Chapter 12 Principles of Bond Valuations and Investments Copyright © 2008 by The McGraw-Hill...

Chapter 12Chapter 12

Principles of Bond Principles of Bond Valuations and Valuations and

InvestmentsInvestments

Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Objectives Objectives

1.1. Describe how the valuation of a bond is Describe how the valuation of a bond is based on present value techniques.based on present value techniques.

2.2. Explain the differences among various Explain the differences among various concepts of yield such as yield to concepts of yield such as yield to maturity, yield to call, and anticipated maturity, yield to call, and anticipated realized yield.realized yield.

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Objectives continued Objectives continued

3.3. Describe the techniques for anticipating Describe the techniques for anticipating changes in interest rates.changes in interest rates.

4.4. Develop an investment strategy for Develop an investment strategy for investing in bonds.investing in bonds.

5.5. Describe how bond swaps may be used Describe how bond swaps may be used to increase after-tax returns.to increase after-tax returns.

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Principles of Bond Valuation and Principles of Bond Valuation and InvestmentInvestment

Fundamentals of the Bond Valuation ProcessFundamentals of the Bond Valuation Process

Rates of ReturnRates of Return

The Movement of Interest RatesThe Movement of Interest Rates

Investment Strategy: Interest Rate Investment Strategy: Interest Rate ConsiderationsConsiderations

Bond SwapsBond Swaps

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Fundamentals of the Bond Fundamentals of the Bond Valuation ProcessValuation Process

The price of a bond represents the present value of future interest payments plus the present value of the par value of the bond at maturity

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VV = = Market value or price of the bondMarket value or price of the bondnn = = Number of periodsNumber of periodstt = = Each periodEach period

CCtt = = Coupon or interest payment for each period, tCoupon or interest payment for each period, t

PPnn = = Par or maturity valuePar or maturity valueii = = Interest rate in the marketInterest rate in the market

n

tn

nt

i

P

i

CV

1 11

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Assume a bond pays 10% interest or $100 for 20 Assume a bond pays 10% interest or $100 for 20 years and has a par or maturity value of $1,000.years and has a par or maturity value of $1,000.

The interest rate in the marketplace is assumed The interest rate in the marketplace is assumed to be 12%.to be 12%.

The present value of the bond, using annual The present value of the bond, using annual compounding, is:compounding, is:

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Assume a bond pays 10% interest or $100 for 20 Assume a bond pays 10% interest or $100 for 20 years and has a par or maturity value of $1,000.years and has a par or maturity value of $1,000.


The present value of the bond, using annual The present value of the bond, using annual compounding, is:compounding, is:

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Present Value of an Annuity of $1 Present Value of an Annuity of $1 (coupon payments)(coupon payments)

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Present Value of an Single Amount of $1 Present Value of an Single Amount of $1 (par or maturity value)(par or maturity value)

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Calculating Bond Prices Using Tables

Present Value of Coupon Payments (Ct) Present value of Maturity Value (Pn) (from Table 12-1 or Appendix D) (from Table 12-2 or Appendix C)

n = 20, i = 12 % n = 20, i = 12%

$100 x 7.469 = $746.90 $1,000 x 0.104 = $104.00

Present value of coupon payments = $746.90 Present value of maturity value = $104.00 Value of bond = $850.90

nn

nt

tt

t

i

P

i

CV

)1()1(1

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Calculating Bond PricesCalculating Bond PricesUsing ExcelUsing Excel

Please click on the Excel iconPlease click on the Excel icon

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Other Methods of Calculating Other Methods of Calculating Bond PricesBond Prices

Using financial calculatorUsing financial calculator

Using the Internet (Online bond Using the Internet (Online bond calculations)calculations)

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Assume a bond pays 10% interest (5% Assume a bond pays 10% interest (5% semiannually, or $50 every six months, for 20 semiannually, or $50 every six months, for 20 years and has a par or maturity value of $1,000.years and has a par or maturity value of $1,000.


The present value of the bond, using semiannual The present value of the bond, using semiannual compounding, is:compounding, is:

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Assume a bond pays 10% interest (5% Assume a bond pays 10% interest (5% semiannually, or $50 every six months, for 20 semiannually, or $50 every six months, for 20 years and has a par or maturity value of $1,000.years and has a par or maturity value of $1,000.


