金融学精编版(第二版)课后答案

CHAPTER 15OPTIONS AND CONTINGENT CLAIMSObjectives•How to use options to modify one’s exposure to investment risk.•To understand the pricing relationships that exist among calls, puts, stocks and bonds.•To explain the binomial and Black-Scholes option-pricing models and apply them to the valuation of corporate bonds and other contingent claims.•To explore the range of financial decisions that can be fruitfully analyzed in terms of options.Outline15.1 How Options Work15.2 Investing with Options15.3 The Put-Call Parity Relation15.4 Volatility and Option Prices15.5 Two-State (Binomial) Option-Pricing15.6 Dynamic Replication and the Binomial Model15.7 The Black-Scholes Model15.8 Implied Volatility15.9 Contingent Claims Analysis of Corporate Debt and Equity15.10 Credit Guarantees15.11 Other Applications of Option-Pricing Methodologythe maturity of the option, and C the price of the call.•One can create a synthetic option from the underlying stock and the risk-free asset through a dynamic replication strategy that is self-financing after the initial investment. By the Law of One Price, the option’s price is given by the formula:where:C = price of the callS = price of the stockE = exercise pricer = risk-free interest rate (the annualized continuously compounded rate on a safe asset with the same maturity as the option)T = time to maturity of the option in yearsσ= standard deviation of the annualized continuously compounded rate of return on the stockd = continuous dividend yield on the stockln = natural logarithme = the base of the natural log function (approximately 2.71828)N(d1) = the probability that a random draw from a standard normal distribution will be less than d1.•The same methodology used to price options can be used to value many other contingent claims, including corporate stocks and bonds, loan guarantees, and the “real options” imbedded in investments in research and development and flexible manufacturing technology.Solutions to Problems at End of ChapterPayoff Diagrams1. Graph the payoff for a European put option with exercise price E, written on a stock with value S, when:a. You hold a long position (i.e., you buy the put)b. You hold a short position (i.e., you sell the put)SOLUTION: a.b.2.Graph the payoff to a portfolio holding one European call option and one European put option, each with the same expiration date and each with exercise price E, when both options are on a stock with value S.Investing with options3. The risk-free one –year rate of interest is 4%, and the Globalex stock index is at 100. The price of one-year European call options on the Globalex stock index with an exercise price of 104 is 8% of the current price of the index. Assume that the expected dividend yield on the stocks in the Globalex index is zero. You have $1million to invest for the next year. You plan to investenough of your money in one-year T-bills to insure that you will at least get back your original $1 million, and you will use the rest of your money to buy Globalex call options.a. Assuming that you can invest fractional amounts in Globalex options,show the payoff diagram for your investment. Measure the Globalex index on the horizontal axis and the portfolio rate of return on the vertical axis. What is the slope of the payoff line to the right of an index value of 104? b. If you think that there is a probability of .5 that the Globalex index a year from now will be up 12%, a probability of .25 that it will be up 40%, and a probability of .25 that it will be down 20%, what is the probability distribution of your portfolio rate of return?SOLUTION:a.To insure that you will at least get back your original $1 million, you need toinvestin T-bills.You can buy46.538,961$04.1000,000,1$1000,000,1$=+=+f r 69.4807854.461,38$10008.46.538,961$000,000,1$==⨯-options.The slope of the payoff line to the right of an index value of 104 is 4807.69, as seen from the graph:b.Put-Call Parity4.a.Show how one can replicate a one-year pure discount bond with a facevalue of $100 using a share of stock, a put and a call.b.Suppose that S=$100, P=$10, and C=$15. What must be the one-year interest rate?c.Show that if the one-year risk-free interest rate is lower than in youranswer to part b, there would be an arbitrage opportunity. (Hint: The price of the pure discount bond would be too high).SOLUTION:a.To replicate a one-year pure discount bond with a face value of $100, buy ashare of stock, and a European put with exercise price $100, and sell aEuropean call with an exercise price $100.b.S = $100, P = $10, and C = $15.E/(1+r) = S + P- C$100/(1+r) = $100 + $10 - $15 = $95r = 100/95 -1 = .053 or 5.3%c.If r = 4%, then one could make risk-free arbitrage profits by borrowing at 4%and investing in synthetic 1-year pure discount bonds consisting of a share of stock, a European put with exercise price $100, and a short position in aEuropean call with an exercise price $100. The synthetic bond would cost $95 and pay off $100 at maturity in 1 year. The principal and interest on the $95 it costs to buy this synthetic bond would be $95 x 1.04 = $98.8. Thus there would be a pure arbitrage profit of $1.20 per bond a year from now with zero initial outlay of funds.5. A 90-day European call option on a share of the stock of Toshiro Corporation is currently trading at 2,000 yen whereas the current price of the share itself is 2, 400 yen. 90-day zero-coupon securities issued by the government of Japan are selling for 9, 855 yen per 10, 000 yen face value. Infer the price of a 90-day European put option on this stock if both the call and put have a common exercise price of 500 yen.SOLUTION:Using the expression for put-call parity, P =-S + E/(1+r)T + CS is the share price, P is the price of the put, C is the price of the call and E is the common exercise price.Since government bonds are selling at . 9855 per 1 yen of face value, this is thediscount factor for computing the PV of the exercise price. There is no need to compute the riskless rate, r.Substituting in the parity equation we get:P = -2,400 + 500 x .9855 +2,000 = 92.75 yen6. Gordon Gekko has assembled a portfolio consisting of ten 90-day US Treasury bills, each having a face value of $1, 000 and a current price of $990.10, and 200 90-day European call options, each written on a share of Paramount stock and having an exercise price of $50.00. Gekko is offering to trade you this portfolio for 300 shares of Paramount stock, which is currently valued at $215.00 a share.If 90-day European put options on Paramount stock with a $50.00 exercise price are currently valued at $25.00,a.Infer the value of the calls in Gekko’s portfolio.b.Determine whether you should accept Gekko’s offer.SOLUTION:ing put-call parity, the current price of a call is found to be approximately$190.50 as follows:C =S - E/(1+r)T + P= $215 - $50 x .9901 + $25 = $190.495b.The v alue of Gekko’s portfolio is 10 x $990.10 + 200 x $190.495 = $48,000But the value of 300 shares is $64,500. We should reject Gekko’s offer.7. The stock of Kakkonen, Ltd., a hot tuna distributor, currently lists for $500.00 a share, whereas one-year European call options on this stock, with an exercise price of $200.00, sell for $400.00 and European put options with a similar expiration date and exercise price sell for $84.57.a.Infer the yield on a one-year, zero-coupon U.S. government bond soldtoday.b.If this yield is actually at 9%, construct a profitable trade to exploit thepotential for arbitrage.SOLUTION:ing put-call parity, we can infer the riskless yield to be approximately 8.36%as follows:A portfolio consisting of a share of the stock, a put, and a short position in acall is equivalent to a 1-year T-bill with a face value of E. Therefore the price of such a T-bill would have to be $184.57:E/(1+r)T = S + P- C = $500.00 +$84.57 -$400.00 = $184.571+r= 200/184.57 = 1.0836r= .0836 or 8.36%b.There are many ways to exploit the violation of the Law of One Price to makearbitrage profits. Since the risk-free interest rate is 9%, and the implied interest rate on the replicating portfolio is 8.36%, we could go short the replicating portfolio and invest the proceeds in T-bills. For example, at current prices,short-sell a “unit” portfolio, which consists of long positions in one put and one share and writing one call, to earn immediate revenue of $184.57. The portfolio you sold short requires payment of $200 one year from now. If you invest the $184.57 in one-year T-bills you will have 1.09x $184.57 = $201.18 a year from now. Thus you will earn a risk-free arbitrage profit of $1.18 with no outlay of your own money.Two-State Option Pricing8. Derive the formula for the price of a put option using the two-state model. SOLUTION:To price the put option, we create a synthetic option by selling short a fraction (denote the fraction “a”) and len d $b in risk-free asset. Denote the price of the stock S, the price of the put option P, the stock price when the next period is an “up” to be uS, the stock price when the next period is a “down” to be dS, the payoffs of the put option in each state Pu and Pd, and the risk-free interest r.We solve for (a, b) in 1) and 2) We find:andSo that the price of the put optionuP b r a S u =⨯++⨯⨯-)1(d P b r a S d =⨯++⨯⨯-)1(Sd u P P a d u ⨯---=)()1()(r d u P d P u b u d +⨯-⨯-⨯=⎥⎦⎤⎢⎣⎡⨯⎪⎭⎫ ⎝⎛---+⨯⎪⎭⎫ ⎝⎛--+⨯+=+⨯-=d u P d u r u P d u d r r b S a P 1)1)1(19. The share value of Drummond, Griffin and McNabb, a New Orleanspublishing house, is currently trading at $100.00 but is expected, 90 days from today, to rise to $150.00 or to decline to $50.00, depending on critical reviews of its new biography of Ezra Pound. Assuming the risk-free interest rate over the next 90 days is 1%, can you value a European call option written on a share of DGM stock if the option carries an exercise price of $85.00?SOLUTION:Should the value of DBM stock rise to $150 in 90 days, the call will be worth $65.00 at that date, but if DBM stock falls to $50.00 the call will be worthless at expiration. Using the 2-state option pricing model, we find that the call is worth $32.82:To replicate the call using the stock and risk-free borrowing we buy x shares ofstock and borrow y. We findthe values for x and y by setting up two equations, one for each of the possible payoffs of the call at expiration:The solution to this set of two equations is x = .65 and y = $32.50/1.01 = $32.18 Thus, we can replicate the call option by buying .65 of a share of stock (at a cost of $65) and borrowing $32.18.The price of the call option is $32.82: C = .65 x $100 - $32.18 = $32.82The Black-Scholes Formula 10.a. Use the Black-Scholes formula to find the price of a 3-month European call option on a non-dividend- paying stock with a current price of $50.Assume the exercise price is $51, the continuously compounded risk-free interest rate is 8% per year, and σ is .4.b. What is the composition of the initial replicating portfolio for this call option?c. Use the put-call parity relation to find the Black-Scholes formula for the price of the corresponding put option.SOLUTION:a. The price of the call is $3.987. Since the present value of the exercise price is01.1506501.1150=⨯-⨯=⨯-⨯y x y x 4$5.504.4.4.=⨯⨯⨯=⨯⨯⨯=T S C σapproximately equal to the current stock price, we could use the linearapproximation to the Black-Scholes formula:b.The hedge ratio, which is the number of shares of stock you must buy, equalsN(d1), and the amount to borrow is N(d2) times the PV of the exercise price.To find N(d1) and N(d2) you must compute d1 and d2 and then apply the N( ) function (i.e., the standard normal cumulative density function). You can either use NORMDIST in Excel or use a statistical table to do this. The hedge ratio is .54, which means you would buy .54 of a share of stock for $27. The amount to borrow is $23.c. From put-call parity: P = -S + E e0.02 + C = -$50 + $51.01 + $4 = $5.0111. As a financial analyst at Yew and Associates, a Singaporean investment house, you are asked by a client if she should purchase European call options on Rattan, Ltd. stock, which are currently selling in U.S. dollars for $30.00. These options have an exercise price of $50.00. Rattan stock currently exhibits a share price of $55.00, and the estimated rate of return variance of the stock is .04.If these options expire in 25 days and the risk-free interest rate over that period is 5% per year, what do you advise your client to do?SOLUTION:We can apply the Black-Scholes formula, where S = $55, E = $50, σ = .2, T =25/365, r = .05. We find thatC = $5.20. This is a lot less than $30, so clearly the options are not worth buying.Valuation of Corporate Securities with the Two-State Model12. Lorre and Greenstreet, Inc., a purveyor of antique statues, currently has corporate assets valued at$100,000 and must repay $50, 000, the aggregate face value of zero-coupon bonds sold to private investors, in 90 days. An independent appraisal of a newly acquired antique falcon from Malta will be publicly released at that time, and the value of the firm’s assets is expected to increase to $170,000 if the falcon is certified as genuine, but to decline to a mere $45, 000 if the antique is found to be a fake. The firm will declare bankruptcy in this latter circumstance and shareholders will surrender the assets of the firm to its creditors.a.Can you express the current aggregate value of equity in Lorre andGreenstreet as a contingent expression of the value of the firm’s assets and the face value of its outstanding debt?b.Is there a relation between the expression you have derived for equity anda 90-day European call option written upon the aggregate value of thefirm’s assets?c.Can you express the current aggregate value of the bonds issued by Lorreand Greenstreet in terms of the value of the firm’s assets and the facevalue of its outstanding debt?d.Is there a relation among the current value of the bonds the firm hasissued, the current value of riskless bonds with the same term to maturity and face value, and a European put option written on the aggregate value of the firm’s assets? What would the implication of such a relationship be for expressing the value of risky debt in terms of risk-free debt andcollateral?SOLUTION:a.The aggregate value of the firm’s equity in 90 d ays is E1 = max (V1 -B, 0)where E1 and V1 are, respectively, the aggregate values in 90 days of thefirm’s equity and assets, and where B is the aggregate face value of the firm’s debt.The current value of the equity can be expressed as:E = xV - ywhere x is the fraction of the value of the firm that one must purchase toreplicate the payoffs from the equity, and y is the amount that must beborrowed. We find the values for x and y by setting up two equations, one for each of the possible payoffs of the equity 90 days from now:170000x - y(1+r) = 120,00045000x - y(1+r) = 0The solution to this set of two equations is x = 120/125 = .96 and y =$43,200/(1+r), where r is the risk-free 90-day interest rate. Thus, we canreplicate the equity by buying 96% of the firm’s assets (at a cost of $96,000) and borrowing the present value of $43,200. The current value of the equity is therefore:E = $96,000 -$43,200/(1+r)b.They are exactly analogous. The call value is analogous to the aggregate valueof equity, the share price is analogous to the aggregate value of the firm’sassets, and the exercise price is analogou s to the face value of the firm’s debt.In effect, the firm’s shareholders hold a call option on the firm’s assets, which they can exercise by repaying the face value of the debt.c.In the presence of limited corporate liability, the realized aggregate payoff tothe firm’s creditors in 90 days, D1, can be written as:D1 = min (V1,B).d.The difference in value between the firm’s bonds and the correspondingdefault-free bonds equals the value of a European put on the firm’s assets. This relation implies the limit ed liability that stockholders have to sell the firm’s assets at the debt’s face value, which also implies that the value of risk-free debt equals the sum of the value of the risky debt and the value of collateral.13. Gephardt, Army and Gore, a vaudeville booking agency, has issued zero-coupon corporate debt this week, consisting of 80 bonds, each with a face value of $1,000 and a term to maturity of one year. Industry analysts predict that the value of GAG assets will be $160,000 in one year if Rupert Murdoch succeeds in purchasing and converting the Washington Press Club into a comedy venue, $130,000 if Murdoch buys the club but retains its current scheduling, and $20,000 if Murdoch builds an alternative comedy venue in Washington. Industry analysts also predict that aggregate value of the assets of a second firm in the field of comedy entertainment, Yelstin Yuks, Ltd., will have the values of $100,000, $100,000, and $40,000 in these respective circumstances. Assuming that investors can purchase portfolios comprised of shares of the assets of GAG and YY Ltd., as well as buying or short –selling one-year, zero-coupon, government bonds at the risk-free annual rate of .10, thena.Infer the three alternative values for aggregate equity in GAG, one yearfrom today.b.Devise a portfolio that is a perfect substitute for the payoffs given by aportfolio composed only of equity in GAG.c.Determine the current market value of a share of equity in GAG, assuming10,000 shares of GAG stock are outstanding, the current market value of GAG assets is $120,000, and the current market value of YY Ltd., assets is $85,725.d.Determine the current market value of a bond issued by GAG, assuming80 bonds are issued, under these circumstances. What of the yield tomaturity on each such bond?SOLUTION:a.In the first circumstance, the value of aggregate equity in GAG is $160,000-$80,000=$80,000.In the second circumstance, the value of aggregate equity in GAG is $130,000-$80,000=$50,000.In the third circumstance, the value of aggregate equity in GAG is 0.b.Suppose that the replicating portfolio consists of buying x units of the GAGasset, y units of the YY asset, and z units of the government bond (with a face value of $100,000). The payoff of this portfolio will exactly match that of the GAG equity, that gives:160,000x + 100,000y + 100,000z = 80,000130,000x + 100,000y + 100,000z = 50,00020,000x + 40,000y +100,000z = 0solving the equations, we have x = 1, y = -1, z = 0.2c.We define three types of pure contingent claims: at the end of one year, AD1will pay off $1 if and only if Rupert Murdoch succeeds in purchasing andconverting the Washington Press Club into a comedy venue; AD2 will pay off $1 if and only if Murdoch buys the club but retains its current scheduling; AD3 will pay off $1 if and only if Murdoch builds an alternative comedy venue in Washington. Denote the prices as of today of the three pure contingent claims as p1, p2 and p3, respectively.From the value equation of the GAG asset, YY asset and the government bond, we have:GAG: 160,000p1 + 130,000p2 + 20,000p3 = 120,000YY: 100,000p1 + 100,000p2 + 40,000p3 = 85,725Government bond: 100,000p1 + 100,000p2 + 100,000p3 = 100,000/(1+10%) = 90,909Solve the equations, we have p1 = 0.3774, p2=0.4453, p3=0.0864The total value of GAG equity is80,000p1 + 50,000p2 = $52457The per share price of equity is $5.25.d.The value of the bond and the value of the equity add up to the value of theasset, so,V bond = V asset– V equity = 120,000 – 52547 = $67543The yield-to-maturity of bond is (80,000-67543)/67543 = 18.4%。

