公司理财汇总整理

第一章

1.1 1The three questions

1）What long-term investments

Fixed Assets1 Tangible 2 Intangible 2）How can the firm raise the money

Current Liabilities;Long-Term Debt;Shareholders’ Equity

3）How much short-term cash flow does a company need to pay its bills?

2Balance Sheet

1)A=S+B Total Value of Assets=Shareholders’ Equity+The Capital Budgeting Decision 2) NWC:Current Assets-Current Liabilities

3Capital structure(P4)

The answer to this involves the firm’s Capital structure,which represents the proportions of the firm’s financing from current and long-term debt and equity这一问题又涉及到资金结构，它表示公司短期及长期负债与股东权益的比例

The Capital Structure decision can be viewed as how best to slice up a the pie. v=B+S

4Cash Flow v.s. Net Income

cash flow 现金流量：是指一定会计期间企业现金和现金等价物的流入和流出。 net income净收益：是指企业当期利润总额减去所得税后的金额 price价格，

Cash Flow：Identification of Cash Flow;Timing of Cash Flow;Risk of Cash Flow(P7-8) Net Income

① In business, what remains after subtracting all the costs (namely, business, depreciation, interest, and taxes) from a company's revenues. Net income is sometimes called the bottom line. also called earnings or net profit.

② For an individual, gross income minus taxes, allowances, and

deductions. An individual's net income is used to determine how much income tax is owed.

1.2payoff(p9)

1-12Debt and Equity as Contingent ClaimsPayoff to debt holdersIf the value of the firm is more than $F, debt holders get a maximum of $F. $FPayoff to shareholdersIf the value of the firm is less than $F, share holders get nothing. $FValue of the firm (X)Debt holders are promised $F. $FValue of the firm (X)If the value of the firm is more than $F, share If the value of the firm is less than $F, they holders get everything get the whatever the firm if worth. above $F. Algebraically, the bondholder’s Algebraically, the shareholder’s claim is: Min[$F,$X]claim is: Max[0,$X –$F]McGraw-Hill/IrwinCopyright ?2002 by The McGraw-Hill Companies, Inc. All rights reserved. 1-13Combined Payoffs to Debt and EquityCombined Payoffs to debt holders and shareholdersIf the value of the firm is lessthan $F, the shareholder’s claim is: Max[0,$X –$F] = $0 and the debt holder’s claim is Min[$F,$X] = $X. The sum of these is = $XPayoff to shareholders$FPayoff to debt holders$FValue of the firm (X)Debt holders are promised $F. If the value of the firm is morethan $F, the shareholder’s claim is: Max[0,$X –$F] = $X –$Fand the debt holder’s claim is:Min[$F,$X] = $F. The sum of these is = $XMcGraw-Hill/IrwinCopyright ?2002 by The McGraw-Hill Companies, Inc. All rights reserved. 1.3The corprate Firm(p10)

The sole proprietorship（个体业主制）-A sole proprietorship is a business owned by one person

? The Partnership--General Partnership，Limited Partnership ? The Corporation

? Advantages and Disadvantages：①Liquidity and Marketability of Ownership

②Control③Liability④Continuity of Existence⑤Tax Considerations

The partnership合伙制：A two or more person can get toghter and form a partnership The corporation公司制

1-16A Comparison of Partnership and CorporationsCorporationLiquidityShares can easily be exchanged.Usually each share gets one votePartnershipSubject to substantial restrictions.General Partner is in charge; limited partners may have some voting rights.Partners pay taxes on distributions.All net cash flow is distributed to partners.General partners may have unlimited liability. Limited partners enjoy limited liability.Limited lifeVoting RightsTaxationReinvestment DoubleBroad latitudeLiabilityLimited liabilityContinuity McGraw-Hill/IrwinPerpetual lifeCopyright ?2002 by The McGraw-Hill Companies, Inc. All rights reserved.

1.4Goals of the Corporate Firm

The traditional answer is that the managers of the corporation are obliged to make efforts to maximize shareholder wealth.

1.5Financial Markets

? Primary Market

– When a corporation issues securities, cash flows from investors to the firm. – Usually an underwriter is involved

? Secondary Markets

– Involve the sale of “used” securities from one investor to another.

– Securities may be exchange traded or trade over-the-counter in a dealer market.

