Answers and Solutions to Select End-of-Chapter Problems

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1 Bond Evaluation, Selection, and Management, Second Edition by R. Stafford Johnson Copyright 2010 R. Stafford Johnson Answers and Solutions to Select End-of-Chapter Problems CHAPTER 1 1. In the private sector, real assets consist of both the tangible and intangible capital goods, as well as human capital, which are combined with labor to form the business. The business, in turn, transforms ideas into the production and sale of goods or services that will generate a future stream of earnings. The financial assets, on the other hand, consist of the financial claims on the earnings. These claims are sold to raise the funds necessary to acquire and develop the real assets. In the public sector, the federal government s capital expenditures and state and local governments capital expenditures represent the development of real assets that these units of government often finance through the sale of financial claims on either the revenue generated from a particular public sector project or from future tax revenues. 2. The financial market can be described as a market for loanable funds; that is, a market where there is a supply and demand for loanable funds. The supply of loanable funds comes from the savings of households, the retained earnings of businesses, and the surpluses of units of government. The demand for loanable funds comes from businesses who need to raise funds to finance their capital purchases of equipment, plants, and inventories; households who need to purchase houses, cars, and other consumer durables; and the Treasury, federal agencies, and municipal governments who need to finance the construction of public facilities, projects, and operations. The exchange of loanable funds from savers to borrowers is done either directly through the selling of financial claims (stock, bonds, commercial paper, etc.) or indirectly through financial institutions. 11. Securitized assets are claims on a portfolio of loans. In creating a securitized asset, an intermediary will put together a package of loans of a certain type (mortgages, auto loans, credit cards, etc.). The institution then sells claims on the package to investors, with the claim being secured by the package of assets securitized assets. The package of loans, in turn, generates interest and principal that is passed on to the investors who purchased the securitized asset. 16. An efficient market can be defined as one in which all information on which investors base their investment decisions are reflected in the security s price. In an efficient market, speculators, on average, would not earn abnormal returns. An inefficient market is one in which the information the market receives is asymmetrical: some investors have information that others don t, or some investors receive information earlier than others. In this market, the market price 771

2 772 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS is not equal to its equilibrium value at all times, and there are opportunities for speculators to earn abnormal returns. 18. For an instrument to be liquid it must be highly marketable and have little, if any, short-run risk. Thus, the difference between marketability and liquidity is the latter s feature of low or zero risk that makes the security cashlike. CHAPTER 2 1. V 0 = V 0 = V 0 = 5 t=1 5 t=1 5 t=1 80 (1.08) t + 1,000 (1.08) 5 = (1.06) t + 1,000 (1.06) 5 = (1.10) t + 1,000 (1.10) 5 = 80 [ 1 (1/1.08) 5.08 [ 1 (1/1.06) 5.06 [ 1 (1/1.10) 5.10 ] + 1,000 (1.08) 5 = $1,000 ] + 1,000 (1.06) =$1, ] + 1,000 (1.10) =$ The problem shows the inverse relationship that exists between the price of a bond and its rate of return. From 8% to 6%, the percentage change in value is 8.425%; from 8% to 10%, the percentage change in value is 7.582%. 2. $1,000, $1,147.20, $ From 8% to 6%, the percentage change in value is 14.72%; from 8% to 10%, the percentage change in value is %. Comment: The percentage changes in value for given changes in yields are greater for the 10-year bond than the 5-year bond. This illustrates the bond price relation that the greater the maturity on a bond the greater its price sensitivity to interest rate changes. 3. $680.58, $747.26, $ From 8% to 6%, the percentage change in value is %; from 8% to 10%, the percentage change in value is 8.766%. Comment: The percentage changes in value for given changes in yields are greater for the 5-year, zero-coupon bond than the 5-year, 8% coupon bond than. This illustrates the bond price relation that the lower the coupon rate on a bond, the greater its price sensitivity to interest rate changes. 4. Values, Effective rates: Semiannual: $960.44, %; Monthly: $959.86, %; Weekly: $959.76, %. 5. Monthly: ; Weekly: ; Daily: ; Continuous: Yields Values

3 Answers and Solutions to Select End-of-Chapter Problems a. Yields Values b. The price change when the yield increases from 8% to 8.5% is c. The price change when the yield decreases from 8% to 7.5% is d. The capital gain and capital loss in b and c are not equal in absolute value. This suggests that gains and losses are not symmetrical. 8. Full price = $1,147.45; Accrued interest = $50; Clean price = $1, Purchase price = $968.30, Selling price (full) = $1, a. The dealer would offer to buy the bonds from investors at $951.25: ((95 + (4/32))/100) ($1,000) = (95.125/100)($1,000) = $ b. The dealer would be willing to sell the bond for $1, : ( /100)($1,000) = $1, c. The dealer would be willing to buy the bond for $975: (97.5/100)($1,000) = $975. d. The dealer would sell the bond for $947.87: $1,000/(1.055) = $ e. The dealer is willing to sell the bond for $9,943: $10,000[1.04(52/360)] = $9, %, $924.18; 10.5%, V 0 = ; Effective yield = 12.36% 14. ARTM = %, V 0 = $ ARTC = % 16. a: Discount yield = 4.8%; b: YTM = 5.039%; c: Logarithmic return = 4.916%. 17. b: Yield = 8%: 18. c: Bond equivalent yield = 9.013% 19. a: $938.55; c: 1,046.23; d: HD value = $1,451.78, TR = 11.52% 20. a: TR = 10%; b: TR = 10.67%; c: TR = 9.43% 21. a: $98.75; b: $ a: S 1 =.06; S 2 =.08; b: YTM 4 = 4 (1 + y 1 )(1 + f 11 )(1 + f 12 )(1 + f 13 ) 1 YTM 4 = 4 (1 + y 2 ) 2 (1 + f 12 )(1 + f 13 ) 1 YTM 4 = 4 (1 + y 1 )(1 + f 21 ) 2 (1 + f 13 ) 1 YTM 4 = 4 (1 + y 1 )(1 + f 31 ) 3 1