金融学第二版课后习题答案
金融学第二版课后习题答案：深入理解金融学知识
金融学是一个涉及广泛的领域，涵盖了货币、银行、投资、风险管理等多个方面。

对于学习金融学的学生来说，课后习题是巩固知识、提高理解的重要途径。

本文将以金融学第二版课后习题答案为标题，深入探讨金融学知识的重要性和
应用。

首先，金融学知识对于个人和企业来说都是非常重要的。

对于个人来说，理解
金融学知识可以帮助他们更好地管理个人财务，进行投资和理财规划。

而对于
企业来说，金融学知识可以帮助他们进行资金管理、风险管理和投资决策，从
而更好地实现经营目标。

其次，金融学知识的应用范围非常广泛。

无论是在银行、证券公司、保险公司
等金融机构，还是在企业、政府和非营利组织，金融学知识都有着重要的应用
价值。

只有深入理解金融学知识，才能更好地应对各种金融风险和挑战，实现
财务目标。

金融学第二版课后习题答案提供了学生们检验自己掌握程度的重要途径。

通过
仔细分析和思考课后习题答案，学生们可以更好地理解金融学知识，发现自己
的不足之处，并及时进行补充和提高。

这对于他们将来在金融领域的发展和应
用都是非常有益的。

总之，金融学知识对于个人和企业来说都是非常重要的，它的应用范围也非常
广泛。

通过深入理解金融学知识，我们可以更好地管理个人和企业财务，更好
地应对各种金融风险和挑战。

金融学第二版课后习题答案为我们提供了一个重
要的学习工具，帮助我们更好地掌握金融学知识，实现个人和企业的财务目标。

金融学第二版课后习题答案【篇一：王重润公司金融学第二版课后答案】业有几种组织方式？各有什么特点？（ 1）有两种，有限责任公司和股份有限责任公司（ 2）有限责任公司特点：有限责任公司是指股东以其出资额为限对公司承担责任，公司以其全部资产对公司的债务承担责任的企业法人；有限责任公司注册资本的最低限额为人民币3万元；其资本并不必分为等额股份，也不公开发行股票，股东持有的公司股票可以再公司内部股东之间自由转让，若向公司以外的人转让，须经过公司股东的同意；公司设立手续简便，而且公司无须向社会公开公司财务状况。

（ 3）股份有限责任公司特点：1、有限责任2、永续存在3、股份有限责任公司的股东人数不得少于法律规定的数目，我国规定设立股份有限公司，应当有2人以上200人以下为发起人4、股份有限责任公司的全部资本划分为等额的股份，通过向社会公开发行的办法筹集资金，任何人在缴纳了股款之后，都可以成为公司股东，没有资格限制。

5、可转让性6、易于筹资2题：为什么我国《公司法》允许存在一人有限责任公司？一人有限责任公司与个人独资企业有何不同？答：1.就立法初衷而言，许可自然人投资设立一人有限责任公司的重要考虑是减少实质上的一人公司的设立，简化和明晰股权归属，减少纷争。

以往由于我国《公司法》禁止设立一人公司，使得投资人通过各种途径设立或形成的实质上的一人公司大量存在，挂名股东与真实股东之间的投资权益纠纷以及挂名股东与公司债权人之间的债务纠纷不断，令工商行政管理部门和司法机关无所适从。

在修订《公司法》的过程中，法律委员会、法制工作委员会会同国务院法制办、工商总局、国资委、人民银行和最高人民法院反复研究认为：从实际情况看，一个股东的出资额占公司资本的绝大多数而其他股东只占象征性的极少数，或者一个股东拉上自己的亲朋好友作挂名股东的有限责任公司，即实质上的一人公司，已是客观存在，也很难禁止。

