第06章資本成本(武漢大學(xué)公司金融學(xué))

1、1公司金融 武漢大學(xué)經(jīng)濟(jì)與管理學(xué)院2第六章 資本成本一、資本成本概念剖析二、權(quán)益成本(Cost of Equity)三、債務(wù)成本(Cost of Debt)四、加權(quán)平均資本成本 (WACC)3 資本成本是公司使用資本所付出的代價(jià)。 站在投資者的角度，資本成本是投資者投資于某一項(xiàng)目或企業(yè)的機(jī)會(huì)成本，可以用投資者要求的必要報(bào)酬率（Required rate of Return）來(lái)度量。 公司金融中的基本假設(shè)是，投資者向企業(yè)提供資金，他們期望有一定的投資回報(bào)，這種回報(bào)就構(gòu)成了公司的融資成本。資本成本是投資與融資相溝通的橋梁。一、資本成本概念剖析4 資本成本直接影響公司價(jià)值，公司價(jià)值就是用資本成本折現(xiàn)

2、的一系列現(xiàn)金流。對(duì)資本成本的研究形成公司股東價(jià)值最大化前提下公司金融學(xué)的基礎(chǔ)內(nèi)容：如何投資（資本預(yù)算）？如何融資（資本結(jié)構(gòu)決策）？為投資者提供多少回報(bào)（股利政策決策）？ 資本成本如何估算還是投資學(xué)的核心內(nèi)容。在有效資本市場(chǎng)中，投資者期望的回報(bào)率，就是投資者的機(jī)會(huì)成本，即公司資本成本。 資本成本同時(shí)也是宏觀金融學(xué)研究的基礎(chǔ)。宏觀金融運(yùn)行的目的是促使有效金融市場(chǎng)的形成，使公司和投資者之間的資源配置有序化，宏觀金融的目標(biāo)歸根到底是為了促使一個(gè)國(guó)家的資本成本最小化。資本成本是金融學(xué)理論的核心5A Digest on Different Terminology We have used differen

3、t terminology such as required rate of return, the appropriate discount rate, the cost of capital and the opportunity cost of capital. They all mean essentially the same thing.6 Firms can raise capital for their projects either by issuing debt or issuing equity. These different sources of capital (e

4、quity or debt) will have different opportunity costs associated.（企業(yè)可以通過(guò)發(fā)行債券或股票為投資項(xiàng)目籌集資金，不同的資金來(lái)源具有不同的成本） One of the most important measures of cost of capital is Weighted Average Cost of Capital (WACC) which takes into account all the above.（衡量企業(yè)資金成本的一個(gè)重要指標(biāo)是加權(quán)平均資本成本-WACC）Equity and Debt7二、權(quán)益成本（Cost o

5、f Equity） Calculating the cost of equity is more difficult than calculating the cost of debt.（權(quán)益成本的計(jì)算比債務(wù)成本的計(jì)算要更為困難） There is no way of directly observing the return that the firms equity investors (shareholders) require on their investment. Hence, it must be somehow estimated.（權(quán)益成本的估計(jì)有不同的方法）8權(quán)益成本的估計(jì)

6、方法Source: Graham and Harvey (2001), The theory and practice of corporate finance: evidence from the field, Journal of Financial Economics 60, 187-243.9Gordon Growth Model Approach For a publicly traded company, we can observe the market price and the recent dividend payment. However, the growth rate

7、 of dividend payments needs to be estimated. There are three possible ways of estimating the growth rate: Use historical growth rates to predict the future growth rate Use analysts forecasts of future growth rates Use earnings retention： g = Retention Ratio x ROE （ Use historical ROE numbers to calc

8、ulate ROE ）10Gordon Growth Model Approach Advantages Easy to understand and easy to use Simplicity Disadvantages Mostly applicable to dividend paying firms Assumes that the dividend growth rate is constant Very sensitive to estimated growth rate Does not consider risk explicitly (No allowance for th

9、e uncertainty about the estimated growth rate)11The CAPM Approach 上式中，RE 為股東持有股票所期望獲得的收益即權(quán)益成本；Rf為無(wú)風(fēng)險(xiǎn)收益率； RM 為市場(chǎng)收益率，實(shí)踐中一般取大盤(pán)指數(shù)的收益率；RM Rf為市場(chǎng)風(fēng)險(xiǎn)溢價(jià)；E（beta ）表示股票相對(duì)于市場(chǎng)特有的風(fēng)險(xiǎn)。()EfEMfRRRR 資本資產(chǎn)定價(jià)模型（Capital Asset Pricing Model - CAPM）12Example Suppose the stock of Stansfield Enterprises, a publisher of PowerPoi

