1．优先股与长期债务的相似点是什么？其与权盗的相似点又是什么？ 1. What are the similarities between preferred stock and long-term debt? What are the similarities between it and the thieves?
答：优先股像长期债务一样，它承诺向持有者每年支付固定的收益。从这个角度讲，优先股类似于无服期的债券，即永久债券。优先股另一个与长期债务相似的特点是：它没有购予其持有者参与公司决策的权利。 A: Preferred stock, like long-term debt, promises to pay a fixed annual return to the holder. From this perspective, preferred shares are similar to bonds with no expiration date, i.e., perpetual bonds. Another feature of preferred equity that is similar to long-term debt is that it does not give its holders the right to participate in the company's decision-making.
优先股是一种权益投资，公司保留向优先股股东支付股利的自主权，支付股利并不是公司的合同义务。若无法支付，公司并不会破产，而在公司破产的情况下，优先股对公司资产的求惶权优先于普通股，但位于债券之后。优先股股息和股票红利均不能在税前扣除，从而不能像债券利息那样起到减免税收的作用。 Preferred stock is an equity investment, and the company retains the autonomy to pay dividends to preferred shareholders, and the payment of dividends is not a contractual obligation of the company. If it is unable to pay, the company will not go bankrupt, and in the event of corporate bankruptcy, preferred stock has priority over common stock over the company's assets, but after the bonds. Neither preference stock dividends nor stock dividends are deductible before tax, so they cannot be tax-deductible like bond interest.
4．如果发生严重的经济衰退，你预期商业票据的收盗率与短期国库券的收益率之差将加何变化？ 4. In the event of a severe recession, how do you expect the difference between the rate of theft of commercial paper and the yield of short-term Treasury bills to change?
答：它们的收益率之差将会扩大。经济的恶化会增加信用风险，即增加违约的可能性，因此，对于具有较高违约风险的供务证券，投资者将要求更高的滥价。 A: The difference in their yields will widen. A deterioration in the economy increases credit risk, i.e., increases the likelihood of default, and as a result, investors will demand higher overpricing for supply securities with a higher risk of default.
5．普通股、优先股以及公司债券之间的主要区别是什么？ 5. What are the main differences between common stock, preferred stock, and corporate bonds?
答：普通股、优先股以及公司债券之间的主要区别如下表所示： A: The main differences between common stock, preferred stock, and corporate bonds are shown in the table below:
6．为什么与低税率等级的投资者相比，高税率等级的投资在更倾向于投资市政债券？ 6. Why are investments in higher tax brackets more inclined to invest in municipal bonds than investors in lower tax brackets?
答：市政债券的利息是免税的。当面临更高的边际税牽时，高收入的投资者更倾向于投资免税的证券。 A: Interest on municipal bonds is tax-free. When faced with higher marginal taxes, high-income investors are more inclined to invest in tax-free securities.
9．某公司以每股 40 美元的价格物入一股优先股，并在当年末以同样的价格售出，同时还获得了 4 美元的年末股利，假设该公司的税率等级为30%30 \%，请计算该公司的税后收盗率。 9. If a company acquires one preferred stock at $40 per share and sells it at the same price at the end of the year, while also receiving a year-end dividend of $4, calculate the company's after-tax rate, assuming the company's tax bracket is 30%30 \% .
答：税前总收益为 4 美元。从优先股股息中扣除70%70 \%之后， A: The gross income before taxes is $4. 70%70 \% After deducting the dividends from the preferred shares, 应税收益为： After that, the taxable income is:0.30 xx4=1.200.30 \times 4=1.20（美元）。 Taxable income is: 0.30 xx4=1.200.30 \times 4=1.20 (USD). 因此，应交税金为： (United States dollars). Therefore, the tax payable is:0.30 xx1.20=0.360.30 \times 1.20=0.36（美元）; Therefore, the tax payable is: 0.30 xx1.20=0.360.30 \times 1.20=0.36 (USD);税后收益为： (United States dollars); After-tax income is:4.00-0.36=3.644.00-0.36=3.64（美元）; After-tax income is: 4.00-0.36=3.644.00-0.36=3.64 (USD); 故收益率为： (United States dollars); Therefore, the rate of return is:3.64//40.00=9.10%3.64 / 40.00=9.10 \%， A: The gross income before taxes is $4. After deducting the dividends on preferred shares, the taxable income is: 0.30 xx4=1.200.30 \times 4=1.20 (USD). 70%70 \% Therefore, the tax payable is: 0.30 xx1.20=0.360.30 \times 1.20=0.36 (USD); After-tax income is: 4.00-0.36=3.644.00-0.36=3.64 (USD); Therefore, the rate of return is: 3.64//40.00=9.10%3.64 / 40.00=9.10 \% ,
11．下表中有 3 只股票A、B、C\mathrm{A} 、 \mathrm{~B} 、 \mathrm{C}，其中P_(t)\mathrm{P}_{\mathrm{t}}表示 t 时刻的股价，Q_(i)\mathrm{Q}_{\mathrm{i}}表示 t 时刻发行在外的股票数量，股票 C在上一期由一股分拆成两股。 11. There are 3 stocks A、B、C\mathrm{A} 、 \mathrm{~B} 、 \mathrm{C} in the table below, which P_(t)\mathrm{P}_{\mathrm{t}} represents the share price at time t, the Q_(i)\mathrm{Q}_{\mathrm{i}} number of shares outstanding at time t, and stock C was split from one share to two shares in the previous period.
