• Types of financial statements : Balance sheet, income statement, statement of cash
flows, and the statement of changes in shareholder’s equity.
• Balance sheet : Assets(current assets includes inventories,receivables etc. longterm
includes depreciation, bookvalue of assets, goodwill, intangibleassets, amortization,
impairment charge) = liabilities(longterm liabilities includes deferred taxes) +
shareholders’ equity(includes market capitalization = total market value of firm’s
equity = the market price per share × the number of shares).
Value of Equity
• market-to-book value ratio(price-to-book ratio)= Market
. If low,
Book Value of Equity
called value stocks. if higher, called growth stocks.
Total Debt . Enterprise
• Debt-Equity Ratio= Total
Equity
Value=Market Value of Equity + Debt − Cash. Current ratio =
CurrentAsset . Quick ratio = CurrentAssets−Inventories
CurrentLiabilities
CurrentLiabilities
• Gross Profit = Net Sales − Cost of Sales.
• EBIT = Earning before interest and taxes. EPS(Earning per share) =
Net Income
Shares Outstanding
Profit . Operating margin = Operating Profit . Net Profit
• Gross Margin = Gross
Sales
Sales
Margin = Net Income . Accounts Receivable Days = Accounts Receivable .
Total Sales
Average Daily Sales
Accounts Payable
. Inventory
Accounts Payable days =
Average daily purchases
Inventory
. Return on Equity(ROE) =
AverageDailyCost of Goods Sold
Net Income
. Return on Assets(ROA) = Net Income . Price-Earning
Book Value of Equity
Total Assets
Market Capitalization
Share Price
ratio(P/E ratio) =
.
=
Net Income
Earning per Share
Net Income
Sales
Total Assets
.
ROE =
×
×
Sales
Total Assets
Total Equity
|
{z
}
|
{z
}
{z
}
|
Asset Turnover
Net Profit Margin
Equity Multiplier
|
{z
}
Return on Assets
Retained Earning = Net Income − Dividends.
Arbitrage = practice of buying and selling equivalent goods in different markets to
take advantage of a price difference. Therefore, no arbitrage price of a security
implies Price = P V . The bond’s return = Gain
. If no arbitrage, all risk-free
Cost
investments should offers the same return and N P V must be zero.
Separation Principle states we can separate the firm’s investment decision from its
financing choice.
days=
•
•
•
•
• Price of stock. P0 =
Div1 +P1
1+rE
rE =
Div1 + P1
Div1
P0
| {z }
P0
−1
(1)
P1 − P0
+
|
Dividend Yield
P0
{z
(2)
}
• Expected Return = E[R] =
R pR × R
P
2
• V ar(r) =
r pr × (r − E[r])
p
• SD(r) = V ar(r) = Volatility
1
• Using empirical distribution of realized returns, R = T
PT
2
1
• V ar(R) = T −1
t=1 (Rt − R)
PT
t=1
Rt
SD(individual risk)
• SD(Average of Independent, Identical risks = √
number of observations
• small stocks have had higher volatility and higher average returns than large
stocks, which have had higher volatility and higher average returns than bonds.
• Variation in a stocks return due to firm-specific news is called idiosyncratic risk.
This type of risk is also called firm-specific, unique, or diversifiable risk. It is risk
that is independent of other shocks in the economy
• Systematic risk is risk due to market-wide news that affects all stocks
simultaneously. Systematic risk is also called market or undiversifiable risk. It is
risk that is common to all stocks.
• If a firm moves independently, there is no systematic risk.
• Diversification eliminates idiosyncratic risk but does not eliminate systematic risk
because investors can eliminate idiosyncratic risk, they do not require a risk
premium for taking it on.
• An efficient portfolio is a portfolio that contains only systematic risk and cannot
be diversified further
• If the market portfolio is efficient, we can measure the systematic risk of a security
by its beta ().The beta of a security is the sensitivity of the securitys return to the
return of the overall market.
