公司理财 罗斯 习题集

1、课堂练习1Consider two securities that pay risk-free cash flows over the next two years and that have the current market prices shown here:a. What is the no-arbitrage price of a security that pays cash flows of $100 in one year and $100 in two years?b. What is the no-arbitrage price of a security that pa

2、ys cash flows of $100 in one year and $500 in two years?c. Suppose a security with cash flows of $50 in one year and $100 in two years is trading for a price of $130. What arbitrage opportunity is available?课堂练习2某公司如果不从事任何新的项目，则其每年预期盈利为1亿美元。该公司面临这样一个投资机会：在今天立即投资1500万美元并在一年后投资500万美元，两年后，这一新的投资每年将为公司带

3、来1000万美元的盈利。假设该公司有2000万股普通股票，贴现率为15%，求：当公司不从事任何新的投资项目时每股股票的价格是多少？投资项目的价值是多少？如果公司进行该投资项目，每股股票的价格是多少？课堂练习3 某公司如果不从事新的投资项目，它每年的每股盈利为4元，在此情形下，公司把所有的盈利当作股利分发出去（假设第一笔股利刚好在一年后收到）。在另一种情形中，假设距今三年后的每一年，公司将其盈利的25%投资于新的项目，每一个投资项目将在一年后获得40%的收益率（直至永远）。设贴现率为14%，分别求公司在不从事新的投资项目和从事新的投资项目时的股票价格。课堂练习4 某公司市盈率为12，股利支付比率

4、40%，股价为32美元。如果股利支付比率变为60%，股价为多少？课堂练习5Prices of zero-coupon, default-free securities with face values of $1000 are summarized in the following table:Suppose you observe that a three-year, default-free security with an annual coupon rate of 10% and a face value of $1000 has a price today of $1183.50.

5、Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not?练习1解答a. This security has the same cash flows as a portfolio of one share of B1 and one share of B2. Therefore, its no-arbitrage price is 94 + 85 = $179.b. This security has

6、the same cash flows as a portfolio of one share of B1 and five shares of B2. Therefore, its no-arbitrage price is 94 + 5 85 = $519c. There is an arbitrage opportunity because the no-arbitrage price should be $132 (94 / 2 + 85). One should buy two shares of the security at $130/share and sell one sha

7、re of B1 and two shares of B2. Total profit would be $4 (94 + 85 2 130 2).练习2解答（1）摇钱树的价值：PV = C1 / r= $100,000,000 / 0.15= $666,666,666.67每股股票价格= $666,666,666.67 / 20,000,000= $33.33（2）NPVGO =C0 + C1 +C2 / r / (1+r)T=-$15,000,000 -$5,000,000 / 1.15 + $10,000,000 / 0.15 / (1.15) =$38,623,188.41（3）每股股

8、票价格= （1）+ NPVGO / (股数)= $33.33 + $38,623,188.41 / 20,000,000= $35.26练习3解答 P = Div / r = 4 / 0.14 = 28.57 g = (0.25) (0.4)= 0.1 NPVGO = (Investment + Return / r) / (r g) / (1+r)2 = (-1 + 0.40 / .14) / (0.14 0.1) / (1.14)2 = 35.73P = PV(EPS) + NPVGO= 28.57 + 35.73= 64.30 练习4解答Using dividend model, pri

9、ce of a stock can be written as P = D/(k g)Or it can be written as P = E*PO/(k g) where PO is the dividend payout ratio and denotes multiplicationRearranging terms we get, P/E = PO/(k g)Substituting values 12 = .4/(k g) 1/(k g) = 12/0.4 1/(k g) = 30P = E*PO/(k g)Now substituting P = $32, PO = 40%, 1

10、/(k g) = 30 we get32 = E*.4*30 E = 8/3If the dividend payout ratio were 60%P = E*PO/(k g)P = (8/3)*.6*30 = $48练习5解答First, figure out if the price of the coupon bond is consistent with the zero coupon yields implied by the other securities.练习5解答According to these zero coupon yields, the price of the

11、coupon bond should be:The price of the coupon bond is too low, so there is an arbitrage opportunity. To take advantage of it:课堂练习6考虑两个互斥投资项目，现金流如下：年份 项目A 项目B0 -5000 -1000001 3500 650002 3500 65000课堂练习6（1）两个项目的IRR分别是多少？（2）仅仅根据IRR，你会选择哪个项目？（3）你根据（2）做出决策时忽略了什么？（4）如何克服这一问题？请计算。（5）根据（4）的结果，你会选择哪一个项目？假设贴现

12、率为15%。（6）根据NPV法则，你会选择哪一个项目？假设贴现率为15%。课堂练习7课堂练习7课堂练习8课堂练习8课堂练习9课堂练习10练习6解答a.Set the projects cash flows, discounted at the internal rate of return (IRR), equal to zero. Solve for the IRR. IRR(Project A) = C0 + C1 / (1+IRR) + C2 / (1+IRR)20 = -$5,000 + $3,500 / (1+IRR) + $3,500 / (1+IRR)2IRR = 0.2569T