根据我国的实际情况，并研究借鉴国外的通行做法，应当允许一个自然人投资设立有限责任公司。

CHAPTER 8VALUATION OF KNOWN CASH FLOWS: BONDSObjectives«To show how to value con tracts and securities that promise a stream of cash flows that areknown with certa inty.«To un dersta nd the shape of the yield curve .«To un dersta nd how bond prices and yields cha nge over time.Outline8.1 Us ing Prese nt Value Formulas to Value Known Cash Flows8.2 The Basic Build ing Blocks: Pure Discou nt Bonds8.3 Coupon Bo nds, Curre nt Yield, and Yield to Maturity8.4 Readi ng Bond Listi ngs8.5 Why Yields for the Same Maturity Differ8.6 The Behavior of Bond Prices over TimeSummary* A cha nge in market in terest rates causes a cha nge in the opposite directi on in the market values of all exist ing con tracts promisi ng fixed payme nts in the future.* The market prices of $1 to be received at every possible date in the future are the basic building blocks for valuing all other streams of known cash flows. These prices are inferred from the observed market prices of traded bonds and the n applied to other streams of known cash flows to value them.* An equivale nt valuati on can be carried out by appl ying a discou nted cash flow formula with a differe nt discou nt rate for each future time period.* Differe nces in the prices of fixed-i ncome securities of a give n maturity arise from differe nces in coup on rates, default risk, tax treatme nt, callability, con vertibility, and other features.* Over time the prices of bonds con verge towards their face value. Before maturity, however, bond prices can fluctuatea great deal as a result of cha nges in market in terest rates.Solutions to Problems at End of ChapterBond Valuation with a Flat Term Structure1. Suppose you want to know the price of a 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity is 8%. What is the price?b. What is the price if coupons are paid semiannually, and the yield to maturity is 8% per year?c. Now you have been told that the yield to maturity is 7% per year. What is the price? Could you have guessedthe answer without calculating it? What if coupons are paid semiannually?c. Price = 100. When the coup on rate and yield to maturity are the same, the bond sells at par value (i.e. the price equalsthe face value of the bon d).2. Assume six months ago the US Treasury yield curve was flat at a rate of 4% per year (with annualcompounding) and you bought a 30-year US Treasury bond. Today it is flat at a rate of 5% per year. What rate of return did you earn on your initial investment: a. If the bond was a 4% coupon bond? b. If the bond was a zero coupon bond?c. How do your answer change if compounding is semiannual? SOLUTION: a and b.Coupon = 4% 30 4 ? 100 4 PV =100 Zero coupon30 4 ? 100 0 PV =30.83Step 2: Find prices of the bonds today: Coupon = 4% 29.5 5?100 4 84.74 Zero coupon29.5 5 ? 100 0 23.71Step 3: Find rates of retur n:Rate of retur n = (coup on + cha nge in price)/in itial price4% coupon bond: r = (4 + 84.74 —100)/100 = -0.1126 or —11.26%Zero-coupon bon d: r = (0 + 23.71 —30.83)/30.83 = -0.2309 or -23.09%. Note that the zero-coupon bo nd is more sen sitive to yield cha nges tha n the 4% coup on bond. c.Step 1: Find prices of the bonds six mon ths ago:Coup on=4% 60 2 ?100 2 PV =100 Zero coupon 60 2 ? 100 0 PV =30.48 Step 2: Find prices of the bonds today:Coup on=4% 59 2.5? 100 2 84.66 Zero coupon59 2.5 ?10023.30SOLUTION:a. With coup ons paid once a year:Price = 93.29b. With coup ons paid twice a year:Price = 93.20Step 3: Find rates of retur n:Rate of return = (coupon + change in price) / initial price4% coupon bond: r = (2 + 84.66 -100)/100 = -0.1334 or -13.34%Zero coupon bond: r = (0 + 23.30 - 30.48)/30.48 = -0.2356 or -23.56%. Note that the zero-coupon bond is more sen sitive to yield cha nges tha n the 4% coup on bond.Bond Valuatio n With a Non-Flat Term Structure3. Suppose you observe the following prices for zero-coupon bonds (pure discount bonds) that have no risk of default:a. What should be the price of a 2-year coupon bond that pays a 6% coupon rate, assuming coupon paymentsare made once a year starting one year from now?b. Find the missing entry in the table.c. What should be the yield to maturity of the 2-year coupon bond in Part a?d. Why are your answers to parts b and c of this question different?SOLUTION:a. Present value of first year's cash flow = 6 x .97 = 5.82Prese nt value of sec ond year's cash flow = 106 x .90 = 95.4Total prese nt value = 101.22 b^Th^y^^tomaturityon^^^^arzerocoupo^bon^wrt^pr^eof9^an^facevalu^of1^3i^5^^^^^^^^2 I ? I -90 I 100 I 0 1 i = 5.41%c. The yield to maturity on a 2-year 6% coup on bond with price of 101.22 isd. The two bonds are differe nt because they have differe nt coup on rates. Thus they have differe nt yields to maturity.Coupon Stripping4. You would like to create a 2-year synthetic zero-coupon bond. Assume you are aware of the following information: 1-year zero- coupon bonds are trading for $0.93 per dollar of face value and 2-year 7% coupon bonds (annual payments) are selling at $985.30 (Face value = $1,000).a. What are the two cash flows from the 2-year coupon bond?b. Assume you can purchase the 2-year coupon bond and unbundle the two cash flows and sell them.i. How much will you receive from the sale of the first payment?ii. How much do you need to receive from the sale of the 2-year Treasury strip to break even?SOLUTION:a. $70 at the end of the first year and $1070 at the end of year 2.b. i. I would receive .93 x $70 = $65.10 from the sale of the first payment.ii. To break even, I would need to receive $985.30- $65.10 = $920.20 from the sale of the 2-year strip.The Law of One price and Bond Pricing5. Assume that all of the bonds listed in the following table are the same except for their pattern of promised cash flows over time. Prices are quoted per $1 of face value. Use the information in the table and the Law of One Price to infer the values of the missing entries. Assume that coupon payments are annual.6% 2 years 5.5%0 2 years7% 2 years0 1 year $0.95From Bond 1 and Bond 4, we can get the miss ing en tries for the 2-year zero-coup on bond. We know from bond 1 that:2 21.0092 = 0.06/1.055 +1.06/(1.055) . This is also equal to 0.06/(1+z 1) + 1.06/(1+z 2) where z 1 and Z2 are the yields to maturity on on e-year zero-coup on and two-year zero-coup on bonds respectively. From bond 4 , we have z 1, we can find z2.1.0092 -0.06/1.0526 = 1.06/(1+z 2)2, hence z = 5.51%.To get the price P per $1 face value of the 2-year zero-coup on bond, using the same reasoning:1.0092 -0.06x0.95 = 1.06xP, he nee P = 0.8983To find the entries for bond 3: first find the price, then the yield to maturity. To find the price, we can use z 1 and Z2 found earlier: PV of coupon payment in year 1: 0.07 x 0.95 = 0.0665PV of coupon + pri ncipal payme nts in year 2: 1.07 x 0.8983 =0.9612「otal prese nt value of bond 3 二 1.02772 ? 0.07 -1.0277 1 i = 5.50%Hence the table becomes:6% 2 years $1.0092 5.5%0 2 years $0.8983 5.51%SOLUTION:Bond 1:Bond 4:Bond Features and Bond Valuation6. What effect would adding the following features have on the market price of a similar bond which does not have this feature?a. 10-year bond is callable by the company after 5 years (compare to a 10-year non-callable bond);b. bond is convertible into 10 shares of common stock at any time (compare to a non-convertible bond);c. 10-year bond can be “ put back ” to the company after 3 years at par (puttable boiumipare to a 10year non-puttablebond)d. 25-year bond has tax-exempt coupon paymentsSOLUTION:a. The callable bond would have a lower price tha n the non-callable bond to compe nsate the bon dholders for gra nti ng theissuer the right to call the bon ds.b. The con vertible bond would have a higher price because it gives the bon dholders the right to con vert their bonds intoshares of stock.c. The puttable bond would have a higher price because it gives the bondholders the right to sell their bonds back to the issuerat par.d. The bond with the tax-exempt coup on has a higher price because the bon dholder is exempted from pay ing taxes on thecoup ons. (Coup ons are usually con sidered and taxed as pers onal in come).Inferring the Value of a Bond Guarantee7. Suppose that the yield curve on dollar bonds that are free of the risk of default is flat at 6% per year. A 2-year 10% coupon bond (with annual coupons and $1,000 face value) issued by Dafolto Corporation is rates B, and it is currently trading at a market price of $918. Aside from its risk of default, the Dafolto bond has no other financially significant features. How much should an investor be willing to pay for a guarantee against Dafolto ' s defaulting on this bond?The difference between the price of the bond if it were free of default and its actual price (with risk of default) is the value of a guarantee against default: 1073.3-918 = $155.3The implied Value of a Call Provision and Convertibility8. Suppose that the yield curve on bonds that are free of the risk of default is flat at 5% per year. A 20-year default-free coupon bond (with annual coupons and $1,000 face value) that becomes callable after 10 years is trading at par and has a coupon rate of 5.5%.a. What is the implied value of the call provision?b. A Safeco Corporation bond which is otherwise identical to the callable 5.5% coupon bond describedabove, is also convertible into 10 shares of Safeco stock at any time up to the bond ' s maturity. If its yield to maturity is currently 3.5% per year, what is the implied value of the conversion feature?SOLUTION:a. We have to find the price of the bond if it were only free of the risk of default.The bond is traded at par value, hence the differe nee betwee n the value calculated above and the actual traded value is the implied value of the call provisio n: 1062.3 T000 = $62.3Note that the call provisi on decreases the value of the bond.b. We have to find the price of the Safeco Corporati on:This bond has the same features as the 5.5% default free callable bond described above, plus an additional feature: it is con vertible into stocks. Hence the implied value of the con versi on feature is the differe nee betwee n the values of both bonds: 1284.2-1000 = $284.25. Note that the con version feature in creases the value of the bond.Changes in Interest Rates and Bond Prices9. All else being equal, if interest rates rise along the entire yield curve, you should expect that:i. Bond prices will fallii. Bond prices will riseiii. Prices on long-term bonds will fall more than prices on short-term bonds.iv. Prices on long-term bonds will rise more than prices on short-term bondsa. ii and iv are correctb. We can ' t be certain that prices will changec. Only i is correctd. Only ii is correcte. i and iii are correctSOLUTION:The correct an swer is e.Bond prices are in versely proporti onal to yields hence whe n yields in crease, bond prices fall. Lon g-term bonds are more sen sitive to yield cha nges tha n short-term bon ds.。

第一章思考题A、B、C详解1.1 答案详解：A金银作为自然的产物，其只有在人类社会出现之后才作为货币，因此金银天然不是货币，B选项错误。

货币的本质是一般等价物，贝壳、铜在历史上都曾经做过货币，因此C选项错误。

金银只有在作为货币使用时才能作为一般等价物。

D选项也错误。

综合，A说法正确。

1.2 答案详解：A纸币是由国家发行的、强制使用的货币符号。

纸币的发行数量、面值等等都是由国家决定的，体现着一个国家的货币政策。

但是，货币的购买力不是由国家或者法律决定的，而是由货币发行数量和经济发展状况决定的。

如果生产力水平不变，社会生产出的总的商品数量不变，而流通中的货币数量为原来的两倍，那么商品的价格也会变成原来的两倍，此时每种面值的货币只代表原来一半的价值。

因此选A。

1.3 答案详解：ACDF在商品交换过程中，价值形式的发展经历的四个阶段有简单的价值形式、扩大的价值形式、相对价值形式、一般价值形式。

参见第一章第一节有关内容1.4 答案详解：银行券指由银行发行的以信用作为保证的可以兑现的银行票据，是以银行信用为担保所产生的一种信用工具银行券有其自身的发展历程。

开始时为安全的缘故，一些人将金银交由从事货币兑换业务的商铺保存，商铺则给客户开出相应收据，并承诺随时提取原有数量的金银；后来，由于交易和支付日益频繁，人们可以使用保管凭条进行直接收付，这就是银行券的雏形。

随着商业信用的不断扩大和发展，商业票据的运用范围日益广泛，但持票人只能到期才能兑现自己所持有的商业票据。

为了解决持票人临时需要资金的问题，银行进行金融创新，开展贴现业务，并且当银行的现款不足以支付持票人时，银行可以使用自己发行的银行券来支付。

1.5 答案详解：当货币在生活中日益重要时，一般说来，作为货币的商品有如下四个基本特征：一是价值比较高，这样可用较少的媒介完成较大量的商品交换；二是易于分割，一方面分割之后不会减少它的价值，另一方面分割成本较低，以便于同价值高低不等的商品交换；三是易于保存，即在保存过程中不会损失价值，费用很低；四是便于携带，以利于扩大化的商品交易。