The present value of the bond, using semiannual The present value of the bond, using semiannual compounding, is:compounding, is:

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Excerpts from Bond Value TableExcerpts from Bond Value Table

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Rates of ReturnRates of Return

Current YieldCurrent Yield Yield to Maturity Yield to Maturity Yield to CallYield to Call Anticipated Realized YieldAnticipated Realized Yield Reinvestment AssumptionReinvestment Assumption

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Current YieldCurrent Yield Annual interest payment divided by Annual interest payment divided by

price of bond price of bond

Example:Example:• 10% coupon rate $1,000 par value bond 10% coupon rate $1,000 par value bond

selling at $950selling at $950

Ignores capital gains or lossesIgnores capital gains or losses

%53.10950$

100$yieldCurrent

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Yield to maturity (YTM)Yield to maturity (YTM) Measure of return that considersMeasure of return that considers

• Annual interest rate receivedAnnual interest rate received

• Difference between current bond price and maturity Difference between current bond price and maturity valuevalue

• Number of years to maturityNumber of years to maturity

The interest rate at which you can discount theThe interest rate at which you can discount the• Future coupon payments andFuture coupon payments and

• Maturity valueMaturity value

• To arrive at quoted price of the bondTo arrive at quoted price of the bond

Assumption: all coupons are reinvested at the same Assumption: all coupons are reinvested at the same (YTM) rate.(YTM) rate.

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Yield to Maturity ExampleYield to Maturity Example Assume the market price of the bond is $850.90, Assume the market price of the bond is $850.90,

coupon or interest payment is $100, maturity coupon or interest payment is $100, maturity value is $1,000 and number of periods is 20.value is $1,000 and number of periods is 20.

What interest rate will force the future cash What interest rate will force the future cash inflows to equal $850.90?inflows to equal $850.90?

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The Formula for Approximate The Formula for Approximate Yield to MaturityYield to Maturity

Pn-V

n (0.6) V+ (0.4) Pn

Approximare yield to maturity

V = Market value or price of the bond n = Number of periods

Ct = Coupon or interest payment for each period, t

Pn = Par or maturity value

Ct

+++

Y

Y

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Yield to CallYield to Call To the extent a debt instrument may To the extent a debt instrument may

be called in before maturity, a be called in before maturity, a separate calculation for yield to call separate calculation for yield to call may be necessarymay be necessary

Yield to call value is determined by: Yield to call value is determined by: • the coupon rate, the coupon rate, • the length of time to the call date,the length of time to the call date,• the call price, and the call price, and • the market price.the market price.

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Yield to Call ExampleYield to Call Example 20-year bond was initially issued at 11.5% interest rate, 20-year bond was initially issued at 11.5% interest rate,

and was callable at $1,090 five years after issueand was callable at $1,090 five years after issue

Two years later, the yield to maturity on the bond is Two years later, the yield to maturity on the bond is 9.48%, and the bond is selling for $1,1809.48%, and the bond is selling for $1,180

An investor who buys the bond two years after issue An investor who buys the bond two years after issue can have his bond called back after three more years at can have his bond called back after three more years at $1,090$1,090

To compute yield to call, determine the approximate To compute yield to call, determine the approximate interest rate that will equate a $1,180 investment today interest rate that will equate a $1,180 investment today with $115 (11.5%) per year for the next three years with $115 (11.5%) per year for the next three years plus a payoff or call price value of $1,090 at the end of plus a payoff or call price value of $1,090 at the end of three years.three years.

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Yield to Call Example continuedYield to Call Example continued

Yield to call = 7.43%Yield to call = 7.43%• 205 basis points less than yield to 205 basis points less than yield to

maturitymaturity

If market price is equal to or greater If market price is equal to or greater than call price, investor should do a than call price, investor should do a separate calculation for yield to callseparate calculation for yield to call

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Yield to Call Calculation -An Alternative Method Click on the Bonds iconClick on the Bonds icon

Y = yield to maturity expressed in %

R = coupon rate (or i)

P = price of the bond.

