金融数学引论答案第二版

合集下载

金融学习题集及参考答案解析word版第二版

金融学习题集及参考答案解析（第二版）金融学习题集（第二版）带★内容为非金融学专业选做题目第一章货币概述一、单项选择题（在每小题列出的四个备选项中只有一个是最符合题目要求的，请将其代码写在题后的括弧内。

）1．金融的本源性要素是【】A. 货币B. 资金C. 资本D. 市场2．商品价值最原始的表现形式是【】A. 货币价值形式B. 一般价值形式C.总和的或扩大的价值形式D. 简单的或偶然的价值形式3．一切商品的价值共同表现在某一种从商品世界中分离出来而充当一般等价物的商品上时，价值表现形式为【】A. 货币价值形式B. 一般价值形式C.总和的或扩大的价值形式D. 简单的或偶然的价值形式4．价值形式的最高阶段是【】A. 货币价值形式B. 一般价值形式C.总和的或扩大的价值形式D. 简单的或偶然的价值形式5．货币最早的形态是【】A. 实物货币B.代用货币C.信用货币D. 电子货币6．最适宜的实物货币是【】A. 天然贝B. 大理石C. 贵金属D. 硬质合金硬币7．中国最早的货币是【】A. 银圆B. 铜钱C. 金属刀币D. 贝币8．信用货币本身的价值与其货币价值的关系是【】A. 本身价值大于其货币价值B.本身价值等于其货币价值C. 本身价值小于其货币价值D. 无法确定9．在货币层次中M0是指【】A. 投放的现金B. 回笼的现金C. 流通的现金D. 贮藏的现金10．从近期来看，我国货币供给量相含层次指标系列中观察和控制的重点是【】A. M0B. M1C. M2D. M0和M111．从中长期来看，我国货币供给量相含层次指标系列中观察和控制的重点是【】A. M0B. M1C. M2D. M0和M112．货币在表现商品价值并衡量商品价值量的大小时，发挥的职能是【】A. 价值尺度B. 流通手段C. 贮藏手段D. 支付手段13．货币在充当商品流通媒介时发挥的职能是【】A. 价值尺度B. 流通手段C. 贮藏手段D. 支付手段14．当货币退出流通领域，被持有者当作独立的价值形态和社会财富的绝对值化身而保存起来时，货币发挥的职能是【】A. 价值尺度B. 流通手段C. 贮藏手段D. 支付手段15．货币在支付租金、赋税、工资等的时候发挥的职能是【】A. 价值尺度B. 流通手段C. 贮藏手段D. 支付手段16．观念货币可以发挥的职能是【】A. 价值尺度B. 流通手段C. 贮藏手段D. 支付手段17．货币最基本、最重要的职能是【】A. 价值尺度B. 流通手段C. 贮藏手段D. 支付手段18．“劣币驱逐良币现象”产生的货币制度背景是【】A. 银本位B. 平行本位C. 双本位D. 金本位19．最早实行金币本位制的国家是【】A. 美国B. 英国C. 中国D. 德国20．人民币是【】A. 实物货币B. 代用货币C. 金属货币D. 信用货币二、多项选择题（在小题列出的五个备选项中，至少有二个是符合题目要求的，请将其代码写在题后的括弧内。

金融学第二版讲义大纲及课后习题答案详解第八章

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.。

《金融学(第二版)》讲义大纲及课后习题答案详解十四章

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%.。

金融学第二版课后习题答案

金融学第二版课后习题答案金融学第二版课后习题答案金融学是一门研究金融市场、金融机构和金融工具的学科，它对于理解和解决现代金融问题具有重要意义。

而课后习题则是帮助学生巩固所学知识、提高解决问题能力的重要工具。

本文将为读者提供金融学第二版课后习题的答案，以帮助读者更好地理解金融学的概念和理论。

第一章：金融的基本概念和职能1. 金融的基本概念是指金融的定义和范围。

金融的定义是指金融活动和金融制度的总称。

金融的范围包括金融市场、金融机构和金融工具等。

2. 金融的职能是指金融对于经济发展和社会进步的作用。

金融的主要职能包括储蓄和融资、支付和结算、风险管理和信息中介等。

第二章：金融市场1. 金融市场的分类包括货币市场、资本市场和衍生品市场等。

货币市场是指短期资金融通的市场，资本市场是指长期资金融通的市场，衍生品市场是指金融衍生品交易的市场。

2. 金融市场的功能包括资源配置、风险管理和信息传递等。

资源配置是指将资金从供给者转移给需求者的过程，风险管理是指通过金融市场进行风险的转移和分散，信息传递是指金融市场通过价格和交易信息传递经济信息。

第三章：金融机构1. 金融机构的分类包括银行、非银行金融机构和金融市场机构等。

银行是最重要的金融机构，它包括商业银行、中央银行和政策性银行等。

2. 金融机构的职能包括储蓄和融资、支付和结算、风险管理和信息中介等。

储蓄和融资是指金融机构接受存款并提供贷款的过程，支付和结算是指金融机构提供支付和结算服务的过程，风险管理是指金融机构通过风险评估和风险转移来管理风险，信息中介是指金融机构通过收集、加工和传递信息来提供金融服务。

第四章：金融工具1. 金融工具的分类包括货币工具、债券、股票和衍生品等。

货币工具是指短期借贷和短期投资的金融工具，债券是指借款人向债权人发行的债务凭证，股票是指公司向股东发行的所有权凭证，衍生品是指衍生自其他金融资产的金融工具。

2. 金融工具的特点包括流动性、收益性和风险性等。

金融数学引论答案 .docx

第一章习题答案1.设总量函数为A(t) = t2 + 2/ + 3 o试计算累积函数a(t)和第n个吋段的利息【仇°解：把t =()代入得4(()) = 3于是：4(t) t? + 2t + 3啲=丽=3In = 4(北)一A(n一1)=(n2 + 2n + 3) — ((n — I)2 + 2(n — 1) + 3))= 2n+l2.对以下两种情况计算从t时刻到冗(£ < n)时刻的利息：(1)厶(0 < r < n);(2)/r =2r(0<r <n).解：(1)I = A(n) - A(t)—In + in-1+ • • • + A+l n(n + 1) t(t + 1)=2 2I = A(n) - A(t)n n=乞h = 土hk=t+l A：=t+13.已知累积函数的形式为：Q(t) = at2 +几若0时刻投入的100元累积到3吋刻为172元,试计算：5时刻投入的10()元在10时刻的终值。

解：由题意得。

(0) = 1, «(3) = = L72=> a = 0.0& 6=14(5) = 100>1(10) = 4(0) • «(10) = 4⑸• W = 100 x 3 = 300.a(5)4.分别对以下两种总量函数计算订和讪:(1) A(t) = 100 + 5t; (2) A(t) = 100(1 + 0.1尸・解：(1)_ 4(5) - 4(4)5 _ 4(4)5二面-.17% . 4(10)-4(9)210 =—4(9)—5=—^ 3.45%145⑵_ 4(5) - 4(4)5 - 4⑷_ 100(1 + 0.1)5 - 100(1 + 0.1)4 = 100(1+ 0.1)4=10%. 4(10) —4(9)皿=_ 100(1+ O.1)10-100(1+ 0.1)9 = 100(1 + 0.1)9=10%5•设4(4) = 1000, i n = O.Oln.试计算4(7)。

金融学第二版讲义大纲及课后习题答案详解第十章

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%。

《金融数学》(第二版)练习题(修订版)