第二章

Accounting Statements and Cash Flow (会计报表与现金流量) 2.1 The Balance Sheet(资产负债表)

The balance sheet is an accountant′s snapshot of the Firm′s accounting value on a particular date，as though the firm stood momentarily still.

Asset=Liabilities + Stockholders′ equity 资产=负债+股东权益

分析资产负债表时应注意三个问题：accounting liquid（会计流动性）、debt versus equity（债务与权益）、Value versus cost（市价与成本）

Accounting Liquidity refers to the ease and quickness with

Which assets can be converted to cash. 会计流动性是指资产变现的方便与快捷程度。

Current assets（流动资产） are the most liquid and include cash and those assets that will be turned into cash within a year from the date of the balance sheet. Fixed assets（固定资产）are the least liquid kind of assets. It include tangible and intangible fixed assets. Tangible fixed (有形资产)assets include property，plant，and equipment. These assets do not convert to cash from normal business activity，and they are not usually used to pay expense， such as payroll. Intangible assets（无形资产） have no physical existence but can be very valuable. Debt versus Equity（债务与权益） Value versus Cost（市价与成本）

企业资产的会计价值通常是指置存价值（carry value）或账面价值（book value）。 2.2

1、The income statement measures performance over a specific period of time ,say,a year.The accounting definition of income is Revenue - Expense=Income

2、One number of particular importance is earnings before interest and taxes(EBIT),which summarizes earnings before taxes and financing costs. 3、Generally Accepted Accounting Principles(GAAP) The matching principal of GAAP dictates that revenues be matched with expenses. Thus, income is reported when it is earned, even though no cash flow may have occurred

4、Non Cash Items Depreciation is the most apparent. No firm ever writes a check for “depreciation”. Another noncash item is deferred taxes, which does not represent a cash flow.

5、 Time and Costs In the short run, certain equipment, resources, and commitments of the firm are fixed, but the firm can vary such inputs as labor and raw materials.

In the long run, all inputs of production (and hence costs) are variable.

Financial accountants do not distinguish between variable costs and fixed costs. Instead, accounting costs usually fit into a classification that distinguishes product costs from period costs 2．3Tax tate书上没有，找不到 Average Tax tate Maringal Tax tate 2、4

Net Working Capital Net Working Capital ?Current Assets - Current LiabilitiesNWC is usually growing with the firm 2.5 Financial Cash Flow

? In finance, the most important item that can be extracted from financial

statements is the actual cash flow of the firm.

? Since there is no magic in finance, it must be the case that the cash from

received from the firm’s assets must equal the cash flows to the firm’s

creditors and stockholders.

CF(A)?CF(B)?CF(S)2.6 Summary and Conclusions

? Financial statements provide important information regarding the value of

the firm.

? You should keep in mind:

– Measures of profitability do not take risk or timing of cash flows

into account.

Financial ratios are linked to one another

The statement of cash flows Cash Flow activities from operating

Cash flow activities from investing Cash flow from financing activities

第四章

1Future Value:未来值：The total amount due at the end of the investment is call the Future Value (FV).

In the one-period case, the formula for FV can be written as: FV = C0×(1 + r) 要求已经三个 求另一个；FV C r T

例题 If we deposit $5,000 today in an account paying 10%, how long does it take to grow to

$10,000$10,000? T(1.10)??2 $10,000?$5,000?(1.10)T$5,000ln20.6931 ln(1.10)T?ln2T???7.27 years ln(1.10)0.0953

例题Assume the total cost of a college education will be $50,000 when your child enters college in 12 years. You have $5,000 to invest today. What rate of interest must you earn on your investment to cover the cost of your child’s education? About 21.15%.

$50,000

(1?r)12??10$50,000?$5,000?(1?r)12 $5,000

(1?r)?10112r?10112?1?1.2115?1?.2115

2,PV:Present Value:现值：Refers to the discounted value of future cash flows to the appropriate discount rate

C

PV?11?r

3、The Net Present Value (NPV) of an investment is the present value of the expected cash flows,

T

less the cost of the investment.

? Suppose an investment that promises to pay $10,000 in one year is offered for sale for

$9,500. Your interest rate is 5%. Should you buy?

