投资学10版习题答案.docx

1、投资学10版习题答案CHAPTER 14: BOND PRICES AND YIELDSPROBLEM SETS 1. a. Catastrophe bondA bond that allows the issuer to transfer “catastrophe risk” from the firm to the capital markets. Investors in these bonds receive a compensation for taking on the risk in the form of higher coupon rates. In the event of

2、 a catastrophe, the bondholders will receive only part or perhaps none of the principal payment due to them at maturity. Disaster can be defined by total insured losses or by criteria such as wind speed in a hurricane or Richter level in an earthquake. b. EurobondA bond that is denominated in one cu

3、rrency, usually that of the issuer, but sold in other national markets.c. Zero-coupon bondA bond that makes no coupon payments. Investors receive par value at the maturity date but receive no interest payments until then. These bonds are issued at prices below par value, and the investors return com

4、es from the difference between issue price and the payment of par value at maturity (capital gain).d. Samurai bondYen-dominated bonds sold in Japan by non-Japanese issuers.e. Junk bondA bond with a low credit rating due to its high default risk; also known as high-yield bonds.f. Convertible bondA bo

5、nd that gives the bondholders an option to exchange the bond for a specified number of shares of common stock of the firm.g. Serial bondsBonds issued with staggered maturity dates. As bonds mature sequentially, the principal repayment burden for the firm is spread over time.h. Equipment obligation b

6、ondA collateralized bond for which the collateral is equipment owned by the firm. If the firm defaults on the bond, the bondholders would receive the equipment.i. Original issue discount bondA bond issued at a discount to the face value.j. Indexed bond A bond that makes payments that are tied to a g

7、eneral price index or the price of a particular commodity.k. Callable bondA bond that gives the issuer the option to repurchase the bond at a specified call price before the maturity date.l. Puttable bondA bond that gives the bondholder the option to sell back the bond at a specified put price befor

8、e the maturity date.2. The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should be higher.3. Zero coupon bonds provide no coupons to be reinvested. Therefore, the investors proceeds from the bond are indepe

9、ndent of the rate at which coupons could be reinvested (if they were paid). There is no reinvestment rate uncertainty with zeros.4. A bonds coupon interest payments and principal repayment are not affected by changes in market rates. Consequently, if market rates increase, bond investors in the seco

10、ndary markets are not willing to pay as much for a claim on a given bonds fixed interest and principal payments as they would if market rates were lower. This relationship is apparent from the inverse relationship between interest rates and present value. An increase in the discount rate (i.e., the

11、market rate. decreases the present value of the future cash flows.5. Annual coupon rate: 4.80% $48 Coupon payments Current yield: 6. a. Effective annual rate for 3-month T-bill:b. Effective annual interest rate for coupon bond paying 5% semiannually:(1.05.21 = 0.1025 or 10.25%Therefore the coupon bo

12、nd has the higher effective annual interest rate.7. The effective annual yield on the semiannual coupon bonds is 8.16%. If the annual coupon bonds are to sell at par they must offer the same yield, which requires an annual coupon rate of 8.16%.8. The bond price will be lower. As time passes, the bon

13、d price, which is now above par value, will approach par.9. Yield to maturity: Using a financial calculator, enter the following:n = 3; PV = 953.10; FV = 1000; PMT = 80; COMP iThis results in: YTM = 9.88%Realized compound yield: First, find the future value (FV. of reinvested coupons and principal:F

14、V = ($80 * 1.10 *1.12. + ($80 * 1.12. + $1,080 = $1,268.16Then find the rate (yrealized . that makes the FV of the purchase price equal to $1,268.16:$953.10 (1 + yrealized .3 = $1,268.16 yrealized = 9.99% or approximately 10%Using a financial calculator, enter the following: N = 3; PV = 953.10; FV =

15、 1,268.16; PMT = 0; COMP I. Answer is 9.99%.10.a.Zero coupon8% coupon10% couponCurrent prices$463.19$1,000.00$1,134.20b. Price 1 year from now$500.25$1,000.00$1,124.94Price increase$ 37.06$ 0.00 $ 9.26Coupon income$ 0.00$ 80.00$100.00Pretax income$ 37.06$ 80.00$ 90.74Pretax rate of return8.00%8.00%8

16、.00%Taxes*$ 11.12$ 24.00$ 28.15After-tax income$ 25.94$ 56.00$ 62.59After-tax rate of return5.60%5.60%5.52%c. Price 1 year from now$543.93$1,065.15$1,195.46Price increase$ 80.74$ 65.15$ 61.26Coupon income$ 0.00$ 80.00$100.00Pretax income$ 80.74$145.15$161.26Pretax rate of return17.43%14.52%14.22%Tax

