Equity Flashcards
Expression to explain sources of percieved mispricing
Ve - P = (V-P) + (Ve-V)
- Ve: Estimated value
- P: Market price
- V: Intrinsic value
5-Steps of the Valuation Process
- Understanding the business
- Forecasting company performance
- Selecting appropriate valuation model
- Convert forecasts to a valuation
- Apply valuation conclusions (make a recommendation)
Types of Valuation Analysis
- Absolute valuation: NPV of dividends, FCFE, FCFF, Etc. (or valuation of assets like a lumber company)
- Relative valuation model
- Component valuation: Sum of the parts (can lead to a conglomerate discount)
Holding Period Return
r = [(Dh + Ph) / Po] -1
- Dh: Dividend
- Ph: Price at end of holding period
- Po: Price at beginning of holding period
Expected Return Components (2)
- Required return
- Return from convergence of price to value (mispricing between Vo and Po or “Alpha”)
Return from Convergence of Price to Value
- Second component of return
- (Vo - Po) / Po
Vo: Intrinsic value (analyst estimate)
Po: Price in the market
Convert Annual Holding Period Return to Semi-annual
Semiannual HPr = [(1 + HPr)^1/2] - 1
This can then be done to convert any HPr to whatever period you want.
Convert Annual HPr to Total Return over X Years
Then Annualize that Return
HPr (over x years) = [(1 + HPr)^X] -1
HPr annual = [(1 + HPr over x years)^1/x] -1
Internal Rate of Return (Intrinsic Value)
Vo = D1 / (Ko - G)
- Ko: Required return
- D1: Dividend next year
- G: Growth rate of Dividend
Internal Rate of Return (Required Return)
Ko = (D1 / PmkT) + G
- assumes PmkT is = IV (efficient market)
Convert ROE to a Dividend Growth Rate (G)
G = ROE X (1-PayOut)
Equity Risk Premium - Market
Individual Public Stock Required Return (ERP)
Individual Private Stock Required Return (ERP)
3 is a buildup method
- ERP = RoE(MrkT) - Rf%
- Ri = Rf% + β(ERP)
- Ri(private) = Rf% + ERP(MrkT) +- other risks or premiums appropriate for i
Beta
β = CovMrkT / VarMrkT
Historical Estimates for ERP
Average difference between Rf% and market returns
- tends to be counter-cyclical*
- Subject to survivorship bias*
- geometric vs. arithmetic?*
Forward Looking Estimates for ERP (GGM)
ERP (GGM) = (D1/Po) + G - Rf%
-Gordon growth model must rely on developed markets
Macroeconomic / Supply-Side Model (ERP)
Ibbotson Chen Model
ERP = {[(1+EInfL)(1+EGrEPS)(1+EGPE) - 1] + EinC} - ERf%
- EInfL: Expected inflation (Δbetween Treasury Bonds and TIPS)*
- EGrepS: Growth in EPS (or Growth in GDP)*
- EGpE: Growth in PE (Expected increases or decreases of market is overvalued)*
- EinC: Growth in income (can be market yield)*
Multifactor Models
- Required Return
- Risk Premium
Required Return = Rf% + (risk premium) + (risk premium2) + …
Risk Premium = (Factor sensitivity X Factor Risk Premium)
- factor sensitivity = factor β
Fama - French Model
Ri = Rf% + βi(mrktRMRF) + βi(sizeSMB) + βi(valueHMI)
- RMRF: Market Risk Premium*
- SMB: Small cap return Premium*
- HML: Value return premium (*
- Explains why small cap stocks have a higher return than CAPM would predict?*
Pastor Stambaugh Model (PSM) to determine Ri
Ri = Rf% + βi(mrktRMRF) + βi(sizeSMB) + βi(valueHMI) + β(liqLIQ)
- RMRF: Market Risk Premium*
- SMB: Small cap return Premium*
- HML: Value return premium*
- LIQ: Liquidity*
- Explains why small cap stocks have a higher return than CAPM would predict?*
Five Factor BIRR Model (macroeconomic model)
CTYIBM
- Economic _not _ Fundamental factors
- Confidence risk: unexpected Δ in Δ of Jnk and govt bonds
- Time horizon risk: unexpected Δin Δ of R% on 2-yr and 30-d gvt bonds
- Inflation risk: unexpected Δ in inflation
- Business cycle risk: Unexpected Δ in business activity
- Market timing risk: % of total return on MrkT not explained by first 4 factors.
59:16
Blume Adjusted Beta
Adjusted β = (2/3)(β) + (1/3)(1)
Unlevering Beta and then Relevering Beta for Comparisons
- βu = ( 1 / 1+DE )βe
- βe = (1 + DE)βu
When is DDM Suitable?
