Time Value of Money Flashcards
PV of a cash flow (C) that arrives n periods from now
PV=C/(1+r)^(n)
FV
FV=C*(1+r)^(n)
PV of a perpetuity of constant CF
PV=C/r
How to calculate PV of perpetuity with constant CF if first comes at t=0
PV=C/r*(1-r)
How to calculate PV of perpetuity with constant CF if first comes at t=2
PV=(C/r)/(1-r)
PV of perpetuity with constant growing rate
PV=C/(r-g), provided that r>g
PV of a constant annuity
PV=(C/r)(1-(1/(1+r)^(n)))
PV of a growing annuity
PV=(C/r)(1-((1+g)/(1+r))^(n))
Shortcut for PV of growing annuity if r=g
PV=C*(n/(1+r))
Constant Annuity Formula
PV=PMT*((1-(1/(1+r)^(n)))/r)
Special Case: Constant Dividend Growth
-P(0)=D(1)/(Re-g)
-Re=D(1)/P(0)+g
Dividend Payout Rate
Dividend payout rate = 1-retention rate
b Variable
Fraction of earnings retained
Sustainable Growth Rate
G=retention rate * return on new investment
Price of Dividend Formula with Retention
P(0)=D(1)/(Re-g)=(E(1)(1-b))/(Re-B*ROI)
Dividend Formula with Retention
D(t)=E(t)(1-b)
Enterprise Value Equation
EV=(Market Value of Equity)+Debt-Cash=PV(Future Cash Flows)
Price Using EV
P(0)=(EV-Debt+Cash)/(# of shares)
If a firm wants to increase its share price, should it cut its dividend
and invest more, or should it cut investment and increase its
dividend?
-Cutting the firm’s dividend to increase investment will raise
the stock price if, and only if, the new investments have a
positive NPV.
-Conversely, the firm can decrease dividend payout but it’s stock
price could go up.
FCF for EV Calculations
-FCF=EBIT(1-tau)+DEPR-CAPEX-ΔWC
-Use WACC to discount FCF in FCF Model
R(wacc)=ReE/(D+E) + RdD/(D+E)
where:
Re is equity cost of capital
E is Equity
D is Debt
Rd is YTM
Terminal Value Calculation
FCF(t)*(1+Rwacc)/(Rwacc-g)
Discount this value back using previous year as power
Price to Earnings Ratio
P/E= Market Price per Share/Earnings per Share
