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Chapter 7

By Scott Gonzalez,2014-06-29 08:54
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Chapter 7 ...

    Chapter 7

    Bonds and Their Valuation

    LEARNING OBJECTIVES

     ? List the four main classifications of bonds and differentiate among them. After reading this chapter, students should be able to: ? Identify the key characteristics common to all bonds.

    ? Calculate the value of a bond with annual or semiannual interest

    payments.

? Explain why the market value of an outstanding fixed-rate bond will fall

    when interest rates rise on new bonds of equal risk, or vice versa.

? Calculate the current yield, the yield to maturity, and/or the yield to

    call on a bond.

? Differentiate between interest rate risk, reinvestment rate risk, and

    default risk.

? List major types of corporate bonds and distinguish among them.

? Explain the importance of bond ratings and list some of the criteria

    used to rate bonds.

? Differentiate among the following terms: Insolvent, liquidation, and

    reorganization.

? Read and understand the information provided on the bond market page of

    your newspaper.

     Learning Objectives: 7 - 1

    LECTURE SUGGESTIONS

This chapter serves two purposes. First, it provides important and useful

    information on bonds per se. Second, it provides a good example of the use of

    time value concepts, so it reinforces the topics covered in Chapter 6.

    We begin our lecture with a discussion of the different types of bonds

    and their characteristics. Then we move on to how bond values are established,

    how yields are determined, the effects of changing interest rates on bond

    prices, and the riskiness inherent in different types of bonds.

    The details of what we cover, and the way we cover it, can be seen by

    scanning Blueprints, Chapter 7. For other suggestions about the lecture,

    please see the “Lecture Suggestions” in Chapter 2, where we describe how we

    conduct our classes.

DAYS ON CHAPTER: 4 OF 58 DAYS (50-minute periods)

    Lecture Suggestions: 7 - 2

    ANSWERS TO END-OF-CHAPTER QUESTIONS

7-1 Yes, the statement is true.

7-2 False. Short-term bond prices are less sensitive than long-term bond

    prices to interest rate changes because funds invested in short-term

    bonds can be reinvested at the new interest rate sooner than funds tied

    up in long-term bonds.

7-3 The price of the bond will fall and its YTM will rise if interest rates

    rise. If the bond still has a long term to maturity, its YTM will

    reflect long-term rates. Of course, the bond’s price will be less

    affected by a change in interest rates if it has been outstanding a long

    time and matures shortly. While this is true, it should be noted that

    the YTM will increase only for buyers who purchase the bond after the

    change in interest rates and not for buyers who purchased previous to

    the change.

    If the bond is purchased and held to maturity, the bondholder’s YTM will

    not change, regardless of what happens to interest rates.

7-4 If interest rates decline significantly, the values of callable bonds

    will not rise by as much as those of bonds without the call provision.

    It is likely that the bonds would be called by the issuer before

    maturity, so that the issuer can take advantage of the new, lower rates.

7-5 From the corporation’s viewpoint, one important factor in establishing a

    sinking fund is that its own bonds generally have a higher yield than do

    government bonds; hence, the company saves more interest by retiring its

    own bonds than it could earn by buying government bonds. This factor

    causes firms to favor the second procedure. Investors also would prefer

    the annual retirement procedure if they thought that interest rates were

    more likely to rise than to fall, but they would prefer the government

    bond purchase program if they thought rates were likely to fall. In

    addition, bondholders recognize that, under the government bond purchase

    scheme, each bondholder would be entitled to a given amount of cash from

    the liquidation of the sinking fund if the firm should go into default,

    whereas under the annual retirement plan, some of the holders would

    receive a cash benefit while others would benefit only indirectly from

    the fact that there would be fewer bonds outstanding.

    On balance, investors seem to have little reason for choosing one

    method over the other, while the annual retirement method is clearly

    more beneficial to the firm. The consequence has been a pronounced

    trend toward annual retirement and away from the accumulation scheme.

7-6 a. If a bond’s price increases, its YTM decreases.

     Answers and Solutions: 7 - 3

b. If a company’s bonds are downgraded by the rating agencies, its YTM

    increases.

    c. If a change in the bankruptcy code made it more difficult for

    bondholders to receive payments in the event a firm declared

    bankruptcy, then the bond’s YTM would increase.

d. If the economy entered a recession, then the possibility of a firm

    defaulting on its bond would increase; consequently, its YTM would

    increase.

e. If a bond were to become subordinated to another debt issue, then the

    bond’s YTM would increase.

