公司财务原理principles of corporate finance(11th...
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百度⼀一下 帮助公司财务原理Principles of Corporate Finance(11th edition)_课后习题答案Chap0033
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公司财务原理Principles of Corporate Finance(11th edition)_课后习题答案Chap003
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第11版,课后习题答案,第3章
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Chapter 03 - Valuing Bonds
3-1
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
CHAPTER 3 CHAPTER 3 Valuing Bonds Valuing Bonds
Answers to Problem Sets Answers to Problem Sets 1. a. Does not change. The coupon rate is set at time of issuance. b. Price falls. Market yields and prices are inversely related. c. Yield rises. Market yields and prices are inversely related.
Est. Time: 01-05 2. a. If the coupon rate is higher than the yield, then investors must be
expecting a decline in the capital value of the bond over its remaining life. Thus, the bond’s price must be greater than its face value.
b. Conversely, if the yield is greater than the coupon, the price will be below face value and it will rise over the remaining life of the bond. Est. Time: 01-05 3. The yield over six months is 2.7/2 = 1.35%.
The six-month coupon payment is $6.25/2 = $3.125. There are 18 years between today (2012) and 2030; since coupon payments are
listed every six months, there will be 36 payment periods. Therefore, PV = $3.125 / 1.0135 + $3.125 / (1.0135)2 + . . . $103.125 / (1.0135)36
= $150.35.
Est. Time: 01-05 4. Yields to maturity are about 4.3% for the 2% coupon, 4.2% for the 4% coupon,
and 3.9% for the 8% coupon. The 8% bond had the shortest duration (7.65 years), the 2% bond the longest (9.07 years).The 4% bond had a duration of 8.42 years.
Est. Time: 01-05 5. a. Fall. Example: Assume a one-year, 10% bond. If the interest rate is 10%,
the bond is worth $110/1.1 = $100. If the interest rate rises to 15%, the bond is
worth $110/1.15 = $95.65.
Chapter 03 - Valuing Bonds
3-2
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
b. Less (e.g., see 5a—if the bond yield is 15% but the coupon rate is lower at 10%, the price of the bond is less than $100).
c. Less (e.g., with r = 5%, one-year 10% bond is worth $110/1.05 = $104.76). d. Higher (e.g., if r = 10%, one-year 10% bond is worth $110/1.1 = $100,
while one-year 8% bond is worth $108/1.1 = $98.18).
e. No. Low-coupon bonds have longer durations (unless there is only one period to maturity) and are therefore more volatile (e.g., if r falls from 10% to 5%, the value of a two-year 10% bond rises from $100 to $109.3 (a rise of 9.3%). The value of a two-year 5% bond rises from $91.3 to $100 (a rise of 9.5%).
Est. Time: 01-05 6. a. Spot interest rates. Yield to maturity is a complicated average of the
separate spot rates of interest.
b. Bond prices. The bond price is determined by the bond’s cash flows and the spot rates of interest. Once you know the bond price and the bond’s cash flows, it is possible to calculate the yield to maturity.
Est. Time: 01-05
7. a. 4%; each bond will have the same yield to maturity. b. PV = $80/(1.04) + $1,080/(1.04)2 = $1,075.44.
Est. Time: 01-05
8. a.
Chapter 03 - Valuing Bonds
PV ! "221 1
1051
5rr ###$
b. PV ! "21105
15
yy ##
#$
c. Less (it is between the one-year and two-year spot rates). Est. Time: 01-05 9. a. The two-year spot rate is r2 = (100/99.523).5 – 1 = 0.24%.
The three-year spot rate is r3 = (100/98.937).33 – 1 = 0.36%. The four-year spot rate is r4 = (100/97.904).25 – 1 = 0.53%. The five-year spot rate is r5 = (100/96.034).2 – 1 = 0.81%.
3-3
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
b. Upward-sloping.
c. Higher (the yield on the bond is a complicated average of the separate spot rates).
Est. Time: 01-05
10. a. Price today is $108.425; price after one year is $106.930. b. Return = (8 + 106.930)/108.425 - 1 = .06, or 6%.
c. If a bond’s yield to maturity is unchanged, the return to the bondholder is equal to the yield.
