financial management chapter 07 im 10th ed

8/2/2019 Financial Management Chapter 07 IM 10th Ed

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Prof. Rushen Chahal

CHAPTER 7

Bonds Valuation

CHAPTER ORIENTATION

This chapter introduces the concepts that underlie asset valuation. We are specificallyconcerned with bonds. We also look at the concept of the bondholder's expected rate of returnon 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 eventof liquidation than do other senior debtholders.

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

D. Eurobonds: bonds issued in a country different from the one in whosecurrency 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 asubstantial discount from their $1,000 face value with a zero or very lowcoupon.

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

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

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.

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Prof. Rushen Chahal

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 thefirm's assets before the preferred and common stockholders. Also, bondholders must be paid interest due them before dividends can be distributedto the stockholders.

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

D. The contractual agreement of the bond specifies a coupon interest rate that isexpressed either as a percent of the par value or as a flat amount of interestwhich 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 thespecific 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 bond’s market price.

H. Bond ratings

1. Three primary rating agencies exist—Moody’s, Standard & Poor’s, andFitch 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 firm’s bond rating tells much about the cost of funds and the firm’s access tothe 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 isdetermined by its historical cost rather than its current worth.

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

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

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Prof. Rushen Chahal

D. Intrinsic value is the value based upon the expected cash flows from theinvestment, 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 OverviewA. 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 valueequation, the value of an asset is found as follows:

V = ∑= +

N

1tt

t

k) (1

$C

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 paymentsand maturity value discounted at the bondholder's required rate of return. Thismay be expressed as:

V b

= ∑= +

++

N

1t N

bt

b

t

)k (1

$M

)k (1

$I

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

M = the par value of the bond at maturity

k b

= the required rate of return for the bondholder

N = the number of periods to maturity

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Prof. Rushen Chahal

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

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Prof. Rushen Chahal

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

V

b

=

∑=

+

+

+

2N

1t

2N

b

t

b

t

2k 1

$M

2k 1

2

$I

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

A. We compute the bondholder's expected rate of return by finding the discountrate 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. Thechange 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) equalsthe 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 couponrate, 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 relationshipA bondholder owning a long-term bond is exposed to greater interest rate risk than when owning a short-term bond.

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Prof. Rushen Chahal

E. Fifth relationship

The sensitivity of a bond's value to changing interest rates depends not only onthe length of time to maturity, but also on the pattern of cash flows provided bythe 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 percentagechange in a bond price in response to a given percentage change in theinterest rate, the longer the duration.

2. Calculating duration

duration =

0

t b

t

1

P

)k (1

tC

+∑=

n

t

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

k b = 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 costminus accumulated depreciation. Liquidation value is the dollar sum that could berealized if the assets were sold individually and not as part of a going concern. Marketvalue is the observed value for an asset in the marketplace where buyers and sellersnegotiate a mutually acceptable price. Intrinsic value is the present value of the asset'sexpected 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 theinvestor. Hence, the terms value and present value are synonymous.

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

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

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Prof. Rushen Chahal

7-5. (a) The par value is the amount stated on the face of the bond. This value does notchange and, therefore, is completely independent of the market value.However, the market value may change with changing economic conditionsand 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 interestto be received in each payment period. On the other hand, the investor'srequired rate of return is equivalent to the bond’s current yield to maturity,which changes with the changing bond's market price. This rate may be alteredas 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, arehonored before those of both common stock and preferred stock. However, differenttypes 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 andforce it into bankruptcy. Thus, the bondholder's claim on income is more likely to behonored than that of common and preferred stockholders, whose dividends are paid atthe discretion of the firm's management.

7-7. Ratings involve a judgment about the future risk potential of the bond. Although theydeal 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 capitalmarkets.

For the financial manager, bond ratings are extremely important. They provide anindicator 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 areunsecured, 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 aresult 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 prohibitionof any additional encumbrance of assets. This prohibits the future issuance of securedlong-term debt that would further tie up the firm's assets and leave the bondholdersless 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.

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Prof. Rushen Chahal

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 themortgage bondholders with a margin of safety in the event the market value of thesecured property declines. In the case of foreclosure, the trustees have the power to sellthe 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 generalcreditors, 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, inthis case bonds, issued in a country different from the one in whose currencythe bond is denominated. For example, a bond that is issued in Europe or inAsia by an American company and that pays interest and principal to thelender in U.S. dollars would be considered a Eurobond. Thus, even if the bondis not issued in Europe, it merely needs to be sold in a country different fromthe 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 lowcoupon. 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 recordof 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 purchasinga security at the prevailing market price. Thus, the expected rate of return is the ratethat 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 rateof return is higher than the coupon interest rate, the bond will be issued at a discount tothe 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'srequired rate of return. The premium is the excess of the market value over the facevalue 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 allowsthe bondholder to realize an effective yield equal to their required rate of return.