CHAPTER 16CAPITAL STRUCTUREObjectives•To understand how a firm can create value through its financing decisions. •To show how to take account of a firm’s financing mix in evaluating investment decisions.Outline16.1 Internal versus External Financing16.2 Equity Financing16.3 Debt Financing16.4 The Irrelevance of Capital Structure in a Frictionless Environment16.5 Creating Value through Financing Decisions16.6 Reducing Costs16.7 Dealing with Conflicts of Interest16.8 Creating New Opportunities for Stakeholders16.9 Financing Decisions in Practice16.10 How to Evaluate Levered InvestmentsSummary•External financing subjects a corporation’s investment plans more directly to the discipline of the capital market than internal financing does.•Debt financing in its broadest sense includes loans and debt securities, such as bonds and mortgages, as well as other promises of future payment by the corporation, such as accounts payable, leases, and pensions.•In a frictionless financial environment, where there are no taxes or transaction costs, and contracts are costless to make and enforce, the wealth of shareholders is the same no matter what capital structure the firm adopts.•In the real world there are a number of frictions that can cause capital structure policy to have an effect on the wealth of shareholders. These include taxes, regulations, and conflicts of interest between the stakeholders of the firm. A firm’s management might therefore be able to create shareholder val ue through its capital structure decisions in one of three ways:•By reducing tax costs or the costs of burdensome regulations.•By reducing potential conflicts of interest among various stakeholders in the firm.•By providing stakeholders with financial assets not otherwise available tothem.•There are three alternative methods used in estimating the net present value of an investment project to take account of financial leverage: the adjusted present value method, the flows to equity method, and the weighted average cost of capital methodSolutions to Problems at End of ChapterDebt-Equity Mix1. Divido Corporation is an all-equity financed firm with a total market value of $100 million.The company holds $10 million in cash-equivalents and has $90 million in other assets.There are 1,000,000 shares of Divido common stock outstanding, each with a market price of $100.Divido Corporation has decided to issue $20 million of bonds and to repurchase $20 million worth of its stock.a.What will be the impact on the price of its shares and on the wealth of itsshareholders?Why?b.Assume that Divido’s EBIT has an equal probability of being $20 million,or $12 million, or $4million.Show the impact of the financial restructuring on the probability distribution of earnings per share in the absence oftaxes.Why does the fact that the equity becomes riskier not necessarily affect shareholder wealth?SOLUTION:a.In an M&M frictionless environment, where there are no taxes and contractsare costless to make and enforce, the wealth of shareholders is the same no matter what capital structure the firm adopts. In such an environment, neither the stock price nor shareholders’ wealth would be affected. In the real world Divido’s management might be ab le to create shareholder value by issuing debt and repurchasing shares in two ways:By reducing tax costsBy reducing the free cash flow available to management and exposing itself to greater market discipline.b.The formula for EPS without debt is:EPS all equity =EBIT1,000,000 sharesThe interest payments will be $1.2 million per year (.06 x $20 million)regardless of the realized value of EBIT. The number of shares outstanding after exchanging debt for equity will be 800,000. EPS with debt is therefore: EPS with debt = Net Earnings= EBIT – $1.2 million800,000 shares 800,000 sharesAlthough the shares of stock become riskier with debt financing, the expected earnings per share go up. In a frictionless financial environment, the net effect is to leave the price of the stock unaffected.Leasing2. Plentilease and Nolease are virtually identical corporations.The only difference between them is that Plentilease leases most of its plant and equipment whereas Nolease buys its plant and equipment and finances it by pare and contrast their market-value balance sheets.SOLUTION:Market-Value Balance Sheets of Nolease and Plentilease CorporationsThe main difference between the bonds and the lease as a form of debtfinancing is who bears the risk associated with the residual market value of the leased asset at the end of the term of the lease. Since Nolease Corporation has bought its equipment, it bears this risk. In Plentilease’s case, however, it is the lessor that bears this residual-value risk.Pension Liabilities3. Europens and Asiapens are virtually identical corporations.The only difference between them is that Europens has a completely unfunded pension plan, and Asiapens has a fully funded pension pare and contrast their market-value balance sheets.What difference does the funding status of the pension plan make to the stakeholders of these two corporations?SOLUTION:Balance Sheets of Asiapens and Europens CorporationsAsiapens has funded its pension plan by issuing bonds and investing the funds raised in a segregated pool of pension fund assets. These pension assets take the form of a diversified portfolio of stocks and bonds issued by othercompanies and serve as collateral for the pension benefits promised byAsiapens to its employees. In the case of Europens, there is no segregated poolof pension assets. The pension promises of Europens are backed by the assets of the company itself. Therefore, the employees of Asiapens are more secure about receiving their promised pension benefits, since the benefits arecollateralized by a more diversified portfolio of assets. In the case of bothcompanies, however, any unfunded pension liability reduces shareholdersequity.4. Comfort Shoe Company of England has decided to spin off its Tango Dance Shoe Division as a separate corporation in the United States.The assets of the Tango Dance Shoe Division have the same operating risk characteristics as those of Comfort.The capital structure of Comfort has been 40% debt and 60% equity in terms of marketing values, and is considered by management to be optimal.The required return on Comfort’s assets (if unlevered) is 16% per year, and the interest rate that the firm (and the division) must currently pay on their debt is 10% per year.Sales revenue for the Tango Shoe Division is expected to remain indefinitely at last year’s level of $10 million.Variable costs are 55% of sales.Annual depreciation is $1 million, which is exactly matched each year by new investments.The corporate tax rate is 40%.a.How much is the Tango Shoe Division worth in unlevered form?b.If the Tango Shoe Division is spun off with $5 million in debt, how muchwould it be worth?c.What rate of return will the shareholders of the Tango Shoe Divisionrequire?d.Show that the market value of the equity of the new firm would be justifiedby the earnings to the shareholders.SOLUTION:a.The unlevered free cash flow for the Tango Shoe Division would be (in$millions):Sales: $10.0Var. Cost: -5.5Depreciation - 1.0Taxable Income $ 3.5Taxes (@40%) -1.4After-Tax Income $2.1Depreciation 1.0Investment -1.0Free Cash Flow $2.1 millionUnlevered, Tango is worth: $2.1 million / 0.16 = $13.125 millionb.If Tango had $5 million of debt, its total value would be:Market Value with Debt = Market Value without Debt + PV of Interest Tax ShieldV L = V U + T x B= $13.125 + (.4 x 5) = $15.125 millionTango Equity = $15.125 - $5 = $10.125 millionc.Tango’s cost of equity capital would be .1778k e = k + (1-T)(k - r)D/E = .16 + (1-.4)(.16-.10)x 5/10.125 = .1778d.The value of the equity should be the present value of the expected net incomediscounted at the required rate of return on equity. The expected net income will be the unlevered cash flow less the after-tax cost of the interest of the debt: $2.1 - (.6) (.1 x $5) = $2.1 - $.3 = $1.8 million per yearS = $1.8 million / .1778 = $10.125 million5. Based on the above problem, Suppose that Foxtrot Dance Shoes makes custom designed dance shoes and is a competitor of Tango Dance Shoes. Foxtrot has similar risks and characteristics as Tango except that it is completely unlevered.Fearful that Tango Dance Shoes may try to take over Foxtrot in order to control their niche in the market, Foxtrot decides to lever the firm to buy back stock.a.If there are currently 500,000 shares outstanding, what is the value ofFoxtrot’s stock?b.How many shares can Foxtrot buy back and at what value if it is willing toborrow 30% of the value of the firm?c.What if it is willing to borrow 40% of the value of the firm?d.Should Foxtrot borrow more?SOLUTION:a.Current price per share: $13.125 million /.5 million shares = $26.25 per shareb.@30% debtAmount to borrow: 30% of 13.125 million = $3.9375 millionPV of Tax Shield = .4 x $3.9375 million = $1.575 millionValue of levered firm = $13.125 + $1.575 = $14.7 millionValue of equity in levered firm = $14.7 million $3.9375 million = $10.7625 millionTo compute the number of shares Foxtrot can repurchase, we need to know the price per share.If Foxtrot can repurchase shares at the existing price of $26.25 then the number of shares retired will be$3.9375 million/$26.25 per share = .15 million shares. This will leave .35million shares outstanding, and the price of each share will be $10.7625million/.35 million = $30.75.If the PV of the tax shield gets incorporated in the price of the shares before the repurchase, then the price of the shares will increase by $1.575 million/.5million = $3.15. So the price of the repurchased shares will be$26.25 + $3.15 = $29.40.Then the number of shares retired will be $3.9375 million/$29.40 per share = 133,929 shares. This will leave 366,071 shares outstanding each with a price of $29.40.c.@40% debtAmount to borrow: 40% of $13.125 million = $5.25 millionPV of Tax Shield = .4 x $5.25 million = $2.1 millionValue of levered firm = $13.125 + $2.1 = $15.225 millionValue of equity in levered firm = $15.225 million $5.25 million = $9.975 millionIf Foxtrot can repurchase shares at the existing price of $26.25 then the number of shares retired will be$5.25 million/$26.25 per share = .2 million shares. This will leave .3 million shares outstanding, and the price of each share will be $9.975 million/.3 million = $33.25.If the PV of the tax shield gets incorporated in the price of the shares before the repurchase, then the price of the shares will increase by $2.1 million/.5 million = $4.20. So the price of the repurchased shares will be$26.25 + $4.20 = $30.45.Then the number of shares retired will be $5.25million/$30.45 per share =172,414 shares. This will leave 327,586 shares outstanding each with a price of $30.45.d. Foxtrot’s management must trade off the tax savings due to additional debtfinancing against the costs of financial distress that rise with the degree of debt financing.6. Hanna-Charles Company needs to add a new fleet of vehicles for their sales force.The purchasing manager has been working with a local car dealership to get the best value for the company dollar.After some negotiations, a local dealer has offered Hanna-Charles two options:1) a three year lease on the fleet of cars or 2) 15% off the top to purchase outright. Option 2 would cost Hanna-Charles company about 5% less than the lease option in terms of present value.a.What are the advantages and disadvantages of leasing?b.Which option should the purchasing manager at Hanna-Charles pursueand why?SOLUTION:a.Advantages:The lessor bears all the residual-value riskTax BenefitsNo disposal concerns (or resale) when life of equipment is expended.Disadvantages:No ownership while maintaining maintenance responsibilityb.Lease or Buy:Hanna-Charles company should lease. Although they may spend more with the lease, they do not bear the residual-value risk.7. Havem and Needem companies are exactly the same differing only in their capital structures.Havem is an unlevered firm issuing only stocks whereas Needem issues stocks and bonds. Neither firm pays corporate taxes. Havem pays out all of its yearly earnings in the form of dividends and has 1 million shares outstanding.Its market capitalization rate is 11% and the firm is currently valued at$180 million.Needem is identical except that 40% of its value is in bonds and has 500,000 shares outstanding. Needem’s bonds are risk free and pay a coupon of 9% per year and are rolled over every year.a.What is the value of Needem’s shares?b.As an investor forecasting the upcoming year, you examine Havem andNeedem using three possible states of the economy that are all equallylikely: normal, bad, and exceptional.Assuming the earnings will be the same, one half, and one and a half respectively, produce a table that shows the earnings and the earnings per share for both Havem and Needem in all three scenarios.SOLUTION:a.Needem has $72 million in debt and $108 million in equity. Since there are500,000 shares, the value of each share is $216.b.Expected EBIT = $180 million x 11% = $19.8 million per yearInterest expense for Needem = $72 million x .09 = $6.48 million per yearb EBIT – Interest Expense8. Using the foregoing example, let us now assume that Havem and Needem must pay taxes at the rate of 40% annually.Given the same distribution of possible outcomes as previously:a.What are the possible after-tax cash flows for Havem and Needem?b.What are the values of the shares?c.If one was not risk averse, which company would that person invest in? SOLUTION:a.After-tax CF Havem = (1 -Tax Rate) EBIT = Net incomeNet income Needem = (1 -Tax Rate) (EBIT - Int. Pmt.)CF Needem = (1 -Tax Rate) (EBIT) + Tax Rate x Int. PmtCF Needem (bad) = (.60) $9.9 + (.40) x 6.48 = $8.532 millionCF Needem (normal) = (.60) $19.8 + (.40) x 6.48 = $14.472 millionCF Needem (except.) = (.60) $29.7 + (.40) x 6.48 = $20.412 millionb.The equity of Havem will be worth $11.88 million /.11 = $108 million or $108per shareThe total value of Needem’s debt + equity will be $108,000,000 + .4 x $72,000,000 = $136.8 million.Needem’s equity will be worth $136,800,000- $72,000,000 = $64.8 million.Since there are .5 million shares of Needem, each will be worth $129.60.c.Needem.9. The Griffey-Lang Food Company faces a difficult problem.In management’s effort to grow the business, they accrued a debt of $150 million while the value of the company is only $125 million.Management must come up with a plan to alleviate the situation in one year or face certain bankruptcy. Also upcoming are labor relations meetings with the union to discuss employee benefits and pension funds. Griffey-Lang at this time has three choices they can pursue: 1) Launch a new, relatively untested product that if successful (probability of .12) will allow G-L to increase the value of the company to $200 million, 2) Sell off two food production plants in an effort to reduce some of the debt and the value of the company thus making it even (.45 probability of success), or do nothing (probability of failure = 1.0).a.As a creditor, what would you like Griffey-Lang to do, and why?b.As an investor?c.As an employee?SOLUTION:a.As a Creditor:Option 2 best suits the creditor. Option 2 allows the creditor to regain some value through the sale of plant and equipment.b.As a shareholder:The shareholders have nothing to lose and everything to gain by taking a big chance with the new product.c.As an Employee:Selling off two production plants will eliminate jobs. Doing nothing means certain bankruptcy and may result in liquidation of the firm and the loss of all the jobs. For the employees, the best choice is option 1.。

