公司理财 罗斯 第9 版Chap015
罗斯《公司理财》(第9版)课后习题(第13~15章)【圣才出品】

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。
公司理财罗斯第九版课后习题答案

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 Corporate Finance

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。
公司理财 斯蒂芬A罗斯 第九版精要

Invests in assets (B)
Current assets Fixed assets Firm issues securities (A) Retained cash flows (F)
Financial markets
Short-term debt
Cash flow from firm (C) Dividends and debt payments (E) Taxes (D) Long-term debt Equity shares
1-1
Chapter Outline
1.1 What is Corporate Finance?
1.2 The Corporate Firm
1.3 The Importance of Cash Flows
1.4 The Goal of Financial Management 1.5 The Agency Problem and Control of the Corporation 1.6 Regulation
1-10
Forms of Business Organization
The Sole Proprietorship The Partnership
General Partnership Limited Partnership
The Corporation
1-11
A Comparison
Know
the basic types of financial management decisions and the role of the Financial Manager Know the financial implications of the various forms of business organization Know the goal of financial management Understand the conflicts of interest that can arise between owners and managers Understand the various regulations that firms face
罗斯《公司理财》第9版英文原书课后部分章节答案

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。
精编版罗斯《公司理财》中文版第九版课件资料

现值是指未来一定时间的特定货币按一定利率折算 到现在的价值。
终值是指现在一定数额的资金按一定的利率计算的 一定时间后的价值。
2.1资金时间价值观念
复利终值与现值
复利终值,是指一次性的收、付款项经过若干期的使用 后,所获得的包括本金和利息在内的未来价值。
因为永续年金无终止时间,所以不存在终值问题,永续 年金推倒公式如下:
2.1资金时间价值观念
资金时间价值计算中的几个特殊问题
不等额系列款项现值的计算:为求得不等额的系列付 款的现值之和,可以先计算每次付款的复利现值, 然后加总。
年金与不等额的系列付款混合情况下的现值:如果在 一组不等额的系列款项中,有部分是连续发生的 等额付款,则可分段计算其年金现值及复利现值, 然后加总。
式中: 是第j种证券的预期报酬率; 是第j种证券在全部投 资额中的比重;m是组合中证券种类总数。
2.2风险与收益权衡观念
组合投资的风险及度量。证券组合的风险不仅仅取决 于组合内各种证券的风险,还取决于各个证券之 间的关系。投资组合报酬率概率分布的标准差的 计算公式为:
式中:m是组合内证券种类总数; 是第j种证券在投资总额中 占的比例; 是第k种证券在投资总额中占的比例; 是第j种 证券与第k种证券报酬率的协方差。
1.4公司理财的原则与职能
公司理财原则
资金合理配置原则 财务收支平衡原则 成本-效益原则 风险与收益均衡原则 利益关系协调原则
1.4公司理财的原则与职能
公司理财职能
财务预测 财务决策 财务预算 财务控制 财务分析
1.5公司理财环境
公司理财的宏观环境
经济环境
公司理财精要版(罗斯第9版)-15筹集资本

系列1
100
93.39 101.04
70.9793.64
74
50
45.15
40.48
21.08
0
(2)破发率的显著提高彻底打破“新股不败神话”;
这里将新股破发定义为上市首日的平均价低于发 行价。据此定义,2010年新股破发率为6.91%, 2011年升至25.62%。
下表为2010~2011年破发新股的申购损益率
2011年 51.51 4.32 % -6.66 %
-0.29 % 15.35 % -9.92 % -1.02 % -1.52 %
平均 48.25 2.85 % -4.97 %
-0.17 % 10.55 % -4.59 % -0.61 % -0.74 %
注:上市首日涨幅是上市首日均价相对发行价的涨幅,收益率是指中签率乘以股价涨幅(中证指数有限公司) 24
• Google是第一家将这种方式用于股票发行 的大公司
15-14
绿鞋条款与牢笼协议
• 绿鞋条款(Green Shoe provision) – 允许承销团成员从发行者那里额外购买不超过发 行额15%的证券 – 允许证券发行被超额认购 – 为承销商执行价格稳定职能提供了保护
• 牢笼协议(Lockup agreements)/限售协议 – 限制内部人士在IPO之后特定一段时间内不能对 外出售股份 – 通常,美国的牢笼锁定期为180天。 – 当牢笼期满时,由于市场预期会有大量股份解限资本(VC)
• 含义:指愿意融资给相对年轻、新创立公 司并换以股权的私有资本
• 通常都需要一些实际的指导 • 公司通常都有“退出”战略
– 出售公司 – VC从出售所得中获利 – 使公司上市 – VC从IPO中获利
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】
【圣才出品】](https://img.taocdn.com/s3/m/e1dcbc711fb91a37f111f18583d049649b660eea.png)
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。
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0
$0
$0
$1,000
30
1
2
29
$1,000 F $174.11 PV T 30 (1 r ) (1.06)
15-11
Floating Rate Bonds
Coupon rate floats depending on some index value Examples – adjustable rate mortgages and inflationlinked Treasuries There is less price risk with floating rate bonds.
Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm, and stockholders have no legal recourse if dividends are not paid An all-equity firm cannot go bankrupt
15-13
Securitized Bonds
Also called asset-backed bonds Bondholders receive interest and principal payments from a specific asset rather than a specific company or government Mortgage backed securities are the best-known type of securitized bond, but others include
15-8
Zero Coupon Bonds
Make no periodic interest payments (coupon rate = 0%) The entire yield to maturity comes from the difference between the purchase price and the par value Cannot sell for more than par value Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) Treasury Bills and principal-only Treasury strips are good examples of zeroes
Secured debt versus a debenture Subordinated debenture versus senior debt A bond with a sinking fund versus one without A callable bond versus a non-callable bond
Chapter 15
Long-Term Financing: An Introduction
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
15-12
Other Bond Types
Income bonds Convertible bonds Put bonds There are many other types of provisions that can be added to a bond, and many bonds have several provisions – it is important to recognize how these provisions affect required returns.
15-6
Bond Classifications
Registered vs. Bearer Forms Security
Collateral – secured by financial securities Mortgage – secured by real property, normally land or buildings Debentures – unsecured Notes – unsecured debt with original maturity less than 10 years
15-9
Pure Discouபைடு நூலகம்t Bonds
Information needed for valuing pure discount bonds: Time to maturity (T) = Maturity date - today’s date Face value (F) Discount rate (r)
15-3
Features of Preferred Stock
Dividends
Stated dividend must be paid before dividends can be paid to common stockholders. Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely. Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid.
Car loans Credit cards
15-14
15.4 Long-Term Syndicated Bank Loans
Large money-center banks frequently have more demand for loans than they have supply. Small regional banks are often in the opposite situation. As a result, a lager money center bank may arrange a loan with a firm or country and then sell portions of the loan to a syndicate of other banks. A syndicated loan may be publicly traded. Syndicated loans are always rated investment grade. However, a leveraged syndicated loan is junk.
15-5
The Bond Indenture
Contract between the company and the bondholders that includes:
The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions Call provisions Details of protective covenants
$0
0
$0
$0
$F
T
1
2
T 1
Present value of a pure discount bond at time 0:
F PV T (1 r )
15-10
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.
The coupon floats, so it is less likely to differ substantially from the yield to maturity.
Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor.”
Seniority
15-7
Required Yields
The coupon rate depends on the risk characteristics of the bond when issued. Which bonds will have the higher coupon, all else equal?
Preferred stock generally does not carry voting rights.
15-4
Debt versus Equity