⎧kt,
1.18
假设利息力为 δt
=
⎪
⎨ ⎪⎩
1 25
kt
2
,
0<t ≤5 ，期初存入单位 1 在第 10 年末将会累积到 2.7183。试求 k。
5 < t ≤ 10
1.19
已知利息力为 δt
=
1 2+t
，一笔金额为
1
的投资从 t=0
开始的前
n
年赚取的总利息是
8。试求
n。
1.20 1996 年 1 月 1 日，某投资者向一个基金存入 1000，该基金在 t 时刻的利息力为 0.1(t −1)2 ，求 1998 年 1 月 1 日的累积值。
1.7 基金 A 以每月复利一次的名义利率 12 %累积。基金 B 以 δt = t / 6 的利息力累积。在零时刻，分别存入 1 到两个基金中。请问何时两个基金的金额
1
将相等。
1.8
基金
A
以δ t
=
a
+ bt
的利息力累积。基金
B
以δ t
=
g
+
ht
的利息力累积。基金
A
与基金
B
在零时刻和
n
时刻相等。已知 a
3
2.2 某人将在 10 年后退休。他打算从现在开始每年初向一种基金存入 2000 元，如果基金的收益率为 6%，试计算他在退休时可以积存多少退休金。 2.3 某人从 2000 年 3 月 1 日起，每月末可以领取 200 元，2010 年 5 月末是最后一次领取。如果每月复利一次的年名义利率为 6%，试计算：（1）年金的现值；（2）年金的终值；（3）年金在 2005 年 12 月 31 日的值。 2.4 某人在今后的 20 年内，每年初向一基金存入 10000 元。从第 30 年开始，每年末可以领取一笔退休金。该基金的收益率为 6%。（1）如果限期领取 20 年，每次可以领取多少？（2）如果无限期地领下去（当他死亡后，由其继承人领取），每次可以领取多少？ 2.5 某人留下了 10 万元的遗产，遗嘱规定，该笔遗产前 5 年的利息收入由其长子领取，第二个 5 年的利息由其次子领取，从第 11 年开始，剩余遗产全部归第三个儿子。如果年实际利率为 8%，试计算三个儿子在该笔遗产中分别占多大份额？ 2.6 如果年实际利率为 i，那么一笔在 36 年内每年末支付 4000 元的年金，与另一笔在 18 年内每年末支付 5000 元的年金将有相等的现值。试计算 1000 元的投资在年实际利率为 i 时，经过多长时间可以翻番。 2.7 借款人原计划在每月末偿付 1000 元，用 5 年的时间还清贷款。每月复利一次的年名义利率为 12%。如果他现在希望一次性支付 60000 元还清贷款，他应该在何时偿还？ 2.8 投资者每月初往基金存入一笔款项，5 年后可以积存到 60000 元。如果前 2 年每次存入 1000 元，后 3 年每次存入 500 元。试计算每月复利一次的名义利率。 2.9 投资者每年末向一基金存入 2000 元，如果在前 2 年的投资按 6%的年实际利率计算，在后两年的投资按 5%的年实际利率计算，投资者在第 4 年末可以积存多少价值？ 2.10 一项 10 年期的年金，在前 5 年的每季度末付款 1000 元，后 5 年的每季度末付款 2000 元。如果年实际利率为 5%，试计算该项年金的现值。 2.11 一项每 3 年末支付 1 元的永续年金，其现值为 125/91，试确定年实际利率是多少？ 2.12 某人将一笔遗产（每年末可以领取的永续年金）捐赠给了四家慈善机构 A，B，C 和 D。在前 n 年，每次领取的款项由 A、B、C 三家平均分享，n 年以后，剩余部分均由 D 领取。试确定当(1 + i) n 为多少时，A、B、C、D 四家在该遗产中享有的现值相等。假设年实际利率为 8%。 2.13 一项永续年金在每月初付款 1 元，如果每年结转四次利息的年名义利率为 4%，试计算该项年金的现值。

国际金融第二版课后答案(全)

国际金融第二版课后答案（全）国际金融习题答案第一章国际收支本章重要概念国际收支：国际收支是指一国或地区居民与非居民在一定时期内全部经济交易的货币价值之和。

它体现的是一国的对外经济交往，是货币的、流量的、事后的概念。

国际收支平衡表：国际收支平衡表是将国际收支根据复式记账原则和特定账户分类原则编制出来的会计报表。

它可分为经常项目、资本和金融项目以及错误和遗漏项目三大类。

丁伯根原则：1962年，荷兰经济学家丁伯根在其所著的《经济政策：原理与设计》一书中提出：要实现若干个独立的政策目标，至少需要相互独立的若干个有效的政策工具。

这一观点被称为“丁伯根原则”。

米德冲突：英国经济学家米德于1951年在其名著《国际收支》当中最早提出了固定汇率制度下内外均衡冲突问题。

米德指出，如果我们假定失业与通货膨胀是两种独立的情况，那么，单一的支出调整政策（包括财政、货币政策）无法实现内部均衡和外部均衡的目标。

分派原则：这一原则由蒙代尔提出，它的含义是：每一目标应当指派给对这一目标有相对最大的影响力，因而在影响政策目标上有相对优势的工具。

自主性交易：亦称事前交易，是指交易当事人自主地为某项动机而进行的交易。

国际收支失衡：国际收支失衡是指自主性交易发生逆差或顺差，需要用补偿性交易来弥补。

它有不同的分类，根据时间标准进行分类，可分为静态失衡和动态失衡；根据国际收支的内容，可分为总量失衡和结构失衡；根据国际收支失衡时所采取的经济政策，可分为实际失衡和潜在失衡。

复习思考题1．一国国际收支平衡表的经常账户是赤字的同时，该国的国际收支是否可能盈余，为什么？答：可能，通常人们所讲的国际收支盈余或赤字就是指综合差额的盈余或赤字.这里综合差额的盈余或赤字不仅包括经常账户，还包括资本与金融账户，这里，资本与金融账户和经常账户之间具有融资关系。

