ࡱ> _a^q` a]bjbjqPqP v::Tqzzz$---P-.|L./04(1(1(11:1:1:'L)L)L)L)L)L)L$ROhQMLzX;7>1:X;X;ML(1(1bL???X;rR(1z(1'L?X;'L??rJTX"zCK(1"/ M"9-<6J'LxL0LJVNR>NRCKNRzCK1:"S:?k::1:1:1:MLML?^1:1:1:LX;X;X;X;&-- SOLUTIONS MANUAL CHAPTER 12 PRINCIPLES OF BOND VALUATION AND INVESTMENT Answers to Text Discussion Questions 1. Why are bonds not necessarily a conservative investment? 12-1. Since bond prices are sensitive to interest rate changes, capital gains or losses are possible even though interest is paid regularly. 2. How can the market price of a bond be described in terms of present value? 12-2. The price of a bond is the present value of the annuity created by the interest payments plus the present value of the lump sum of principal returned at maturity. 3. Why does a bond price change when interest rates change? 12-3. Since the bond has a fixed return (the interest promised) based on the bond contract, the market price of a bond changes to reflect changes in market interest rates. A bond's price changes to indicate the present value of future cash return, both interest and principal based on market interest rates (discount factors). Floating rate bonds are an exception to this principle. 4. Why is current yield not a good indicator of bond returns? (Relate your answer to maturity considerations.) 12-4. The current yield does not consider the length of time to maturity. A dollar received this year is worth more than dollars received in future years. 5. Describe how yield to maturity is the same concept as the internal rate of return (or true yield) on an investment. 12-5. Yield to maturity is the same concept as internal rate of return or true yield because it is the interest rate (i) at which you can discount the future coupon payments (Ct) and maturity value (Pn) to arrive at a known current value (V) of the bond. 6. What is the significance of the yield-to-call calculation? 12-6. If a bond is callable, the yield to call calculation shows what the yield for that time period would be as compared to yield to maturity (which you may never get to) or some other length of time. 7. What is the bond reinvestment assumption? Is this necessarily correct? 12-7. It is assumed that funds are reinvested at the yield from the investment. This is not necessarily the case. Reinvestment may take place at a higher or lower rate (as will be discussed in the next chapter). 8. What is the meaning of term structure of interest rates? 12-8. The term structure of interest rates depicts the relationship between maturity and interest rates. It is sometimes called a yield curve because yields on existing securities, having maturities anywhere from three months to 30 years, are plotted on a graph to develop the curve. 9. What does an ascending term structure pattern tend to indicate? 12-9. When the term structure is in an ascending posture (short-term rates are lower than long-term rates), it is a general signal that interest rates will rise in the future. 10. Explain the general meaning of the expectations hypothesis as it relates to the term structure of interest rates. 12-10. The hypothesis is that any long-term rate is an average of the expectation of future short-term rates over the applicable time horizon. Thus, if lenders expect short-term rates to be continually increasing in the future, they will demand higher long-term rates. Conversely, if they anticipate short-term rates to be declining, they will accept lower long-term rates. 11. Explain the liquidity preference theory as it relates to the term structure of interest rates. 12-11. The shape of the term structure of interest rates tends to be upward sloping more than any other pattern. This reflects recognition of the fact that long-term maturity obligations are subject to greater price change movements when interest rates change. Because of the increased risk of holding longer-term maturities, investors demand a higher return to hold long-term securities relative to short-term securities. This is called the liquidity preference theory of interest rates. Since short-term securities are more easily turned into cash without the risk of large price changes, investors will pay a higher price and receive a lower yield. 12. How might the market segmentation theory help to explain why short-term rates on government securities increase when bank loan demand becomes high? 12-12. When bank loan demand becomes high, banks are likely to partially withdraw from investments in government securities. Since banks are an important part of the short-term side of the market, their reduced demand will likely drive up short-term rates on government securities. 13. Under what circumstances would the yield spread on different classes of debt obligations tend to be largest? 