Introduction To Bonds

INTRODUCTION TO BONDS
AND THEIR VALUATION

Alan Anderson, Ph.D.
ECI Risk Training
www.ecirisktraining.com

(c) ECI RISK TRAINING 2009
www.ecirisktraining.com 1

WHAT IS A BOND?

A bond is a debt instrument that provides
a periodic stream of interest payments to
investors while repaying the borrowed
principal on a specified maturity date


BOND TERMINOLOGY

Face (par) value:

the price of a bond when first issued

(often a multiple of $1,000)


Coupon rate:

The periodic interest payments promised
to bondholders are a fixed percentage of
a bond’s face value; this percentage is
known as the coupon rate


Coupon:

the dollar value of the periodic
interest promised to bondholders;
this equals the coupon rate times
the face value of the bond


Maturity

The time until the principal
is scheduled to be repaid


Call Provisions

Some bonds contain a provision that
enables the issuer to buy the bond
back from the bondholder at a pre-
specified price prior to maturity


A bond containing such a
provision is said to be callable


This call option is known as
an embedded option, since
it can’t be bought or sold
separately from the bond


Put Provisions

Some bonds contain a provision that
enables the buyer to sell the bond
back to the issuer at a pre-specified
price prior to maturity


A bond containing such a
provision is said to be putable


Sinking Fund Provisions

Some bonds are issued with a
provision that requires the issuer
to buy back a fixed percentage
of the bonds each year


CONVERTIBLE BONDS
A convertible bond contains an embedded
option; the holder has the right to convert
the bond into a pre-determined number of
shares of stock


BOND ISSUERS
Bonds can be categorized
according to their issuers:

Treasury Bonds
Corporate Bonds
Municipal Bonds
Foreign Bonds

TREASURY BONDS

Treasury bonds are issued by the U.S.
government to finance its deficits


These are free of default risk, which
is the risk that the investor will not
receive all promised payments


They are also not taxed by
state and local governments


CORPORATE BONDS
Corporations can raise funds by issuing
debt in the form of corporate bonds

These bonds offer a higher promised
coupon rate than Treasuries, but expose
investors to default risk


Ratings agencies, such as Standard and
Poor’s and Moody’s, rank corporate issuers
according to their likelihood of default


The riskiest corporations offer the
highest coupon rates to investors
as compensation for default risk


MUNICIPAL BONDS

A municipal bond is issued by a state or
local government; as a result, they carry
little or no default risk

They also offer an extremely favorable
tax treatment to investors


A municipal bond is not
taxed at the Federal level

It is also not taxed by the
issuing municipality


As a result, municipal bonds offer
very low coupon rates to investors


FOREIGN BONDS

Foreign bonds are issued by foreign
governments and corporations

These may be denominated in dollars
or in a foreign currency


ILLUSTRATING A
BOND’S CASH FLOWS

A bond’s cash flows may
be shown with a time line


EXAMPLE

Suppose that a bond is issued with:

a face value of $1,000
a coupon rate of 4%
a maturity of four years


With a face value of $1,000, the
bond will make an annual coupon
payment of:

4%* $1,000 = $40


On the bond’s maturity date, the bond pays:

one final $40 coupon
the face value of $1,000

Therefore, the final cash flow totals $1,040


This is shown as follows:


where:

VB = the bond’s price or value
rd = the interest rate used to compute
the present value of the bond’s cash
flows; this is known as the discount
rate

NOTE
The appropriate discount rate to use for
pricing a bond depends on several factors,
including the bond’s default risk and maturity


PRICING BONDS

A bond’s price equals the present value
of its expected future cash flows


EXAMPLE
Referring to the previous example,
suppose that the appropriate
discount rate for this bond is 4%.

What is the price of this bond?


PRICING BONDS
WITH FORMULAS
A bond may be priced with the
following formula:

N
INT M
VB = +
t =1 (1 + rd ) (1 + rd )
t N


where:
INT = the periodic coupon or
interest payment
rd = the discount rate
M = the bond’s par or face value
N = the number of periods until the
bond’s maturity date

In this example, the price is computed as:

40 40 40 1, 040
1
+ 2
+ 3
+ 4
(1.04) (1.04) (1.04) (1.04)


This equals:

38.4615 + 36.9822 + 35.5599
+ 888.9964 = $1,000.00


At a discount rate of 5%, the price is:

40 40 40 1, 040
1
+ 2
+ 3
+ 4
(1.05) (1.05) (1.05) (1.05)


This equals:

38.0952 + 36.2812 + 34.5535
+ 855.6106 = $964.54


At a discount rate of 3%, the price is:

40 40 40 1, 040
1
+ 2
+ 3
+ 4
(1.03) (1.03) (1.03) (1.03)


This equals:

38.8350 + 37.7038 + 36.6057
+ 924.0265 = $1,037.17


These results show the following
important relationship:

If rd > coupon rate, VB < face value
If rd = coupon rate, VB = face value
If rd < coupon rate, VB > face value


These results also demonstrate that there
is an inverse relationship between interest
rates and bond prices:

when rates rise, bond prices fall
when rates fall, bond prices rise


NOTE

A bond that sells for less than its face
value is known as a discount bond

A bond that sells for more than its face
value is known as a premium bond


ZERO COUPON BONDS

A zero-coupon bond does not make any
coupon payments; instead, it is sold to
investors at a discount from face value


The difference between the
price paid for the bond and the
face value represents the return
to the investor

This is known as a capital gain


The pricing formula for
a zero coupon bond is:

M
VB =
(1 + rd ) N


EXAMPLE
A one-year zero-coupon bond
is issued with a face value of
$1,000. The discount rate for
this bond is 8%. What is the
market price of this bond?


M 1, 000
VB = = = $925.93
(1 + rd ) N
(1 + .08)1


Introduction To Bonds

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