chapter 07 im 10th ed

CHAPTER 7

CHAPTER 7

Bonds Valuation

CHAPTER ORIENTATION

This chapter introduces the concepts that underlie asset valuation. We are specifically concerned with bonds. We also look at the concept of the bondholder's expected rate of return on an investment.CHAPTER OUTLINE

I.Types of bonds

A.Debentures: unsecured long-term debt.

B.Subordinated debentures: bonds that have a lower claim on assets in the event of liquidation than do other senior debtholders.

C.Mortgage bonds: bonds secured by a lien on specific assets of the firm, such as real estate.

D.Eurobonds: bonds issued in a country different from the one in whose currency the bond is denominated; for instance, a bond issued in Europe or Asia that pays interest and principal in U.S. dollars.

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

1.The disadvantages are, when the bond matures, the issuing firm will face an extremely large nondeductible cash outflow much greater than the cash inflow they experienced when the bonds were first issued.

2.Zero and low coupon bonds are not callable and can be retired only at maturity.

3.On the other hand, annual cash outflows associated with interest payments do not occur with zero coupon bonds.

F.Junk bonds: bonds rated BB or below.

II.Terminology and characteristics of bonds

A.A bond is a long-term promissory note that promises to pay the bondholder a predetermined, fixed amount of interest each year until maturity. At maturity, the principal will be paid to the bondholder.

B.In the case of a firm's insolvency, a bondholder has a priority of claim to the firm's assets before the preferred and common stockholders. Also, bondholders must be paid interest due them before dividends can be distributed to the stockholders.

C.A bond's par value is the amount that will be repaid by the firm when the bond matures, usually $1,000.

D.The contractual agreement of the bond specifies a coupon interest rate that is expressed either as a percent of the par value or as a flat amount of interest which the borrowing firm promises to pay the bondholder each year. For example: A $1,000 par value bond specifying a coupon interest rate of 9 percent is equivalent to an annual interest payment of $90.

E.The bond has a maturity date, at which time the borrowing firm is committed to repay the loan principal.

F.An indenture (or trust deed) is the legal agreement between the firm issuing the bonds and the bond trustee who represents the bondholders. It provides the specific terms of the bond agreement such as the rights and responsibilities of both parties.

G.The current yield on a bond refers to the ratio of annual interest payment to the bonds market price.

H.Bond ratings

1. Three primary rating agencies existMoodys, Standard & Poors, and Fitch Investor Services.

2. Bond ratings are simply judgments about the future risk potential of the bond in question. Bond ratings are extremely important in that a firms bond rating tells much about the cost of funds and the firms access to the debt market.

3.The different ratings and their implications are described.

III.Definitions of value

A.Book value is the value of an asset shown on a firm's balance sheet which is determined by its historical cost rather than its current worth.

B.Liquidation value is the amount that could be realized if an asset is sold individually and not as part of a going concern.

C.Market value is the observed value of an asset in the marketplace where buyers and sellers negotiate an acceptable price for the asset.

D.Intrinsic value is the value based upon the expected cash flows from the investment, the riskiness of the asset, and the investor's required rate of return. It is the value in the eyes of the investor and is the same as the present value of expected future cash flows to be received from the investment.

IV.Valuation: An Overview

A.The value of an asset is a function of three elements:

1.The amount and timing of the asset's expected cash flows

2.The riskiness of these cash flows

3.The investors' required rate of return for undertaking the investment

B.Expected cash flows are used in measuring the returns from an investment.

V.Valuation: The Basic Process

The value of an asset is found by computing the present value of all the future cash flows expected to be received from the asset. Expressed as a general present value equation, the value of an asset is found as follows:

V=

where Ct

=the cash flow to be received at time t

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

k=the investor's required rate of return

N=the number of periods

VI.Bond Valuation

A.The value of a bond is simply the present value of the future interest payments and maturity value discounted at the bondholder's required rate of return. This may be expressed as:

Vb=

where It =the dollar interest to be received in each payment

M=the par value of the bond at maturity

kb=the required rate of return for the bondholder

N=the number of periods to maturity

In other words, we are discounting the expected future cash flows to the present at the appropriate discount rate (required rate of return).

