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第五章 债券和股票的定价,主讲:肖淑芳 北京理工大学管理与经济学院 2004年2月,Corporate Finance Ross Westerfield Jaffe,Sixth Edition,Chapter Outline,5.1 Definition and Example of a Bond 5.2 How to Value Bonds 5.3 Bond Concepts 5.4 The Present Value of Common Stocks 5.5 Estimates of Parameters in the Dividend-Discount Model 5.6 Growth Opportunities 5.7 The Dividend Growth Model and the NPVGO Model 5.8 Price Earnings Ratio 5.9 Stock Market Reporting 5.10 Summary and Conclusions,第五章 债券和股票的定价,5.1 不同的价值概念 用货币时间价值的原理,可以对各种证券的价值进行估计。定价理论是公司理财各章内容的一个基础,公司的主要决策(筹资决策中资本成本的计算、证券投资决策中证券内在价值的计算)都与定价有关。 利用贴现的方法对债券和股票定价的准确程度是不同的。,5.1 不同的价值概念,(1)清算价值和持续经营价值 清算价值(liquidation value)是一项资产或一组资产从正在运营的组织中分离出来单独出售所获得的货币额。,5.1 不同的价值概念,如果一项或一组资产、一个公司的清算价值远高于其持续经营价值(市值),这些资产也就没有继续持有的必要,这个公司也就没有继续营运的意义。 若市值低于清算价值,公司将成为被收购的对象,并购者会发现有利可图。,5.1 不同的价值概念,持续经营价值(going -concern value) 资产的持续经营价值是,指资产作为按现行用途或转换为相关用途继续使用的有用物品,在其出售时所能获得的现金流量。 作为一个公司的续营价值,是指公司作为一个正在持续经营的营业组织整体在出售时所能获得的现金流量,而不是公司内部各项资产续营价值相加之和。,5.1 不同的价值概念,(2)帐面价值 资产帐面价值(book value)是资产的入帐价值(历史成本原则所决定的),即资产的成本减去累计折旧; 公司的帐面价值等于资产总额减去负债和优先股之和。 资产帐面价值应用的是会计准则,将购置成本分摊到每一年的结果; 股票市值反映的是公司未来现金流量的贴现值。 每股帐面价值与每股市值相比来反映股票被高估或低估了。,5.1 不同的价值概念,(3)内在价值和市场价值 市场价值(market value)是资产交易时的市场价格;对公司而言,市场价值是清算价值和持续经营价值两者中较大者。 市场价值被表现为供求双方在交易时所达到的均衡价格。 市场价值是以公平的交易市场和交易活动存在为前提的,若资产没有可供交易的公平市场,它也就没有市场价值。,5.1 不同的价值概念,内在价值(intrinsic value)是指在对所有影响价值的因素(资产、收益、管理)都正确估价后所得到的证券价值,是证券的经济价值。 若市场是有效率的,信息是完全的,则证券时价(current market price)应围绕其内在价值上下波动。,5.1 不同的价值概念,资产的内在价值是将资产能带来的未来现金流量折为现值,也称为资本化价值。资产的内在价值也是一种交换价值,是按未来售出价格衡量的现金或现金等价物。 将未来所取得的现金流量折为现值,意味着内在价值已扣除了按一定贴现率所计算的投资报酬。 将内在价值再与现时市场价值比较尚有正数余额,说明在该资产上能够取得超过贴现率水平的超额报酬,这正是购买或持有的目的。,5.1 不同的价值概念,除了比较证券的内在价值与市场价值外,还可以比较证券的预期收益率与应得收益率来进行证券投资决策。 例如股票的预期收益率与赢得收益率。 证券分析师的目标是发现内在价值低于市场价值的证券,5.1 不同的价值概念,证券估价的基本方法,是将证券投资者获得的现金流量按投资者要求的报酬率折现,计算其现值。这是一种考虑了各种风险后计算证券应有价值的方法。基本计算公式为: PV=Ct /(1+k)t (t=1,2,3, , ,n) 其中:PV证券现值 Ct第t期的预期现金流量 k贴现率 n投资受益期间,Valuation of Bonds and Stock First Principles: Value of financial securities = PV of expected future cash flows To value bonds and stocks we need to: Estimate future cash flows: Size (how much) and Timing (when) Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the security.,5.1 不同的价值概念,5.2 债券估价(Bond),影响债券内在价值的因素有: 债券面值(face value) 息票率(coupon rate) 贴现率(discount rate) 债券期限等。,Definition and Example of a Bond,Consider a U.S. government bond listed as 6 3/8 of December 2009. The Par Value of the bond is $1,000. Coupon payments are made semi-annually (June 30 and December 31 for this particular bond). Since the coupon rate is 6 3/8 the payment is $31.875. On January 1, 2002 the size and timing of cash flows are:,How to Value Bonds,Identify the size and timing of cash flows. Discount at the correct discount rate. If you know the price of a bond and the size and timing of cash flows, the yield to maturity is the discount rate. Yield to maturity (YTM) is the discount rate that equates the price of a bond with the discounted value of its coupons and face (par) value. In other words, value = price when r = YTM. The yield to maturity represents the current market interest rate for a bond.,5.2 债券估价,5.2.1 纯贴息债券(pure discount bond) 零息债券(zero coupon bond) 贴息发行债券 以低于面值的价格出售、不支付利息、到期还本的债券,是一种以价格增殖的形式作为投资者回报的债券。 (P77),Pure Discount Bonds,Information needed for valuing pure discount bonds: Time to maturity (T) = Maturity date - todays date Face value (F) Discount rate (r),Present value of a pure discount bond at time 0:,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%.,5.2 债券估价,5.2.2 平息债券(nonzero coupon bond) 平息债券是指在债券发行期内定期支付利息(复利),到期还本的债券。 例51(P78-79),Level-Coupon Bonds,Information needed to value level-coupon bonds: Coupon payment dates and time to maturity (T) Coupon payment (C) per period and Face value (F) Discount rate,Value of a Level-coupon bond = PV of coupon payment annuity + PV of face value,Level-Coupon Bonds: Example,Find the present value (as of January 1, 2002), of a 6-3/8 coupon T-bond with semi-annual payments, and a maturity date of December 2009 if the YTM is 5-percent. On January 1, 2002 the size and timing of cash flows are:,5.2 债券估价,5.2.3 一次还本付息(不计复利)的债券 其债券内在价值为: F+(F r T) P = (1+ r )T =(F+F r T)PVIF r . T,5.2 债券估价,5.2.4 永久债券(perpetual bond) 无还本期、定期支付利息直到永远的债券。例如,英国统一公债(CONSOL)、美国举债建造巴拿马运河的债券。 其债券内在价值 为 P=C/ r,5.3 与债券价值有关的几个问题,5.3.1 利率与债券价格(Interest and rates and bond prices ) 例5-2(P80) 市场利率上升,债券价格下降; 市场利率下降,债券价格上升。 例如:2002年第八次降息,目前银行3年和5年期存款的利率分别为2.52%和2.79%,扣税后,实际利率分别为2.016%和2.232%。而3年和5年期国债利率分别为2.89%和3.14%。由于降息后新发行债券的利率必然降低,已发行债券的内在价值均有所提高(固定利率)。,5.3 与债券价值有关的几个问题,The selling ways of Level-Coupon Bonds (1)When coupon rate = YTM, price = par value. (2)When coupon rate YTM, price par value (3)When coupon rate YTM, price par value,Interest and rates and bond prices,800,1000,1100,1200,1300,$1400,0,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,Discount Rate,Bond Value,When the YTM coupon, the bond trades at a premium.,When the YTM = coupon, the bond trades at par.,When the YTM coupon, the bond trades at a discount.,5.3 与债券价值有关的几个问题,5.3.2 债券的到期收益率(Yield to Maturity) 计算债券价格已知时收益率为的到期收益率。 到期收益率是债券按当前市价购买并持有至到期日所产生的预期报酬率,具体就是使债券预期现金流量的现值等于债券市场价格的贴现率。 (P80,D2),5.3 与债券价值有关的几个问题,YTM, Bond Value, and Discount Rate On July 1, 1998 a U.S. government bond is listed as 6 3/8s of December 2009 selling for 99.3125% of par value ($1000) in the Wall Street Journal. The bondholder has a claim to the following cash flows:,6/98 12/98 6/99 6/09 12/09 | | | | | | | | | | $31.875 $31.875 $31.875 $1031.875,5.3 与债券价值有关的几个问题,When discounted at the yield to maturity, the price (PV) of this bond is $993.125. The relationship between present value and discount rate.,5.3 与债券价值有关的几个问题,5.3 与债券价值有关的几个问题,A bond with longer maturity has higher relative (%) price change than one with shorter maturity when interest rate (YTM) changes. All other features are identical. A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.,Maturity and Bond Price Volatility,Consider two otherwise identical bonds. The long-maturity bond will have much more volatility with respect to changes in the discount rate,Figure (Price Risk),Coupon Rate and Bond Price Volatility,Consider two otherwise identical bonds. The low-coupon bond will have much more volatility with respect to changes in the discount rate,5.3 与债券价值有关的几个问题,长期债券有更高的利率敏感性的原因: 债券价值的一大部分来源于面值($1000)。