Lecture 7use of CAPM for calculating

cost of Capital for risky projectand efficient market

By Muhammad Shafiq.forshaf@gmail com

:// . . /http www slideshare net forshaf

Basic terms• You get compensated for taking on systematic risk measured by beta. Std

Dev measure volatility due to both systematic and unsystematic risk.• Beta Means: A measure of the volatility, or systematic risk, of a security or a

portfolio in comparison to the market as a whole. Beta is used in the capital asset pricing model (CAPM), a model that calculates the expected return of an asset based on its beta and expected market returns

• Beta is calculated using regression analysis, and you can think of beta as the tendency of a security's returns to respond to swings in the market.

• A beta of 1 indicates that the security's price will move with the market. A beta of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20% more volatile than the market

Introduction: Cost of Capital Expected return on a portfolio of all the company’s existing securities. It is the opportunity for investment in the firm’s assets Hence, the appropriate discount for the firm’s risk projects If company has no debt outstanding then the cost of capital is just the

expected rate of return on firm’s stock Eg

a company has beta of about 0.55, risk free rate is 7.4 and market risk premium is 8% then CAPM would imply rate of return:

r= rf +[(Beta (rm)] =.074+ .55*.08

Cost of Capital and risk factor• Two project, never have the same expected rate of return• Based on the risk factor• More the risk, higher the expected rate of return

Security market line showing RoR on project

11.8 company CoC

7.4

project beta Average beta of company investment=0.55

Figure showing a comparison between the company CoC and the RoR under the CAPM at 11.8% returns. It is correct only if project beta 0.55 . **correct discount rate increase with increase of beta. Company should accept the project with the rate of return above security line

Perfect pitch and the cost of capital• If true cost of capital depends on risk of project then why time is

spent on estimating more time on company CoC (Cost of Capital):Two reasons:

• Company CoC is good starting point to estimate a project (whether more risky or less risky).

• For average risky or less risky project company CoC is considered the best rate

Debt and the Company CoC(Cost of Capital)• Portfolio usually includes debt and equity, so, it is blend of two• Suppose the company market value Balance Sheet looks as:

• CoC is different as we can calculate: company CoC = rD D/V + rE E/V

=7.5*.30 + 15 *.70 = 12.75%rD = Ror on debt D = Debt V = value rE required rate on equity E = equityThis Blended measure of company is weighted average cost of Capital (WACC)

Debt D=30 at 7.5%

Equity E=70 at 15% Asset Value 100

Firm Value value=100 Asset Value 100

Calculating WACC• Calculating WACC is bit complicated than our last exampleSuppose: Interest is a tax-deductible expense for corporations so after tax Cost of Debt is (1- t) rD, where Tc is the marginal corporate tax rate.If Te = 35%. Then after tax WACC is:After tax WACC = (1-tc) rD D/V + rE E/V

rD = Ror on debt D = Debt V = value rE required rate on equity E = equity

Measuring the cost of equity• To calculate the weighted-average CoC, you need an estimate of cost

of equity• You decide to use CAPM as most US companies do; CAPM says;

expected stock return= rf = + Beta (rm - rf)

Estimating beta• Future beta are estimated by historical evidence• We fit a line through the points(different dots).• Slope of the line is an estimate of beta; tells how much on average the

stock price changed when the market index are 1% higher/lower.• Small risk from market but specific/non systematic risk.• R squared (R2) provides the proportion of total variation in the stock’s

return that can be explained by market movement.

Estimating beta• Generally returns obscure beta• Hence, statisticians calculate standard error of the estimated beta to

shoe the extent of possible mismeasurement• Then they setup confidence Interval of the value plus or minus two

standard error.example. Confidence interval for PTCL beta is 0.34 plus or minus1.96* .029. if you state that the true beta for PTCL company is between 0.29 and 0.4, you have 95% chance of being right.• Financial managers often turn their attention toward industry betas

The expected return on Pakistan State Oil (PSO)• You are asked to calculate CoC of PSO. We have two clues about the true

beta: one PSO direct estimate is 0.45 and average industry estimate is 0.86. so we use industry average as Financial manager. Next issue is to estimate the risk free interest rate, we can get it from central Bank (State bank of Pakistan) T-bills rate which is on average 7.31.