B.If interest payments are received semiannually (as with most bonds), the valuation equation becomes:

Vb=

VII.Bondholder's Expected Rate of Return (Yield to Maturity)

A. We compute the bondholder's expected rate of return by finding the discount rate that gets the present value of the future interest payments and principal payment just equal to the bond's current market price.

B. The bondholder's expected rate of return is also the rate the investor will earn if the bond is held to maturity, provided, of course, that the company issuing the bond does not default on the payments.

VIII.Bond Value: Five Important Relationships

A.First relationship

A decrease in interest rates (required rates of return) will cause the value of a bond to increase; an interest rate increase will cause a decrease in value. The change in value caused by changing interest rates is called interest rate risk.

B.Second relationship

1.If the bondholder's required rate of return (current interest rate) equals the coupon interest rate, the bond will sell at par, or maturity value.

2.If the bondholder's required rate of return exceeds the bond's coupon rate, the bond will sell below par value or at a "discount."

3. If the bondholder's required rate of return is less than the bond's coupon rate, the bond will sell above par value or at a "premium."

C.Third relationship

As the maturity date approaches, the market value of a bond approaches its par value.

1.The premium bond sells for less as maturity approaches.

2.The discount bond sells for more as maturity approaches.

D.Fourth relationship

A bondholder owning a long-term bond is exposed to greater interest rate risk than when owning a short-term bond.

E.Fifth relationship

The sensitivity of a bond's value to changing interest rates depends not only on the length of time to maturity, but also on the pattern of cash flows provided by the bond.

1.The duration of a bond is simply a measure of the responsiveness of its price to a change in interest rates. The greater the relative percentage change in a bond price in response to a given percentage change in the interest rate, the longer the duration.

2.Calculating duration

duration=

where t=the year the cash flow is to be received

N=the number of years to maturity

Ct=the cash flow to be received in year t

kb=the bondholder's required rate of return

P0=the bond's present value

ANSWERS TO

END-OF-CHAPTER QUESTIONS

7-1.Book value is the asset's historical value and is represented on the balance sheet as cost minus accumulated depreciation. Liquidation value is the dollar sum that could be realized if the assets were sold individually and not as part of a going concern. Market value is the observed value for an asset in the marketplace where buyers and sellers negotiate a mutually acceptable price. Intrinsic value is the present value of the asset's expected future cash flows discounted at an appropriate discount rate.

7-2.The value of a security is equal to the present value of cash flows to be received by the investor. Hence, the terms value and present value are synonymous.

7-3.The first two factors affecting asset value (the asset characteristics) are the asset's expected cash flows and the riskiness of these cash flows. The third consideration is the investor's required rate of return. The required rate of return reflects the investor's risk-return preference.

7-4.The relationship is inverse. As the required rate of return increases, the value of the security decreases, and a decrease in the required rate of return results in a price increase.

7-5.(a)The par value is the amount stated on the face of the bond. This value does not change and, therefore, is completely independent of the market value. However, the market value may change with changing economic conditions and changes within the firm.

(b)The coupon interest rate is the rate of interest that is contractually specified in the bond indenture. As such, this rate is constant throughout the life of the bond. The coupon interest rate indicates to the investor the amount of interest to be received in each payment period. On the other hand, the investor's required rate of return is equivalent to the bonds current yield to maturity, which changes with the changing bond's market price. This rate may be altered as economic conditions change and/or the investor's attitude toward the risk-return trade-off is altered.

7-6.In the case of insolvency, claims of debt holders in general, including bonds, are honored before those of both common stock and preferred stock. However, different types of debt may also have a hierarchy among themselves as to the order of their claim on assets.