$10,000NPV??$9,500? 1.05 NPV??$9,500?$9,523.81 NPV?$23.81

In the one-period case, the formula for NPV can be written as: NPV??Cost?PVIf we had not undertaken the positive NPV project considered on the last slide, and instead invested our $9,500 elsewhere at 5-percent, our FV would be less than the $10,000 the investment promised and we would be unambiguously worse off in FV terms as well: $9,500×(1.05) = $9,975 < $10,000

4、Compounding Periods 复利期限 m?Tr?? FV?C0??1???m?

For example, if you invest $50 for 3 years at 12% compounded semi-annually, your investment will grow to 2?3?.12?6FV?$50??1? ??$50?(1.06)?$70.932??

5、Effective Annual Interest Rates：有效年利率

A reasonable question to ask in the above example is what is the effective annual rate of interest on that investment?

.122?3)?$50?(1.06)6?$70.93 FV?$50?(1?2The Effective Annual Interest Rate (EAR) is the annual rate that would give us the same end-of-investment wealth after 3 years:

$70.93

(1?EAR)3?$50?(1?EAR)3?$70.93 $5013 ?$70.93???1?.1236 EAR???$50?

So, investing at 12.36% compounded annually is the same as investing at 12% compounded semiannually

? The general formula for the future value of an investment compounded continuously over

many periods can be written as: 公式 FV = C0×e^rT

Where C0 is cash flow at date 0, r is the stated annual interest rate,

T is the number of periods over which the cash is invested, and

e is a transcendental number approximately equal to 2.718. ex is a key on your calculator 4.4

（概念）

? Perpetuity

– A constant stream of cash flows that lasts forever.

? Growing perpetuity

– A stream of cash flows that grows at a constant rate forever.

? Annuity

– A stream of constant cash flows that lasts for a fixed number of periods.

? Growing annuity

– A stream of cash flows that grows at a constant rate for a fixed number of

periods.

Perpetuity

A constant stream of cash flows that lasts forever. 公式

C PV?r

Example

What is the value of a British consol that promises to pay ￡15 each year, every year until the sun turns into a red giant and burns the planet to a crisp? The interest rate is 10-percent

?5??50 PV?.10

Growing Perpetuity

A growing stream of cash flows that lasts forever. 公式

C PV?r?gExample

The expected dividend next year is $1.30 and dividends are expected to grow at 5% forever. If the discount rate is 10%, what is the value of this promised dividend stream?

$1.30

PV??$26.00.10?.05

Annuity （年金最重要）

A constant stream of cash flows with a fixed maturity.

CCCC???? PV?(1?r)(1?r)2(1?r)3(1?r)T

The formula for the present value of an annuity is:

PV?C?1?1?T?r?(1?r)??

Example

If you can afford a $400 monthly car payment, how much car can you afford if interest rates are 7% on 36-month loans? ?$400?1PV?1??$12,954.59?36? .07/12?(1?.0712)?

Growing Annuity

A growing stream of cash flows with a fixed maturity.

CC?(1?g)C?(1?g)T?1 PV?????2T(1?r)(1?r)(1?r)

The formula for the present value of a growing annuity: T????C1?g

?PV??1????r?g??(1?r) ?????

A defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by 3-percent each year. What is the present value at retirement if the discount rate is 10-percent?

40 $20,000??1.03?????$265,121.57?1?? PV?.10?.03???1.10???

4.5 What Is a Firm Worth?

? 公司价值决定未来现金流：a firm should be worth the present value of the firm’s cash

flows.

第五章

5.1 definition and example of bond

definition: bond is a legally binding agreement between a borrower and lender.

– Specifies the principal amount of the loan.

– Specifies the size and timing of the cash flows:

? In dollar terms (fixed-rate borrowing) ? As a formula (adjustable-rate borrowing)

5.2 how to value bond: P106—109

A: method : (1): identify the size and timing of cash flow

(2): discount at the correct discount rate

B: several bounds:

(1): pure discount bounds（纯贴现债券）: the pure discount bond is perhaps the

Fsimplest kind of bond.

PV?(1?r)T

(2):level—coupon bonds（票面利息）: Information needed to value level-coupon bonds: ①Coupon payment dates and time to maturity (T) ;②Coupon payment (C) per period and Face value (F) ;③Discount rate. （文字说明对照PPT） ?CCC?FPV???...????21?r（1? r））?(1?r)T?(1?r)T(3):consols（金边债券/永久公债）: a consol is perpetuity. consols are bonds that never stop paying a coupon, have no financial maturity date, and therefore never mature.