CHAPTE R 14FORWARD AND FUTURE S PRICE SObjectives∙ To explain the economic role of futures markets∙To show what information can and cannot be inferred from forward and futures prices.Outline14.1 Distinctions Between Forward and Futures Contracts14.2 The Economic Function of Futures Markets14.3 The Role of Speculators14.4 Relation Between Commodity Spot and Futures Prices14.5 Extracting Information from Commodity Futures Prices14.6 Spot-Futures Price Parity for Gold14.7 Financial Futures14.8 The Implied Risk-Free Rate14.9 The Forward Price Is Not a Forecast of the Spot Price14.10 Forward-Spot Parity with Cash Payouts14.11 Implied Dividends14.12 The Foreign-Exchange Parity Relation14.13 The Role of Expectations in Determining Exchange RatesSummary∙ Futures contracts make it possible to separate the decision of whether to physically store a commodity from thedecision to have financial exposure to its price changes.∙ Speculators in futures markets improve the informational content of futures prices and make futures marketsmore liquid than they would otherwise be.∙ The futures price of wheat cannot exceed the spot price by more than the cost of carry:∙ The forward-spot price parity relation for gold is that the forward price equals the spot price times the cost ofcarry:This relation is maintained by the force of arbitrage . ∙One can infer the implied cost of carry and the implied storage costs from the observed spot and forward prices and the risk-free interest rate. ∙ The forward-spot parity relation for stocks is that the forward price equals the spot price times 1 plus the risk-free rate less the expected cash dividend.This relation can therefore be used to infer the implied dividend from the observed spot and forward prices and the risk-free interest rate.∙ The forward-spot price parity relation for the dollar/yen exchange rate involves two interest rates:where F is the forward price of the yen, S is the current spot price, r Y is the yen interest rate, and r $ is the dollarinterest rate.∙If the forward dollar/yen exchange rate is an unbiased forecast of the future spot exchange rate, then one can infer that forecast either from the forward rate or from the dollar-denominated and yen-denominated risk-free interest rates. F S C-≤F S r s =++()1F S r D=+-()1F r S r Y11+=+$Solutions to Problems at End of ChapterForward Contracts and Forward-Spot Parity.1. Suppose that you are planning a trip to E ngland. The trip is a year from now, and you have reserved a hotel room in London at a price of ₤ 50 per day. You do not have to pay for the room in advance. The exchange rate is currently $1.50 to the pound sterling.a.E xplain several possible ways that you could completely hedge the exchange rate risk in this situation.b.Suppose that r₤=.12 and r$=.08. Because S=$1.50, what must the forward price of the pound be?c.Show that if F is $0.10 higher than in your answer to part b, there would be an arbitrage opportunity. SOLUTION:a.Ways to hedge the exchange rate risk:Pay for the room in advanceBuy the pounds you will need in the forward market.Invest the present value of the rental payments in a pound-denominated riskless asset.b. F = S (1+r$)/(1+r£) = $1.50 x 1.08/1.12 = $1.4464 per poundc.If F is $1.55 then arbitrage profits can be made by borrowing dollars, investing in pounds and selling themforward at the inflated forward price. After paying off principle and interest on the dollars borrowed, you would have pure arbitrage profits left over. For example,Borrow $1.50,Convert it into 1 pound,Invest it in pound-denominated bonds to have 1.12 pounds a year from now,Sell 1.12 pounds forward at $1.55 per pound to have $1.736 a year from now,After 1 year, pay off the principle and interest on the loan ($1.50x 1.08 = $1.62).This series of transactions leaves you with $.116 a year from now with no initial outlay of your money.Forward-Spot Parity Relation with Known Cash Payouts2. Suppose that the Treasury yield curve is flat at an interest rate of 7% per year (compounded semiannually).a.What is the spot price of a 30-year Treasury bond with an 8% coupon rate assuming coupons are paidsemiannually?b.What is the forward price of the bond for delivery six months from now?c.Show that if the forward price is $1 lower than in your answer to part b, there should be an arbitrageopportunity.SOLUTION:b. The forward price for delivery six months from now is $1,124.089:F = S(1+r) - C = $1,124.724 x 1.035 - 40 =$1,124.089c. If the forward price is only $1,123.089, then arbitrage profits can be made by selling the bond short and buying itforward at the low forward price. It can be described as follows:Sell short a bond at $1,124.724; buy it forward at $1,123.089; invest the proceeds of the short sale to earn 3.5% for6 monthsAfter 6 months, take delivery of the bond and cover your short saleForward-Spot Parity Relation with Uncertain Dividends3. A stock has a spot price of $100; the riskless interest rate is 7% per year (compounded annually), and the expected dividend on the stock is $3, to be received a year from now.a.What should be the one-year futures price?b.If the futures price is $1 higher than your answer to part a, what might that imply about the expected dividend? SOLUTION:a.S = $100, r = .07, D = $3. F = S ( 1+r) - D = $104b.If F is $105, that might imply that D is really only $2.Storage Costs versus Dividend Yield4. Compare the forward-spot price-parity relation for gold to the one for stocks. Is it fair to say that stocks have a negative storage cost equal to the dividend yield?SOLUTIONOne could definitely say that stocks have a negative storage cost equal to the dividend.5. Suppose you are a distributor of canola seed and you observe the spot price of canola to be $7.45 per bushel while the futures price for delivery one month from today is $7.60. Assuming a $.10 per bushel carrying cost, what would you do to hedge your price uncertainty?SOLUTIONWe see that F> S+C. If you short the futures contract, you can sell your seed at $7.60 per bushel.6. Infer the spot price of an ounce of gold if you observe the price of one ounce of gold for forward delivery in three months is $435.00, the interest rate on a 91-day Treasury bill is 1% and the quarterly carrying cost as a percentage of the spot price is .2%.SOLUTIONDeduce from the futures price parity condition for gold that F = S0 (1 + r + s) so that S0 = $429.84.7. You are a dealer in kryptonite and are contemplating a trade in a forward contract. You observe that the current spot price per ounce of kryptonite is $180.00, the forward price for delivery of one ounce of kryptonite in one year is $205.20, and annual carrying costs of the metal are 4% of the current spot price.a.Can you infer the annual return on a riskless zero-coupon security implied by the Law of One Price?b.Can you describe a trading strategy that would generate arbitrage profits for you if the annual return on theriskless security is only 5%? What would your arbitrage profit be, per ounce of kryptonite?SOLUTIONa.By no-arbitrage, we require that the riskless rate r satisfy:F = S0 (1 + r + s)205.2 = 180 (1 +r +.04) = 187.2 + 180rr = 18/180 = .10 or 10%b.The implicit risk-free rate that you can earn by buying kryptonite, storing it, and selling it forward at $205.2 perounce is 10%. If the riskless borrowing rate is five percent, you should borrow at that rate and invest in hedged kryptonite. If you buy an ounce of kryptonite for $180, you will get $205.2 for it for sure a year from now. If you borrow the $180, you will have to pay principal and interest of $180 x 1.05 plus another .04 x $180 in storage costs.This totals $196.2, thus leaving you with $9 in arbitrage profits.8. Calculate the implicit cost of carrying an ounce of gold and the implied storage cost per ounce of gold if the current spot price of gold per ounce is $425.00, the forward price of an ounce of gold for delivery in 273 days is $460.00, the yield over 91 days on a zero-coupon Treasury bill is 2% and the term structure of interest rates is flat. SOLUTIONFirst, we solve it assuming a simple compounding method for the risk free interest rate. Over 273 days, the Risk free rate is 2%*3=6%. Therefore we have,F = S (1 + r + s )460 = 425 (1.06 + s)s = (460 - 450.5)/425 = 9.5/425 = .02235 for 273 daysThus the carrying costs are roughly 8.24% for 273 days or 10.98% per year.Second, we solve it assuming we need to compound the interest rates. The risk free rate over 273 days will be(1+2%)3-1=6.12%.plug in the above formulae we get s=.021145 for 273 days.Thus the carrying costs are roughly 8.23% for 273 days or 11.13% per year.9. The forward price for a share of stock to be delivered in 182 days is $410.00, whereas the current yield on a 91-day T-bill is 2%. If the term structure of interest rates is fiat, what spot price for the stock is implied by the Law of One Price?SOLUTIONF = $410; r = .02 per quarter.S = F/(1+r)2 = $394.0810. You observe that the one-year forward price of a share of stock in Kramer,Inc.,a New York tour-bus company and purveyor of fine clothing, is $45.00 while the spot price of a share is $41.00. If the riskless yield on a one-year zero-coupon government bond is 5%:a.What is the forward price implied by the Law of One Price?b.Can you devise a trading strategy to generate arbitrage profits? How much would you earn per share?SOLUTIONa.The no-arbitrage value of the forward price is F = $43.05.b.The observed forward price is excessive. Consider short-selling a forward contract and taking a long position ina portfolio consisting of one stock and the sale of a bond with face value of F. Future liabilities for this positionare zero, while the current cash inflow is $1.86.11. Infer the yield on a 273-day, zero-coupon Japanese government security if the spot price of a share of stock in Mifune and Associates is 4,750 yen whereas the forward price for delivery of a share in 273 days is 5,000 yen.SOLUTIONThe implied yield over the 273 day term is r = 5.26%.12. On your first day of trading in Vietnamese forward contracts, you observe that the share price of Giap Industries is currently 54, 000 dong while the one-year forward price is 60, 000 dong. If the yield on a one-year riskless security is fifteen percent, are arbitrage profits possible in this market? If not, explain why not. If so, devise an appropriate trading strategy.SOLUTIONArbitrage profits would seem to be possible, since the no-arbitrage forward price implied by these parameters isF = $62,100.The futures contract is underpriced, relative to this no-arbitrage value. Consider taking a long position in the forward contract and simultaneously selling a share of Giap stock and buying a riskless bond with a face value equal to the observed forward price. The liabilities from these joint positions are zero, while the current cash inflow is $1826.09.13. The share price of Schleifer and Associates, a financial consultancy in Moscow, is currently 10, 000 roubles whereas the forward price for delivery of a share in 182 days is 11,000 roubles. If the yield on a riskless zero-coupon security with term to maturity of 182 days is 15%, infer the expected dividend to be paid by Schleifer and Associates over the next six months.SOLUTIONThe implied dividend is 500 roubles.14. The spot rate of exchange of yen for Canadian dollars is currently 113 yen per dollar but the one-year forward rate is 110 yen per dollar. Determine the yield on a one-year zero-coupon Canadian government security if the corresponding yield on a Japanese government security is 2.21%.SOLUTIONThe implied Canadian rate over this term is approximately 5.00%.。

