corporate finance Chap006newWord文档下载推荐.docx

1、 To compute the yield to maturity, use trial and error to solve for r in the following equation: r = 9.119% Using a financial calculator, compute the yield to maturity by enteringn = 6, PV = （）950, FV = 1,000, PMT = 80; compute i = 9.119%. Verify the solution as follows:（difference due to rounding）5

2、. In order for the bond to sell at par, the coupon rate must equal the yield to maturity. Since Circular bonds yield 9.119%, this must be the coupon rate.6. a. Current yield = coupon/price = $80/$1,100 = 0.0727 = 7.27%b. To compute the yield to maturity, use trial and error to solve for r in the fol

3、lowing equation: r = 6.3662%n = 8, PV = （）1,100, FV = 1,000, PMT = 80; compute i = 6.3662%.7. When the bond is selling at face value, its yield to maturity equals its coupon rate. This firms bonds are selling at a yield to maturity of 9.25%. So the coupon rate on the new bonds must be 9.25% if they

4、are to sell at face value.8. The bond pays a coupon of 8.75%, which means annual interest is $87.50. The bond is selling for 144 19/32 = $1,445.9375. Therefore, the current yield is $87.50/$1445.9375 = 6.05%. The current yield exceeds the yield to maturity on the bond because the bond is selling at

5、a premium. At maturity the holder of the bond will receive only the $1,000 face value, reducing the total return on investment.9. Bond 1: Year 1: Year 2: Using a financial calculator: PMT = 80, FV = 1,000, i = 10%, n = 10; compute PV0 = $877.11. PMT = 80, FV = 1,000, i = 10%, n = 9; compute PV1 = $8

6、84.82. Rate of return = Bond 2: PMT = 120, FV = 1,000, i = 10%, n = 10; compute PV0 = $1,122.89. PMT = 120, FV = 1,000, i = 10%, n = 9; compute PV1 = $1,115.18. Both bonds provide the same rate of return.10. a. If yield to maturity = 8%, price will be $1,000.b. Rate of return = c. Real return = 1 =

7、11. a. With a par value of $1,000 and a coupon rate of 8%, the bondholder receives $80 per year.b. c. If the yield to maturity is 6%, the bond will sell for:12. a. To compute the yield to maturity, use trial and error to solve for r in the following equation: r = 8.971%n = 30, PV = （）900, FV = 1,000

8、, PMT = 80; compute i = 8.971%.b. Since the bond is selling for face value, the yield to maturity = 8.000%. c. To compute the yield to maturity, use trial and error to solve for r in the following equation: r = 7.180%n = 30, PV = （）1,100, FV = 1,000, PMT = 80; compute i = 7.180%. 061013. a. To compu

9、te the yield to maturity, use trial and error to solve for r in the following equation: r = 4.483%n = 60, PV = （）900, FV = 1,000, PMT = 40; compute i = 4.483%. Therefore, the annualized bond equivalent yield to maturity is: 4.483% 2 = 8.966%b. Since the bond is selling for face value, the semiannual

10、 yield = 4%. Therefore, the annualized bond equivalent yield to maturity is 4% 2 = 8%.c. To compute the yield to maturity, use trial and error to solve for r in the following equation: r = 3.592%n = 60, PV = （）1,100, FV = 1,000, PMT = 40; compute i = 3.592%. 3.592% 2 = 7.184%14. In each case, we sol

11、ve the following equation for the missing variable: Price = $1,000/（1 + y）maturityPriceMaturity （Years）Yield to Maturity$300.0030.00 4.095%15.64 8.000%$385.5410.00 10.000%15. PV of perpetuity = coupon payment/rate of return PV = C/r = $60/0.06 = $1,000.00 If the required rate of return is 10%, the b

12、ond sells for: PV = C/r = $60/0.10 = $600.0016. Current yield = 0.098375, so bond price can be solved from the following:$90/price = 0.098375 price = $914.87To compute the remaining maturity, solve for t in the following equation: t = 20.0 Using a financial calculator, compute the remaining maturity