5.3 Bond Concepts

First principles: value of financial securities=pv of expected future cash flows (1) bond prices and market interest rates:

That bond prices fall with a rise in interest rates and rise with a fall in interest rates.

(2) When coupon rate = YTM(Yield to Maturity), price = par value. (3) bond maturity and bond’s price change: 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. (4) bond coupon and bond’s price change:

A lower coupon bond has a higher relative price change than a higher coupon bond when YTM changes. All other features are identical.

5.4 The Present Value of Common Stocks (1)Dividends versus Capital Gains

12(2)Valuation of Different Type of Stocks

0121.Zero Growth(零增长)

0

2.Constant Growth（固定增长率） Div1P0?

r?g

?DivN?1?

???T3.Differential Growth（变动增长率）

C?(1?g1)??r?g2?? P?1???T?Nr?g(1?r)(1?r) ?1?5.5 Estimates ofParameters in the Dividend-Discount Model

1)Where does gcome from?G=Retentionratio*Return on retained earnings 2)Where does rcome from?R=Div1/P0+g

Div3DivDivP?????3(1?r)(1?r)(1?r)DivP?r

5.6

The Dividend Growth Model and NPVGO Model P= EPS/(r )+NPVGO 一、

1.Cash Cow

2.Net Present Value (per share) of Growth Opportunities 二、

Calculate NPVGO 三、

Does a higher Retention Ratio Benefit Shareholders? P= Div/(R-g)

g =RR*ROE(Where RR is Retention Ratio) Div=Payoutratio*EPS=(1-RR)*EPS

p =Div/(R-g)=((1-RR)*EPS)/(R-(RR*ROE))

ROE>R,Higher retention ratio ,better for shareholders ROE

? 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 quarter’s earnings

(2)Price/Cash Flow Ratio

? cash flow = net income + depreciation = cash flow from

operations or operating cash flow

(3)Price/Sales

? current stock price divided by annual sales per share

(4)Price/Book (a.k.a Market to Book Ratio)

? price divided by book value of equity, which is measured as

assets - liabilities

Price per shareP/E ratio?EPS 第6章

6.1Why Use Net Present Value

1、 Estimating NPV:

– 1. Estimate future cash flows: how much? and when?

– (Future cash flows of real-world projects are invariably . In other words, cash

flows can only be estimated , rather than known . Imagine that the managers of Alpha expect the cash floe of the project to be $107 next year. That is , the cash flow could be higher , say $117 ,or lower, say $97.) – 2. Estimate discount rate

– 3. Estimate initial costs

? 2、Minimum Acceptance Criteria: Accept if NPV > 0 ? Ranking Criteria: Choose the highest NPV ?

3、three Good Attributes of the NPV Rule ? 1. Uses cash flows

? 2. Uses ALL cash flows of the project ? 3. Discounts ALL cash flows properly

6.2 The payback period rule

1. Definition:

Payback period=number of years to recover initial costs

2.Criterion:

Acceptance---set by management Ranking---set by managent

3.Problems with the Payback Method:

(1)Does not consider the timing of the cash flows within the payback period. (2)Ignores all cash flows occurring after the payback period. (3)Arbitrary standard for payback period.

4.Advantage of payback period

(1)Easy to understand and quick decision. (2)Quick result. (3)Small projects.

(4)Small firm difficult to finance.

6.3 The discounted payback period rule

The discounted payback period method:折现回收期法

Aware of the pitfalls of payback,some decision makers use a variant called the discounted payback period method.

缺陷：At first glance discounted payback may seem like an attractive alternative,but on closer inspection we see that it has some of the same major falws as payback.Like payback,discounted payback first requires us to make a somewhat magical choice of an arbitrary cutoff period,and then it ignores all of the flows after that date

6.5 The internal rate of return

Definition(下定义)：IRR is the rate that causes the NPV of the project to be zero。 General criterion（一般准则）：Accept the project if IRR is greater than the discount rate. Reject the project if IRR is less than the discount rate.若内部收益率大于贴现率，项目可以接受；若内部收益率小于贴现率，项目不能接受。这就是基本的内部收益率法则

6.6 Problems with the IRR Approach

1.Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.

