Fund.finance Lecture 3 Valuing Bond 2011 Revised

8/13/2019 Fund.finance Lecture 3 Valuing Bond 2011 Revised

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Present Value of Future Cash Flows

Link Risk & Return

Expected Returnon Assets

Valuation2


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)r+(1CF+...+

)r+(1CF+

)r+(1CF=P n

n

2

2

1

10

P0 = Price of asset at time 0 (today)

CFt = Cash flow expected at time t

r = Discount rate (reflecting assets risk)

n = Number of discounting periods (usually years)

This model can express the price of any asset at

t = 0 mathematically.

Marginal benefitof owningthe asset: right to receive the

cash flows

Marginal cost:opportunitycost of owning the asset3


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A bond is a long term security that obligates the

issuer to make specified interest and principal

payments to the holder on specified dates.

Bonds are sometimes called fixedincome securities.

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The face valueof a bond, which the borrower repaysat maturity.

Par value

The datewhen a bonds life endsand the borrower

must make the final interest payment and repay theprincipal/par value.

Maturity Date

A fixed amount of interestthat a bond promises to payinvestors each period.

Coupon payments

The rate derived by dividing the bonds annual coupon

payment by its par value.

Coupon interest rate

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WARNING

The coupon rate IS NOTthe discount rate used in the

Present Value calculations.

The coupon rate merely tells us what cash flow the bondwill produce.

Since the coupon rate is listed as a %, this misconceptionis quite common.

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Based onissuer

Governmentbonds

Municipalbonds

Corporatebonds

Foreign bonds

Based oncouponrate

Fixed rate

Floating rate

Zerocoupon

Based onprotection

Secured

Unsecured

Based onotherfeatures

Convertible

Exchangeable

Etc.

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Issued by Federal governments Have no default risk but still have interest rate risk Used to fund budget deficits If 1 year < maturity < 10 years: Treasury Notes Maturity > 10 years: Treasury Bonds

Treasury Bonds

Issued by corporations Have default risk and interest rate risk Different corporate bonds have different levels of

default risk

Corporate Bonds

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Issued by local and state government Have default risk and interest risk. In general, interest on municipal bonds tax-free

Municipal Bonds

Issued by either foreign governments or foreign

corporations. Have default risk and interest rate risk. Can issued in either in a currency or in investors home

currency Can be exposed to currency risk

Foreign Bonds

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Coupon payments are fixedat stated rate

Fixed

Rate Bonds

coupon tied to prime rate, LIBOR, Treasury rate or other interestrate

Floating rate = benchmark rate + spread Floating rate can also be tied to the inflation rate: TIPS, for example

Floating Rate Bonds

Zero-coupon bonds pay no interest Also known as Discount bonds or pure discount bonds Sell below par value Treasury Bills (Tbills) Treasury STRIPs

Zero Coupon Bonds

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Unsecured bonds (debentures) are backed only by general faithand credit of issuer

Secured bonds are backed by specific assets (collateral) Mortgage bonds, collateral trust bonds, equipment trust

certificates

Secured vs. Unsecured Bonds

A provision in a bond contract that gives the issuer the right toredeem the bonds under specified terms prior to normal

maturity dates

Call provision

A provision in a bond contract that requires the issuers to retire

a portion of the bond issue each year.

Sinking Funds

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Convertible bonds, in addition to paying coupon, offers the right to convert the bondinto common stock of the issuer of the bond

Exchangeable bonds are convertible in shares of a company other than the issuers

Convertible and Exchangeable Bonds

Callable bonds: bond issuer has the right to repurchase the bonds at a specified price(call price).

Firms could retire and reissue debt if interest rates fall. Putable bonds: the investors have the right to sell the bonds to the issuer at the put

price.

Callable and Putable Bonds

Sinking fund provisions: the issuer is required to gradually repurchase outstandingbonds.

Protective covenants: requirements the bond issuer must meet Positive and negative covenants

Protection from Default Risk

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A bond that pay interest only if it is earned

Income bond

A bond that has interest payments based on

an inflation index so as to protect hodlers frominflation

Indexed/purchasing power bond

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Assuming annual interest:

)r+(1

M

+)r+(1

C

+...+)r+(1

C

+)r+(1

C

=P nn210

)r+(1M

+rr

C=

nn

1

11

Bond Price = PV of coupons + PV of principal

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Example

What is the price of a 5.5 % annual coupon bond, with a$1,000 face value, which matures in 3 years? Assume arequired return of 3.5%.

03.056,1$

)035.1(

055,1

)035.1(

55

)035.1(

55321

PV

PV15


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Example (continued)

What is the price of the bond if the required rate of return is 5.5%?

000,1$

)055.1(

055,1

)055.1(

55

)055.1(

55

321

PV

PV

Example (continued)

What is the price of the bond if the required rate of return is 15 %?