a.计算第 1 期(t=0(t=0到t=1)3t=1) 3只股票的价格加权指数的收益率。 b.第 2 年，价格加权指数的除数将会发生什么变化？ a. Calculate the return of the price-weighted index for period (t=0(t=0 1 to t=1)3t=1) 3 a stock. b. What will happen to the divisor of the price-weighted index in Year 2? c.计算第 2 期(t=1(\mathrm{t}=1到t=2)\mathrm{t}=2)的收益率。 答：a.在t=0\mathrm{t}=0时，价格加权指数为：(90+50+100)//3=80(90+50+100) / 3=80在 .t=1\mathrm{t}=1时，价格加权指数为：(95+45+110)//3=83.333(95+45+110) / 3=83.333. 故其收益率为：(83.333//80)-1=4.17%(83.333 / 80)-1=4.17 \%。 b.股票分拆前，股票 C 价格为 110 ，故价格加权指数为：250//3=83.333250 / 3=83.333. 股票分拆后，股票 C 价格降为 55 。因此，必须找到一个新的除数 d ，满足： c. Calculate the yield of t=2)\mathrm{t}=2) the 2nd installment (t=1(\mathrm{t}=1 . Answer: a. At t=0\mathrm{t}=0 , the price-weighted index is: (90+50+100)//3=80(90+50+100) / 3=80 at t=1\mathrm{t}=1 , the price-weighted index is: (95+45+110)//3=83.333(95+45+110) / 3=83.333 . Therefore, its yield is: (83.333//80)-1=4.17%(83.333 / 80)-1=4.17 \% . b. Before the stock split, the price of stock C was 110, so the price-weighted index was: 250//3=83.333250 / 3=83.333 . After the stock split, the price of stock C drops to 55. Therefore, a new divisor d must be found, satisfying: 83.333=(95+45+55)//d=>d=2.34083.333=(95+45+55) / d \Rightarrow d=2.340 c.第二期收益率为雪。因为每股收益分别为零，故指数保持不变。 12．用第 11 题的数据，计算 3 只股票的下列排数在第 1 期的收益率。 a.市值加权指数。 b.等权重指数。 答：a.t=0\mathrm{t}=0时总市值为：(9000+10000+20000)=39000(9000+10000+20000)=39000（美元）； t=0\mathrm{t}=0 The total market capitalization is: (9000+10000+20000)=39000(9000+10000+20000)=39000 (USD); t=1t=1时总市值为：(9500+9000+22000)=40500(9500+9000+22000)=40500（美元）。 故市值加权指数收益率=(40500//39000)-1=3.85%=(40500 / 39000)-1=3.85 \%。 b.每只股票收益率分别如下： t=1t=1 The total market capitalization is: (9500+9000+22000)=40500(9500+9000+22000)=40500 (USD). Therefore, the market capitalization-weighted index yield =(40500//39000)-1=3.85%=(40500 / 39000)-1=3.85 \% . b. The yields of each stock are as follows: r_(A)=(95//90)-1=0.0556\mathrm{r}_{\mathrm{A}}=(95 / 90)-1=0.0556 r_(B)=(45//50)-1=-0.10\mathrm{r}_{\mathrm{B}}=(45 / 50)-1=-0.10 r_(C)=(110//100)-1=0.10\mathrm{r}_{\mathrm{C}}=(110 / 100)-1=0.10 故等权重指数收益率为：[0.0556+(-0.10)+0.10]//3=0.0185=1.85%[0.0556+(-0.10)+0.10] / 3=0.0185=1.85 \%。 13.某投资者的税率等级为30%30 \%，若公司债券提供9%9 \%的收盖率，要想使该投资者偏好市政债拳，市政债絭应提供的收益率最低为多少？ Therefore, the yield of the equal-weighted index is: [0.0556+(-0.10)+0.10]//3=0.0185=1.85%[0.0556+(-0.10)+0.10] / 3=0.0185=1.85 \%30%30 \% If the corporate bond provides 9%9 \% a coverage ratio, what is the minimum yield that the municipal bond should provide in order to make the investor prefer the municipal bond?