独立项目：是其接收或者放弃的决策不受其他项目投资决策影响的投资项目。 Mutually Exclusive Projects: only one of several potential projects can be chosen. 互斥项目：是只能在一些潜在的项目选择只有一个。

2.Two general problems affecting both independent and mutually exclusive projects Problem 1:Investing or Financing 1)Investing

Accept: IRRs >discount rate 内部收益率>贴现率 Reject :IRRs< discount rate 2)Financing

Accept: IRRs < discount rate 内部收益率<贴现率 Reject : IRRs > discount rate

Problem 2:Multiple Rates of Return Mixture

1) NPV Rule：

Accept a project if the NPV is greater than zero; Reject a project if NPV is less than zero. NPV=-cost+

?i?1nCi i(1?r)2) Modified IRR (MIRR)

3)The Guarantee against Multiple IRRs General Rules Number of Flows IRRs First cash flow is negative and 1 all remaining cash flows are positive. IRR Criterion Accept if IRR>r Reject if IRR0 Reject if NPV<0 First cash flow is positive and all remaining cash flows are negative. Some cash flows after first are positive and some cash flows after first are negative.

1 Accept if IRRr No valid IRR Accept if NPV>0 Reject if NPV<0 Accept if NPV>0 Reject if NPV<0 May be more than 1 3.Problems Specific to Mutually Exclusive Projects ( 1).The Scale Problem:

Example with incremental IRR.

Incremental IRR is the IRR on the incremental investment from choosing the large project instead of the small one.

Furthermore, we can calculate the NPV for incremental Cash Flows.

In review, we can handle this example (or any mutually exclusive example) in one of three ways:

1. Compare the NPVs of the two choices.

2. Compare the incremental NPV from making the large-budget picture instead of the small-budget picture.

3. Compare the incremental IRR to the discount rate.

(2).The Timing Problem

We can select the better project with one of three different methods: 1. Compare NPVs of the two projects

2. Compare incremental IRR to discount rate. 3. Calculate NPV on incremental cash flows.

The IRR probably survives because it fills a need that the NPV does not. People seem to want a rule that summarizes the information about a project in a single rate of return.

To their credit, however, companies that employ the IRR approach seem to understand its deficiencies.

6.8 The Practice of Capital Budgeting

1.IRR 2.NPV 3.Payback

第10章

1Individual Securities(单个证券):

1.The characteristics of Individual Securities（单个证券的特点） ①return（期望收益） ②risk（风险）

10.2Expected Return,Variance,and Covariance（期望收益、方差、协方差）

1.Expected Return（期望收益）：Arithmetic mean of historical return（算术平均的

历史回归）

2. Variance and standard Deviation（方差与标准差）

Var(R)?ExpectedSD(R)?Var(R)

valueof(R?R)2

3. Covariance and Correlation（协方差和相关系数）

?AB?Cov(RA.RB)?Expectedvalueof[(RA?RA)?(RB?RB)]

?AB?Corr(RA.RB)?Cov(RA.RB)

?A??B

10.3 The Return and Risk for Portfolios

1. The expected return on a portfolio is simply a weighted average of the expected returns on the individual securities.(组合的期望收益是构成组合的各个证券的期望收益的简单加权平均) Expected return on portfolio(组合的期望收益)=XARA+XBRB=RP 2. The variance of the portfolio(投资组合的方差)

Var(portfolio)=X2A?2A+2XAXB?A,B+XB?B

22

3. The diversification effect Variance

of

super,slow+Xslow?22portfolio’s

slow

return=X2super?2super+2XsuperXslow?super,slow?As long as ?<1,the standard deviation of a portfolio of two securities is less than the weighted average of the standard deviations of the individual securities.(当由两种证券构成投资组合时，只要?AB<1，组合的标准差就小于这两种证券

各自的标准差的加权平均数)

10.4

The efficient set for two assets两种资产组合的有效集

图：1.Portfolio1 is composed of 90 percent slowpoke and 10 percent supertech.(p=-0.1639).

