Topic 2 :VALUATION AND

CHARACTERISTICS OF BONDS

Contents :Contents :1. Definition of Bonds2. Terminology & Characteristics of

Bonds3. Definition and determinants of value4. Bond Valuation5. Yield to Maturity (YTM)6. Important factors in bond

relationship

Definition of Bonds…Definition of Bonds… A type of debt (long-term promissory note)

issued by the borrower, promising to pay fixed coupon (interest) payments at fixed intervals (6 months, 1 year etc ) and pay the par value at maturity.

0 1 2 . . . n

$I $I $I $I $I $I+$M

Example: Example: Par value = $1,000Coupon = 6.5% on par value per year,

or $65 per year ($32.50 every six months).Maturity = 28 years (matures in 2038).Issued by AT&T.

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0 1 2 … 28 (2010) (2011) (2012) (2038)

$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000

Types of BondsTypes of Bonds

DebenturesSubordinated DebenturesMortgage BondsEurobondsZero and Very Low Coupon BondsJunk Bonds (High-Yield Bonds)

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DebenturesDebenturesAny unsecured long-term debtViewed as more risky than secured bonds and

provide a higher yield than secured bonds

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Subordinated DebentureSubordinated DebentureUnsecured “junior” debt

The claims of subordinated debentures are honored only after the claims of secured debt and unsubordinated debentures have been satisfied.

Mortgage BondMortgage BondA bond secured by a lien on real propertyTypically, the value of the real property is greater

than that of the bonds issued.

EurobondsEurobondsSecurities (bonds) issued in a country different from the

one in whose currency the bond is denominatedexample – Bond issued in Asia by an American company

that pays interest and principal to the lender in US dollars. Why do this?◦The borrowing rates are lower◦To avoid SEC regulations.

Zero and Very Low Coupon BondsZero and Very Low Coupon BondsIssued at a substantial discount from the $1,000 face value

that pay no or very low coupon rate (interest). Cannot sell for more than par value

Return comes from appreciation of the bond. The entire yield-to-maturity comes from the difference between the purchase price and the par value

Make no periodic interest payments (coupon rate = 0%)

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Disadvantage:• Issuer faces large cash outflow in excess of the cash inflow when the

bond was issued Advantages:

• Cash outflows don’t occur with zero coupon bonds and are relatively low level with low coupon bonds

• Strong investor demand tends to bid up prices and yields are bid down.

Junk Bonds (High-Yield Bonds)Junk Bonds (High-Yield Bonds)High risk debt with ratings of BB or below by

Moody’s and Standard & Poor’s

High yield — typically pay 3%-5% more than AAA grade long-term bonds

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Terminology & Characteristic of Bonds..Terminology & Characteristic of Bonds..1. Par Value (M) : the bond’s face value that is

returned to the bondholder at maturity, usually $1000

2. Coupon Interest Rate ( I ) : percentage of the par value of the bond will be paid out annually

3. Maturity ( n ) : The length of time until the bond issuer returns the par value to the bondholder and terminates the bond

Example : Par Value : RM1000, Interest 5%(annually), Maturity 4 years

0 1 2 3 4

RM50 RM50 RM50 RM50RM1000

Terminology & Characteristic of Bonds..Terminology & Characteristic of Bonds..

4. Claims on Asset and Income : bonds have a claim on Assets and Income that comes ahead of common stock and preferred stock

5. Current Yield : the ratio of the annual interest payment to the bond’s market price

Current Yield : annual interest payment market price of the bond

Terminology & Characteristic of Bonds..Terminology & Characteristic of Bonds..6. Indenture : the legal agreement (bond contract) between

the firm issuing the bonds and the bond trustee who represents the bondholders

Lists all of the bond’s features: - coupon, par value, maturity, etc.

Lists restrictive provisions which are designed to protect bondholders.

Describes repayment provisions.

Terminology & Characteristic of Bonds..Terminology & Characteristic of Bonds..

7. Bond Ratings : the ratings involve a judgment about the future risk potential of the bond. The poorer the bond rating (BBB,CCC) the higher the rate of return demanded in the capital markets. They are affected by:

- a greater reliance on equity as opposed to debt in financing the firm - profitable operations - a low variability in past earnings - large firm size - little use of subordinated debt

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High Grade◦ Moody’s Aaa and S&P AAA – capacity to pay is extremely strong◦ Moody’s Aa and S&P AA – capacity to pay is very strong

Medium Grade◦ Moody’s A and S&P A – capacity to pay is strong, but more susceptible

to changes in circumstances◦ Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse

conditions will have more impact on the firm’s ability to pay Low Grade

◦ Moody’s Ba, B, Caa and Ca◦ S&P BB, B, CCC, CC◦ Considered speculative with respect to capacity to pay. The “B” ratings

are the lowest degree of speculation. Very Low Grade

◦ Moody’s C and S&P C – income bonds with no interest being paid◦ Moody’s D and S&P D – in default with principal and interest in

arrears

ValueValueBook value: value of an asset as shown on a firm’s

balance sheetLiquidation value: the dollar sum that could be

realized if an asset were sold individually and not as part of a going concern.

