FORMULA SHEET FOR THE FINAL
=1+(D/E)
Earnings Per Share (EPS) = Net Income / Total shares
Dividends per Share (DPS) = Total Dividends / Total shares
Net Income = Cash Dividends + Addition to retained earnings
Dividend Payout Ratio = Cash Dividends / Net Income
Net Working Capital (NWC) = Current Assets (CA) - Current Liabilities (CL)
1/4
CFFA = OCF - NET CAPITAL SPENDING - CHANGE IN NWC
Net Capital Sp. = Ending net fixed assets - Beginning net fixed assets + Depreciation
Change in NWC = Ending NWC - Beginning NWC
CF to creditors = Interest Paid - Net new borrowing
CF to stockholders = Dividends paid - Net new equity raised
CFFA = CF to creditors + CF to stockholders
OCF FORMULAS
1) OCF = EBIT+DEPRECIATION-TAXES
2) OCF = (SALES-COSTS)x(1-T) + DxT
3) OCF = NET INCOME + DEPRECIATION
Depreciation tax shield = Depreciation x T
Straight-line depreciation "D" = (Initial cost – ending book value) / number of years
Book value of an asset = initial cost – accumulated depreciation
After-tax salvage = salvage – T(salvage – book value)
NPV = PV of future cash flows - cost
PI = PV of future cash flows / cost
AAR = Average Net Income / Average Book Value
FV = PV (1+r)t
Annuity Present Value
1
⎡
1
−
⎢
(1 + r ) t
PV = C ⎢
r
⎢
⎢⎣
PV = FV/(1+r)t
r = (FV / PV)1/t – 1
t = Ln(FV / PV) / Ln(1 + r)
Annuity Future Value
Annual Percentage Rate
1
APR = m ⎡(1 + EAR) m - 1⎤
⎢⎣
⎥⎦
Effective Annual Rate
m
APR ⎤
⎡
EAR = ⎢1 +
−1
m ⎥⎦
⎣
⎡ (1 + r )t − 1⎤
FV = C ⎢
⎥
r
⎣
⎦
PV for a perpetuity = C / r
2/4
⎤
⎥
⎥
⎥
⎥⎦
1
⎡
1
⎢ (1 + r) t
Bond Value = C ⎢
r
⎢
⎢⎣
⎤
⎥
F
⎥+
t
⎥ (1 + r)
⎥⎦
Fisher Effect:
(1 + R) = (1 + r)(1 + h), where,
R = nominal rate, r = real rate, h = expected inflation rate
P0 is the PV of all expected
future dividends:
P0 =
Constant Dividend Case:
D1
D2
D3
+
+
+ ...
(1 + R)1 (1 + R) 2 (1 + R) 3
Dividend Growth Model:
P0 =
P0 =
D
R
Using DGM to find R:
D 0 (1 + g)
D1
=
R -g
R -g
rearrange and solve for R
D 0 (1 + g)
D
= 1
R -g
R -g
P0 =
R=
D 0 (1 + g)
D
+g= 1 +g
P0
P0
Dividend yield =
D1
P0
Capital gains yield = g
3/4
Historical variance = sum of squared deviations from the mean / (number of observations – 1)
Historical Standard deviation = square root of the historical variance
Expected Return:
n
E ( R) = ∑ pi Ri
i =1
Expected Variance:
n
σ 2 = ∑ pi ( Ri − E ( R )) 2
i =1
Expected Standard deviation:
σ = σ2
(pi is the probability of state i occurring)
Return of a portfolio in state i :
m
For example, let's say we have 2 assets: A and B and 2 states: boom and
recession. Then the portfolio return in each state is calculated as:
j
Rportfolio,boom
= wAxRA,boom
+ wBxRB,boom
Rportfolio,recession = wAxRA,recession + wBxRB,recession
R portfolio,i = ∑ w j R j ,i
where wj is the portfolio weight for asset j
Rj,i is the return of asset j in state i
VU = EBIT(1-T) / RU
Value of an unlevered firm (assuming perpetual cash flows) :
M&M Proposition I
Without Taxes
V L = VU
With taxes
VL = VU + DTC
M&M Proposition II
WACC = R A = (E/V)RE + (D/V)RD
WACC = R A = (E/V)RE + (D/V)(RD)(1-TC)
RE = RA + (RA – RD)(D/E)
Capital Asset Pricing Model (SML)
E(RA) = Rf + βA(E(RM) – Rf)
Cost /Req. Return of Equity RE:
Dividend growth model
P0 =
D1
RE − g
RE =
D1
+g
P0
CAPM
RE = R f + β E ( E ( RM ) − R f )
Cost/Req. Return Debt: R D = YTM on debt
Cost/Req. Return Preferred: R P = D / P0
Weighted Average Cost of Capital a.k.a. WACC = W ExRE + W DxRD(1-TC) + W PxRP
V=E+D+P; W E=E/V; W D=D/V; W P=D/V
Page 4
RE = RU + (RU – RD)(D/E)(1-TC)