公司理财 罗斯 第9 版Chap015

罗斯《公司理财》（第9版）课后习题第13章风险、资本成本和资本预算一、概念题1．资产贝塔（asset beta）答：资产贝塔是指企业总资产的贝塔系数。

除非完全依靠权益融资，否则不能把资产贝塔看作普通股的贝塔系数。

其公式为：其中，β权益是杠杆企业权益的贝塔。

公式包括两部分，即负债的贝塔乘以负债在资本结构中的百分比；权益的贝塔乘以权益在资本结构中的百分比。

这个组合包括企业的负债和权益，所以组合贝塔就是资产贝塔。

在实际中，负债的贝塔很低，一般假设为零。

若假设负债的贝塔为零，则：对于杠杆企业，权益／（负债+权益）一定小于1，所以β资产<β权益，将上式变形，有：有财务杠杆的情况下，权益贝塔一定大于资产贝塔。

2．经营杠杆（operating leverage）答：经营杠杆是指由于固定成本的存在而导致息税前利润变动大于产销业务量变动的杠杆效应。

对经营杠杆的计量最常用的指标是经营杠杆系数或经营杠杆度。

经营杠杆系数，是指息税前利润变动率相当于销售量变动率的倍数。

用公式可以表示为：式中，EBIT为息税前利润；F为固定成本。

经营杠杆系数不是固定不变的。

当企业的固定成本总额、单位产品的变动成本、销售价格、销售数量等因素发生变动时，经营杠杆系数也会发生变动。

经营杠杆系数越高，对经营杠杆利益的影响就越强，经营杠杆风险也就越高。

经营杠杆越大，企业的贝塔系数就越大。

3．权益资本成本（cost of equity capital）答：权益资本成本就是投资股东要求的回报率，用CAPM模型表示股票的期望收益率为：其中，R F是无风险利率；是市场组合的期望收益率与无风险利率之差，也称为期望超额市场收益率或市场风险溢价。

所以要估计企业权益资本成本，需要知道以下三个变量：①无风险利率；②市场风险溢价；③公司权益的贝塔系数。

4．加权平均资本成本（weighted average cost of capital，r WACC）答：平均资本成本是权益资本成本和债务资本成本的加权平均，所以，通常称之为加权平均资本成本，r WACC，其计算公式如下：式中的权数分别是权益占总价值的比重，即和负债占总价值的比重，即。

罗斯《公司理财》第9版精要版英文原书课后部分章节答案详细»1 / 17 CH5 11，13，18，19，20 11. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = $1,000,000 / (1.10) 80 = $488.19 13. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for r, we get: r = (FV / PV) 1 / t –1 r = ($1,260,000 / $150) 1/112 – 1 = .0840 or 8.40% To find the FV of the first prize, we use: FV = PV(1 + r) t FV = $1,260,000(1.0840) 33 = $18,056,409.94 18. To find the FV of a lump sum, we use: FV = PV(1 + r) t FV = $4,000(1.11) 45 = $438,120.97 FV = $4,000(1.11) 35 = $154,299.40 Better start early! 19. We need to find the FV of a lump sum. However, the money will only be invested for six years, so the number of periods is six. FV = PV(1 + r) t FV = $20,000(1.084)6 = $32,449.33 20. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln($75,000 / $10,000) / ln(1.11) = 19.31 So, the money must be invested for 19.31 years. However, you will not receive the money for another two years. From now, you’ll wait: 2 years + 19.31 years = 21.31 years CH6 16，24，27，42，58 16. For this problem, we simply need to find the FV of a lump sum using the equation: FV = PV(1 + r) t 2 / 17 It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = $2,100[1 + (.084/2)] 34 = $8,505.93 24. This problem requires us to find the FVA. The equation to find the FVA is: FV A = C{[(1 + r) t – 1] / r} FV A = $300[{[1 + (.10/12) ] 360 – 1} / (.10/12)] = $678,146.38 27. The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get: EAR = [1 + (APR / m)] m – 1 EAR = [1 + (.11/4)] 4 – 1 = .1146 or 11.46% And now we use the EAR to find the PV of each cash flow as a lump sum and add them together: PV = $725 / 1.1146 + $980 / 1.1146 2 + $1,360 / 1.1146 4 = $2,320.36 42. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $1,150 monthly payments is: PVA = $1,150[(1 – {1 / [1 + (.0635/12)]} 360 ) / (.0635/12)] = $184,817.42 The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The amount of principal you will still owe is: $240,000 – 184,817.42 = $55,182.58 This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be: Balloon payment = $55,182.58[1 + (.0635/12)] 360 = $368,936.54 58. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: PV = $99 + $450{1 –[1 / (1 + .07/12) 12(3) ]} / (.07/12) = $14,672.91 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: PV = $23,000 / [1 + (.07/12)] 12(3) = $18,654.82 The PV of the decision to purchase is: $32,000 – 18,654.82 = $13,345.18 3 / 17 In this case, it is cheaper to buy the car than leasing it since the PV of the purchase cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be: $32,000 – PV of resale price = $14,672.91 PV of resale price = $17,327.09 The resale price that would make the PV of the lease versus buy decision is the FV ofthis value, so: Breakeven resale price = $17,327.09[1 + (.07/12)] 12(3) = $21,363.01 CH7 3，18，21，22，31 3. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = $75({1 – [1/(1 + .0875)] 10 } / .0875) + $1,000[1 / (1 + .0875) 10 ] = $918.89 We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PV A equation, it is common to abbreviate the equations as: PVIF R,t = 1 / (1 + r) t which stands for Present Value Interest Factor PVIFA R,t = ({1 – [1/(1 + r)] t } / r ) which stands for Present Value Interest Factor of an Annuity These abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key. 18. The bond price equation for this bond is: P 0 = $1,068 = $46(PVIFA R%,18 ) + $1,000(PVIF R%,18 ) Using a spreadsheet, financial calculator, or trial and error we find: R = 4.06% This is the semiannual interest rate, so the YTM is: YTM = 2 4.06% = 8.12% The current yield is: Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + 0.0406) 2 – 1 = .0829 or 8.29% 20. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $74/2 × 2/6 = $12.33 And we calculate the clean price as: 4 / 17 Clean price = Dirty price –Accrued interest = $968 –12.33 = $955.67 21. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $68/2 × 4/6 = $22.67 And we calculate the dirty price as: Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.67 22. To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0755 = $80/P 0 P 0 = $80/.0755 = $1,059.60 Now that we have the price of the bond, the bond price equation is: P = $1,059.60 = $80[(1 – (1/1.072) t ) / .072 ] + $1,000/1.072 t We can solve this equation for t as follows: $1,059.60(1.072) t = $1,111.11(1.072) t –1,111.11 + 1,000 111.11 = 51.51(1.072) t 2.1570 = 1.072 t t = log 2.1570 / log 1.072 = 11.06 11 years The bond has 11 years to maturity.31. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is: P M = $1,100(PVIFA 3.5%,16 )(PVIF 3.5%,12 ) + $1,400(PVIFA 3.5%,12 )(PVIF 3.5%,28 ) + $20,000(PVIF 3.5%,40 ) P M = $19,018.78 Notice that for the coupon payments of $1,400, we found the PV A for the coupon payments, and then discounted the lump sum back to today. Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the PV of the par, or: P N = $20,000(PVIF 3.5%,40 ) = $5,051.45 CH8 4，18，20，22，24 4. Using the constant growth model, we find the price of the stock today is: P 0 = D 1 / (R – g) = $3.04 / (.11 – .038) = $42.22 5 / 17 18. The priceof a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 20, so we can find the price of the stock in Year 19, one year before the first dividend payment. Doing so, we get: P 19 = $20.00 / .064 P 19 = $312.50 The price of the stock today is the PV of the stock price in the future, so the price today will be: P 0 = $312.50 / (1.064) 19 P 0 = $96.15 20. We can use the two-stage dividend growth model for this problem, which is: P 0 = [D 0 (1 + g 1 )/(R – g 1 )]{1 – [(1 + g 1 )/(1 + R)] T }+ [(1 + g 1 )/(1 + R)] T [D 0 (1 + g 2 )/(R –g 2 )] P 0 = [$1.25(1.28)/(.13 – .28)][1 –(1.28/1.13) 8 ] + [(1.28)/(1.13)] 8 [$1.25(1.06)/(.13 – .06)] P 0 = $69.55 22. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield. W: P 0 = D 0 (1 + g) / (R – g) = $4.50(1.10)/(.19 – .10) = $55.00 Dividend yield = D 1 /P 0 = $4.50(1.10)/$55.00 = .09 or 9% Capital gains yield = .19 – .09 = .10 or 10% X: P 0 = D 0 (1 + g) / (R – g) = $4.50/(.19 – 0) = $23.68 Dividend yield = D 1 /P 0 = $4.50/$23.68 = .19 or 19% Capital gains yield = .19 – .19 = 0% Y: P 0 = D 0 (1 + g) / (R – g) = $4.50(1 – .05)/(.19 + .05) = $17.81 Dividend yield = D 1 /P 0 = $4.50(0.95)/$17.81 = .24 or 24% Capital gains yield = .19 – .24 = –.05 or –5% Z: P 2 = D 2 (1 + g) / (R – g) = D 0 (1 + g 1 ) 2 (1 +g 2 )/(R – g 2 ) = $4.50(1.20) 2 (1.12)/(.19 – .12) = $103.68 P 0 = $4.50 (1.20) / (1.19) + $4.50(1.20) 2 / (1.19) 2 + $103.68 / (1.19) 2 = $82.33 Dividend yield = D 1 /P 0 = $4.50(1.20)/$82.33 = .066 or 6.6% Capital gains yield = .19 – .066 = .124 or 12.4% In all cases, the required return is 19%, but the return is distributed differently between current income and capital gains. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time. 24. Here we have a stock with supernormal growth, but the dividend growth changes every year for the first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be: 6 / 17 P 3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08 The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so: P 0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.11 2 + $2.45(1.20)(1.15)(1.10)/1.11 3 + $65.08/1.11 3 P 0 = $55.70 CH9 3，4，6，9，15 3. Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 of recapturing the initial investment, so the payback for Project A is: Payback = 1 + ($21,000 / $25,000) = 1.84 years Project B has cash flows of: Cash flows = $14,000 + 17,000 + 24,000 = $55,000 during this first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is: B: Payback = 3 + ($5,000 / $270,000) = 3.019 years Using the payback criterion and a cutoff of 3 years, accept project A and reject project B. 4. When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21 Value today of Year 2 cash flow = $5,300/1.14 2 = $4,078.18 Value today of Year 3 cash flow = $6,100/1.14 3 = $4,117.33 V alue today of Year 4 cash flow = $7,400/1.14 4 = $4,381.39 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is: Discounted payback= 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years For an initial cost of $10,000, the discounted payback is: Discounted payback = 2 + ($10,000 –3,684.21 – 4,078.18)/$4,117.33 = 2.54 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback. If the initial cost is $13,000, the discounted payback is: Discounted payback = 3 + ($13,000 – 3,684.21 – 4,078.18 – 4,117.33) / $4,381.39 = 3.26 years 7 / 17 6. Our definition of AAR is the average net income divided by the average book value. The average net income for this project is: Average net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325 And the average book value is: Average book value = ($15,000,000 + 0) / 2 = $7,500,000 So, the AAR for this project is: AAR = Average net income / Average book value = $1,836,325 / $7,500,000 = .2448 or 24.48% 9. The NPV of a project is the PV of the outflows minus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = –$138,000 + $28,500(PVIFA 8%, 9 ) = $40,036.31 At an 8 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 20 percent required return is: NPV = –$138,000 + $28,500(PVIFA 20%, 9 ) = –$23,117.45 At a 20 percent required return, the NPV is negative, so we would reject the project. We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = –$138,000 + $28,500(PVIFA IRR, 9 ) IRR = 14.59% 15. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The equation for the profitability index at a required return of 10 percent is: PI = [$7,300/1.1 + $6,900/1.1 2 + $5,700/1.1 3 ] / $14,000 = 1.187 The equation for the profitability index at a required return of 15 percent is: PI = [$7,300/1.15 + $6,900/1.15 2 + $5,700/1.15 3 ] / $14,000 = 1.094 The equation for the profitability index at a required return of 22 percent is: PI = [$7,300/1.22 + $6,900/1.22 2 + $5,700/1.22 3 ] / $14,000 = 0.983 8 / 17 We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one. We would reject the project if the required return were 22 percent since the PI。

