CorpFi Exam 2

Define covariance and correlation.

-covariance is the expected product of the deviations of two returns from their means Cov(Ri,Rj) = E[(Ri-ui)*(Rj-uj)] -correlation equals the covariance of the returns of two securities divided by the SD of the returns of each Corr(Ri,Rj) = Cov(Ri,Rj)/[Vol(Ri)*Vol(Rj)] The correlation is always between -1 (perfectly negatively correlated) and 1 (perfectly positively correlated). independent events have 0 corrlelation

difficulties of using historical data to predict the future

-the future might not be like the past -data set is limited

what are the conditions of a perfect capital market?

1. investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows 2. there are no taxes, transaction costs, or issuance costs associated with securities trading 3. a firm's financing decisions do not change the cash flows generated by its investments, nor do they reveal any new information about them

the CAPM depends on what 3 assumptions about investor behavior

1. investors can buy and sell all securities at competitive market prices, (with no taxes or transaction costs) and can borrow and lend at the risk free rate 2. investors hold only efficient portfolios of traded securities (i.e., they maximize their returns for a given risk level 3. investors have homogeneous expectations regarding the volatilities, correlations, and expected returns of securities

what are the three levels of market efficiency considered under the various forms of the EMH? How do they differ?

1. weak form: prices reflect the record of past prices 2. semi-strong form: stock prices reflect all publicly available easily interpretable information. competition will be fierce. EMH should hold very well 3. strong form: in addition to publicly available easily interpretable information, stock prices also reflect private or difficult to interpret information. if information is limited, then the EMH won't strictly hold. But over time if the information is available, others will spend time and effort to get it, and the degree of "inefficiency" should be limited by the cost of obtaining the information

risk premium

A risk premium is the return in excess of the risk-free rate of return an investment is expected to yield; an asset's risk premium is a form of compensation for investors who tolerate the extra risk, compared to that of a risk-free asset, in a given investment. Rp = Ri - Rf

Value-at-Risk

A threshold value such that the probability of loss on the portfolio over the given time horizon exceeds this value, assuming normal markets and no trading in the portfolio Value at risk (VaR) is a statistic that measures and quantifies the level of financial risk within a firm, portfolio or position over a specific time frame. This metric is most commonly used by investment and commercial banks to determine the extent and occurrence ratio of potential losses in their institutional portfolios. Risk managers use VaR to measure and control the level of risk exposure. One can apply VaR calculations to specific positions or whole portfolios or to measure firm-wide risk exposure. VaR modeling determines the potential for loss in the entity being assessed and the probability of occurrence for the defined loss. One measures VaR by assessing the amount of potential loss, the probability of occurrence for the amount of loss, and the timeframe. For example, a financial firm may determine an asset has a 3% one-month VaR of 2%, representing a 3% chance of the asset declining in value by 2% during the one-month time frame. The conversion of the 3% chance of occurrence to a daily ratio places the odds of a 2% loss at one day per month.

the risk free rate is 5%. the equity risk premium is 6%. we own 3 stocks: 20% of our portfolio is in stock ABC with a Beta of 0.75; 50% of our portfolio is in stock XYZ with a Beta of 1.25; and 30% of our portfolio is in stock PQR with a Beta of 0.30. what is the expected return of our portfolio?

Beta = .2*.75 + .5*1.25 + .3*.3 = .865 risk free rate = 5% equity risk premium = 6% expected return = .05 + .865*.06 = 10.19%

the risk free rate is 3%. the equity risk premium for the stock market portfolio is 5%, and the variance of the market portfolio is 17.5%. the covariance of the returns of a firms stock and the market portfolio is 26.25%. calculate the expected return of an investment in the firms stock using CAPM

Beta = Cov(Ri,Rmkt)/Var(Rmkt) =.2625/.175 = 1.5 The expected return = Re is: Re = Rf + B*[E(Rmkt)-Rf] Re = .03 + 1.5*(.05) = 10.5%

define the Beta of a security. give the formula for Beta

Beta is a measure of the sensitivity of a stock's return to the return of the overall market. specifically, Beta is the expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio Beta = [Vol(Ri)*Corr(Ri,Rmkt)]/Vol(Rmkt) = Cov(Ri,Rmkt)/Var(Rmkt)

You are given the following information about a firm: -Long-term debt outstanding = $200,000 -long term debt is risk free and financed at an interest rate of 8% -number of shares of common stock: 50,000 -price per share: $16 -book value per share: $12 -stock's beta: 1.10 -the expected market return: 12% Assuming PCM, what is the company's weighted average cost of capital?

