Chapter 6 Valuation and Chapter 6 Valuation and Characteristics of BondsCharacteristics of Bonds

LEARNNG OBJECTIVESLEARNNG OBJECTIVESAfter reading this chapter you should be able toAfter reading this chapter you should be able to1.1.            Distinguish between different kinds of bonds.Distinguish between different kinds of bonds.2.2.            Explain the more popular features of bonds.Explain the more popular features of bonds.3.3.            Define the term value as used for several different purposes.Define the term value as used for several different purposes.4.4.            Describe the basic process for valuing assets.Describe the basic process for valuing assets.5.5.            Estimate the value of a bond.Estimate the value of a bond.6.6.            Compute a bondholder’s expected rate of return.Compute a bondholder’s expected rate of return.7.7.            Explain three important relationships that exist in bond valuation.Explain three important relationships that exist in bond valuation.

OBJECTIVE 1 OBJECTIVE 1 TYPES OF BONDS TYPES OF BONDS A A bondbond is a type of debt or long-term promissory note, issued is a type of debt or long-term promissory note, issued by the borrower, promising to pay its holder a predetermined and fixed by the borrower, promising to pay its holder a predetermined and fixed amount of interest per year. amount of interest per year. However, there are a wide variety of such However, there are a wide variety of such creatures. Just to mention a few, we have creatures. Just to mention a few, we have · · DebenturesDebentures · · Subordinated debenturesSubordinated debentures · · Mortgage bondsMortgage bonds · · EurobondsEurobonds · · Zero and very low coupon bondsZero and very low coupon bonds · · Junk bondsJunk bondsWe will briefly explain each of these types of bonds. We will briefly explain each of these types of bonds.

··DebenturesDebentures The term The term debentures debentures applied to applied to any unsecured long-term debt. any unsecured long-term debt.

··Subordinated debenturesSubordinated debentures

Many firms have more than one issue of debentures outstanding. Many firms have more than one issue of debentures outstanding. In this case a hierarchy may be specified, in which some In this case a hierarchy may be specified, in which some debentures are given debentures are given subordinated standing in case of insolvency.subordinated standing in case of insolvency.

··Mortgage bondsMortgage bonds A A mortgage bond mortgage bond is a is a bond secured by a lien on real propertybond secured by a lien on real property. .

··EurobondsEurobonds

Eurobonds Eurobonds are not so much a different type of security as they are are not so much a different type of security as they are securities, in this case securities, in this case bonds, issued in a country different from the one bonds, issued in a country different from the one in whose currency the bond is denominated.in whose currency the bond is denominated.

··Zero and very low coupon bondsZero and very low coupon bonds

Zero and very low coupon bonds Zero and very low coupon bonds allowallow the issuing firm to issue the issuing firm to issue bonds at a substantial discount from their $1,000 face value with a zero bonds at a substantial discount from their $1,000 face value with a zero

or very low coupon rate.or very low coupon rate.

··Junk bondsJunk bonds Junk bonds Junk bonds are high-risk debt with ratings of BB or below by are high-risk debt with ratings of BB or below by Moody’s and Standard and Poor’s. Junk bonds are also called Moody’s and Standard and Poor’s. Junk bonds are also called high-high-yield bondsyield bonds for the high interest rates they pay the investor, typically for the high interest rates they pay the investor, typically having an interesting rate of between 3 and 5 percent more than AAA having an interesting rate of between 3 and 5 percent more than AAA grade long-term debt.grade long-term debt.

BACK TO THE FUNDATIONSBACK TO THE FUNDATIONS Axiom 1: Axiom 1: The Risk-Return Trade-off——We Won’t The Risk-Return Trade-off——We Won’t Take on Additional Risk Unless We Except to be Take on Additional Risk Unless We Except to be Compensated with Additional Return.Compensated with Additional Return.