13、he IRR of project A is 25.69%. IRR(Project B) = C0 + C1 / (1+IRR) + C2 / (1+IRR)20 = -$100,000 + $65,000 / (1+IRR) + $65,000 / (1+IRR)2IRR = 0.1943The IRR of project B is 19.43%. 练习6解答Choose project A because it has a higher IRR than project B. The difference in scale was ignored. Project B has a su

14、bstantially larger initial investment than project A has. Thus, the simple IRR calculation may not lead to the best decision. 练习6解答Calculate the incremental IRR. The incremental IRR is the IRR on the incremental investment from choosing the larger project instead of the smaller project. The incremen

15、tal cash flows are the differences between the cash flows of project B and those of project A. Always subtract the project with the smaller initial cash outflow from the project with the larger initial cash outflow. In this way, the initial incremental cash flow will be negative. 练习6解答B A ：-$95,000

16、$61,500 $61,500Next, find the IRR of those incremental cash flows. IRR(B A) = C0 + C1 / (1+IRR) + C2 / (1+IRR)20 = -$95,000 + $61,500 / (1+IRR) + $61,500 / (1+IRR)2IRR = 0.191练习6解答For investing-type projects, accept the larger project when the incremental rate of return is greater than the discount

17、rate. Therefore, choose project B since the incremental IRR (19.1%) is greater than the 15 percent discount rate. 练习6解答Calculate the NPV of each project. NPV(Project A) = -$5,000 + $3,500 / (1.15) + $3,500 / (1.15)2= $689.98The NPV of project A is $689.98.NPV(Project B) = -$100,000 + $65,000 / (1.15

18、) + $65,000 / (1.15)2= $5,671.08The NPV of project B is $5,671.08.Since the NPV of project B, $5,671.08, is greater than the NPV of project A, $689.98, choose project B. 练习7解答练习7解答练习7解答练习7解答练习10解答6 + 1.2 (16 6) = 18%6 + 0.5 (16 6) = 11%PV = $1,000/0.11 = $9,090.91PV = $1,000/0.16 = $6,250The differe

19、nce, $2,840.91, is the amount you will overpay if you erroneously assume that beta is 0.5 rather than 1.Using the SML: 4 = 6 + b(16 6) b = 2/10 = 0.2课堂练习11某公司的权益市场价值为2000万美元，债务的市场价值为1000万美元。债务的成本为每年14%，一年期国库券的收益率为8%，预期下一年市场组合的收益率为18%，该公司的贝塔为0.9，假设无税。（1）该公司的负债-权益比是多少？（2）该公司的加权平均资本成本是多少？（3）假设有一个全权益的公司

20、与该公司在其他方面都一样，全权益公司的资本成本是多少？课堂练习12某公司负债-权益比为2.5，加权平均资本成本为15%，税前债务成本为10%，公司税率为35%。（1）该公司的权益资本成本？（2）该公司无杠杆权益资本成本？（3）如果该公司的负债-权益比变为0.75，其加权平均资本成本是多少？课堂练习13（1）什么是直接和间接的破产成本？请简单解释。（2）财务困境成本及代理成本的存在怎样影响有公司税时的MM定理？（3）什么是权益代理成本？课堂练习14M公司负债-权益比为2/3，无杠杆权益资本成本为16%，税前负债的成本为10%。销售收入预计将一直保持在每年19,740,000美元，可变成本为销售额

21、的60%，公司税率为40%。该公司在每年末把所有盈利当做股利分发出去。（1）如果M公司完全由权益融资，其价值是多少？（2）对M公司杠杆权益的要求回报率是多少？（3）使用加权平均资本成本法计算M公司的价值，其权益和负债的价值分别为多少？（4）使用权益现金流法计算M公司权益的价值。练习11解答（1）Debt-Equity Ratio = Market Value of Debt / Market Value of Equity= $10 million / $20 million = （2）According to the CAPM:rS = rf + bSE(rm) rf = 0.08 + 0.