2. Portfolio2 is composed of 50 percent slowpoke and 50

percent supertech.(p=-0.1639)

3. Portfolio3 is composed of 10 percent slowpoke and 90 percent supertech.(p=-0.1639)

P<=0,backward bending always occurs(会出现后弯)；p>0, backward bending may or may not occur(可能出现也有可能不出现后弯)。

4.nonsystematic risk can be diversified away (非系统性风险可以消除)；systematic risk can not be delimitated (系统性风险不可以消除)。

10.5：The Efficient Set for Many Securities 多种资产组合的有效集 1、

无限多种组合但所有只能是落在有效区域内。 2、多种资产组合的期望收益。 3、投资组合方差的矩阵计算表。

10.6 Diversification:An Example

1.Variance portfolio=N?(

1111?varvarcov)+N(N-1)()=()+(1-)cov 22NNNNof

2.Variance of portfolio(when N??)=cov

10.7 Riskless Borrowing and lending 无风险的借和贷

1.由一种风险资产和一种无风险资产构成的投资组合的收益率：是两种资产收益的加权平均数。

2. 由一种风险资产和一种无风险资产构成的投资组合的风险：X2risky?risky 3. 35% in risk assets(风险资产)，65% in risk-free assets(无风险资产)

4.该图说明了一个要点：通过按照无风险利率进行接入或贷出，任何投资者持有的风险资产的投资组合都将是点A。无论投资者的风险厌恶程度如何，他绝不会选择风险资产有效集中的其他点，也绝不会选择可行集内部的任何点。

10.8：Market Equilibrium市场均衡

在一个具有共同期望的世界中，所有的投资者都会持有A点所代表的风险资产组合。 10.9Relationship between Risk and Expected Return (CAPM) 期望收益与风险之间的关系：资本定价模型 1Beta

1)Beta measures the responsiveness of a security to movements in the market portfolio 贝塔系数是度量一种证券对于市场组合变动的反应程度的指标 2)The actual definition of beta is

2?i?Cov(Ri，RM)?(R2M)

其中分子是第i种证券的收益与市场组合收益之间的协方差，分母是市场组合收益的方差 3）①One usefull property is that the average beta across all securities,when weighted by the proportion of each securiy’s market value to that the market portfolio,is 1.That is,即证券市场的一般证券的贝塔系数为1

②增加一个一个贝塔系数大于1的股票，将增加投资组合的风险

?X?i?1iNi?1

③增加有一个负贝塔系数的股票，将降低投资组合的风险 2CAPM资本资产定价模型

They posit that,under plausible conditions,the replation between expected return and beta can be represented by the following equation: Capital-Asset-pricing Model

R??RF??X(RM?RF)

?Expected = Risk-free rate + Beat of the X Difference between expected return on security return on market and risk-free a security rate 3The three lines

10-39Estimating ??with regressionSecurity Returnsneic LitisretacraChSlope = ?iReturn on market %Ri= ?i+ ?iRm+eiMcGraw-Hill/IrwinCopyright ?2002 by The McGraw-Hill Companies, Inc. All rights reserved.

第十一章 一．概念

A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree.

An unsystematic risk is a risk that specifically affects a single asset or small group of assets. 二.公式

11.1 .Return on any security consists of two parts:R=R+U ?R:expected returns ?U:unexpected or risked returns 11.2 R=R+m+?

?m：systematic risk ??:unsystematic risk 11.3 systematic risk and betas :R=R+?(

R-)+? MRm

—

?i?Cov(Ri,RM)?2(RM)

11.5 betas and expected returns

II

11-23Profit (收益SML

R?R?βF?βGDPFGDP?βSFS?εProfit (收益 Relationship Between ?& Expected ReturnProfit (收益Expected returnSMLProfit (收益ADBC?RFR?RF?β(RP?RF)McGraw-Hill/IrwinCopyright ?2002 by The McGraw-Hill Companies, Inc. All rights reserved. 三．结论

The APT assumes that stock returns are generated according to factor models such as:

1.As securities are added to the portfolio, the unsystematic risks of the individual securities offset each other. A fully diversified portfolio has no unsystematic risk. 2.The CAPM can be viewed as a special case of the APT.

3.Empirical models try to capture the relations between returns and stock attributes that can be measured directly from the data without appeal to theory. 第十二章

The Cost of Equity Capital 权益资本成本 Firm with excess cash Shareholder invests Pay cash dividend in financial asset A firm with excess cash can either pay a dividend or make a capital investment Shareholder’s Invest in project 对上图解释说明： Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk. The Cost of Equity ①From the firm’s perspective, the expected return is the Cost of Equity Capital:R i?RF?βi(RM?RF)②To estimate a firm’s cost of equity capital, we need to know three things: Terminal Value 1. The risk-free rate, RF 2.The market risk premium,RM3.The company beta, Cov(Ri,RM)σi,Mβi??2Var(RM)σM?RF

Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects

Project IRR SMLGood A projects B C Bad projects 2.5

Firm’s risk (beta)

30% 5%

Estimation of Beta

Theoretically, the calculation of beta is straightforward:

Problems：

1. Betas may vary over time.

2. The sample size may be inadequate.

3. Betas are influenced by changing financial leverage and business risk.

Solutions

– Problems 1 and 2 (above) can be moderated by more sophisticated statistical

techniques.