12-13. The yield spread represents the difference in returns for different classes of bonds based on ratings. The yield spread tends to be largest when there is a low degree of confidence in the economy as in the early phases of a recession as investors attempt to shift out of low grade securities into strong instruments. 14. List the six principles associated with bond-pricing relationships. 12-14. 1. Bond prices and interest rates are inversely related. 2. Prices of long-term bonds are more sensitive to a change in yields to maturity than short-term bonds. 3. Bond price sensitivity increases at a decreasing rate as maturity increases. 4. Bond prices are more sensitive to a decline in market yield to maturity than to a rise in market yield to maturity. 5. Prices of low coupon bonds are more sensitive to a change in yields to maturity than high coupon bonds. 6. Bond prices are more sensitive when yields to maturity are low than when yields to maturity are high. 15. How do margin requirements affect investor strategy for bonds? 12-15. Borrowing to purchase bonds requires relatively little margin. For government securities, the amount be put down may be as little as 5 percent and for corporate bonds, it may be 30 percent. The leverage available can affect returns dramatically. Investors may use margin to enhance percentage returns if they expect interest rates to go down, but margin can also cause large percentage losses if they are wrong and interest rates go up. 16. Explain the benefits derived from investing in deep discount bonds. 12-16. Deep discount bonds have almost no change of being called away even if prices go up because the value is already far removed from par. Secondly, deep discount bonds offer the opportunity for higher price increases than high coupon bonds if interest rates decline. 17. What is a bond swap investment strategy? Explain how it might relate to tax planning. 12-17. The term "Swap" refers to the procedure of selling out of a given bond position and immediately buying into another one with similar attributes in an attempt to improve overall portfolio return or performance. For tax planning purposes, you might sell a bond on which you have a large loss and take a reduction against other income. You then take the proceeds from the sale and reinvest in a bond of equal risk, and you will have increased your total cash returns because of tax benefits. PROBLEMS Bond price 1. Given a 10-year bond that sold for $1,000 with a 13 percent coupon rate, what would be the price of the bond if interest rates in the marketplace on similar bonds are now 10 percent? Interest is paid semiannually. Assume a 10-year time period. 12-1. PV of $65 semiannually for n = 20 and i = 5% (table 12-1 or Appendix D) $65 12.462 = $810.03 PV of $1,000 semiannually for n = 20 and i = 5% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  Bond price 2. Given a 15-year bond that sold for $1,000 with a 9 percent coupon rate, what would be the price of the bond if interest rates in the marketplace on similar bonds are now 12 percent? Interest is paid semiannually. Assume a 15-year time period. 12-2. PV of $45 semiannually for n = 30 and i = 6% (Table 12-1 or Appendix D) $45 13.765 = $619.43 PV of $1,000 semiannually for n = 30 and i = 6% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  Bond price 3. Given the facts in problem 2, what would be the price if interest rates go down to 8 percent? (Once again, do a semiannual analysis.) 12-3. PV of $45 semiannually for n = 30 and i = 4% (Table 12-1 or Appendix D) $45 17.292 = $778.14 PV of $1,000 semiannually for n = 30 and i = 4% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  Use of bond table 4. Using Table 123, determine the price of a a. 10 percent coupon rate bond, with 20 years to maturity and a 14 percent yield to maturity. b. 12 percent coupon rate bond with 10 years to maturity and an 8 percent yield to maturity. 12-4. a) 73.34% $1,000 = $ 733.40 b) 127.18% $1,000 = $1,271.80 Use of bond table 5. Using Table 123: Assume you bought a bond with a 10 percent coupon rate with 20 years to maturity at a yield to maturity of 14 percent. Further assume 10 years later the yield to maturity is 8 percent. Determine the price of the bond that you initially paid and the bond price with 10 years remaining to maturity. Also, compute the dollar and percentage profit related to the bond over the 10-year holding period. 12-5. 