Capital Budgeting
NPV : Σt=1nCFt/(i + r)t - outlay
IRR : Σt=1nCFt/(i + r)t = outlay
Payback Period : number of years to recover original investment, based on cashflows
Discounted Payback Period : number of years to recover original investment, based on discounted cashflows
NPV profile: shows a project's NPV graph as function of various discount rates
Profitability Index = PV of future cash flow / initial investment
= 1 + ( NPV / initial investment )
Cost of Capital
WACC = wdrd(1 + t) + wprp + were
Cost of Preferred Stock
Pp = Dp/rp
Cost of Debt
calculate the ytm of bond
Cost of Equity
cost of debt + risk premium
CPAM: ri = rf + β(rm-rf)
PV model: P0 = D1/(re-g)
Pure play method
Unlevered beta of the company:
βu,comparable or called βassets
Levered beta of the company:
βL,comparable or called βequity
Find unlevered beta:
βu,comparable = βL,comparable / [1 + (1 - Tcomparable)Dcomparable/Ecomparable]
Lever this beta to get βproject
βL,project = βu,comparable [1+ (1 - Tproj)Dproj/Eproj]
Leverage
Degree of Operating Leverage (DOL): measure of operating risk
Operating leverage involves using a large proportion of fixed costs to variable costs in the operations of the firm.
% change Operating Income
DOL = -------------------------------------
% change sales
Q(P-V) P: price
= ------------------------ V: variable operating cost
Q(P-V) - F F: Fixed operating cost
Fixed operating cost, such as factory depreciation
Degree of Financial Leverage (DOL): measure of financial risk
% change net Income
DFL = --------------------------------------
% change Operating Income
Q(P-V) P: price
= ------------------------ V: variable operating cost
Q(P-V) - F -C C: Fixed financial cost
Fixed financial cost, such as interest payment
EBIT
DFL = ------------------------
EBIT - Interest
Since interest is a fixed expense, DFL magnifies returns.
DTL = DOL x DFL
Q(P-V) P: price
= ------------------------ V: variable operating cost
Q(P-V) - F -C F: Fixed operating cost
Break-Even Point Operating Breakeven Point
F + C F
Qbe = --------------- Qobe = -----------
P - V P - V
Dividend Payment Chronology:
dividend declaration date:
the day dividend is declared
ex-dividend date ( ex-date ) :
the 1st day that a share trades without dividend
holder of record date:
two business days after the ex-dividend date, the date that a shareholder listed in the corp. record will be deemed to have ownership of the shares for purpose of receiving the upcoming dividend
payment date:
the day company sends out dividend payment
treasury stock: shares that have been issued and then repurchased
money market yield:
FV - Price 360
------------- * ------------------------------------
Price number of days to maturity
bond equiv. yield: state bond yields into annual yield
FV - Price 365
------------- * ------------------------------------
Price number of days to maturity
Portfolio risk and return:
Pt + Dt
holding period return: R = ---------- - 1
Po
1
arithmetic/mean return: R = ---- Σt=1T Rt
T
geometric mean return: R = T√πt=1T (1+ Rt) - 1
Portfolio Management
For two asset portfolio,
σp 2= w12σ12+ w22σ2 2 + 2w1w2 COV(R1,R2)
COV(R1,R2) = ρ12σ1σ2
Efficient Frontier is combinations of 2 stocks
Utilities Theory and Indifference Curves
Capital Allocation line: risk free asset + risky portfolio
Capital Market line: risk free asset + market portfolio
E(Rp) = Rf + σp/σm [E(Rm) - Rf]
CML with different lending and borrowing rates
systematic risk: risk that cannot be avoided
non-systematic risk: risk that is local
total variance = systematic variance + non-systematic variance
beta: it is a measure of volatility or systematic risk, of a security or a portfolio, compared to market as a whole
βi = ρimσi/σm E(Ri) = Rf + βi [E(Rm) - Rf]
Security market line: use systematic risk, applies to any security
CAL, CML: use total risk, applies to efficient portfolio only
Portfolio performance evaluation:
Sharpe ratio = (Rp-Rf)/σp
Treynor ratio = (Rp-Rf)/βp
M-squared(M2) = (Rp - Rf)σm/σf - [E(Rm) - Rf]
Jensen's Alpha = Rp - [Rf + βp(E(Rm) - Rf)]
Application of Sharpe ratio
The greater a portfolio's sharpe ratio, the better its risk adjusted performance has been. If the addition of a new security lowers the sharpe ratio, it should not be added to the portfolio.