公司理财第九版罗斯课后案例答案 Case Solutions CorporateFinance1. 案例一：公司资金需求分析问题：一家公司需要资金支持其新项目。

通过分析现金流量，推断该公司是否需要向外部借款或筹集其他资金。

解答：为了确定公司是否需要外部资金，我们需要分析公司的现金流量状况。

首先，我们需要计算公司的净现金流量（净收入加上非现金项目）。

然后，我们需要将净现金流量与项目的投资现金流量进行对比。

假设公司预计在项目开始时投资100万美元，并在项目运营期为5年。

预计该项目每年将产生50万美元的净现金流量。

现在，我们需要进行以下计算：净现金流量 = 年度现金流量 - 年度投资现金流量年度投资现金流量 = 100万美元年度现金流量 = 50万美元净现金流量 = 50万美元 - 100万美元 = -50万美元根据计算结果，公司的净现金流量为负数（即净现金流出），意味着公司每年都会亏损50万美元。

因此，公司需要从外部筹集资金以支持项目的运营。

2. 案例二：公司股权融资问题：一家公司正在考虑通过股权融资来筹集资金。

根据公司的财务数据和资本结构分析，我们需要确定公司最佳的股权融资方案。

解答：为了确定最佳的股权融资方案，我们需要参考公司的财务数据和资本结构分析。

首先，我们需要计算公司的资本结构比例，即股本占总资本的比例。

然后，我们将不同的股权融资方案与资本结构比例进行对比，选择最佳的方案。

假设公司当前的资本结构比例为60%的股本和40%的债务，在当前的资本结构下，公司的加权平均资本成本（WACC）为10%。

现在，我们需要进行以下计算：•方案一：以新股发行筹集1000万美元，并将其用于项目投资。

在这种方案下，公司的资本结构比例将发生变化。

假设公司的股本增加至80%，债务比例减少至20%。

根据资本结构比例的变化，WACC也将发生变化。

新的WACC可以通过以下公式计算得出：新的WACC = (股本比例 * 股本成本) + (债务比例 * 债务成本)假设公司的股本成本为12%，债务成本为8%：新的WACC = (0.8 * 12%) + (0.2 * 8%) = 9.6%•方案二：以新股发行筹集5000万美元，并将其用于项目投资。