CAPM states: Re = Rf + B*[E(Rmkt) - Rf] Re = 8% + 1.1*(12%-8%) = 12.4% Debt = 200,000 Equity = 50,000*16 = 800,000 so debt = 20%/equity = 80% WACC = [E/(D+E)]*Re + [D/(E+D)]*Rd WACC = (80%*12.4%) + (20%*8%) WACC = 11.52%

M&M II

Cost of capital of levered equity increases as the firm's market value of debt to equity ratio increases.

assume your firm operates in a PCM. the MV of the debt is originally $300 million, and the firm's total MV of assets is originally $1.5 billion. the equity costs of capital is 15%, and the debt cost of capital is 5%. your firm has decided to invest in a new IT reporting system which requires $400 million upfront in investment. the decision is to finance 25% of this project by issuing new shares of stock and to finance 75% of this project with new debt at the same 5% cost of capital. determine the equity cost of capital for your firm after the new $400 million upfront investment, assuming PCM

D = $300 mm, A = $1500 mm = D+E So, E = $1200 mm R(pretax WACC) = [E/(E+D)]*Re + [E/(E+D)]*Rd = (1200/500)*.15 + (300/1500)*.13 = 13% Since PCM, R(pretax WACC) does not change with different capital structure when issuing more debt New D = 300 + .75*400 = $600 mm New E = 1200 + .25*400 = $1300 mm New A = D+E = $1900 mm R(pretax WACC) = .13 = (13/19)*Re + (6/19)*.05 Re = 16.7%

let E(Re), E(Ru) and E(Rd) represent the expected returns on levered equity, unlevered equity, and debt respectively. let E and D equal the market value of equity and market value of debt, respectively, of a firm. give the formula for E(Re), which demonstrates the effect of leverage on E(Re).

E(Re) = E(Ru) + (D/E)*E(Ru-Rd) Note: this demonstrates the Modigliani-Miller Proposition II -- the cost of capital of levered equity E(Re) increases as the firms' market value of debt to equity ratio increases

you are the CFO of Value Corp with the following capital structure: -outstanding debt: $200 million financed at an interest rate of 4% which includes a 100 basis point credit spread -number of outstanding shares of stock: 25 million -book value of equity: $600 million -current share price: $40 -Beta of a firm's stock is 1.2, volatility of historical return of Value Corp's shares is 25% -expected return of the market: 9% -firm's tax rate: 20% you as the CFO have been asked to consider financing a major project for Value Corp. the project requires upfront costs followed by positive cash flows each year after. you plan to fund the project with internal financing without modifying the proportions of debt and equity in your firm. the project has an 11% IRR based on analysis. given capital constraints you will accept the project ONLY IF the project IRR exceed's the firm's opportunity cost of capital by at least 2.5%. your firm is not in PCM. Would you accept or reject this project?

MV equity = $40*25 mm shares = $1000 mm A = D+E = $200 mm + $1000 mm = $1200 mm Tau(c = 20%; Beta=1.2; Rd=4% Therefore, Rf=3% due to 100 bp credit spread FInd R(after-tax WACC) or after-tax opportunity cost of capital since not in PCM. R(WACC) = [E/(E+D)]*Re + [D/(E+D)]*Rd*(1-Tau) = (1000/1200)*Re + (200/1200)*.04*(1-.20) need Re: Re = Rf + B*[E(Rmkt)-Rf] = .3 + 1.2*(.09-.03) = 10.2% Therefore, R(WACC) = 5/6(.102) + 1/6(.04)(.8) = 9.03%, which is the opportunity cost of capital for Value Corp. IRR of project = 11% vs. 11.53% hurdle rate (9.03% + 2.5%) Since 11% IRR is less than the 11.53% hurdle rate, REJECT the new project

3 risk measures

-volatility -semi variance -expected tail loss

correlation

Measure of common risk shared by stocks that does not depend on volatility. Equals the covariance of the returns of two securities divided by the standard deviation of each stock's return. Value is always between -1 (perfectly negatively correlated) and +1 (perfectly positively correlated).

semi-variance

Measures the possibility of returns below the mean. Therefore, semi-variance is a measure of downside risk.

what are the two forms of bankruptcy

1. liquidation of the firm - the firms assets are sold at auction and the proceeds go to the creditors 2. reorganization - all collection attempts are automatically suspended, and management continues to run the business while proposing a reorganization plan that specifies the treatment of each creditor of the firm, which is usually a combination of cash and equity of the firm. generally speaking, this total is less than the amount owed to the creditors, but more than they would expect to receive in an auction of the firm's assets. creditors must vote to accept the plan, and it must be approved by a bankruptcy court

you have a portfolio of three stocks with the following weights and financial statistics. (correlation means the correlation of the return of the stock with the return of the portfolio). the risk free rate is 2.5%. Calculate the Sharpe Ratio of your stock portfolio