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Prof. Rushen Chahal

7-13. A change in current interest rates (required rate of return) causes a change in themarket value of a bond. However, the impact on value is greater for long-term bondsthan it is for short-term bonds. The reason long-term bond prices fluctuate more thanshort-term bond prices in response to interest rate changes is simple. Assume aninvestor 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 belocked 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 thelower return for only 2 years and not the full 10 years. At the end of year 2, theinvestor would receive the maturity value of $1,000 and could buy a bond offering thehigher 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 aninvestment.

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

SOLUTIONS TO

END-OF-CHAPTER PROBLEMS

7-1A. Value (V b) = ∑= +

++

12

1t12t .12) (1

$1,000

.12) (1

$80

121280

1000CPT → ANSWER -752.23

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Prof. Rushen Chahal

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

Value (V b) =16

16

1tt (1.04)

$1,000

(1.04)

$45 +∑

=

16

445

1000CPT → ANSWER -1,058.26

If interest is paid annually:

Value (V b) = ∑=

+8

1t8t (1.08)

$1,000

(1.08)

$90

8890

1000CPT → ANSWER -1,057.47

7-3A. $900 = ∑= +

++

20

1t20

bt

b /2)k (1

$1,000

/2)k (1

$40

20

900401000CPT → ANSWER 4.79% semiannual rate

The rate is equivalent to 9.6 percent annual rate compounded semiannually, or 9.8

percent (1.0482

- 1) compounded annually.

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Prof. Rushen Chahal

7-4A. $945 = 20 b

20

1tt

b )k (1

$1,000

)k (1

$90

++

+∑=

2094590

1000CPT → ANSWER 9.63%

7-5A. $1,150 = ∑= +

++

12

1t12

bt

b )k (1

$1,000

)k (1

$70

121150

70


7-6A. a. $1,085 = ∑= +

++

15

1t15

bt

b )k (1

$1,000

)k (1

$80

151085

801000CPT → ANSWER 7.06%

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Prof. Rushen Chahal

b. V b = ∑=

+15

1t15t (1.10)

$1,000

(1.10)

$80

151080

1000CPT → ANSWER -847.88

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

7-7A. a. Value

Par Value $1,000.00Coupon $ 100.00Required Rate of Return 0.12Years to Maturity 15

Market Value $ 863.78

b. Value at Alternative Rates of ReturnRequired Rate of Return 0.15


Required Rate of Return 0.08Market Value $1,171.19

c. As required rates of return change, the price of the bond changes, which is theresult 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 lesshis/her required rate of return below that of the coupon rate, the greater the premium will be.

d. Value at Alternative Maturity DatesYears to Maturity 5Required Rate of Return 0.15

Market Value $ 832.39Required Rate of Return 0.08

Market Value $1,079.85

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

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Prof. Rushen Chahal

7-8A. $1,250 = ∑= +

++

15

1t15

bt

b )k (1

$1,000

)k (1

$90

151250

901000CPT → ANSWER 6.36%

7-9A.(a) V b = ∑=

+20

1t20t (1.09)

$1,000

(1.09)

$110

209

110

1000CPT → ANSWER -1,182.57

(b) (i) V b = ∑=

+20

1t20t (1.12)

$1,000

(1.12)

$110

2012

1101000CPT → ANSWER -925.31

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Prof. Rushen Chahal

(b) (ii) V b = ∑=

+20

1t20t (1.06)

$1,000

(1.06)

$110

20

6110

1000CPT → ANSWER -1,573.50

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

7-10A.Value Bond P

Par Value $1,000.00Coupon $ 100.00Required Rate of Return 8%Years to Maturity 5

Market Value $ 1,079.85

Value Bond QPar Value $1,000.00Coupon $ 70.00Required Rate of Return 8%Years to Maturity 5


Value Bond R Par Value $1,000.00Coupon $ 120.00Required Rate of Return 8%Years to Maturity 10


Value Bond SPar Value $1,000.00Coupon $ 80.00Required Rate of Return 8%Years to Maturity 10


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Prof. Rushen Chahal

Value Bond TPar Value $1,000.00Coupon $ 65.00Required Rate of Return 8%Years to Maturity 15


Bond P Q R S T

$1,079.85 $960.07 $1,268.40 $1,000.00 $871.61

Years Ct t*PV(Ct) Ct t*PV(Ct) Ct t*PV(Ct) Ct t*PV(Ct) Ct t*PV(Ct)