罗斯《公司理财》第9版精要版英文原书课后部分章节答案详细»1 / 17 CH5 11，13，18，19，20 11. To find the PV of a lump sum, we use: PV = FV / (1 + r) t PV = $1,000,000 / (1.10) 80 = $488.19 13. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for r, we get: r = (FV / PV) 1 / t –1 r = ($1,260,000 / $150) 1/112 – 1 = .0840 or 8.40% To find the FV of the first prize, we use: FV = PV(1 + r) t FV = $1,260,000(1.0840) 33 = $18,056,409.94 18. To find the FV of a lump sum, we use: FV = PV(1 + r) t FV = $4,000(1.11) 45 = $438,120.97 FV = $4,000(1.11) 35 = $154,299.40 Better start early! 19. We need to find the FV of a lump sum. However, the money will only be invested for six years, so the number of periods is six. FV = PV(1 + r) t FV = $20,000(1.084)6 = $32,449.33 20. To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r) t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) t = ln($75,000 / $10,000) / ln(1.11) = 19.31 So, the money must be invested for 19.31 years. However, you will not receive the money for another two years. From now, you’ll wait: 2 years + 19.31 years = 21.31 years CH6 16，24，27，42，58 16. For this problem, we simply need to find the FV of a lump sum using the equation: FV = PV(1 + r) t 2 / 17 It is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get: FV = $2,100[1 + (.084/2)] 34 = $8,505.93 24. This problem requires us to find the FV A. The equation to find the FV A is: FV A = C{[(1 + r) t – 1] / r} FV A = $300[{[1 + (.10/12) ] 360 – 1} / (.10/12)] = $678,146.38 27. The cash flows are annual and the compounding period is quarterly, so we need to calculate the EAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get: EAR = [1 + (APR / m)] m – 1 EAR = [1 + (.11/4)] 4 – 1 = .1146 or 11.46% And now we use the EAR to find the PV of each cash flow as a lump sum and add them together: PV = $725 / 1.1146 + $980 / 1.1146 2 + $1,360 / 1.1146 4 = $2,320.36 42. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $1,150 monthly payments is: PV A = $1,150[(1 – {1 / [1 + (.0635/12)]} 360 ) / (.0635/12)] = $184,817.42 The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The amount of principal you will still owe is: $240,000 – 184,817.42 = $55,182.58 This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be: Balloon payment = $55,182.58[1 + (.0635/12)] 360 = $368,936.54 58. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: PV = $99 + $450{1 –[1 / (1 + .07/12) 12(3) ]} / (.07/12) = $14,672.91 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: PV = $23,000 / [1 + (.07/12)] 12(3) = $18,654.82 The PV of the decision to purchase is: $32,000 – 18,654.82 = $13,345.18 3 / 17 In this case, it is cheaper to buy the car than leasing it since the PV of the purchase cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be: $32,000 – PV of resale price = $14,672.91 PV of resale price = $17,327.09 The resale price that would make the PV of the lease versus buy decision is the FV ofthis value, so: Breakeven resale price = $17,327.09[1 + (.07/12)] 12(3) = $21,363.01 CH7 3，18，21，22，31 3. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = $75({1 – [1/(1 + .0875)] 10 } / .0875) + $1,000[1 / (1 + .0875) 10 ] = $918.89 We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PV A equation, it is common to abbreviate the equations as: PVIF R,t = 1 / (1 + r) t which stands for Present V alue Interest Factor PVIFA R,t = ({1 – [1/(1 + r)] t } / r ) which stands for Present V alue Interest Factor of an Annuity These abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key. 18. The bond price equation for this bond is: P 0 = $1,068 = $46(PVIFA R%,18 ) + $1,000(PVIF R%,18 ) Using a spreadsheet, financial calculator, or trial and error we find: R = 4.06% This is thesemiannual interest rate, so the YTM is: YTM = 2 4.06% = 8.12% The current yield is:Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61% The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter: Effective annual yield = (1 + 0.0406) 2 – 1 = .0829 or 8.29% 20. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $74/2 × 2/6 = $12.33 And we calculate the clean price as: 4 / 17 Clean price = Dirty price –Accrued interest = $968 –12.33 = $955.67 21. Accrued interest is the coupon payment for the period times the fraction of the period that has passed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is: Accrued interest = $68/2 × 4/6 = $22.67 And we calculate the dirty price as: Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.67 22. To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0755 = $80/P 0 P 0 = $80/.0755 = $1,059.60 Now that we have the price of the bond, the bond price equation is: P = $1,059.60 = $80[(1 – (1/1.072) t ) / .072 ] + $1,000/1.072 t We can solve this equation for t as follows: $1,059.60(1.072) t = $1,111.11(1.072) t –1,111.11 + 1,000 111.11 = 51.51(1.072) t2.1570 = 1.072 t t = log 2.1570 / log 1.072 = 11.06 11 years The bond has 11 years to maturity.31. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is: P M = $1,100(PVIFA 3.5%,16 )(PVIF 3.5%,12 ) + $1,400(PVIFA3.5%,12 )(PVIF 3.5%,28 ) + $20,000(PVIF 3.5%,40 ) P M = $19,018.78 Notice that for the coupon payments of $1,400, we found the PV A for the coupon payments, and then discounted the lump sum back to today. Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the PV of the par, or: P N = $20,000(PVIF3.5%,40 ) = $5,051.45 CH8 4，18，20，22，244. Using the constant growth model, we find the price of the stock today is: P 0 = D 1 / (R – g) = $3.04 / (.11 – .038) = $42.22 5 / 17 18. The price of a share of preferred stock is the dividend payment divided by the required return. We know the dividend payment in Year 20, so we can find the price of the stock in Y ear 19, one year before the first dividend payment. Doing so, we get: P 19 = $20.00 / .064 P 19 = $312.50 The price of the stock today is the PV of the stock price in the future, so the price today will be: P 0 = $312.50 / (1.064) 19 P 0 = $96.15 20. We can use the two-stage dividend growth model for this problem, which is: P 0 = [D 0 (1 + g 1 )/(R – g 1 )]{1 – [(1 + g 1 )/(1 + R)] T }+ [(1 + g 1 )/(1 + R)] T [D 0 (1 + g 2 )/(R –g 2 )] P0 = [$1.25(1.28)/(.13 –.28)][1 –(1.28/1.13) 8 ] + [(1.28)/(1.13)] 8 [$1.25(1.06)/(.13 – .06)] P 0 = $69.55 22. We are asked to find the dividend yield and capital gains yield for each of the stocks. All of the stocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield. W: P 0 = D 0 (1 + g) / (R – g) = $4.50(1.10)/(.19 – .10) = $55.00 Dividend yield = D 1 /P 0 = $4.50(1.10)/$55.00 = .09 or 9% Capital gains yield = .19 – .09 = .10 or 10% X: P 0 = D 0 (1 + g) / (R – g) = $4.50/(.19 – 0) = $23.68 Dividend yield = D 1 /P 0 = $4.50/$23.68 = .19 or 19% Capital gains yield = .19 – .19 = 0% Y: P 0 = D 0 (1 + g) / (R – g) = $4.50(1 – .05)/(.19 + .05) = $17.81 Dividend yield = D 1 /P 0 = $4.50(0.95)/$17.81 = .24 or 24% Capital gains yield = .19 – .24 = –.05 or –5% Z: P 2 = D 2 (1 + g) / (R – g) = D 0 (1 + g 1 ) 2 (1 +g 2 )/(R – g 2 ) = $4.50(1.20) 2 (1.12)/(.19 – .12) = $103.68 P 0 = $4.50 (1.20) / (1.19) + $4.50(1.20) 2 / (1.19) 2 + $103.68 / (1.19) 2 = $82.33 Dividend yield = D 1 /P 0 = $4.50(1.20)/$82.33 = .066 or 6.6% Capital gains yield = .19 – .066 = .124 or 12.4% In all cases, the required return is 19%, but the return is distributed differently between current income and capital gains. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time. 24. Here we have a stock with supernormal growth, but the dividend growth changes every year for the first four years. We can find the price of the stock in Y ear 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Y ear 3 will be the dividend in Y ear 4, divided by the required return minus the constant dividend growth rate. So, the price in Y ear 3 will be: 6 / 17 P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08 The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Y ear 3, so: P 0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.11 2 + $2.45(1.20)(1.15)(1.10)/1.11 3 + $65.08/1.11 3 P 0 = $55.70 CH9 3，4，6，9，15 3. Project A has cash flows of $19,000 in Y ear 1, so the cash flows are short by $21,000 of recapturing the initial investment, so the payback for Project A is: Payback = 1 + ($21,000 / $25,000) = 1.84 years Project B has cash flows of: Cash flows = $14,000 + 17,000 + 24,000 = $55,000 during this first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is: B: Payback = 3 + ($5,000 / $270,000) = 3.019 years Using the payback criterion and a cutoff of 3 years, accept project A and reject project B. 4. When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: V alue today of Y ear 1 cash flow = $4,200/1.14 = $3,684.21 V alue today of Y ear 2 cash flow = $5,300/1.14 2 = $4,078.18 V alue today of Y ear 3 cash flow = $6,100/1.14 3 = $4,117.33 V alue today of Y ear 4 cash flow = $7,400/1.14 4 = $4,381.39 To findthe discounted payback, we use these values to find the payback period. The discounted first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is: Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years For an initial cost of $10,000, the discounted payback is: Discounted payback = 2 + ($10,000 –3,684.21 –4,078.18)/$4,117.33 = 2.54 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Y ear 1 and Y ear 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Y ear 3 to get the fractional portion of the discounted payback. If the initial cost is $13,000, the discounted payback is: Discounted payback = 3 + ($13,000 – 3,684.21 – 4,078.18 – 4,117.33) / $4,381.39 = 3.26 years 7 / 17 6. Our definition of AAR is the average net income divided by the average book value. The average net income for this project is: A verage net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325 And the average book value is: A verage book value = ($15,000,000 + 0) / 2 = $7,500,000 So, the AAR for this project is: AAR = A verage net income / A verage book value = $1,836,325 / $7,500,000 = .2448 or 24.48% 9. The NPV of a project is the PV of the outflows minus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = –$138,000 + $28,500(PVIFA 8%, 9 ) = $40,036.31 At an 8 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 20 percent required return is: NPV = –$138,000 + $28,500(PVIFA 20%, 9 ) = –$23,117.45 At a 20 percent required return, the NPV is negative, so we would reject the project. We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = –$138,000 + $28,500(PVIFA IRR, 9 ) IRR = 14.59% 15. The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The equation for the profitability index at a required return of 10 percent is: PI = [$7,300/1.1 + $6,900/1.1 2 + $5,700/1.1 3 ] / $14,000 = 1.187 The equation for the profitability index at a required return of 15 percent is: PI = [$7,300/1.15 + $6,900/1.15 2 + $5,700/1.15 3 ] / $14,000 = 1.094 The equation for the profitability index at a required return of 22 percent is: PI = [$7,300/1.22 + $6,900/1.22 2 + $5,700/1.22 3 ] / $14,000 = 0.983 8 / 17 We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one. We would reject the project if the required return were 22 percent since the PI。

罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]（股票估值）【圣才出品】罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]第9章股票估值9.1复习笔记1．不同类型股票的估值（1）零增长股利股利不变时，一股股票的价格由下式给出：在这里假定Div1=Div2=…=Div。

（2）固定增长率股利如果股利以恒定的速率增长，那么一股股票的价格就为：式中，g是增长率；Div是第一期期末的股利。

（3）变动增长率股利2．股利折现模型中的参数估计（1）对增长率g的估计有效估计增长率的方法是：g=留存收益比率×留存收益收益率（ROE）只要公司保持其股利支付率不变，g就可以表示公司的股利增长率以及盈利增长率。

（2）对折现率R的估计对于折现率R的估计为：R=Div/P0+g该式表明总收益率R由两部分组成。

其中，第一部分被称为股利收益率，是预期的现金股利与当前的价格之比。

3．增长机会每股股价可以写做：该式表明，每股股价可以看做两部分的加和。

第一部分（EPS/R）是当公司满足于现状，而将其盈利全部发放给投资者时的价值；第二部分是当公司将盈利留存并用于投资新项目时的新增价值。

当公司投资于正NPVGO的增长机会时，公司价值增加。

反之，当公司选择负NPVGO 的投资机会时，公司价值降低。

但是，不管项目的NPV是正的还是负的，盈利和股利都是增长的。

不应该折现利润来获得每股价格，因为有部分盈利被用于再投资了。

只有股利被分到股东手中，也只有股利可以加以折现以获得股票价格。

4．市盈率即股票的市盈率是三个因素的函数：（1）增长机会。

拥有强劲增长机会的公司具有高市盈率。

（2）风险。

低风险股票具有高市盈率。

（3）会计方法。

采用保守会计方法的公司具有高市盈率。

5．股票市场交易商：持有一项存货，然后准备在任何时点进行买卖。

经纪人：将买者和卖者撮合在一起，但并不持有存货。

9.2课后习题详解一、概念题1．股利支付率（payout ratio）答：股利支付率一般指公司发放给普通股股东的现金股利占总利润的比例。

====Word行业资料分享--可编辑版本--双击可删====附录B各章习题及部分习题答案APPENDIX B目录Contents第一部分公司理财概览第三部分未来现金流量估价第1章公司理财导论3 第5章估价导论：货币的时间价值39 概念复习和重要的思考题 4 本章复习与自测题40微型案例麦吉糕点公司 5 本章复习与自测题解答40第2章财务报表、税和现金流量6 概念复习和重要的思考题40 本章复习与自测题7 思考和练习题41本章复习与自测题解答7 第6章贴现现金流量估价43概念复习和重要的思考题8 本章复习与自测题44思考和练习题9 本章复习与自测题解答44微型案例Sunset Boards公司的现金流量和概念复习和重要的思考题46财务报表13 思考和练习题4652第二部分财务报表与长期财务计划微型案例读MBA的决策第7章利率和债券估价54第3章利用财务报表17 本章复习与自测题55本章复习与自测题18 本章复习与自测题解答55本章复习与自测题解答19 概念复习和重要的思考题55概念复习和重要的思考题20 思考和练习题56思考和练习题21 微型案例基于债券发行的S&S飞机公司的微型案例针对S&S飞机公司的财务比率扩张计划59分析24 第8章股票估价60第4章长期财务计划与增长27 本章复习与自测题61本章复习与自测题28 本章复习与自测题解答61本章复习与自测题解答28 概念复习和重要的思考题61概念复习和重要的思考题29 思考和练习题62思考和练习题30 微型案例Ragan公司的股票估价64微型案例S&S飞机公司的比率与财务计划35III第四部分资本预算第9章净现值与其他投资准绳69 第六部分资本成本与长期财务政策第14章资本成本111本章复习与自测题70 本章复习与自测题112本章复习与自测题解答概念复习和重要的思考题7071本章复习与自测题解答概念复习和重要的思考题112112思考和练习题73 思考和练习题113第10章资本性投资决策77 第15章筹集资本117 本章复习与自测题78 本章复习与自测题118本章复习与自测题解答概念复习和重要的思考题7880本章复习与自测题解答概念复习和重要的思考题118118思考和练习题80 思考和练习题120微型案例贝壳共和电子公司（一）85 微型案例S&S飞机公司的上市121 第11章项目分析与评估86 第16章财务杠杆和资本结构政策123 本章复习与自测题87 本章复习与自测题124本章复习与自测题解答概念复习和重要的思考题8787本章复习与自测题解答概念复习和重要的思考题124124思考和练习题88 思考和练习题125微型案例贝壳共和电子公司（二）第五部分风险与报酬第12章资本市场历史的一些启示95 91 微型案例斯蒂芬森房地产公司的资本重组127第17章股利和股利政策129概念复习和重要的思考题130本章复习与自测题96 思考和练习题130本章复习与自测题解答概念复习和重要的思考题思考和练习题97 9696微型案例电子计时公司133第七部分短期财务计划与管理微型案例S&S飞机公司的职位99 第18章短期财务与计划137第13章报酬、风险与证券市场线101 本章复习与自测题138 本章复习与自测题102 本章复习与自测题解答138本章复习与自测题解答概念复习和重要的思考题102103概念复习和重要的思考题139思考和练习题140思考和练习题104 微型案例Piepkorn制造公司的营运成本管微型案例高露洁棕榄公司的 值108 理145IV第19章现金和流动性管理147本章复习与自测题148本章复习与自测题解答148概念复习和重要的思考题148思考和练习题149微型案例Webb公司的现金管理150 第20章信用和存货管理151本章复习与自测题152本章复习与自测题解答152概念复习和重要的思考题152思考和练习题153微型案例豪利特实业公司的信用政策155第八部分公司理财专题第21章国际公司理财159本章复习与自测题160本章复习与自测题解答160概念复习和重要的思考题160思考和练习题161微型案例S&S飞机公司的国际化经营163 部分习题答案165PART 1第一部分公司理财概览====Word行业资料分享--可编辑版本--双击可删====第1章公司理财导论CHAPTER 14附录概念复习和重要的思考题1.财务管理决策过程财务管理决策有哪三种类型？就每一种类型，举出一个相关的企业交易实例。