10、nt presentations, has a beta of 2.5. The firm is 100-percent equity financed. Assume a risk-free rate of 5-percent and a market risk premium of 10-percent. What is the appropriate discount rate for an expansion of this firm?%105 . 2%5R%30R13Example (continued) Suppose Stansfield Enterprises is evalu

11、ating the following non-mutually exclusive projects. Each costs $100 and lasts one year.ProjectProject Projects Estimated Cash Flows Next YearIRRNPV at 30%A2.5$15050%$15.38B2.5$13030%$0C2.5$11010%-$15.3814CAPM 方法的優(yōu)缺點(diǎn) Advantages Explicitly adjusts for risk Does not assume steady dividend growth Disad

12、vantages Sensitive to estimates of the market risk premium and beta Uses past to predict the future15Estimation of Beta Theoretically, the calculation of beta is straightforward:2,)(),(MMiMMiRVarRRCov 回歸方法（Regression techniques ）：Beta - Sensitivity of a stocks return to the return on the market port

13、folio.)(fMfERRRR16影響高低的因素分析 Business Risk（經(jīng)營(yíng)風(fēng)險(xiǎn)） Cyclicity of Revenues（收入的周期性） Operating Leverage（經(jīng)營(yíng)杠桿） Financial Risk（財(cái)務(wù)風(fēng)險(xiǎn)） Financial Leverage（財(cái)務(wù)杠桿）17收入的周期性 有些企業(yè)的收入具有明顯的周期性，即這些企業(yè)在商業(yè)周期的擴(kuò)張階段經(jīng)營(yíng)得很好，而在商業(yè)周期的緊縮階段經(jīng)營(yíng)得很差。 Empirical evidence suggests that retailers and automotive firms fluctuate with the busin

14、ess cycle.（經(jīng)驗(yàn)證據(jù)表明零售企業(yè)和汽車(chē)企業(yè)隨商業(yè)周期的波動(dòng)大） Transportation firms and utilities are less dependent upon the business cycle.（交通運(yùn)輸及公用事業(yè)類(lèi)企業(yè)與商業(yè)周期相關(guān)性不大） 由于貝塔是股票收益率與市場(chǎng)收益率的標(biāo)準(zhǔn)協(xié)方差，所以周期性強(qiáng)的股票必然具有較高的貝塔系數(shù)。18Operating Leverage（經(jīng)營(yíng)杠桿） 企業(yè)收入的周期性對(duì)貝塔起決定性作用，而經(jīng)營(yíng)杠桿又將這種作用進(jìn)一步放大。經(jīng)營(yíng)杠桿是公司EBIT對(duì)銷(xiāo)售收入波動(dòng)的反映程度。 The degree of operating lever

15、age is given by:SalesSalesEBITEBITEBITDOL/銷(xiāo)售額變化的百分比變化的百分比 例如，Piece Grain 固定成本為10萬(wàn)元，當(dāng)銷(xiāo)售收入由30萬(wàn)元增加到36萬(wàn)元時(shí)(增加20%)，變動(dòng)成本由18萬(wàn)元增加到21.6萬(wàn)元，則： EBIT由2萬(wàn)元增加到4.4萬(wàn)元(增加120%) 公司經(jīng)營(yíng)杠桿：DOL=120%/20%=6（倍）19經(jīng)營(yíng)杠桿與固定成本 當(dāng)產(chǎn)品價(jià)格保持不變時(shí)，經(jīng)營(yíng)杠桿可以寫(xiě)成：TFCQAVCPQAVCPDOL)()( 因此，只要TFC0，DOL就大于1；TFC越大，DOL就越大，表明企業(yè)經(jīng)營(yíng)風(fēng)險(xiǎn)越大。20銷(xiāo)售收入變化對(duì)EBIT的影響Volume$Fi

16、xed costsTotal costs EBIT VolumeOperating leverage increases as fixed costs rise and variable costs fall.Fixed costsTotal costs21Financial Leverage （財(cái)務(wù)杠桿） 經(jīng)營(yíng)杠桿與企業(yè)固定成本有關(guān)，而財(cái)務(wù)杠桿與企業(yè)籌集資金所產(chǎn)生的利息費(fèi)用有關(guān)。 財(cái)務(wù)杠桿是每股收益（EPS）相對(duì)于EBIT變動(dòng)的反映程度，用公式表示為：EBITEBITEPSEPSEBITDFL/變化的百分比每股收益變化的百分比.IntEBITEBIT其中，Int.為利息支出。若公司沒(méi)有負(fù)債，

