Second semester Flashcards
Equity cost of capital
The expected return of other investments available in the market with equivalent risk to the firms shares
Condition under which an investor is willing to buy stock (Formula div discount model)
P0 = Div1 + P1/rE
Total return rE (dividend discount model)
Div1+p1/p0 -1 = Div1/P0 + P1-P0/P0 (Dividend gain + capital gain)
Dividend yield (%)
The expected annual dividend of the stock divided by its current price (Dividend/price)
Capital gain
Difference between expected sale price and purchase price for the stock (p1-p0)
P0 for multiyear investor (formula) dividend discount model
P0= (Div1/1+rE) +(Div2/(1+rE)^2 +… Divn/(1+rE)^n + Pn/(1+re)^n
Constant dividend growth model P0 (formula)
P0=Div1/rE-g
Dividend payout rate (dividend per share)
Div/Earnings x shares outstanding
In what three ways can firms increase dividends?
1) increase its earnings (net income)
2) It can increase its dividend payout rate
3) It can decrease its shares outstanding
New investment (formula) profit
Earnings x Retention rate
Retention rate
The fraction of current earnings that the firm retains
Earnings growth rate (formula)
Change in earnings /Earnings = Retention rate x Return on new investment
Dividend discount model with constant long term growth
P0 = Div1/1+rE + Div2/(1+re)^2
Share purchase
The firm uses excess cash to buy back its own stock
Discount free cash flow model
Determines the total value of the firm to all investors
Enterprise value Discount free cash flow model formula
Market value of equity +debt - cash
Discount free cash flow model formula
V0 = PV(Future free cash flow of firm)
Weighted average cost of capital
The average cost of capital the firm must pay to all of its invetors both debt and equity holders (The effective after tax cost of capital of the firm)
Valuation multiple
The ratio of the value to some measure of the firms scale
Example:
1) The price earning ratio multiple
2) Enterprise Value Multiples
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Efficient market hypothesis
Competition among investors works to eliminate all positive NPV trading opportunities
Key implications for corporate managers
1) Focus on NPV and free cash flow
2) Avoid accounting illusions
3) use financial transactions to support investment
Probability distribution
Assigns a probability Pr that each possible return R will occur
Expected (mean) return formula
E(R)=SumR PrxR
Calculating realized annual returns formula 1+Rannual=
1+ Rannual = (1+ RQ1)(1+RQ2)(1+RQ3)(1+RQ4) = quarterly dividend rate
Average annual return
Is simply the average of the realized returns ofeach year
Average annual return of a security (formula)
1/T x (R1+R2+RT)
Standard error
Is the standard deviation of the estimated value of the mean of the actual distribution around its true value; That is the standard deviation of the average return
Standard error of the estimate of the expected return (formula)
SD(average of independend identical risk) = SD(individual risk)/sqroot Numer of observations
Common risk
Risk is perfectly correlated ; E.g Earthquake hits all houses
Independent risk
Risks without correlation Example: Thief breaks into one specific house
Firm-specific news
Is good or bad news about the company itself. For example, a firm might announce that it has been successful in gaining the market share within its industry
Market wide news
Is news about the economy as a whole and therefore affects all stock
Identifying systematic risk
Finding a portfolio that ocntains only systematic risk. Changes in this portfolio will correspond to systematic shocks to the economy (Efficient portfolio)
Efficient portfolio
Cannot be diversified further, bo way to reduce the risk without reducing the return
Beta
measures the sensitivity of a security to market wide risk factors
Market risk premium
E(r(mrk))-risk free interest rate
Estimating the cost of capital of an investment from its beta (cost of capital)
r1=risk free interest rate + beta1 x Market risk premium =rf+betax(E(Rmkt)-rf)
Xi (formula) (portfolio weights)
Value of investment i /Total value of portfolio
Expected return of a portfolio
the weighted average of the expected returns of the invstements within it using the portfolio weights
Efficient portfolio
offer investors the highest possible expected return for a given level of risk
Efficient frontier
highest possible expected return for a given level of volatility
sharpe ratio
Steepest possible tangent line on portfolio for return(y) risk(x) (risk-reward ratio)
Three main assumptions of the capital asset pricing model
Investors trade securities at competitive market prices (without incurring traxes or transaction costs) and can borrow and lend at the risk free rate
Investors choose efficient portfolios
Investors have homogeneous expectations regarding the volatilities, correlations and expected returns of securities