罗斯《公司理财》第9版笔记和课后习题（含考研真题）详解[视频详解]第15章长期融资:简介15.1复习笔记长期融资的基本来源为：普通股、优先股和长期负债。

具体来说，长期融资的基本方式主要包括普通股、优先股、长期债券、长期借款和留存收益等。

按资金来源于公司内部还是外部划分，其中前四种属于外部融资方式；留存收益属于内部融资方式。

按所筹集的资金是自有的还是借入的划分，普通股、优先股和留存收益属于自有资金，长期债券和长期借款属于借入资金。

本章主要介绍几种不同类型的长期融资方式。

一、普通股融资1．普通股概述（1）定义：普通股通常指那些在股利和破产清算方面不具有任何特殊优先权的股票，是股份有限公司发行的最基本、标准的股份。

普通股的持有人是公司的股东，他们是公司的最终所有者，对公司的经营收益或公司清算时的资产分配拥有最后的请求权，是公司风险的主要承担者。

（2）特点①与其他筹资方式相比，普通股筹资具有如下优点：a．所筹集的资本具有永久性，无到期日，不需归还。

b．没有固定的股利负担，股利支付与否和支付多少，视公司有无盈利和经营需要而定。

c．能增加公司的信誉，增强公司的举债能力。

d．由于普通股的预期收益较高并可一定程度地抵销通货膨胀的影响，因此普通股筹资容易吸收资金。

②普通股融资的缺点a．资本成本较高。

首先，从投资者的角度讲，投资于普通股风险较高，相应地所要求的投资报酬率也较高；其次，对于筹资公司来讲，普通股股利从税后利润中支付，不像债券利息那样作为费用从税前支付，因而不具有抵税作用；最后，普通股的发行费用一般也高于其他筹资方式。