但是，随着国际金融一体化的发展，资本和金融账户与经常账户之间的这种融资关系正逐渐发生深刻变化。

一方面，资本和金融账户为经常账户提供融资受到诸多因素的制约。

金融学第二版讲义大纲及课后习题答案详解十六章

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 inv estme nt decisi ons.Outline16.1 In ternal versus Exter nal Financing16.2 Equity Financing16.3 Debt Finan ci ng16.4 The Irrelevance of Capital Structure in a Frictionless Environment16.5 Creati ng Value through Financing Decisi ons16.6 Reduci ng Costs16.7 Dealing with Conflicts of Interest16.8 Creat ing New Opport un ities for Stakeholders16.9 Financing Decisi ons in Practice16.10 How to Evaluate Levered Inv estme ntsSummary•Exter nal financing subjects a corporati on investme nt pla ns 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 corporati on, such as acco unts payable, leases, and pensions.•In a frictionless financial environment, where there are no taxes or transaction costs, and con tracts are costless to make and en force, 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 shareholdere/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 alter native methods used in estimat ing the net prese nt value of an inv estme nt project to take acco unt of finan cial leverage: the adjusted prese nt 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 assetsThere are 1,000,000 shares of Divido common stock outstanding, each with a market price of $100.ivido 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 Divid6s EBIT has an equal probability of being $20 million, or $12million, or $4million .Show the impact of the financial restructuring on theprobability distribution of earnings per share in the absence of taxes .Why does the fact that the equity becomes riskier not necessarily affect shareholder wealth? SOLUTION:a. In an M&M fricti onl ess en vir onment, where there are no taxes and con tracts arecostless to make and en force, the wealth of shareholders is the same no matter what capital structure the firm adopts. In such an environment, neitherthe stock price nor shareholders ' wealth would be affected. In the real world Divido ' s management might bieab create shareholder value by issuing debt andrepurchas ing shares in two ways:By reduc ing tax costsBy reduc ing the free cash flow available to man ageme nt and expos ing itself togreater market discipli ne.b. The formula for EPS without debt is:EPS all equity =1,000,000 sharesThe in terest payme nts will be $1.2 millio n per year (.06 x $20 milli on) regardless of the realized value ofEBIT. The nu mber of shares outsta nding after excha nging debt for equity will be 800,000. EPSwith debt is therefore:EPS w ith debt = Net Earnings = EBIT —$1.2 millio n800,000 shares 800,000 sharesProbability Distribute n of Divido EBIT an d'PSState of theEconomy EBIT All equity With $20 million of debtAlthough 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 un affected.Leasing2. Plentilease and Nolease are virtually identical corporationSThe 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 borrowing・ Compare and contrast their market-value balance sheets・SOLUTION:Market-Value Bala nee Sheets of Nolease and Ple ntilease Corporati ons a. Nolease CorporationThe main differe nee betwee n the bonds and the lease as a form of debt financing 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,howe、lessor that bears this residual-value risk.Pension Liabilities3. Europens and Asiapens are virtually identical corporationSThe only difference between them is that Europens has a completely unfunded pension plan, and Asiapens has a fully funded pension plaCompare and contrast their market-value balance sheetsWhat difference does the funding status of the pension plan make to the stakeholders of these two corporations?SOLUTION:Bala nee Sheets of Asiape ns and Europe ns Corporatio ns a. Asiape ns Bala nee SheetAsiapens 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 adiversified portfolio of stocks and bonds issued by other eompa nies and serve ascollateral for the pension ben efits promised byAsiape ns to its employees. In the ease of Europe ns, there is no segregated pool ofpension assets. The pension promises of Europens are backed by the assets of thecompany itself. Therefore, the employees of Asiapens are more secure about receiving their promised pension benefits, since the benefits are collateralized by a more diversified portfolio of assets. In the case of both companies, however, any unfunded pension liability reduces shareholders equity.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 $5 million in debt, how much would it be worth?c. What rate of return will the shareholders of the Tango Shoe Division require?d. Show that the market value of the equity of the new firm would be justified by the earningsto the shareholders.a. The unievered free cash flow for the Tango Shoe Division would be (in$millio ns):Sales: $10.0Var. Cost: -5.5Depreciatio n -1.0Taxable In come $ 3.5Taxes (@40%) -1.4After-Tax In come $2.1Depreciatio n 1.0Inv estme nt -1.0Free Cash Flow $2.1 millionUni evered, Tan go is worth: $2.1 millio n / 0.16 = $13.125 millio nb. If Tango had $5 million of debt, its total value would be:Market Value with Debt = Market Value without Debt + PV of In terest Tax Shield V L = V U + T x B=$13.125 + (.4 x 5) = $15.125 millio nTango Equity = $15.125 - $5 = $10.125 millionc. Tan go' 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 prese nt value of the expected net in come disco unted at the required rate of retur n on equity. The expected net in come will be the uni evered cash flow less the after-tax cost of the in terest of the debt:$2.1 - (.6) (.1 x $5) = $2.1 - $.3 = $1.8 millio n per yearS = $1.8 million / .1778 = $10.125 million5. Based on the above problem, Suppose that Foxtrot Dance Shoes makes custom desig ned dance shoes and is a competitor of Tango Dance Shoes. Foxtrot has similar risks and characteristics as Tango except that it is completely unievered. Fearful that Tango Dance Shoes may try to take over Foxtrot in order to con trol their ni che 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 of Foxtrot ' stock?b. How many shares can Foxtrot buy back and at what value if it is willing to borrow 30% ofthe value of the firm?c. What if it is willing to borrow 40% of the value of the firm?d. Should Foxtrot borrow more?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 millio nValue of equity in levered firm = $14.7 million - $3.9375 million = $10.7625 millio nTo compute the nu mber of shares Foxtrot can repurchase, we n eed 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 .35 millio n shares outsta nding, and the price of each share will be $10.7625 million/.35 million = $30.75.If the PV of the tax shield gets in corporated in the price of the shares before therepurchase, the n the price of the shares will in crease by $1.575 millio n/.5 millio n 二$3.15. So the price of the repurchased shares will be$26.25 + $3.15 = $29.40.Then the nu mber of shares retired will be $3.9375 millio n/$29.40 per share = 133,929 shares. This will leave 366,071 shares outsta nding 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 millio nValue of equity in levered firm = $15.225 million - $5.25 million = $9.975 millio n If 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 sharesoutstanding, and the price of each share will be $9.975 million/.3 million =$33.25.If the PV of the tax shield gets in corporated in the price of the shares before therepurchase, the n the price of the shares will in crease by $2.1 millio n/.5 millio n =$4.20.So the price of the repurchased shares will be$26.25 + $4.20 = $30.45.Then the nu mber of shares retired will be $5.25milli on/$30.45 per share = 172,414shares. This will leave 327,586 shares outsta nding each with a price of $30.45.d. Foxtrot ' s management must trade off the tax savings due to additional debt financingagainst 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 forceThe purchasing manager has been working with a local car dealership to get the best value for the company dollaAfter some negotiations, a local dealer has offered Hanna-Charles two options) 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 pursue and why? SOLUTION:a. Advantages:The lessor bears all the residual-value riskTax Ben efitsNo disposal concerns (or resale) whe n life of equipme nt is expe nded. Disadva ntages:No own ership while mai nta ining maintenance resp on sibilityb. Lease or Buy:Hann a-Charles compa ny should lease. Although they may spe nd 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 ・H avem 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 outstandingIts 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 ・ NeedeEnbonds are risk free and pay a coupon of 9% per year and are rolled over every year.a. What is the value of Neederhs shares?b. As an investor forecasting the upcoming year, you examine Havem and Needemusing three possible states of the economy that are all equally likely: normal, bad, and exceptionalAssuming 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 are 500,000shares, the value of each share is $216.b. Expected EBIT = $180 million x 11% = $19.8 million per yearIn terest expe nse for Needem = $72 millio n x .09 = $6.48 millio n per yearEBIT Tnterest 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 in come Net in come Needem = (1 -Tax Rate) (EBIT - Int. Pmt.) CF Needem = (1 -Tax Rate) (EBIT) + Tax Rate x Int. Pmt CF Needem (bad) = (.60) $9.9 + (.40) x 6.48 = $8.532 millionCF Needem (n ormal) = (.60) $19.8 + (.40) x 6.48 = $14.472 million CF 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 $108 per share The total value of Needem ' s debt + equity will be $108,000,000 + .4 x $72,000,000 = $136.8 millio n.Needem' s equity will be worth $136,800,000$72,000,000 = $64.8 millio n. Since there are .5 millio n shares of Needem, each will be worth $129.60.Kc. 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 millionM. anagement 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 certainbankruptcy and may result in liquidation of the firm and the loss of all the jobs. For the employees, the best choice is option 1.。

金融数学引论答案第一章__北京大学出版[1]

第一章习题答案1. 设总量函数为A(t) = t 2 + 2t + 3 。

试计算累积函数a(t) 和第n 个时段的利息I n 。

解: 把t = 0 代入得A(0) = 3 于是:a(t) =A(t)/A(0)=（t 2 + 2t + 3）/3I n = A(n) − A(n − 1)= (n 2 + 2n + 3) − ((n − 1)2+ 2(n − 1) + 3))= 2n + 12. 对以下两种情况计算从t 时刻到n(t < n) 时刻的利息: (1)I r (0 < r <n); (2)I r = 2r (0 < r < n).解: ()n n-1t 11I A(n)A(t)I I I n(n 1)/2t(t 1)/2+=-=+++=+-+・・・ (2)1t 11I A(n)A(t) 22n n k k t I ++=+=-==-∑3. 已知累积函数的形式为: 2a(t) at b =+。

若0 时刻投入的100 元累积到3 时刻为172 元，试计算：5 时刻投入的100 元在10 时刻的终值。

解: 由题意得a(0) = 1, a(3) =A(3)/A(0)= 1.72⇒ a = 0.08, b = 1∴ A(5) = 100A(10) = A(0) ・ a(10) = A(5) ・ a(10)/a(5)= 100 × 3 = 300.4. 分别对以下两种总量函数计算i 5 和i 10 :(1) A(t) = 100 + 5t; (2)t A(t) 100(1 0.1)=+.解：(1)i 5 =(A(5) − A(4))/A(4)=5120≈ 4.17%i 10 =(A(10) − A(9))/A(9)=5145≈ 3.45%(2)i 5 =(A(5) − A(4))/A(4)()()()544109109100(1 0.1)100(1 0.1) 10%100(1 0.1)100(1 0.1)100(1 0.1)i (A 10A 9)/A 9 10%100(1 0.1)+-+==++-+=-==+5.设()n A 4 1000, i 0.01n ==. 试计算A(7) 。

《金融学(第二版)》讲义大纲及课后习题答案详解第13章

CHAPTER 13THE CAPITAL ASSET PRICING MODELObjectives•Explain 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 CAPMSummary•The 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, and•Mix 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 selection•To 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 theCML 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: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 = 2.4e 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% to a 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).。