4 774 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS 24. a: f 11 = 8.62%; b: (1) Sell X short at $945; (2) buy 945/870 = issues of Y; (3) after one year, cover short bond: cost = $1,000; (4) at the end of year 2 (one year after covering the short position) receive (1.0862)1,000 = from original 2-year bond. Rate on one-year investment made one year from the present period: R 11 = (1, ,000)/1,000 = 8.62%. 25. Use f mt rule: Short in t-bond and long in m + t bond. For example, for f 11 : Short in 1-year bond (t) and long in 2-year (m + t) bond. After one year, you would cover your short position using your funds and then one year later you would collect on the original 2-year bond investment. Thus, the strategy results in a one-year investment to be made one year from now. 26. f 91,91 = 4.25% Strategy: Prices on the T-bills per $100 face value are P(91) = 100/ (1.0375) 91/365 = and P(182) = 100/(1.04) 182/365 = To lock in an implied forward rate on a 91-day investment to be made 91 days from now, one could: (1) Short the 91-day bill: borrow the bill and sell it for (or borrow at 3.75% interest). (2) Use proceeds from the short sale to buy / = issues of the 182-day bill. (3) At the end of 91 days, cover the short position: cost = 100 (equivalent of an 100 investment made 91 days in the future. (4) At the end of 182 days (91 days after covering the short position) collect on the 182-day investment: (100) = Annualized rate on 91-day investment made 91 days from now would be 4.25%. CHAPTER 3 2. a. Expansionary open market operation: Central bank buys bonds, decreasing the bond supply and shifting the bond supply curve to the left. The impact would be an increase in bond prices and a decrease in interest rates. Intuitively, as the central bank buys bonds, they will push the price of bond up and the interest rate down. b. Economic recession: In an economic recession, there is less capital formation and therefore fewer bonds are sold. This leads to a decrease in bond supply and a leftward shift in the bond supply curve. The decrease in supply initially leads to an excess demand for bonds, given fewer bonds; this excess demand increases bond prices and lowers interest rates. The recession may also lead to a decrease in bond demand, shifting the bond demand curve to the left. This would, in turn, cause bond prices to fall and rates to increase. If the supply effect dominates the demand effect, then rates will fall; if the demand effect dominates, then rates will increase. c. Treasury financing of a deficit: With a government deficit, the Treasury will have to sell more bonds to finance the shortfall. Their sale of bonds will increase the supply of bonds, shifting the bond supply curve to the right, and initially creating an excess supply of bonds. This excess supply will force bond prices down and interest rates up.

5 Answers and Solutions to Select End-of-Chapter Problems 775 d. Economic expansion: In a period of economic expansion, there is an increase in capital formation and therefore more bonds are being sold to finance the capital expansion. This leads to an increase in bond supply and a rightward shift in the bond supply curve. The increase in supply initially leads to an excess supply for bonds, decreasing bond prices and increasing interest rates. The expansion may also lead to an increase in bond demand, shifting the bond demand curve to the right. This would, in turn, cause bond prices to rise and rates to decrease. If the supply effect dominates the demand effect, then rates will increase; if the demand effect dominates, then rates will decrease. 3. The increased riskiness on the one bond would cause its demand to decrease, shifting its bond demand curve to the left. That bond s riskiness would also make the other bond more attractive, increasing its demand and shifting its demand curve to the right. At the new equilibriums, the riskier bond s price is lower and its rate greater than the other. The different risk associated with bonds leads to a market adjustment in which at the new equilibrium there is a positive risk premium. 4. The markets are defined in terms of their risk premium, RP: RP = YTM on risky bond YTM on risk-free bond. By definition, a risk-neutral market is one in which the RP is zero, a risk-averse market is one with a positive RP, and a risk-loving market is one in which the RP is negative. 5. a. The expected dollar return on the risky bond is $775 [.75($1,000) +.25($100)]. In a risk-neutral market, the risk premium is equal to zero. As a result, the price of the risky bond is found by discounting its $775 by the risk-free rate of 5%. In this problem, the price of the risky bond is $ (= 775/1.05). b. In a risk-averse market, investors would not want the risky bond when it is priced to equal the risk-free rate. This would cause the demand for the risky bond to decrease, decreasing its price and increasing its yields, and also cause the demand for the risk-free bond to increase, causing its price to increase and its yield to fall. In this problem, the price of the risky bond would fall below $ , resulting in an expected yield that exceeds the initial risk-free yield of 5%, and the price of the risk-free bond would rise above $952.35, resulting in a risk-free yield lower than 5%. Combined, these market adjustments would result in a positive risk premium: RP = E(YTM on risky bond) YTM on risk-free bond > 0. c. In a risk-loving market, investors would want the risky bond when it is priced to equal the risk-free rate. This would cause the demand for the risky bond to increase, increasing its price and lowering its yields, and also cause the demand for the risk-free bond to decrease, causing its price to decrease and its yield to rise. In this problem, the price of the risky bond would increase above $ , resulting in an expected yield that is less than the initial risk-free yield of 5%, and the price of the risk-free bond would fall below $952.35, resulting in a risk-free yield greater than 5%. Combined, these