Bonds also have a claim on income that comes ahead of common and preferred stock. If interest on bonds is not paid, the bond trustees can classify the firm insolvent and force it into bankruptcy. Thus, the bondholder's claim on income is more likely to be honored than that of common and preferred stockholders, whose dividends are paid at the discretion of the firm's management.

7-7.Ratings involve a judgment about the future risk potential of the bond. Although they deal with expectations, several historical factors seem to play a significant role in their determination. Bond ratings are favorably affected by (1) a greater reliance on equity, and not debt, in financing the firm, (2) profitable operations, (3) a low variability in past earnings, (4) large firm size, and (5) little use of subordinated debt. In turn, the rating a bond receives affects the rate of return demanded on the bond by the investors. The poorer the bond rating, the higher the rate of return demanded in the capital markets.

For the financial manager, bond ratings are extremely important. They provide an indicator of default risk that in turn affects the rate of return that must be paid on borrowed funds.

7-8.The term debentures applies to any unsecured long-term debt. Because these bonds are unsecured, the earning ability of the issuing corporation is of great concern to the bondholder. They are also viewed as being more risky than secured bonds and as a result must provide investors with a higher yield than secured bonds provide. Often the issuing firm attempts to provide some protection to the holder through the prohibition of any additional encumbrance of assets. This prohibits the future issuance of secured long-term debt that would further tie up the firm's assets and leave the bondholders less protected. To the issuing firm, the major advantage of debentures is that no property has to be secured by them. This allows the firm to issue debt and still preserve some future borrowing power.

A mortgage bond is a bond secured by a lien on real property. Typically, the value of the real property is greater than that of the mortgage bonds issued. This provides the mortgage bondholders with a margin of safety in the event the market value of the secured property declines. In the case of foreclosure, the trustees have the power to sell the secured property and use the proceeds to pay the bondholders. In the event that the proceeds from this sale do not cover the bonds, the bondholders become general creditors, similar to debenture bondholders, for the unpaid portion of the debt.

7-9.(a)Eurobonds are not so much a different type of security as they are securities, in this case bonds, issued in a country different from the one in whose currency the bond is denominated. For example, a bond that is issued in Europe or in Asia by an American company and that pays interest and principal to the lender in U.S. dollars would be considered a Eurobond. Thus, even if the bond is not issued in Europe, it merely needs to be sold in a country different from the one in whose currency it is denominated to be considered a Eurobond.

(b)Zero and very low coupon bonds allow the issuing firm to issue bonds at a substantial discount from their $1,000 face value with a zero or very low coupon. The investor receives a large part (or all on the zero coupon bond) of the return from the appreciation of the bond at maturity.

(c)Junk bonds refer to any bond with a rating of BB or below. The major participants in this market are new firms that do not have an established record of performance. Many junk bonds have been issued to finance corporate buyouts.

7-10.The expected rate of return is the rate of return that may be expected from purchasing a security at the prevailing market price. Thus, the expected rate of return is the rate that equates the present value of future cash flows with the actual selling price of the security in the market.

7-11.When the coupon interest rate does not equal the bondholder's required rate of return, the bond will be issued at either a premium or discount. If the investor's required rate of return is higher than the coupon interest rate, the bond will be issued at a discount to the investor. If the coupon rate is higher that the investor's required rate, the bond will be issued at a premium.

7-12.A premium bond is issued when the coupon rate is higher than the bondholder's required rate of return. The premium is the excess of the market value over the face value of the bond. A discount bond is issued when the bondholder's required rate of return is higher than the coupon rate. The discount is the excess of the face value of the bond over the market value.

Over time, the premium or discount on a bond is amortized. This amortization allows the bondholder to realize an effective yield equal to their required rate of return.

