公司理財(cái) 羅斯 習(xí)題集

1、課堂練習(xí)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?課堂練習(xí)2某公司如果不從事任何新的項(xiàng)目，則其每年預(yù)期盈利為1億美元。該公司面臨這樣一個(gè)投資機(jī)會(huì)：在今天立即投資1500萬美元并在一年后投資500萬美元，兩年后，這一新的投資每年將為公司帶

3、來1000萬美元的盈利。假設(shè)該公司有2000萬股普通股票，貼現(xiàn)率為15%，求：當(dāng)公司不從事任何新的投資項(xiàng)目時(shí)每股股票的價(jià)格是多少？投資項(xiàng)目的價(jià)值是多少？如果公司進(jìn)行該投資項(xiàng)目，每股股票的價(jià)格是多少？課堂練習(xí)3 某公司如果不從事新的投資項(xiàng)目，它每年的每股盈利為4元，在此情形下，公司把所有的盈利當(dāng)作股利分發(fā)出去（假設(shè)第一筆股利剛好在一年后收到）。在另一種情形中，假設(shè)距今三年后的每一年，公司將其盈利的25%投資于新的項(xiàng)目，每一個(gè)投資項(xiàng)目將在一年后獲得40%的收益率（直至永遠(yuǎn)）。設(shè)貼現(xiàn)率為14%，分別求公司在不從事新的投資項(xiàng)目和從事新的投資項(xiàng)目時(shí)的股票價(jià)格。課堂練習(xí)4 某公司市盈率為12，股利支付比率

4、40%，股價(jià)為32美元。如果股利支付比率變?yōu)?0%，股價(jià)為多少？課堂練習(xí)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?練習(xí)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).練習(xí)2解答（1）搖錢樹的價(jià)值：PV = C1 / r= $100,000,000 / 0.15= $666,666,666.67每股股票價(jià)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、票價(jià)格= （1）+ NPVGO / (股數(shù))= $33.33 + $38,623,188.41 / 20,000,000= $35.26練習(xí)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 練習(xí)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練習(xí)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.練習(xí)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:課堂練習(xí)6考慮兩個(gè)互斥投資項(xiàng)目，現(xiàn)金流如下：年份 項(xiàng)目A 項(xiàng)目B0 -5000 -1000001 3500 650002 3500 65000課堂練習(xí)6（1）兩個(gè)項(xiàng)目的IRR分別是多少？（2）僅僅根據(jù)IRR，你會(huì)選擇哪個(gè)項(xiàng)目？（3）你根據(jù)（2）做出決策時(shí)忽略了什么？（4）如何克服這一問題？請(qǐng)計(jì)算。（5）根據(jù)（4）的結(jié)果，你會(huì)選擇哪一個(gè)項(xiàng)目？假設(shè)貼現(xiàn)

12、率為15%。（6）根據(jù)NPV法則，你會(huì)選擇哪一個(gè)項(xiàng)目？假設(shè)貼現(xiàn)率為15%。課堂練習(xí)7課堂練習(xí)7課堂練習(xí)8課堂練習(xí)8課堂練習(xí)9課堂練習(xí)10練習(xí)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%. 練習(xí)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. 練習(xí)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. 練習(xí)6解答B(yǎng) 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練習(xí)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. 練習(xí)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. 練習(xí)7解答練習(xí)7解答練習(xí)7解答練習(xí)7解答練習(xí)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課堂練習(xí)11某公司的權(quán)益市場(chǎng)價(jià)值為2000萬美元，債務(wù)的市場(chǎng)價(jià)值為1000萬美元。債務(wù)的成本為每年14%，一年期國(guó)庫(kù)券的收益率為8%，預(yù)期下一年市場(chǎng)組合的收益率為18%，該公司的貝塔為0.9，假設(shè)無稅。（1）該公司的負(fù)債-權(quán)益比是多少？（2）該公司的加權(quán)平均資本成本是多少？（3）假設(shè)有一個(gè)全權(quán)益的公司

20、與該公司在其他方面都一樣，全權(quán)益公司的資本成本是多少？課堂練習(xí)12某公司負(fù)債-權(quán)益比為2.5，加權(quán)平均資本成本為15%，稅前債務(wù)成本為10%，公司稅率為35%。（1）該公司的權(quán)益資本成本？（2）該公司無杠桿權(quán)益資本成本？（3）如果該公司的負(fù)債-權(quán)益比變?yōu)?.75，其加權(quán)平均資本成本是多少？課堂練習(xí)13（1）什么是直接和間接的破產(chǎn)成本？請(qǐng)簡(jiǎn)單解釋。（2）財(cái)務(wù)困境成本及代理成本的存在怎樣影響有公司稅時(shí)的MM定理？（3）什么是權(quán)益代理成本？課堂練習(xí)14M公司負(fù)債-權(quán)益比為2/3，無杠桿權(quán)益資本成本為16%，稅前負(fù)債的成本為10%。銷售收入預(yù)計(jì)將一直保持在每年19,740,000美元，可變成本為銷售額

21、的60%，公司稅率為40%。該公司在每年末把所有盈利當(dāng)做股利分發(fā)出去。（1）如果M公司完全由權(quán)益融資，其價(jià)值是多少？（2）對(duì)M公司杠桿權(quán)益的要求回報(bào)率是多少？（3）使用加權(quán)平均資本成本法計(jì)算M公司的價(jià)值，其權(quán)益和負(fù)債的價(jià)值分別為多少？（4）使用權(quán)益現(xiàn)金流法計(jì)算M公司權(quán)益的價(jià)值。練習(xí)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.練習(xí)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練習(xí)12解答B(yǎng) / 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練習(xí)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練習(xí)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%.練習(xí)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練習(xí)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.練習(xí)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:練習(xí)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.練習(xí)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.練習(xí)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.練習(xí)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%.練習(xí)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練習(xí)14解答B(yǎng) / 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