CHAPTER 10AN OVERVIEW OF RISK MANAGEMENTObjectives« To explore how risk affects finan cial decisi on-mak ing.« To provide a con ceptual framework for the man ageme nt of risk.«To explain how the financial system facilitates the efficient allocation of risk-bearing.Outline10.1 What Is Risk?10.2 Risk and Econo mic Decisi ons10.3 The Risk Ma nageme nt Process10.4 The Three Dime nsions of Risk Tran sfer10.5 Risk Tran sfer and Econo mic Efficie ncy10.6 In stituti ons for Risk Man ageme nt10.7 Portfolio Theory: Quan titative An alysis for Optimal Risk Man ageme nt10.8 Probability Distributions of ReturnsSummary* Risk is defined as uncertainty that matters to people. Risk management is the process of formulating the benefit- cost trade-offs of risk-reduction and deciding on a course of action to take. Portfolio theory is the quantitative analysis of those trade-offs to find an optimal course of action.* All risks are ultimately borne by people in their capacity as consumers, stakeholders of firms and other econo mic orga ni zati ons, or taxpayers.* The risk in ess of an asset or a tra nsacti on cannot be assessed in isolati on or in the abstract; it depe nds on the specific frame of refere nee. In on e con text, the purchase or sale of a particular asset may add to one ' s risk exposure; in another, the same transaction may be risk-reducing.* Speculators are in vestors who take positi ons that in crease their exposure to certa in risks in the hope of in creas ing their wealth. In con trast, hedgers take positi ons to reduce their exposures. The same pers on can be a speculator on some exposures and a hedger on others.* Many resource-allocation decisions, such as saving, investment, and financing decisions, are significantly in flue need by the prese nee of risk and therefore are partly risk-ma nageme nt decisi ons.* We disti nguish among five major categories of risk exposures for households: sick ness, disability, and death job loss; consumer-durable asset risk ; liability risk ; and financial asset risk .* Firms face several categories of risks: production risk , price risk of outputs , and price risk of in puts .* There are five steps in the risk-management process: risk identification, risk assessment, selection of riskman ageme nt tech ni ques, impleme ntati on, review.* There are four techniques of risk management: r isk avoidanee, loss prevention and control, risk retention, risk tra nsfer.* There are three dimensions of risk transfer: hedging , insuring , and diversifying .* Diversificati on improves welfare by spread ing risks among many people, so that the existi ng un certa inty matters less. * From society ' s perspective-n^ageme nt in stituti ons con tribute to econo mic efficie ncy in two importa nt ways. First, they shift risk away from those who are least willing or able to bear it to those who are most willing to bear it. Second, they cause a reallocation of resources to production and consumption in accordance with the new distribution of risk-bearing.By allowing people to reduce their exposure to the risk of undertaking certain bus in ess ven tures, they may en courage en trepre neurial behavior that can have a ben efit to society.* Over the cen turies, various econo mic orga ni zati ons and con tractual arra ngeme nts have evolved to facilitate a more efficient allocation of risk-bearing by expanding the scope of diversification and the types of risk that are shifted.* Among the factors limit ing the efficie nt allocati on of risks are tra nsacti ons costs and problems of adverse selecti on and moral hazard.Solutions to Problems at End of ChapterOn the Nature of Risk and Risk Management1. Suppose that you and a friend have decided to go to a movie together next Saturday. You will select any movie for which tickets are available when you get to the theater. Is this a risky situation for you? Explain. Now suppose that your friend has already purchased a ticket for a movie that is going to be released this Saturday. Why is this a risky situation? How would you deal with the risk?SOLUTION:No, the uncertainty doesn ' t represienncteriysokusdo not care which movie you see. However, if your friend has a ticket already, and if you wait till Saturday to buy yours, the show may be sold out. To eliminate the risk that you may not be able to sit with your friend and see the same movie, you might buy your ticket in advance.2. Suppose you are aware of the following investment opportunity: You could open a coffee shop around the corner from your home for $25,000. If business is strong, you could net $15,000 in after-tax cash flows each year over the next 5 years.a. If you knew for certain the business would be a success, would this be a risky investment?b. Now assume this is a risky venture and that there is a 50% chance it is a success and a 50% chance you gobankrupt within 2 years. You decide to go ahead and invest. If the business subsequently goes bankrupt, did you make the wrong decision based on the information you had at the time? Why or why not?SOLUTION:a. No, this investment would not be risky.b. No, you did not make a “ wrong ” decision. When you made your decision, you did not know for certain that thecompany would go bankrupt. You decided to invest for many reasons, including the possibility of making a lot of money.Given your tolerance for risk and the fact that you based our decision on the information available at the time, your decision was not wrong and may have been optimal at the time.3. Suppose you are a pension fund manager and you know today that you need to make a $100,000 payment in 3 months.a. What would be a risk-free investment for you?b. If you had to make that payment in 20 years instead, what would be a risk free investment?c. What do you conclude from your answers to Parts a and b of this question?SOLUTION:a. A risk-free investment for you would be a Treasury Bill (default risk free) which matures in exactly 3 months.b. A risk-free investment would be a zero coupon U.S. Treasury security maturing in 20 years and which would have thesame single payment of $100,000.c. Because risk is dependent upon circumstances, what is risk-free for one individual may be risky for another too. There canbe any number of risk-free investments depending upon circumstances. Your investment time horizon is critical tochoosing the best risk-free investment (so payments in can exactly match payments out so that you are left with no risk).4. Is it riskier to make a loan denominated in dollars or in yen?SOLUTION:It depends on the context. For people whose income and expenses are denominated in dollars (perhaps because they live in the U.S), denominating a loan in yen would be riskier than denominating it in dollars. But for someone whose income and expenses are denominated in yen, denominating the loan in yen would be less risky than in dollars.5. Which risk management technique has been chosen in each of the following situations?« Installing a smoke detector in your home« Investing savings in T-bills rather than in stocks« Deciding not to purchase collision insurance on your car« Purchasing a life insurance policy for yourselfSOLUTION:« Loss preve nti on and con trol.・Risk avoida nee« Risk rete nti on・Risk tran sfer6. You are considering a choice between investing $1,000 in a conventional one-year T-Bill offering an interest rate of 8% and a one-year Index 丄inked Inflation Plus T-Bill offering 3% plus the rate of inflation.a. Which is the safer investment?b. Which offers the higher expected return?c. What is the real return on the Index 丄inked Bond?SOLUTION:a. The inflation-indexed T-Bill offers a fixed real rate of return of 3% over the life of the investment. The realreturn on the conventional T- Bill ' s real return depends upon the expected rate of inflation over the life of thein vestme nt. The safer in vestme nt is the In flati on Plus T-Bill.b. The real rate of return on the conventional T-Bill depends upon the expected rate of inflation over the life of thein vestme nt. You do not know which expected retur n is higher unl ess you know what in flati on is expected to be.c. The real retur n on the in dex-l in ked T-Bill is 3%.Hedging and Insurance7. Suppose you are interested in financing your new home purchase. You have your choice of a myriad financing options. You could enter into any one of the following agreements: 8% fixed rate for 7 years, 8.5% fixed rate for 15 years, 9% fixed for 30 years. In addition, you could finance with a 30-year variable rate that begins at 5% and increases and decreases with the prime rate, or you could finance with a 30year variable rate that begins at 6% with ceilings of 2% per year to a maximum of 12% and no minimum.a. Suppose you believe that interest rates are on the rise. If you want to completely eliminate your risk of risinginterest rates for the longest period of time, which option should you choose?b. Would you consider that hedging or insuring? Why?c. What does you r risk management decision “ cost ” you in terms of quoted interest rates during the firstyear?SOLUTION:a. You would choose the 30-year fixed rate at 9%.b. That would be a hedge because you have elim in ated both the upside (decli ning rates) or dow nside ( rising rates).c. This costs me at least 4% since I could get a variable rate loa n at 5%.8. Referring to the information in problem 7, answer the following:a. Suppose you believe interest rates are going to fall, which option should you choose?b. What risk do you face in that transaction?c. How might you insure against that risk? What does that cost you (in terms of quoted interest rates?). SOLUTION:a. You would want one of the variable rate options, in particular the variable loan tied to the prime rate, currently equal to5%.b. You face the risk of rising rates.c. You could in sure aga inst that risk by purchas ing the opti on to have a 12% ceil ing on the rate (2% in crease per year.This option cost you 1% (the difference between 6% and 5%).9. Suppose you are thinking of investing in real estate. How might you achieve a diversified real estate investment?SOLUTION:« You could own several differe nt build ings in the same gen eral area.« You could own several differe nt build ings in differe nt geographic areas.« You could sell some of your equity own ership to other owners to lower your own in dividual exposure to decli ning market values.10. Suppose the following represents the historical returns for Microsoft and Lotus Development Corporation:Historical ReturnsYear MSFT LOTS110%9%215%12%3-12%-7%420%18%57%5%a. What is the mean return for Microsoft? For Lotus?b. What is the standard deviation of returns for Microsoft? For Lotus?c. Suppose the returns for Microsoft and Lotus have normally distributed returns with means and standarddeviations calculated above. For each stock, determine the range of returns within one expected standard deviation of the mean and within two standard deviations of the mean.SOLUTION:a. Mea n return Microsoft: 8.0%; Lotus: 7.4%b. If you use the formula for the sta ndard deviati on based on a sample of size n:You find that the standard deviations are: MSFT: 10.94%; Lotus: 8.357%.However, if you use the formula for the population standard deviation:You find that the standard deviations are: MSFT 12.23% and LOTS 9.34%.c. Range of returns within 1 standard deviation Microsoft: -2.94% to +18.94% Range of returns within 1 standarddeviation Lotus: -0.957% to + 15.76% Range of returns within 2 standard deviations Microsoft: -13.88% to+29.88% Range of returns within 1 standard deviation Lotus: -9.31% to + 24.11%。