7-13.A change in current interest rates (required rate of return) causes a change in the market value of a bond. However, the impact on value is greater for long-term bonds than it is for short-term bonds. The reason long-term bond prices fluctuate more than short-term bond prices in response to interest rate changes is simple. Assume an investor bought a 10-year bond yielding a 12 percent interest rate. If the current interest rate for bonds of similar risk increased to 15 percent, the investor would be locked into the lower rate for 10 years. If, on the other hand, a shorter-term bond had been purchased, say one maturing in 2 years, the investor would have to accept the lower return for only 2 years and not the full 10 years. At the end of year 2, the investor would receive the maturity value of $1,000 and could buy a bond offering the higher 15 percent rate for the remaining 8 years. Thus, interest rate risk is determined, at least in part, by the length of time an investor is required to commit to an investment.

7-14.The duration of a bond is simply a measure of the responsiveness of its price to a change in interest rates. The greater the relative percentage change in a bond price in response to a given percentage change in the interest rate, the longer the duration.

SOLUTIONS TO

END-OF-CHAPTER PROBLEMS7-1A.Value (Vb)=

12 EQ \x(N)

12 EQ \x(I/Y)

80 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER-752.23

7-2A.If the interest is paid semiannually:

Value (Vb)=

16 EQ \x(N)

4 EQ \x(I/Y)

45 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER-1,058.26

If interest is paid annually:

Value (Vb)=

8 EQ \x(N)

8 EQ \x(I/Y)

90 EQ \x(PMT)

1000 EQ \x(FV)


7-3A.$900 =

20 EQ \x(N)

900 EQ \x(+/-) EQ \x(PV)

40 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(I/Y) (ANSWER4.79%semiannual rate

The rate is equivalent to 9.6 percent annual rate compounded semiannually, or 9.8 percent (1.0482 - 1) compounded annually.

7-4A.$945 =

20 EQ \x(N)

945 EQ \x(+/-) EQ \x(PV)

90 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(I/Y) (ANSWER9.63%

7-5A.$1,150 =

12 EQ \x(N)

1150 EQ \x(+/-) EQ \x(PV)

70 EQ \x(PMT)

1000 EQ \x(FV)


7-6A.a.$1,085 =

15 EQ \x(N)

1085 EQ \x(+/-) EQ \x(PV)

80 EQ \x(PMT)

1000 EQ \x(FV)


b.Vb =

15 EQ \x(N)

10 EQ \x(I/Y)

80 EQ \x(PMT)

1000 EQ \x(FV)


c.Since the expected rate of return, 7.06 percent, is less than your required rate of return of 10 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,085, exceeds the value of the security to the investor of $847.88.

7-7A.a.Value

Par Value$1,000.00

Coupon$ 100.00

Required Rate of Return0.12

Years to Maturity15

Market Value$ 863.78

b.Value at Alternative Rates of Return




Market Value$1,171.19

c.As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk." Thus, the greater the investor's required rate of return, the greater will be his/her discount on the bond. Conversely, the less his/her required rate of return below that of the coupon rate, the greater the premium will be.

d.Value at Alternative Maturity Dates

Years to Maturity5





e.The longer the maturity of the bond, the greater the interest rate risk the investor is exposed to, resulting in greater premiums and discounts.

7-8A.$1,250=

15 EQ \x(N)

1250 EQ \x(+/-) EQ \x(PV)

90 EQ \x(PMT)

1000 EQ \x(FV)


7-9A.(a)Vb =

20 EQ \x(N)

9 EQ \x(I/Y)

110 EQ \x(PMT)

1000 EQ \x(FV)


(b)(i)Vb=

20 EQ \x(N)

12 EQ \x(I/Y)

110 EQ \x(PMT)

1000 EQ \x(FV)


(b)(ii)Vb=

20 EQ \x(N)

6 EQ \x(I/Y)

110 EQ \x(PMT)

1000 EQ \x(FV)


(c)We see that value is inversely related to the investor's required rate of return.

7-10A.