答：公司债券税后收益率为：0.09 xx(1-0.30)=0.0630=6.30%0.09 \times(1-0.30)=0.0630=6.30 \%。因此，市政债券应提供的收盗率最低为6.30%6.30 \%。 A: The after-tax yield of corporate bonds is: 0.09 xx(1-0.30)=0.0630=6.30%0.09 \times(1-0.30)=0.0630=6.30 \% Therefore, municipal bonds should offer a minimum rate of 6.30%6.30 \% theft.
14．某短期市政债券的收益率为4%4 \%，当投资者的税率等级分别为0、10%、20%0 、 10 \% 、 20 \%和30%30 \%时，该市政债券的应税等值收益率分別为遙少？ 14. What is the taxable equivalent yield of a short-term municipal bond when the investor's tax bracket is 0、10%、20%0 、 10 \% 、 20 \% the same 30%30 \% ? 4%4 \%
答：教材式（2－2）表明，应税等值收益率为：r=r_(n)//(1-t)\mathrm{r}=\mathrm{r}_{\mathrm{n}} /(1-\mathrm{t})。 Answer: Textbook formula (2-2) shows that the taxable equivalent rate of return is: r=r_(n)//(1-t)\mathrm{r}=\mathrm{r}_{\mathrm{n}} /(1-\mathrm{t})
第一部分 绪论 Part I: Introduction
因此，税率等级为 0 时，r=4%//(1-0)=4.00%\mathrm{r}=4 \% /(1-0)=4.00 \%； 税率等级为10%10 \%时，r=4%//(1-10%)=4.44%\mathrm{r}=4 \% /(1-10 \%)=4.44 \%； 税率等级为20%20 \%时，r=4%//(1-20%)=5.00%\mathrm{r}=4 \% /(1-20 \%)=5.00 \%； 税率等级为30%30 \%时，r=4%//(1-30%)=5.71%\mathrm{r}=4 \% /(1-30 \%)=5.71 \%。 Therefore, when the tax band is 0, r=4%//(1-0)=4.00%\mathrm{r}=4 \% /(1-0)=4.00 \% ; The tax rate bracket is 10%10 \% , r=4%//(1-10%)=4.44%\mathrm{r}=4 \% /(1-10 \%)=4.44 \% ; The tax rate bracket is 20%20 \% , r=4%//(1-20%)=5.00%\mathrm{r}=4 \% /(1-20 \%)=5.00 \% ; The tax band is 30%30 \% . r=4%//(1-30%)=5.71%\mathrm{r}=4 \% /(1-30 \%)=5.71 \%
16.下列各项中瀞种证券的售价将会更高？a.利率 16.Will the selling price of any of the following securities be higher? a. Interest Rate9%9 \%的 10 年期长期国债和利率10%10 \%的 10 年期长期国债。 b．期展 3 个月行权价格每服 40 美元的看暴期权和期限 3 个月行权价格每服 35 美元的看暴期权。 The 10-year Treasury note. b. Futures 3-month strike price $40 per term and 3-month strike price $35 per term option. c．行权价恪每股 50 美元的看跌期权和标的物为另一只股票行权价格每股 60 美元的看跌期权（股票和期权的其他相关特点均相同）。 c. A put option with an exercise price of $50 per share and a put option with an underlying asset of another stock with an exercise price of $60 per share (the stock and the option have the same other relevant characteristics).
答：a．息票率较高的债券，即利率10%10 \%的 10 年期长期国债。 b.行权价格较低的看深期权，即期限 3 个月行权价格每服 35 美元的看添期权。 The 10-year Treasury note. b. A short option with a low strike price, that is, a call option with a term of 3 months and an exercise price of $35 per service. c.行权价格较高的股票的看跌期权。 c. A put option on a stock with a higher strike price.