• Since, CAPM is short term model. It works period to period and ask for short term rate. Can a project use CAPM rate for 1 year to 10 year in future

• FM can use long term rate in risk free rate or retains the difference between the market risk premium and short term T-bills.

• Suppose you decide to use a market risk premium of 10% and risk ree rate is 7.37% then we can calculate as:

• Cost of Equity= expected stock return= rf = + Beta (rm - rf)= 7.4+0.86*10 = 16%

PSO after tax weighted average cost of Capital• If calculate WACC then the company cost of debt was about 9% with

34% a corporate tax rate, the after tax cost of debt was:• rD (1-tc)=9*(1-0.34)= 5.94% • The ratio of debt to overall company value was D/V =7% therefore

After tax WACC = (1-tc) rD D/V + rE E/V =(1-0.34)*9*0.07+16*0.93= 15.29%

Note: the formula is using debt which always less than equity. Not suggested for acute calculation

PSO asset beta(β)• After tax WACC depends on average risk of the company asst but also

depends on tax and financing.• Direct measure is called the beta of assetWe calculate the asset beta as a blend of the separate betas of debt (βD) and equity (βE). For Pakistan State oil company we have (βE)=0.86 and (βD) =0.1610 Weights are the fraction of debt and equity financing, D/V=0.07 and E/V= 0.93 then asset beta will be:

Asset beta ((βa) = (βD) (D/V) + (βE) (E/V) = 0.16*0.07+ 0.86*0.93 = 0.81

Analyzing project risk

Copyright © 2013 CFA Institute16

1. Introduction• The cost of capital is the cost of using the funds of creditors and

owners.• Creating value requires investing in capital projects that provide a

return greater than the project’s cost of capital.• When we view the firm as a whole, the firm creates value when it provides a

return greater than its cost of capital.

• Estimating the cost of capital is challenging.• We must estimate it because it cannot be observed.• We must make a number of assumptions.• For a given project, a firm’s financial manager must estimate its cost of capital.

Copyright © 2013 CFA Institute17

2. Cost of capital• The cost of capital is the rate of return that the suppliers of capital—

bondholders and owners—require as compensation for their contributions of capital.

• This cost reflects the opportunity costs of the suppliers of capital.

• The cost of capital is a marginal cost: the cost of raising additional capital.

• The weighted average cost of capital (WACC) is the cost of raising additional capital, with the weights representing the proportion of each source of financing that is used.

• Also known as the marginal cost of capital (MCC).

CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a

security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the

security.Works for both individual assets and portfolios

• A model that describes the relationship between risk and expected return and that is used in the pricing of risky securities.

• default model for risk in equity valuation and corporate finance.• The general idea behind CAPM is that investors need to be

compensated in two ways: time value of money and risk

Capital Asset Pricing Model (CAPM)

Definition: Efficient Capital Markets• In an efficient capital market, security prices adjust

rapidly to the arrival of new information, therefore the current prices of securities reflect all information about the security

• Whether markets are efficient has been extensively researched and remains controversial

Corporate Financing Decisions and Efficient Capital Markets

• An efficient market is one in which current market prices reflect all available information.

• What information is available? Depends on costs/benefits of collection/evaluation/use of information.

• We will see that the EMH has strong implications for investors/firms/financial managers.

Preview – An Efficient Market• Because information is reflected in prices immediately,

investors should only expect to obtain an equilibrium rate of expected return (as predicted by the SML). Awareness of information when it is released does the investor no good. The price adjusts before the investor can trade on it.

• Firms should expect to receive a fair value for securities they issue.

• Financial managers cannot time issues of securities.• A firm can sell as many shares of stock or as many bonds as it

wants without fear of depressing the price.• Stock and bond markets cannot (barring fraud) be affected by

firms artificially increasing earnings (cooking the books).

