Chapter 5

Bonds and Their Valuation

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.

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

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.

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.

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

The value of a bond is a function of three elements.

1. The amount and timing of the asset’s expected cash flow2. The riskiness of these cash flows3. The investor’s required rate of return for undertaking the

investment

Bond ValuationSay 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

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

tN

dt

db r

ValuePar

r

PMTInterestAnnualV

1 )1()1(

IN OUR EXAMPLE…

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

t= 0 t=10

801,000

t= 2

80t= 180

t=9

80. . . . . . . . . . . . .

IN OUR EXAMPLE…

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

t= 0 t=10

801,000

t= 2

80t= 180

t=9

80. . . . . . . . . . . . .

IN OUR EXAMPLE…

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

t= 0 t=10

801,000

t= 2

80t= 180

t=9

80. . . . . . . . . . . . .

Bond Valuation with Semi-annual CompoundingWhat 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]

Vb Annual InterstPMT

(1 rd2

)tParValue

(1 rd2

)Nt1

N

Bond Valuation with Semi-annual Compounding (Cont.)

FV = 1,000 N = 10 x 2 = 20I/Y = rd = 6% P/Y = 2, C/Y = 2PMT = 80/2 = $40CPT PV = $1,148.77[Compared to $1,147.20 with annual interest payment]

t= 0 t=20

401,000

t= 2

40t= 140

t=19

40. . . . . . . ……………….. . . . . .

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

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)?

PV = -1,200FV = 1,000PMT = 80n = 10P/Y = C/Y = 1CPT i = YTM = 5.38%

t= 0-1,200

t=10

801,000

t= 2

80t= 180

t=9

80. . . . . . . . . . . . .

Yield to Maturity (Cont.)2. What if the bond pays semi-annual payments of $40?

PV = -1,200FV = 1,000PMT = 40n = 10x2 = 20P/Y = C/Y = 2CPT i = YTM = 5.39%

t= 0-1,200

t=20

401,000

t= 2

40t= 140

t=19

40. . . . . . . . . . . .

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 = $80Market price of bond = $1,200

Current yieldCY Annual Interest PMT

MarketPr iceof Bond

80

12006.67%

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 = -1,150FV = Call Price = 1,350PMT = 150n = 2P/Y = C/Y = 1CPT i = YTC = 20.92%

Bond Value: Three Important Relationships

A. First relationship1. 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 relationship1. If the bondholder’s required rate of return (current interest rate) equals the

coupon interest rate, the bond will sell at par , or maturity value2. 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.

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?

FV = 10,000i = 8% or n = 5P/Y = C/Y = 1CPT PV =$6,805.83

t=5

10,000t= 0PV =?

t= 2t= 1 t=3 t=4

PV FV

(1 kb )N

10,000

(1 0.08)5 $6,805.83

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

PV of these interest payments is

t=

90t= 0PV =?

t= 2

90t= 190

. . . . . . . . . . . . . . . . . . . .

PVconsul PMT

i

90

0.07$1,285.71