M = the number of years to Call date.

The relation is:

MYiY

RP

M

i

1001

100

1001

1

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Anticipated Realized YieldAnticipated Realized Yield

Return over the expected holding Return over the expected holding periodperiod

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The Formula for Approximate Anticipated Realized Yield

r

r

rt

PVn

VPC

)4.0()6.0(

rY == = Coupon payment

= Realized price V = Market price

YYrr = Anticipated realized yield = Anticipated realized yield

CCt t = Coupon payment= Coupon payment

PPr r = Realized price= Realized price

V = Market priceV = Market price nnr r = Number of periods to realization= Number of periods to realization

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Reinvestment AssumptionReinvestment Assumption

Yield to MaturityYield to Maturity Yield to CallYield to Call Anticipated Realized YieldAnticipated Realized Yield

Assume that the Assume that the determined ratedetermined rate also also represents an represents an appropriate rateappropriate rate for for reinvestment of funds.reinvestment of funds.

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Computing Bond YieldsComputing Bond YieldsYield Measure Purpose

Nominal Yield Measures the coupon rateCurrent yield Measures current income rate

Promised yield to maturity

Measures expected rate of return for bond held to maturity

Promised yield to call

Measures expected rate of return for bond held to first call date

Realized (horizon) yield

Measures expected rate of return for a bond likely to be sold prior to maturity.

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The Movement of Interest RatesThe Movement of Interest Rates

Investors wishing to make substantial Investors wishing to make substantial profit in bond market must try to profit in bond market must try to anticipate direction of interest ratesanticipate direction of interest rates

Short-term rates may not move in the Short-term rates may not move in the same direction as long-term ratessame direction as long-term rates

Interest rates Interest rates —— coincident indicator coincident indicator

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Factors Influencing Interest RatesFactors Influencing Interest Rates

Inflationary expectationsInflationary expectations Demand for funds by:Demand for funds by:

• IndividualsIndividuals• BusinessesBusinesses• GovernmentGovernment

Desire for savingsDesire for savings Federal Reserve policyFederal Reserve policy

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Term Structure of Interest RatesTerm Structure of Interest Rates

Depicts the relationship between Depicts the relationship between maturity and interest ratesmaturity and interest rates

Sometimes called the yield curveSometimes called the yield curve

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Maturity

Yield

c

Maturity

Yield

a

Yield

Maturityb

Maturity

Yield

d

Normal

Figure 12-1 Term Structure of Interest Figure 12-1 Term Structure of Interest RatesRates

Inverted

Humped Flat

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Investment Strategy: Interest-Investment Strategy: Interest-Rate ConsiderationsRate Considerations

Bond-Pricing Rules Bond-Pricing Rules Example of Interest-Rate ChangeExample of Interest-Rate Change Deep Discount verses Par BondsDeep Discount verses Par Bonds Yield Spread ConsiderationsYield Spread Considerations

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Expectations HypothesisExpectations Hypothesis

Any long-term rate is an average of Any long-term rate is an average of the expectations of future short-term the expectations of future short-term rates over the applicable time rates over the applicable time horizonhorizon

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Liquidity Preference TheoryLiquidity Preference Theory

The shape of the term structure The shape of the term structure curve tends to be upward sloping curve tends to be upward sloping more than any other pattern.more than any other pattern.

Reflects recognition that long Reflects recognition that long maturity obligations are subject to maturity obligations are subject to greater price-change movements greater price-change movements when interest rates changewhen interest rates change

• Investors demand higher return for Investors demand higher return for holding longer-term maturitiesholding longer-term maturities

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Market Segmentation TheoryMarket Segmentation Theory

Banks prefer short-term liquid Banks prefer short-term liquid securitiessecurities

Life insurance companies prefer Life insurance companies prefer long-term bondslong-term bonds

These two institutions often put These two institutions often put pressure on short-term and long-pressure on short-term and long-term ratesterm rates

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Relative Volatility of Short-Term Relative Volatility of Short-Term and Long-Term Interest Ratesand Long-Term Interest Rates