22、9( 0.18 0.08 = 0.17The cost of equity (rS) is 17%.weighted average cost of capital equals:rwacc = B / (B+S) rB + S / (B+S)rS= (1/3)(0.14) + (2/3)(0.17) = 0.16（3）According to Modigliani-Miller Proposition II (No Taxes): rS = r0 + (B/S)(r0 rB)Thus: 0.17 = r0 + (1/2)(r0 0.14)Solving for r0:r0 = 0.16The

23、refore, the cost of capital for an otherwise identical all-equity firm is 16%. This is consistent with Modigliani-Millers proposition that, in the absence of taxes, the cost of capital for an all-equity firm is equal to the weighted average cost of capital of an otherwise identical levered firm.练习12

24、解答In a world with corporate taxes, a firms weighted average cost of capital (rwacc) is equal to:rwacc = B / (B+S)(1 TC) rB + S / (B+S)rSwhere B / (B+S) = the firms debt-to-value ratioS / (B+S)= the firms equity-to-value ratiorB= the pre-tax cost of debtrS = the cost of equity for a levered firm.TC =

25、 the corporate tax rate练习12解答B / S = 2.5Solving for B: B = (2.5 * S)The above formula for rwacc uses the following ratio: B / (B+S)Since B = (2.5 * S):B/ (B+S)= (2.5 * S) / (2.5 * S) + S= (2.5 * S) / (3.5 * S)= (2.5 / 3.5)= 0.7143练习12解答rwacc= B / (B+S)(1 TC) rB + S / (B+S)rS 0.15= (0.7143)(1 0.35)(0

26、.10) + (0.2857)(rS)rS = 0.3625According to Modigliani-Miller Proposition II with corporate taxes:rS = r0 + (B/S)(r0 rB)(1 TC)where r0 = the cost of equity for an unlevered firmrS = the cost of equity for a levered firmrB = the pre-tax cost of debt TC = the corporate tax rateB/S = the firms debt-to-e

27、quity ratio练习12解答rS = r0 + (B/S)(r0 rB)(1 TC) 0.3625 = r0 + (2.5)(r0 0.10)(1 0.35)r0 = 0.20Therefore, the unlevered cost of equity is 20%.练习12解答rS = r0 + (B/S)(r0 rB)(1 TC) = 0.20 + (0.75)(0.20 0.10)(1 0.35) = 0.2488If debt-to-equity ratio is 0.75:B / S = 0.75Solving for B: B = (0.75 * S)A firms deb

28、t-to-value ratio is:B / (B+S),Since B = (0.75 * S): debt-to-value ratio = (0.75 * S) / (0.75 * S) + S = (0.75 * S) / (1.75 * S)= (0.75 / 1.75) = 0.4286练习12解答 the weighted average cost of capital (rwacc) is:rwacc= B / (B+S)(1 TC) rB + S /(B+S)rS= (0.4286)(1 0.35)(0.10) + (0.5714)(0.2488)= 0.17Therefo

29、re, the weighted average cost of capital (rwacc) is 17% if the firms debt-to-equity ratio is 0.75.练习13解答（1）Direct Costs:Legal and administrative costs: Costs associated with the litigation arising from a liquidation or bankruptcy. These costs include lawyers fees, courtroom costs, and expert witness

30、 fees.Indirect Costs:Impaired ability to conduct business: Incentive to under-invest:Milking the property:练习13解答（2）Modigliani and Millers theory with corporate taxes indicates that, since there is a positive tax advantage of debt, the firm should maximize the amount of debt in its capital structure.

31、 In reality, however, no firm adopts an all-debt financing strategy. MMs theory ignores both the financial distress and agency costs of debt. The marginal costs of debt continue to increase with the amount of debt in the firms capital structure so that, at some point, the marginal costs of additiona

32、l debt will outweigh its marginal tax benefits. Therefore, there is an optimal level of debt for every firm at the point where the marginal tax benefits of the debt equal the marginal increase in financial distress and agency costs.练习13解答（3）There are two major sources of the agency costs of equity:S

33、hirkingManagers with small equity holdings have a tendency to reduce their work effort, thereby hurting both the debt holders and outside equity holders.More PerquisitesSince management receives all the benefits of increased perquisites but only shoulder a fraction of the cost, managers have an ince

34、ntive to overspend on luxury items at the expense of debt holders and outside equity holders.练习14解答（1）If M were financed entirely by equity, the value of the firm would be equal to the present value of its unlevered after-tax earnings, discounted at its unlevered cost of capital of 16%.VU= $4,737,60

35、0 / 0.16 = $29,610,000Therefore, M Company would be worth $29,610,000 as an unlevered firm.练习14解答（2）According to Modigliani-Miller Proposition II with corporate taxes:rS = r0 + (B/S)(r0 rB)(1 TC)= 0.16 + (2/3)(0.16 0.10)(1 0.40)= 0.184The required return on Ms levered equity (rS) is 18.4%.练习14解答（3）I

36、n a world with corporate taxes, a firms weighted average cost of capital (rwacc) equals:rwacc = B / (B+S)(1 TC) rB + S / (B+S)rSwhere B / (B+S) = the firms debt-to-value ratioS / (B+S)= the firms equity-to-value ratiorB= the pre-tax cost of debtrS = the cost of equityTC = the corporate tax rate练习14解答B / S = 2/3Solving for B: B = (2/3)(S)A firms debt-to-value ratio is:B / (B+S)Since B = (2/3)(S):Ms debt-to-value ratio = (2/3