6 776 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS market adjustments would result in a negative risk premium: RP = E(YTM on risky bond) YTM on risk-free bond < The decrease in the liquidity on the one bond would cause its demand to decrease, shifting its bond demand curve to the left. The decrease in that bond s liquidity would also make the other bond relatively more liquid, increasing its demand and shifting its demand curve to the right. Once the markets adjust to the liquidity difference between the bonds, then the less liquid bond s price would be lower and its rate greater than the more liquid bond. Thus, the difference in liquidity between the bonds leads to a market adjustment in which there is a difference between rates due to their different liquidity features. 7. If investors know with certainty the probabilities and payoffs on the risky bond, then they would know that by buying a number of such bonds they would earn $775 per bond. That is, if they bought 100 risky bonds, 75 of the bonds would pay $1,000 and 25 would pay $100, yielding an average return of $775 ([(75)($1,000) + (25)($100)]/100 = $775). Or, if they were to buy risky bonds for the next 100 periods, then in 75 of the periods they would get a payoff of $1,000 and in 25 of the periods, they would get $100, yielding an average payoff of $750. To be assured that they would earn an average of $750 per bond, investors would have to buy a sufficient number of bonds (e.g., 100) or have sufficient number of time periods (e.g., 100). Buying a sufficient number of bonds now or over time can therefore eliminate the risk of a loss. For there to be a sufficient number of such bonds, in turn, requires a big enough market, which is a liquidity or marketability requirement. Such a requirement is not the case for the risk-free bond. Thus, for liquidity or marketability reasons, investors may price the so-called risky bond at a price to yield a rate above the risk-free bond of 5%. 8. ATY = 5.2%; P 0 = 1, CHAPTER 4 1. a. Outline: Decrease in capital formation (S-T and L-T) Fewer bonds sold (S-T and L-T) Excess demand for bonds (S-T and L-T) Bond prices increase and rates decrease. Downward shift in YCs b. Outline: Increase in capital formation (S-T and L-T) More bonds sold (S-T and L-T) Excess supply of bonds (S-T and L-T) Bond prices decrease and rates increase. Upward shift in YCs c. Outline: Central bank buys S-T Treasuries (T-bills) T-bill prices increase and rates decrease Substitution effect in which the demand for S-T corporate securities increase, causing their prices to increase and their yields to decrease. Tendency for YCs to become positively sloped. d. Outline: Treasury sells L-T Treasuries (T-bonds) T-bond prices decrease and yields increase Substitution effect in which the demand for L-T corporate securities decreases, causing their prices to decrease and their rates to increase. Tendency for YCs to become positively sloped.

7 Answers and Solutions to Select End-of-Chapter Problems 777 e. Outline: Treasury buys L-T Treasuries (T-bonds) T-bond prices increase and yields decrease Substitution effect in which the demand for L-T corporate securities increases, causing their prices to increase and their rates to decrease. Tendency for YCs to become negatively sloped. 2. a. The combination of investors preferring short-term bonds investments, while corporations prefer to sell long-term bonds, would lead to an excess demand for short-term bonds and an excess supply for long-term claims. An equilibrium adjustment would have to occur in both markets. Specifically, the excess supply in the long-term market would force issuers to lower their bond prices, thus increasing bond yields and inducing some investors to change their short-term investment demands. In the short-term market, the excess demand would cause bond prices to increase and rates to fall, inducing some corporations to finance their long-term assets by selling short-term claims. Ultimately, equilibriums in both markets would be reached with long-term rates higher than short-term rates, a premium necessary to compensate investors and borrowers/issuers for the risk they ve assumed. b. In this case, the combination of investors preferring long-term bonds, while corporations prefer to sell short-term bonds, would lead to an excess supply for short-term bonds and an excess demand for long-term claims. The excess supply in the short-term market would force issuers to lower their bond prices, thus increasing bond yields and inducing some investors to change their longterm investment demands. In the long-term market, the excess demand would cause bond prices to increase and rates to fall, inducing some corporations to finance their long-term assets by selling long-term claims. Equilibriums in both markets would be reached with long-term rates lower than short-term rates. 3. Investors with horizon dates of two years can buy the two-year bond with an annual rate of 6%, or they can buy the one-year bond yielding 6%, then reinvest the principal and interest one year later in another one-year bond expected to yield 8%. In a risk-neutral market, such investors would prefer the latter investment since it yields a higher expected average annual rate for the two years of 7% ([(1.06)(1.08)] 1/2 1). Similarly, investors with one-year horizon dates would also find it more advantageous to buy a one-year bond yielding 6% than a two-year bond (priced at $890 = $1,000/ ) that they would sell one year later to earn an expected rate of only 4.037% (E(P 11 ) = 1,000/1.08 = $925.93; E(R) = (925.93/890) 1 =.0437). Thus, in a risk-neutral market with an expectation of higher rates next year, both investors with one-year horizon dates and investors with two-year horizon dates would purchase oneyear instead of two-year bonds. If enough investors do this, an increase in the demand for one-year bonds and a decrease in the demand for two-year bonds would occur until the average annual rate on the two-year bond is equal to the equivalent annual rate from the series of one-year investments (or the one-year bond s rate is equal to the rate expected on the two-year bond held one year). 5. a. Outline: (1) Given HD = 2 years, investors would prefer a series of one-year bonds at 10% (= [(1.08)(1.12)] 1/2 1) to a two-year bond at 8% (also