1 $100 $93 $70 $65 $120 $111 $80 $74 $65 $602 100 171 70 120 120 206 80 137 65 1113 100 238 70 167 120 286 80 191 65 1554 100 294 70 206 120 353 80 235 65 191

5 1,100 3,743 1,070 3,641 120 408 80 272 65 2216 120 454 80 302 65 2467 120 490 80 327 65 2658 120 519 80 346 65 2819 120 540 80 360 65 29310 1,120 5,188 1,080 5,002 65 30111 65 30712 65 31013 65 31114 65 31015 1,065 5,036

)t(* C PV t

Sumof 4,539 4,198 8,554 7,247 8,398

Duration 4.20 4.37 6.74 7.25 9.63

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Prof. Rushen Chahal

7-11A. a.$1,100 = ∑= +

++

7

1t7

bt

b )k (1

$1,000

)k (1

$90

7

110090


b. V b = ∑=

+7

1t7t (1.07)

$1,000

(1.07)

$90

77

90

1000CPT → ANSWER -1,107.79

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

7-12A. a. $915 = ∑= +

++

12

1t12

bt

b )k (1

$1,000

)k (1

$50

1291550


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

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Prof. Rushen Chahal

7-13A.Value Bond I

Par Value $1,000.00Coupon $ 130.00Required Rate of Return 7%

Years to Maturity 7Market Value $ 1,323.36

Value Bond IIPar Value $1,000.00Coupon $ 90.00Required Rate of Return 7%Years to Maturity 6


Value Bond III

Par Value $1,000.00Coupon $ 110.00Required Rate of Return 7%Years to Maturity 12


Value Bond IVPar Value $1,000.00Coupon $ 125.00Required Rate of Return 7%Years to Maturity 5


Value Bond VPar Value $1,000.00Coupon $ 80.00Required Rate of Return 7%Years to Maturity 10


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Prof. Rushen Chahal

Bond I II III IV V

BondValue $1,323.36 $1,095.33 $1,317.71 $1,225.51 $1,070.24

Years Ct tPV(Ct) Ct tPV(Ct) Ct tPV(Ct) Ct tPV(Ct) Ct tPV(Ct)

1 $130 $121 $90 $84 $110 $103 $125 $117 $80 $752 $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 $520 1,090 $4,358 $110 $440 $80 $320

7 1,130 $4,926 $110 $480 $80 $349

8 $110 $512 $80 $372

9 $110 $538 $80 $392

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

11 1,110 $5,801

12

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

Duration 5.27 4.94 7.30 4.11 7.35

7-14A.(a) V b = ∑=

+15

1t15t (1.09)

$1,000

(1.09)

$85

159

851000CPT → ANSWER -959.70

(b) (i) V b = ∑=

+15

1t15t (1.11)

$1,000

(1.11)

$85

1511

851000CPT → ANSWER -820.23

(b) (ii) V b = ∑=

+15

1t15t (1.07)

$1,000

(1.07)

$85

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Prof. Rushen Chahal

157

851000CPT → ANSWER -1,136.62

(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 returndecreases to 7%, you should purchase the bond.