Equity cost of capital formula
E(Ri) = Rf + betai x(E(Rm) - RF)
market capitalization
The total market value of a firms outstanding shares (value of all shares you can buy combined)
Value-Weighted Portfolio
A portfolio in which each security is held in proportion to its market capitalization
Passive portfolio
A portfolio that is not rebalanced in resoponse to price changes
Active portfolio
The portfolio is frequent balanced with
Index funds
Mutual funds that invest in the S&P 500 etc
Exchange traded funds
Trade directly on an exchange but represent ownership in a portfolio in stocks
How to invest in an index in practice
You invest a mutual fund company. You will be a shareholder of the mutual company. That mutual company can invest in efts too
How to estimate the historical risk premium
Estimate the risk premium (E(Rmrk) - rf) using the historical average exess return of the market over the risk free interest rate
Debt betas
Debt betas are difficult to estimate because corporate bonds are traded infrequently. One appx is to use estimates of betas of bond indices by rating category
Dividend discount model
Focuses on total discounted value of future dividends of firms. Has several limitations
Total payout model
Ignores the firms choice between dividend and share repurchases, Values all of the firms equity, rather than a single share
PV0 total payout model (formula)
= PV(future total dividends and repurchases)/Shares outstanding
PV0 share price (discount free cash flow formula)
Pv0 = P0 = PV(Future cash flows)+ cash – debt / shares outstanding
Change in earnings
New investment x Return on new investment
Dividend formula
Earnings per share x payout ratio
Limitations of the dividend discount model
Forecasting a firms dividend growth rate and future dividends is not easy
Little change in growth rate estimation may lead to big changes
Discounted free cash flows model
Determines the value of the firm to all investors, including both equity and debt holders
Free cash flow
Unlevered net income + Depreciation
−CapitalExpenditures − IncreasesinNetWorkingCapital
the cash flow available for the company to repay creditors or pay dividends and interest to investors
V0 Formla (PV)
FCF/1+Weighted average cost of capital + FCF2/(1+WAAC)^2…+ Vn(Terminal value)/(1+waac)^n
Ebit
Earnings before interest and taxes
Forward price earnings ratio Formula
Dividend payout rate/rE-g or P0(share price)/EPS
The ratio is used for valuing companies and to find out whether they are overvalued or undervalued
Multiples formula
Vo/EBITDA = (FCF/EBITDA)/re-gfcf
Expected return on investment
Sum of all Probabilities x Returns
Variance/volatity of investment
Sum of all probabilities x (Return - mean return)^2
Realized return
Dividend yield + capital gain rate
Sensitivity of systematic risk beta
measures sensitivity of individual stocks against systematic shocks (market)
The expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio.
Covariance definition
The expected product of the deviations of two returns from their means
Covariance formula (2 stocks)
Cov(Ri,Rj) = E[(Ri − E[Ri])(Rj − E[Rj])] /N-1
Correlation definition
A measure of the common risk shared by stocks that does not depend on their volatility (that means that the risk of two stocks combined is less than the individual risk of both stocks)
Correlation formula
Corr(Ri,Rj) = Cov(Ri,Rj) / SD(Ri) x SD(Rj)
Variance portfolio (formula)
x1^2Var(R1) + x2^2Var(R2) + 2x1x2Cov(R1,R2)
Weighted average covariance of each stock in the portfolio
variance of equally weighted portfolio formula
v^2/N +(1-1/N) x cov (v = variance)
Expected return formula (portfolio + risk free investments)
(1-x) *rf + xE(Rp)
Standard Deviation (portfolio + risk free investments)
xSD(Rp)
Sharpe ratio formula
tan(alpha) = E(r)-rf/omega (Omega = SD)
incremental change in sharpe ratio formula
𝐀𝐝𝐝𝐢𝐭𝐢𝐨𝐧𝐚𝐥𝐑𝐞𝐭𝐮𝐫𝐧𝐅𝐫𝐨𝐦𝐈𝐧𝐯𝐞𝐬𝐭𝐢𝐧𝐠𝐆𝐌 /𝐈𝐧𝐜𝐫𝐞𝐦𝐞𝐧𝐭𝐚𝐥𝐕𝐨𝐥𝐚𝐭𝐢𝐥𝐢𝐭𝐲 𝐟𝐫𝐨𝐦𝐢𝐧𝐯𝐞𝐬𝐭𝐢𝐧𝐠𝐆𝐌
E(RGM)-rf/SD(RGM) x corr(RGM, RP)
beta formula
Cov(Ri,Rp)/Var(Rp) or change in market/change in stock)
OR Corr x SD1/SD2
alpha definition
represents a risk-adjusted performance measure for the historical returns.
(If alpha is positive the stock has performed better than predicted by the CAPM)
(f αlpha is negative, the stock’s historical return is below the SML.)
alpha formula
α=𝐸 𝑟 −{𝑟𝑓+β[𝐸 𝑟𝑀 −𝑟𝑓]}
Debt cost of capital: default probability formula
rd = (1 − p)y + p(y − L) = y − pL
y= yield to maturity rd= default probability L= expected loss rate
Debt cost of capital CAPM formula
d = risk free+(Debt Beta) X (Market Risk Premium)
Projects cost of capital ru
ru= E/E+D *rE + D/E+D *rD
Asset (unlevered) beta formula
βU = E/(E+D)βE + D/(E+D)βD
Net debt
Net Debt = Debt − Excess Cash and short-term investments
Operating leverage formula
Operating leverage = fixed cost / variable costs.