OBJECTIVE 2 OBJECTIVE 2 TERMINOLOGY AND CHARACTERISTICS OF TERMINOLOGY AND CHARACTERISTICS OF BONDSBONDS

Some of the more important terms and characteristics that you might Some of the more important terms and characteristics that you might hear about bonds are as follows:hear about bonds are as follows:▪Claims on assets and income▪Claims on assets and income▪Par value▪Par value▪Coupon interest rate▪Coupon interest rate▪Maturity▪Maturity▪Indenture▪Indenture▪Current yield▪Current yield▪Bond ratings▪Bond ratingsLet’s consider each in turn.Let’s consider each in turn.

··Claims on Assets and IncomeClaims on Assets and Income In the case of insolvency, claims of debt in general, including In the case of insolvency, claims of debt in general, including bonds, are honored before those of both common stock and preferred bonds, are honored before those of both common stock and preferred stock. However, different types of debt may also have a hierarchy stock. However, different types of debt may also have a hierarchy among themselves as to the order of their claim on assets.among themselves as to the order of their claim on assets. Bonds also have a claim on income that comes ahead of common Bonds also have a claim on income that comes ahead of common and preferred stock. In general if interest on bonds is not paid, the bond and preferred stock. In general if interest on bonds is not paid, the bond trustees can classify the firm as insolvent and force it into bankruptcy. trustees can classify the firm as insolvent and force it into bankruptcy. Thus, the bondholder’s claim on income is more likely to be honored Thus, the bondholder’s claim on income is more likely to be honored than that of common and preferred stockholders, whose dividends are than that of common and preferred stockholders, whose dividends are paid at the discretion of the firm’s management.paid at the discretion of the firm’s management.

··Par valuePar value

The The par value of a bondpar value of a bond is its is its face value that is returned the face value that is returned the bondholder at maturity.bondholder at maturity.

··Coupon Interest RateCoupon Interest Rate The The coupon interest ratecoupon interest rate on a bond indicates the percentage of on a bond indicates the percentage of the par value of the bond that will be paid out annually in the form of the par value of the bond that will be paid out annually in the form of interest. interest.

··MaturityMaturity

The The maturity maturity of a bond indicates of a bond indicates the length of time until the bond the length of time until the bond issuer returns the par value to the bondholder and terminates or issuer returns the par value to the bondholder and terminates or redeems the bond.redeems the bond.

··IndentureIndentureAn An Indenture Indenture is the is the legal agreement between the firm issuing the legal agreement between the firm issuing the bonds and the bond trustee who represents the bondholdersbonds and the bond trustee who represents the bondholders . .

··Current yieldCurrent yield

The The current yield current yield on a bond refers to the on a bond refers to the ratio of the annual ratio of the annual interest payment to the bond’s current market priceinterest payment to the bond’s current market price. .

··Bond RatingsBond Ratings These ratings involve a judgment about the future risk potential of the These ratings involve a judgment about the future risk potential of the bond.bond.Bond ratings are favorably affected by Bond ratings are favorably affected by (1) a greater reliance on equity as opposed to debt in financing the firm, (1) a greater reliance on equity as opposed to debt in financing the firm, (2) profitable operations, (2) profitable operations, (3) a low variability in past earnings, (3) a low variability in past earnings, (4) large firm size, and (4) large firm size, and (5) little use of subordinated debt. (5) little use of subordinated debt. The poorer the bond rating, the higher the rate of return demanded in the The poorer the bond rating, the higher the rate of return demanded in the capital markets. capital markets. Table 6-1 provides an example and description of these ratings. Table 6-1 provides an example and description of these ratings.