StockPrice Overreaction and

reversion

Early response

Delayed response

Efficient marketresponse to new

information

Days before (–) and

after(+) announcement

Public announcement day

Reaction of Stock Price to New Information in Efficient and Inefficient Markets

–30 –20 –10 0 +10 +20 +30

Market Efficiency• Weak Form Efficiency

• A capital market is said to be weakly efficient or to satisfy weak-form efficiency if current prices fully incorporate the information in past prices (more generally trading information).

• In a financial market that is weak form efficient, investors can't trade on the basis of past returns and expect abnormal profits.

Market Efficiency• Semi-Strong Form Efficiency

• A market is said to be semi-strong form efficient if current market prices fully incorporate all publicly available information (e.g., information in the WSJ).

• Since past prices are publicly available information, if a market is semi-strong form efficient, it is necessarily weak form efficient.

• In a market that is semi-strong form efficient investors cannot trade based on publicly available information and expect profits in excess of an equilibrium expected return (as specified by, for example, the SML).

Corporate Insider Trading• Corporate insiders include major corporate officers, directors, and

owners of 10% or more of any equity class of securities• Insiders must report to the SEC each month on their transactions in

the stock of the firm for which they are insiders• These insider trades are made public about six weeks later and

allowed to be studied

Role of Corporate Insider Trading• Corporate insiders generally experience above-average profits

especially on purchase transaction• This implies that many insiders had private information from which

they derived above-average returns on their company stock

Corporate Insider Trading• Studies showed that public investors who traded with the insiders

based on announced transactions would have enjoyed excess risk-adjusted returns (after commissions), but the markets now seem to have eliminated this inefficiency (soon after it was discovered)

Corporate Insider Trading• Other studies indicate that you can increase returns from using

insider trading information by combining it with key financial ratios and considering what group of insiders is doing the buying and selling

Stock Exchange Specialists• Specialists have monopolistic access to information about unfilled

limit orders• You would expect specialists to derive above-average returns from

this information• The data generally supports this expectation

Security Analysts• Tests have considered whether it is possible to identify a set of

analysts who have the ability to select undervalued stocks• This looks at whether, after a stock selection by an analyst is made

known, a significant abnormal return is available to those who follow their recommendations

Professional Money Managers• Trained professionals, working full time at investment management• If any investor can achieve above-average returns, it should be this

group• If any non-insider can obtain inside information, it would be this

group due to the extensive management interviews that they conduct

Performance of Professional Money Managers• Most tests examine mutual funds• New tests also examine trust departments, insurance companies, and

investment advisors• Risk-adjusted, after expenses, returns of mutual funds generally show

that most funds did not match aggregate market performance

Implications of Efficient Capital Markets• Overall results indicate the capital markets are efficient as related to

numerous sets of information• There are substantial instances where the market fails to rapidly

adjust to public information

Efficient Markets and Technical Analysis• Assumptions of technical analysis directly oppose the notion of

efficient markets• Technicians believe that new information is not immediately available

to everyone, but disseminated from the informed professional first to the aggressive investing public and then to the masses

Efficient Markets and Technical Analysis• Technicians also believe that investors do not analyze information and

act immediately - it takes time• Therefore, stock prices move to a new equilibrium after the release of

new information in a gradual manner, causing trends in stock price movements that persist for periods

Efficient Markets and Fundamental Analysis• Fundamental analysts believe that there is a basic intrinsic value for

the aggregate stock market, various industries, or individual securities and these values depend on underlying economic factors

• Investors should determine the intrinsic value of an investment at a point in time and compare it to the market price

Why Should Capital Markets Be Efficient?

The assumptions of an efficient market• 1. A large number of competing profit-maximizing

participants analyze and value securities, each independently of the others

• 2. New information regarding securities comes to the market in a random fashion, new information is not predictable.

• 3. Profit-maximizing investors adjust security prices rapidly to reflect the effect of new information

Conclusion: random unpredictable information + large competing investors react to news

Thank you very much for your time and discussion