11

Chapter Twelve

Principles of Bond Valuations and Investments

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.

22

Bond: Players and FactorsBond: Players and Factors

Indebted entityIndebted entity InvestorsInvestors Certificate (or bond)Certificate (or bond)

• Interest rate (coupon rate) Interest rate (coupon rate)

• Coupon payment dates (semi-annually)Coupon payment dates (semi-annually)

• Maturity date Maturity date

33

Fundaments of the Bond Valuation Fundaments of the Bond Valuation ProcessProcessRates 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

44

YieldYield

Principal (amount invested)Principal (amount invested) Dollar amount of return on investmentDollar amount of return on investment Percentage return (at an annual rate)Percentage return (at an annual rate)

55

Current YieldCurrent Yield

Current bond priceCurrent bond price Annual coupon rate Annual coupon rate Ignores capital gains or losses.Ignores capital gains or losses.

Current Yield Calculation

Current Yield =

X100%ceMarket_Pri

st_Paidlar_IntereAnnual_Dol

77

Current Yield Calculation - Current Yield Calculation - ExampleExample

An example might be a 10% coupon rate An example might be a 10% coupon rate $1000 par value bond selling for $950.$1000 par value bond selling for $950.

The current yield would be:The current yield would be:

$100 / $950 = 10.53%$100 / $950 = 10.53%

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Yield to maturity (YTM)Yield to maturity (YTM)

Return (coupon payments received)Return (coupon payments received)

Maturity valueMaturity value

Market price Market price

YTM equates the sum of the present YTM equates the sum of the present value of the cash flows of the bond with value of the cash flows of the bond with its market price (IRR)its market price (IRR)

99

Risk vs. Expected ReturnRisk vs. Expected Return

Rate of return (high/Low)Rate of return (high/Low) Degree of riskDegree of risk

• Default riskDefault risk• Bond ratings Bond ratings

Calculating Bond Prices and YTM Method 1 - 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

1111

Calculating Bond Prices – Calculating Bond Prices – Method 2 – Using EquationMethod 2 – Using Equation

Based on the principle of:Based on the principle of:

Time value of moneyTime value of money Present ValuePresent Value Future ValueFuture Value Interest rateInterest rate

------------------

Fundamentals of the Bond Valuation Process – The Value of a Bond

V

n

t 1 + V = Market value or price of the bond n = Number of periods t = Each period C t = Coupon or interest payment for each period, t Pn= Par or maturity value i = interest rate in the market

Ct Pn

(1+i)n

(1+i)t

1313

Yield to Maturity (YTM)Yield to Maturity (YTM)

Current market priceCurrent market price Par valuePar value Coupon interest rateCoupon interest rate Time to maturityTime to maturity

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

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

Call dateCall date 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,

and and • the market price.the market price.

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Yield to Call ExampleYield to Call Example

Assume a 20-year bond was initially issued Assume a 20-year bond was initially issued at 11.5% interest rate, and after two years, at 11.5% interest rate, and after two years, rates have dropped. Let us assume the bond rates have dropped. Let us assume the bond is currently selling for $1,180, and the yield is currently selling for $1,180, and the yield to maturity on the bond is 9.48%. However, to maturity on the bond is 9.48%. However, the investor who purchases the bond for the investor who purchases the bond for $1,180 may not be able to hold the bond for $1,180 may not be able to hold the bond for the remaining 18 years the remaining 18 years becausebecause the issue the issue can be called. Under theses circumstances, can be called. Under theses circumstances, yield to maturity may not be the appropriate yield to maturity may not be the appropriate measure of return over the expected measure of return over the expected holding period. holding period.

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Yield to Call Calculation – Example cont.Yield to Call Calculation – Example cont.

In the present case, we assume the bond In the present case, we assume the bond can be called at $1,090 five years after can be called at $1,090 five years after issue. Thus, the investor who buys the issue. Thus, the investor who buys the bond two years after issue can have his bond two years after issue can have his bond called back after three more years at bond called back after three more years at $1,090. To compute yield to call, we $1,090. To compute yield to call, we determine the approximate interest rate determine the approximate interest rate that will equate a $1,180 investment today that will equate a $1,180 investment today with $115 (11.5%) per year for the next with $115 (11.5%) per year for the next three years plus a payoff or call price value three years plus a payoff or call price value of $1,090 at the end of three years.of $1,090 at the end of three years.

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

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

2020Maturity

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

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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

2222

Investment Strategy: Interest-Rate Considerations (7 rules) (7 rules)

Bond Pricing Rules

• 1. Bond prices and interest rates are

inversely related.

• 2. Prices of long-term bonds are more

sensitive to a change in yields to maturity

than short-term bonds.

• 3. Bond price sensitivity increases at a

decreasing rate as maturity increases.

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Investment Strategy: Interest-Rate

Considerations (cont.)

• 4. Bond prices are more sensitive to a 4. 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 YTM.YTM.

• 5. Prices of low-coupon bonds are more 5. 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.

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Investment Strategy: Interest-Rate

Considerations (cont.)

• 6. Bond prices are more sensitive when 6. Bond prices are more sensitive when YTM is low than when YTM is high.YTM is low than when YTM is high.

• 7. Margin trading magnifies profits and 7. Margin trading magnifies profits and losses of bond investments by a factor losses of bond investments by a factor of 1/(margin requirement).of 1/(margin requirement).

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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

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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.

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

New York Stock ExchangeNew York Stock Exchange

U.S. Securities and U.S. Securities and

Exchange CommissionExchange Commission

Terms Used in Bond CalculatorsTerms Used in Bond Calculators

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Click on the following hyperlinksClick on the following hyperlinks

1. 1. Treasury DirectTreasury Direct

2. 2. Public debtPublic debt

3. 3. Online Financial TutorialOnline Financial Tutorial