17、es$ 19.86$ 37.03$ 42.25After-tax income$ 60.88$108.12$119.01After-tax rate of return13.14%10.81%10.49%* In computing taxes, we assume that the 10% coupon bond was issued at par and that the decrease in price when the bond is sold at year-end is treated as a capital loss and therefore is not treated

18、as an offset to ordinary income. In computing taxes for the zero coupon bond, $37.06 is taxed as ordinary income (see part (b); the remainder of the price increase is taxed as a capital gain.11. a. On a financial calculator, enter the following:n = 40; FV = 1000; PV = 950; PMT = 40You will find that

19、 the yield to maturity on a semiannual basis is 4.26%. This implies a bond equivalent yield to maturity equal to: 4.26% * 2 = 8.52%Effective annual yield to maturity = (1.0426)2 1 = 0.0870 = 8.70%b. Since the bond is selling at par, the yield to maturity on a semiannual basis is the same as the semi

20、annual coupon rate, i.e., 4%. The bond equivalent yield to maturity is 8%.Effective annual yield to maturity = (1.04)2 1 = 0.0816 = 8.16%c. Keeping other inputs unchanged but setting PV = 1050, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semiannual basis.Effective annual yiel

21、d to maturity = (1.0376)2 1 = 0.0766 = 7.66%12. Since the bond payments are now made annually instead of semiannually, the bond equivalent yield to maturity is the same as the effective annual yield to maturity. On a financial calculator, n = 20; FV = 1000; PV = price; PMT = 80The resulting yields f

22、or the three bonds are:Bond PriceBond Equivalent Yield =Effective Annual Yield$9508.53%1,0008.001,0507.51The yields computed in this case are lower than the yields calculated with semiannual payments. All else equal, bonds with annual payments are less attractive to investors because more time elaps

23、es before payments are received. If the bond price is the same with annual payments, then the bonds yield to maturity is lower.13.PriceMaturity (years.Bond EquivalentYTM$400.0020.004.688%500.0020.003.526500.0010.007.177385.5410.0010.000463.1910.008.000400.0011.918.00014. a. The bond pays $50 every 6

24、 months. The current price is:$50 Annuity factor (4%, 6) + $1,000 PV factor (4%, 6) = $1,052.42Alternatively, PMT = $50; FV = $1,000; I = 4; N = 6. Solve for PV = $1,052.42.If the market interest rate remains 4% per half year, price six months from now is:$50 Annuity factor (4%, 5) + $1,000 PV facto

25、r (4%, 5) = $1,044.52Alternatively, PMT = $50; FV = $1,000; I = 4; N = 5. Solve for PV = $1,044.52.b. Rate of return15. The reported bond price is: $1,001.250However, 15 days have passed since the last semiannual coupon was paid, so:Accrued interest = $35 * (15/182) = $2.885The invoice price is the

26、reported price plus accrued interest: $1,004.1416. If the yield to maturity is greater than the current yield, then the bond offers the prospect of price appreciation as it approaches its maturity date. Therefore, the bond must be selling below par value.17. The coupon rate is less than 9%. If coupo

27、n divided by price equals 9%, and price is less than par, then price divided by par is less than 9%.18.TimeInflation in Year Just EndedPar ValueCouponPaymentPrincipalRepayment0$1,000.0012%1,020.00$40.80$ 0.0023%$1,050.60$42.02$ 0.0031%$1,061.11$42.44$1,061.11The nominal rate of return and real rate

28、of return on the bond in each year are computed as follows: Nominal rate of return = Real rate of return = Second YearThird YearNominal returnReal returnThe real rate of return in each year is precisely the 4% real yield on the bond.19. The price schedule is as follows:YearRemaining Maturity (T).Con

29、stant Yield Value $1,000/(1.08)TImputed Interest (increase in constantyield value)0 (now)20 years$214.55119231.71$17.16218250.2518.54191925.93200 1,000.0074.0720. The bond is issued at a price of $800. Therefore, its yield to maturity is: 6.8245%Therefore, using the constant yield method, we find th

30、at the price in one year (when maturity falls to 9 years) will be (at an unchanged yield. $814.60, representing an increase of $14.60. Total taxable income is: $40.00 + $14.60 = $54.6021. a. The bond sells for $1,124.72 based on the 3.5% yield to maturity.n = 60; i = 3.5; FV = 1000; PMT = 40Therefore, yield to call is 3.368% semiannually, 6.736% annually.n = 10 semiannual periods; PV = 1124.72; FV = 1100; PMT = 40b. If the call price were $1,050, we would set FV = 1,050 and redo part (a) to find that yield to call is 2.976% semiannually, 5.95