17、則Int. =0，財(cái)務(wù)杠桿就等于1；一般情況下，公司有負(fù)債， Int. 為正，所以財(cái)務(wù)杠桿大于1。22財(cái)務(wù)杠桿與貝塔 公司有負(fù)債的情況下財(cái)務(wù)杠桿大于1，表明EBIT100%的變化被放大為每股收益高于100%的變化，從而使股東面臨了更大風(fēng)險(xiǎn)（財(cái)務(wù)風(fēng)險(xiǎn)）。 由于債務(wù)的使用增加了股東遭受的風(fēng)險(xiǎn)，因此股東需要有更高的回報(bào)，意味著權(quán)益成本增加。23資產(chǎn)貝塔與權(quán)益貝塔 有負(fù)債情況下，公司資產(chǎn)貝塔可以表示為債務(wù)貝塔與權(quán)益貝塔的加權(quán)平均，即： 一般情況下債務(wù)的貝塔很小，假定Debt 等于0，則權(quán)益貝塔可以寫(xiě)成：Asset = Debt + EquityDebt Debt+ Debt + EquityEquit

18、y EquityAssetEquityEquityDebt)1 ( 因此，債務(wù)的使用使得權(quán)益貝塔大于資產(chǎn)貝塔。24Financial Leverage and Beta: ExampleConsider Grand Sport, Inc., which is currently all-equity and has a beta of 0.90.The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity.Since the firm will remain in the same

19、 industry, its asset beta should remain 0.90.However, assuming a zero beta for its debt, its equity beta would become twice as large:Asset = 0.90 = 1 + 11 EquityEquity = 2 0.90 = 1.8025Using an Industry Beta（行業(yè)貝塔的運(yùn)用）（行業(yè)貝塔的運(yùn)用） 根據(jù)企業(yè)自身歷史數(shù)據(jù)估算貝塔系數(shù)是一種常用的方法，也可以運(yùn)用整個(gè)行業(yè)的貝塔系數(shù)估算企業(yè)的貝塔系數(shù)（有人認(rèn)為這種方法更好）。 運(yùn)用行業(yè)貝塔的基本原則：

20、 如果企業(yè)經(jīng)營(yíng)特點(diǎn)與所在行業(yè)其他企業(yè)的經(jīng)營(yíng)十分類(lèi)似，可以考慮運(yùn)用行業(yè)貝塔； 如果企業(yè)的經(jīng)營(yíng)特點(diǎn)與所在行業(yè)內(nèi)其他企業(yè)的經(jīng)營(yíng)有根本性差異，則應(yīng)該根據(jù)企業(yè)自身歷史數(shù)據(jù)估算企業(yè)貝塔； 還要注意運(yùn)用財(cái)務(wù)杠桿對(duì)行業(yè)貝塔進(jìn)行調(diào)整。26Stability of Beta（貝塔的穩(wěn)定性） 如果企業(yè)改變業(yè)務(wù)，貝塔系數(shù)一般隨之改變。但如果企業(yè)不改變行業(yè)，貝塔系數(shù)會(huì)不會(huì)改變？ 大多數(shù)研究結(jié)果表明：一般情況下，當(dāng)企業(yè)不改變業(yè)務(wù)時(shí)，其貝塔系數(shù)保持穩(wěn)定。 但在一些特定情況下，即使企業(yè)不改變行業(yè)，其貝塔系數(shù)也會(huì)改變，如： 企業(yè)生產(chǎn)的產(chǎn)品系列發(fā)生了大的變化； 企業(yè)所采用的技術(shù)發(fā)生很大變遷； 政府的管制放松：如解除對(duì)航空業(yè)的管制

21、會(huì)使航空公司貝塔系數(shù)變大； 財(cái)務(wù)杠桿的變化； 等等。27股票流動(dòng)性與權(quán)益成本 The idea that the expected return on a stock and the firms cost of capital are positively related to risk is fundamental. Recently a number of academics have argued that the expected return on a stock and the firms cost of capital are negatively related to the

22、liquidity of the firms shares as well.28Liquidity and the Cost of CapitalCost of CapitalLiquidityAn increase in liquidity, i.e. a reduction in trading costs, lowers a firms cost of capital.29What the Corporation Can Do The corporation has an incentive to lower trading costs since this would result i