09.783$

)15.1(

055,1

)15.1(

55

)15.1(

55321

PV

PV16


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6% coupon ratefor both

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Bond prices move inversely to yields (interest rates)


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r > Coupon InterestRate

P0< par value DISCOUNT

r < Coupon InterestRate

P0 > par value PREMIUM

r = Coupon Interest

Rate

P0 =par value PAR VALUE

What happens to bond values if the required return is not equal tothe coupon rate?

The bond's price will differ from its par value.

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880

900

920

940

960

980

1,000

1,020

1,040

1,060

1,080

0 5 10 15 20 25 30

Bond

Price

Time to Maturity

Price path for Premium

Bond

Price path for DiscountBond

TodayMaturity

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Bond prices converge to par value (plus final coupon) with

passage of time


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SEMIANNUAL COMPOUNDING

Example (continued)

Determine the price of a 5.5 % annual coupon bond, with a$1,000 face value, which matures in 3 years?

What is the price of the bond if the required rate of return is3.5% AND the coupons are paid semi-annually?

49.056,1$

)0175.1(

50.027,1

)0175.1(

50.27...)0175.1(

50.27

)0175.1(

50.276521

PV

PV

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SEMIANNUAL COMPOUNDING (CONT.)

Example (continued)

Question:How did the calculation change, given semi-annual coupons versus annual coupon payments?

Time Periods

Paying coupons twice a year,

instead of once doubles the total

number of cash flows to be

discounted in the PV formula.

Discoun t Rate

Since the time periods are now

half years, the discount rate is

also changed from the annual

rate to the half year rate.

nr

MC

r

C

r

C

r

C

2321 )2

1(

2....

)2

1(

2

)2

1(

2

)2

1(

2Price

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SEMIANNUAL COMPOUNDING (CONT.)

nr

MC

r

C

r

C

r

C

2321 )2

1(

2....

)2

1(

2

)2

1(

2

)2

1(

2Price

22

)r+(1M

+

rr

C=

nn 22

221

11

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Interest rate for which the presentvalue of the bonds couponpayments and principal equal thebond price.

YTM

Estimate the rate of return

investors earn if they buy at P0and hold it until maturity

YTM

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n

r

MC

r

C

r

CPV

)1(

)(....

)1()1( 21

YIELD TO MATURITY (YTM) (CONT.)

Calculating Yield to Maturity (YTM=r)

If you are given the price of a bond (PV) and the coupon rate,

the yield to maturity can be found by solving for r.

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YIELD TO MATURITY (YTM) (CONT.)

Example

What is the YTM of a 5.5 % annual coupon bond, with a

$1,000 face value, which matures in 3 years? The market price

of the bond is $1,056.03.

03.056,1$

)1(

055,1

)1(

55

)1(

55

321

PV

rrr

PV

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WARNING

Calculating YTM by hand can be very tedious.

It is highly recommended that you learn to use the IRR

or YTM or i functions on a financial calculator.

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The amount obtained by dividing the bondscoupon by its current market price (which

does not always equal its par value).

CurrentYield

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Interest rate risk: the risk of a decline in bonds value(bond price)due to an increase in interest rate.

Interest rate risk is higher on bonds with long maturitiesthan on those maturing in near future.

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C Discount Rate

Bon

dValue

Par

Short Maturity Bond

Long Maturity Bond

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For a given change in yields, longer maturity bonds have

largerprice changes. Bond price volatility is positively relatedto maturity


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Discount Rate

BondV

alue

High Coupon Bond

Low Coupon Bond

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For a given change in yields, higher coupon issues showsmaller price fluctuation . Bond price volatility is inverselyrelated to coupon.


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Reinvestment rate risk: the risk of decline in income froma bond portfolio due to the decrease in interest rate.

Reinvestment rate risk is higher on bonds with shortmaturities than those with longer maturities.

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Interest rate risk

Interest rate risk relates tothe value of the bond

portfolio.

Investors hold long-termbonds will face significantinterest rate risk, but will

not face muchreinvestment rate risk.

Reinvestmentrisk

Reinvestment rate riskrelates to the i ncomeof the

bond portfolio.

Otherwise, investors holdshort- termbonds will face

significant reinvestmentrate risk, but will not facemuch interest rate risk.

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Approximately, the difference between an

investments stated or nominal return and theinflation rate.

Real return

The stated return offered by an investmentunadjusted for the effects of inflation.

Nominal return

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Bond ratings: grades assigned to bond issues based ondegree of default risk

Investment-grade bonds

Moodys Aaa to Baa3 ratings S&P and Fitch AAA to BBB-

ratings

Junk bonds Moodys Ba1 to Caa1 or lower

S&P and Fitch BB to CCC+ orlower

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TUTORIALQUESTIONS

CHAPTER 5TEXTBOOK:

QUESTIONS FOR REVIEW CHAPTER 1, 2, 3, 4, 5

PRATICE PROBLEMS 7, 17, 20, 21, 22, 23 AND 25

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Fund.finance Lecture 3 Valuing Bond 2011 Revised