Sharpe Ratio = [E(Rp)-Rf]/SD(Rp) E(Rp) = .35*.07 + .25*.12 + .4*.1 = .0945 SD(Rp) = weighted average[SD(Ri)*Corr(Ri,RP)] = .35*.15*.4 + .25*.28*.5 + .4*.2*.6 SD(Rp) = .104 Sharpe Ratio = (.0945-.025)/.104 = .6683

the volatility of a portfolio equally weighted with large cap stocks, small cap stocks, and bonds is 13.2%. using E(Rp) = 9.17%, calculate the Sharpe ratio of this portfolio.

Sharpe Ratio = [E(Rp)-Rf]/Vol(Rp) =(.0917-.01)/.132 = .6189

the risk free rate is 3% and the equity risk premium is 5%. Google has volatility of 26% and a Beta of 1.45. Southwest Airlines has a Beta of 0.83. Its total volatility is 40%. Which firm has greater risk? Which firm has the lower equity cost of capital?

Southwest Airlines has higher total volatility, therefore higher risk. Google expected return = .03 + 1.45*.05 = 10.25% = equity cost of capital Southwest expected return = .03 + .83*.05 = 7.15% Southwest Air has a greater total risk and a lower equity cost of capital. Why? a firm's equity cost of capital is determined by its systematic risk, not its total risk (remember, investors don't get paid for firm specific risk)

diversification

Spreading out investments to reduce risk the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce risk or volatility by investing in a variety of assets.

Southwest Airlines has a zero debt beta, a 0.98 unlevered beta, and a .15 market debt/equity ratio. calculate its equity beta

Be = Bu* [1+(D/E)] Be = .98*1.15 = 1.13

let Be equal the equity beta of a firm, Bd be the debt beta, and let Bu equal the beta of the firm if it is unlevered. express the unlevered beta as a function of the equity and debt betas and the firm's market value debt to equity ratio. assuming the firm can borrow with no risk of default, express the equity beta as a function of the unlevered beta and the firm's market value debt to equity ratio.

Bu = [E/(D+E)]*Be + [D/(D+E)]*Bd if the risk of default is zero (Bd=0) then: Be = Bu*[1+(D/E)]

market value balance sheet

a balance sheet where all assets, including intangible assets, are reflected, and all assets and liabilities are valued at market value

what is the difference between a firm in economic distress and a firm in financial distress?

a firm is in financial distress when it is having difficulty meeting its debt obligations. a firm is in economic distress when there is a significant decline in the value of the firm's assets, whether or not it is also in financial distress is due to its leverage

what is a firm's marginal tax rate?

a firm's (or individual's) marginal tax rate is the tax rate it will pay on the next $1 of income

M&M I

In a perfect capital market, total value of firm equals the Market Value of the total cash flows generated by its assets and is not affected by its capital structure. Market Value Balance Sheet: 1. All assets are included such as intangible assets like brand, reputation, and human capital. 2. All assets and liabilities are assessed at market value (current cost vs historical cost or book value).

1978 Bankruptcy Reform Act

PCM: ownership transferred from shareholders to debtholders or creditors Debtholders stand first in line (M& MII)

what is the key advantage that the Tail Value-at-Risk (TVaR) risk measure has over the Value-at-Risk (VaR) risk measure?

Value-at-Risk does not measure how bad the results can get if the outcome is beyond the calculated cut-off percentile. TVaR was developed to overcome that disadvantage. it measures the expected loss given that the loss is beyond the calculated percentile (e.g., given that the loss exceeds the 95th percentile)

taking into account the interest tax shield, what is a firm's weighted average cost of capital?

