Introduction To Bonds

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

INTRODUCTION TO BONDS

AND THEIR VALUATION

Alan Anderson, Ph.D.

ECI Risk Training

www.ecirisktraining.com


A bond is a debt instrument that providesa periodic stream of interest payments toinvestors while repaying the borrowedprincipal on a specified maturity date

WHAT IS A BOND?


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 promisedto bondholders are a fixed percentage ofa bond’s face value; this percentage isknown as the coupon rate


Coupon:

the dollar value of the periodicinterest promised to bondholders;this equals the coupon rate timesthe face value of the bond


Maturity

The time until the principalis scheduled to be repaid


Call Provisions

Some bonds contain a provision thatenables the issuer to buy the bondback from the bondholder at a pre-specified price prior to maturity


A bond containing such aprovision is said to be callable


This call option is known asan embedded option, sinceit can’t be bought or soldseparately from the bond


Put Provisions

Some bonds contain a provision thatenables the buyer to sell the bondback to the issuer at a pre-specifiedprice prior to maturity


A bond containing such aprovision is said to be putable


Sinking Fund Provisions

Some bonds are issued with aprovision that requires the issuerto buy back a fixed percentageof the bonds each year


CONVERTIBLE BONDS

A convertible bond contains an embeddedoption; the holder has the right to convertthe bond into a pre-determined number ofshares of stock


BOND ISSUERS

Bonds can be categorizedaccording 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, whichis the risk that the investor will notreceive all promised payments


They are also not taxed bystate and local governments


CORPORATE BONDS

Corporations can raise funds by issuingdebt in the form of corporate bonds

These bonds offer a higher promisedcoupon rate than Treasuries, but exposeinvestors to default risk


Ratings agencies, such as Standard andPoor’s and Moody’s, rank corporate issuersaccording to their likelihood of default


The riskiest corporations offer thehighest coupon rates to investorsas compensation for default risk


MUNICIPAL BONDS

A municipal bond is issued by a state orlocal government; as a result, they carrylittle or no default risk

They also offer an extremely favorabletax treatment to investors


A municipal bond is nottaxed at the Federal level

It is also not taxed by theissuing municipality


As a result, municipal bonds offervery low coupon rates to investors


FOREIGN BONDS

Foreign bonds are issued by foreigngovernments and corporations

These may be denominated in dollarsor in a foreign currency


ILLUSTRATING A

BOND’S CASH FLOWS

A bond’s cash flows maybe 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, thebond will make an annual couponpayment 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 computethe present value of the bond’s cashflows; this is known as the discount

rate


NOTE

The appropriate discount rate to use forpricing 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 appropriatediscount rate for this bond is 4%.

What is the price of this bond?


PRICING BONDS

WITH FORMULAS

A bond may be priced with thefollowing formula:

VB =INT

(1+ rd )t+

M

(1+ rd )N

t=1

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 thebond’s maturity date


In this example, the price is computed as:

40

(1.04)1+

40

(1.04)2+

40

(1.04)3+1,040

(1.04)4


This equals:

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


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

40

(1.05)1+

40

(1.05)2+

40

(1.05)3+1,040

(1.05)4


This equals:

38.0952 + 36.2812 + 34.5535+ 855.6106 = $964.54


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

40

(1.03)1+

40

(1.03)2+

40

(1.03)3+1,040

(1.03)4


This equals:

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


These results show the followingimportant 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 thereis an inverse relationship between interestrates and bond prices:

when rates rise, bond prices fall

when rates fall, bond prices rise


NOTE

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

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


ZERO COUPON BONDS

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


The difference between theprice paid for the bond and theface value represents the returnto the investor

This is known as a capital gain


The pricing formula fora zero coupon bond is:

VB =M

(1+ rd )N


EXAMPLE

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


VB =M

(1+ rd )N=

1,000

(1+ .08)1= $925.93

Economy & Finance

Introduction To Bonds