Value Bond P

Par Value$1,000.00

Coupon$ 100.00

Required Rate of Return8%

Years to Maturity5

Market Value$ 1,079.85

Value Bond Q

Par Value$1,000.00

Coupon$ 70.00


Years to Maturity5


Value Bond R

Par Value$1,000.00

Coupon$ 120.00


Years to Maturity10


Value Bond S

Par Value$1,000.00

Coupon$ 80.00


Years to Maturity10


Value Bond T

Par Value$1,000.00

Coupon$ 65.00


Years to Maturity15


BondPQRST

EQ \a(Bond,value) $1,079.85$960.07$1,268.40$1,000.00$871.61

YearsCtt*PV(Ct)Ctt*PV(Ct)Ctt*PV(Ct)Ctt*PV(Ct)Ctt*PV(Ct)

1$100$93$70$65$120$111$80$74$65$60

2100171701201202068013765111

3100238701671202868019165155

4100294702061203538023565191

51,1003,7431,0703,6411204088027265221

6

1204548030265246

7

1204908032765265

8

1205198034665281

9

1205408036065293

10

1,1205,1881,0805,00265301

11

65307

12

65310

13

65311

14

65310

15

1,0655,036

4,539

4,198

8,554

7,247

8,398

Duration

4.20

4.37

6.74

7.25

9.63

7-11A.a.$1,100 =

7 EQ \x(N)

1100 EQ \x(+/-) EQ \x(PV)

90 EQ \x(PMT)

1000 EQ \x(FV)


b.Vb =

7 EQ \x(N)

7 EQ \x(I/Y)

90 EQ \x(PMT)

1000 EQ \x(FV)


c.Since the expected rate of return, 7.14 percent, is more than your required rate of return of 7 percent, the bond is an acceptable investment. This fact is also evident because the market price, $1,100, is less than the value of the security to the investor of $1,107.79.

7-12A.a.$915=

12 EQ \x(N)

915 EQ \x(+/-) EQ \x(PV)

50 EQ \x(PMT)

1000 EQ \x(FV)


b.Since the required rate of return(9%) is greater than the expected rate of return(6%), you should not purchase the bond.

7-13A.

Value Bond I

Par Value$1,000.00

Coupon$ 130.00


Years to Maturity 7


Value Bond II

Par Value$1,000.00

Coupon$ 90.00


Years to Maturity6


Value Bond III

Par Value$1,000.00

Coupon$ 110.00


Years to Maturity12


Value Bond IV

Par Value$1,000.00

Coupon$ 125.00


Years to Maturity5


Value Bond V

Par Value$1,000.00

Coupon$ 80.00


Years to Maturity10


BondIIIIIIIVV

Bond Value$1,323.36$1,095.33$1,317.71$1,225.51$1,070.24

YearsCttPV(Ct)CttPV(Ct)CttPV(Ct)CttPV(Ct)CttPV(Ct)

1$130$121$90$84$110$103$125$117$80$75

2$130$227$90$157$110$192$125$218$80$140

3$130$318$90$220$110$269$125$306$80$196

4$130$397$90$275$110$336$125$381$80$244

5$130$463$90$321$110$392$1,125$4,011$80$285

6$130$5201,090$4,358$110$440$80$320

71,130$4,926$110$480$80$349

8$110$512$80$372

9$110$538$80$392

10$110$559$1,080$5,490

111,110$5,801

12

Sum of

t*PV(Ct)$6,973$5,415$9,622$5,033$7,863

Duration5.27 4.94 7.30 4.11 7.35

7-14A.(a)Vb =

15 EQ \x(N)

9 EQ \x(I/Y)

85 EQ \x(PMT)

1000 EQ \x(FV)


(b)(i)Vb=

15 EQ \x(N)

11 EQ \x(I/Y)

85 EQ \x(PMT)

1000 EQ \x(FV)


(b)(ii)Vb=

15 EQ \x(N)

7 EQ \x(I/Y)

85 EQ \x(PMT)

1000 EQ \x(FV)


(c)As long as the required rate of return is less than the expected rate of return of 9%, you should purchase the bond Thus, if your required rate of return decreases to 7%, you should purchase the bond.