WACC = [E/(E+D)]*(equity cost of capital) + [D/(E+D)]*(pre-tax debt cost of capital)*(1-marginal tax rate) where E and D represent the market value of the firm's equity and debt respectively

a firm has an equity cost of capital of 15%, a debt cost of capital (before taxes) of 6%, and a marginal tax rate of 35%. its ratio of its market value debt to equity is 25%. calculate the firs=ms weighted average cost of capital, after taking into account taxes

WACC = [E/(E+D)]*(equity cost of capital) + [D/(E+D)]*(pre-tax debt cost of capital)*(1-marginal tax rate) WACC = .8*15% + .2*6%*(1-.35) = 12.78%

security market line

a linear relationship, starting at the risk free rate (with zero volatility), going through the market portfolio (Beta=1) and on upward showing the relationship between a stocks expected return and its Beta according to the CAPM. in other words, it is a graphical representation of this formula: E(Ri)=Ri=Rf+B*[E(Rmkt)-Rf] ---B=1 if you are at the mkt portfolio--- Re = Rf + B*[E(Rmkt) - Rf] EX: Beta of portfolio = .865 Rf = 5% equity risk premium = 6% Expected return = .5 + .865*.1

how do agency costs of leverage change as a firm's leverage increases?

agency costs of leverage only occur when there is a change of financial distress, so these costs increase as leverage increases, because that increases the probability of financial distress

what is the alpha of a stock?

alpha is the difference between a stock's historical actual return and its expected return predicted by the security market line alpha = E(Rs) - Rs E(Ri)=Ri=Rf+Bi*[E(Rmkt)-Rf] as demand goes up, price goes up, and expected return goes up

firm-specific risk

an event or activity relevant to the firm itself; good or bad news regarding the firm aka: -diversifiable -independent -idiosyncratic risk premium = 0 (you can diversify out of it)

what are potential agency benefits of leverage?

benefits that may arise due to enhanced incentives for managers to run the firm in a more efficient and effective manner due to concentration of ownership -managers know that the firm needs to meet debt obligations (make interest payments); "free cash flow" -managers will be more efficient and effective -managers, and others, are more assertive/aggressive in their actions to keep the company running (maintain business, be competitive)

define the beta of a security

beta is a measure of the sensitivity of a stock's return to the return of the overall market. specifically, beta is the expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio

how does debt affect the equity cost of capital in PCM and non-PCM?

choice of debt or equity financing will not affect the total value of a firm, its cost of capital, or its share price

what are agency costs of leverage?

costs that arise due to conflicts of interest between shareholders and creditors of a firm. these conflicts are most likely to occur when a firm is in financial distress, and managers may take actions that benefit shareholders at the expense of creditors. one example is overinvestment: taking on risky investments to try to increase returns for shareholders at the expense of creditors another example is underinvestment: passing up potential opportunities that require large upfront investments to mitigate: -issue short term vs. long term debt (limits time frame to exploit opportunities) -bond covenants

how does Monte Carlo simulation differ from deterministic anaylsis?

deterministic analysis involves a 'single point estimate' which illustrates the outcome of one trial at a time (i.e., revising one assumption at a time for 'sensitivity testing') Monte Carlo simulation allows one to see all possible outcome values for enhanced decision-making analysis. the process is also called 'stochastic modeling' whereby a random number generator is used to simulate a distribution of value (e.g., interest rate scenarios)

list some of the indirect costs of financial distress or bankruptcy

direct: -lawyers -accountants -investments appraisers -investment bankers indirect: -loss of customers -loss of suppliers -loss of employees (or expensive retention packages) -loss of receivables -fire sale of assets to raise cash -delayed liquidation (and continued bad decisions by the managers) -costs to creditors whose own firms are hurt because the value of their assets (the bonds of the firm in financial distress) goes down

what is the difference between levered and unlevered equity?

equity in a firm with no outstanding debt is called unlevered equity. equity in a firm that has debt outstanding is called levered equity

optimal levels of debt

firms use internal financing (RE) firms use external financing (issue debt), varies by industry

thinking back to what we learned in the first part of this course, how would financial managers use the WACC when deciding which projects or products to approve?

as we learned in the first part of this course, when evaluating projects financial managers should make their decisions based on the NPV decision rule, in order to maximize the value of the firm. the WACC is the discount rate that the financial manager uses to compute the NPV of the cash flows when applying the NPV decision rule. in other words, WACC Is the Opportunity Cost of Capital.

define default

default occurs when a firm fails to make promised interest of principal payments on its debt. default need not occur as long as the present value of the firm's assets exceeds the present value of the firm's liabilities (that is default depends on the relative value of a firm's assets and liabilities, not on its cash flows)

equity risk premium or Market risk premium

expected return of the market - risk free rate Equity risk premium refers to the excess return that investing in the stock market provides over a risk-free rate. This excess return compensates investors for taking on the relatively higher risk of equity investing. The size of the premium varies depending on the level of risk in a particular portfolio and also changes over time as market risk fluctuates. As a rule, high-risk investments are compensated with a higher premium.

how does the lemon principle potentially affect corporate financing decisions?