- Company is dividend paying
- Board has established div policy that is clear and related to profitability
- Investor is not taking control
DDM Formula for Single Period
DDM Formula for Multi Periods
Single: Vo = D1/(1+r)^1 + P1/(1+r)^1 Or Vo = D1+P1 / (1+r)^1
Multi: Vo = D1/(1+r)^1 + … (Dn+Pn)/(1+r)^n
r: required rate of return on the stock
DDM GGM Equation
Vo = D1 / (r-G)
D1 = Do(1+G)
Using GGM to Forecast Dividend in n-Period
Dt = Do(1+G)^t
- Do = Most recent dividend*
- t = The number of the future period*
GGM with Negative Growth Rate
Vo = D1/r-(-G)
- This means the denominator will grow (stock value will fall)
Vo based on PVoGO
Vo = E1/r + PVGO
DO NOT FORGET THAT E1 is not Eo
- E1: All earnings of a no-growth company are distributed*
- E1/r: Value of no growth company*
- PVGO: Present Value of Growth Opportunities*
Solving for PVoGO
MrktP = EPS/r + PVoGO
- Use EPS to solve for no-growth and use PVoGO as the variable.
Leading Price to Earnings Ratio / Expressed with GGM
Po / E1 or (D1/E1) / (r-G) or (D1/r-G) / E1
E1: EPS
Lagging Price to Earnings Ratio / Expressed with GGM
Po / Eo **or ** [Do(1+G)/Eo] / r-G or (D1/r-G) / Eo
Two Stage DDM Model
Vo = {∑[Do(1+Gs)^t] / (1+r)^t} + {[Do(1+Gs)^n(1+Gl)] / [(1+r)^n(r-Gl)]}
- Gs = growth rate in first period*
- Gl= growth rate in second period*
H-DDM Model (high growth model)
Vo = [Do(1+Gl) + DoH(Gs-Gl)] / r-Gl
DO NOT FORGET THAT THE FIRST Do IS MULTIPLIED BY LONG TERM GROWTH RATE!
- H = Half-life of the high growth rate period*
- Gl = Normal Dividend Growth rate after year H*
- Gs = Initial short term dividend growth rate*
Sustainable growth rate
G = b X ROE
b = retention rate
Free Cash Flow to the Firm (FCFF)
FCFF = NI + NCC + int(1-Tr) - FCInv - WCInv
DON’T FORGET THAT WCInv INCLUDES ALL CURRENT ASSETS EXCEPT CASH
Free Cash Flow to Equity (FCFE)
FFCE = NI + NCC - FCInv - WCInv + Net Borrowing
FCFF Valution to Estimate Firm Value / Equity Value
Firm Value = ∑ FCFFt / (1+WACC)^t
Equity Value = Firm Value - MVdebt
THIS IS A TWO-STEP PROCESS - DON’T FORGET TO REMOVE THE MARKET VALUE OF THE DEBT.
WACC based on MV of Debt and Equity
WACC = (MVdebt / MVdebt+MVeq)(Rd)(1-Tr) + (MVeq / MVdebt+MVeq)(Re)
FCFE Valuation to Estimate Firm Value (constant growth rate)
Firm Value = FCFF1 / WACC-G
or
Firm Value = FCFFo(1+G) / WACC-G
Value of Equity using FCFE
- No Growth
- Constant Growth
Ve = ∑ FCFEt / (1+r)^t
Ve = FCFE1 / r-G
Two Stage FCFF Valuation Model
2-stage FCFF = ∑FCFFt/(1+WACC)^t + (FCFFn+1)(1) / (WACC-G)(1+WACC)^n
Two Stage FCFE Valuation Model
Ve = ∑FCFEt / (1+r)^t + (FCFEn+1)(1) / (r-G)(1+r)^n
Law of One Price
Two identical assets should have the same price
Normalized EPS (two methods)
- Historical Average: Average EPS over a full business cycle
- Average ROE: Average ROE X Current BV per share
Earnings Yield
EY = EPS/Price
Allows for calcuating multiples across companies with negative EPS because price cannot be negative.