8 778 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS holds for investors with HD = 1 year). (2) Market Response: Demand for 2-year bonds would decrease, causing their price to decrease and their yield to increase, and the demand for 1-year bonds would increase, causing their price to increase and their yield to decrease. Impact: Tendency for YC to become positively sloped. Outline: (1) Given the expectation of higher rates in the future, borrowers wishing to finance 2-year assets would prefer to issue two-year bonds at 8% rather than sell a series of one-year bonds at 10% = [(1.08)(1.12)] 1/2 1. (2) Market Response: The supply of 2-year bonds would increase, causing their price to decrease and their yield to increase, and the supply of 1-year bonds would decrease, causing their price to increase and their yield to decrease. Impact: Tendency for YC to become positively sloped, complementing the impact of investors response to the expectation. b. Outline: (1) Given HD = 2 years, investors would prefer a 2-year bond at 10% to a series of one-year bonds at 9% (= [(1.10)(1.08)] 1/2 1) (also holds for investors with HD = 1 year). (2) Market Response: Demand for 2-year bonds would increase, causing their price to increase and their yield to decrease, and the demand for 1-year bonds would decrease, causing their price to decrease and their yield to increase. Impact: Tendency for YC to become negatively sloped. Outline: (1) Given the expectation of lower rates in the future, borrowers wishing to finance 2-year assets would prefer to issue a series of one-year bonds at 9% (= [(1.08)(1.10)] 1/2 1) to two-year bonds at 10%. (2) Market response: The supply of 2-year bonds would decrease, causing their price to increase and their yield to decrease, and the supply of 1-year bonds would increase, causing their price to decrease and their yield to increase. Impact: Tendency for YC to become negatively sloped, complementing the impact of investors response to the expectation. c. Outline: (1) Given HD = 2 years, investors would be indifferent to a 2-year bond at 7% and a series of one-year bonds at 7% (= [(1.06) (1.08)] 1/2 1) (also holds for investors with HD = 1 year). (2) Market response: No change in the yield curve. Outline: (1) Given HD = 2 years, borrowers would be indifferent to issuing a 2-year bond at 7% and a series of one-year bonds at 7% (= [(1.06) (1.08)] 1/2 1). (2) Market response: No change in the yield curve. 6. a. f 11 = 9%, f 21 = 8.5%, f 31 = 7%, f 41 = 5.751%. b. f 12 = 8%, f 22 = 6.01%, f 32 = 4.69%. c. The expected rate of return from buying a three-year bond and selling it one year later is equal to the yield on the one-year bond of 7% if the implied forward rate, f 21, is used as the expected rate on a two-year bond one year later: P 3 = 100/(1.08) 3 = ; E(P 21 ) = 100/(1.085) 2 = ; E(R) = ( /79.383) 1 =.07. d. The expected rate of return from buying a bond of any maturity and selling it one year later is equal to the yield on the one-year bond of 7% if the implied forward rate is used as the expected rate on the bond one year later.

9 Answers and Solutions to Select End-of-Chapter Problems 779 e. The expected rate of return from buying a four-year bond and selling it two years later is equal to the yield on the two-year bond of 8% if the implied forward rate, f 22, is used as the expected rate on a two-year bond two years later: P 4 = 100/(1.07) 4 = ; E(P 22 ) = 100/(1.0601) 2 = ; E(R) = ( / ) 1/2 1=.08. f. The expected rate of return from buying a bond of any maturity and selling it two years later is equal to the yield on the two-year bond of 8% if the implied forward rate is used as the expected rate on the bond two years later. 7. a. P 0 = b. f 11 = 7.002%, f 21 = %, f 31 = % c. E(P 31 ) = d. If bonds are equal to their equilibrium prices and the implied forward rates are used as estimate of future rates, then the one-year expected rates will be equal to the current one-year rate. The one-year expected rate on the four-year, 7% bond held one year is 6% the same as the one-year rate: E(R) = =.06 e. f 12 = %; f 22 = % f. The expected price on the four-year, 7% coupon bond two years later is ( = [7/( ) + (107/( ) 2 ] = ). Assuming that the $7 coupon is reinvested to year 2 at f 11 of 7%, the expected rate of return for holding the four-year, 7% bond two years is 6.5% the same as the two-year spot rate: [ ] 7(1.07) /2 E(R 22 ) = 1 = (1) A contractionary open market operation in which the central bank sells shortterm government securities. (2) A Treasury purchase of long-term Treasury securities. (3) A poorly hedged economy in which investors prefer long-term investments and borrowers prefer short-term. (4) A market expectation of lower interest rates. 9. The liquidity premium theory (LPT) posits that there is a liquidity premium for long-term bonds over short-term bonds because the prices of long-term securities tend to be more volatile and therefore more risky than short-term securities. According to LPT, if investors were risk averse, then they would require some additional return (liquidity premium) in order to hold long-term bonds instead of short-term ones. The yield curves in Questions 6 and 7 had no risk premium factored in to compensate investors for the additional volatility they assumed from buying long-term bonds. Thus a liquidity premium would need to be added to longer-term yields to reflect the additional risk associated with the longer-term bonds. 10. (1) The market expects higher interest rates in the future. (2) The market expects lower interest rates in the future. (3) Expected rates for holding bonds for a