– Problem 3 can be lessened by adjusting for changes in business and financial

risk.

– Look at average beta estimates of comparable firms in the industry.

Cov(Ri,RM)σi2β??2Var(RM)σMStability of Beta

? ?

Most analysts argue that betas are generally stable for firms remaining in the same

industry.

That’s not to say that a firm’s beta can’t change.

– Changes in product line – Changes in technology

– Deregulation

– Changes in financial leverage

Using an Industry Beta

? It is frequently argued that one can better estimate a firm’s beta by involving the whole

industry.

? If you believe that the operations of the firm are similar to the operations of the rest of the

industry, you should use the industry beta.

? If you believe that the operations of the firm are fundamentally different from the

operations of the rest of the industry, you should use the firm’s beta. ? Don’t forget about adjustments for financial leverage.

Determinants of Beta

?

Business Risk

– Cyclicity of Revenues – Operating Leverage Financial Risk

– Financial Leverage

?

①Cyclicality of Revenues

? Highly cyclical stocks have high betas.

– Empirical evidence suggests that retailers and automotive firms fluctuate with the

business cycle.

– Transportation firms and utilities are less dependent upon the business cycle.

? Note that cyclicality is not the same as variability—stocks with high standard deviations

need not have high betas.

– Movie studios have revenues that are variable, depending upon whether they

produce “hits” or “flops”, but their revenues are not especially dependent upon the business cycle.

②Operating Leverage

? The degree of operating leverage measures how sensitive a firm (or project) is to its fixed

costs.

? Operating leverage increases as fixed costs rise and variable costs fall. ? Operating leverage magnifies the effect of cyclicity on beta. ? The degree of operating leverage is given by:

Change in EBITSalesDOL??

EBITChange in Sales

$ Total costs Fixed

? EBIT ? Volume

Fixed costs

Volume

Operating leverage increases as fixed costs rise and variable costs fall. ③Financial Leverage and Beta

? Operating leverage refers to the sensitivity to the firm’s fixed costs of production. ? Financial leverage is the sensitivity of a firm’s fixed costs of financing.

? The relationship between the betas of the firm’s debt, equity, and assets is given by:

DebtEquity βAsset??βDebt??βEquityDebt?EquityDebt?Equity

Financial leverage always increases the equity beta relative to the asset beta

Extensions of the Basic Model

? ?

The Firm versus the Project The Cost of Capital with Debt

Capital Budgeting & Project Risk

Project IRR The SML can tell us why: SMLHurdle rate

RF?βFIRM(RM?RF)Incorrectly rejected positive NPV projects rf

?FIRM

Firm’s risk (beta)

A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value.

The Cost of Capital with Debt

?

?

The Weighted Average Cost of Capital is given by:

?S??B?rWACC???r??S???rB?(1?TC)?S?B??S?B?It is because interest expense is tax-deductible that we multiply the last term by (1- TC)

Liquidity, Expected Returns and the Cost of Capital

?

? ?

The cost of trading an illiquid stock reduces the total return that an investor receives.

Investors thus will demand a high expected return when investing in stocks with high trading costs.

This high expected return implies a high cost of capital to the firm.

Liquidity and the Cost of Capital

Cost of Capit-al

Liquidity

第22章 Options and Corporate finance

option期权：An option is a contract giving its owner the right to buy or sell an asset at a fixed

price on or before a given date.（期权是一种赋予持有人在某给定日期或该日期之前的任何时间以固定价格购进或售出一种资产之权力的合约） 重要名词：

In-the-Money(价内期权):The exercise price is less than the spot price of the underlying asset. At-the-Money(平价期权):The exercise price is equal to the spot price of the underlying asset. Out-of-the-Money(价外期权):The exercise price is more than the spot price of the underlying asset.

Exercise Price(执行价格)：The fixed price in the option contract at which the holder can buy or sell the underlying asset is called the Exercise Price.

Expiration date(到期日):The maturity date of the option is referred to as the Expiration Date . After the date , the option is dead.

