【文章內(nèi)容簡介】 1( / ????? ????????? nwn fy Mfy fCfy fCfy fCPV ? 與債券價值有關(guān)的幾個問題 當 f=1時，上式計算結(jié)果為到期實際收益率； 當 f≥2時，上式計算結(jié)果為名義收益率。 對不同債券的收益率進行比較時，應采用同一收益率，實際收益率或名義收益率。 股票估價（普通股） 股票估價與債券估價基本原理相同，也是由其未來 現(xiàn)金流量貼現(xiàn) 所決定。 股票未來現(xiàn)金流量有二類，一是支付的股利，二是出售股票時的售價。與債券現(xiàn)金流量不同，股票現(xiàn)金流量有更大的不確定性。 股票估價（普通股） 股票定價的基本模型 問題：股票內(nèi)在價值是等于 ①下一期股利和下一期股票出售價格的現(xiàn)值總和還是 ②以后所有各期股利的現(xiàn)值？ （ P82） 股票估價（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 + … . = ??? ?1ttt)r1(Di v 股票估價（普通股） 公式（ 54）可以認為是股票估價的 一般模型 。用該公式計算股票內(nèi)在價值時，通常假設公司在未來某個時候支付股利，當公司清算或被并購時，也會支付清算股利或回購股票而發(fā)生現(xiàn)金支付。若公司從不支付任何現(xiàn)金股利或其他形式的股利，則股票價值等于零。 用公式（ 54）對股票估價是否忽視了資本利得？ 否。因為股票未來的售價依賴于未來紅利的預測。 股票估價（普通股） ? The value of mon 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. 股票估價（普通股） The three dividend growth models apply to firms in different stages of its life cycle. ? Young panies 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. 股票估價（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. 股票估價（普通股） 不同類型股票的價值 (P82) （ 1）零成長股票（ no growth or zero growth stock） Case 1: Zero Growth ? Assume that dividends will remain at the same level forever rPrrrPD i v)1(D i v)1(D i v)1(D i v03322110???????? ?D i v???? ?321 D ivD ivD iv? 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 panies surprisingly well 股票估價（普通股） （ 2）固定成長股票（ constant growth） 股利以固定的比例 g增長，則未來第 t期的預期股利 Dt=D0（ 1+g） t. Case 2: Constant Growth )1(D ivD iv 01 g??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: grP?? 10 D ivAssume that dividends will grow at a constant rate, g, forever. . 2022 )1(D i v)1(D i vD i v gg ????3023 )1(D i v)1(D i vD i v gg ????. . . 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)() = $ Price = Divl / (r g) = ($) / (.) = $. 股票估價（普通股） （ 3）非固定成長股票（階段性增長 growth phases） 因為公司有生命周期，在不同階段紅利分派會有不同。早期公司有好的投資機會，紅利率低，增長速度快；成熟期，好的投資機會不多，紅利率較高，增長速度較慢。 有一些股票（例如高科技企業(yè)）的價值會在短短幾年內(nèi)飛速增長（甚至 g＞ r），但接近成熟期時會減慢其增長速度，即股票價值從超常增長率到正常增長率（固定增長）之間有一個轉(zhuǎn)變。 股票估價（普通股） 例如， Value Line Investment Survey 對半導體行業(yè)和電器行業(yè) 19951998年期間的資產(chǎn)收益率、紅利分派率和每股盈利增長率進行了調(diào)查。 結(jié)果半導體行業(yè)的資產(chǎn)收益率、紅利分派率和每股盈利增長率分別為 18%、 %和 %；而電器行業(yè)的則分別為 %、 %和 %。 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 bees 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 )(1D ivD iv 101 g??? Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter 210112 )(1D i v)(1D i vD i v gg ????NNN gg )(1D i v)(1D i vD i v 1011 ???? ?)(1)(1D i v)(1D i vD i v 21021 ggg NNN ??????. . . . . . Case 3: Differential Growth )(1D iv 10 g?? Dividends will grow at rate g1 for N years and grow at rate g2 thereafter 210 )(1D iv g?Ng )(1D iv 10 ? )(1)(1D iv)(1D iv2102gggNN????… 0 1 2 … N N+1 … Case 3: Differential Growth We can value this as the sum of: an Nyear annuity growing at rate g1 ??????????? TTA rggrCP)1()1(1 11plus the discounted value of a perpetuity growing at rate g2 that starts in year N+1 NB rgrP)1(D iv21