10 780 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS specified period (e.g., one year, two years) will be equal to the applicable current rate if expected rates are equal to implied forward. If investors expect future rate to be less than the applicable implied forward rate, then they would expect their holding period yields to exceed the current rates. Thus, the implied forward rates can be used as a cutoff rate in evaluating and selecting bonds. (4) The preferred habitat theory posits that investors and borrowers will move away from their preferred maturity segment if rates are attractive enough to compensate them for foregoing their preferences. CHAPTER 5 1. During recessions investors are more concerned with safety than during expansionary times. As a result, a relatively low demand for lower grade bonds and a high demand for higher grades occur, leading to lower prices for the lower grade bonds and thus a higher interest premium. On the other hand, during periods of economic expansion there is usually less concern about default. This tends to increase the demand for lower grade bonds relative to higher grade, causing a smaller premium. 2. The negatively sloped yield curve for low-grade bonds suggests that investors have more concern over the repayment of principal (or the issuer s ability to refinance at favorable rates) than they do about the issuer meeting interest payments. This concern would explain the low demand and higher yields for short-term bonds, in which principal payment is due relatively soon compared to long-term bonds. 8. TR 4 = %; TR 10 = 9.889% 10. a %; b % 11. a. 10%; b. 10%. c. Since the TR stays at 10% at the different rates, there is no market risk. 12. The eight-year, 8.5% coupon bond given a flat yield curve at 10% has Macaulay duration of The bond s modified duration is Comment: This problem illustrates how an investor with an HD = 6 years can eliminate, or at least minimize, market risk by buying a bond that has a duration equal to the HD of a. For zero-coupon bonds, Macaulay s duration is equal to the bond s maturity. b. w 1 = 1/3 and w 2 = 2/ Bond Period Coupon, C P F Period Yield, y Periods to Maturity, M Payments per Year, n Modified Duration Macaulay Duration Convexity a b c d e f

11 Answers and Solutions to Select End-of-Chapter Problems 781 CHAPTER 6 4. Even though it is true that a sinking fund provision benefits bondholders by allaying their concern over the ability of the issuer to pay the principal, many sinking funds have a provision that allows the issuer to buy up the requisite amount of bonds either at a stipulated call price or in the secondary market at its market price. This sinking fund call option provision benefits the issuer and is a disadvantage to the bondholder. 5. The average life is 8.5 years. 7. YTM = 14.64% 8. Call protection means that the bond cannot be called. Refunding protection means that the bond cannot be called from the proceeds of certain types of refunding debt. Bonds that have refunding protection may still be called. 9. The initial year s call price is equal to the offering price of $950 plus the $100 coupon: $1,050. The call price will then decrease by $2.50 each year [= ($1,050 $1,000)/20] to equal $1,000 at the end of year 20. The call price will be equal to $1,000 for years 21 through A release and substitution provision allows the issuer of a mortgage bond to sell the collateral in order to retire the bond; that is, the proceeds from the asset sale are used to retire the bond. 13. (1) A provision requiring the issuer to deliver to the trustee the pledged securities. (2) A provision allowing the company to retain its voting right if the collateral is the stock of one of its subsidiaries. (3) A provision requiring that the company maintains the value of its securities, positing addition collateral if the collateral decreases in value. (4) A provision allowing the company to withdraw the collateral provided there is an acceptable substitute. 15. The creditworthiness of debentures can be improved with protective covenants, subordination, and credit enhancements. 16. The guarantee does not eliminate the risk but shifts it from the corporation to the insurer. 19. The board of directors hires the managers and officers of a corporation. Since the board represents the stockholders, this arrangement can create a moral hazard in which the managers may engage in activities that could be detrimental to the bondholders. Since bondholders cannot necessarily seek redress from managers after they ve made decisions that could harm them, they need to include in the bond indenture protective covenants that place restrictions on the company. 20. Some of the standard covenants specify the financial criterion that must be met before borrowers can incur additional debt (debt limitation) or pay dividends (dividend limitations). Other possible covenants include limitations on liens, borrowing from subsidiaries, asset sales, mergers and acquisitions, and leasing. 22. (a) A company is considered insolvent if the value of its liabilities exceeds the value of its assets; it is considered in default if it cannot meet its obligations.

