计算

Chapter 3

1. Calculate the present value of $1,000 zero-coupon bond with 5 years to maturity if the required annual interest rate is 6%.（计算1000美元零息债券的现值5年到期如果所需的年利率为6%。）

Solution: PV(现值) ? FV（）/(1 ? i)n, where

FV ? 1000, i ? 0.06, n ? 5 PV ? 747.25 grand prize is

3. Consider a bond with a 7% annual coupon and a face value of $1,000. Complete the following table:（考虑将以每年7%的息票，面值为1000美元的债券。完成下面的表格：）

Years to Maturity 3 3 6 9 9

Discount Rate

5 7 7 7 9

Current Price

What relationship do you observe between yield to maturity and the current market value?（有什么关系，你观察到期收益率与市场价值之间的关系吗？）

Solution:

Years to Maturity Yield to Maturity Current Price 3 3 6 9 9

5 7 7 5 9

$1,054.46 $1,000.00 $1,000.00 $1,142.16 $ 880.10

When yield to maturity is above the coupon rate, the band’s current price is below its face

value. The opposite holds true when yield to maturity is below the coupon rate. For a given maturity, the bond’s current price falls as yield to maturity rises. For a given yield to maturity, a bond’s value rises as its maturity increases. When yield to maturity equals the coupon rate, a bond’s current price equals its face value regardless of years to maturity.（当到期收益率高于票面利率，债券的市价低于其票面

价值。相反，当到期收益率低于票面利率。对于一个给定的期限，债券的当前价格下跌到期收益率上升。对于一个给定的到期收益率，债券的价值上升，其成熟度的增加。当到期收益率等于票面利率，债券的当前价格等于其面值无论年到期。）

4. Consider a coupon bond that has a $1,000 per value and a coupon rate of 10%. The bond is

currently selling for $1,150 and has 8 years to maturity. What is the bond’s yield to maturity?（考虑

一个息票债券，有一个1000美元的价值和10%的息票率。债券目前的售价为1150美元，8年内到期。债券的到期收益率是什么？）p43

6. What is the price of a perpetuity that has a coupon of $50 per year and a yield to maturity of 2.5%? If the yield to maturity doubles, what will happen to its price?（一个永久的有息每年50美元和2.5%的到期收益率的价格是多少？如果到期收益率增加一倍，其价格会发生什么？）

Solution: To calculate the bond’s yield to maturity using a financial calculator: N ? 8; PMT ? 1000 ? 0.10 ? 100; FV ? 1000; PV ? 1150 Compute I : I ? 7.44

Solution: Pc=C/ic,=50/2.5%=$2000

The price is $2000. 9.

If the yield to maturity doubles, its price will cut in half.

A 10-year, 7% coupon bond with a face value of $1,000 is currently selling for $871.65. Compute your rate of return if you sell the bond next year for $880.10.

Solution: （一个10年，以1000美元的面值7%的息票债券目前的售价为871.65美元。计算你

的回报率，如果你卖债券明年880.10美元。）

R?

C?Pt?1?Pt70?880.10?871.65??0.09,or9%.

Pt871.65Chapter 8

3. If you want to earn an annualized discount rate of 3.5%, what is the most you can pay for a

91-day Treasury bill that pays $5,000 at maturity?（如果你想获得每年3.5%的折现率，你可以支付91天的国库支付5000美元的账单，成熟时最？）

Solution:

$5,000?A360??.035

$5,00091$5,000?A?44.24

A?$4,955.76

4. What is the annualized discount rate % and investment rate % on a Treasury bill that you purchase for $9,900 that will mature in 91 days for $10,000?（年贴现率和投资率% %在财政部的比尔，你以9900美元的价格收购，将成熟的91天为10000美元，是什么？）

Solution: Discount Rate

? ?

$10,000?$9,900360??0.03956?3.956%

$10,00091$10,000?$9,900365??0.04052?4.052%

$9,90091Investment Rate(投资率) ? ?