13、 by enteringPV = （）914.87, FV = 1,000, PMT = 90, i = 10; compute n = 20.0 years.17. Solve the following equation for PMT: PMT = $80.00 Using a financial calculator, compute the annual payment by enteringn = 9, PV = （）1,065.15, FV = 1,000, i = 7; compute PMT = $80.00.Since the annual payment is $80,

14、the coupon rate is 8%.18. a. The coupon rate must be 7% because the bonds were issued at face value with a yield to maturity of 7%. Now the price is: b. The investors pay $641.01 for the bond. They expect to receive the promised coupons plus $800 at maturity. We calculate the yield to maturity based

15、 on these expectations by solving the following equation for r: r = 12.87% Using a financial calculator, enter n = 8, PV = （）641.01, FV = 800, PMT = 70; then compute i = 12.87%.19. a. At a price of $1,200 and remaining maturity of 9 years, find the bonds yield to maturity by solving for r in the fol

16、lowing equation: r = 5.165% Using a financial calculator, enter n = 9, PV = （）1,200, FV = 1,000, PMT = 80; then compute i = 5.165%. b. Rate of return = 20. 21. a., b.Price of Each Bond at Different Yields to MaturityMaturity of BondYield4 Years8 Years30 Years7% $1,033.87 $1,059.71 $1,124.098% $1,000

17、.009% $967.60 $944.65 $897.26 c. The table shows that prices of longer-term bonds are more sensitive to changes in interest rates.22. The price of the bond at the end of the year depends on the interest rate at that time. With 1 year until maturity, the bond price will be $1,080/（1 + r）. a. Price =

18、$1,080/1.06 = $1,018.87 Rate of return = $80 + （$1,018.87 $1,000）/$1,000 = 0.0989 = 9.89% b. Price = $1,080/1.08 = $1,000.00 Rate of return = $80 + （$1,000 $1,000）/$1,000 = 0.0800 = 8.00% c. Price = $1,080/1.10 = $981.82 Rate of return = $80 + （$981.82 $1,000）/$1,000 = 0.0618 = 6.18%23. The original

19、 price of the bond is computed as follows:After 1 year, the maturity of the bond will be 29 years, and its price will be:The capital loss on the bond is $74.07. The rate of return is therefore: （$40 $74.07）/$627.73 = 0.0543 = 5.43%24. The bonds yield to maturity will increase from 7.5% to 7.8% when

20、the perceived default risk increases. The bond price will fall:Initial price = New price = 25. The nominal rate of return is 7% （$70/$1,000）. The real rate of return is 1.07/（1 + inflation） 1. a. 1.07/1.02 1 = 0.0392 = 4.902% b. 1.07/1.04 1 = 0.0192 = 2.885% c. 1.07/1.06 1 = 0.009434 = 0.9434% d. 1.

21、07/1.08 1 = 0.00926 = 0.926%26. The principal value of the bond will increase by the inflation rate, and since the coupon is 4% of the principal, the coupon will also increase along with the general level of prices. The total cash flow provided by the bond will be: 1,000 （1 + inflation rate） + coupo

22、n rate 1,000 （1 + inflation rate） Since the bond is purchased for face value, or $1,000, total dollar nominal return is therefore the increase in the principal due to the inflation indexing, plus coupon income: Income = （$1,000 inflation rate） + coupon rate $1,000 （1 + inflation rate） Finally: Nomin

23、al rate of return = income/$1,000a. Nominal rate of return = Real rate of return = b. Nominal rate of return = c. Nominal rate of return = d. Nominal rate of return = 27.First-Year Cash FlowSecond-Year Cash Flowa.$40 1.02 = $40.80$1,040 1.022 = $1,082.016b.$40 1.04 = $41.60$1,040 1.042 = $1,124.864c.$40 1.06 = $42.40$1,040 1.062 = $1,168.544d.$40 1.08 = $43.20$1,040 1.082 = $1,213.05628. The coupon bond will fall from an initial price of $1,000 （when yield t