若一年内收回,该面值的现值受利率变化影响较小;但即使利率只有很小的变化,若重复计算到30 年中,对现值的影响也会很大。,5.3 与债券价值有关的几个问题,利率较低的债券有较高风险的原因: 债券的价值取决于利息的现值和本金的现值。在到期日相同的情况下,利率较低的债券的价值更多的取决于到期收回面值的大小,因此在利率变化较大时,该部分现值的变化更大。 而利率较高的债券会在早期收回更多的现金,所以其价值相对于贴现率来说变化的敏感性要小一些。,5.3 与债券价值有关的几个问题,在美国大多数债券的期限是30年的。 近几年有更长期限的债券发行: 1995年,南方贝尔发行了100年期债券; 1993年,沃尔玛、可口可乐等发行了100年期债券; 1997年,某公司发行了1000年期的债券。 原因:发行方想锁定低利率。,5.3 与债券价值有关的几个问题,到期日 利率 价格 价格 价格 价格 12/31/95 7/31/96 变化幅度 8/31/97 变化幅度 7.00% 1000.00 800.00 -20.0% 997.20 24.7% 6.75% 976.25 886.25 -9.2% 985.00 11.1% 2033 7.50% 1040.00 960.00 -7.7% 996.20 3.8%,南方贝尔与其他两种30年期债券的利率风险比较,5.3 与债券价值有关的几个问题,国债到期收益率的计算: 央行发布的关于统一采用债券收益率计算方法有关事项的通知公布了统一的债券收益率的计算公式。对不处于最后付息周期的固定利率附息债券的到期收益率采取复利的方法,计算公式为: 式中:y到期收益率 PV债券全价(债券内在价值) f债券每年的利息支付频率 W=D/(365/f) M债券面值 D从债券交割日距下一次付息日的实际天数 n剩余的付息次数 n-1剩余的付息周期 C当期债券票面年利息,5.3 与债券价值有关的几个问题,当f=1时,上式计算结果为到期实际收益率; 当f2时,上式计算结果为名义收益率。 对不同债券的收益率进行比较时,应采用同一收益率,实际收益率或名义收益率。,5.4 股票估价(普通股),股票估价与债券估价基本原理相同,也是由其未来现金流量贴现所决定。 股票未来现金流量有二类,一是支付的股利,二是出售股票时的售价。与债券现金流量不同,股票现金流量有更大的不确定性。,5.4 股票估价(普通股),5.4.1 股票定价的基本模型 问题:股票内在价值是等于 下一期股利和下一期股票出售价格的现值总和还是 以后所有各期股利的现值? (P82),5.4 股票估价(普通股),For a single holding period: PV0 = (Divl + P1 ) / (l+r) What determines P1? P1 = PV1 = (Div2 + P2) / (l+r) Therefore PV0 = Divl / (l+r)+ Div2 / (l+r)2 + P2 / (l+r)2 Eventually results in: PV0 = Div1 / (l+r) + Div2 / (l+r)2 + Div3 / (l+r)3 + . =,5.4 股票估价(普通股),公式(5-4)可以认为是股票估价的一般模型。用该公式计算股票内在价值时,通常假设公司在未来某个时候支付股利,当公司清算或被并购时,也会支付清算股利或回购股票而发生现金支付。若公司从不支付任何现金股利或其他形式的股利,则股票价值等于零。 用公式(5-4)对股票估价是否忽视了资本利得? 否。因为股票未来的售价依赖于未来红利的预测。,5.4 股票估价(普通股),The value of common stock depends only on the timing, size, and riskiness of expected future dividends. How do we estimate future dividends? We introduce three models for estimating future dividends: zero growth, constant dividend growth, differential growth.,5.4 股票估价(普通股),The three dividend growth models apply to firms in different stages of its life cycle. Young companies usually have a high growth rate. After a while they slow down and grow at a more normal rate. Finally, they may shrink or go out of business entirely.,5.4 股票估价(普通股),The caveats with the dividend growth models. First, growth is hard to forecast and the growth rate has a large impact on estimated firm value. Second, it is dividends, not earnings, that should be used.,5.4 股票估价(普通股),5.4.2 不同类型股票的价值 (P82) (1)零成长股票(no growth or zero growth stock),Case 1: Zero Growth,Assume that dividends will remain at the same level forever,Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:,The zero growth model fits many mature companies surprisingly well,5.4 股票估价(普通股),(2)固定成长股票(constant growth) 股利以固定的比例g增长,则未来第t期的预期股利Dt=D0(1+g)t.,Case 2: Constant Growth,Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:,Assume that dividends will grow at a constant rate, g, forever. i.e.,.,.,.,Case 2: Constant Growth,Example of a constant growth stock: Suppose a firm just paid a dividend of $10 per share. Future dividends are expected to increase at a 5% annual rate. The required return is 25% per year. The value of the firm is estimated as: Divl = Div0 (1 + g) = ($10)(1.05) = $10.50 Price = Divl / (r g) = ($10.50) / (.25.05) = $52.50.,5.4 股票估价(普通股),(3)非固定成长股票(阶段性增长 growth phases) 因为公司有生命周期,在不同阶段红利分派会有不同。