《⾦融学（第⼆版）》讲义⼤纲及课后习题答案详解⼗三章CHAPTER 13THE CAPITAL ASSET PRICING MODELObjectivesExplain the theory behind the CAPM.Explain how to use the CAPM to establish benchmarks for measuring the performance of investment portfolios. Explain how to infer from the CAPM the correct risk-adjusted discount rate to use in discounted-cash-flow valuation models. Explain the APT and its relationship to the CAPM.Outline13.1 The Capital Asset Pricing Model in Brief13.2 Determinants of the Risk Premium on the Market Portfolio13.3 Beta and Risk Premiums on Individual Securities13.4 Using the CAPM in Portfolio Selection13.5 Valuation and Regulating Rates of Return13.6 Extensions, Modifications, and Alternatives to the CAPMSummaryThe CAPM has three main implications:In equilibrium, ev eryone’s relative holding of risky assets are the same as in the market portfolio.The size of the risk-premium of the market portfolio is determined by the risk-aversion of investors.The risk premium on any asset is equal to its beta times the risk premium on the market portfolio.Whether or not the CAPM is strictly true, it provides a rationale for a very simple passive portfolio strategy: Diversify your holdings of risky assets in the proportions of the market portfolio, andMix this portfolio with the risk-free asset to achieve a desired risk-reward combination.The CAPM is used in portfolio management primarily in two ways:To establish a logical and convenient starting point in asset allocation and security selectionTo establish a benchmark for evaluating portfolio management ability on a risk-adjusted basis.In corporate finance the CAPM is used to determine the appropriate risk-adjusted discount rate in valuation models of the firm and in capital budgeting decisions. The CAPM is also used to establish a “fair” rate of return on invested capital for regulated firms and in cost-plus pricing.Today few financial scholars consider the CAPM in its simplest form to be an accurate model for explaining or predicting risk premiums on risky assets. However, modified versions of the model are still a central feature of the theory and practice of finance.The APT gives a rationale for the expected return-beta relationship that relies on the condition that there be no arbitrage profit opportunities; the CAPM requires that investors be portfolio optimizers. The APT and CAPM are not incompatible; rather, they complement each other.Solutions to Problems at End of ChapterComposition of the Market Portfolio1. Capital markets in Flatland exhibit trade in four securities, the stocks X, Y and Z, and a risklessgovernment security. Evaluated at current prices in US dollars, the total market values of these assets are, respectively, $24 billion, $36 billion, $24 billion and $16 billion.a. Determine the relative proportions of each asset in the market portfolio.b. If one trader with a $100,000 portfolio holds $40,000 in the riskless security, $15,000 in X, $12,000 in Y, and$33,000 in Z, determine the holdings of the three risky assets of a second trader who invests $20, 000 of a $200, 000 portfolio in the riskless security.SOLUTION:The total value of all assets in the economy is 100 billion dollars. a. The proportions of each asset relative to the value of all assets are, respectively, .24 (X), .36 (Y),b. .24 (Z) and .16 (riskless bond.) The proportions of each risky asset to the total value of all risky assets are, respectively, (2/7) (X), (3/7) (Y) and (2/7) (Z).c. . Ignore the question as it appears in the First Edition of the textbook. Instead, the question should be: If aninvestor has $100,000 with $30,000 invested in the riskless asset, how much is invested in securities X, Y, and Z? The answer to this question is $20,000 in X and Z, and $30,000 in Y.Implications of CAPM2. The riskless rate of interest is .06 per year, and the expected rate of return on the market portfolio is .15 per year.a. According to the CAPM , what is the efficient way for an investor to achieve an expected rate of returnof .10 per year?b. If the standard deviation of the rate of return on the market portfolio is .20, what is the standarddeviation on the above portfolio?c. Draw the CML and locate the foregoing portfolio on the same graph.d. Draw the SML and locate the foregoing portfolio on the same graph.e. Estimate the value of a stock with an expected dividend per share of $5 this coming year, an expecteddividend growth rate of 4% per year forever, and a beta of .8. If its market price is less than the value you have estimated, i.e., if it is under-priced, what is true of its mean rate of return?SOLUTION: a.So one would hold a portfolio that is 4/9 invested in the market portfolio and 5/9 in the riskless asset. b.c. The formula for the CML is9415.)1(06.10.)()1()(=+-=?+-?=x xx x r E x r r E M f 08889.)20(.94==?=M x σσσσσ45.06.)()(+=-+=MfM f r r E r r Ed. The formula for the SML ise. Use constant growth rate DDM and find r using the SML relationIf the market price of the stock is less than this, then its expected return is higher than the 13.2% required rate.()ββ09.06.)()(+=-+=f M f r r E r r E 35.54$04.132.504.510=-=-=-=r g r D P 132.8.09.06.09.06.=?+=+=βr3. If the CAPM is valid, which of the following situations is possible? Explain. Consider each situation independently. a.PortfolioExpected ReturnBeta A 0.20 1.4B 0.25 1.2b.PortfolioExpected ReturnStandard DeviationA 0.300.35B 0.400.25c.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A 0.160.12d.Portfolio Expected ReturnStandard DeviationRisk-free 0.100Market 0.180.24A0.200.22SOLUTION:a. Impossible. Since the risk premium on the market portfolio is positive, a security with a higher beta must have ahigher expected return.b. Possible. Since portfolios A & B are not necessarily efficient, A can have a higher standard deviation and alower expected return than B.c. Impossible. Portfolio A lies above the CML, implying that the CML is not efficient. If the standard deviation ofA is .12, then according to the CML its expected return cannot be greater than .14.d. Impossible. Portfolio A has a lower standard deviation and a higher mean return than the market portfolio,implying that the market portfolio is not efficient.4. If the Treasury bill rate is currently 4% and the expected return to the market portfolio over the same period is 12%, determine the risk premium on the market. If the standard deviation of the return on the market is .20, what is the equation of the Capital Market Line?SOLUTION: The risk premium on the market portfolio is .08. The slope of the CML is .08/.2 = .4. Thus, the equation of the CML is:Determinants of the Market Risk Premium5. Consider an economy in which the expected return on the market portfolio over a particular period is .25, the standard deviation of the return to the market portfolio over this same period is .25, and the averagedegree of risk aversion among traders is 3. If the government wishes to issue risk-free zero-coupon bonds with a term to maturity of one period and a face value per bond of $100,000, how much can the government expect to receive per bond? []σσσ4.04.)()(+=++=MfMf r rE r r ESOLUTION:According to the CAPM, E(r M) - r f = Aσ2, so that r f = E(r M) - Aσ2.Substituting into this formula we find: r f = .25 – 3 x .252 = .0625Therefore the revenue raised by the government per bond issued is $100,000 = $94,117.651.06256. . Norma Swanson has invested 40% of her wealth in MGM stock and 60% in Industrial Light and Magic stock. Norma believes the returns to these stocks have a correlation of .06 and that their respective means and standard deviations are: MGM ILMExpected Return (%) 10 15Standard Deviation (%) 15 25a.Determine the expected value and standard deviation of the return on Norma’s portfolio.b.Would a risk-averse investor such as Norma prefer a portfolio composed entirely of only MGM stock? Ofonly ILM stock? Why or why not?SOLUTION:a.The expected return is .13, and the standard deviation is .1649.b. A risk averse investor will not want to hold a portfolio composed entirely of MGM or of ILM stock, becauseone can, in general, achieve the same expected return with a lower standard deviation by combining a portfolio of MGM and ILM with the risk-free asset.7. Consider a portfolio exhibiting an expected return of 20% in an economy in which the riskless interest rate is 8%, the expected return to the market portfolio is thirteen percent, and the standard deviation of the return to the market portfolio is .25. Assuming this portfolio is efficient, determine:a.its beta.b.the standard deviation of its return.c.its correlation with the market return.SOLUTION:/doc/ad5801fd700abb68a982fb59.html e the security market line to infer that the beta of this portfolio is 2.4:.20 = .08 + β(.13 - .08)β = (.20 - .08)/(.13 - .08) = .12/.05 = 2.4/doc/ad5801fd700abb68a982fb59.html e the capital market line to infer that the standard deviation of the yield to this portfolio is .6:.20 = .08+ (.13 - .08) σ = .08+ .2 σ.25σ = .12/.2 = .6c.By definition the following relationships hold:β = cov/σ2Mρ = covσiσMwhere ρ denotes the correlation coefficient. We know that β = 2.4, σM = .25, and σi = .6.So from the definition of β, we get that the cov is 2.4 x .252 = .15. Substituting this into the definition of ρ: ρ = cov = .15 __ = 1σiσM .6 x .25Application of CAPM to Corporate Finance8. . The Suzuki Motor Company is contemplating issuing stock to finance investment in producing a new sports-utility vehicle, the Seppuku. Financial analysts within Suzuki forecast that this investment will have precisely the same risk as the market portfolio, where the annual return to the market portfolio is expected to be 15% and the current risk-free interest rate is 5%. The analysts further believe that the expected return to the Seppuku project will be 20% annually. Derive the maximal beta value that would induce Suzuki to issue the stock.SOLUTION:The project would be on the borderline if its required return were 20% per year. Since the risk-free rate is 5% and the risk premium on the market portfolio is 10%, the required return would be 20% if the beta were 1.5.9. . Roobel and Associates, a firm of financial analysts specializing in Russian financial markets, forecasts that the stock of the Yablonsky Toy Company will be worth 1,000 roubles per share one year from today. If the riskless interest rate on Russian government securities is 10% and the expected return to the market portfolio is 18% determine how much you would pay for a share of Yablonsky stock today if:a.the beta of Yablonsky is 3.b.the beta of Yablonsky is 0.5.SOLUTION:Use the security market line in each case to determine a required rate of return, then infer the current price from the forecasted price of 1,000 roubles and the required rate of return you have determined.a.If beta is 3, the required return is .10+ 3x.08 = .34. You would pay 1,000/1.34 = 746.27 roubles;b.If beta is .5, the required return is .10+ .5x.08 = .14. You would pay 1,000/1.14 = 877.19 roubles.Application of CAPM to Portfolio Management10. Suppose that the stock of the new cologne manufacturer, Eau de Rodman, Inc., has been forecast to havea return with standard deviation .30 and a correlation with the market portfolio of .9. If the standard deviation of the yield on the market is .20, determine the relative holdings of the market portfolio and Eau de Rodman stock to form a portfolio with a beta of 1.8.SOLUTION: By definition:β = cov/σ2Mρ = covσrσMTherefore, β = ρσr/σM. The beta of Rodman stock is therefore .9x.3/.2 = 1.35.The beta of a portfolio is a weighted average of the betas of the component securities. Let A be a fraction of the portfolio invested in Rodman stock to produce a beta of 1.8. Then we have:1.35A + (1-A) = 1.8.35A = .8A = 2.286So the portfolio would have to have 228.6% invested in Rodman stock and a short position in the market portfolio equal to 128.6%.11. The current price of a share of stock in the Vo Giap Clothing Company of Vietnam is 50 dong and its expected yield over the year is 14%. The market risk premium in Vietnam is 8% and the riskless interest rate 6%. What would happen to the stock’s current price if its expected future payout remains co nstant while the covariance of its rate of return with the market portfolio falls by 50%?SOLUTION:Deduce that the expected future price of a share of Vo Giap is 57 dong, so that a reduction in this stock’s beta of 50% implies, by the security market relation, that the required yield on Vo Giap is now 10%, so that its current share price rises by 3.64% toa new value of 51.82 dong.12. Suppose that you believe that the price of a share of IBM stock a year from today will be equal to the sumof the price of a share of General Motors stock plus the price of a share of Exxon, and further you believethat the price of a share of IBM stock in one year will be $100 whereas the price of a share of General Motors today is $30. If the annualized yield on 91-day T-bills (the riskless rate you use) is 5%, the expected yield on the market is 15%, the variance of the market portfolio is 1, and the beta of IBM is 2, what price would you be willing to pay for one share of Exxon stock today?SOLUTION:Expected return = .05 + 2(.15 - .05) = 25%; (100 - x)/x = .25 → x = $80Deduce that the current price of a share of IBM stock is $80, so that the upper bound on the price of a share of Exxon is ($80 -$30 = $50).13. Ascertain whether the following quotation is true or false, and state why:“When arbitrage is absent from financial markets, and investors are each concerned with only the risk and return to their portfolios, then each investor can eliminate all the riskiness of his investments through diversification, and as a consequence the expected yield on each available asset will depend only on the covariance of its yield with the covariance of the yield on the diversified portfolio of risky assets each investor holds.”SOLUTION:False. You cannot eliminate all risk through diversification, only the unsystematic risk.Application of CAPM to Measuring Portfolio Performance14. During the most recent 5-year period, the Pizzaro mutual fund earned an average annualized rate of return of 12% and had an annualized standard deviation of 30%. The average risk-free rate was 5% per year. The average rate of return in the market index over that same period was 10% per year and the standard deviation was 20%. How well did Pizzaro perform on a risk-adjusted basis?SOLUTION:Compute the ratio of average excess return to standard deviation for Pizzaro and compare it to that of the market portfolio: Pizzaro risk-adjusted performance ratio = (.12-.05)/.30 = .233Market portfolio risk-adjusted performance ratio = (.1-.05)/.2 = .250So, on a risk-adjusted basis, Pizzaro did worse than the market index.Challenge ProblemCAPM with only 2 Risky Assets15. There are only two risky assets in the economy: stocks and real estate and their relative supplies are 50% stocks and 50% real estate. Thus, the market portfolio will be half stocks and half real estate. The standard deviations are .20 for stocks, .20 for real estate, and the correlation between them is 0. The coefficient of relative risk aversion of the average market participant (A) is 3. r f is .08 per year.a.According to the CAPM what must be the equilibrium risk premium on the market portfolio, on stocks,and on real estate?b.Draw the Capital Market Line. What is its slope? Where is the point representing stocks located relativeto the CML?c.Draw the SML. What is its formula? Where is the point representing stocks located relative to the SML? SOLUTION: a.The market portfolio consists of half stocks and half real estate. It has a standard deviation of .1414, computedas follows:σ2M = w2σ2s + (1-w)2σ2r+ 2 w(1-w) cov s,rσ2M = 2 x (1/2)2 .22 = .02σM = .1414The equilibrium risk premium on the market portfolio is E(r M)-r f = Aσ2M = 3x.02 = .06.The market portfolio’s expected rate of return is also a weighted average of the expected rates of return on stocks and real estate, where the weights are each 1/2. Stocks and real estate must have the same risk premiumbecause they have the same standard deviation and correlation with the market. Therefore the risk premium on stocks and real estate must be .06, the same as the market portfolio’s risk premium.b.The slope of the CML is .06/.1414 = .424. The point representing stocks is M, it is to the right of the CML.equaling to 1.The formula is: E(r) = r f + (E(r M) –r f).。