SOLUTION TO INTEGRATIVE PROBLEM

1.Young Corp. Bond Value (Vb)=

10 EQ \x(N)

6 EQ \x(I/Y)

78 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER-$1,132.48

Thomas Resorts Bond Value (Vb)=

17 EQ \x(N)

9 EQ \x(I/Y)

75.00 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER-$871.85

Entertainment, Inc. Bond Value (Vb)=

4 EQ \x(N)

8 EQ \x(I/Y)

79.75 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER-$999.17

2.Young Corporation: $1,030=

10 EQ \x(N)

1,030 EQ \x(+/-) EQ \x(PV)

78 EQ \x(PMT)

1000 EQ \x(FV)


Thomas Resorts: $973=

17 EQ \x(N)

973 EQ \x(+/-) EQ \x(PV)

75.00 EQ \x(PMT)

1000 EQ \x(FV)


Entertainment, Inc.: $1,035=

4 EQ \x(N)

1,035 EQ \x(+/-) EQ \x(PV)

79.75 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(I/Y) (ANSWER 6.94%

3.i.Young Corp. Bond Value (Vb)=

10 EQ \x(N)

9 EQ \x(I/Y)

78 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER- $922.99

(Vb)=

17 EQ \x(N)

12 EQ \x(I/Y)

75.00 EQ \x(PMT)

1000 EQ \x(FV)



4 EQ \x(N)

11 EQ \x(I/Y)

79.75 EQ \x(PMT)

1000 EQ \x(FV)


3.iiYoung Corp. Bond Value (Vb)=

10 EQ \x(N)

3 EQ \x(I/Y)

78 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER- $1,409.45

(Vb)=

17 EQ \x(N)

6 EQ \x(I/Y)

75.00 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER- $1,157.16


4 EQ \x(N)

5 EQ \x(I/Y)

79.75 EQ \x(PMT)

1000 EQ \x(FV)

EQ \x(PV) (ANSWER- $1,105.49

4.As the interest rates rise and fall, we see the different effects on the bond prices depending on the length of time to maturity and whether the investor's required rate of return is above or below the coupon interest rate. If the investors required rate of return is above the coupon interest rate, the bond will sell at a discount (below par value), but if the investors required rate of return is below the coupon interest rate, the bond will sell at a price above its par value (premium).

5.Duration of bonds

Young Corp.Thomas ResortsEntertainment, Inc.

Bond Value$1,030.00$ 973.00$1,035.00

Required rate of return6%9%8%

YearCtt* PV(Ct)Ctt* PV(Ct)Ctt* PV(Ct)

1$ 78.00$ 73.58$ 75.00$ 68.81$ 79.75$ 73.84

278.00138.8475.00126.2579.75136.75

378.00196.4775.00173.7479.75189.92

478.00247.1375.00212.531,079.753,174.59

578.00291.4375.00243.72

678.00329.9275.00268.32

778.00363.1275.00287.19

878.00391.5175.00301.12

978.00415.5175.00310.79

101,078.006,019.5075.00316.81

1175.00319.71

1275.00319.98

1375.00318.02

1475.00314.21

1575.00308.86

1675.00302.24

171,075.004222.86

Sum of t*PV(Ct)8,467.028,415.173,575.11

Duration8.228.653.45

The value of the Entertainment, Inc. bonds will be less sensitive to interest rate changes than will Young Corporation and Thomas Resorts bonds.

6.Although the Young Corporation bonds and the Thomas Resorts bonds have different terms to maturity, the duration of the two bonds is very similar. These two bonds will likely have similar sensitivity to changes in interest rates as evidenced by their duration values.

7.The Entertainment, Inc. and Thomas Resorts bonds have lower expected rates of return than your required rate of return. Young Corporations expected rate of return is greater than your required rate of return. So we would buy Young Corporation and not Entertainment, Inc. or Thomas Resorts.