following the lemon principle would imply that when a firm issues more equity, buyers will assume the firm is overvalued and the share price will drop (this is, in fact, borne out by research on the effect of new equity issues). therefore, financial managers will prefer to fund new projects first through retained earnings, then debt, and lastly by issuing equity This is called Pecking Order Theory

if the Beta of a stock decreases, what happens to its stock price?

if Beta decreases, then systematic risk has decreased. therefore, investors don't demand as high a return as they did before Beta decreased, so the stock price goes up

what is the difference between homogeneous expectations and rational expectations?

if investors have homogeneous expectations regarding the volatilities, correlations, and expected returns of securities the all value them the same. with rational expectations investors may have different information regarding expected returns, correlations, and volatilities, but they correctly interpret that information and the information contained in market prices and they adjust their estimates of expected returns in a rational way

what is the implication for the role of financial managers of a firm? (in context of Trade-Off theory of firm value)

in PCM, the capital structure doesn't matter. but capital markets are imperfect, and financial managers must balance the costs and benefits of these imperfections to find the optimum capital structure

how does capital structure affect the WACC in PCM?

no effect?

calculate the Correlation of Small cap stocks to Large cap stocks. calculate the Correlation of Small cap stocks to Bonds. if you held a portfolio of only Small cap stocks and wanted to lower your volatility, which other portfolio is the better diversifier?

for small cap and large cap stocks: Corr(Ri,Rj) = Cov(Ri,Rj)/[Vol(Ri)*Vol(Rj)] =.0308/(.22*.175) = 0.8 for small cap stocks and bonds: Corr = .00264/(.22*.06) = .2 since the correlation of bonds to small cap stocks is lower than the correlation of small cap stocks to large cap stocks, bonds provide better diversification.

debt in high vs. low growth firms

high growth firms: tech, pharm low growth firms: retail, auto, airlines Answer: low growth firms (b/c of the earnings, the EBIT) High growth firms tend to have higher P/E ratio because MV of equity is typically higher -Higher P/E ratio = MV equity/NI = Share price/EPS -Leverage = D/A = D/(A+D)

what type of risk can be eliminated through diversification?

idiosyncratic risks (firm specific)

the risk free rate is 5% and the equity risk premium is 8%. the price of a share of XYZ corp stock (which pays no dividends) is expected to be $40 one year from now. the equity Beta of XYZ Corp is between zero and one. what is the price range of a share of XYZ Corp stock today?

if Beta equaled one, the expected return would be 13%. Then, price for a share of stock would be 40/1.13 = $35.40. But Beta is less than one, so investors expect a return lower than for the market as a whole. This means the price of a share of XYZ Corp stock must be greater than $35.40. If Beta equaled zero, the expected return would be the risk free rate, 5%. then the stock price would be 40/1.05 = $38.10. the stock is not risk free, so investors will pay less than $38.10 per share. Therefore, the price of a share of XYZ Corp is between $35.40-$38.10

semi-variance

if the Var(R) = E[(R-u)^2], then the downside semi-variance is defined as follows: E{[min(0,R-u)]^2}. This illustrates the downside risk to be analyzed when designing risk management strategies

in PCM, how is a firm's WACC affected by its capital structure?

in PCM, a firm's WACC is not affected by its capital structure

in PCM, how does leverage affect the average cost of capital of a firm?

in PCM, the financing of a new project with debt or equity will not affect the total value of a firm, nor its share price, nor the firm's average cost of capital. the average cost of capital for a levered firm will be the same as for the firm if it were unlevered. debt merely changes the allocation of cash flows between debt and equity investors. in other words, in PCM the savings from the low expected returns on debt (the debt cost of capital) will be exactly offset by the higher equity cost of capital which will be demanded by investors due to their increased risk resulting from the borrowing. this is the conservation of value principle, which states that in PCM financial transactions neither add nor destroy value

State Modigliani-Miller Proposition I

in a PCM, the total value of a firm is equal to the market value of the total cash flows generated by the firms' assets, and it is not affected by its choice of capital structure

what happens to debt holders in default?

in default, debt holders are given certain rights to the assets of the firm. in bankruptcy, the debt holders take over ownership of the firm

what is the general formula for calculating the value that the interest tax shield adds to a corporation? why, in practice, is this value difficult to calculate?

in general terms the interest tax shield for any year equals the firm's marginal tax rate times its interest payments. the value that the interest tax shield adds to a corporation is the present value of the interest tax shield for all future years, which equals the sum of the present values of the marginal tax rate times the interest expense for all future years in practice the value of the interest tax shield is difficult to calculate because the amount of a firm's debt changes over time, the interest rates on debt change over time, and the firm's marginal tax rates may change over time

asymmetric information

information that a firm's managers know about a firm and its future cash flows that is not known by investors