早期公司有好的投资机会,红利率低,增长速度快;成熟期,好的投资机会不多,红利率较高,增长速度较慢。 有一些股票(例如高科技企业)的价值会在短短几年内飞速增长(甚至gr),但接近成熟期时会减慢其增长速度,即股票价值从超常增长率到正常增长率(固定增长)之间有一个转变。,5.4 股票估价(普通股),例如,Value Line Investment Survey 对半导体行业和电器行业1995-1998年期间的资产收益率、红利分派率和每股盈利增长率进行了调查。 结果半导体行业的资产收益率、红利分派率和每股盈利增长率分别为18%、4.3%和8.3%;而电器行业的则分别为7.6%、70.8%和3.8%。,Case 3: Differential Growth,Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. To value a Differential Growth Stock, we need to: Estimate future dividends in the foreseeable future. Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.,Case 3: Differential Growth,Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter,.,.,.,.,.,.,Case 3: Differential Growth,Dividends will grow at rate g1 for N years and grow at rate g2 thereafter,0 1 2,N N+1,Case 3: Differential Growth,We can value this as the sum of: an N-year annuity growing at rate g1,plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1,Case 3: Differential Growth,To value a Differential Growth Stock, we can use,Or we can cash flow it out.,A Differential Growth Example,A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. The required return is 12% What is the stock worth?,With the Formula,A Differential Growth Example (continued),0 1 2 3 4,0 1 2 3,The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.,图52 (P83)零增长、固定增长和变动增长率的模型比较 图53(P84)-变动增长率的例子,5.4股票估价(普通股),5.4 股票估价(普通股),影响非固定成长股票高速增长期长度的因素: (1)公司收益的增长率相对于稳定增长率而言越高,高增长时期就越长。例如,目前增长率为40%的公司的高增长率时期要长于增长率只有14%的公司。 (2)公司的规模越大,高增长时期就越短。因为规模是促使公司趋于稳定增长的最强有力的因素。 (3)行业进入壁垒越强,高增长时期就越长。,5.5 股票定价模型中有关参数的估计,5.5.1 增长率g (1)利用公司的基本因素确定增长率g(P85) 当部分盈余没有当作股利支付给投资者,即部分盈余被保留时,下一年的盈余可用下式估计 下一年盈余=今年盈余+今年留存收益 今年留存收益的回报率,上式两端同除以“今年盈利”,则有,下一年盈利 今年盈利 今年留存收益 = + 今年留存收 益回报率 今年盈利 今年盈利 今年盈利 1+g=1+留存收益率留存收益回报率 g=留存收益率留存收益回报率 其中的“留存收益回报率”的确定,可假定近期选择的项目与其他年度投资项目有着同样的回报,即可利用历史上的权益报酬率(ROE)来估计现有的留存收益的预期回报率。,例56(P86) P公司财务报告有2000000元盈利,计划留存收益率为40%,公司历史上权益报率(ROE)为16%,求P公司盈利增长率(股利增长率与盈利增长率同比例)。 公司现保留800000元(200000040%),假设历史ROE是对未来回报率的恰当估计,则 盈利预计增长128000(80000016%),盈利增长率为 盈利增长率=128000/2000000=0.064=6.4% 即下一年的盈利=2000000 1.064=2128000 用公式计算, 则 G=40% 16%=0.064=6.4%,5.5 股票定价模型中有关参数的估计,(2)几何平均法 在过去若干年内股利增长较稳定的情况下,也可以用过去一定时期内股利增长率的几何平均数作为g的估计值,计算公式为 g =nDn/D0 1 =n(1+g1)(1+g2) (1+gt)(1+gn) 1 其中:Dn第n期股利 D0第一期股利 g t第t期的股利增长率,5.5 股票定价模型中有关参数的估计,Formula for Firms Growth Rate,决定增长率的因素: 总体经济环境 企业所处行业的成长性 企业的客户所处行业的成长性 收购可能带来的协同效应 企业的历史增长率 在一定的竞争条件下,包括技术、产品线、市场、定价、销售、市场营销等方面,管理者对未来发展的预期,Formula for Firms Growth Rate,选择长期增长率的方法是考虑宏观经济因素: 根据人口增长率确定国内生产总值的增长率 根据国内生产总值的增长率确定各行业长期加权平均增长率 根据具体行业情况确定其长期增长率 对企业所属行业的细分行业进行类似的分析 确定该企业的长期增长率,5.5.2贴现率r D1 D1 由P0= 可得 r = + g r g P0 其中的g可根据前面介绍的方法来估计,Po可根据公开的股利和股票价格信息来计算。 