20 years, 14 percent 73.34% $1,000 = $ 733.40 10 years, 8 percent 113.50% $1,000 = $1,135.00  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Current yield 6. What is the current yield of an 8 percent coupon rate bond priced at $877.60? $80 / $877.60 = 9.12% Yield to maturity 7. What is the yield to maturity for the data in problem 6? Assume there are 10 years left to maturity. It is a $1,000 par value bond. Use the trial-and-error approach with annual analysis. [Hint: Because the bond is trading for less than par value, you can assume the interest rate (i) for which you are solving is greater than the coupon rate of 8 percent.] Since the interest rate must be greater than 8%, we will try 9% as a first approximation. PV of $80 annually for n = 10, i = 9% (Table 12-1 or Appendix D) $80 6.418 = $513.44 PV of $1,000 annually for n = 10, i = 9% (Table 12-2 or Appendix D)  EMBED Equation.DSMT4  At a 9% discount rate, the answer is $935.44. This is higher than our desired value of $877.60. In order to bring the value down, we will use a higher interest rate. Lets try 10%. PV of $80 annually for n = 10, i = 10% (Table 12-1 or Appendix D) $80 6.145 = $491.60 PV of $1,000 annually for n = 10, i = 10% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  A 10% discount rate provides the bond price of $877.60. Ten percent is the yield to maturity. Yield to maturity 8. What is the yield to maturity for a 10 percent coupon rate bond priced at $1,090.90? Assume there are 20 years left to maturity. It is a $1,000 par value bond. Use the trial-and-error approach with annual analysis. (Hint: Because the bond is trading at a price above par value, first decide whether your initial calculation should be at an interest rate above or below the coupon rate.) 12-8. With the bond trading above par value, the discount rate must be below the coupon rate of 10%. Lets try 9%. PV of $100 annually for n = 20, i = 9% (Table 12-1 or Appendix D) $100 9.129 = $912.90 PV of $1,000 annually for n = 20, i = 9% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  Since 9% provides the desired bond value of $1,090.90, it is the yield to maturity. Comparison of yields 9. What is the current yield in problem 8? Why is it slightly higher than the yield to maturity? 12-9. $100/$1,090.90 = 9.17% It is higher than yield to maturity because it does not take into consideration the fact that the bond price will decline from $1,090.90 to $1,000 over the next 20 years. This factor lowers the yield to maturity. Current yield and yield to maturity comparison 10. A 15-year, 7 percent coupon rate bond is selling for $839.27. a. What is the current yield? b. What is the yield to maturity using the trial-and-error approach with annual calculations? c. Why is the current yield higher/lower than the yield to maturity? 12-10. a) Current Yield  EMBED Equation.DSMT4  b) Since the bond is trading below par value, the yield to maturity (interest rate) must be above 7 percent. Lets try 8 percent. PV of $80 annually for n = 15, i = 8% (Table 12-1 or Appendix D) $70 8.559 = $599.13 PV of $1000 for n = 15, i = 8% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  At an 8% discount rate, the answer is $914.13. This is higher than our desired value of $839.27. In order to bring the value down, we must use a higher interest rate. Lets try 9%. PV of $80 annually for n = 15, i = 9% (Table 12-1 or Appendix D) $70 8.061 = $564.27 PV of $1000 for n = 15, i = 9% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  A 9% discount rate provides the bond price $839.27. 9% is the yield to maturity. Approximate yield to maturity 11. What is the approximate yield to maturity of a 14 percent coupon rate, $1,000 par value bond priced at $1,160 if it has 16 years to maturity? Use Formula 122. 12-11.  EMBED Equation.DSMT4  The calculation is done on an annual basis.  EMBED Equation.DSMT4  Yield to call 12. a. Using the facts given in problem 11, what would be the yield to call if the call can be made in four years at a price of $1,080? Use Formula 123. b. Explain why the answer is lower in part a than in problem 11. c. Given a call value of $1,080 in four years, is it likely that the bond price would actually get to $1,160? 12-12. a)  EMBED Equation.DSMT4  The calculation is done on an annual basis.  EMBED Equation.DSMT4  b) Because the bond is callable at $1,080 in four years, the investor must consider the $80 loss in value over four years from $1,160 to $1,080 ($20 per year). This substantially reduces yield. In problem 11, there is also a loss in value from $1,160 to $1,000, but it takes place over 16 years (only $10 per year). The normal amortization of the premium over the life of the bond has less of a negative effect on yield. c) No. The threat of the call will likely keep the price closer to $1,080 (though with four years to call, a littler higher value than $1,080 may be possible if the yield on the bond is well above market rates). Anticipated realized yield 13. a. Using the facts given in problem 11, what would be the anticipated realized yield if the forecast is that the bond can be sold in three years for $1,280? Use Formula 124. Continue to assume the bond has a 14 percent coupon rate ($140) and a current price of $1,160. b. Now break down the anticipated realized yield between current yield and capital appreciation. ( Hint: Compute current yield and subtract this from anticipated realized yield to determine capital appreciation.) 