12 782 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS Technically, default and insolvency are dependent: A company with liabilities exceeding assets will inevitably be in default when the future income from its assets is insufficient to cover future obligations on its liabilities. (b) A company can be illiquid and not insolvent. A company with assets that are not expected to generate a return for some time in the futures may very well be a solvent company. 25. The investment banker underwriting a bond issue bears the risk that the price of the issue could decrease during the time the bonds are being sold. A classic example discussed in the chapter was the $1 billion bond issue of IBM in (1) Commercial paper is usually sold as a zero-coupon bond; (2) many have maturities less than 270 days to avoid registration; (3) CP is sold either directly (direct paper) or through dealers (dealer paper); (4) many CP issues include credit enhancements such as lines of credit. 32. Reverse inquiry is when institutional investors indicate to agents the type of maturity they want. The agent will inform the corporation of the investor s request; the corporation could then agree to sell the notes with that maturity from its MTN program, even if they are not posted. 33. As a source of financing, MTNs provide corporations with flexibility in their financing choices. Corporations selling an MTN through a shelf registration are able to enter the market constantly or intermittently, with the flexibility to finance a number of different short-, intermediate-, and long-term projects over a two-year period. CHAPTER 7 2. Year Inflation Inflation-Adjusted Principal TIP Cash Flow 1 2% $ $ % $ $ % $ $ % $ $ $ a. S.5 = 5%, S 1 = 5.25%, S 1.5 = 6.03%, S 2 = 6.55%, S 2.5 = 7.08%, S 3 = 7.62%. b. P.5 = , P 1 = , P 1.5 = , P 2 = , P 2.5 = , P 3 = ; total value of the strips = c. An arbitrage exists by buying the three-year note for 100, stripping it into six zero coupons, and selling the strips for d. If the actual yield curve matches the theoretical spot yield curve, then the proceeds from the sale of the strips would be equal to the cost of the threeyear note of 100. Thus, no arbitrage exists: P.5 = , P 1 = ,

13 Answers and Solutions to Select End-of-Chapter Problems 783 P 1.5 = , P 2 = , P 2.5 = , P 3 = ; total value of the strips = 100. e. If the yield curve had yields equal to the YTMs on the Treasury securities, arbitrageurs could buy a T-note, strip it, and sell the strips for a risk-free profit. In contrast, if the yields on the yield curve were equal to the spot rates estimated from bootstrapping, then the arbitrage profit would be zero. Thus, the process of stripping will change the supply and demand for bonds, causing their yields to move to their theoretical spot yield curve levels. 6. a. 2.84% or ; b billion; c %; d %; e..042%. 8. Income comes from two sources: carry income and position profit. Carry income is the difference between the interest dealers earn from holding the securities and the interest they pay on the funds they borrow to purchase the securities. The position profit of dealers comes from long positions, as well as short positions. In a long position, a dealer purchases the securities and then holds them until a customer comes along. The dealer will realize a position profit if rates decrease and prices increase during the time she holds the securities. In contrast, in a short position, the dealer borrows securities and sells them hoping that rates will subsequently increase and prices will fall by the time he purchases the securities. 9. On-the-run issues are recently issued Treasury securities; they are the most liquid securities with a very narrow bid-ask spread. Off-the-run issues are Treasury securities issued earlier; they are not quite as liquid and can have slightly wider spreads. 10. The interdealer market is a market in which dealers trade amongst themselves. The market functions through government security brokers. 11. Under a repurchase agreement (RP), the holder of a security, such as a dealer, sells securities to another party, often a financial institution, with an agreement to buy the securities back at a later date and price. To the seller/repurchaser, the RP represents a collateralized loan, with the underlying securities serving as the collateral. To the buyer/reseller, the RP represents a secured investment. Their position is referred to as a reverse repo. 12. a. The dealer would buy the notes and then per the repurchase agreement sell the acquired notes on the repurchase agreement with an agreement to buy them back the next day. b. Interest = ($100,000,000)(.03)(1/360) = $8,333; Selling price = $99,991,667; Repurchase price = $100,000,000. c. The dealer could use an open repo. CHAPTER 8 2. In evaluating the creditworthiness of a GO bond, investors need to review the legal opinion to determine the state or local government s unlimited taxing authority. The legal opinion should identify if there are any statutory or

14 784 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS constitutional limitations on the jurisdiction s taxing power, as well as any priority of claims on general funds. The legal opinion should also specify what the bondholders redress is in the case of a default and whether there are any statutory or constitutional questions involved. Municipal defaults are usually handled through a restructuring, which makes the security and priorities as defined in the indenture and explained in the legal opinion important in establishing the type of new debt the holder will receive. 3. Municipal anticipation notes are municipal securities sold to obtain funds in lieu of anticipated revenues. They include tax-anticipation notes (TANs), revenueanticipation notes (RANs), grant-anticipation notes (GANs), bond-anticipation notes (BANs), and municipal tax-exempt commercial paper. TANs and RANs are used to cover regular recurring government expenses. BANs are used as temporary financing or construction financing for long-term projects, with the principal paid from the proceeds from the sale of a long-term municipal bond. 4. If the tax rate increases, then more investors will find tax-exempt bonds relatively attractive; by contrast, if tax rates decrease, tax-exempt bonds become less attractive. 5. Until the Tax Reform Act of 1986, commercial banks were one of the larger purchasers of municipals. The lowering of the top corporate tax rate from 46% to 35%, though, led to a sizable reduction in their investments in municipal bonds. 6. Revenue bonds are used to finance capital projects such as roads, bridges, tunnels, airports, hospitals, power-generating facilities, water treatment plants, municipal buildings, university buildings, educational programs, inner-city housing development, and student loan programs. 7. Industrial revenue bonds are used by state and local governments to support private-public sector projects. They are often sold to finance the expansion of an area s industrial base or to attract new industries. Typically, the government or authority floats a bond issue and then uses the proceeds to build a plant or an industrial facility; it then leases the facility to a company or provides a low interest loan for the company to acquire the asset. Comment: Because of the tax-exempt status of municipal bonds, this type of financial arrangement benefits all parties: investors receive a higher after-tax yield, corporations receive lower interest rates on loans or lower rental rates, and the area benefits from a new or expanding industry. 8. For revenue bonds, some of the important provisions specified in the official statement and legal opinion that investors should consider are: (1) Whether the issuer can increase the tax or user s fee underlying the revenue source. (2) Whether the issuer can incur additional debt secured by the revenue of the project (referred to as minimum revenue clauses) or under what conditions new debt can be incurred. (3) How the revenues of the project are to be directed if they are to be paid to bondholders after operating expenses but before other expenses (this is called