Table 6-1Table 6-1 Standard and Poor’s Corporate Bond RatingsStandard and Poor’s Corporate Bond RatingsAAAAAA This is the highest rating assigned by Standard and Poor’s for debt obligation and This is the highest rating assigned by Standard and Poor’s for debt obligation and indicates an extremely strong capacity to pay principal and interest.indicates an extremely strong capacity to pay principal and interest.AA AA Bonds rated AA also qualify as high-quality debt obligations. Their capacity to pay Bonds rated AA also qualify as high-quality debt obligations. Their capacity to pay principal and interest is very strong, and in the majority of instances they differ from AAA principal and interest is very strong, and in the majority of instances they differ from AAA issues only in small degree.issues only in small degree.AA Bonds rated A have a strong capacity to pay principal and interest, although they Bonds rated A have a strong capacity to pay principal and interest, although they are somewhat susceptible to the adverse effects of changes in circumstances and are somewhat susceptible to the adverse effects of changes in circumstances and economic conditions.economic conditions.BBBBBB Bonds rated BBB are regarded as having an adequate capacity to pay principal Bonds rated BBB are regarded as having an adequate capacity to pay principal and interest. Whereas they normally exhibit adequate protection parameters, adverse and interest. Whereas they normally exhibit adequate protection parameters, adverse economic conditions or changing circumstances are more likely to lead to a weakened economic conditions or changing circumstances are more likely to lead to a weakened capacity to pay principal and interest for bonds in this category than for bonds n the A capacity to pay principal and interest for bonds in this category than for bonds n the A category.category.BB BB Bonds rated BB, B, CCC, and CC are regarded, on balance, as Bonds rated BB, B, CCC, and CC are regarded, on balance, as B B predominantly speculative with respect to the issuer’s capacity to pay predominantly speculative with respect to the issuer’s capacity to payCCCCCC interest and repay principal in accordance with the terms of the obligation. interest and repay principal in accordance with the terms of the obligation.CCCC BB indicates the lowest degree of speculation and CC the highest. While such BB indicates the lowest degree of speculation and CC the highest. While such bonds will likely have some quality and protective characteristics, these are outweighed bonds will likely have some quality and protective characteristics, these are outweighed by large uncertainties or major risk exposures to adverse conditions.by large uncertainties or major risk exposures to adverse conditions.C C The rating C is reserved for income bonds on which no interest is being paid The rating C is reserved for income bonds on which no interest is being paidD D Bonds rated D are in default, and payment of principal and/or interest is in arrears. Bonds rated D are in default, and payment of principal and/or interest is in arrears. Plus (+) or Minus (-): To provide more detailed indications of credit quality,Plus (+) or Minus (-): To provide more detailed indications of credit quality,the ratings from AA to BB may be modified by the addition of a plus or minus sign to show the ratings from AA to BB may be modified by the addition of a plus or minus sign to show

relative standing within the major rating categories. relative standing within the major rating categories.

OBJECTIVE 3 OBJECTIVE 3 DEFINITIONS OF VALUEDEFINITIONS OF VALUE

··Book valueBook value is the is the value of an asset as shown on a firm’s balance sheetvalue of an asset as shown on a firm’s balance sheet. .

··Liquidation valueLiquidation value is the is the dollar sum that could be realized if an asset were dollar sum that could be realized if an asset were

sold individually and not as part of a going concernsold individually and not as part of a going concern. .

··The The intrinsic or economic valueintrinsic or economic value of an asset ,also called the of an asset ,also called the fair fair

valuevalue ——is the present value of the asset’s expected future cash ——is the present value of the asset’s expected future cash flows. This value is the amount an investor should be willing to pay, flows. This value is the amount an investor should be willing to pay, given the amount, timing, and riskiness of future cash flows. given the amount, timing, and riskiness of future cash flows.

BACK TO THE FUNDATIONSBACK TO THE FUNDATIONSAxiom 6: Efficient Capital Markets——The Markets Are Quick and Axiom 6: Efficient Capital Markets——The Markets Are Quick and the Prices Are Rightthe Prices Are Right. In an efficient market, the price reflects all . In an efficient market, the price reflects all available public information about the security, and therefore it is priced available public information about the security, and therefore it is priced fairly.fairly.