    7-7 As an investor with a short investment horizon, I would view the 20-year

    Treasury security as being more risky than the 1-year Treasury security.

    If I bought the 20-year security, I would bear a considerable amount of

    interest rate risk. Since my investment horizon is only one year, I

    would have to sell the 20-year security one year from now, and the price

    I would receive for it would depend on what happened to interest rates

    during that year. However, if I purchased the 1-year security I would

    be assured of receiving my principal at the end of that one year, which

    is the 1-year Treasury’s maturity date.

    Answers and Solutions: 7 - 4

    SOLUTIONS TO END-OF-CHAPTER PROBLEMS

    7-1 With your financial calculator, enter the following:

    N = 10; I = YTM = 9%; PMT = 0.08 ? 1,000 = 80; FV = 1000; PV = V = ? BPV = $935.82.

    7-2 With your financial calculator, enter the following to find YTM:

    N = 10 ? 2 = 20; PV = -1100; PMT = 0.08/2 ? 1,000 = 40; FV = 1000; I = YTM = ?

    YTM = 3.31% ? 2 = 6.62%.

    With your financial calculator, enter the following to find YTC:

    N = 5 ? 2 = 10; PV = -1100; PMT = 0.08/2 ? 1,000 = 40; FV = 1050; I = YTC = ?

    YTC = 3.24% ? 2 = 6.49%.

    7-3 The problem asks you to find the price of a bond, given the following

    facts: N = 16; I = 8.5/2 = 4.25; PMT = 45; FV = 1000.

    With a financial calculator, solve for PV = $1,028.60.

    7-4 V

     = $985; M = $1,000; Int = 0.07 ? $1,000 = $70. B

     a. Current yield = Annual interest/Current price of bond

     = $70/$985.00

     = 7.11%.

     b. N = 10; PV = -985; PMT = 70; FV = 1000; YTM = ?

     Solve for I = YTM = 7.2157% ? 7.22%.

     c. N = 7; I = 7.2157; PMT = 70; FV = 1000; PV = ?

     Solve for V

     = PV = $988.46. B

7-5 a. 1. 5%: Bond L: Input N = 15, I = 5, PMT = 100, FV = 1000, PV = ?,

    PV = $1,518.98.

    Bond S: Change N = 1, PV = ? PV = $1,047.62.

    2. 8%: Bond L: From Bond S inputs, change N = 15 and I = 8, PV = ?,

    PV = $1,171.19.

    Bond S: Change N = 1, PV = ? PV = $1,018.52. Answers and Solutions: 7 - 5

    3. 12%: Bond L: From Bond S inputs, change N = 15 and I = 12, PV = ?,

    PV = $863.78.

    Bond S: Change N = 1, PV = ? PV = $982.14.

    b. Think about a bond that matures in one month. Its present value is

    influenced primarily by the maturity value, which will be received in

    only one month. Even if interest rates double, the price of the bond

    will still be close to $1,000. A 1-year bond’s value would fluctuate

    more than the one-month bond’s value because of the difference in the

    timing of receipts. However, its value would still be fairly close

    to $1,000 even if interest rates doubled. A long-term bond paying

    semiannual coupons, on the other hand, will be dominated by distant

    receipts, receipts that are multiplied by 1/(1 + kt/2), and if k ddincreases, these multipliers will decrease significantly. Another

    way to view this problem is from an opportunity point of view. A 1-

    month bond can be reinvested at the new rate very quickly, and hence

    the opportunity to invest at this new rate is not lost; however, the

    long-term bond locks in subnormal returns for a long period of time.

    N7-6 a. VINTM = ?B?tN(1?k)(1?k)t1?dd

    M = $1,000. I = 0.09($1,000) = $90.

    1. V = $829: Input N = 4, PV = -829, PMT = 90, FV = 1000, I = ? I = B14.99%.

    2. V = $1,104: Change PV = -1104, I = ? I = 6.00%. B

    b. Yes. At a price of $829, the yield to maturity, 15 percent, is

    greater than your required rate of return of 12 percent. If your

    required rate of return were 12 percent, you should be willing to buy

    the bond at any price below $908.88.

    7-7 The rate of return is approximately 15.03 percent, found with a

    calculator using the following inputs:

N = 6; PV = -1000; PMT = 140; FV = 1090; I = ? Solve for I = 15.03%.