15 Answers and Solutions to Select End-of-Chapter Problems 785 a net revenue structured revenue bond) or to bondholders first (this is called a gross revenue structured bond). (4) Whether there are any additional collateral or guarantees. 9. (a) Serial issue: Many municipals are sold as a serial issue, with the bond issue broken into different maturities. (b) Insured bonds: Insured municipal bonds are ones secured by an insurance company. (c) Letter-of-credit-backed municipal bonds are municipals secured by a letter of credit from a commercial bank. (d) Mello-Roos bonds are municipal securities issued by local governments in California that are not backed by the full faith and credit of the government. (e) Refunded bonds are municipal bonds secured by an escrow fund consisting of high-quality securities such as Treasuries and federal agencies. There are also refunded municipals backed by an escrow fund consisting of a mix of Treasuries and non-treasuries such as municipals. (f) Moral obligation bonds are bonds issued without the legislature approving appropriation. The bonds are therefore considered backed by the permissive authority of the legislature to raise funds, but not the mandatory authority. CHAPTER 9 2. Today, dealers and brokers form the core of the primary and secondary markets for CDs, selling new CDs and trading and maintaining inventories in existing ones. Money-market funds, banks, bank trust departments, state and local governments, foreign governments and central banks, and corporations are the major investors in CDs. 3. In 1961, First Bank of New York issued a negotiable CD that was accompanied by an announcement by First Boston Corporation and Salomon Brothers that they would stand ready to buy and sell the CDs, thus creating a secondary market for CDs. The secondary market provided a way for banks to circumvent Regulation Q and offer investors rates competitive with other money market securities. Specifically, with Federal Reserve Regulation Q setting the maximum rates on longer term CDs (e.g., six months), and with those rates set relatively higher than shorter term CDs (e.g., three months), the existence of a secondary market meant that an investor could earn a rate higher than either a short- or longer-term CD by buying a longer term CD and selling it later in the secondary market at a higher price associated with the short-term maturity. 4. Bank notes are similar to medium-term notes. They are sold as a program consisting of a number of notes with different maturities typically ranging from one to five years and offered either continuously or intermittently. They differ from corporate MTNs in that they are not registered with the SEC, unless it is the bank s holding company, and not the individual bank, issuing the MTN. 5. Banker s acceptances (BAs) are time drafts (postdated checks) guaranteed by a bank guaranteed postdated checks. The guarantee of the bank improves the credit quality of the draft, making it marketable. BAs are used to finance the purchase of goods that have to be transferred from a seller to the buyer.

16 786 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS They are often created in international business transactions where finished goods or commodities have to be shipped. The use of BAs to finance transactions is known as acceptance financing and banks that create BAs are referred to as accepting banks. 6. The U.S. company would obtain a letter of credit (LOC) from its bank. The LOC would say that the bank would pay the German company $20 million if the U.S. company failed to do so. The LOC would then be sent by the U.S. bank to the German company s bank. Upon receipt of the LOC, the German bank would notify the German manufacturing company who would then ship the drilling equipment. The German company would then present the shipping documents to the German bank and receive the present value of $20 million in local currency from the bank. The German bank would then present a time draft to the U.S. bank who would stamp accepted on it, thus creating the BA. The U.S. company would sign the note and receive the shipping documents. At this point, the German bank is the holder of the BA. The bank can hold the BA as an investment or sell it to the American bank at a price equal to the present value of $20 million. If the German bank opts for the latter, then the U.S. bank holds the BA and can either retain it or sell it to an investor such as a money market fund or a BA dealer. If all goes well, at maturity the U.S. company will present the shipping documents to the shipping company to obtain the drilling equipment, as well as deposit the $20 million funds in its bank; whoever is holding the BA on the due date will present it to the U.S. bank to be paid. 10. A unit investment trust has a specified number of fixed-income securities that are rarely changed, and the fund usually has a fixed life. A unit investment trust is formed by a sponsor who buys a specified number of securities, deposits them with a trustee, and then sells claims on the security, known as redeemable trust certificates, at their net asset value plus a commission fee. The financial institution would purchase $100 million worth of 10-year Treasury bonds, place them in a trust, and then issue 100,000 redeemable trust certificates at net asset value of $1,000 plus commission: NAV = ($100,000,000/100,000) = $1,000. The financial institution s sale of trust certificates provides the proceeds to purchase the $100 million of T-bonds. 11. Hedge funds are structured so that they can be largely unregulated. To achieve this, they are often set up as limited partnerships. By federal law, as limited partnerships, hedge funds are limited to no more than 99 limited partners each with annual incomes of at least $200,000 or a net worth of at least $1 million (excluding home), or to no more than 499 limited partners each with a net worth of at least $5 million. Many funds or partners are also domiciled offshore to circumvent regulations. Hedge funds acquire funds from many different individual and institutional sources; the minimum investments range from $100,000 to $20 million, with the average investment being $1 million. 18. $1,425, (a) Bank investment contracts (BIC) are deposit obligations with a guaranteed rate and fixed maturity; they are similar to a GIC. (b) Stable value investment is the term used to describe investments in bank investment contracts and