5. The price of 182-day commercial paper is $7,840. If the annualized investment rate is

4.093%, what will the paper pay at maturity?（182天的商业票据的价格是7840美元。如果按年投资率是4.093%，在成熟时，本文将到期支付什么？）

Solution: Let B ? what will be paid at maturity

[(B?$7,840)/($7,840)]?(365/182)?0.04093[(B?$7,840)/($7,840)]?2.0055?0.04093(B?$7,840)?2.0055?320.89B?$7,840?B?160B?$8,000

Chapter 9

1. A bond pays $80 per year in interest (8% coupon). The bond has 5 years before it matures at

which time it will pay $1,000. Assuming a discount rate of 10%, what should be the price of the bond (Review Chapter 3)?（债券支付每年80美元的利息（8%票）。5年的债券到期时将支付1000美元之前。假设一个10%的折扣率，什么应该是债券的价格（章3）？）p43

Solution: $924.18

4. A 2-year $1,000 par zero-coupon bond is currently priced at $819.00. A 2-year $1,000 annuity is currently priced at $1,712.52. If you want to invest $10,000 in one of the two securities,

which is a better buy? You can assume（2年的1000美元面值的零息票债券目前售价为819美元。2

年1000美元的年金目前售价为1712.52美元。如果你想投资10000美元在一个证券，这是一个更好的购买？你可以假设）

Solution: With PV ? $819, FV ? $1,000, PMT ? 0 and N ? 2, the yield to maturity on

the two-year zero-coupon bonds is 10.5% for the two-year annuities, PV ? $1,712.52, PMT ? 0, FV ? $2,000 and N ? 2 gives a

yield to maturity of 8.07%. The zero-coupon bonds are the better buy.

10. A 10-year, 1,000 par value bond with a 5% annual coupon is trading to yield 6%. What is the current yield?（一个10年，1000面值的债券以5%的年利息是交易的收益率6%。现在的产量是多少？） Solution: The current price of the bond is computed as follows:

PMT ? 50; N ? 10; FV ? 1000; I ? 6 Compute PV; PV ? 926.40 The current yield ? 50/926.40 ? 5.4%

11. A $1,000 par bond with an annual coupon has only 1 year until maturity. Its current yield is 6.713% and its yield to maturity is 10%. What is the price of the bond?（一种面值1000美元的债券年利率只有1年直到成熟。目前的收益率是6.713%，其到期收益率是10%。债券的价格是多少？）

Solution:

a. CY ? 0.06713 ? Coupon/Price, or Coupon ? 0.06713 ? Price b. Price ? (Coupon ? 1000)/1.10.

Substituting from (1), Price ? (0.06713 ? Price ? 1000)/1.10 Solve for Price, Price ? $968.17

Chapter 10

5. Suppose Microsoft, Inc. was trading at $27.29 per share. At that time, It pays an annual

dividend of $0.32 per share, and analysts have set a 1-year target price around $33.30 per share. What is the expected return on this stock?（微软公司认为，交易价格为每股27.29美元。

当时，它支付的年度股息每股0.32美元，分析师已将一年的目标价每股33.30美元左右。对这只股票的期望回报率是多少？）

Solution:

Expected return?33.30?0.32?27.29?0.2319?23.2%

27.29 7. Huskie Motor’s just paid an annual dividend of $1.00 per share. Management has promised

shareholders to increase dividends a constant rate of 5%. If the required return is 12%, what is the current price per share?（西伯利亚爱斯基摩狗运动只是支付的年度股息每股1美元。管理承诺股东增加派息恒定速度5%。如果所要求的回报是12%，当前每股的价格是多少？）

Solution:

P0?D0(1?g)1.00(1?0.05)??$15.00

ke?g0.12?0.0512. Analysts are projecting that CB Railways will have earnings per share of $3.90. If the

average industry ratio is about 25, what is the current price of CB Railways?（分析人士预计，

CB铁路将有每股3.90美元。如果行业平均比例约为25，CB铁路目前的价格是多少？）

Solution:

Price ? 3.90 ? 25 ? $97.50

16. Compute the price of a share of stock that pays a $1 per year dividend and that you expect to

be able to sell in one year for $20, assuming you require a 15% return. （计算股票支付每年1美元的股息，你希望能够出售一年以20美元的价格，如果你需要一个15%的回报。）

Solution:

$1/(1 ? 0.15) ? $20/(1 ? 0.15) ? $18.26

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