    7-8 a. Using a financial calculator, input the following:

    N = 20, PV = -1100, PMT = 60, FV = 1000, and solve for I = 5.1849%.

    However, this is a periodic rate. The nominal annual rate =

    5.1849%(2) = 10.3699% ? 10.37%.

    b. The current yield = $120/$1,100 = 10.91%. Answers and Solutions: 7 - 6 c. YTM = Current Yield + Capital Gains (Loss) Yield

    10.37% = 10.91% + Capital Loss Yield

d. Using a financial calculator, input the following:

    N = 8, PV = -1100, PMT = 60, FV = 1060, and solve for I = 5.0748%. -0.54% = Capital Loss Yield.

    However, this is a periodic rate. The nominal annual rate =

    5.0748%(2) = 10.1495% ? 10.15%.

     7-9 The problem asks you to solve for the YTM, given the following facts:

N = 5, PMT = 80, and FV = 1000. In order to solve for I we need PV.

    However, you are also given that the current yield is equal to 8.21%.

    Given this information, we can find PV.

    Current yield = Annual interest/Current price

     0.0821 = $80/PV

     PV = $80/0.0821 = $974.42.

Now, solve for the YTM with a financial calculator:

    N = 5, PV = -974.42, PMT = 80, and FV = 1000. Solve for I = YTM = 8.65%.

    7-10 The problem asks you to solve for the current yield, given the following

    facts: N = 14, I = 10.5883/2 = 5.29415, PV = -1020, and FV = 1000. In

    order to solve for the current yield we need to find PMT. With a

    financial calculator, we find PMT = $55.00. However, because the bond

    is a semiannual coupon bond this amount needs to be multiplied by 2 to

    obtain the annual interest payment: $55.00(2) = $110.00. Finally, find

    the current yield as follows:

Current yield = Annual interest/Current price = $110/$1,020 = 10.78%.

    7-11 The bond is selling at a large premium, which means that its coupon rate

    is much higher than the going rate of interest. Therefore, the bond is

    likely to be called--it is more likely to be called than to remain

    outstanding until it matures. Thus, it will probably provide a return

    equal to the YTC rather than the YTM. So, there is no point in

    calculating the YTM--just calculate the YTC. Enter these values:

N = 10, PV = -1353.54, PMT = 70, FV = 1050, and then solve for I.

    The periodic rate is 3.2366 percent, so the nominal YTC is 2 ? 3.2366% =

    6.4733% ? 6.47%. This would be close to the going rate, and it is about

    what the firm would have to pay on new bonds.

    7-12 a. To find the YTM:

    N = 10, PV = -1175, PMT = 110, FV = 1000

    I = YTM = 8.35%.

b. To find the YTC, if called in Year 5:

     Answers and Solutions: 7 - 7

    N = 5, PV = -1175, PMT = 110, FV = 1090

    I = YTC = 8.13%.

    c. The bonds are selling at a premium which indicates that interest rates

    have fallen since the bonds were originally issued. Assuming that

    interest rates do not change from the present level, investors would

    expect to earn the yield to call. (Note that the YTC is less than the

     YTM.)

     If called in Year 6:

    d. Similarly from above, YTC can be found, if called in each subsequent N = 6, PV = -1175, PMT = 110, FV = 1080

    year. I = YTM = 8.27%.

    If called in Year 7:

    N = 7, PV = -1175, PMT = 110, FV = 1070

    I = YTM = 8.37%.

    If called in Year 8:

    N = 8, PV = -1175, PMT = 110, FV = 1060

    I = YTM = 8.46%.

    If called in Year 9:

    N = 9, PV = -1175, PMT = 110, FV = 1050

    I = YTM = 8.53%.

    According to these calculations, the latest investors might expect a

    call of the bonds is in Year 6. This is the last year that the

    expected YTC will be less than the expected YTM. At this time, the

    firm still finds an advantage to calling the bonds, rather than

    seeing them to maturity.

    7-13 First, we must find the amount of money we can expect to sell this bond

    for in 5 years. This is found using the fact that in five years, there

    will be 15 years remaining until the bond matures and that the expected

    YTM for this bond at that time will be 8.5%.

N = 15, I = 8.5, PMT = 90, FV = 1000

    PV = -$1,041.52. V = $1,041.52. B

    This is the value of the bond in 5 years. Therefore, we can solve for

    the maximum price we would be willing to pay for this bond today,

    subject to our required rate of return of 10%.