Est. Time: 01-05 11. a. False. Duration depends on the coupon as well as the maturity. b. False. Given the yield to maturity, volatility is proportional to duration.
c. True. A lower coupon rate means longer duration and therefore higher volatility.
d. False. A higher interest rate reduces the relative present value of (distant)
principal repayments.
Est. Time: 01-05
Chapter 03 - Valuing Bonds
12.
YearYear CC PV(CPV(C ))
Proportion Proportion
of Total of Total
ValueValue
Proportion Proportion
× Time× Time VolatilityVolatility
3-4
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 03 - Valuing Bonds
16.
YearYear CCtt PV(CPV(C tt)) ValueValue × Time× Time VolatilityVolatility
Security ASecurity A 1 40 37.04 0.3593 0.3593
2 40 34.29 0.3327 0.6654
3 40 31.75 0.3080 0.9241
V = 103.08
a. $10,231.64(1.026)10,000
(1.026)0.0261
0.0261275PV 2020
!"#$
%&'
()
*)!
b. Interest Interest
Rate Rate PVPV of of
Interest Interest PV of PV of
Face Value Face Value PV of Bond PV of Bond
1.0% $5,221.54 $9,050.63
1.00
$14,272.17 2.0% 4,962.53 8,195.44 13,157.97
Duration = 1.94871.9487 1.801.80
Security BSecurity B 1 20 18.52 0.1414 0.1414
2 20 17.15 0.1310 0.2619
3 120 95.26 0.7276 2.1828
V = 130.93 1.00 Duration = 2.58612.5861 2.392.39
Security CSecurity C 1 10 9.26 0.0881 0.0881
2 10 8.57 0.0815 0.1631
3 110 87.32 0.8304 2.4912
V = 105.15 1.00 Duration = 2.74242.7424 2.542.54
Est. Time: 06-10 13. 7.01%; the extra return that you earn for investing for two years rather than one
year is 1.062
/1.05 – 1 = .0701. Est. Time: 01-05 14. a. Real rate = 1.10/1.05 – 1 = .0476, or 4.76%.
b. The real rate does not change. The nominal rate increases to 1.0476 × 1.07 – 1 = .1209, or 12.09%.
Est. Time: 01-05 15. With annual coupon payments:
!"#$
%&'
(
)*)!
1010 (1.06)100
(1.06)0.061
0.0615PV €92.64
Est. Time: 01-05
3-5
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
1.0% $5,221.54 $9,050.63 $14,272.17 2.0% 4,962.53 8,195.44 13,157.97 3.0% 4,721.38 7,424.70 12,146.08 4.0% 4,496.64 6,729.71 11,226.36 5.0% 4,287.02 6,102.71 10,389.73 6.0% 4,091.31 5,536.76 9,628.06 7.0% 3,908.41 5,025.66 8,934.07 8.0% 3,737.34 4,563.87 8,301.21 9.0% 3,577.18 4,146.43 7,723.61
10.0% 3,427.11 3,768.89 7,196.00 11.0% 3,286.36 3,427.29 6,713.64
12.0% 3,154.23 3,118.05 6,272.28 13.0% 3,030.09 2,837.97 5,868.06 14.0% 2,913.35 2,584.19 5,497.54 15.0% 2,803.49 2,354.13 5,157.62
Est. Time: 06-10
17. Purchase price for a six-year government bond with 5% annual coupon:
1,108.34(1.03)1,000
(1.03)0.031
0.03150PV 66 $!"#
$
%&'
(
)*)!
The price one year later is equal to the present value of the remaining five years
of the bond:
1,091.59(1.03)1,000
(1.03)0.031
0.03150PV 55 $!"#
$
%&'
(
)*)!
Rate of return = [$50 + ($1,091.59 – $1,108.34)]/$1,108.34 = 3.00%
Price one year later (yield = 2%):
1,141.40(1.02)1,000
(1.02)0.021
0.02150PV 55 $!"#
$
%&'
(
)*)!
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