23、n a lower cost of capital. A stock split would increase the liquidity of the shares, but it would also reduce the adverse selection costs thereby lowering bid-ask spreads. Companies can also facilitate stock purchases through the Internet. Direct stock purchase plans and dividend reinvestment plans

24、handles on-line allow small investors the opportunity to buy securities cheaply. The companies can also disclose more information. Especially to security analysts, to narrow the gap between informed and uninformed traders. This should reduce spreads. This idea is a new one and empirical evidence is

25、not yet in.30作業(yè) 選取一家上市公司，采取兩種方法估計(jì)其貝塔系數(shù)。31三、債務(wù)成本 The cost of debt is the return that lenders require on a companys debt. One can use the YTM calculated using market prices for companys bonds as the cost of debt before taxes, RD.32稅前成本與稅后成本 However, we should incorporate the tax into the cost of debt.

26、 Because of the tax shield of interest, the cost of debt after taxes: RD= RD（1Tc） 例如，投資者認(rèn)購(gòu)公司發(fā)行利率為10%的債券，公司所得稅為33%，則債務(wù)稅前成本為10%，稅后成本為10% （1-33%）=6.7%。投資者獲得了10%的收益率，但公司資本成本只有6.7%。33債務(wù)成本與權(quán)益成本的討論 會(huì)計(jì)方法上的處理會(huì)計(jì)利潤(rùn)的核算扣除利息費(fèi)用（EBITDA、EBIT、NOI、NI），但是沒(méi)有考慮權(quán)益成本；經(jīng)濟(jì)增加值：EVA= EBIT（1-Tc）-WACC總資本 在金融學(xué)中的差異債務(wù)成本高還是權(quán)益成本高？選擇債務(wù)融

27、資還是股權(quán)融資？增加債務(wù)融資對(duì)權(quán)益成本的影響34四、加權(quán)平均資本成本 (WACC) The cost of capital is the weighted average cost of capital using the current capital structure weights:WACC(1)EDCEDRRTVVD is the market value of debt outstandingE is the market value of equity outstandingV is the total market value of the firm (=D + E)TC is

28、 the marginal corporate tax rate35Weighted Average Cost of Capital (WACC) WACC is the overall return that the firm must earn on its existing assets to maintain the value of its stock. So if we were evaluating the cash flows from a proposed investment by this firm, this is the discount rate we would

29、use.36WACC - Example Technology Spying Systems (TSS) is a company that monitors communications between suspected individuals for the government. It is currently considering developing a new advanced system to monitor email exchanges more efficiently. The additional details about the firm are as foll

30、ows: The common stock of the firm has a beta of 1.2. The marginal tax rates for the firm are 30%. The market risk premium and the risk free rate are 8% and 6%, respectively.37WACC - Example It currently has the following capital structure. 3,000 outstanding 8 percent semiannual-coupon bonds with par

31、 value of $1,000 and 20 years to maturity which sells for 103 percent of par. $2,000,000 in 9% APR bank loans with semiannual payments. 90,000 outstanding common shares of stock which sells for $45 per share. 13,000 shares of 7 percent preferred stock outstanding with a face value of $100 which curr

32、ently sells for $108 per share. Should the firm accept the project if the IRR of the project is 10%?38Step 1a: Find The Costs of Debt The after tax YTM on the bond is the required rate of return on the debt of the firm from the issuance of this debenture. YTM = 7.703%(APR) Required Rate of Return =

33、7.85% (EAR) x (1-0.3) = 5.50% The after tax EAR on the bank loan is the required rate of return on the bank loan of the firm. EAR = 9.200% Required Rate of Return = 9.200% x (1-0.3) = 6.442%39Step 1b: Find The Costs of Equity The required rate of return on the common stock of the firm can be found u

34、sing CAPM:()6%1.208%15.600%EfMfERRRRR The required rate of return on the common stock of the firm is 15.600%. The required return on the preferred stock of the firm can be found as follows:0/$7 / $1086.481%PRDP40Step 2a: Market Values of Debt The market value of bonds can be found by multiplying the

35、 number of debentures outstanding by the price per bond. 3,000 x $1,030 = $3.090M The market value of the bank loan is given in the question. $2.000M41Step 2b: Market Values of Equity The market value of common stocks can be found by multiplying the number of common stocks outstanding by the price per share. 90,000 x $45 = $4.050M The market value of preferred stocks can be found by multiplying the number of preferred stocks ou