b．以普通股筹资会增加新股东，这可能分散公司的控制权；另外，新股东分享公司未发行新股前积累的盈余，会降低普通股的每股净收益，从而可能引发股价的下跌。

2．普通股的价值计量（1）市场价值、账面价值和重置价值①市场价值。

市场价值是指把该资产视为一种商品在市场上公开竞争，在供求关系平衡状态下确定的价值。

公司理财习题答案第十五章Chapter 15: Capital Structure: Basic Concepts15.1 a. The value of Nadus’ stock is ($20)(5,000) = $100,000. Since Nadus is an all-equityfirm, $100,000 is also the value of the firm.b. The value of any firm is the sum of the market value of its bonds and the marketvalue of its stocks, i.e. V=B+S, For Logis, the value of the stock is not yet known,nor is the value of the firm. The market value of Logis’ bonds is $25,000. Thus,the value of Logis’ stock isS=V - $25,000.c. Costs:Nadus: 0.20 ($100,000) = $20,000Logis: 0.20 (V - $25,000)Returns: You are entitled to 20% of the net income of each firm.Nadus: 0.20 ($350,000) = $70,000Logis: 0.20 [$350,000-0.12($25,000)] = $69,400d. From the standpoint of the stockholders, Logis is riskier. If you hold Logis stock,you can receive returns only after the bondholders have been paid.e. In this problem, positive signs denote negative signs denote all cash inflows and alloutflows. You should expect the immediate flows to be on net negative (anoutflow). The future flows should be on net positive (an inflow).Immediate flows:Borrow from the bank an amount equal to 20% of Logis’ debt$5,000Buy 20% of Nadus’ stock -20,000Total Immediate Flows -$15,000Future flows:Pay the interest on the loan 0.12 ($5,000) -$600Receive 20% of Nadus’ net income 70,000Total Future Flows $69,400f. Since the returns from the purchase of the Logis stock are the same as the returns inthe strategy you constructed in part e, the two investments must cost the same.Cost of the strategy = Cost of Logis stock$15,000 = 0.20 (V-$25,000)Therefore, V=$100,000Note: This is an application of MM-Proposition I, In this MM world with no taxesand no financial distress costs, the value of an levered firm will equal the value ofan un-levered firm. Thus, capital structure does not matter.g. If the value of the Logis firm is $135,000 then the value of Logis stock is $110,000(= $135,000 - $25,000). If that is true, purchasing 20% of Logis’ stock would costyou $22,000 ( = 0.20 x $110,000). You will receive the same return as before($69,400). You can receive the same return for only $15,000 by following thestrategy in part e. Thus, if Logis is worth $135,000, you should borrow on yourown account an amount equal to 20% of Logis’ debt and purchase 20% of Nadus’stock.15.2 a. B=$10 million S=$20 millionTherefore, B/S=$10 / $20 = 1/2b. The required return is the firm’s after-tax overall cost of capital. In this no tax world,that is simplyrBVrSVr 0B S =+Use CAPM to find the required return on equity. Sr = 8% + (0.9)(10%) = 17%The cost of debt is 14%.Therefore,r$10 m illion$30 m illion0.14$20 m illion$30 m illion0.1716% 0=+=15.3 You expect to earn a 20% return on your investment of $25,000. Thus, you are earning$5,000 (=$25,000 x 0.20) per year. Since you borrowed $75,000, you will be makinginterest payments of $7,500 (=$75,000 x 0.10) per annum. Your share of the stock must earn $12,500 (= $5,000 + $7,500). The return without leverage is 0.125 (=$12,500 /$100,000).15.4 The firms are identical except for their capital structures. Thus, under MM-Proposition Itheir market values must be the same regardless of their capital structures. If they are not equal, the lower valued stock is a better purchase.Market values:Levered: V=$275 million + $100 x 4.5 million = $725 millionUnlevered: V= $80 x 10 million = $800 millionSince Levered’s market value is less than Unlevered’s market value, you should buyLevered’s stock. To understand why, construct the strategies that were presented in thetext. Suppose you want to own 5% of the equity of each firm.Strategy One: Buy 5% of Unlevered’s equityStrategy Two: Buy 5% of Levered’s equityStrategy Three: Create the dollar returns of Levered through borrowing an amount equal to 5% of Levered’s debt and purchasing 5% of Unlevered’s stock. If youfollow this strategy you will own what amounts to 5% of the equity ofLevered. The reason why is that the dollar returns will be identical topurchasing 5% of Levered outright.Dollar Investment Dollar Return Strategy One: -(0.05)($800) (0.05)($96)Strategy Two: -(0.05)($450) (0.05)[$96 - (0.08)($275)]Strategy Three:Borrow (0.05)($275) -[(0.05) ($275)] (0.08)Buy Unlevered -(0.05)($800) (0.05)($96)Net $ Flows -(0.05)($525) (0.05)[$96 - (0.08)($275)] Note: Dollar amounts are in millions.Note: Negative signs denote outflows and positive denotes inflows.Since the payoffs to strategies Two and Three are identical, their costs should be the same.Yet, strategy three is more expensive than strategy two ($26.25 million versus $22.5公司理财习题答案第十五章million). Thus, Levered’s stock is underpriced relative to Unlevered’s stock. You should purchase Levered’s s tock.15.5 a. In this MM world, the market value of Veblen must be the same as the market valueof Knight. If they are not equal, an investor can improve his net returns throughborrowing and buying Veblen stock. To understand the improvement, construct thestrategies discussed in the text. The investor already owns 0.0058343 (=$10,000 /$1,714,000) of the equity of Knight. Suppose he is willing to purchase the sameamount of Veblen’s equity.Strategy One (SI): Buy 0.58343% of Veblen’s equit y.Strategy Two (SII): Continue to hold the 0.58343% of Knight’s equity.Strategy Three (SIII): Create the dollar returns of Knight through borrowing anamount equal to 0.58343% of Knight’s debt and purchasing0.58343% of Veblen’s stock. If you follow this strategy youwill own what amounts to 0.58343% of the equity of Knight.The reason why is that the dollar returns will be identical topurchasing 0.58343% of Knight outright.Dollar Investment Dollar Return SI: -(0.0058343)($2.4) (0.0058343)($0.3)SII: -(0.0058343)($1.714) (0.0058343)($0.24)SIII:Borrow (0.0058343)($1) -[(0.0058343) ($1)] (0.06)Buy Veblen -(0.0058343)($2.4) (0.0058343)($0.3)Net $ Flows -(0.0058343)($1.4) (0.0058343)($0.24) Note: Dollar amounts are in millions.Note: Negative signs denote outflows and positive denotes inflows.Since strategies Two and Three have the same payoffs, they should cost the same.Strategy three is cheaper, thus, Knight stock is overpriced relative to Veblen stock.An investor can benefit by selling the Knight stock, borrowing an amount equal to0.0058343 of Knights debt and buying the same portion of Veblen stock. Theinvestor’s dollar returns will be identical to holding the Knight stock, but the costwill be less.b. Modigliani and Miller argue that everyone would attempt to construct the strategy.Investors would attempt to follow the strategy and the act of them doing so willlower the market value of Knight and raise the market value of Veblen until theyare equal.15.6 Each lady has purchased shares of the all-equity NLAW and borrowed or lent to create thenet dollar returns she desires. Once NLAW becomes levered, the return that the ladiesreceive for owning stock will be decreased by the interest payments. Thus, to continue to receive the same net dollar returns, each lady must rebalance her portfolio. The easiestapproach to this problem is to consider each lady individually. Determine the dollarreturns that the investor would receive from an all-equity NLAW. Determine what she will receive from the firm if it is levered. Then adjust her borrowing or lending position tocreate the returns she received from the all-equity firm.Before looking at the women’s positions, look at the firm value.All-equity: V=100,000 x $50 = $5,000,000Levered: V=$1,000,000 + 80,000 x $50 = $5,000,000Remember, the firm repurchased 20,000 shares.The income of the firm is unknown. Since we need it to compute the investor’s returns, we will denote it as Y. Assume that the income of the firm does not change due to the capital restructuring and that it is constant for the foreseeable future.Ms. A before rebalancing: Ms. A owns $10,000 worth of NLAW stock. That ownership represents ownership of 0.002 (=$10,000/$5,000,000) of the all-equity firm. That ownership entitles her to receive 0.002 of the firm’s income; i.e. her dollar return is 0.002Y. Also, Ms. A has borrowed $2,000. That loan will require her to make an interest payment of $400 ($2,000 x 0.20). Thus, the dollar investment and dollar return positions of Ms. A are:Dollar Investment Dollar Return NLAW Stock -$10,000 0.002YBorrowing 2,000 -$400Net -$8,000 0.002Y-$400Note: Negative signs denote outflows and positive denotes inflows.Ms. A after rebalancing: After rebalancing, Ms. A will want to receive net dollar returnsof 0.002Y-$400. The only way to receive the 0.002Y is to own 0.002 of NLAW’s stock. Examine the returns she will receive from the levered NLAW if she owns 0.002 of thef irm’s equity. She will receive (0.002) [Y - ($1,000,000)(0.20)] = 0.002Y - $400. This is exactly the dollar return she desires! Therefore, Ms. A should own 0.002 of the levered firm’s equity and neither lends nor borrow. Owning 0.002 of the firm’s equi ty means she has $8,000 (= 0.0002 x $4,000,000) invested in NLAW stock.Dollar Investment Dollar Return NLAW stock -$8,000 0.002Y - $400Ms. B before rebalancing: Ms. B owns $50,000 worth of NLAW stock. That ownership represents ownership of 0.01 (=$50,000/$5,000,000) of the all-equity firm. That ownership entitles her to receive 0.01 of the firm’s income; i.e. her dollar return is 0.01Y. Also, Ms. B has lent $6,000. That loan will generate interest income for her of the amount $1,200 (=$6,000 x 0.20). Thus, the dollar investment and dollar return positions of Ms. B are:Dollar Investment Dollar Return NLAW Stock -$50,000 0.01YLending -6,000 $1,200Net -$56,000 0.01Y + $1,200Ms. B after rebalancing: After rebalancing, Ms. B will want to receive net dollar returns of 0.01Y + $1,200. The only way to receive the 0.01Y is to own 0.01 of NLAW’s stock. Examine the returns she will receive from the levered NLAW if she owns 0.01 of the firm’s equity. She will receive (0.01) [Y - ($1,000,000) (0.20)] = 0.01Y - $2,000. This is not the return which Ms. B desires, so she must lend enough money to generate interest income of $3,200 (=$2,000 + $1,200). Since the interest rate is 20% she must lend公司理财习题答案第十五章$16,000 (= $3,200 / 0.20). The 0.01 equity interest of Ms. B means she will have $40,000 (=0.01 x $4,000,000) invested in NLAW.Dollar Investment Dollar ReturnNLAW Stock -$40,000 0.01Y - $2,000Lending -16,000 $3,200Net -$56,000 0.01Y + $1,200Ms. C before rebalancing: Ms. C owns $20,000 worth of NLAW stock. That ownershiprepresents ownership of 0.004 (=$20,000 / $5,000,000) of the all-equity firm. Thatownership entitles her to receive 0.004 of the firm’s income; i.e. her dollar return is 0.004Y.The dollar investment and dollar return positions of Ms. A are:Dollar Investment Dollar ReturnNLAW Stock -$20,000 0.004YMs. C after rebalancing: After rebalancing, Ms. C will want to receive net dollar returns of0.004Y. The only way to receive the 0.004Y is to ow n 0.004 of NLAW’s stock. Examinethe returns she will receive from the levered NLAW if she owns 0.004 of the firm’s equity.She will receive (0.004) [Y - ($1,000,000) (0.20)] = 0.004Y - $800. This is not the dollar return she desires. Therefore, Ms. C must lend enough money to offset the $800 she loses once the firm becomes levered. Since the interest rate is 20% she must lend $4,000 (=$800 / 0.20). The 0.004 equity interest of Ms. C means she will have $16,000 (0.004 x$4,000,000) invested in NLAW.Dollar Investment Dollar ReturnNLAW Stock -$16,000 0.004Y - $800Lending -4,000 $800Net -$20,000 0.004Y15.7 a. Since Rayburn is currently an all-equity firm, the value of the firm’s assets equalsthe value of its equity. Under MM-Proposition One, the value of a firm will notchange due to a capital structure change, and the overall cost of capital will remainunchanged. Therefore, Rayburn’s overall cost of capital is 18%.b. MM-Proposition Two states r r(B/S)(r r)=+-.S00BApplying this formula you can find the cost of equity.r = 18% + ($400,000 / $1,600,000) (18% - 10%) = 20%Sc. In accordance with Proposition Two, the expected return on Rayburn’s equity willrise with the amount of leverage. This rise occurs because of the risk which the debt adds.15.8 a.b.i. According to efficient markets, Strom’s stock price will rise immediately toreflect the NPV of the project.ii. The NPV of the facilities that Strom is buying isNPV= -$300,000 + ($120,000 / 0.15) = $500,000The sum of the old assets and the NPV of the new facilities is the new value ofthe firm ($5.5 million). Since new shares have not yet been sold, the price of theoutstanding shares must rise. The new price is $5,500,000 / 250,000 = $22.iii. Strom needed to raise $300,000 through the sale of stock that sells for $22.Thus, Strom sold 13,636.364 (=$300,000 / $22) shares.iv.v.vi. The returns available to the shareholders are the sum of the returns from each portion of the firm.Total earnings = $750,000 + $120,000 = $870,000Return = ($870,000 / $5,800,000) = 15%Note: The returns to the shareholder had to be the same since r0 was unchangedand the firm added no debt.c.i.Under efficient markets the price of the shares must rise to reflect the NPV of thenew facilities. The value will be the same as with all-equity financing because1. Strom purchased the same competitor and2. In this MM world debt is no better or no worse than equity.