SOLUTION TO INTEGRATIVE PROBLEM

1. Young Corp. Bond Value (V b) = ∑= +

++

10

1t10t )06. 1(

000,1$

)06.1(

00.78$

106

781000CPT → ANSWER -$1,132.48

Thomas Resorts Bond Value (V b) = ∑= +

++

17

1t17t )09. 1(

000,1$

)09.1(

00.75$

179

75.001000CPT → ANSWER -$871.85

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Prof. Rushen Chahal

Entertainment, Inc. Bond Value (V b) =4

4

1tt .08) (1

$1,000

.08) (1

$79.75

++

+∑=

48

79.751000CPT → ANSWER -$999.17

2. Young Corporation: $1,030 = ∑= +

++

10

110

bt

b )k (1

$1,000

)k (1

$78

t

101,030

78


Thomas Resorts: $973 = ∑= +

++

17

117

bt

b )k (1

$1,000

)k (1

$75

t

17973

75.001000CPT

→ ANSWER 7.79%

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Prof. Rushen Chahal

Entertainment, Inc.: $1,035 = 4 b

4

1tt

b )k (1

$1,000

)k (1

$79.75

++

+∑=

41,035

79.751000CPT → ANSWER 6.94%

3. i. Young Corp. Bond Value (V b) = ∑= +

++

10

110t .09) (1

$1,000

.09) (1

$78

t

109

781000

CPT → ANSWER - $922.99

ValueBond

ResortsThomas(V b) = ∑

= ++

+

17

1t17t )12. 1(

000,1$

)12.1(

00.75$

1712

75.001000CPT → ANSWER - $679.62

Entertainment, Inc. Bond Value (V b) = ∑= +++

4

1t4t )11. 1(

000,1$ )11. 1(

75.79$

411

79.751000CPT → ANSWER - $906.15

3. ii Young Corp. Bond Value (V b) = ∑= +

+

+

10

1t

10t .03) (1

$1,000

.03) (1

$78

103

781000CPT → ANSWER - $1,409.45

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Prof. Rushen Chahal

ValueBond

ResortsThomas(V b) = ∑

= ++

+

17

1t17t .06) (1

$1,000

.06) (1

$75.00

176

75.001000CPT → ANSWER - $1,157.16

Entertainment, Inc. Bond Value (V b) = ∑= +

++

4

1t4t .05) (1

$1,000

.05)(1

$79.75

45

79.751000CPT

→ ANSWER - $1,105.49

4. As the interest rates rise and fall, we see the different effects on the bond pricesdepending 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 investor’s required rate of return is above the coupon interest rate, the bond will sell at a discount (below par value), but if the investor’s required rate of return is below the coupon interest rate, the bond will sell at a price above its par value (premium).

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Prof. Rushen Chahal

5. Duration of bonds

Young Corp. Thomas Resorts Entertainment, Inc.

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

Required rate of return 6% 9% 8%

Year Ct t* PV(Ct) Ct t* PV(Ct) Ct t* PV(Ct)

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

2 78.00 138.84 75.00 126.25 79.75 136.75

3 78.00 196.47 75.00 173.74 79.75 189.92

4 78.00 247.13 75.00 212.53 1,079.75 3,174.59

5 78.00 291.43 75.00 243.72

6 78.00 329.92 75.00 268.32

7 78.00 363.12 75.00 287.198 78.00 391.51 75.00 301.12

9 78.00 415.51 75.00 310.79

10 1,078.00 6,019.50 75.00 316.81

11 75.00 319.71

12 75.00 319.98

13 75.00 318.02

14 75.00 314.21

15 75.00 308.86

16 75.00 302.24

17 1,075.00 4222.86

Sum of t*PV(Ct) 8,467.02 8,415.17 3,575.11

Duration 8.22 8.65 3.45

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

6. Although the Young Corporation bonds and the Thomas Resorts bonds have differentterms to maturity, the duration of the two bonds is very similar. These two bonds willlikely 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 returnthan your required rate of return. Young Corporation’s expected rate of return isgreater than your required rate of return. So we would buy Young Corporation and notEntertainment, Inc. or Thomas Resorts.

195



Prof. Rushen Chahal

Solutions to Problem Set B

7-1B. Value (V b) = ∑= +

++

10

1t10t .15) (1

$1,000

.15) (1

$90

101590

1000CPT → ANSWER -698.87

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

Value (V b) = ∑=

+22

1t22t (1.045)

$1,000

(1.045)

$50

224.550

1000CPT → ANSWER -1068.92

If interest is paid annually:

Value (V b) = ∑=

+11

1t

11t

(1.09)

$1,000

(1.09)

$100

119

1001000CPT → ANSWER -1068.05

196



Prof. Rushen Chahal

7-3B. $950 = ∑= +

++

16

1t16

bt

b /2)k (1

$1,000

/2)k (1

$45

16

950451000CPT → ANSWER 4.96%

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

1t20

bt

b )k (1

$1,000

)k (1

$100

20975100

1000CPT → ANSWER 10.30%

7-5B. $1,175 = ∑= +

++

15

1t15

bt

b )k (1

$1,000

)k (1

$80

151175

801000CPT → ANSWER 6.18%

197



Prof. Rushen Chahal

7-6B. a. $1,100 = ∑= +

++

14

1t14

bt

b )k (1

$1,000

)k (1

$90

141100

901000CPT → ANSWER 7.80%

b. V b = ∑=

+14

1t14t (1.10)

$1,000

(1.10)

$90

141090

1000CPT → ANSWER -926.33

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

7-7B.

a. ValuePar Value $1,000.00Coupon $ 80.00Required Rate of Return 7%Years to Maturity 20


b. Value at Alternative Rates of ReturnRequired Rate of Return 10%


Required Rate of Return 6%Market Value $1,229.40

c. As required rates of return change, the price of the bond changes, which is theresult 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 lesshis/her required rate of return is below that of the coupon rate, the greater the premium will be.