《金融学(第二版)》讲义大纲及课后习题答案详解第七章

《金融学〔第二版〕》讲义大纲及课后习题答案详解第七章CHAPTER 7PRINCIPLES OF ASSET VALUATIONObjectives? Understand why asset valuation is important in finance.? Explain the Law of One Price as the principle underlying all asset-valuation procedures. ? Explain the meaning and role of valuation models.? Explain how information gets reflected in security prices.Outline7.1 The Relation Between an Asset’s Value and Its Price 7.2 Value Maximization and Financial Decisions 7.3 The Law of One Price and Arbitrage7.4 Arbitrage and the Prices of Financial Assets 7.5 Exchange Rates and Triangular Arbitrage 7.6 Interest Rates and the Law of One Price 7.7 Valuation Using Comparables 7.8 Valuation Models7.9 Accounting Measures of Value7.10 How Information Gets Reflected in Security Prices 7.11 The Efficient Markets HypothesisSummary? In finance the measure of an asset’s value is the price it would fetch if it were sold in a competitive market. Theability to accurately value assets is at the heart of the discipline of finance because many personal and corporate financial decisions can be made by selecting the alternative that maximizes value.? The Law of One Price states that in a competitive market, if two assets are equivalent they will tend to have thesame price. The law is enforced by a process called arbitrage, the purchase and immediate sale of equivalent assets in order to earn a sure profit from a difference in their prices.? Even if arbitrage cannot be carried out in practice to enforce the Law of One Price, unknown asset values canstill be inferred from the prices of comparable assets whose prices are known.? The quantitative method used to infer an asset’s value from information about the prices of comparable assets iscalled a valuation model. The best valuation model to employ varies with the information available and the intended use of the estimated value. ? The book value of an asset or a liability as reported in a firm’s financial statements often differs from its currentmarket value.? In making most financial decisions, it is a good idea to start by assuming that for assets that are bought and soldin competitive markets, price is a pretty accurate reflection of fundamental value. This assumption is generally warranted precisely because there are many well-informed professionals looking for mispriced assets who profit by eliminating discrepancies between the market prices and the fundamental values of assets. The proposition that an asset’s current price fully reflects all publicly-available information about future economic fundamentals affecting the asset’s value is known as the Efficient Markets Hypothesis.? The prices of traded assets reflect information about the fundamental economic determinants of their value.Analysts are constantly searching for assets whose prices are different from their fundamental value in order to buy/sell these “bargains.〞 In deciding the best strategy for the purchase/sale of a “bargain,〞 theanalyst has to evaluate the accuracy of her information. The market price of an asset reflects the weighted average of all analysts opinions with heavier weights for analysts who control large amounts of money and for those analysts who have better than average information.Instructor’s ManualChapter 7 Page 106Solutions to Problems at End of ChapterLaw of One Price and Arbitrage1. IBX stock is trading for $35 on the NYSE and $33 on the Tokyo Stock Exchange. Assume that the costs of buying and selling the stock are negligible. a. How could you make an arbitrage profit?b. Over time what would you expect to happen to the stock prices in New York and Tokyo?c. Now assume that the cost of buying or selling shares of IBX is 1% per transaction. How does this affectyour answer?SOLUTION:a. Buy IBX stock in Tokyo and simultaneously sell them in NY. Your arbitrage profit is $2 per share.b. The prices would converge.c. Instead of the prices becoming exactly equal, there can remain a 2% discrepancy between them, roughly $.70 inthis case.2. Suppose you live in the state of Taxachusetts which has a 16% sales tax on liquor. A neighboring state called Taxfree has no tax on liquor. The price of a case of beer is $25 in Taxfree and it is $29 in Taxachusetts.a. Is this a violation of the Law of One Price?b. Are liquor stores in Taxachusetts near the border with Taxfree going to prosper?SOLUTION:a. This is not a violation of the Law of One Price because it is due to a tax imposed in one state but not in the other.Illegal arbitrage will probably occur, with lawbreakers buying large quantities of liquor in Taxfree and selling it in Taxachusetts without paying the tax.b. It is likely that liquor stores will locate in Taxfree near the border with Taxachusetts. Residents of both stateswill buy their liquor in the stores located in Taxfree, and liquor stores in Taxachusetts will go out of business.Triangular Arbitrage3. Suppose the price of gold is 155 marks per ounce.a. If the dollar price of gold is $100 per ounce, what should you expect the dollar price of a mark to be?b. If it actually only costs $0.60 to purchase one mark, how could one make arbitrage profits?SOLUTION:a. $100 buys the same amount of gold (1 ounce) as 155 DM, so 1 DM should cost 100/155 or $.645.b. The marks are “cheaper〞 than they should be, so the arbitrage transaction requires you to buy marks at thecheap price, use them to purchase gold, and sell the gold for dollars. Example:1. Start with $1 million, which you borrow for only enough time to carry out the arbitrage transaction.2. Use the million dollars to buy 1,666,667 marks (1,000,000 / 0.60)3. Buy 10,752.69 ounces of gold (1,666,667 / 155)4. Sell the gold for $1,075,269 (10752.69 x 100)Your risk-free arbitrage profit is $75,269.4. You observe that the dollar price of the Italian lira is $0.0006 and the dollar price of the yen is $0.01. What must be the exchange rate between lira and yen for there to be no arbitrage opportunity?SOLUTION:.0006$/lira?.06Yen/lira.01$/YenInstructor’s ManualChapter 7 Page 1075. Fill in the missing exchange rates in the following table: US dollar British pound German mark Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 German mark DM2.0 Japanese ￥100 Yen SOLUTION: US dollar British pound German mark Japanese Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 1 = .67 / 2 = .67 / 100 German mark DM2.0 = 2 / .67 1 = 2 / 100 Japanese ￥100 = 100 / .67 = 100 / 2 1 Yen US dollar British pound German mark Japanese Yen US dollar $1 $1.50 $.5 $.01 British pound ￡0.67 ￡1 ￡.33 ￡.0067 German mark DM2.0 DM3.0 DM1.0 DM.02 Japanese ￥100 ￥150 ￥50 ￥1 Yen Valuation Using Comparables6. Suppose you own a home that you purchased four years ago for $475,000. The tax assessor’s office has just informed you that they are increasing the taxable value of your home to $525,000. a. How might you gather information to help you appeal the new assessment?b. Suppose the house next door is comparable to yours except that it has one fewer bedroom. It just sold for$490,000. How might you use that information to argue your case? What inference must you make about the value of an additional bedroom?SOLUTION:a. You should retrieve as much information as you can about recent sales of comparable homes. If you canconvince the assessor’s office that your home is comparable (and the market value of the recent sales is less than $525,000) you should have a good case. You can gather the information about home sales from a real estate broker.b. The difference between your house’s assessed value and the actual market value of the home next door is$35,000 ($525,000 - $490,000). If you can convince the tax assessor’s office that the value of a bedroom is less than $35,000, then the assessor must agree that your home is worth less than $525,000. For example, if comparable sales figures show that one additional bedroom (all else reasonably equivalent) is worth only $10,000, then you should be able to argue that your home is worth $500,000 rather than $525,000.7. The P/E ratio of ITT Corporation is currently 6 while the P/E ratio of the S&P 500 is 10. What might account for the difference? SOLUTION: There are several possible reasons:? ITT may be riskier than the S&P500 either because it is in a relatively risky industry or has a relatively higherdebt ratio.? ITT’s reported earnings may be higher than they are expected to be in the future, or they may be inflated due tospecial accounting methods used by ITT.Instructor’s ManualChapter 7 Page 1088. Suppose you are chief financial officer of a private toy company. The chief executive officer has asked you to come up with an estimate for the company’s price per share. Your company’s earnings per share were $2.00 in the year just ended. You know that you should look at public company comparables, however, they seem to fall into two camps. Those with P/E ratios of 8x earnings and those with P/E ratios of 14x earnings. You are perplexed at the difference until you notice that on average, the lower P/E companies have higher leverage than the higher P/E group. The 8x P/E group has a debt/equity ratio of 2:1. The 14x P/E group has a debt/equityratio of 1:1. If your toy company has a debt/equity ratio of 1.5:1, what might you tell the CEO about your company’s equity value per share? SOLUTION:It would be reasonable to apply a P/E of 11x earnings (= (8 + 14) / 2) because your leverage is midway between the two groups. Hence, your company’s price per share would be: 11x $2.00 = $22.00 per share.9. Assume that you have operated your business for 15 years. Sales for the most recent fiscal year were $12,000,000. Net income for the most recent fiscal year was $1,000,000. Your book value is $10,500,000. A similar company recently sold for the following statistics: Multiple of Sales: 0.8x Multiple of Net Income 12x Multiple of Book Value 0.9xa. What is an appropriate range of value for your company?b. If you know that your company has future investment opportunities that are far more profitable than thecompany above, what does that say about your company’s likely valuation? SOLUTION:a. Multiple of Sales: .8x = $12 million x .8 Multiple of Net Income 12x = $1 million x 12 Multiple of Book Value .9x = $10.5 million x .9 An appropriate range might be 9 to 12 millionb. Higher end of the range = $9.6 million = $12 million = $9.45 millionEfficient Markets Hypothesis10. The price of Fuddy Co. stock recently jumped when the sudden unexpected death of its CEO was announced. What might account for such a market reaction?SOLUTION:Investors may believe that the company’s future prospects look better(i.e., either higher earnings or less risky) without the deceased CEO.11. Your analysis leads you to believe that the price of Outel’s stock should be $25 per share. Its current market price is $30.a. If you do not believe that you have access to special information about the company, what do you do?b. If you are an analyst with much better than average information, what do you do?SOLUTION:a. If you believe that the market for Outel stock is an informationally efficient one then the $30 market price(which is a weighted average of the valuations of all analysts) is the best estimate of the stock’s true value. You should question whether your own analysis is correct.b. You sell the stock because you think you have superior information. Real Interest Rate Parity12. Assume that the world-wide risk-free real rate of interest is 3% per year. Inflation in Switzerland is 2% per year and in the United States it is 5% per year. Assuming there is no uncertainty about inflation, what are the implied nominal interest rates denominated in Swiss francs and in US dollars?SOLUTION: Switzerland: (1.03 x 1.02) =1.0506 hence nominal interest rate = 5.06% US: (1.03 x 1.05) = 1 .0815 hence nominal interest rate = 8.15%Instructor’s ManualChapter 7 Page 109Integrative Problem13. Suppose an aunt has passed away and bequeathed to you and your siblings (one brother, one sister) a variety of assets. The original cost of these assets follows:ITEM COST WHEN PURCHASEDJewelry $500 by Grandmother 75 years ago House 1,200,000 10 years ago Stocks and Bonds 1,000,000 3 years ago Vintage (used) Car 200,000 2 months ago Furniture 15,000 various dates during last 40 yearsBecause you are taking a course in finance, your siblings put you in charge of dividing the assets fairly among the three of you. Before you start, your brother approaches you and says: “I’d really like the car for myself, so when you divide up the assets, just give me the car and deduct the $200,000 from my share.〞Hearing that, your sister says: “That sounds fair, because I really like the jewelry and you can assign that to me and deduct the $500 from my share.〞You have always loved your aunt’s house and its furnishings, so you would like to keep the house and the furniture.a. How do you respond to your brother and sister’s requests? Justify your responses.b. How would you go about determining appropriate values for each asset?SOLUTION:a. Because the market price of the car is close to the what your brother is willing to give up for it, your brother’srequest is reasonable. It is, however, quite possible (even likely), that the antique jewelry is worth much more today than what your relative’s grandmother paid for it in the past. Assigning only its acquisition cost to your sister’s share is quite likely a gross miscalculation. If she wants the jewelry, she should be “charged〞 an amount equal to today’s market value. It does not matter that your sister does not want to sell the jewelry for a profit, because the jewelry has VALUE even if you do not sell it. Fairness is all about equal VALUE.b. You would probably have to hire a professional appraiser for the furniture and the jewelry. You can look up thevalue of the stocks and bonds in a financial newspaper. You can estimate the value of the house by inquiring for how much similar houses in the same neighborhood have recently been sold. The car was purchased only twomonths ago, so it is probably reasonable to assume that the current market price is very close to what your distant relative paid for the car. Instructor’s ManualChapter 7 Page 110。