公司理财习题答案第十五章ii.iii. The cost of equity will be the earnings after interest and taxes divided by the market value of common. Since Strom pays no taxes, the cost of equity is simplythe earnings after interest (EAI) divided by the market value of common.EAI = $750,000 + $120,000 - $300,000 (0.10) = $840,000Cost of equity = $840,000 / $5,500,000 = 15.27%iv. The debt causes the equity of the firm to be riskier. Remember, stockholders are residual owners of the firm.v. MM-Proposition Two states,r r(B/S)(r r)15%($300,000/$5,500,000)(15%10%)15.27% =+-=+-=S00Bd. Examine the final balance sheet for the firm and you will see that the price is $22under each plan.15.9 a. The market value of the firm will be the present value of Gulf’s earning s after thenew plant is built. Since the firm is an all-equity firm, the overall required return isthe required return on equity.Annual earnings = Original plant + New Plant= $27 million + $3 million = $30 millionValue = $30 million / 0.1 = $300 millionb. Gulf Power is in an MM world (no taxes, no costs of financial distress). Therefore,the value of the firm is unchanged by a change in the capital structure.c. The overall required rate of return is also unchanged by the capital structurechange. Thus, according to MM-Proposition Two, r r(B/S)(r r)=+-. TheS00B firm is valued at $300 million of which $20 million is debt. The remaining $280million is the value of the stock.r S = 10% + ($20 million / $280 million) (10% - 8%) = 10.14%15.10 a. False. Leverage increases both the risks of the stock and its expected return. MMpoint out that these two effects exactly cancel out each other and leave the price ofthe stock and the value of the firm invariant to leverage. Since leverage is beingreduced in this firm, the risk of the shares is lower; however, the price of the stockremains the same in accordance with MM.b. False. If moderate borrowing does not affect the probability of financial distress,then the required return on equity is proportional to the debt-equity ratio [i.e.=+-]. Increasing the amount of debt will increase the return on r r(B/S)(r r)S00Bequity.15.11 a.i. Individuals can borrow at the same interest rate at which firms borrow.ii. There are no taxes.iii. There are no costs of financial distress.b.i. If firms are able to borrow at a rate that is lower than that at which individualsborrow, then it is possible to increase the firm’s value through borrowing. Asthe text discussed, since investors can purchase securities on margin, theindividuals’ effective rate is probably no higher than that of the firms.ii. In the presence of corporate taxes, the value of the firm is positively related to the level of debt. Since interest payments are deductible, increasing debtminimizes tax expenditure and thus maximizes the value of the firm for thestockholders. As will be shown in the next chapter, personal taxes offset thepositive effect of debt.iii. Because these costs are substantial and stockholders eventually bear them, they are incentives to lower the amount of debt. This implies that the capital structuremay matter. This topic will also be discussed more fully in the next chapter. 15.12 a and b.Total investment in the firm’s assets = $10 x 1million x 1% = $0.1 million3 choices of financing 20% debt 40% debt 60% debtTotal asset investment 0.1 0.1 0.1x ROA (15%) 0.015 0.015 0.015- Interest 0.2 x 0.1 x0.1 0.4 x 0.1 x 0.1 0.6 x 0.1 x 0.1Profit after interest 0.013 0.011 0.009/ Investment in equity 0.1 x 0.8 0.1 x 0.6 0.1 x 0.4ROE 16.25% 18.33% 22.5%Susan can expect to earn $0.013 million, $0.011 million, and $0.009 million,respectively, from the correspondent three scenarios of financing choices, i.e.borrowing 20%, 40%, or 60% of the total investment. The respective returns onequity are 16.25%, 18.33% and 22.5%.c. From part a and b, we can see that in an MM with no tax world, higher leveragebrings about higher return on equity. The high ROE is due to the increased risk ofequity while the WACC remains unchanged. See below.WACC for 20% debt = 16.25% x 0.8 + 10% x 0.2 = 15%WACC for 40% debt = 18.33% x 0.6 + 10% x 0.4 = 15%WACC for 60% debt = 22.5% x 0.4 + 10% x 0.6 = 15%This example is a case of homemade leverage, so the results are parallel to that of aleveraged firm.15.13 Suppose individuals can borrow at the same rate as the corporation, there is no needfor the firm to change its capital structure because of the different forecasts ofearnings growth rates, as investors can always duplicate the leverage by creatinghomemade leverage. Different expectation of earnings growth rates can affect theexpected return on assets. But this change is the result of the change in expectedoperating performance of the corporation and/or other macroeconomic factors. Theleverage ratio is irrelevant here since we are in an MM without tax world.公司理财习题答案第十五章15.14 a. current debt = 0.75 / 10% = $7.5 millioncurrent equity = 7.5 / 40% = $18.75 millionTotal firm value = 7.5 + 18.75 = $26.25 millionb. r s = earnings after interest/total equity value = $(3.75 - .75)/$18.75 = 16%r B =10%r 0 = (.4/1.4)(10%) + (1/1.4)(16%) = 14.29%r S after repurchase = 14.29% + (50%)(14.29% - 10%) = 16.44%So, the return on equity would increase from 16% to 16.44% with the completion of the planned stock repurchase.c. The stock price wouldn’t change because in an MM world, there’s no added value toa change in firm leverage. In other words, it’s a zero NPV transaction.15.15 a. Since V V T B L U C =+,V =V T B U L C -. L V = $1,700,000, B = $500,000 and C T =0.34. Therefore, the value of the unlevered firm isU V = $1,700,000 - (0.34)($500,000) = $1,530,000b. Equity holders earn 20% after-tax in an all-equity firm. That amount is $306,000(=$1,530,000 x 0.20). The yearly, after-tax interest expense in the levered firm is$33,000 [=$500,000 x 0.10 (1-0.34)]. Thus, the after-tax earnings of the equityholders in a levered firm are $273,000 (=$306,000 - $33,000). This amount is thefirm’s net income.15.16 The initial market value of the equity is given as $3,500,000. On a per share basis this is$20 (=$3,500,000 / 175,000). The firm buys back $1,000,000 worth of shares, or 50,000 (= $1,000,000 / $20) shares.In this MM world with taxes,V V T B L U C =+= $3,500,000 + (0.3) ($1,000,000) = $3,800,000Since V = B + S, the market value of the equity is $2,800,000 (= $3,800,000 - $1,000,000).15.17 a. Since Streiber is an all-equity firm,V = EBIT (1 - C T ) / 0r = $2,500,000 (1 - 0.34) / 0.20 = $8,250,000b. V V T B L U C =+= $8,250,000 + (0.34)($600,000) = $8,454,000c. The presence of debt creates a tax shield for the firm. That tax shield has value andaccounts for the increase in the value of the firm.d. You are making the MM assumptions:i. No personal taxesii. No costs of financial distressiii. Debt level of the firm is constant through time15.18 a. In this MM world with no financial distress costs, the value of the levered firm isgiven by V V T B L U C =+. The value of the unlevered firm is V = EBIT (1 - C T ) / r 0.The market value of the debt of Olbet is B = $200,000 / 0.08 = $2,500,000.Therefore, V = $1,200,000 (1 - 0.35) / 0.12 + ($2,500,000) (0.35) = $7,375,000b. Since debt adds to the value of the firm, it implies that the firm should be financedentirely with debt if it wishes to maximize its value.c. This conclusion is incorrect because it does not consider the costs of financialdistress or other agency costs that might offset the positive contribution of the debt. These costs will be discussed in further detail in the next chapter.15.19 a. Since Green is currently an all-equity firm, the value of the firm is the value of itsoutstanding equity, $10 million. The value of the firm must also equal the PV ofthe after-tax earnings, discounted at the overall required return. The after-taxearnings are simply ($1,500,000) (1 - 0.4) = $900,000. Thus, $10,000,000 =$900,000 / 0r0r = 0.09b. With 500,000 shares outstanding, the current price of a share is $20 (=$10,000,000 / 500,000). Green’s market value balance sheet isTherefore, at the announcement, the value of the firm will rise by the PV of the tax shield (PVTS). The PVTS is ($2,000,000) (0.4) = $800,000. Since the value of the firm has risen $800,000 and the debt has not yet been issued, the price of Green stock must rise to reflect the increase in firm value. Since the firm is worth $10,800,000 (=$10,000,000 + 800,000) and there are 500,000 shares outstanding,the price of a share rises to $21.60 (= $10,800,000 / 500,000). price of the stock rises to $21.60. Thus, Green will retire $2,000,000 / $21.60 = $92,592.59 shares. e. After the restructuring, the value of the firm will still be $10,800,000. Debt will be $2,000,000 and the 407,407.41 (=500,000 - 92,592.59) outstanding shares of stockwill sell for $21.60. )T -)(1r (B /S)(r r r C B 00S -+= = 0.09 + ($2,000,000 / $8,800,000) (0.09 - 0.06) (1 - 0.4) = 9.41%15.20 a.million $20.83$100.3515.0)65.0(4$B T r )T EBIT(1B T V V C 0C C U L =⨯+=+-=+= b.公司理财习题答案第十五章Answers to End-of-Chapter Problems B-15112.48%V )T EBIT(1r V S )T (1r V Br L C S L C B L WACC =-=+-= c. r r (B /S)(r r )(1-T S 00B C =+-)= 0.15 + [10 / (20.83 - 10)] (0.65) (0.15 - 0.10) = 18.01%15.21 a. r S = 0r + (B / S)( 0r – B r )(1 – C T )= 15% + (2.5)(15% – 11%)(1– 35%)= 21.50%b. If there is no debt, WACC r = r S = 15%c. S r = 15% + 0.75 (15% – 11%)(1 – 35%)= 16.95%B/S = 0.75, B = 0.75SB/(B+S) = 0.75S/(0.75S +S)= 0.75 /1.75S/(B+S) = 1– (0.75 /1.75) = (1/1.75)r WACC = (0.75/1.75)(0.11)(1– 0.35) + (1/1.75)(16.95%)= 12.75%S r = 15% + 1.5 (15% – 11%)(1 – 35%)= 18.90%B/S = 1.5, B = 1.5SB/(B+S) = 1.5S/(1.5S +S)= 1.5/2.5S /(B+S) = 1 – (1.5/2.5)WACC r = (1.5/2.5)(0.11)(1 – 0.35) + (1/2.5)(0.1890)= 11.85%15.22 Since this is an all-equity firm, the WACC = S r .$240,00025.0)4.01(000,100$r )T EBIT(1V S C U =-=-=If the firm borrows to repurchase its own shares, then the value of GT will be: L V = U V + C T B()$440,000000,500$4.025.0)6.0(000,100$=⨯+=。

