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INTRODUCTION TO BONDS
AND THEIR VALUATION
Alan Anderson, Ph.D.
ECI Risk Training
www.ecirisktraining.com
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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?
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BOND TERMINOLOGY
Face (par) value:
the price of a bond when first issued
(often a multiple of $1,000)
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Coupon rate:
The periodic interest payments promisedto bondholders are a fixed percentage ofa bond’s face value; this percentage isknown as the coupon rate
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Coupon:
the dollar value of the periodicinterest promised to bondholders;this equals the coupon rate timesthe face value of the bond
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Maturity
The time until the principalis scheduled to be repaid
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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
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A bond containing such aprovision is said to be callable
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This call option is known asan embedded option, sinceit can’t be bought or soldseparately from the bond
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Put Provisions
Some bonds contain a provision thatenables the buyer to sell the bondback to the issuer at a pre-specifiedprice prior to maturity
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A bond containing such aprovision is said to be putable
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Sinking Fund Provisions
Some bonds are issued with aprovision that requires the issuerto buy back a fixed percentageof the bonds each year
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CONVERTIBLE BONDS
A convertible bond contains an embeddedoption; the holder has the right to convertthe bond into a pre-determined number ofshares of stock
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BOND ISSUERS
Bonds can be categorizedaccording to their issuers:
Treasury Bonds
Corporate Bonds
Municipal Bonds
Foreign Bonds
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TREASURY BONDS
Treasury bonds are issued by the U.S.government to finance its deficits
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These are free of default risk, whichis the risk that the investor will notreceive all promised payments
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They are also not taxed bystate and local governments
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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
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Ratings agencies, such as Standard andPoor’s and Moody’s, rank corporate issuersaccording to their likelihood of default
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The riskiest corporations offer thehighest coupon rates to investorsas compensation for default risk
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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
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A municipal bond is nottaxed at the Federal level
It is also not taxed by theissuing municipality
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As a result, municipal bonds offervery low coupon rates to investors
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FOREIGN BONDS
Foreign bonds are issued by foreigngovernments and corporations
These may be denominated in dollarsor in a foreign currency
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ILLUSTRATING A
BOND’S CASH FLOWS
A bond’s cash flows maybe shown with a time line
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EXAMPLE
Suppose that a bond is issued with:
a face value of $1,000
a coupon rate of 4%
a maturity of four years
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With a face value of $1,000, thebond will make an annual couponpayment of:
4%* $1,000 = $40
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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
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This is shown as follows:
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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
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NOTE
The appropriate discount rate to use forpricing a bond depends on several factors,including the bond’s default risk and maturity
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PRICING BONDS
A bond’s price equals the present value
of its expected future cash flows
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EXAMPLE
Referring to the previous example,suppose that the appropriatediscount rate for this bond is 4%.
What is the price of this bond?
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PRICING BONDS
WITH FORMULAS
A bond may be priced with thefollowing formula:
VB =INT
(1+ rd )t+
M
(1+ rd )N
t=1
N
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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
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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
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This equals:
38.4615 + 36.9822 + 35.5599+ 888.9964 = $1,000.00
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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
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This equals:
38.0952 + 36.2812 + 34.5535+ 855.6106 = $964.54
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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
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This equals:
38.8350 + 37.7038 + 36.6057+ 924.0265 = $1,037.17
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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
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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
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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
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ZERO COUPON BONDS
A zero-coupon bond does not make anycoupon payments; instead, it is sold toinvestors at a discount from face value
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The difference between theprice paid for the bond and theface value represents the returnto the investor
This is known as a capital gain
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The pricing formula fora zero coupon bond is:
VB =M
(1+ rd )N
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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?
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VB =M
(1+ rd )N=
1,000
(1+ .08)1= $925.93
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