VALUATION: AN OVERVIEWVALUATION: AN OVERVIEWFor our purposes, For our purposes, the value of an asset is its intrinsic value or the the value of an asset is its intrinsic value or the present value of its expected future cash flowspresent value of its expected future cash flows, where these cash flows , where these cash flows are discounted back to the present using the investor's required rate of are discounted back to the present using the investor's required rate of return. This statement is true for valuing all assets and serves as the return. This statement is true for valuing all assets and serves as the basis of almost all that we do in finance. Thus, value is affected by basis of almost all that we do in finance. Thus, value is affected by three elements:three elements: 1. The amount and timing of the asset's expected cash flows 1. The amount and timing of the asset's expected cash flows 2. The riskiness of these cash flows 2. The riskiness of these cash flows 3. The investor's required rate of return for undertaking the 3. The investor's required rate of return for undertaking the investmentinvestment

BACK TO THE FUNDATIONSBACK TO THE FUNDATIONSAxiom 1: The Risk-Return Trade-off--We Won’t Take on Additional Axiom 1: The Risk-Return Trade-off--We Won’t Take on Additional Risk Unless We Expect to Be Compensated With Additional Risk Unless We Expect to Be Compensated With Additional Return. Return. Axiom 2: The Time Value of Money--A Dollar Received Today Is Axiom 2: The Time Value of Money--A Dollar Received Today Is Worth More Than a Dollar Received in the Future.Worth More Than a Dollar Received in the Future.Axiom 3: Cash—Not Profits--is King. Axiom 3: Cash—Not Profits--is King.

The value of an asset involves:The value of an asset involves: 1. Assessing the asset's characteristics, which include the amount 1. Assessing the asset's characteristics, which include the amount and timing of the expected cash flows and the riskiness of these cash and timing of the expected cash flows and the riskiness of these cash flows;flows; 2.Determining the investor's required rate of return, which embodies 2.Determining the investor's required rate of return, which embodies the investor's attitude about assuming risk and perception of the the investor's attitude about assuming risk and perception of the riskiness of the asset; andriskiness of the asset; and 3. Discounting the expected cash flows back to the present, using 3. Discounting the expected cash flows back to the present, using

the investor’s required rate of return as the discount rate.the investor’s required rate of return as the discount rate.

OBJECTIVE 4: VALUATION: THE BACIS PROCESSOBJECTIVE 4: VALUATION: THE BACIS PROCESS

AA basic security valuation model can be defined mathematically basic security valuation model can be defined mathematically as follows: as follows: V = C V = C

11/(1+k)/(1+k)1 1 + C+ C22/(1+k)/(1+k)

2 2 ++… … + C+ Cn n /(1+k)/(1+k)nn （（ 6-26-2 ））

where Cwhere Ct t = cash flow to be received at time= cash flow to be received at time t t

V = the intrinsic value or present value of an asset V = the intrinsic value or present value of an asset producing expected future cash flows, producing expected future cash flows, CCtt, in years 1 through , in years 1 through nn

KK=the investor’s required rate of return=the investor’s required rate of return

n

tt

t

k

C

1 )1(

n

tt

t

k

C

1 )1(

n

tt

t

k

C

1 )1(

n

tt

t

k

C

1 )1(

• Using equation (6-2), there are three basic steps in the valuation process: Step l: Estimate the Ct in equation (6-2), which is the amount

and timing of the future cash flows the security is expected to provide.Step 2: Determine k, the investor's required rate of return.Step 3: Calculate the intrinsic value, V, as the present value of expected future cash flows discounted at the investor's required rate of return.

OBJECTIVE 5: BOND VALUTIONOBJECTIVE 5: BOND VALUTIONThe valuation process for a bond, as depicted in Figure 6-2, requires The valuation process for a bond, as depicted in Figure 6-2, requires knowledge of three essential elements: knowledge of three essential elements: (1)the amount of the cash flows to be received by the investor, (1)the amount of the cash flows to be received by the investor, (2)the maturity date of the loan, and (2)the maturity date of the loan, and (3)the investor’s required rate of return. (3)the investor’s required rate of return.