金融学第二版课后复习思考题参考答案

⾦融学第⼆版课后复习思考题参考答案第⼀章货币与货币制度⼀、单项选择题1.B2.C3.B4.C5.A6.B7.C⼆、多项选择题1.ACDE2.CDE3.CD4.ABCD5.ABCDE6.ABCD三、简答题1. 货币的职能有哪些？价值尺度；流通⼿段；⽀付⼿段；贮藏⼿段；世界货币2. ⼈民币制度包括哪些内容？（1）⼈民币是我国的法定货币；（2）⼈民币是我国唯⼀的合法通货；（3）⼈民币的发⾏权集中于中央银⾏；（4）⼈民币以商品物资作为发⾏的⾸要保证，也以⼤量的政府政府债券、商业票据、商业银⾏票据等为发⾏的信⽤保证，还有黄⾦、外汇储备等也是⼈民币发⾏的现⾦保证；（5）⼈民币实⾏有管理的货币制度；（6）⼈民币称为可兑换货币。

3. 货币制度的构成要素是什么？货币材料；货币单位；各种通货的铸造、发⾏和流通程序；准备制度4. 不兑现的信⽤货币制度有哪些特点？（1）不兑现信⽤货币⼀般由中央银⾏发⾏，并由国家赋予其⽆限法偿能⼒，这是不兑现信⽤货币制度最基本的特点；（2）信⽤货币不与任何⾦属保持等价关系，也不能兑换黄⾦；（3）货币通过信⽤程序投⼊流通领域；（4）信⽤货币制度是⼀种管理货币制度；5. 钱、货币、通货、现⾦是⼀回事吗?银⾏卡是货币吗?不⼀样。

（1）钱的概念在不同场景下有很多不同的意思。

可以是个收⼊的概念、也可以是个财富的概念，也可以特指现⾦货币；（2）货币是在商品劳务交换与债券债务清偿时，被社会公众所普遍接受的东西。

（3）通货是流通中的货币，指流通与银⾏体系之外的货币。

范围⼩于货币。

（4）现⾦就是现钞，包括纸币、硬币。

现⾦是货币的⼀部分，流动性很强，对⼈们的⽇常消费影响很⼤。

（5）银⾏卡本⾝也称为“塑料货币”，包括信⽤卡、⽀票卡，记账卡、⾃动出纳机卡等。

银⾏卡可以⽤于存取款和转账⽀付。

在发达西⽅国家，各种银⾏卡正在取代现钞和⽀票，称为经济⽣活中⼴泛的⽀付⼯具，因此现代社会银⾏卡也是货币6.社会经济⽣活中为什么离不开货币？为什么⾃古⾄今，⼈们⼜往往把⾦钱看做说万恶之源？（1）社会经济⽣活离不开货币，货币的产⽣和发展都有其客观必然性。

博迪莫顿版金融学(第二版)课后习题答案,DOC

金融学（第二版）答案博迪默顿第一章课后习题答案一.我的生活目标：●完成学业●退休3，当我结5，?2，现在消费更多为以后比如买房，买车或储蓄留置很少的钱还是现在消费很少，甚至少于我的许多朋友二.答案样例：净值＝资产－负债$__________(很可能会被低估)资产包括:经常帐户余额储蓄存款帐户余额家具设备，首饰类（如表）车（如果有的话）负债包括：学生贷款信用卡结余的差额各种租用金的协定（不包括转租）应付车款在计算净值时学生会特别地排除了他们一生潜在的赚钱能力的价值三．一个单身汉之需要养活他自己，所以他可以独立自主的作出金融决策。

如果他不想购买健康保险（而愿意承担由这个决定而带来的金融风险）那么除了这个单身汉自身，没谁会受这个决定的影响。

另外，他不需要在家庭成员之间分配收入这件事上做任何决定。

单身汉是很灵活自由的，可以选择住在几乎任何地方。

他主要是在今天的消费（开支）和为明天储蓄之间做出权衡决策。

既然他只需要养活他自己，那么他储蓄的重要性就比对一家之主的重要性小。

有许多孩子的一家之长必须在这些家庭成员中分配资源[或者说是收入].他们必须随时准备着处理各种风险,比如说潜在财政危机的突然发生[诸如家庭成员经历的严重健康问题,或者因为火灾和其他疏忽导致的保险问题].因为在一般一个家庭里人会比较多,有些人生病或受伤的风险就会更大.并且因为家庭中有许多依赖性的个体,所以薪水收入者得认真地考虑生活和残疾保险.还有,家庭并不像个体那样富有机动性,这是因为有了适龄儿童的缘b.1银行借贷2汽车经销商借贷或租赁3个人储蓄C（略）d你应该从可选择的融资方式中选择成本最小的一种。

当你分析的时候，你应该考虑以下方面：1你是否有足够的现金储蓄去购买？为了买车，你必须放弃的利息？你付现金和贷款所付是否不同？2对于不同的贷款方式，首付金额是多少？月付多少？付多久？相关利息是多少？整个贷款是按月还清，还是期末一次还清？税收和保险费是否包括在月付款中？3对于不同的租赁方式，首付金额是多少？月付多少？付多久？在租赁期末你是否拥有车？如果不拥有，买车要花多少？在租赁期末你是否必须得买车？你是否拥有优先购买权？如果你不买车你是否得付钱？相关利息是多少？税收和保险费是否包括在月付款中？是否有里程限制？七．a为学生们提供个人服务可能是个低成本的选择。