Marie's Goods Store had EBIT of $1.5 billion in 2017. in calendar year 2017 the outstanding debt was $5 billion and the cost of debt was 5%. Marie's Goods has a marginal tax rate of 40% -What is the interest tax shield in calendar year 2017? -Without leverage in 2017, Marie's Goods Store would have had 'Net Income' equal to $900 million. Determine 'Net Income' in 2017 based on Marie's Goods Store having the leverage as discussed above.

interest expenses = O/S debt*cost of debt = $5 billion*.05 = $250 million in 2017 Interest Tax Shield = Corp Tax Rate * Interest Expenses = .4($250 mm) = $100 mm W/o leverage ($mm) -EBIT: $1500 -Int Exp: 0 -Pretax Income: $1500 -Taxes: -$600 -Net Income: $900 W/ leverage ($mm) -EBIT: $1500 -Int Exp: -$250 -Pretax Income: $1250 -Taxes: -$500 -Net Income: $750 mm shortcut: Net Income (w/leverage) = $900 mm (NI w/o leverage) -250 interest expenses +100 interest tax shield = $750 mm

in PCM, how does leverage affect the risk of owning the equity of a firm?

leverage increases the risk of owning equity in a firm because the lenders (the bond holders) will be paid first. this increases the volatility of returns to equity holders, even if there is no risk of default. investors in the firm's equity will demand a higher return to compensate them for this increased risk (volatility). this is true even if there is no risk of default

which firms in theory would have higher leverage if they took advantage of the interest tax shield in their corporate structure -- high or low growth firms?

low growth firms would, in theory, have higher leverage. this is because the interest tax shield is a function of current earnings before interest and taxes. the value of high growth firms will generally be a bigger multiple of current earnings than for low growth firms. therefore, its optimal level of debt, which is a function of current earnings, will be a lower ratio to the market value of the firm

systematic risk

market wide risk: an event or activity that affects the entire market (fed reserve announcements, recession, tariffs); things that affect the economy on a macro scale aka: -systematic -undiversifiable -common risk risk premium exists: can't do anything about it because it affects everything

beta

measure of how a stock might move relative to the market Bi = Cov(Ri,Rp)/Var(Rp) low beta: utility company, food processing (not as cyclical) high beta: auto industry, home building, steel firm (cyclical)

expected tail loss

measures the expected loss in the worst X% of the outcomes, or expected losses of outcomes below a certain threshold

which is the more common form of bankruptcy

reorganization

under the CAPM, what is the opportunity cost of capital for investing in a project for a firm whose Beta is B, assuming the firm has no debt?

since we can only add value to a company by investing in projects whose expected return exceeds the expected return required by investors (thereby raising the price of the stock to reflect this new opportunity) it follows that the opportunity cost of capital for investing in a project at a firm with no debt whose beta is B equals the risk free rate Rf plus Beta times the equity risk premium. recall, the equity risk premium is the expected return of the market minus the risk free rate Opp Cost of Cap = Rf + B*[E(mkt) - Rf]

efficient markets hypothesis (EMH)

states that securities will be fairly priced, based on their future expected cash flows, given all information available to investors. competition among investors eliminates all positive NPV trading opportunities

define systematic risk and idiosyncratic risk. which of these can be eliminated through diversification?

systematic risk is risk that is common to all securities in the market. idiosyncratic risk, or firm specific risk, is risk that is specific to one firm. examples would be bad management, lawsuits, defective products, etc.

define the Sharpe ratio. give the formula. what can be said about the Sharpe ratio of the Efficient Portfolio?

the Sharpe ratio is a measure of reward (excess return) to volatility (SD of the portfolio) provided by a portfolio = [E(Rp)-Rf] / Vol(Rp) the Efficient Portfolio is the portfolio on the efficient frontier that has the highest possible Sharpe ratio. under CAPM, it is the market portfolio (the S&P500)

opportunity cost of capital for a firm

the best available rate offered by the market for a security of comparable risk and term to the investment opportunity being considered Ri = Rf + B*[E(Rmkt)-Rf]

what is the Beta of a portfolio of stocks? (give the formula)

the beta of a portfolio of stocks is the weighted average sum of the betas in the portfolio = sum(Xi*Bi) where Xi is the percentage of the portfolio made up of investment i and Bi is the beta of investment i

the risk free rate is 4%. the equity risk premium is 6%. the volatility of the market portfolio is 18%. an investor invests 25% of his portfolio in the risk free asset, and the remaining 75% in the market portfolio. what is the expected return and the volatility of this investor's portfolio?

