Download Equations from Damodaran

EQUATIONS OF THE BOOK “INVESTMENT VALUATION”, 2ND ED. BY DAMODARAN
t n
Value  
CFt
t 1 (1 
r)t
t  n CF
Value of Equity  
t 1
t n
Value of Firm  
to Equity
(1  k e ) t
CF to Firm
t 1 (1  WACC
CAPM
)t
E(R) = Rf + B (Rm- Rf)
Cost of Equity = E(Ri) = Rf + Equity Beta * (E(Rm) - Rf)
Cost of equity = Risk-free rate + Beta * (U.S. risk premium) + Country risk premium
Cost of equity = Risk-free rate + Beta * (U.S. risk premium + Default spread)
Relative standard deviation country x = Standard deviation country x / Standard deviation U.S.
Equity risk premium country x = Risk premium U.S. * Relative standard deviation country x
Country risk premium = Country default spread * ( Std. Dev. equity / Std. Dev. country bond)
E(Return)=Riskfree Rate+ Вeta (US premium) + λ (Country risk premium)
λ =% of revenues domesticallyfirm / % of revenues domesticallyavg firm
BETA ESTIMATION
Rj = a + b Rm
BL = Bu (1+ ((1-t) D/E)
BL = Bu (1+ ((1-t)D/E) - Bdebt (1-t) (D/E)
ii 1k Bi
Operating Incomei
Operating Income Firm
Changes in earnings firm, t = a + B * Changes in earnings Market, t
Interest Coverage Ratio = EBIT / Interest Expenses
Pre-tax cost of debt = Risk free rate US + Country default spread EM. MRK
+ Company default spread Company synthetic rating
MV of debt = Int. Exp. (1/r – 1 / r(1+r) n) + BV of debt / (1+r) n
Market value of equity = number of shares * price per share
1  Inflation Peso 

1  Inflation USD 
Cost of capital= (1  Cost of CapitalUSD)
Straight bond component = Market value of bond
Conversion option = Book value of bond at issuance – Straight bond component
Cost of PS = Preferred dividend per share / Market price per preferred share
CASH FLOW DEFINITIONS
EBIT (1 – tax rate)
- (Capital Expenditures – Depreciation)
- Change in non-cash working capital
= Free Cash Flow to Firm (FCFF)
Net Income
- (Capital Expenditures – Depreciation)
- Change in non-cash Working Capital
- (Principal Repaid – New Debt Issued)
- Preferred Dividend
+ Dividends and Stock Buybacks
= Free Cash Flow to Equity
Revenues
(-) Operating Expenses
= Operating Income
(-) Financial Expenses
(-) Taxes
= Net Income before Extraordinary Items
(-) or (+) Extraordinary Losses (Profits)
R&D, OPERATING LEASE ADJUSTMENTS
Adjusted operating income = Operating income + Current year’s R&D expense – Amortization
of research asset
Adjusted net income = Net income + Current year’s R&D expense – Amortization of research
asset
Debt Value of Operating Leases = PV of Operating Lease Expenses at the pre-tax cost of debt
Adjusted debt = Debt + Present value of lease commitments
Adjusted Operating Earnings = Operating Earnings + Operating Lease Expenses - Depreciation
on Leased Asset
Adjusted Net Capital Expenditures = Net Capital Expenditures + Current year’s R&D expenses Amortization of Research Asset
Adjusted Net Cap Ex = Net Capital Expenditures + Acquisitions of other firms - Amortization of
such acquisitions
GROWTH ESTIMATION – DIFFERENT MODELS
Net Income
- (1- δ) (Capital Expenditures - Depreciation)
- (1- δ) Working Capital Needs
= Free Cash flow to Equity
δ = Debt/Capital Ratio
Reinvestment Rate = Retained Earnings/ Current Earnings = Retention Ratio
Return on Investment = ROE = Net Income/Book Value of Equity
gEPS
= Retained Earningst-1/ NIt-1 * ROE
= Retention Ratio * ROE
= b * ROE
gEPS= b *ROEt+1 +(ROEt+1– ROEt) ROEt
gEPS= b *ROEt+1 + (ROEt+1– ROEt)(BV of Equityt )/ ROEt (BV of Equityt)
ROE = ROC + D/E (ROC - i (1-t))
BV of capital = BV of Debt + BV of Equity
Reinvestment Rate = (Net Capital Expenditures + Change in WC)/EBIT(1-t)
Return on Investment = ROC = EBIT(1-t)/(BV of Debt + BV of Equity)
gEBIT
= (Net Capital Expenditures + Change in WC)/EBIT(1-t) * ROC
Expected Growth Rate = ROCt+1 * Reinvestment rate
+(ROCt+1 – ROCt)/ROCt
Value = Expected Cash Flow Next Period / (r - g)
Stable Growth Payout Ratio = 1 - g/ ROE
Reinvestment Rate = Growth in Operating Income/ROC
Value of Bond = PV of coupons at market interest rate + PV of face value of bond at market
interest rate
RELATIVE VALUATION
P0 
DPS1
r  gn
P0
Payout Ratio * (1  g n )
 PE =
EPS0
r-g
n
Value
Market Value of Equity + Market Value of Debt

EBITDA Earnings before Interest, Taxes and Depreciation
Enterprise Value Market Value of Equity + Market Value of Debt - Cash

EBITDA
Earnings before Interest, Taxes and Depreciation
FCFF = EBIT (1-t) - (Cex - Depr) -  Working Capital
= (EBITDA - Depr) (1-t) - (Cex - Depr) -  Working Capital
= EBITDA (1-t) + Depr (t) - Cex -  Working Capital
Value =
EBITDA (1 - t) + Depr (t) - Cex -  Working Capital
WACC - g
Value
(1 - t)
Depr (t)/EBITDA CEx/EBITDA  Working Capital/EB ITDA
=
+
EBITDA WACC - g
WACC - g
WACC - g
WACC - g
Price/Book Value =
P0 
Market Value of Equity
Book Value of Equity
BV0 * ROE * Payout Ratio * (1  g n )
r-gn
P0
ROE * Payout Ratio * (1  g n )
 PBV =
BV0
r-g
n
P0
ROE * Payout Ratio
 PBV =
BV0
r-g
n
g = (1 - Payout ratio) * ROE
P0
ROE - g n
 PBV =
BV0
r-g
n
V0 =
FCFF1
WACC - g
V0 FCFF1/BV
=
BV WACC - g
V0
ROC - g
=
BV WACC - g
n Price/ Sales= Market Value of Equity
Total Revenues
P0 
DPS1
r  gn
P0
Net Profit Margin * Payout Ratio * (1  g n )
 PS =
Sales 0
r-g
n
Value/ Sales=
Market Value of Equity + Market Value of Debt-Cash
Total Revenues
MERGERS AND ACQUSITIONS
Value of Control = Value of firm, with restructuring - Value of firm, without restructuring
Value of Control = Value of Firm - Status Quo
Value of Synergy = Value of Firm - Change of Control
V(AB) > V(A) + V(B)
the cause of synergy.