Justified Price
JP = (Benchmark value of own historical PE) X (Most recent EPS)
Common Shareholder’s Equity (for BV)
CSE = (Shareholder EQ) - (Value of Equity Claims Senior to Common)
Justified P/B ratio based on Fundamentals
Po/Bo = ROE-G / r-G
Justfied P/B Ratio from Residual Income
Po/Bo = 1 + (PV of Expected Future Residual Earnings)/Bo
P/S based on Forecasted Fundamentals
Po/So = [(Eo/So)(1-b)(1+G)] / r-G
b = retention rate
1-b = payout ratio
Justified P/CF based on Forcasted Fundamentals
Vo = [(1+G)FCFEo] / r-G
Trailing Dividend Yield (two methods)
- Consistent quarterly payor = (Most recent Qtrly Div X 4) / Po
- Semiannual payor (inconsistent) = (Dividends over last 12 months) / Po
Enterprise Value vs. Total Invested Capital (TIC)
EV = MVd + MVe +MVpe - Cash - STInv
TIC = EV + Cash + STInv
Cash and ST Investments are considered nonearning assets
Standardized Unexpected Earnings
SUE = (EPSt - eEPSt) / σ(EPSt - eEPSt)
- σ(EPSt - eEPSt): SDev of suprises over some period*
- The more common surprises are the less the impact.*
Harmonic Mean (for multiples and everything else)
Xh = n / ∑(1/Xi)
Justified Price/Sales Ratio
Po/So = [(Eo/So)(1-b)(1+G)] / r-G
Underlying Earnings
EPS + Extraordinary items (one time charges and such)
- Core, continuing or persistent earnings
When to use relative strength indicators
Patterns of persistence and reversals exist in stock returns that may be shown to depend on the investor’s time horizon
Economic Value Added (EVA)
EVA = NOPAT - (WACC X Total Capital)
Residual Income Model (hint: solve for Vo rather than Po/Bo)
Vo = Bo + ∑RIt / (1+r)^t
- Bo: Book Value per share*
- RI: Residual Income*
Single Stage Residual Income Valuation (like Justified P/B from fundamentals)
Vo = Bo + (ROE-r) / r-G
Bo: Current Book Value per share
Multistage Residual Income Valuation (hint: like Po/Bo from RI + the future Pn-Bn)
Vo = Bo + ∑ RIt/(1+r)^t + (Pn - Bn)/(1+r)^n
- Pn: expected price at n period*
- Bn: expected BV per share at n period*
- For long periods the second term can be excluded*
When is Residual Income Models Appropriate?
- When expected free cash flows are expected to be negative for the foreseeable future.
- When dividends are uneven
RI models will show declining value when RI is negative and rising value if RI is positive.
Residual Income Persistence Factors (high vs. low)
Low: extreme ROEs, Extreme Special Items, Extreme Accruals
High: Low dividend payouts, High historical persistence in industry
Forecasted Book Value
B1 = Bo + E1 - D1
Economic Value Added (EVA)
EVA = NOPAT - (C% X TC)
C% = Cost of Capital
TC = Total Capital
Market Value Added (MVA)
MVA = Market Value - Invested Capital
- Market value of Equity (share price X #shares)
- Market Value of Debt (could be a given discount)*
Solve for implied growth rate in residual income
G = r - [(ROE - r)XBo / (Vo - Bo)]
Clean surplus relationship
Ending BV = Beg BV + NI - Divs
- Can be broken by currency translation adjustments*
- Certain Pension adjustements*
- Fair value changes in some financial instruments (not held for trading)*
Capitalized Cash Flow Method
Is the same as FCFE or FCFF method but use normalized FCF measures
- CCM = FCFE(1+G) / r-G
- CCM = FCFF(1+G) / WACC-G
Degree of Financial Leverage
= Ave Assets / Ave Equity
- True nature excludes accrued unearned income
- Don’t forget these ratios need an average value
Porters 5-Forces
- Threat of new entrants
- Bargaining power of suppliers
- Bargaining power of buyers
- Threat of substitutes
- Rivalry among competitors
REBBS
Factors that aren’t in the 5-forces
- Industry growth rate
- Technology and innovation
- Government
- Complementary products and services
Work into FCFF from EBITDA
EBITDA - Depreciation (this is an expense) = EBIT
EBIT X (1-tr) = After tax EBIT
atEBIT + Dep - Wc - Capex + Net borrowing = FCFF
Which cash flow model to be used for a highly leveraged firm or one with a changing capital structure?
FCFF
Public vs. Private Firms Valuation Issues
- Privates are smaller and more risky
- Lack of access to public markets may limit growth
- Shallower depth of management
- Management tends to have longer-term views because quarterlies aren’t as big of an issue.
Calculate adjustment for Control and Marketability for Private Firm
- Calculate DLOC (Discount for Lack of Control)
- Calculate DLOM (Discount for Lack of Marketability)
- DLOC = 1 - [1/1+control premium]
- Total discount = 1 - [(1-DLOC)(1-DLOM)]
- Remember that this is important when valuing an investment where A will not be taking a controlling interest in T.*
Issues with Size Premium for private firms
- Premium may be understated if taken from very smallest public firms because it includes a distressed discount.
When calculating two-stage growth valuations don’t forget what?
The terminal value is added to the last cash flow. It is not discounted back an extra year. E.G. A three year high growth rate followed by a continuous low growth rate. The terminal value is added to the third cash flow. It is NOT a cash flow on its own.
Leading P/E ratio versus Lagging P/E ratio
- P/Eo = lagging and should be higher than leading
- P/E1 = Should be lower because denominator is growing by 1+g
EBITDA ratios should include equity or EV?
EV because EBITDA is a flow to all investors not just equity holders. It includes the profits that will be distributed to equity as well as debt.
Real Required Rate of Return (inflating or volatile economy)
= Real country return + Industry + Size - leverage
- look out for inflation numbers. If real country return is provided, ignore the inflation data.