《金融学(第二版)》讲义大纲及课后习题答案详解第九章

CHAPTER 9VALUATION OF COMMON STOCKSObjectives∙To explain the theory and application of the discounted cash flow valuation method as applied to the equity of a firm.Outline9.1 Reading Stock Listings9.2 The Discounted Dividend Model9.3 Earnings and Investment Opportunities9.4 A Reconsideration of the Price/Earnings Multiple Approach9.5 Does Dividend Policy Affect the Value of a Share?Summary∙The discounted cash flow (DCF) method of valuing assets consists of discounting expected future cash flows ata risk-adjusted discount rate.∙The discounted dividend model (DDM) for valuing shares of stock starts from the observation that an investor in common stock expects a rate of return (consisting of cash dividends and price appreciation) that is equal to the market capitalization rate. The resulting formula shows that the current price of a share is the present value of all expected future dividends.∙In the constant growth rate DDM, the growth rate of dividends is also the expected rate of price appreciation.∙Growth per se does not add value to a share’s current price. What adds value is the opportunity to invest in projects that yield a rate of return in excess of the market capitalization rate.∙In a “frictionless” financial envir onment, where there are no taxes and no transaction costs, the wealth of shareholders is the same no matter what dividend policy the firm adopts.∙In the real world there are a number of frictions that can cause dividend policy to have an effect on the wealth of shareholders. These include taxes, regulations, the costs of external finance, and the information content of dividends.Solutions to Problems at End of Chapter1.The DDM Corporation has just paid a cash dividend (D0) of $2 per share. It has consistently increased its cash dividends in the past by 5% per year, and you expect it to continue to do so. You estimate that the market capitalization rate for this stock should be 13% per year.a.What is your estimate of the intrinsic value of a share (derived using the DDM model)?b.Suppose that the actual price of a share is $20. By how much would you have to adjust each of thefollowing model parameters to “justify” this observed price:i.The growth rate of dividendsii.The market capitalization rateSOLUTION:a.P0 = D0(1+g)/(k-g) = 2(1+0.05)/(0.13-0.05) = $26.25b.If the actual price of the share is $20, then some of our input parameters might need some adjustments:i.Assuming all other parameters are left as given, then solving for g =(.13 x 20 – 2)/(2+20) = 0.0273= 2.73%ii.Similarly, solving for k = 2(1.05)/20 + 0.05 = 0.155 = 15.5%2.The Rusty Clipper Fishing Corporation is expected to pay a cash dividend of $5 per share this year. You estimate that the market capitalization rate for this stock should be 10% per year. If its current price is $25 per share, what can you infer about its expected growth rate of dividends?SOLUTION:D1 = $5; k = 10%; P0= $25Hence g = 0.1 - 5/25 = -0.1 = -10%3. The Constant Growth Corporation (CGC) has expected earnings per share (E1) of $5. It has a history of paying cash dividends equal to 20% of earnings. The market capitalization rate for CGC’s stock is 15% per year, and the expected ROE on the firm’s future investments is 17% per year? U sing the constant growth rate discounted dividend model,a. What is the expected growth rate of dividends?b. What is the model’s estimate of the present value of the stock?c. If the model is right, what is the expected price of a share a year from now?d.Suppose that the current price of a share is $50.By how much would you have to adjust each of the following model parameters to “justify” this observed price:i.The expected ROE on the firm’s future investments.ii.The market capitalization rateiii.The dividend payout ratio.SOLUTION:a. g = earnings retention ratio x ROE = .8 x .17 = .136 = 13.6%b. P0 = D1/(k-g)D1 = .2 x $5 = $1 per shareP0 = $1/(.15 -.136) = $1/.014 = $71.43c. The stock price grows at the same rate as dividends, i.e., 13.6% per year:P1 = P0 x (1 + g) = $71.43 x 1.136 = $81.14d.If the market is efficient then the $50 price represents the best estimate of the stock’s true value. To “justify” thisprice, one of the input parameters in the model needs to be adjusted:i.Assuming all other parameters are correct, if we were to adjust for the ROE:50 = D1/(k-g), where g = 0.8 x ROESolving for g, then for ROE: g = .15 – 1/50 = 0.13 = 13%,hence ROE is equal to 13/0.8 = 16.25%ii. If we were to adjust the market capitalization k then:k = 1/50 + .136 = .156 = 15.6%iii.Dividend payout ratio x E1 = 50 x (.15-.136) = 0.7,hence Dividend payout ratio = 0.7/5=0.14 = 14%4. The stock of Slogro Corporation is currently selling for $10 per share. Earnings per share in the coming year are expected to be $2 per share. The company has a policy of paying out 60% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This situation is expected to continue forever.a. Assuming the current market price of the stock reflects its intrinsic value as computed using the constantgrowth rate DDM, what rate of return do Slogro’s investors require?b. By how much does its value exceed what it would be if all earnings were paid as dividends and nothingwere reinvested?c. If Slogro were to cut its dividend payout ratio to 25%, what would happen to its stock price? What ifSlogro eliminated the dividend altogether?d. Suppose that Slogro wishes to maintain its current 60% dividend payout policy but that it also wishes toinvest an amount each year equal to that year’s total earnings. All the money would be invested inprojects earning 20% per year. One way that Slogro could do so would be to issue an amount of new stock each year equal to one-half that year’s earnings. What do you think would be the effect of this policy on the current stock price?SOLUTION:a. P0 = $10, E1 = $2, b = .4, ROE = .2k = D1/P0 + gD1 = .6 x $2 = $1.20g = b x ROE = .4 x .2 = .08Therefore, k = $1.20/$10 + .08 = .12 + .08 = .2 or 20%b. If all earnings were paid as dividends its price would be:P0 = $2/.2 = $10Thus, its price is the same whether it reinvests or not. This is because k = ROE.c. Since k = ROE, the stock price would be unaffected by cutting the dividend and investing the additionalearnings.d.Again, this should have no impact on the stock’s price since the NPV of the investments would be zero (the IRRof those projects (20%) is equal to the investors’ required rate of return, hence the firm’s c ost of capital).5. The Corporation currently pays no cash dividends, and it is not expected to for the next 5 years. Its sales have been growing at 25% per year.a.Can you apply the constant growth rate DDM to estimate its intrinsic value? Explain.b.It is expected to pay its first cash dividend $1 per share 5 years from now. It its market capitalization rateis 20% and its dividends are expected to grow by 10% per year, what would you estimate its intrinsic value to be?c.If its current market price is $100 per share, what would you infer the expected growth rate of its futuredividends to be?SOLUTION:a.Yes, we can apply the DDM model even if the company doesn’t pay dividends for the first 5 years. Thecompany will eventually have to pay dividends in the future.b.P4 = D5/(k-g) = 1/(.2-.1) = $10P0 = 10/1.24 = $4.82c.If P0 = $100 then P4 = 100 x 1.24 = 207.36 and g = 0.2 – 1/207.36 = 19.518%6. The Digital Growth Corp. pays no cash dividends currently and is not expected to for the next 5 years. Its latest EPS was $10, all of which was reinvested in the company. The firm’s expected ROE for the next 5 years is 20% per year, and during this time it is expected to continue to reinvest all of its earnings. Starting 6 years from now, the firm’s ROE on new investments is expected to fall to 15%, and the company is expected to start paying out 40% of its earnings in cash dividends, which it will continue to do forever after. DG’s market capitalization rate is 15% per year.a. What is your estimate of DG’s int rinsic value per share?b. Assuming its current market price is equal to its intrinsic value, what do you expect to happen to its priceover the next year? The year after?c. What effect would it have on your estimate of DG’s intrinsic value if you expecte d DG to pay out only20% of earnings starting in year 6?56P0 = P5/(1+k)5 = $180.82/1.155 = $89.90b.The price should rise by 15% per year until year 5 after which it will grow at the dividends’ growth rate g (=9%).c. Since ROE =k, the dividend payout ratio will have no effect on current price.7. The 2Stage Co. just paid a dividend of $1 per share. The dividend is expected to grow at a rate of 25% per year for the next 3 years and then to level off to 5% per year forever. You think the appropriate market capitalization rate is 20% per year.a. What is your estimate of the intrinsic value of a share of the stock?b. If the market price of a share is equal to this intrinsic value, what is the expected dividend yield?c. What do you expect its price to be one year from now? Is the implied capital gain consistent with yourestimate of the dividend yield and the market capitalization rate?P 3 = D 4/(k – g) = 2.05078/(.20 -.05) = $13.67P 0 = D 1/(1+k) + D 2/(1+k)2 + (D 3 + P 3)/(1+k)3 = $1.25/1.2 + $1.5625/1.22 + ($1.953 + $13.67)/1.23 = $11.17 b. If the market price of a share is equal to this intrinsic value, the expected dividend yield is D 1/P 0, which is1.25/11.17 = .1119 or 11.2%c. Its price one year from now = P 1 = D 2/(1+k) + (D 3 + P 3)/(1+k)2 = $1.5625/1.2 + ($1.953 + $13.67)/1.22 =$12.15.The implied capital gain is $12.15 - $11.17 = $.98, which is 8.8% of the price P 0. Thus the dividend yield plusthe capital gain rate add up to 20%, which is k.8. The Bearded ladies’ Stock guide offers the following method for selecting stocks:Compute the stock’s PEG ratio by dividing its P/E mu ltiple by its growth rate of earnings. Select only those stocks whose PEG ratio is in the lowest quartile.a. If the stock is fairly priced according to the constant-growth-rate DDM, what should be its PEG ratio asa function of the following three variables: the stock’s market capitalization rate (k), the expectedprofitability of its future investments (ROE), and its plowback ratio (b)? (Assume the P/E ratio used in computing PEG is the ratio of the stock’s current price to its expected earnings per share, P 0/E 1)b. Assume the CAPM and the DDM are valid. The risk free rate is .04 and the risk premium on the marketportfolio is .06. What should be the relationship between the PEG for a stock whose ROE is .10 and a stock whose ROE is .15, assuming the two stocks have the same beta (equal to 1) and plowback ratio (equal to .6)?c. What do you think of the Bearded Ladies’ method?SOLUTION:a. If the DDM holds we know that P 0 = D 1 / (k-g), furthermore, we know that g = b x ROE and D 1=(1-b) E 1b(ROE)(k -b(ROE))b (ROE)b E k -b(ROE)E )b (g E P PEG -=⨯-==1111110b. The values of k for each of the stocks will be: k = .04 + .06 beta = .04 + .06 =.1PEG 1= (1-.6) / (.6 x .10 x (.1 - .6 x .10)) = 166.67PEG 2= (1-.6) / (.6 x .15 x (.1 - .6 x .15)) = 444.44PEG 1 < PEG 2c. As we can see in part b, the PEG rule would lead us to choose the stock with the lowest ROE.In general, if the stock market is informally efficient, then any stock will offer an expected rate of return that is commensurate with the stock’s perceived market risk, regardless of the stock’s PEG.Using the Internet for Stock Pricing9. Pick a company whose stock is traded on the NYSE. Use one of the stock valuation models discussed in this chapter together with information that you can find by searching the Internet to compute an intrinsic value for the s tock. Compare your estimate of intrinsic value with the stock’s actual price. Would you be willing to make an investment decision on the basis of your research? Why or why not?SOLUTION:One simple model that we can use to value a company is to find the average P/E multiple of the industry in which the company operates and multiply it by the expected earnings per share of that company. The difference between this intrinsic value and the actual market value of the stock can be explained by the difference between our assumptions regarding the company’s future investment opportunities and the market’s expectations. For example, if the market value of the stock is higher than the intrinsic value found, then this difference reflects the investors’ belief that the company will have a greater-than-average future investments opportunities with a rate of return greater than the market capitalization rate for this particular industry. If markets are efficient, then this market value is supposed to be the “real” value o f the company, and represents the view of the majority of investors, hence I would be reluctant to follow my own findings of the intrinsic value as a basis for an investment decision.Dividend Policy10. 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. What would be the impact on Di vido’s stock price and on the wealth of its shareholders of each of the following decisions? Consider each decision separately.a. The company pays a cash dividend of $10 per share.b. The company repurchases 100,000 shares.c. The company pays a 10% stock dividend.d. The company has a 2-for-1 stock split.e. The company invests $10 million in an expansion that has an expected IRR equal to the firm’s cost ofcapital.SOLUTION:a.The stock price falls by $10, but shareholder wealth remains the same in a frictionless world becauseshareholders receive $10 in cash on each share they own. In the real world, shareholder’s wealth may decline because personal taxes may have to be paid on the cash dividend.b.The stock price is unchanged and so is shareholder wealth. Some of the shareholders who sold their shares mayhave to pay taxes on their capital gains in the real world.c.The number of shares outstanding rises to 1,100,000, and the stock price falls to $90.909 (=$100MM/$1.1MM)per share. Shareholder wealth is unchanged: instead of having one share at $100, now the shareholder will have1.1 shares at $90.909/share (1.1 x 90.909 = 100)d.The number of shares outstanding rises to 2,000,000, and the stock price falls to $50 per share. Theoretically,shareholder wealth is unchanged.e.The composition of the firm’s assets changes. Cash falls by $10 million and other assets go up by the sameamount. There is no change in either the stock price or in shareholder wealth.11. It has been found empirically, that on average the total market value of their stock rises when firms announce a stock split. What hypotheses might you offer to explain this phenomenon?SOLUTION:Theoretically, when a firm announces a stock-split, the number of shares doubles (if 2-to-1 stock split) and the market value per share drops by half. Empirically, we have observed a small increase in market value of the stock after the announcement of a stock-split. This can be explained by the informational content of the split. Outside investors may interpret this stock dividend as a positive sign that the company is doing well, hence increasing the price of the stock. Another possible interpretation is that since the price per share is now lower after the split, it can become more affordable for some investors.12. Suppose that a company has had an extraordinarily profitable year, and it announces that it will use most of its net cash inflow to buy back shares of its stock in the market. Would you expect the price of its stock to rise or fall when the announcement is made? Explain.SOLUTION:Theoretically, the price of the stock should not change after a stock repurchase. But the announcement could send a positive signal to investors that the company has been doing very well and has enough cash to buy back shares as a form of dividends. This might increase the price of the stock after the announcement.。