EXAMPLEEXAMPLEConsider a bond issued by American Airlines with a maturity date of Consider a bond issued by American Airlines with a maturity date of 2016 and a stated coupon rate of 9 percent. In 1996, with 20 years left 2016 and a stated coupon rate of 9 percent. In 1996, with 20 years left to maturity, investors owning the bonds were requiring an 8.4 percent to maturity, investors owning the bonds were requiring an 8.4 percent rate of return. We can calculate the value of the bonds to these rate of return. We can calculate the value of the bonds to these investors using the following three-step valuation procedure: investors using the following three-step valuation procedure:

··Step 1: Estimate the amount and timing of the expected future cash flows. Two Step 1: Estimate the amount and timing of the expected future cash flows. Two

type of cash flows are received by the bondholder: type of cash flows are received by the bondholder: a.a.            Annual interest payments equal to the coupon rate of interest times the face Annual interest payments equal to the coupon rate of interest times the face value of the bond. In this example the bond’s coupon interest rate is 9 percent; value of the bond. In this example the bond’s coupon interest rate is 9 percent; thus the annual interest payment is $90=0.09thus the annual interest payment is $90=0.09××$1,000. Assuming that 1996 interest $1,000. Assuming that 1996 interest payments have already been made, these cash flows will be received by the payments have already been made, these cash flows will be received by the bondholder in each of the 20 years before the bond matures (1997 through 2016 = bondholder in each of the 20 years before the bond matures (1997 through 2016 = 20 years). 20 years). Figure 6-2 Data Requirements for Bond Valuation Figure 6-2 Data Requirements for Bond Valuation b. The face value of the bond of $l,000 to be received in 2016. To summarize, the b. The face value of the bond of $l,000 to be received in 2016. To summarize, the cash flows received by the bondholder are as follows: cash flows received by the bondholder are as follows: YEARS 1 2 3 4 … 19 20YEARS 1 2 3 4 … 19 20 $90 $90 $90 $90 … $90 $90 $90 $90 $90 $90 … $90 $90 +$1,000+$1,000 $1,090 $1,090

·· Step 2: Determine the investor's required rate of return by evaluating Step 2: Determine the investor's required rate of return by evaluating

the riskiness of the bond's future cash flows. An 8.4 percent required rate the riskiness of the bond's future cash flows. An 8.4 percent required rate of return for the bondholders is given. In Chapter 8, we will learn how this of return for the bondholders is given. In Chapter 8, we will learn how this rate is determined. For now, simply realize that the investor’s required rate is determined. For now, simply realize that the investor’s required rate of return is equal to a rate earned on a risk-free security plus a risk rate of return is equal to a rate earned on a risk-free security plus a risk premium for assuming risk.premium for assuming risk.

·· Step 3: Calculate the intrinsic value of the bond as the present value Step 3: Calculate the intrinsic value of the bond as the present value

of the expected future interest and principal payments discounted at the of the expected future interest and principal payments discounted at the

investor's required rate of return.investor's required rate of return. The present value of American Airlines bonds is found as follows:The present value of American Airlines bonds is found as follows:bond value = bond value = VVb b =$ interest in yare 1/(1+required rate of return)=$ interest in yare 1/(1+required rate of return)11

+$ interest in year 2/(1+required rate of return) +$ interest in year 2/(1+required rate of return)2 (6-3a)2 (6-3a)

+ …+$ interest in year 20/(1+required rate of return) + …+$ interest in year 20/(1+required rate of return)2020

+$ par value of bond/(1+required rate of return) +$ par value of bond/(1+required rate of return)2020

