Time Value of Money

Question 1

PV of a cash flow (C) that arrives n periods from now

Answer 1

PV=C/(1+r)^(n)

Question 2

FV

Answer 2

FV=C*(1+r)^(n)

Question 3

PV of a perpetuity of constant CF

Answer 3

PV=C/r

Question 4

How to calculate PV of perpetuity with constant CF if first comes at t=0

Answer 4

PV=C/r*(1-r)

Question 5

How to calculate PV of perpetuity with constant CF if first comes at t=2

Answer 5

PV=(C/r)/(1-r)

Question 6

PV of perpetuity with constant growing rate

Answer 6

PV=C/(r-g), provided that r>g

Question 7

PV of a constant annuity

Answer 7

PV=(C/r)(1-(1/(1+r)^(n)))

Question 8

PV of a growing annuity

Answer 8

PV=(C/r)(1-((1+g)/(1+r))^(n))

Question 9

Shortcut for PV of growing annuity if r=g

Answer 9

PV=C*(n/(1+r))

Question 10

Constant Annuity Formula

Answer 10

PV=PMT*((1-(1/(1+r)^(n)))/r)

Question 11

Special Case: Constant Dividend Growth

Answer 11

-P(0)=D(1)/(Re-g)
-Re=D(1)/P(0)+g

Question 12

Dividend Payout Rate

Answer 12

Dividend payout rate = 1-retention rate

Question 13

b Variable

Answer 13

Fraction of earnings retained

Question 14

Sustainable Growth Rate

Answer 14

G=retention rate * return on new investment

Question 15

Price of Dividend Formula with Retention

Answer 15

P(0)=D(1)/(Re-g)=(E(1)(1-b))/(Re-B*ROI)

Question 16

Dividend Formula with Retention

Answer 16

D(t)=E(t)(1-b)

Question 17

Enterprise Value Equation

Answer 17

EV=(Market Value of Equity)+Debt-Cash=PV(Future Cash Flows)

Question 18

Price Using EV

Answer 18

P(0)=(EV-Debt+Cash)/(# of shares)

Question 19

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?

Answer 19

-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.

Question 20

FCF for EV Calculations

Answer 20

-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

Question 21

Terminal Value Calculation

Answer 21

FCF(t)*(1+Rwacc)/(Rwacc-g)

Discount this value back using previous year as power

Question 22

Price to Earnings Ratio

Answer 22

P/E= Market Price per Share/Earnings per Share