《金融数学》(第二版)习题参考答案(修订版)

δ0.5 = a' (0.5) / a (0.5) =（0.08*0.5+0.03）/(1+2.5%)=0.06829
∫ 1.15
A(3) = 100⋅ exp⎜⎝⎛⎜
3
t2
0
/ 100dt⎞⎠⎟⎟+
X
= 109.42 +
X
∫ A(6) = (109.42 + X )⋅exp⎛⎜⎜⎝
6t2
3
/ 100dt⎞⎠⎟⎟
第三部分是自55年开始支付5次每次支付2x故有050545500001051053278516由已知115045869228001001由过去法第2期后未偿还本金金额为10001018692288453852次支付的本金金额为001784689由将来法第4期后未偿还本金金额为次支付的利息金额为0015138212517第69期还款额中本金金额为3606929269rvrv故由已知292292094473rv和70期偿还的本金金额比为944186970同样解得01196518由已知前10次付款等于应付利息故十年末的未偿还贷款余额仍为1000第11至20次付款等于应付利息的两倍即本金偿还值等于应付利息值有11101110111011101211101010201000809209209209209210004343885后10期每期付款等于x故206474008104343885519分别用将来法计算两种偿还方式在第5次付款之后的未偿还本金有10005100050051000800kvia487914
200a ×(1+ 0.5%)123 = 33873 123 0.5%
200a ×(1+ 0.5%)70 = 26005 123 0.5%

金融数学引论答案第二版

金融数学引论答案第二版【篇一：北大版金融数学引论第二章答案】>第二章习题答案1．某家庭从子女出生时开始累积大学教育费用5万元。

如果它们前十年每年底存款1000元，后十年每年底存款1000+x 元，年利率7%。

计算x 。

解：s = 1000s?7%+xs?7%20p10p20px = 50000 ? 1000s?7% = 651.72s?p7%102．价值10,000元的新车。

购买者计划分期付款方式：每月底还250元，期限4年。

月结算名利率18%。

计算首次付款金额。

解：设首次付款为x ，则有10000 = x + 250a?p1.5%48解得x = 1489.3613．设有n年期期末年金，其中年金金额为n，实利率i =n解：p v = na?npi= 1nn+2 =(n + 1)nn2n4．已知：a?pn= x，a?p2n= y 。

试用x和y 表示d 。

解： a?p2n= a?pn+ a?p (1 ? d)则nny ? xd = 1 ? ( x ) n5．已知：a?p7= 5.58238, a?= 7.88687, a?= 10.82760。

计算i。

11p18p解：a?p = a?p + a?p v718711解得=i = 6.0%10?p +a∞?p6.证明： 11?v10s。

解：p v = 100a?+ 100a20?8p3% p3% = 2189.7168．某人现年40岁，现在开始每年初在退休金帐号上存入1000元，共计25年。

然后，从65岁开始每年初领取一定的退休金，共计15年。

设前25年的年利率为8%，后15年的年利率7%。

计算每年的退休金。

解：设每年退休金为x，选择65岁年初为比较日=解得x = 8101.658。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

金融数学引论答案第二版【篇一：北大版金融数学引论第二章答案】>第二章习题答案1．某家庭从子女出生时开始累积大学教育费用5万元。

如果它们前十年每年底存款1000元，后十年每年底存款1000+x 元，年利率7%。

计算x 。

解：s = 1000s?7%+xs?7%20p10p20px = 50000 ? 1000s?7% = 651.72s?p7%102．价值10,000元的新车。

购买者计划分期付款方式：每月底还250元，期限4年。

月结算名利率18%。

计算首次付款金额。

试用x和y 表示d 。

解： a?p2n= a?pn+ a?p (1 ? d)则nny ? xd = 1 ? ( x ) n5．已知：a?p7= 5.58238, a?= 7.88687, a?= 10.82760。