17 Answers and Solutions to Select End-of-Chapter Problems 787 guaranteed investment contracts. (c) Bullet contract is the term used to describe a generic GIC. (d) Window GIC refers to a GIC that allows for premium deposits to be made over a specified period, such as a year; they are designed to attract the annual cash flow from a pension or 401(k) plan. (e) Floating-rate GIC contract is a GIC in which the rate is tied to a benchmark rate. CHAPTER Interest Equalization Tax: In 1963, the U.S. government imposed the Interest Equalization Tax (IET) on the price of foreign securities purchased by U.S. investors. The tax was aimed at reducing the interest-rate difference between higher yielding foreign bonds and lower yielding U.S. bonds. Predictably, it led to a decline in the Yankee bond market. It also contributed to the development of the Eurobond market as more foreign borrowers began selling dollar-denominated bonds outside the U.S. The IET was repealed in Foreign Withholding Tax: In the 1970s there was a U.S. foreign withholding tax that imposed a 30% tax on interest payments made by domestic U.S. firms to foreign investors. There was a tax treaty, though, that exempted the withholding tax on interest payments from any Netherlands Antilles subsidiary of a U.S. incorporated company to non-u.s. investors. This tax-treaty led to many U.S. firms issuing dollar-denominated bonds in the Eurobond market through financing subsidiaries in the Netherlands Antilles. During this time, Germany also imposed a withholding tax on German DM-denominated bonds held by nonresidents. Even though the U.S and other countries with withholding taxes granted tax credits to their residents when they paid foreign taxes on the incomes from foreign security holdings, the tax treatments were not always equivalent. In addition, many tax-free investors, such as pension funds, could not take advantage of the credit (or could, but only after complying with costly filing regulations). As a result, during the 1970s and early 1980s, Eurobonds were often more attractive to foreign investors and borrowers than foreign bonds. In 1984, the U.S. and Germany rescinded their withholding tax laws on foreign investments and a number of other countries followed their lead by eliminating or relaxing their tax codes. Even with this trend, though, the Eurobond market had already been established. 4. A corporation or government wanting to issue a Eurobond will usually contact a multinational bank that will form a syndicate of other banks, dealers, and brokers from different countries. The members of the syndicate usually agree to underwrite a portion of the issue, which they usually sell to other banks, brokers, and dealers. The multinational makeup of the syndicate allows the issue to be sold in many countries. 7. In 1984, U.S. corporations were allowed to issue bearer bonds directly to non- U.S. investors. To accommodate U.S. investors, the SEC allows U.S. investors to purchase nonregistered Eurobonds after they are seasoned. Thus, U.S. investors are locked out of initial offerings of Eurobonds, but can acquire them in the secondary market.

18 788 ANSWERS AND SOLUTIONS TO SELECT END-OF-CHAPTER PROBLEMS 8. In a number of countries, commercial banks, instead of investment bankers, underwrite new bonds. In the secondary market, some countries trade bonds exclusively on exchanges, whereas others trade bonds on both the exchanges and through market makers on an OTC market. Bonds sold in different countries also differ in terms of whether they are sold as either registered bonds or bearer bonds. A foreign investor buying a domestic bond may also be subject to special restrictions. These can include special registrations, exchange controls, and foreign withholding taxes. 10. The Eurocurrency market is a market in which funds are intermediated (deposited or loaned) outside the country of the currency in which the funds are denominated. For example, a certificate of deposit denominated in dollars offered by a subsidiary of a U.S. bank incorporated in the Bahamas is a Eurodollar CD. Similarly, a loan made in yen from a bank located in the United States would be an American-yen loan. The Eurocurrency market is one of the largest financial markets. The underlying reason for this is that Eurocurrency loan and deposit rates are often better than the rates on similar domestic loans and deposits because of the differences that exist in banking and security laws among countries. Foreign lending or borrowing, regardless of what currency it is denominated in and what country the lender or borrower is from, is subject to the rules, laws, and customs of the foreign country where the deposits or loans are made. Accordingly, if a country s banking laws are less restrictive, then it is possible for a foreign bank or a foreign subsidiary of a bank to offer more favorable rates on its loans and deposits than it could in its own country by simply intermediating the deposits and loans in that country. 11. (a) In the 1950s, the Soviet Union maintained large dollar deposits in U.S. banks in order to participate in world trade. However, poor political relations, as well as U.S. claims on the Soviet Union originating from the Lend-Lease Policy, led to fears by the Soviet Union that the U.S. government could expropriate their deposits. As a result, the USSR transferred their dollar deposits to banks in Paris and London, thus creating the first modern-day Eurodollar deposit. (b) Under the old Bretton Woods exchange rate system, the central banks of many countries maintain holding of currencies in order to intervene in the foreign currency market to support their exchange rate. The dollar was the major currency held by central banks. This contributed to dollar deposits outside the U.S. (c) In the mid-1960s, U.S. banks began to go after Eurodollar deposits and loans by establishing foreign subsidiaries. What attracted many U.S. banks to the Eurodollar market were the opportunities around Federal Reserve rules. (d) In the late 1970s, many oil-exporting countries used the Eurodollar market, depositing large dollar deposits. Some of these petrodollars were used to make loans to oil-importing counties, leading the dollar deposits from oil revenues to be recycled.