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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)

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=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)

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