate of return for undertaking the
investment

8. Bond Valuation
Say IBM borrowed $100 million by selling 100,000 individual bonds for $1000
each. IBM promised to pay the bondholder an annual interest of $80 for
10 years.
 M = FV = The par value (stated face value) of the bond (usually $1000)
= $1,000
 N = Maturity date – date on which par value must be repaid = 10 years
 CR = Coupon interest rate – issuer pays interest payment to every
bondholder, usually every 6 months or every year
(Note: Most corporate bonds pay interest on a semi-annual basis)
= Interest payment / Par value = 80/1000 = 8%
 I = PMT = Interest payment
= Coupon rate x Par value = 0.08 x 1,000 = $80
 Rd = I/Y = Required rate of return for the bond holder or the bond’s
market rate

9. Bond Valuation
The value of a bond is simply the present value
of the future interest payments and maturity
value discounted at the bondholder’s required
rate of return. This may be expressed as:
Vb = PV of Interest PMTs + PV of Par Value
N
Annual Interest PMT Par Value
Vb = ∑ +
t =1 (1 + rd ) t
(1 + rd ) N

10. IN OUR EXAMPLE…
t= 0 t= 1 t= 2 ............. t=9 t=10
80 80 80 80
1,000
I. Let I/Y = rd = 6% (Note it is lower than coupon rate)
FV = Par Value = $1,000
PMT = $ 80
P/Y =1,
C/Y =1
n = 10
I/Y = rd = 6%
CPT PV = $ 1,147.20 ( Selling at a premium of $147.20 (1147.20-1000)

11. IN OUR EXAMPLE…
t= 0 t= 1 t= 2 ............. t=9 t=10
80 80 80 80
1,000
II. What if I/Y = rd = 10% (Note it is higher than coupon rate)
Then,
FV = Par Value = $1,000
PMT = $ 80
P/Y =1, C/Y =1
n = 10
I/Y = rd = 10%
CPT PV = $877.11 [Selling at a discount of $122.89 (1,000-877.11)]

12. IN OUR EXAMPLE…
t= 0 t= 1 t= 2 ............. t=9 t=10
80 80 80 80
1,000
III. What if I/Y = rd = 8 % (Note it is the same as coupon rate)
Then,
FV = Par Value = $1,000
PMT = $ 80
P/Y =1, C/Y =1
n = 10
I/Y = rd = 8%
CPT PV = $1,000 (Selling at Par value)

13. Bond Valuation with Semi-annual Compounding
What if IBM (in the previous example) pays a semi-annual interest
of $40 ($80/2) for 10 years.
1. Divide annual coupon interest payment by 2 [ 80/2 = $40]
2. Multiply n by 2 [n = 10 x 2 = 20]
3. Divide kb by 2 [ But when we use calculator we still use kb but set
P/Y = 2, C/Y = 2]
N
An a nes M Pr au
n u lI t r tP T a Vl e
b ∑
V= +
r t r N
t=
1
(+ )
1 d
( + d)
1
2 2

14. Bond Valuation with Semi-annual Compounding
(Cont.)
t= 0 t= 1 t= 2 . . . . . . . ……………….. . . . . . t=19 t=20
40 40 40 40
1,000
FV = 1,000
N = 10 x 2 = 20
I/Y = rd = 6%
P/Y = 2, C/Y = 2
PMT = 80/2 = $40
CPT PV = $1,148.77
[Compared to $1,147.20 with annual interest payment]

15. Bondholder’s Expected Rate of Return
(Yield to Maturity)
A. The bondholder’s expected rate of return is the
rate the investor will earn if the bond is held to
maturity, provided, of course, that the company
issuing the bond does not default on the
payments. This is called the Yield to maturity
A. We compute the bondholder’s expected rate of
return by finding the discount rate that gets the
present value of the future interest payments
and principal payment just equal to the bond’s
current market price

16. Yield to Maturity (Cont.)
1. Say, an investor bought a bond in the market place for $1,200 with
a par value of $1,000, annual coupon rate of $80, and matures after
10 years. What is the yield to maturity (YTM)?
t= 0 t= 1 t= 2 ............. t=9 t=10
-1,200 80 80 80 80
1,000
PV = -1,200
FV = 1,000
PMT = 80
n = 10
P/Y = C/Y = 1
CPT i = YTM = 5.38%

17. Yield to Maturity (Cont.)
2. What if the bond pays semi-annual payments of $40?
t= 0 t= 1 t= 2 ............ t=19 t=20
-1,200 40 40 40 40
1,000
PV = -1,200
FV = 1,000
PMT = 40
n = 10x2 = 20
P/Y = C/Y = 2
CPT i = YTM = 5.39%

18. Current Yield
The current yield on a bond refers to the ratio of annual
interest payment to the bond’s market price
Note: Set your decimal places to 4 in your calculator
e.g. Annual interest PMT = $80
Market price of bond = $1,200
A ul n rsP T 8
n a t et M
n Ie 0
C rn i l =Y
u et e C=
r y d = =. 7
6 %
6
Mkt rco od 10
a eP e fB
r i n 20

19. Yield to Call (YTC)
Yield to Call (YTC) is the rate of interest earned on a bond if it
was called before its maturity date.
e.g. current price of a bond is $1,150, with an annual payment
of $150, with remaining 8 years to maturity. The firm can
call the bond in 2 years with a price of $1,350. What is the
YTC if the bond was called?
PV = -1,150
FV = Call Price = 1,350
PMT = 150
n=2
P/Y = C/Y = 1
CPT i = YTC = 20.92%

20. Bond Value: Three Important Relationships
A. First relationship
1. A decrease in interest rates (required rates of return) will cause the value of
a bond to increase; an interest rate increase will cause a decrease in value.
The change in value caused by changing interest rates is called interest rate
risk.
B. Second relationship
1. If the bondholder’s required rate of return (current interest rate) equals the
coupon interest rate, the bond will sell at par , or maturity value
2. If the current interest exceeds the bond’s coupon rate, the bond will sell
below par value or at a “discount”
3. If the current interest rate is less than the bond’s coupon rate, the bond will
sell above par value or at a “premium”
C. Third relationship
A. A bondholder owning a long-term bond is exposed to greater interest rate
risk than when owning a short-term bond.

21. Zero Coupon Bonds
 Only pay par value at maturity
 No interest payment
 Always sells at a discount
e.g. A zero coupon bond with par value of $10,000 and matures in 5 years.
The required rate of return of such bonds is 8%. What is the value of the
bond?
t= 0 t= 1 t= 2 t=3 t=4 t=5
PV =? 10,000
FV = 10,000
i = 8% or FV 1, 0
0 0
0
n=5 PV= = =6 0 . 3
$, 5
8 8
( + b) ( + . 8
1 k N
1 0 )
0 5
P/Y = C/Y = 1
CPT PV =$6,805.83

22. Perpetual Bonds or Consuls
 Only pays interest indefinitely
 No par value at maturity (no maturity)
e.g. Canadian government issued a consul with a stated value of
$1,000 and coupon rate of 9%. The required rate of return of such
consuls is 7%. What is the value of the consul?
Interest payment = Coupon rate x Par Value
= 0.09 x 1,000 = $90
t= 0 t= 1 t= 2 .................... t=∞
PV =? 90 90 90
PV of these interest payments is
PT 9
M 0
Pc nu =
V sl
o = = 1 8. 1
$, 5
2 7
i 07
.0