Market value: the observed value for the asset in the marketplace

Intrinsic or economic value: also called fair value -the present value of the asset’s expected future cash flows

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Efficient MarketEfficient Market

The values of all securities at any instant fully reflect all available public information, which results in the market and the intrinsic value being the same.

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Bond ValuationBond Valuation…… The value of the bond, Vb is

PV [future interest ( I ) and the par value (M)] of the bond. Bond Value = PV of coupons interest + PV of par

3 essential elements in bond valuation - the amount and timing of the cash flows ( I & M) - the time to maturity of the bond (n) - the investor’s required rate of return (kb)

Discount the bond’s cash flows at the investor’s required rate of return. the coupon interest rate (an annuity;PVIFA). the par value payment (a single sum;PVIF).

In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return.

Basic security valuation model can be defined as :

Bond Valuation

Can the intrinsic value of an asset differ from its market value?

Vb = I (PVIFA kb, n) + M (PVIF kb, n)

1 M

Vb = I 1 - (1 + kb)n + (1 + kb)n

kb

Vb : value of bond n : time to maturity I : coupon interest M : par value Kb : investor’s required rate of return

Bond ExampleBond Example

1. Suppose your firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments of 8%. The return on other corporate bonds of similar risk is currently 12%,

◦What would be a fair price for these bonds?

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Solution: Vb = I (PVIFA k, n ) + M (PVIF k, n ) = 80 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 ) = 80 (7.4694) + 1000 (.1037) = $701.25

1Vb = I 1 - (1 + k)n + M / (1 + k)n

k 1 = 80 1 - (1.12 )20 + 1000/ (1.12) 20

.12 = $ 701.23

0 1 2 3 . . . 20

1000 80 80 80 . . . 80

The intrinsic value is the price that investor willing to pay for 12% required rate of return.

If the bond is sold at a price above the bond value (> $701.25)

it is known as overvalued and investor should not buy the bond.

If the bond is sold at a price below the bond value(< $701.25) it is known as undervalued and a wise decision is to invest in those bonds.

Suppose the following condition occurs:a. The required return on bonds increase to 14%.b. The required return on bonds of similar risk

drops to 8%

What is the implication of the above situation on the bond value?

Solutions:a) Vb = I (PVIFA k, n ) + M (PVIF k, n ) = 80 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 ) = 80 (6.6231) + 1000 (.0728)

= $602.65

b) Vb = I (PVIFA k, n ) + M (PVIF k, n ) = 80 (PVIFA .08, 20 ) + 1000 (PVIF .08, 20 ) = 80 (9.8181) + 1000 (.2145)

= $999.95 $1000

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Note:

•If the coupon rate > discount rate, the bond will sell for a premium.

•If the coupon rate < discount rate, the bond will sell for a discount.

•If the coupon rate = discount rate, the bond will sell for a par.

Premium BondPremium BondThe market value of a bond will be above the par or

face value when the investor’s required rate is lower than the coupon interest rate. The bond will sell at a premium or above face value.

The market value of a bond will be below the par or face when the investor’s required rate is greater than the coupon interest rate. The bond will sell at a discount or below face value.

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Discount BondDiscount Bond

Suppose coupons are semi-annual

Formula for semiannually interest payment :

Vb = (I/2) (PVIFA kb/2, 2n) + M (PVIF kb/2, 2n)

1 M

Vb = I/2 1 - (1 + kb/2)2n + (1 + kb/2)2n

kb/2

Mathematical Solution:

Vb = PMT (PVIFA k, n ) + M (PVIF k, n )

= 80/2 (PVIFA .12/2, 20x2 ) + 1000 (PVIF .12/2, 20x2 )

= 40 (15.0463) + 1000 (.0972) = $699.05

Current YieldCurrent YieldThe ratio of the interest payment to the bond’s

current market price.

◦Current Yield = Annual interest payment . Current market price of the bond

Example:A $1,000 bond with 8% coupon rate and currently selling

at $700 has a current yield of

Current yield = $80 / $700 = 11.4 %

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Yield To Maturity• Also known as the expected rate of return (k) on a

bond.• The discount rate that equates the PV of future

cash flow with the current market price of the bond.

• The rate of return investors earn on a bond if they hold it to maturity.

$It $M

(1 + kb)t (1 + kb)nP0 = +

n

t = 1

YTM ExampleYTM Example

• Suppose we paid $898.90 for a $1,000 par 10% coupon bond with 8 years to maturity and semi-annual coupon payments.

• What is our yield to maturity?