2．某市政债券的利率为6.75%6.75 \%，按面值进行交易，業纳税者的联邦和州综合税率等级为34%34 \%，该市政债券的应税等级收益率是多少？ 2. What is the yield of the taxable grade of a municipal bond whose interest rate is 6.75%6.75 \% traded at par and what is the combined federal and state tax rate bracket of the taxpayer? 34%34 \%
答：应税等级收益率为：6.75%//(1-0.34)=10.23%6.75 \% /(1-0.34)=10.23 \%， 3.若预期股市将会大幅增长，股票指数期权市场上的下列哪项交易的风险最大？ A: The yield of the taxable grade is: 6.75%//(1-0.34)=10.23%6.75 \% /(1-0.34)=10.23 \% 3. Which of the following trades in the stock index options market is the riskiest if the stock market is expected to grow substantially? a.出售一份看涨期权 b.出锫一份看跌期权 A. Sell one call option B. Sell one put option c.购买一份看滋期权 d.购买一份看跃期权 c. Buy a call option d. Buy a call option 答：a。随着股票价格升高，看深期权卖方将承担无限的潜在损失。 4.短期市政债券的收益率为4%4 \%，应税债券的收益率为5%5 \%，当你的稳率等级分別为以下情况时，哪一种债券可以提供更高的税后收益率？ a. 0 A: a. As the price of the stock rises, the seller of a deep option will be exposed to unlimited potential losses. 4. The yield on short-term municipal bonds is , 4%4 \% and the yield on taxable bonds is 5%5 \% , which bond can provide a higher after-tax yield when your stability rating is? a. 0 b.10%10 \% c．20%20 \% d．30%30 \% d. 30%30 \% 答：a.应税债券。税率等级为零时，应税债券的税后收益率与税前收益率相同(5%)(5 \%)，这高于市政债券的收益率。 b.应税债券。其税后收篮率为 , which is higher than the yield on municipal bonds. b. Taxable bonds. Its after-tax scoring rate:5%xx(1-10%)=4.5%5 \% \times(1-10 \%)=4.5 \%， c.两种一样。应税债券的税后收益率为 , c. both are the same. The after-tax yield of a taxable bond is:5%xx(1-20%)=4.0%5 \% \times(1-20 \%)=4.0 \%，与市政债券的收益辜相同， d.市政债券。应税债券的税后政益率为 , which is the same as the yield of municipal bonds, d. municipal bonds. The after-tax benefit ratio of taxable bonds5%xx(1-30%)=3.5% < 4.0%5 \% \times(1-30 \%)=3.5 \%<4.0 \%，税率等级在20%20 \%以上时，市政债券会为投资者提供更高的税后收益率。 A: a. Taxable bonds. When the tax bracket is zero, the after-tax yield of taxable bonds is the same (5%)(5 \%) as the pre-tax yield, which is higher than the yield of municipal bonds. b. Taxable bonds. Its after-tax closing rate 5%xx(1-10%)=4.5%5 \% \times(1-10 \%)=4.5 \% is , c. the same for both. The after-tax yield of a taxable bond is 5%xx(1-20%)=4.0%5 \% \times(1-20 \%)=4.0 \% the same as that of a municipal bond, d. municipal bond. The after-tax yield of taxable bonds is , and municipal bonds provide investors with a higher after-tax yield when the 20%20 \% tax bracket is above. 5%xx(1-30%)=3.5% < 4.0%5 \% \times(1-30 \%)=3.5 \%<4.0 \%
5．免税债券的利率为5.6%5.6 \%，应税债券的利率为8%8 \%，两种债券均按面值销售，当投资者的㮱率等级为多少时投资两种债券是无差别的？ 5. The interest rate of tax-exempt bonds is 5.6%5.6 \% , the interest rate of taxable bonds is 8%8 \% , both bonds are sold at face value, when the investor's rate is what is the difference between investing in the two bonds?
答：若税后收益率相等，则0.056=0.08 xx(1-t)0.056=0.08 \times(1-t)，解得t=0.30=30%t=0.30=30 \%。 Answer: If the after-tax rate of return is equal, then 0.056=0.08 xx(1-t)0.056=0.08 \times(1-t) , the solution t=0.30=30%t=0.30=30 \% .