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Investment Strategy: Interest Rate Investment Strategy: Interest Rate ConsiderationsConsiderations

When investor believes interest rates When investor believes interest rates will fallwill fall• Buy long-terms bonds to maximize price Buy long-terms bonds to maximize price

movement with rate changemovement with rate change

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Change in Market Prices of Bonds for Shifts in Change in Market Prices of Bonds for Shifts in Yields to MaturityYields to Maturity

12 Percent Coupon Rate

6 Percent Coupon Rate

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Bond Pricing Rules

1.1. Bond prices and interest rates are Bond prices and interest rates are inversely related.inversely related.

2.2. Prices of long-term bonds are more Prices of long-term bonds are more sensitive to change in YTM than short-sensitive to change in YTM than short-term bonds.term bonds.

3.3. Bond price sensitivity increases at a Bond price sensitivity increases at a decreasing rate as maturity increases.decreasing rate as maturity increases.

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4.4. Bond prices are more sensitive to a Bond prices are more sensitive to a decline in market YTM than to a rise in decline in market YTM than to a rise in market YTMmarket YTM

5.5. Prices of low-coupon bonds are more Prices of low-coupon bonds are more sensitive to a change in YTM than high-sensitive to a change in YTM than high-coupon bonds.coupon bonds.

6.6. Bond prices are more sensitive when YTM Bond prices are more sensitive when YTM IS low than when YTM is high.IS low than when YTM is high.

Bond Pricing Rules continued

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Deep Discount versus Par BondsDeep Discount versus Par Bonds

Significant discount from par valueSignificant discount from par value

Coupon rate significantly less than Coupon rate significantly less than the prevailing rates of fixed-income the prevailing rates of fixed-income securities with similar risk profiles securities with similar risk profiles

Generally trade at lower YTM than Generally trade at lower YTM than bonds selling at close to parbonds selling at close to par

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Yield Spread ConsiderationsYield Spread Considerations

Yield spread between different Yield spread between different grades of bondsgrades of bonds

At certain phases of business cycle, At certain phases of business cycle, yield spread changesyield spread changes• Higher during recessionHigher during recession• Lower during recoveryLower during recovery

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Yield Spread Differentials on Long-Yield Spread Differentials on Long-Term BondsTerm Bonds

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Bond SwapsBond Swaps Investor sells one bond and uses the Investor sells one bond and uses the

proceeds to purchase another bond, often proceeds to purchase another bond, often at the same price. at the same price.

Investors engage in bond swaps Investors engage in bond swaps • to take a tax loss by selling one bond at a to take a tax loss by selling one bond at a

loss but then preserve their investment by loss but then preserve their investment by simultaneously buying a similar bond. simultaneously buying a similar bond.

• to obtain a higher yield and return on their to obtain a higher yield and return on their bond investments.bond investments.

Click on the bonds icon for : :

An Investor's Guide to Bond SwappingAn Investor's Guide to Bond Swapping

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A detailed tutorial of the more A detailed tutorial of the more complex concepts and calculations complex concepts and calculations

for trading bondsfor trading bonds.. Additional/advancedAdditional/advanced

• Bond PricingBond Pricing• Yield Yield

Current YieldCurrent Yield Yield to MaturityYield to Maturity

• Term Structure of Interest RatesTerm Structure of Interest Rates• Duration and much moreDuration and much more

Click on the investopediaClick on the investopedia

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Yield to Maturity – HYPERLINKYield to Maturity – HYPERLINKAdditional/advancedAdditional/advanced

What is my yield to maturity?What is my yield to maturity?

Click on the Bonds icon

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A sample of the numerous useful bond websites – – click on the icons

New York Stock New York Stock Exchange ------Exchange ------

Terms Used in bond Calculators ----------->

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Click on the following hyperlinksClick on the following hyperlinks

1. Treasury Direct1. Treasury Direct

2. Public debt2. Public debt

3. Online Financial 3. Online Financial

TutorialTutorial

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Chapter 12 Principles of Bond Valuations and Investments Copyright © 2008 by The McGraw-Hill...

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Transcript of Chapter 12 Principles of Bond Valuations and Investments Copyright © 2008 by The McGraw-Hill...