12-13. a)  EMBED Equation.DSMT4  The calculation is done on an annual basis.  EMBED Equation.DSMT4  b)  EMBED Equation.DSMT4  Use of bond table 14. An investor places $800,000 in 30-year bonds (12 percent coupon rate), and interest rates decline by 3 percent. Use Table 124 to determine the current value of the portfolio. 12-14.  EMBED Equation.DSMT4  Use of bond table 15. Use Table 124 to describe the worst possible scenario for a $1,000 bond based on yield change, years to maturity, and coupon rate. What would be the price of the bond? 12-15. The worst possible care would be for yield to rise by the maximum amount in the table (+3%), for the longest maturity (30 years), at the lowest coupon rate (6%). A decline of 30.82 percent would take place and the new price of the bond would be $691.80.  EMBED Equation.DSMT4  Expectations hypothesis 16. The following pattern for one-year Treasury bills is expected over the next four years: Year 1 -5% Year 2 -7% Year 3-10% Year 4-11% a. What return would be necessary to induce an investor to buy a two-year security? b. What return would be necessary to induce an investor to buy a three-year security? c. What return would be necessary to induce an investor to buy a four-year security? d. Diagram the term structure of interest rates for years 1 through 4. 12-16. a) 2-year security (5% + 7%)/2 = 6% b) 3-year security (5% + 7% + 10%)/3 = 7.33% c) 4-year security (5% + 7% + 10% + 11%)/4 = 8.25% d) Yield          Margin purchase 17. a. Assume an investor purchases a 10-year, $1,000 bond with a coupon rate of 12 percent. The market rate almost immediately falls to 9 percent. What would be the percentage return on the investment if the buyer borrowed part of the funds with a 25 percent margin requirement? Assume the interest payments on the bond cover the interest expense on the borrowed funds. (You can use Table 123 in this problem to determine the new value of the bond.) b. Assume the same bond in part a is purchased with 25 percent margin, but market rates go up to 14 percent from 12 percent instead of going down to 9 percent. You can once again use Table 123 to determine the price of the bond. What is the percentage loss on the cash investment? 12-17. a) The new bond price is $1,195.10 (Table 12-3 for 10 periods with a 12 percent coupon rate and a 9 percent yield to maturity) Original bond price $1,000.00 Increase in value $ 195.10 Investment (25% margin) = 25% $1000 = $250  EMBED Equation.DSMT4  b) New bond price $894.10 (Table 12-3 for 10 periods with a 12 percent coupon rate and a 14 percent yield to maturity) Original bond price $1,000.00 Decrease in value $ 105.90  EMBED Equation.DSMT4  Deep discount bond 18. Assume an investor is trying to choose between purchasing a deep discount bond or a par value bond. The deep discount bond pays 6 percent interest, has 20 years to maturity, and is currently trading at $656.80 with a 10 percent yield to maturity. It is callable at $1,050. The second bond is selling at its par value of $1,000. It pays 12 percent interest and has 20 years to maturity. Its yield to maturity is also 12 percent. The bond is callable at $1,080. a. If the yield to maturity on the deep discount bond goes down by 2 percent to 8 percent, what will the new price of the bond be? Do semiannual analysis. b. If the yield to maturity on the par value bond goes down by 2 percent to 10 percent, what will the new price of the bond be? Do semiannual analysis. c. Based on the facts in the problem and your answers to parts a and which bond appears to be the better purchase? (Consider the call feature as well as capital appreciation.) 12-18. a) PV of $30 semiannually for n = 40 and i = 4% (Table 12-1 or Appendix D) $30 19.793 = $593.79 PV of $1,000 for n = 40 and i = 4% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  b) PV of $60 semiannually for n = 40 and i = 5% (Table 12-1 or Appendix D) $60 17.160 = $1,029.60 PV of $1,000 for n = 40 and i = 5% (Table 12-2 or Appendix C)  EMBED Equation.DSMT4  c) The deep discount bond is probably the better purchase because a call price of $1,050 will have no influence on the increase in the bond value. The par value bond is callable to $1,080 and this may hold down the potential price appreciation of the bond. Even if both bonds increase in value as indicated in parts (a) and (b), the deep discount bond will have the larger percentage gain. Deep Discount Bond New value (Part A) $801.79 Original value 656.80 Gain in value $144.99 Gain in value $144.99 Original value $656.80 Return = $144.99/$656.80 = 22.08% Par Value Bond New value (Part B) $1,171.60 