·· Semiannual Interest Payments Semiannual Interest Payments

In the preceding American Airlines illustration, the interest payments In the preceding American Airlines illustration, the interest payments were assumed to be paid annually. However, companies typically pay were assumed to be paid annually. However, companies typically pay interest to bondholders semi-annually. interest to bondholders semi-annually. First, thinking in terms of First, thinking in terms of periodsperiods instead of years, a bond with a life of instead of years, a bond with a life of nn years paying interest semiannually has a life of years paying interest semiannually has a life of 2n2n periods. In other periods. In other words, a five-year bond (n=5) that remits its interest on a semiannual words, a five-year bond (n=5) that remits its interest on a semiannual basis actually, makes 10 payments. Yet although the number of periods basis actually, makes 10 payments. Yet although the number of periods has doubled, the has doubled, the dollardollar amount of interest being sent to the investors amount of interest being sent to the investors for each period and the bondholders’ required rate of return are half of for each period and the bondholders’ required rate of return are half of the equivalent annual figures.the equivalent annual figures. I Itt becomes becomes IItt /2 and /2 and kkb b is changed to is changed to kkbb /2; /2;

thus, for semiannual compounding, equation (6-3b) becomesthus, for semiannual compounding, equation (6-3b) becomes (6-4) (6-4)

Alternatively, using the notations introduced in Chapter 5 for Alternatively, using the notations introduced in Chapter 5 for discounting cash flows, the above equation may be restated as follows:discounting cash flows, the above equation may be restated as follows:

V Vb b = ($I= ($I

tt/2)(PVIFA/2)(PVIFAkb/2,2nkb/2,2n) + $M(PVIF) + $M(PVIF

kb/2,2nkb/2,2n) (6-5)) (6-5)

OBJECTIVE 6 OBJECTIVE 6 THE BONDHOLDER’S EXPECTED RATE OF RETURNTHE BONDHOLDER’S EXPECTED RATE OF RETURN (YIELD TO MATURITY) (YIELD TO MATURITY)

To measure the bondholder’s To measure the bondholder’s expected rate of return,expected rate of return, kkbb, we , we

would find the would find the discount rate that equates the present value of the future discount rate that equates the present value of the future cash flows (interest and maturity value) with the current market price of cash flows (interest and maturity value) with the current market price of the bond.the bond. The expected rate of return for a bond is also the The expected rate of return for a bond is also the rate of rate of return the investor will earn if the bond is to maturityreturn the investor will earn if the bond is to maturity, or the , or the yield to yield to maturitymaturity. Thus, when referring to bonds, the terms . Thus, when referring to bonds, the terms expected rate of expected rate of return and yield to maturityreturn and yield to maturity are often used interchangeably. are often used interchangeably.

To illustrate this concept, consider the Brister Corporation’s bonds, To illustrate this concept, consider the Brister Corporation’s bonds, which are selling for $1100. The bonds carry a coupon interest rate of 9 which are selling for $1100. The bonds carry a coupon interest rate of 9 percent and mature in 10 years. (Remember, the coupon rate percent and mature in 10 years. (Remember, the coupon rate determines the interest payment----coupon rate*par value).determines the interest payment----coupon rate*par value).In determining the expected rate of return (In determining the expected rate of return (kkbb), implicit in the current ), implicit in the current

market price, we need to find the rate that discounts the anticipated market price, we need to find the rate that discounts the anticipated cash flows back to a present value of $l,1 00, the current market price cash flows back to a present value of $l,1 00, the current market price ((PP00) for the bond.) for the bond.

Finding the expected rate of return for a bond using the present Finding the expected rate of return for a bond using the present value tables is done by trial and error. We have to keep trying new value tables is done by trial and error. We have to keep trying new rates until we find the discount rate that results in the present value of rates until we find the discount rate that results in the present value of the future interest and maturity value of the bond just equaling the the future interest and maturity value of the bond just equaling the current market value of the bond. If the expected rate is somewhere current market value of the bond. If the expected rate is somewhere between rates in the present value tables, we then must interpolate between rates in the present value tables, we then must interpolate between the rates. between the rates.