Mathematical Solution:Vb = 898.90 n = 16 M= 1000 PMT = 50

k = ?? Vb = PMT (PVIFA k, n ) + M (PVIF k, n ) or

1 Vb = PMT 1 - (1 + k) n + M / (1 + k) n

k

Solve using trial & error….Try k = 12% / 2 = 6%

TIPS: TIPS: Since the Vb < M , so I < k

Mathematical Solution: 1Vb = PMT 1 - (1 + k) n + M / (1 + k) n

k 1898.90 = 50 1 - (1 + .06) 16 + 1000/ (1 + .06) 16

.06

= 505.29 + 393.65 = 898.94

So k = 6% x 2 = 12 %

Other method to calculate YTMOther method to calculate YTM(Approximate method)(Approximate method)

YTM : IM - P

n+

M + P2

I : Coupon Interest

M : Par Value

P : Market Price

n : year

Example 1 :

A bond’s market price is $1100. It has a $1000 par value, will mature in 5 years and pays interest 10% annually. What is your expected rate of return (YTM)?

YTM: 100 + (1000 -1100) / 5

1000 + 1100 / 27.6%=

Example 2 (YTM with semiannual coupon): Suppose a bond with a 10% coupon rate and

semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93.◦Is the YTM more or less than 10%?◦What is the semiannual coupon payment?◦How many periods are there?◦Calculate the YTM.

Zero Coupon BondsZero Coupon Bonds

• No coupon interest payments.• The bond holder’s return is

determined entirely by the price discount.

Zero Coupon - ExampleZero Coupon - Example

• Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity.

• What is your yield to maturity?

0 10

-$508 $1000

Zero ExampleZero Example

Mathematical Solution: PV = FV (PVIF i, n ) 508 = 1000 (PVIF i, 10 ) .508 = (PVIF i, 10 ) [use PVIF table]

PV = FV /(1 + i) 10

508 = 1000 /(1 + i)10

1.9685 = (1 + i)10

i = 7%

0 10

PV = 508 FV = 1000

FIVE IMPORTANT RELATIONSHIPSFIVE IMPORTANT RELATIONSHIPS

FIRST RELATIONSHIP

The value of the bond is inversely related to changes in the investor’s required rate of return (current interest rate) kb

If kb decrease , the value of the bond will increaseIf kb increase , the value of the bond will decrease

SECOND RELATIONSHIP

The market value (Po) will be less than the par value (M) if the investor’s required rate of return (kb) is above the coupon rate (I), but it will be valued above the par value if the investor’s required rate of return (kb) is below the coupon rate (I),

If kb = I , then M = Po

If kb > I , then M > Po (discount bond)If kb < I , then M < Po (premium bond)

THIRD RELATIONSHIP As the maturity approaches, the market value of the bond

approaches its par value

FOURTH RELATIONSHIP Change in price due to changes in interest rates Long term bond have greater interest rate risk than do

short –term bonds Low coupon rate bonds have more price risk than high

coupon rate bonds

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Relationship between bond value & interest rate

FIFTH RELATIONSHIP The sensitivity of a bond’s value to changing - depends on:

Length of time to maturityThe pattern of the cash flows provided by the bond

Exercise : Bonds Valuation (Vb)1) You own a bond that pay $100 in annual interest,

with a $1000 par value. It matures in 15 years. Your required rate of return is 12%. Calculate the value of the bond

2) Telink Corporation bonds pay $55 interest every six month, with a $1000 par value. The bond mature in 20 years. Your required rate of return is 8%. Calculate the value of the bond

Exercise : Bonds Valuation (Vb)3) Calculate the value of a bond that expects to

mature in 10 years and has a $1000 face value. The coupon interest rate is 9% that paid semiannually and the investor’s required rate of return is 16%.

4) A bond have a 10% coupon rate. The interest is paid semiannually and the bond mature in 11 years. Their par value is $1000. If your required rate of return is 10%, what is the value of the bond?

Exercise : Bonds Valuation (Vb)5) S & S has issued a 20-year bonds two years ago at

a coupon rate of 10% compound semi-annually. If the required rate of return is 9% what is the bond value?

6) Super-One Co. has bonds in the market making annual payment, with 16 years of maturity, and selling for $850. At this price the required rate of return is 8 %. What is the coupon rate for Super-One bond?

Exercise : YTM1) Dry Seal plans to issue bonds to expand operations.

The bonds will have a par value of $1,000, a 10-year maturity, and a coupon interest rate of 9%, paid semiannually. Current market conditions are such that the bonds will be sold to net $937.79. What is the yield-to-maturity of these bonds?

2) BCD's $1,000 par value bonds currently sell for $798.50. The coupon rate is 10%, paid semiannually. If the bonds have five years before maturity, what is the yield to maturity or expected rate of return?

3) If you are willing to pay $1,392.05 for a 15-year, $1,000 par value bond that pays 10% interest semiannually, what is your expected rate of return?

4) Lambda Co. has bonds outstanding that mature in 10 years. The bonds have $1,000 par value, pay interest annually at a rate of 9%, and have a current selling price of $1,125. The yield to maturity on the bonds is:

Exercise : YTM