the expected return of a portfolio with x% invested in the market, and (1-x)% invested in the risk free rate is: E(Rp) = (1-X)*Rf + X*R(mkt) = (1-X)*Rf + X*[Rf + [E(Rmkt) - Rf] = Rf + X*[E(Rmkt) - Rf] Here, that is = .04 + .75*.06 = 8.5% The volatility of this portfolio equals X% of the market volatility. Here the volatility equals 75% of the market volatility = .75*.18 = 13.5%

calculate the expected return of a portfolio equally weighted with large cap stocks, small cap stocks, and bonds

the expected return of the equally weighted portfolio of large cap stocks, small cap stocks and bonds: E(Rp) = 1/3* (.11+.12+.045) = 9.17%

what is the interest tax shield?

the interest tax shield is the additional amount the firm would have to pay in taxes if it didn't have any interest payments on debt. In other words, it is the gain to investors from the tax deductibility of interest payments

Capital Market Line

the line drawn from the risk free asset through the efficient portfolio and tangent to the efficient frontier. it shows the highest possible return that can be obtained for any given level of volatility combination of risk-free investments and the market portfolio that represents the set of portfolios with the highest expected return for any given level of vol -when the tangent line goes through the market portfolio, E(Ri)=Ri=Rf+B*[E(Rmkt)-Rf] ---[E(Rmkt)-Rf] = market risk prem note: in the CML we are plotting returns of a portfolio against Total Volatility (don't confuse it with the security market line)

which firms are most affected by the potential costs of financial distress or bankruptcy, those with high or low leverage?

the potential costs of financial distress are difficult to calculate, as they depend on both the probability of financial distress and the magnitude of the costs once a firm is in financial distress. since highly leveraged firms have a higher probability of financial distress, the potential costs of financial distress which affect a firm's value will be higher for them

how do the potential costs of financial distress or bankruptcy affect a firm's value?

the potential costs of financial distress or bankruptcy lower a firm's value because investors factor in these costs and demand to be paid for them in the form of higher returns (i.e., debt holders will demand a higher interest rate). these increased costs of debt affect equity holders because when securities are fairly prices the present value of these costs of financial distress affect the total value of the firm

lemon principle

the principle asserts that when a seller has private information about the value of a good, buyers will discount the price they are willing to pay due to adverse selection

What is a firm's capital structure?

the relative proportion of debt, equity, and other securities the firm has outstanding D=MV of debt E=MV of equity PCM: uses MV A = D+E Ru = [E/(E+D)]*Re + [D/(E+D)]*Rd ----Re = equity cost of capital ----Rd = cost of debt Bu = [E/(E+D)]*Be + [D/(E+D)]*Bd ---Beta: sensitivity of the firm's stock relative to the market shorter term = lower beta higher credit rating = lower beta

volatility

the standard deviation of a return (measures both upside and downside variations)

in looking at historical results to estimate the mean and volatility of a security, what is the standard error? how is it calculated?

the standard error is the standard deviation of the estimated mean around its true value standard error = (SD calculated from historical returns)/(square roor of the # of observations) example: from 1926-2004 we have 79 years of data. the average return for the S&P500 is calculated to be 12.3%. the volatility is calculated to be 20.36%. what is the standard error? SE = .2036/(sqrt 79) = 2.3% A 95% confidence interval is plus/minus 2 standard deviations. So, the 95% confidence interval for the mean return of the S&P500 is 12.3 +/- 4.6%

Trade-Off theory of firm value

the trade off theory states that the value of a levered firm is equal to (the value of the firm without leverage) + (PV of the interest tax shield) - (PV of financial distress costs) + (PV of agency benefits of leverage) - (PV of agency costs of leverage)

what is a firm's weighted cost of capital (WACC)

the weighted average of the firm's equity cost of capital (Re) and debt cost of capital (Rd) WACC = [E/(E+D)]*Re + [D/(E+D)]*Rd

efficient frontier

those combinations of investments that you are considering purchasing that provide the highest possible expected return for a given level of volatility (or, the lowest volatility for a given expected return).

calculate, in dollars, the interest tax shield for the current year for a firm that has earnings before interest and taxes (EBIT) of $5,000,000 and has interest costs of $2,000,000

we are given that the firm's marginal tax rate is 34%. therefore, its tax shield for the year is 34% of $2,000,000 = $680,000

how does capital structure affect the WACC in non-PCM?