例57 (P86) (P87),5.5 股票定价模型中有关参数的估计,5.6 增长机会,Suppose a firm has no positive NPV opportunities and hence does not need retained earnings. The firm generates a constant stream of earnings per share which are paid out as dividends, so that g = 0 and EPS = D. The value of this zero growth firm is: PV0 = EPS / r = D / r,5.6 增长机会,Growth opportunities are opportunities to invest in positive NPV projects. The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100-percent of its earnings as dividends and the net present value of the growth opportunities.,5.6 增长机会,Suppose our nogrowth firm takes its earnings in period 1 and, instead of paying a dividend, invests in a new project at time 1. The discount rate on this new project is r, the same as on the old assets. The project will produce a change in EPS in period 2 and thereafter due to the new project, but otherwise the firm is the same. All earnings are still paid out as dividends, except in period 1.,5.6 增长机会,PV0 = = PV of firm without new project Cost of new project + PV of new project = PV of firm without growth + NPV of growth opportunities = EPS / r + NPVGO,5.6 增长机会,Decomposing firm value into these two components help relate the valuation principles to the goal of the firm. Accepting projects with positive NPV will increase firm value and is consistent with the goal of the firm and the goal of stockholders. Negative NPV projects should be rejected because they reduce firm value. Example 5-8(P88),5.6 增长机会,5.6.1 股利、盈利增长与增长机会(P89) 对于一项有着负的净现值( NPVGO )的项目进行投资而不是把盈利都作为股利的政策,会导致公司盈利和股利的增长,但却会降低公司价值 例59(P89),5.6 增长机会,5.6.2 股利和盈利:那一项应该折现? (P89) 应该对股利而不是盈利进行折现,因为投资人只能从股票的股利中获得好处 若将盈利折现,会使股票价格估计偏高,5.6 增长机会,5.6.3 无股利公司(P89) 不支付股利的公司,用股利折现进行估价其价值应为0,但其股票却以正价位出售 高增长率的公司倾向于低股利支付率:如麦当劳 低增长率的公司倾向于高股利支付率:如公共事业,5.7 股利增长模型与NPVGO模型,We have two ways to value a stock: The dividend discount model. The price of a share of stock can be calculated as the sum of its price as a cash cow plus the per-share value of its growth opportunities.,5.7 股利增长模型与NPVGO模型,5.7.1 股利增长模型(P90) 5.7.2 NPVGO模型(P90-92) (1)单一增长机会每股的价格(P90) (2)所有增长机会的每股价格(P91) (3)“现金牛”的价格(P91) (4)公司股票价格(P92) 所有增长机会的每股价格所有增长机会的每股价格,5.7 股利增长模型与NPVGO模型,Consider a firm that has EPS of $5 at the end of the first year, a dividend-payout ratio of 30%, a discount rate of 16-percent, and a return on retained earnings of 20-percent. The dividend at year one will be $5 .30 = $1.50 per share. The retention ratio is .70 ( = 1 -.30) implying a growth rate in dividends of 14% = .70 20% From the dividend growth model, the price of a share is:,The NPVGO Model,First, we must calculate the value of the firm as a cash cow.,Second, we must calculate the value of the growth opportunities.,Finally,5.8 Price Earnings Ratio,Many analysts frequently relate earnings per share to price. The price earnings ratio is a.k.a the multiple Calculated as current stock price divided by annual EPS The Wall Street Journal uses last 4 quarters earnings Firms whose shares are “in fashion” sell at high multiples. Growth stocks for example. Firms whose shares are out of favor sell at low multiples. Value stocks for example.,Other Price Ratio Analysis,Many analysts frequently relate earnings per share to variables other than price, e.g.: Price/Cash Flow Ratio cash flow = net income + depreciation

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