N = 5, I = 10, PMT = 90, FV = 1041.52

    PV = -$987.87. V = $987.87. B

    We are willing to pay up to $987.87 for this bond today.

    7-14 Before you can solve for the price, we must find the appropriate

    semiannual rate at which to evaluate this bond.

    Answers and Solutions: 7 - 8

     2 EAR = (1 + NOM/2) - 1 20.0816 = (1 + NOM/2) - 1

     NOM = 0.08.

    Semiannual interest rate = 0.08/2 = 0.04 = 4%.

    Solving for price:

    N = 20, I = 4, PMT = 45, FV = 1000

    PV = -$1,067.95. V = $1,067.95. B

    7-15 a. The current yield is defined as the annual coupon payment divided by

    the current price.

    CY = $80/$901.40 = 8.875%.

    b. Solving for YTM:

    N = 9, PV = -901.40, PMT = 80, FV = 1000

    I = YTM = 9.6911%.

    c. Expected capital gains yield can be found as the difference between

    YTM and the current yield.

    CGY = YTM - CY = 9.691% - 8.875% = 0.816%.

    Alternatively, you can solve for the capital gains yield by first

    finding the expected price next year.

    N = 8, I = 9.6911, PMT = 80, FV = 1000

    PV = -$908.76. V = $908.76. B

    Hence, the capital gains yield is the percent price appreciation over

    the next year.

    CGY = (P - P)/P = ($908.76 - $901.40)/$901.40 = 0.816%. 100

    7-16 Using the TIE ratio, we can solve for the firm's current operating

    income.

     TIE = EBIT/Int Exp

     3.2 = EBIT/$10,500,000

    EBIT = $33,600,000.

    Using the same methodology, you can solve for the maximum interest expense the firm can bear without violating its covenant.

    2.5 = $33,600,000/Int Exp

    Max Int Exp = $13,440,000.

    Therefore, the firm can raise debt to the point that its interest expense increases by $2.94 million ($13.44 ? $10.50). The firm can

    raise $25 million at 8%, which would increase the cost of debt by $25 ?

    0.08 = $2 million. Additional debt will be issued at 10%, and the amount of debt to be raised can be found, since we know that only an additional $0.94 million in interest expense can be incurred.

     Answers and Solutions: 7 - 9

Hence, the firm may raise up to $34.4 million in additional debt without Additional Int Exp = Additional Debt ? Cost of debt violating its bond covenants. $0.94 million = Additional Debt ? 0.10 7-17 First, we must find the price Baili paid for this bond. Additional Debt = $9.40 million.

    N = 10, I = 9.79, PMT = 110, FV = 1000

    PV = -$1,075.02. V = $1,075.02. B

    Then to find the one-period return, we must find the sum of the change

    in price and the coupon received divided by the starting price.

    Ending price - Beginning price ? Coupon receivedOne-period return = Beginning price

    One-period return = ($1,060.49 - $1,075.02 + $110)/$1,075.02

    One-period return = 8.88%.

7-18 The answer depends on when one works the problem. We used The Wall

    Street Journal, February 3, 2003:

    a. AT&T’s 8.625%, 2031 bonds had an 8.6 percent current yield. The

    bonds sold at a premium, 100.75% of par, so the coupon interest rate

    would have to be set lower than 8.625% for the bonds to sell at par.

    If we assume the bonds aren’t callable, we can do a rough calculation

    of their YTM. Using a financial calculator, we input the following

    values:

    N = 29 ? 2 = 58, PV = 1.0075 ? -1,000 = -1007.50, PMT =

    0.08625 ? 21,000 = 86.25/2 = 43.125, FV = 1000, and then solve for YTM = k = d

    4.2773% ? 2 = 8.5546%.

    Thus, AT&T would have to set a rate of 8.55 percent on new long-term

    bonds.

    b. The return on AT&T’s bonds is the current yield of 8.6 percent, less

    a small capital loss in 2031. The total return is about 8.55 percent.

    7-19 a. Yield to maturity (YTM):

    With a financial calculator, input N = 28, PV = -1165.75, PMT = 95, FV

    = 1000, I = ? I = k = YTM = 8.00%. d

    Yield to call (YTC):

    With a calculator, input N = 3, PV = -1165.75, PMT = 95, FV = 1090,

    I = ? I = k = YTC = 6.11%. d

    Answers and Solutions: 7 - 10

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