Solutions to Problem Set B7-1B.Value (Vb)

=

10 EQ \x(N)

15 EQ \x(I/Y)

90 EQ \x(PMT)

1000 EQ \x(FV)


7-2B.If the interest is paid semiannually:

Value (Vb)=

22 EQ \x(N)

4.5 EQ \x(I/Y)

50 EQ \x(PMT)

1000 EQ \x(FV)


If interest is paid annually:

Value (Vb)=

11 EQ \x(N)

9 EQ \x(I/Y)

100 EQ \x(PMT)

1000 EQ \x(FV)


7-3B.$950 =

16 EQ \x(N)

950 EQ \x(+/-) EQ \x(PV)

45 EQ \x(PMT)

1000 EQ \x(FV)


The rate is equivalent to 9.92 percent annual rate, compounded semiannually or 10.17 percent (1.04962 - 1) compounded annually.

7-4B.$975 =

20 EQ \x(N)

975 EQ \x(+/-) EQ \x(PV)

100 EQ \x(PMT)

1000 EQ \x(FV)


7-5B.$1,175 =

15 EQ \x(N)

1175 EQ \x(+/-) EQ \x(PV)

80 EQ \x(PMT)

1000 EQ \x(FV)


7-6B.a.$1,100 =

14 EQ \x(N)

1100 EQ \x(+/-) EQ \x(PV)

90 EQ \x(PMT)

1000 EQ \x(FV)


b.Vb =

14 EQ \x(N)

10 EQ \x(I/Y)

90 EQ \x(PMT)

1000 EQ \x(FV)


c.Since the expected rate of return, 7.80 percent, is less than your required rate of return of 10 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,100, exceeds the value of the security to the investor of $926.33.

7-7B.a.Value

Par Value$1,000.00

Coupon$ 80.00


Years to Maturity20


b.Value at Alternative Rates of Return





c.As required rates of return change, the price of the bond changes, which is the result of "interest-rate risk." Thus, the greater the investor's required rate of return, the greater will be his/her discount on the bond. Conversely, the less his/her required rate of return is below that of the coupon rate, the greater the premium will be.

d.Value at Alternative Maturity Dates

Years to Maturity10





e.The longer the maturity of the bond, the greater the interest-rate risk the investor is exposed to, resulting in greater premiums and discounts.

7-8B.$1,110 =

14 EQ \x(N)

1110 EQ \x(+/-) EQ \x(PV)

70 EQ \x(PMT)

1000 EQ \x(FV)


7-9B.(a)Value (Vb)=

+

17 EQ \x(N)

8.5 EQ \x(I/Y)

70 EQ \x(PMT)

1000 EQ \x(FV)


(b)(i)Value (Vb)=

+

17 EQ \x(N)

11 EQ \x(I/Y)

70 EQ \x(PMT)

1000 EQ \x(FV)


(b)(ii)Value (Vb)=

+

17 EQ \x(N)

6 EQ \x(I/Y)

70 EQ \x(PMT)

1000 EQ \x(FV)


(c)We see that value is inversely related to the investor's required rate of return.

7-10B.

Value Bond A

Par Value$1,000.00

Coupon$ 90.00


Years to Maturity5


Value Bond B

Par Value$1,000.00

Coupon$ 60.00


Years to Maturity5


Value Bond C

Par Value$1,000.00

Coupon$ 120.00


Years to Maturity10


Value Bond D

Par Value$1,000.00

Coupon$ 90.00


Years to Maturity15


Value Bond E

Par Value$1,000.00

Coupon$ 75.00


Years to Maturity15


BondABCDE

$1,082.00$959.00$1,351.18$1,182.16$1,045.54

YearsCtt*PV(Ct)Ctt*PV(Ct)Ctt*PV(Ct)Ctt*PV(Ct)Ctt*PV(Ct)1$90$84$60$56$120$112$90$84$75$70