198



Prof. Rushen Chahal

d. Value at Alternative Maturity DatesYears to Maturity 10Required Rate of Return 10%

Market Value $ 877.11Required Rate of Return 6%

Market Value $1,147.20e. 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

1t14

bt

b )k (1

$1,000

)k (1

$70

141110

701000CPT → ANSWER 5.83%

7-9B. (a) Value (V b) =17

17

1t .085)(1

$70

+∑=

+17)085.1(

000,1$

+

178.570

1000CPT → ANSWER -867.62

199



Prof. Rushen Chahal

(b) (i) Value (V b) =17

17

1t .11)(1

$70

+∑=

+17)11.1(

000,1$

+

171170

1000CPT → ANSWER -698.05

(b) (ii) Value (V b) =17

17

1t .06)(1

$70

+∑=

+17)06.1(

000,1$

+

176

701000CPT → ANSWER -1,104.77

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

7-10B.Value Bond A

Par Value $1,000.00Coupon $ 90.00Required Rate of Return 7%

Years to Maturity 5Market Value $ 1,082.00

Value Bond BPar Value $1,000.00Coupon $ 60.00Required Rate of Return 7%Years to Maturity 5


200



Prof. Rushen Chahal

Value Bond CPar Value $1,000.00Coupon $ 120.00Required Rate of Return 7%Years to Maturity 10


Value Bond DPar Value $1,000.00Coupon $ 90.00Required Rate of Return 7%Years to Maturity 15


Value Bond EPar Value $1,000.00

Coupon $ 75.00Required Rate of Return 7%Years to Maturity 15


Bond A B C D E

valueBond

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

Years Ct t*PV(Ct) Ct t*PV(Ct) Ct t*PV(Ct) Ct t*PV(Ct) Ct t*PV(Ct)

1 $90 $84 $60 $56 $120 $112 $90 $84 $75 $70

2 90 157 60 105 120 210 90 157 75 131

3 90 220 60 147 120 294 90 220 75 1844 90 275 60 183 120 366 90 275 75 229

5 1,090 3,886 1,060 3,779 120 428 90 321 75 267

6 120 480 90 360 75 300

7 120 523 90 392 75 327

8 120 559 90 419 75 349

9 120 587 90 441 75 367

10 1,120 5,694 90 458 75 381

11 90 470 75 392

12 90 480 75 400

13 90 486 75 405

14 90 489 75 407

15 1,090 5,926 1,075 5,844

)t(* C PV t

Sumof 4,622 4,270 9,252 10,977 10,053

Duration 4.27 4.45 6.85 9.29 9.62

201



Prof. Rushen Chahal

7-11B. a.$1,350 = ∑= +

++

4

1t4

bt

b )k (1

$1,000

)k (1

$120

41350120


b. V b = ∑=

+4

1t4t (1.09)

$1,000

(1.09)

$120

49

1201000CPT → ANSWER -1,097.19

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

7-12B. a. $915 = ∑= +

++

25

1t25

bt

b )k (1

$1,000

)k (1

$80

2591580


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

202



Prof. Rushen Chahal

7-13B. Value Bond JPar Value $1,000.00Coupon $ 95.00Required Rate of Return 10%Years to Maturity 4

Market Value $984.15

Value Bond PPar Value $1,000.00Coupon $115Required Rate of Return 10%Years to Maturity 12


Value Bond YPar Value $1,000.00Coupon $ 80Required Rate of Return 10%

Years to Maturity 16Market Value $843.53

Value Bond QPar Value $1,000.00Coupon $ 70.00Required Rate of Return 10%Years to Maturity 20

Market Value $744.59

Value Bond ZPar Value $1,000.00Coupon $ 130.00

Required Rate of Return 10%Years to Maturity 15


203



Prof. Rushen Chahal

Bond J P Y Q Z

BondValue $984.15 $1,102.21 $843.53 $744.59 $1,228.18

Years Ct tPV(Ct) Ct tPV(Ct) Ct tPV(Ct) Ct tPV(Ct) Ct tPV(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 $3,181Sum of t*PV(Ct) $3,449 $8,046 $7,581 $7,447 $9,799

Duration 3.50 7.30 8.99 10.00 7.98

7-14B.(a) V b = ∑=

+20

1t20t (1.08)

$1,000

(1.08)

$120

208

120

1000CPT → ANSWER -1,392.73

204



Prof. Rushen Chahal

(b) (i) V b = ∑=

+20

1t20t (1.13)

$1,000

(1.13)

$120

20

131201000CPT → ANSWER -929.75

(b) (ii) V b = ∑=

+20

1t20t (1.06)

$1,000

(1.06)

$120

206

120

1000CPT → ANSWER -1,688.20

(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 returndecreases to 6%, you should purchase the bond.

financial management chapter 07 im 10th ed

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