1、1公司金融 武漢大學經濟與管理學院2第六章 資本成本一、資本成本概念剖析二、權益成本(Cost of Equity)三、債務成本(Cost of Debt)四、加權平均資本成本 (WACC)3 資本成本是公司使用資本所付出的代價。 站在投資者的角度，資本成本是投資者投資于某一項目或企業的機會成本，可以用投資者要求的必要報酬率（Required rate of Return）來度量。 公司金融中的基本假設是，投資者向企業提供資金，他們期望有一定的投資回報，這種回報就構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值，公司價值就是用資本成本折現

2、的一系列現金流。對資本成本的研究形成公司股東價值最大化前提下公司金融學的基礎內容：如何投資（資本預算）？如何融資（資本結構決策）？為投資者提供多少回報（股利政策決策）？ 資本成本如何估算還是投資學的核心內容。在有效資本市場中，投資者期望的回報率，就是投資者的機會成本，即公司資本成本。 資本成本同時也是宏觀金融學研究的基礎。宏觀金融運行的目的是促使有效金融市場的形成，使公司和投資者之間的資源配置有序化，宏觀金融的目標歸根到底是為了促使一個國家的資本成本最小化。資本成本是金融學理論的核心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.（企業可以通過發行債券或股票為投資項目籌集資金，不同的資金來源具有不同的成本） One of the most important measures of cost of capital is Weighted Average Cost of Capital (WACC) which takes into account all the above.（衡量企業資金成本的一個重要指標是加權平均資本成本-WACC）Equity and Debt7二、權益成本（Cost o

5、f Equity） Calculating the cost of equity is more difficult than calculating the cost of debt.（權益成本的計算比債務成本的計算要更為困難） 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.（權益成本的估計有不同的方法）8權益成本的估計

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益成本；Rf為無風險收益率； RM 為市場收益率，實踐中一般取大盤指數的收益率；RM Rf為市場風險溢價；E（beta ）表示股票相對于市場特有的風險。()EfEMfRRRR 資本資產定價模型（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 方法的優缺點 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（經營風險） Cyclicity of Revenues（收入的周期性） Operating Leverage（經營杠桿） Financial Risk（財務風險） Financial Leverage（財務杠桿）17收入的周期性 有些企業的收入具有明顯的周期性，即這些企業在商業周期的擴張階段經營得很好，而在商業周期的緊縮階段經營得很差。 Empirical evidence suggests that retailers and automotive firms fluctuate with the busin

14、ess cycle.（經驗證據表明零售企業和汽車企業隨商業周期的波動大） Transportation firms and utilities are less dependent upon the business cycle.（交通運輸及公用事業類企業與商業周期相關性不大） 由于貝塔是股票收益率與市場收益率的標準協方差，所以周期性強的股票必然具有較高的貝塔系數。18Operating Leverage（經營杠桿） 企業收入的周期性對貝塔起決定性作用，而經營杠桿又將這種作用進一步放大。經營杠桿是公司EBIT對銷售收入波動的反映程度。 The degree of operating lever

15、age is given by:SalesSalesEBITEBITEBITDOL/銷售額變化的百分比變化的百分比 例如，Piece Grain 固定成本為10萬元，當銷售收入由30萬元增加到36萬元時(增加20%)，變動成本由18萬元增加到21.6萬元，則： EBIT由2萬元增加到4.4萬元(增加120%) 公司經營杠桿：DOL=120%/20%=6（倍）19經營杠桿與固定成本 當產品價格保持不變時，經營杠桿可以寫成：TFCQAVCPQAVCPDOL)()( 因此，只要TFC0，DOL就大于1；TFC越大，DOL就越大，表明企業經營風險越大。20銷售收入變化對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 （財務杠桿） 經營杠桿與企業固定成本有關，而財務杠桿與企業籌集資金所產生的利息費用有關。 財務杠桿是每股收益（EPS）相對于EBIT變動的反映程度，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。若公司沒有負債，

17、則Int. =0，財務杠桿就等于1；一般情況下，公司有負債， Int. 為正，所以財務杠桿大于1。22財務杠桿與貝塔 公司有負債的情況下財務杠桿大于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險（財務風險）。 由于債務的使用增加了股東遭受的風險，因此股東需要有更高的回報，意味著權益成本增加。23資產貝塔與權益貝塔 有負債情況下，公司資產貝塔可以表示為債務貝塔與權益貝塔的加權平均，即： 一般情況下債務的貝塔很小，假定Debt 等于0，則權益貝塔可以寫成：Asset = Debt + EquityDebt Debt+ Debt + EquityEquit

18、y EquityAssetEquityEquityDebt)1 ( 因此，債務的使用使得權益貝塔大于資產貝塔。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（行業貝塔的運用）（行業貝塔的運用） 根據企業自身歷史數據估算貝塔系數是一種常用的方法，也可以運用整個行業的貝塔系數估算企業的貝塔系數（有人認為這種方法更好）。 運用行業貝塔的基本原則：

20、 如果企業經營特點與所在行業其他企業的經營十分類似，可以考慮運用行業貝塔； 如果企業的經營特點與所在行業內其他企業的經營有根本性差異，則應該根據企業自身歷史數據估算企業貝塔； 還要注意運用財務杠桿對行業貝塔進行調整。26Stability of Beta（貝塔的穩定性） 如果企業改變業務，貝塔系數一般隨之改變。但如果企業不改變行業，貝塔系數會不會改變？ 大多數研究結果表明：一般情況下，當企業不改變業務時，其貝塔系數保持穩定。 但在一些特定情況下，即使企業不改變行業，其貝塔系數也會改變，如： 企業生產的產品系列發生了大的變化； 企業所采用的技術發生很大變遷； 政府的管制放松：如解除對航空業的管制

21、會使航空公司貝塔系數變大； 財務杠桿的變化； 等等。27股票流動性與權益成本 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 選取一家上市公司，采取兩種方法估計其貝塔系數。31三、債務成本 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，投資者認購公司發行利率為10%的債券，公司所得稅為33%，則債務稅前成本為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債務成本與權益成本的討論 會計方法上的處理會計利潤的核算扣除利息費用（EBITDA、EBIT、NOI、NI），但是沒有考慮權益成本；經濟增加值：EVA= EBIT（1-Tc）-WACC總資本 在金融學中的差異債務成本高還是權益成本高？選擇債務融

27、資還是股權融資？增加債務融資對權益成本的影響34四、加權平均資本成本 (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