CHAPTER 5LIFE-CYCLE FINANCIAL PLANNINGObjectivesIn this chapter you will learn how to analyze:•How much to save for retirement.•Whether to defer taxes or pay them now.•Whether to get a professional degree.•Whether to buy or rent an apartment.•How to minimize estate taxes.Outline5.1 A Life-Cycle Model of Saving5.2 Taking Account of Social Security5.3 Deferring Taxes Through Voluntary Retirement Plans5.4 Should You Invest in a Professional Degree?5.5 Should You Buy or Rent?Summary•In making lifetime saving/consumption decisions:(1) Do the analysis in real terms (constant dollars) to simplify the calculations and to avoid having toforecast inflation.(2) Start by computing the present value of your lifetime resources. The present value of your lifetimespending cannot exceed this amount.•Social security or any other forced saving program will offset voluntary saving. It may have a positive or a negative effect on the present value of your total lifetime resources.•Tax-deferred retirement accounts are advantageous because they allow you to earn a before-tax rate of return until money is withdrawn from the account. They are advantageous if you are in the same tax bracket before and after you retire, and even more so if your tax bracket is lower after you retire. •Getting a professional degree can be evaluated as an investment in human capital. As such, it should be undertaken if the present value of the benefits (such as increase in your earnings) exceeds the present value of the costs (such as tuition and forgone salary.)•In deciding whether to buy or rent an apartment or a consumer durable, choose the alternative with the lower present value of costsSolutions to Problems at End of ChapterSaving for Retirement1. Assume that you are 40 years old and wish to retire at age 65. You expect to be able to average a 6% annual rate of interest on your savings over your lifetime (both prior to retirement and after retirement). You would like to save enough money to provide $8,000 per year beginning at age 66 in retirement income to supplement other sources (social security, pension plans, etc.). Suppose you decide that the extra income needs to be provided for only 15 years (up to age 80). Assume that your first contribution to the savings plan will take place one year from NOW.a.How much must you save each year between now and retirement to achieve your goal?b.If the rate of inflation turns out to be 6% per year between now and retirement, how much willyour first $8000 withdrawal be worth in terms of today’s purchasing power?SOLUTION:a. Age 40 41 65 66 80Time 0 1 25 26 40. . . .X X 8,000 8,000It is a 2 part computation. First compute the amount needed at age 65 to finance the $8,000 per year annuityin terms of today’s purchasing power.2. You are saving for retirement and you come across the following table. It shows the percentage of your current salary that you should save for your retirement in order to retire with an annuity equal to 70% of your salary if you have not yet saved anything. It assumes that your annual salary will remain constant in real terms until retirement, and that you will live for 25 years after retiring. For instance, if you have 35 years left before you retire and earn3.5% per year on your investments, then you should save 17.3% of your current salary.a. Fill in the missing number in Table A.SOLUTION:The method for computing how much saving is needed to reach the desired target (70%) consists of two steps:First compute the amount you need to have accumulated in your personal retirement account when you reach the retirement age. (We’ll do the calculations as percentages of real salary)Then compute the annual amount of saving needed to reach that future value59.79% if you have 15 years to retire29.62% if you have 25 years to retire17.30% if you have 35 years to retireb. Now fill in Table B. It assumes that instead of targeting a 70% replacement rate of preretirement income, your goal is to maintain the same level of consumption spending both before and after retirement.First compute the amount you need to have accumulated in your personal retirement account when you reach the retirement age. (We’ll do the calculations as percentages of real salary)Then compute the annual amount of saving needed to reach that future value85.41% if you have 15 years to retire42.31% if you have 25 years to retire24.72% if you have 35 years to retire3. You are saving for retirement and you come across the following the table. It shows the increase in the annual benefit you can receive in retirement per dollar that you increase your annual retirement saving in the years before retirement. It assumes that you will live for 20 years after retiring. For instance, if you have 30 years left before you retire and earn an interest rate of 3% per year, then you will obtain an increase of $3.20 in your annual retirement benefit for every $1 per year increase in annual saving. Fill in the missing table values.4. George Thriftless is 45 years old, earns $50,000 per year, and expects that his future earnings will keep pace with inflation, but will not exceed inflation. He has not yet saved anything towards his retirement. His company does not offer any pension plan. George pays Social Security taxes equal to 7.5% of his salary, and he assumes that when he retires at age 65, he will receive $12,000 per year in inflation-adjusted Social Security benefits for the rest of his life. His life expectancy is age 85.George buys a book on retirement planning that recommends saving enough so that when private savings and Social Security are combined, he can replace 80% of his preretirement salary. George buys a financial calculator and goes through the following calculations:First, he computes the amount he will need to receive in each year of retirement to replace 80% of his salary: .8 x $50,000 = $40,000.Since he expects to receive $12,000 per year in Social Security benefits, he calculates that he will have to provide the other $28,000 per year from his own retirement fund.Using the 8% interest rate on long-term default-free bonds, George computes the amount he will need to have at age 65 as $274,908 (the present value of $28,000 for 20 years at 8% per year). Then he computes the amount he will have to save in each of the next 20 years to reach that future accumulation as $6,007 (the annual payment that will produce a future value of $274,908 at an interest rate of 8% per year). George feels pretty confident that he can save 12% of his salary (i.e., $6,007/$50,000) in order to insure a comfortable retirement.a.If the expected long-term real interest rate is 3% per year, approximately what is the long-term expected rate of inflation?b.Has George correctly taken account of inflation in his calculations? If not, how would youcorrect him?c.How much should George save in each of the next 20 years (until age 65) if he wants tomaintain a constant level of consumption over the remaining 40 years of his life (from age 45 to age 85)?Ignore income taxes.SOLUTION:a. The long-term expected rate of inflation can be approximated by subtracting the expected real rate ofinterest (3% per year) from the long-term nominal interest rate (8% per year). The expected rate of inflation is therefore approximately 5% per year.The exact value can be calculated using:1+nom= (1+real)(1+inf)hence, the inflation rate is 4.854% per year.b. George has used the nominal interest rate to discount real cash flows. As a result, he has seriouslyunderestimated how much saving he must do to achieve an 80% replacement rate. The time line for this problem is:Age 45 46 65 66 85Time 0 1 20 21 40. . . .X X 28,000 28,000Using the real rate of 3% per year in the calculations results in a needed accumulation at age 65 of $416,569.30:The annual saving needed to achieve this accumulation at a 3% real rate is $15,502.92:So instead of $6,007 per year, George must save $15,502.92 per year. This is 31% of his salary rather than 12%.c. The time line for this problem is:Age 45 46 65 66 85Time 0 1 20 21 40. . . .Inflows 46,250 46,250 12,000 12,000Outflows C CIf George wants to maintain a constant level of consumption both before and after retirement, he must find C , where C is the solution to the following equation:∑∑∑===+=40140212010310001203125046031t t tt t t .,.,.C Equation 1 says that the present value of consumption spending over the next 40 years equals the present value of labor income over the next 20 years (after paying Social Security taxes) plus the present value of Social Security benefits received after retirement.First we find the value on the right side of the equation, the PV of George’s lifetime resources:Step 4: Find PV of lifetime resources as of age 45:688,083.21 + 98,847.56 = 786,930.78So each year between the ages of 46 and 65 George must save $12,205.50, the difference between his income after SS tax ($46,250) and his consumption spending ($34,044.50).Now let us check to make sure that by saving this amount George will indeed have enough to provide the same constant level of consumption spending after retirement as before.Thus, by saving $12,205.50 per year for 20 years earning a real rate of 3% per year, he will have at age 65 an accumulation of $327,966.36.Adding this annuity to the SS benefit we get:$22,044.50 + $12,000 = $34,044.505. George’s company has a defined-benefit pension plan. Suppose the plan pays a benefit equal to 1% of final salary per year of service. George is 40 years old and has worked for the company for 15 years. His last year’s salary was $50,000 and is expected to remain so in real terms until retirement. The expected rate of inflation is 4%.a.If normal retirement age is 65, the interest rate is 8%, and Geor ge’s life expectancy is 80, what isthe present value of his accrued pension benefit?b.What effect should his pension benefit have on George’s planned saving assuming he has a 75%target replacement rate?SOLUTION:a.George’s last year salary $50,000 has a r eal growth rate of 0%, hence it will keep up with inflation untilretirement but not beat it. At retirement, he would have worked for the company for a total of forty years. Hence his annual pension benefit will be equal to 1% x (50,000x 1.0425) x 40 = $53,316.73. We must first find the value of those annual payments in the year when he retires, then discount that back to today.PV65 = $456,363.4140b.For a 75% replacement rate, George expects to have an annual income of 0.75 x 50,000 =$37,500 inreal terms after retirement. Since his pension benefit is providing him with part of his financial needs after retirement, he would only need to worry about the difference between his target income and what the pension is providing him, hence decreasing his planned savings before retirement.6.Analyze the “expert’s” responses to the following questions:Question: How early do you recommend people begin saving for retirement? Would it be too early for my 14-year-old to start saving?Expert: It’s never too early.Question: For a college student , what would you suggest for a savings plan?Expert: I’d suggest deciding on a specific a mount to set aside each month, then making sure you do it, no matter the temptations not to.SOLUTION:a.Because of the time value of money, obviously, the earlier you start saving for retirement the morevalue you’ll have for each dollar saved.Suppose you save $1 at age 15 and you expect to retire at age 65, this dollar will be worth at 8% interest rate $46.9. Of course there’s a trade-off because you’ll also be postponing your spending (enjoying life) to your retirement.b.Again, because of the time value of money, each dollar you save as a college student will earn youmore than a dollar saved later on in your life. That’s why, you must decide on a certain amount you can afford to save and stick with it.Investing in Human Capital7. You are 30 years old and are considering full-time study for an MBA degree. Tuition and other direct costs will be $15,000 per year for two years. In addition you will have to give up a job with a salary of $30,000 per year. Assume tuition is paid and salary received at the end of the year. By how much does your salary have to increase (in real terms) as a result of getting your MBA degree to justify the investment? Assume a real interest rate of 3% per year and ignore taxes. Also assume that the salary increase is a constant real amount that starts after you complete your degree (at the end of the year following graduation) and lasts until retirement at age 65.SOLUTION:Buy or Rent?8. Suppose you currently rent an apartment and have an option to buy it for $200,000. Property taxes are $2,000 per year and are deductible for income tax purposes. Annual maintenance costs on the property are $1,500 per year and are not tax deductible. You expect property taxes and maintenance costs to increase at the rate of inflation. Your income tax rate is 40%, you can earn an after-tax real interest rate of 2% per year, and you plan to keep the apartment forever. What is the “break-even” annual rent such that you would buy it if the rent exceeds this amount? SOLUTION:The after-tax annual outlay if you buy is:$1,500 + .6 x $2,000 = $2,700The PV of this is $2700/.02 = $135,000.The PV of the costs of owning are $135,000 + $200,000 = $335,000.The break-even rent is .02 x $335,000 = $6,700 per year.Buy or lease a car9. You have decided to acquire a new car which costs $30,000. You are considering whether to lease it for 3 years or to purchase it and finance the purchase with a 3-year installment loan. The lease requires no down payment and lasts for 3 years. Lease payments are $400 monthly starting immediately, whereas the installment loan will require monthly payments starting a month from now at an annual percentage rate (APR) of 8%.a.If you expect the resale value of the car to be $20,000 3 years from now, should you buy or leaseit?b.What is the break-even resale price of the car 3 years from now, such that you would beindifferent between buying and leasing it?SOLUTION:a.We have to compare the NPVs of the two alternatives:Since in this case, the car is costing me more, I should choose the first alternative of leasing the car.b. In order to be indifferent among the two alternatives, their respective NPV must be equal, i.e. –12,850.Hence, the PV of the resale price is 30,000-12,850=17,15010. Analyze the following newspaper column:“Many of us who started families late share a nightmare image: having to pay huge college bills just as we’re giving up paychecks and shouldering the ste ep costs of retirement. In fact, the double whammy might not be so bad, assuming the parents have prepared properly. On the plus side, older parents are likely to have enjoyed their best earnings years before the college costs begin, allowing them to put a side more than younger parents can. They’ve also had more years for investments to compound. In the ideal situation, older parents can avoid borrowing to meet college costs, taking the preferred route of earning interest on investments rather than paying i t on student loans.” (Excerpted from Jeff Brown’s Personal Finance column in the Philadelphia Inquirer, May 11, 1998.) SOLUTION:As it is mentioned in the newspaper column, ideally older parents can avoid borrowing to meet college costs provided that they had prepared properly and started saving early in their lives.However, one can argue that with no children in the household, parents have less incentive to save (and enjoy their younger years) and might in fact be faced with this nightmare image of having to pay huge college bills just as they are giving up paychecks.11. Analyze the following newspaper column:“What’s the best age for a person to start collecting Social Security benefits? According to conventional wisdom, retirement starts at age 65. I t’s true that full benefits don’t start until age 65, but 62 year olds can retire and collect 80% of their benefits.Take the hypothetical cases of John and Mary, who have the same birthday and who are both slated to start drawing $1,000 a month in Social Security benefits at age 65. On his 62nd birthday, John decides to go ahead and start claiming his benefits of $800 a month (80% of $1000). Mary decides to wait until she’s 65, when she can claim the full $1000. Three years later, Mary turns 65 and begins receiving $1,000 a month from the Social Security Administration. John continues to receive $800 a month. But he has already been paid $28,800 while Mary received nothing.Five years go by, with Mary drawing $1,000 a month and John $800 a month. At 70, John has received $76,800, compared to Mary’s $60,000. When they reach 77, Mary will pull ahead. So, it seems if a person doesn’t live past 76, it would better to start collecting Social Security benefits at 62. For those who reach their upper 70’s, it pays to wait until they are 65 to collect Social Security. (adapted from 1998, Atlanta Business Chronicle, Gary Summer Contributing writer, June 29, 1998.) SOLUTION:The analysis in this newspaper column ignores the time value of money. The best way to look at this situation is to assume an interest rate, say 5%.The FV at age 65 of the $800 payments that John was taking is:At age 65, when Mary decides to start receiving the benefits from SSA, John has been paid $31,003. Not $28,800 as mentioned in the article.Now, in order to see when Mary will pull ahead, we have to see how many $200 payments (=1000-800) are the $31,003 worth.After 250 month, i.e. at age 85 and 10 months, Mary will eventually pull ahead.Personal Balance Sheets12. Using the finance concepts presented in this chapter, construct a personal balance sheet showing your assets, liabilities and net worth.a.Did you value your assets at cost or at current market value? Why?b.Did you include your human capital as an asset? Why?c.Did you include deferred taxes as a liability? Why?a.I valued my assets at current market value because their cost is irrelevant to me.b.Even though human capital is probably anyone’s biggest asset, I didn’t include it in the balance sheetbecause it’s uncert ain, hard to quantify and I will need to make too many assumptions concerning the PV of my future earnings.c.Once again, I haven’t.Home ownership Over the Life Cycle13. Suppose you buy a house for $200,000 when you are 35 years old. You make a 20% down payment and borrow the other 80% from a mortgage lender. The mortgage loan is at a fixed interest rate of 8% per year for 30 years and requires level annual payments. At age 65, you plan to take out a “reverse-mortgage” loan which will allow you to borrow a constant annual amount for the rest of your life to be paid off by the sale of your house when you die. Your life expectancy is age 85. The interest rate on both the original mortgage loan and the reverse mortgage will be 8% per year.a.Suppose that you expect the inflation rate to be 3% per year and you can rent an equivalenthouse for $10,000 per year. Is it worth buying the house?b.Show how buying the house will affect your assets, liabilities and cash flow over the next 50 years.c.In Making the Most of your money, JB Quinn has written: “ Over the long run, the value ofhomes should follow the inflation rate. But over the time that you won your particular house, its value might rise or fall or stall. You can’t predict. But there are reasons other than profit for owning a house.•Mortgage payments force to save, while rental payments don’t.•You get tax deductions, and can tax-shelter your capital gains.•You’re landlord free.•You know the deep contentment of holding a spot of ground that others can enter by invitation only.•You won’t lose your lease.•You can renovate to suit.• A house is collateral for a loan.Comment.SOLUTION:a.In order to compare the two alternatives, we have to compare their NPVs.Buy Alternative:Basically, this alternative consists of buying the house now at $200,000 and selling it 50 years from now at its market value, accounting for inflation:The FV of the house is:The house will be worth : $876,781 when you are 85.Now, to calculate the NPV of this alternative, we have to discount at 8% to account for the mortgage and the reverse mortgage.Hence the NPV of this option is: -200,000 + 18,694 = -181,306Rent Alternative:We assume that rent will be $10,000 in real terms and hence must be discounted at the real interest rate = 4.854%Hence, it is more economical to buy the house.c. Most of the points mentioned by JB Quinn were discussed in this exercise, namely the fact thatmortgage payments force you to save and that a house can serve as collateral for a loan. She also presents in his discussion some “intangible” benefits from owning a house such as not having a landlord and renovating to suit.。