Original value 1,000.00 Gain in value $ 171.60 Gain in value $ 171.60 = 17.16% Original value $1,000.00 Return = $171.60/$1,000 = 17.16% Tax swap 19. Mr. Conrad bought $10,000 in bonds six months ago. The 10-year bonds were purchased at par with a 10 percent coupon rate. Now interest rates in the market are 13 percent for similar obligations with 10 years to maturity. The rapid rise in interest rates was caused by an unexpected increase in inflation. a. Determine the current value of Mr. Conrads portfolio. Use Table 123 to help accomplish this. b. How large a deduction from other income can Mr. Conrad take if he sells the bonds? c. If he is in a 35 percent tax bracket, what is the tax write-off worth to him? d. Assume he will replace the old 10 percent bonds with 11.9 percent bonds selling at $927. Based on your answer in part a , how many new bonds can be purchased? Round to the nearest whole number. 12-19. a)  EMBED Equation.DSMT4 b) Current value $ 8,347 Purchase price 10,000 Tax loss $1,653 c) Tax loss $1,653 x 35% tax bracket = $578.55 tax write-off d) Proceeds from sales (value of portfolio) $8,347 Price of new bonds $ 927 $8,347/$927 = Number of new bonds (9.004) or 9 Chapter 12 Solution to Investment Advisor Problem Robert Walker failed to follow rule 5, which states that low-coupon rate bonds are more sensitive to interest rate changes than high coupon rate bonds (this same principle can be expressed through rule 6 as well in terms of yield to maturity. Low coupon U.S. government bonds have the greatest price sensitivity because there is no credit risk, and they are exclusively influenced by interest rates. Conversely, high coupon rate bonds (so called junk bonds if their rating is below the first four rating categories are influenced by a multitude of factors. These include earnings outlook, competitive conditions, potential lawsuits, etc. They may well be more influenced by these factors than interest rate changes. This generally makes them a poor candidate for interest rate plays. b. He was selling bonds for a profit before the required 12-month holding period to qualify for a long-term capital gain favorable tax rate. That maximum rate is 15 percent as opposed to 35 percent for short-term capital gains.     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NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A   $70$839.27==$8.34% FMathType 4.0 Equation MathType EFEquation.DSMT49qObjInfo5pEquation Native q_12440222918FM"9M"9Ole x-h@6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  $1,000.315== $315.00$914.13 FMathType 4.0 Equation MathType EFEquation.DSMT49q-h@6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  $1,000CompObj79yiObjInfo:{Equation Native |_1247920690OE=FM"9M"9 .275== $275.00$839.27 FMathType 6.0 Equation MathType EFEquation.DSMT49q²RdDSMT6WinAllBasicCodePagesOle CompObj<>iObjInfo?Equation Native Times New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  y'== Couponpayment(C t )++ ParValue(P n )"-Marketvalue(V)NumberofperiodstoMaturity(n)(0.6)MarketValue(V)+(0.4)ParValue(P n )_12440256861YBFM"9M"9Ole CompObjACiObjInfoD FMathType 4.0 Equation MathType EFEquation.DSMT49q-a@6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  y'== $140++ $1,00Equation Native }_1248025848^GFM"9M"9Ole CompObjFHi0"-$1,16016(0.6)$1,160+(0.4)$1,000== $140++ "-$16016$696++$400== $140"-$10$1,096== $130$1,096==11.86% FMathType 6.0 Equation MathType EFEquation.DSMT49q[¶RLDSMT6WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_EObjInfoIEquation Native _1244025859LFM"9M"9Ole _A  y'== Couponpayment(C t )++ CallPrice(P c )"-Marketvalue(V)NumberofperiodstoCall(n c )(0.6)MarketValue(V)+(0.4)CallPrice(P c ) FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObjKMiObjInfoNEquation Native h_1244462825QFM"9M"9-L@6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  y'== $140++ $1,080"-$1,1604(0.6)$1,160+(0.4)$1,080== $140"- $804$696++$432== $140"-$20$1,128== $120$1,128==10.64%Ole CompObjPRiObjInfoSEquation Native / FMathType 5.0 Equation MathType EFEquation.DSMT49qA tDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  y' r == Couponpayment(C t )++ RealizedPrice(P r )"-Marketvalue(V)Numberofperiodstorealization(n r )(0.6)MarketValue(V)+(0.4)RealizedPrice(P r ) FMathType 4.0 Equation MathType EFEquation.DSMT49q_1244109845VFM"9M"9Ole CompObjUWiObjInfoXEquation Native _1244026927Jc[FM"9M"9Ole CompObjZ\i%w@6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  y' r == $140++ $1,280"-$1,1603(0.6)($1,160)+(0.4)($1,280)== $140"- $1203$696++$512== $140++$40$1,208== $180$1,208==14.90% FMathType 4.0 Equation MathType EFEquation.DSMT49q- @6M6GDSMT4WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A  Currentyield= CObjInfo]Equation Native )_1247920940`FM"9M"9Ole      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