计算i。

11p18p解：a?p = a?p + a?p v718711解得=i = 6.0%10?p +a∞?p6.证明： 11?v10s。

解：p v = 100a?+ 100a20?8p3% p3% = 2189.7168．某人现年40岁，现在开始每年初在退休金帐号上存入1000元，共计25年。

然后，从65岁开始每年初领取一定的退休金，共计15年。

设前25年的年利率为8%，后15年的年利率7%。

计算每年的退休金。

解：设每年退休金为x，选择65岁年初为比较日=解得x = 8101.658。

1解： d = 10%，则 i=1?d? 1 =981 ? v8nnv；nnnn1n1n1ni+ 1? vnn1+i所以nn(1+nni)n(1+i)n?1=(1+i)?1nd=? 1i1+ii+ (1 + i)n所以nn版权所有，翻版必究12.从1980年6月7日开始，每季度年金100元，直至1991年12月7日，季结算名利率6%，计算：1）该年金在1979年9月7日的现值；2）该年金在1992年6月7日的终值。

解：p v = 100a49?p1.5% ? 100a?2p1.5% = 3256.88av = 100s?1.5% ? 100s?p1.5% = 6959.37p213.现有价值相等的两种期末年金a和b。

年金a在第1－10年和第21－30年中每年1元，在第11－20年中每年2元；年金b在第1－10年和第21－30年中每年付款金额为y ，在第11－20年中没有。

已知：v=，计算y 。

102解：因两种年金价值相等，则有a?i+a?iv10=y a? ?iy a10?piv1030p10p30p所以 y =31030.814.已知年金满足：2元的2n期期末年金与3元的n期期末年金的现值之和为36；另外，递延n年的2元n 期期末年金的现值为6。

计算i。

1+v10?2v30= 1解：由题意知，2a?pi+ 3a?pi = 362nn2a?pivn= 6n解得73xi = 8.33%yzp a?p a?p + s?= 15.已a?p a?p + s?p 。

求x，y和z。

知解：由题意得=1 ? v11 (1 + i)z ? vy解得x = 4, y = 7, z = 4117x3153016.化简a15?p (1 + v+ v)。

4.5%解：年金在4月1日的价值为p =2000 = 46444.44 ，则1+4pp v =(1 + i)2+= 41300.657318.某递延永久年金的买价为p ，实利率解：设递延时间为t，有1 p = i vtln解得t = ? ln(1+i)19.从现在开始每年初存入1000元，一直进行20年。

从第三十年底开始每年领取一定的金额x，直至永远。

计算x。

解：设年实利率为i，由两年金的现值相等，有x ?=i29解得x = 1000((1 + i)? (1 + i))301020.某人将遗产以永久年金的方式留给后代a、b、c、和d：前n年，a、b和c三人平分每年的年金，n年后所有年金由d一人继承。

如果四人的遗产份额的现值相同。

计算(1 + i)。

n解： i，那么a,b,c得到的遗产的现值为 i ，而d得到遗产的现值为v。

由题意得 3?pinn1 ? v= v 3nn所以(1 + i)= 4n21.永久期末年金有a、b、c、和d四人分摊，a接受第一个n年，b接受第二个n年，c接受第三个n 年，d接受所有剩余的。

已知：c与a的份额之比为0.49，求b与d的份额之比。

计算最后一次还款的数量和时间。

vnp4.5%41000 100a?解：100an+1?p4.5%v4100016解得 n = 172列价值方程解得+100a?p4.5%xv1 = 1000x = 146.0723.36年的期末年金每次4元，另有18年的期末年金每次5元；两者现值相等。

如果以同样的年利率计算货币的价值在n年内将增加一倍，计算n。

由题意， (1 + i)= 2 解得 n = 91836pn24.某借款人可以选择以下两种还贷方式：每月底还100元，5年还清；k个月后一次还6000元。

已知月结算名利率为12%，计算k。

解：由题意可得方程100a?p1% = 6000(1 + i)?k60解得k = 2925.已知a?pi= 1.75，求i。

2解：由题意得1 ? v= 1.75i2解得i = 9.38%26.某人得到一万元人寿保险赔付。

如果购买10年期末年金可以每年得到1538元，20年的期末年金为每年1072元。

计算年利率。

解：【篇二：金融数学引论北大版第4章答案】现有1000 元贷款计划在5 年内按季度偿还。

已知季换算名利率6%，计算第2 年底的未结贷款余额。

解：设每个季度还款额是r ，有ra(4)5p6%￢ = 1000解得r ，代入b2 的表达式b2 = ra(4)3p6%￢= 635.32 元2 设有10000 元贷款，每年底还款2000 元，已知年利率12% ，计算借款人的还款总额等于原贷款额时的未结贷款余额。

解：n =100002000= 5= 4917.72 元3 某贷款在每季度末偿还1500 元，季换算名利率10% ，如果已知第一年底的未结贷款余额为12000 元，计算最初的贷款额。

解：以季度为时间单位，i = 2.5% 。

b0 = b1 ? v + 1500a4pi ￢= 16514.4 元4 某贷款将在15 年内分期偿还。

前5 年每年底还4000 元，第二个5 年每年底还 3000 元，最后5 年每年底还2000 元。

计算第二次3000 元还款后的未结贷款余额的表达式。

如果已知第4 次还款后的未结贷款余额为5000 元，计算原始贷款金额。

解：设原始贷款额为l ，每次还款为r ，以半年为时间单位，有 ???5000 = ra3p4% ￢l = ra7p4% ￢整理得：l = 5000 ? a￢7pa￢3p= 10814.16 元6 现有20000 元贷款将在12 年内每年底分期偿还。

若(1+i)4 = 2 ，计算第4 次还款后的未结贷款余额。

解：设第4 次还款后的未结贷款余额为l ，每次还款为r ，有 ???20000 = r ? a12pi ￢l = r ? a8pi ￢把(1 + i)4 = 2 代入整理得：l = 5000 ? 1 ? (1 + i)?81 ? (1 + i)?12= 17142.86 元7 20000 元抵押贷款将在20 年内每年分期偿还，在第5 次还款后，因资金短缺，随后的两年内未进行正常还贷。

若借款人从第8 年底重新开始还贷，并在20 年内还清。

计算调整后的每次还款额。

解：设正常每次还款为r ，调整后每次还款x ，以当前时间和第5年底为比较日，有???20000 = ra2￢0pxa1￢3p ? v2 = ra1￢5p整理得：x = 20000 ? a15p ￢a2￢0p? (1 + i)2a1￢3p8 某贷款l 原计划在25 年内分年度等额还清。

但实际上从第6 次到第10 次的还款中每次多付k 元，结果提前5 年还清贷款。

试证明： k =a2￢0p ? a1￢5pa2￢5p a￢5p l证：以第20 年年底为比较日，设每次还款为r ，有???l = ra2￢5pks￢5p (1 + i)10 = ra￢5p整理即得。

9 设bt 表示未结贷款余额，证明：(1) (bt ? bt+1)(bt+2 ? bt+3) = (bt+1 ? bt+2)2;(2) bt + bt+3 bt+1 + bt+2证： (1)(bt ? bt+1)(bt+2 ? bt+3) = (r + bt+11 + i? bt+1) ? (bt+2 ? ((1 + i)bt+2 ? r))=r ? ibt+11 + i? (r ? ibt+2)= (r ? ibt+1) ? r ? i((1 + i)bt+1 ? r)1 + i= (r ? ibt+1)2= (bt+1 ? bt+2)2(2)bt ? bt+1 = r ? ibtr ? ibt+2= bt+2 ? bt+3) bt + bt+3 bt+1 + bt+2默认每次还款额是相同的！10 某贷款按季度分期偿还。

每次1000 元，还期5 年，季换算名利率12%。

计算第6 次还款中的本金量。

解：p6 = b5 ? b6= 1000a20?5p3% ￢ ? 1000a20?6p3% ￢= 641.86 元11 n 年期贷款，每年还款1元。

金融数学引论答案第二版

金融学习题集及参考答案解析word版第二版

金融学第二版讲义大纲及课后习题答案详解第八章

《金融学(第二版)》讲义大纲及课后习题答案详解 十四章

金融学第二版课后习题答案

金融数学引论答案 .docx

金融学第二版讲义大纲及课后习题答案详解第十章

《金融数学》(第二版)练习题(修订版)

国际金融第二版课后答案(全)

金融学第二版讲义大纲及课后习题答案详解十六章

金融数学引论答案第一章__北京大学出版[1]

《金融学(第二版)》讲义大纲及课后习题答案详解 第13章

《金融学(第二版)》讲义大纲及课后习题答案详解 第七章

金融学第二版课后复习思考题参考答案

博迪莫顿版金融学(第二版)课后习题答案,DOC

《金融学(第二版)》讲义大纲及课后习题答案详解 第九章

《金融数学》(第二版)习题参考答案(修订版)

金融数学引论答案第二版

《金融学(第二版)》讲义大纲及课后习题答案详解十四章

《金融学(第二版)》讲义大纲及课后习题答案详解第13章

《金融学(第二版)》讲义大纲及课后习题答案详解第七章

《金融学(第二版)》讲义大纲及课后习题答案详解第九章