罗斯《公司理财》（第9版）笔记和课后习题详解第1章公司理财导论1.1复习笔记公司的首要目标——股东财富最大化决定了公司理财的目标。

公司理财研究的是稀缺资金如何在企业和市场内进行有效配置，它是在股份有限公司已成为现代企业制度最主要组织形式的时代背景下，就公司经营过程中的资金运动进行预测、组织、协调、分析和控制的一种决策与管理活动。

从决策角度来讲，公司理财的决策内容包括投资决策、筹资决策、股利决策和净流动资金决策；从管理角度来讲，公司理财的管理职能主要是指对资金筹集和资金投放的管理。

公司理财的基本内容包括：投资决策（资本预算）、融资决策（资本结构）、短期财务管理（营运资本）。

1．资产负债表资产负债表是总括反映企业某一特定日期财务状况的会计报表，它是根据资产、负债和所有者权益之间的相互关系，按照一定的分类标准和一定的顺序，把企业一定日期的资产、负债和所有者权益各项目予以适当排列，并对日常工作中形成的大量数据进行高度浓缩整理后编制而成的。

资产负债表可以反映资本预算、资本支出、资本结构以及经营中的现金流量管理等方面的内容。

2．资本结构资本结构是指企业各种资本的构成及其比例关系，它有广义和狭义之分。

广义资本结构，亦称财务结构，指企业全部资本的构成，既包括长期资本，也包括短期资本（主要指短期债务资本）。

狭义资本结构，主要指企业长期资本的构成，而不包括短期资本。

通常人们将资本结构表示为债务资本与权益资本的比例关系（D/E）或债务资本在总资本的构成（D/A）。

准确地讲，企业的资本结构应定义为有偿负债与所有者权益的比例。

资本结构是由企业采用各种筹资方式筹集资本形成的。

筹资方式的选择及组合决定着企业资本结构及其变化。

资本结构是企业筹资决策的核心问题。

企业应综合考虑影响资本结构的因素，运用适当方法优化资本结构，从而实现最佳资本结构。

资本结构优化有利于降低资本成本，获取财务杠杆利益。

3．财务经理财务经理是公司管理团队中的重要成员，其主要职责是通过资本预算、融资和资产流动性管理为公司创造价值。

第十五章：长期融资：简介1. The indenture is a legal contract and can run into 100 pages or more. Bond features which would be included are: the basic terms of the bond, the total amount of the bonds issued, description of the property used as security, repayment arrangements, call provisions, convertibility provisions, and details of protective covenants.2.优先股和负债的区别有：1) 在确定公司应纳税收入时，优先股股利不能作为一项利息费用从而免于纳税。

从个人投资者角度分析，优先股股利属于应纳税的普通收入。

对企业投资者而言，他们投资优先股所获得的股利中有70%是可以免缴所得税的。

2) 在破产清算时，优先股次于负债，但优先于普通股。

3) 对于公司来说，没有法律义务一定要支付优先股股利，相反，公司有义务必须支付债券利息。

因此如果没有发放下一年优先股股利，公司一定不是被迫违约的。

优先股的应付股利既可以是“可累积”的，也可以是“非累积”的。

公司也可以无限期拖延（当然股利无限期拖延支付会对股票市场产生负面影响）3. Some firms can benefit from issuing preferred stock. The reasons can be:a. Public utilities can pass the tax disadvantage of issuing preferred stock on to their customers, so there is a substantial amount of straight preferred stock issued by utilities.b. Firms reporting losses to the IRS already don‘t have positive income for any tax deductions, so they are not affected by the tax disadvantage of dividends versus interest payments. They may be willing to issue preferred stock.c. Firms that issue preferred stock can avoid the threat of bankruptcy that exists with debt financing because preferred dividends are not a legal obligation like interest payments on corporate debt.4.不可转换优先股的收益低于公司债券的收益主要有两个原因：1) 如果企业投资者投资优先股股票，其所获得的股利中有70%是可以免缴所得税的，因此企业投资者更愿意购买其他公司的优先股，从而必须对优先股支付升水，这也降低了优先股的收益率。