290157601051202109015775131

390220601471202949022075184

490275601831203669027575229

51,0903,8861,0603,7791204289032175267

6

1204809036075300

7

1205239039275327

8

1205599041975349

9

1205879044175367

10

1,1205,6949045875381

11

9047075392

12

9048075400

13

9048675405

14

9048975407

15

1,0905,9261,0755,844

4,622

4,270

9,252

10,977

10,053

Duration

4.27

4.45

6.85

9.29

9.62

7-11B.a.$1,350 =

4 EQ \x(N)

1350 EQ \x(+/-) EQ \x(PV)

120 EQ \x(PMT)

1000 EQ \x(FV)


b.Vb =

4 EQ \x(N)

9 EQ \x(I/Y)

120 EQ \x(PMT)

1000 EQ \x(FV)


c.Since the expected rate of return, 2.66 percent is much less than your required rate of return of 9 percent, the bond is not an acceptable investment. This fact is also evident because the market price, $1,350, exceeds the value of the security to the investor of $1,097.19.

7-12B.a.$915=

25 EQ \x(N)

915 EQ \x(+/-) EQ \x(PV)

80 EQ \x(PMT)

1000 EQ \x(FV)


b.Since the required rate of return(11%) is greater than the expected rate of return(8.86%), you should not purchase the bond.

7-13B.Value Bond J

Par Value$1,000.00

Coupon$ 95.00


Years to Maturity4

Market Value$984.15

Value Bond P

Par Value$1,000.00

Coupon$115


Years to Maturity12


Value Bond Y

Par Value$1,000.00

Coupon$ 80


Years to Maturity16

Market Value$843.53

Value Bond Q

Par Value$1,000.00

Coupon$ 70.00


Years to Maturity20

Market Value$744.59

Value Bond Z

Par Value$1,000.00

Coupon$ 130.00


Years to Maturity15


BondJPYQZ

Bond Value$984.15$1,102.21$843.53$744.59$1,228.18

YearsCttPV(Ct)CttPV(Ct)CttPV(Ct)CttPV(Ct)CttPV(Ct)

1 $95 $86 $115 $105 $80 $73 $70 $64 $130 $118

2 $95 $157 $115 $190 $80 $132 $70 $116 $130 $215

3 $95 $214 $115 $259 $80 $180 $70 $158 $130 $293

4 $1,095 $2,992 $115 $314 $80 $219 $70 $191 $130 $355

5 $115 $357 $80 $248 $70 $217 $130 $404

6 $115 $389 $80 $271 $70 $237 $130 $440

7 $115 $413 $80 $287 $70 $251 $130 $467

8 $115 $429 $80 $299 $70 $261 $130 $485

9 $115 $439 $80 $305 $70 $267 $130 $496

10 $115 $443 $80 $308 $70 $270 $130 $501

11 $115 $443 $80 $308 $70 $270 $130 $501

12 1,115$4,263 $80 $306 $70 $268 $130 $497

13 $80 $301 $70 $264 $130 $490

14 $80 $295 $70 $258 $130 $479

15 $80 $287 $70 $251 $1,130 $4,058

16 $1,080 $3,761 $70 $244

17 $70 $235

18 $70 $227

19 $70 $217

20 1,070 $3,181

Sum of

t*PV(Ct)$3,449 $8,046 $7,581 $7,447 $9,799

Duration3.50 7.30 8.99 10.00 7.98

7-14B.(a)Vb =

20 EQ \x(N)

8 EQ \x(I/Y)

120 EQ \x(PMT)

1000 EQ \x(FV)


(b)(i)Vb=

20 EQ \x(N)

13 EQ \x(I/Y)

120 EQ \x(PMT)

1000 EQ \x(FV)


(b)(ii)Vb=

20 EQ \x(N)

6 EQ \x(I/Y)

120 EQ \x(PMT)

1000 EQ \x(FV)


(c)As long as the required rate of return is less than the expected rate of return of 8%, you should purchase the bond Thus, if your required rate of return decreases to 6%, you should purchase the bond.

PAGE 203

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chapter 07 im 10th ed

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