期权分类：Call option (看涨期权) 和Put option(看跌期权) Long Position(多方)：Buyer（买入） Call Put Position Buy（+） + — + Sell（—） — Short Position(空方)：Seller (卖出) 对应的四张图：

Profit (收益) 期权费 期权费

Stock Price(股票价格) 执行价格 Stock Price(股票价格)

卖出看跌期权 卖出看涨期权

) Profit (收益Profit (收 执行价格 期权费 Stock Price(股票价格) Stock Price(股票价格) 执行价格 期权费 买入看跌期权 买入看涨期权

期权组合（Combinations of Options）：

Protective put（保护性看涨期权） is the strategy of buying a put and buying the underlying stock

买看跌期权的同时买标的股票的策略 根据两项策略

Price of underlying stock + price of put = price of call +present value of exercise price 标的股票的价格+看跌期权价格=看涨期权价格+行权价的现值 上述关系就是买卖权平价 put-call parity

The relationship is known as put-call parity and is one of the most fundamental relationships concerning options.

买卖权平价表明存在着两种购买保护性看跌期权的途径： 1、 你可以在购买看跌期权的同时买进标的的股票，此时的成本包括标的的股票价格加上看

跌期权价格。

2、 你可以在购买看涨期权的同时买进零息债券，这时，成本包括看涨期权价格加上行权价

格的现值。

为了看清买卖权平价，我们变化以下公式：

标的股票价格=看涨期权价格—看跌期权价格+行权价的现值

Price of underlying stock = price of call—price of put +present value of exercise price 注意，由于看跌期权前面的符号是负号，所以是卖出而不是买入看跌期权。 这种策略叫做Synthetic stock(合成股票)

进一步变化：对销看涨期权策略Cover call stratgy：

Price of underlying stock—price of put = —price of call +present value of exercise price 标的股票的价格—看跌期权价格=—看涨期权价格+行权价的现值

Valuing options看涨期权价值

考虑看涨期权价值上限和下限开始，

Lower bound 下限：股价—执行价 Upper bound上限: 股票价格 The factors determining call-option values 1、Exercise price(执行价格)：An increase in the exercise price reduces the value of the call 执行价格的上升将降低看涨期权的价值。 2、expiration date(到期日)：The value of an American call option must be at least as great as the value of the otherwise identical option whit a shorter term to expiration .(美式期权价值必定不小于期限较短的其他同类的价值) 3、Stock price(股票价格); other things be equal ,the lighter the stock price, the more valuable the call option will be.(在其他条件相同时，股票价格越高，看涨期权的价值越高)

4、The key factor the variability of the underlying assets (关键因素: 标的资产价值的变动性)

The greater the variability of the underlying assets , the more valuable the call –option will be(标的资产价值变动越大，看涨期权越有价值)

5、The interest rate(利率)：Call price are also a function of the level of interest rates.(看涨期权的价格也是利率水平的函数)

Binomial Option Price Model（二差数期权模型）

Value of a call = Stock price *Delta—Amount borrowed

看涨期权价值= 股价 * delta — 借款额 首先决定Delta：Delta?swingofcall（看涨期权的涨落）

Swingofstock（股价的涨落）再决定借款量：（书上有，自己开发）

Risk-Natural Valuation(风险中性评估)

用两种方式评估看涨期权的价值：

1、 Determining the cost if a strategy to duplicate the call . This strategy involves an

investment in a fractional share of stock financed by partial borrowing.(决定复制一个看涨期权策略的成本。该策略涉及通过部分借款投资部分股票)

2、 Calculate the probabilities of a rise and a fall under the assumption of risk-neutrality.(在

假定风险中性的条件下，计算上升和下降的可能性。使用这些可能性，并结合无风险利率，折线看涨期权在到期日的收益)

The Black-Scholes Model

注解：基本见解就是缩短时间期限，股票和借款的特定组合的确可以复制无限小时间水平上的看涨期权。

C?SN(d1)?Ee?rtN(d2)

d1?[ln(S/E)?(r?1/2?2)t]/?2t 和

d2?d1??2t

解释：S= 现行股价 ，E= 看涨期权的执行价格，r=年连续无风险收益率，连续复利 ?= 股票连续收益之方差（每年） t=到期日的时间（年） N(d)=标准正态分布随机变量小于或等于d的概率。

2

本文来源：https://www.bwwdw.com/article/gcrp.html