Assuming that the cost of debt is not equal to the cost of equity capital, the WACC is altered by a change in capital structure. The cost of equity is typically higher than the cost of debt, so increasing equity financing usually increases WACC. While debt does not dilute ownership, interest payments on debt reduce net income and cash flow. This reduction in net income also represents a tax benefit through the lower taxable income.

estimated cost of capital

Ri = Rf + B*market risk premium' Ri = Rf + B*[E(Rmkt)-Rf]

under the Capital Asset Pricing Model (CAPM), what is the expected return of a security with Beta=B?

Expected Return equals the risk free rate plus Beta times the equity risk premium. recall, the equity risk premium is the expected return of the market minus the risk free rate E = Rf + B*[E(mkt) - Rf] Note: this implies stocks can be ranked in a linear fashion according to risk and return. starting at the risk free rate a straight line through the market risk premium (Beta = 1) can be drawn and the expected returns of all stocks should fall on this line according to their particular beta. this line is called the Security Market Line

firm ABC has an equity cost of capital of 15% and a debt cost of capital of 6%. its market value of debt is $200 million, and its total market value of assets is $1 billion. calculate the weighted cost of capital for firm ABC. next, assume ABC borrows $300 million to finance a new project. what is its equity cost of capital after the borrowing, assuming PCM

Firm ABC's weighted average cost of capital equals: WACC = [E/(D+E)]*Re + [D/(D+E)]*Rd Before the additional borrowing this is: .8+15% + .2*6% = 13.2% After the borrowing, the WACC does not change. so after the borrowing: .132 = (800/1300)*(equity cost of capital) + (500/1300)*.06 and, equity cost of capital = 17.7% Note: the equity cost of capital increases to reflect the increased risk to equity investors due to the new debt, while the weighted average cost of capital did not change in perfect capital markets

how do we use correlation to help us achieve diversification within a portfolio?

Recall that the expected return of a portfolio equals: E(Rp) = the weighted average of all E(Ri) The volatility of a portfolio equals: Vol(Rp) = the weighted average of all [Vol(Ri)*Corr(Ri,Rp)] So, if we can replace a stock in the portfolio with another stock with the same expected return, but with a lower product of volatility times correlation with the portfolio then we have reduced the volatility (the risk) of the portfolio without changing the expected return of the portfolio. The greatest benefits of diversification can be achieved by adding stocks to a portfolio which have low, or even negative, correlation to the returns of the portfolio.

variance and volatility of a portfolio (formulas)

Return of a portfolio: Rp = weighted averagre of Ri's E(Rp) = weighted average[E(Ri)] Cov(Ri,Rj) = E[(Ri-ERi)*(Rj-ERj)] Corr(Ri,Rj) = Cov(Ri,Rj)/SD(Ri)*SD(Rj) (if you diversify you want lower correlation) Var of portfolio = weight^2*Var(R1) + Weight^2*Var(R2) SD of portfolio = weighted average[Corr(Ri,Rp)*SD(Ri)]

CAPM and the expected return of a stock or portfolio of stocks under CAPM

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and cost of capital. E(Ri) = Rf + B*[E(Rmkt)-Rf] E(Rmkt) = expected return of the market E(Rmkt)-Rf = market risk premium The beta of a potential investment is a measure of how much risk the investment will add to a portfolio that looks like the market. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce the risk of a portfolio. A stock's beta is then multiplied by the market risk premium, which is the return expected from the market above the risk-free rate. The risk-free rate is then added to the product of the stock's beta and the market risk premium. The result should give an investor the required return or discount rate they can use to find the value of an asset. The goal of the CAPM formula is to evaluate whether a stock is fairly valued when its risk and the time value of money are compared to its expected return.

Tail Value-at-Risk

The VAR plus the expected loss in excess of VAR; when such excess loss occurs Tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the more general value at risk. It quantifies the expected value of the loss given that an event outside a given probability level has occurred. A primary weakness of the VaR measure is that if the adverse outcome is worse than the assumed quantile cutoff, there is no way to measure how bad the outcome actually is. We initially assume that adverse outcomes occur at the lower end of the distribution, as with investment gains or profitability To address this obstacle, Tail-Value-at-Risk, or TVaR, was created to focus on what happens in the adverse tail of the probability distribution. More specifically, TVaR, also known as Conditional Tail Expectation (CTE) or Expected Shortfall, is the expected loss given that the gain/loss is in the lowest 100α% of the probability distribution.

according to the CAPM, if the market is completely efficient, what should the value of alpha be for any stock?

Under the CAPM, in an efficient market the alpha of a stock should be zero