SolutionsCh78.docx

1、SolutionsCh78ANSWERS TO END-OF-CHAPTER QUESTIONS: Chapter 77-1 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 t

2、ied 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 bonds price will be less affected by a change in interest rates if it has been outstanding a

3、 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 bondholders YTM will

4、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

5、take advantage of the new, lower rates. 7-5 From the corporations 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

6、 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 like

7、ly 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

8、 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 consequ

9、ence has been a pronounced trend toward annual retirement and away from the accumulation scheme.7-6 a. If a bonds price increases, its YTM decreases.b. If a companys bonds are downgraded by the rating agencies, its YTM increases.c. If a change in the bankruptcy code made it more difficult for bondho

10、lders to receive payments in the event a firm declared bankruptcy, then the bonds 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 d

11、ebt issue, then the bonds 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 inve

12、stment 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

13、that one year, which is the 1-year Treasurys maturity date.SOLUTIONS TO END-OF-CHAPTER PROBLEMS7-1 With your financial calculator, enter the following:N = 10; I = YTM = 9%; PMT = 0.08 1,000 = 80; FV = 1000; PV = VB = ?PV = $935.82.7-2 With your financial calculator, enter the following to find YTM:N

14、 = 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

15、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 VB = $985; M = $1,000; Int = 0.07 $1,000 = $70. a. Current yield = Annual interest/Current price of bond = $70/$985.00 = 7.11%. b. N = 10; PV = -985; PMT = 70; F

16、V = 1000; YTM = ? Solve for I = YTM = 7.2157% 7.22%. c. N = 7; I = 7.2157; PMT = 70; FV = 1000; PV = ? Solve for VB = PV = $988.46.7-5 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, ch

17、ange N = 15 and I = 8, PV = ?, PV = $1,171.19.Bond S: Change N = 1, PV = ? PV = $1,018.52.3. 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 prim

18、arily 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 bonds value would fluctuate more than the one-month bonds value because of the difference in the timing of receipts. However, its value

19、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 + kd/2)t, and if kd increases, these multipliers will decrease significantly. Another way t

20、o 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.7-6 a. VB = M = $1,000. I = 0.09

21、($1,000) = $90.1. VB = $829: Input N = 4, PV = -829, PMT = 90, FV = 1000, I = ? I = 14.99%.2. VB = $1,104: Change PV = -1104, I = ? I = 6.00%.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 wer

22、e 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

23、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%.c. YTM = Current Yield + Capital Gains (Loss) Yield10.37% = 10.91% + Capital Loss Yield-0.

24、54% = 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%.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

25、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

26、 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.

27、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

28、/$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 retur

29、n 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 t

30、o 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 = 1000I = YTM = 8.35%.b. To find the YTC, if called in Year 5:N = 5, PV = -1175, PMT = 110, FV = 1090I = YTC = 8.13%.c. The bonds are selling at a premium which in

31、dicates 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.)d. Similarly from above, YTC can be found, if called in each s

32、ubsequent year.If called in Year 6:N = 6, PV = -1175, PMT = 110, FV = 1080I = YTM = 8.27%.If called in Year 7:N = 7, PV = -1175, PMT = 110, FV = 1070I = YTM = 8.37%.If called in Year 8:N = 8, PV = -1175, PMT = 110, FV = 1060I = YTM = 8.46%.If called in Year 9:N = 9, PV = -1175, PMT = 110, FV = 1050I = 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