OBJECTIVE 7 OBJECTIVE 7 BOND VALUATION: THERE IMPORTANT BOND VALUATION: THERE IMPORTANT RELATIONSHIPSRELATIONSHIPSWe have now learned to find the value of a bond (We have now learned to find the value of a bond (VVbb), given ), given

(1) the mount of interest payment ((1) the mount of interest payment (IItt),),

(2) the maturity value ((2) the maturity value (MM), ), (3) the length of time to maturity ((3) the length of time to maturity (nn years), and years), and (4) the investor’s required rate of return, (4) the investor’s required rate of return, kkb. .b. .

We also know how to compute the expected rate of return (We also know how to compute the expected rate of return (kkbb), which ), which

also happens to be the current interest rate on the bond, givenalso happens to be the current interest rate on the bond, given (1) the current market value ( (1) the current market value (PP00), ),

(2) the amount of interest payments ( (2) the amount of interest payments (IItt), ),

(3) the maturity value ( (3) the maturity value (MM), and), and (4) the length of time to maturity ( (4) the length of time to maturity (nn years). years). We now have the basics. But let’s go further in our understanding of We now have the basics. But let’s go further in our understanding of bond valuation by studying several important relationships.bond valuation by studying several important relationships.

··First RelationshipFirst Relationship

The value of a bond is inversely related to changes in the investor’s The value of a bond is inversely related to changes in the investor’s present required rate of return (the current interest rate). In other words, present required rate of return (the current interest rate). In other words, as interest rates increase (decrease), the value of the bond decreases as interest rates increase (decrease), the value of the bond decreases (increases). (increases).

··Second RelationshipSecond Relationship

The market value of a bond will be less than the par value if the investor's The market value of a bond will be less than the par value if the investor's required rate of return is above the coupon interest rate; but it will be required rate of return is above the coupon interest rate; but it will be valued above par value if the investor's required rate of return is below valued above par value if the investor's required rate of return is below the coupon interest rate.the coupon interest rate.

··Third RelationshipThird Relationship

Long-term bonds have greater interest rate risk than do short-term Long-term bonds have greater interest rate risk than do short-term bonds.bonds.As already noted, a change in current interest rates (required rate of As already noted, a change in current interest rates (required rate of return) causes an inverse change in the market value of a bond. return) causes an inverse change in the market value of a bond. However, the impact on value is greater for long-term bonds than it is However, the impact on value is greater for long-term bonds than it is for short-term bonds.for short-term bonds.In Figure 6-3 we observed the effect of interest rate changes on a 5-In Figure 6-3 we observed the effect of interest rate changes on a 5-year bond paying a 12 percent coupon interest rate.year bond paying a 12 percent coupon interest rate.

Figure 6-3 Value and Required Rates for a 5-Year Bond at 12 Percent Figure 6-3 Value and Required Rates for a 5-Year Bond at 12 Percent Coupon Rate\ Coupon Rate\

Required rates of return

Mar

ket v

alue

6

800

900

1,000

1,100

1,200

8 10 12 14 16

$1,117

$1,000

$899

MARKET VALUE FOR A 12% COUPON-RATE MARKET VALUE FOR A 12% COUPON-RATE

BOND MATURING IN BOND MATURING IN REOUIRED RATE 5 YEARS 10 YEARS REOUIRED RATE 5 YEARS 10 YEARS

9% $1,116.80 $1,192.16 9% $1,116.80 $1,192.16 12 1,000.00 1,000.00 12 1,000.00 1,000.00 15 899.24 849.28 15 899.24 849.28

Figure 6-4: Market Values of a 5-Year and a 10-Year Bond at Different Required Figure 6-4: Market Values of a 5-Year and a 10-Year Bond at Different Required

RatesRates

Required rates of return

Mar

ket v

alue

6

800

900

1,000

1,100

1,200

8 10 12 14 16

THE ENDTHE END