• Market Risk Premium = Expected Excess return of market portfolio =
E[RM kt ] − rf
• CAPM states that
r = rf + β(E[RM kt − rf )
• Cov(Ri , Rj ) = E[(Ri − E[Ri ])(Rj − E[Rj ])]
P
t (Ri,t − Ri )(Rj,t − Rj )
1
• Cov(Ri , Rj ) = T −1
Cov(R ,R )
i
j
• Corr(R)i, Rj ) = SD(R )SD(R
i
j)
• V ar(Rp ) =
– Investors have homogeneous expectations regarding the volatilities,
correlations, and expected returns of securities.
• The CAPM equation states that the risk premium of any security is equal to the
market risk premium multiplied by the beta of the security.
E[Ri ] = ri = rf +
M kt
βi
|
(E[RM kt ] − rf )
{z
}
Risk Premium for security i
• βi = βiM kt =
Cov(Ri ,RM kt )
V ar(RM kt
• The beta of a portfolio is the weighted-average beta of the securities in the
portfolio.
• In a value-weighted portfolio, the amount invested in each security is proportional
to its market capitalization.
• Beta measures a securitys sensitivity to market risk. Specifically, beta is the
expected change in the return of a security given a 1% change in the return of the
market portfolio.
• Because of default risk, the debt cost of capital, which is its expected return to
investors, is less than its yield to maturity, which is its promised return.
• the debt cost of capital, rd = Y T M − P r(def ault) × Expected Loss Rate
E·rE +D·rD
E+D
EβE +DβD
E+D
• Project cost of capital, rU =
• The beta of project, βU =
• The Weighted cost of capital
D r (1 − τ ) = r −
D τ r
E r +
rW ACC = E+D
E
C
U
E+D D
E+D C D
• αi = E[Ri ] − ri
• When equity is used without debt, the firm is said to be unlevered. Otherwise, the
amount of debt determines the firms leverage.
• Capital markets are said to be perfect if they satisfy three conditions:
– Investors and firms can trade the same set of securities at competitive
market prices equal to the present value of their future cash flows.
– There are no taxes, transaction costs, or issuance costs associated with
security trading.
2
x2
1 V ar(R1 ) + x2 V ar(R2 ) + 2x1 x2 Cov(R1 , R2 )
2
x1 V ar(R1 ) + x2
2 V ar(R2 ) + 2x1 x2 Corr(R1 , R2 )SD(R1 )SD(R2 )
1 (Average Variance of the Individual Stocks) +
n
• V ar(Rp ) =
1 (Average Covariance between the Stocks)
1− n
P
• SD(RP ) =
i xi × SD(Ri ) × Corr(Ri , RP )
• If the portfolio weights are positive, as we lower the covariance or correlation
between the two stocks in a portfolio, we lower the portfolio variance.
• E[RxP ] = rf + x(E[RP ] − rf ) and SD(RxP ) = xSD(RP )
E[RP ]−rf
SD(RP )
Cov(Ri ,RP )
V ar(RP )
• Sharpe Ratio =
• βiP =
• Portfolio is efficient when E[Ri ] = ri for all securities.
ef f
E[Ri ] = ri ≡ rf + βi
• Three main assumptions underlie CAPM
• A firm can change its capital structure at any time by issuing new securities and
using the funds to pay its existing investors. An example is a leveraged
recapitalization in which the firm borrows money (issues debt) and repurchases
shares (or pays a dividend). MM Proposition I implies that such transactions will
not change the share price.
• According to MM Proposition II, the cost of capital for levered equity is
(rU − rD )
rE = rU + D
E
E r +
D r
• rW ACC = rA = rU = E+D
E
E+D D
E β +
D β
• βU = E+D
E
D
E+D
Capital Gain Rate
P
• V ar(Rp ) =
– Investors choose efficient portfolios.
– A firms financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them.
• Total return.
=
– Investors trade securities at competitive market prices (without incurring
taxes or transaction costs) and can borrow and lend at the risk-free rate.
× (E[Ref f ] − rf )
(βU − βD )
• βE = βU + D
E
• A firms net debt is equal to its debt less its holdings of cash and other risk-free
securities
• Leverage can raise a firms expected earnings per share, but it also increases the
volatility of earnings per share. As a result, shareholders are not better off and the
value of equity is unchanged.
•