WAAC
The effective after tax cost of capital of the firm
Unlevered cost of capital
The unlevered cost of capital is the
expected return investors will earn
holding the firm’s assets.
Weighted Average Cost of Capital (WACC) formula
𝑟𝑊𝐴𝐶𝐶 = 𝐸/(𝐸+𝐷)𝑟𝐸 + 𝐷/(𝐸+𝐷)𝑟𝐷*(1−𝑡𝑎𝑥)
Under diversification
There is much evidence that individual investors fail to diversify their portfolios adequately
Familiarity Bias
: Investors favour investments in companies with which they are familiar
Relative wealth concerns
Investors care more about the performance of their portfolios relative to their peers
Hanging on to losers and the disposition effect:
An investor holds on to stocks that have lost their value and sell stocks that have risen in value since the time of purchase
Attention
Individuals are more likely to buy stocks that have recently been in the news and advertising, experienced exceptionally high trading volume, or have had extreme returns
Mood
Sunshine generally has a positive effect on mood, and studies have found that stock returns tend to be higher when it is a sunny day at the location of the stock exchange
Experience
Investors appear to put too much weight on their own experience rather than considering all the historical evidence. As a result, people who grew up and lived during a time of high stock returns are more likely to invest in stocks than are people who experienced times when stocks performed poorly
Information cascade effect
: Traders ignore their own information hoping to profit form the information of others
2) Relative wealth concers
Individuals choose to herd in order to avoid the risk of underperforming their peers
Reputation risk
Professionals may face reputation risk if they stray too far from the actions of their peers
size effect
Small market capitalization stocks have historically earned higher average return than the market portfolio, even after accounting for their higher beta
Exess return and book-to-market ratio
: High book-to-market stocks have historically earned higher average returns than low book-to-book market stocks
momentum strategy
Buying stocks that have had past high returns and (short) selling stocks that have had past low return.
proxy
value for interest as that can not be measured
Behaviour biases
By falling prey to be behavioural biases, investors may hold inefficient portfolios
momentum strategy
Buying stocks that have had past high returns and (short) selling stocks that have had past low returns
Multifactor models of risk:
E(Rs) = rf + betas(E(Rmrk)-rf) + beta * E(Rx1) + Beta E(Rx2) + beta * e(Rx3)
X1 = Market capitalization strategy X2 = Book-to market ratio strategy X3 = past return strategy
Capital gain rate
P1-P0/P0
Share price discounted cash flow model
(PV(FCF) + cash - debt) /shares outstanding
Waac formula
(𝐸/𝐸+𝐷)𝑟(𝐸) + (𝐷/𝐸+𝐷)𝑟(𝐷)*(1−𝑡𝑎𝑥)
What if the current stock price less than P0?
Then you may consider the stock is underpriced →
• people rush in and buy it ,
• And this market behaviour would drive up the stock’s price.
dividend per share
Earnings/shares outstanding x dividend payout rate
Change in earnings formula
New investment x Return on new investment
Consequences of share repurchase
1) The more cash the firm uses to repurchase shares, the less it has available to pay dividends.
2) By repurchasing, the firm decreases the number of shares outstanding, which increases its earnings and dividends per share.
Vn formula (Terminal value)
FCFn+1/rwaac-gfcf = ((1+gfcf)/(rwaac-gfcf)) x FCFn
Vn formula (Terminal value)
FCFn+1/rwaac-gfcf = ((1+gfcf)/(rwaac-gfcf)) x FCFn
Method of Comparables
Estimate the value of the firm based on the value of other, comparable firms or investments that we expect will generate very similar cash flows in the future.
Enterprise value multiples
V0/EBITDA or FCF/EBITDA/rwaac-gfcf
Limitations of multiples
First challenge: how to adjust for differences in expected future growth rates, risk, or differences in accounting policies.
2) Comparables only provide information regarding the value of a firm relative to other firms in the comparison set.
▪ Using multiples will not help us determine if an entire industry is overvalued.
Capital market line
Investors’ optimal asset allocation line. Rational investors form their portfolio at CML.
Effective after tax interest rate (formula)
r(1-Tc)
Determine share price with forward P/E
P/E x EPS = share price
Estimation of shareprice using price to book multiplier
Price/book (ratio) x book value = share price
Marginal contribution to risk formula
SD x Corr
correlation with sharpe ratio formula
corr = sharpe ratio/sharpe ratio
