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Return Concepts:
1. holding period return
2. realized return
3. expected return
4. required return
5. return from convergence
6. discount rate
7. IRR
 1. (Cash flow + any additional gain)/initial investment
 2. Historical return (not future expected), can be calculated as realized return
 3. future return expected by some analyst
 4. minimum return need by investor for given level of risk
 5. return earned when buy/sell mispriced stock and then it converges to the "correct" price
 6. usually same as required rate, used to determine PV
 7. return implied by cash flows

equity risk premium:
definition, how to estimate
 Definition
 equity risk premium = required return  risk free rate
risk free rate usually t bills (short term) or t bonds (long term)
 Estimate
 historic: use past premium
 problems  stationary, upward bias due to survivorship bias
future: model using macroeconomic factors or implied by gordon growth model

estimating required return
single factor: CAPM  required return = rf + beta*(equity premium  rf)
multifactor: return = rf + sensitivity1*premium1 + sens2*prem2 + ...

multifactor models:
famafrench
pastorstambaugh
BIRR
 famafrench
 return = (market index  rf)*sensitivity + (small  big)returns*sens + (high B/M  low B/M)*sens
 pastorstambaugh
 return = same as famafrench + liquidity premium*sensitivity
 BIRR
 aka arbitrage pricing model. could give any of five premiums*sensitivity

buildup method
return = rf + equity risk premium + size premium + company specific premium
does NOT USE BETAS!!

beta estimation for nonpublic or thinly traded firms (pure play)
 identify similar public firm
 estimate beta of that firm
 unlever the beta using public firm's leverage Bu = Bestimate*()
 relever beta using private firm's leverage
 Bprivate = Bu*()

WACC
WACC =

How to discount FCFF and FCFE
 discount FCFF at WACC
 discount FCFE at return on equity

Market value way to find equity value
Equity value = firm value  market value of debt

Porter's five forces
 threat of new entrants
 threat of substitutes
 bargaining power of buyers
 bargaining power of suppliers
 rivalry among competitors

control vs minority perspective in using dividends or FCF
 control use FCF
 minority (just buying 1 share) use dividends

Dividend discount models:
Gordon growth model
two stage model
H model
 Gordon growth model:
 two stage: discount cash flows, then use GGM at the end. can also use trailing P/E*EPS at time t to estimate terminal value
 H model:

Present value of growth opportunities
P0 = E1/r + PVGO
PVGO/P0 = % of price attributed to future growth
Divide through by E1 for PVGO for P/E ratio

Calculate sustainable growth rate
g = b*ROE where b = plowback ratio

What financial statement data is used for DuPont analysis
Use current IS data and beginning of period BS data (do NOT average BS data)

FCFF, FCFE calculation from:
NI
CFO
EBIT
EBITDA
FCFE = FCFF + net borrowing  interest*(1tax)
NI: FCFF = NI + Non Cash Charges  change in working capital + interest*(1tax)  FCInv
CFO: FCFF = CFO + interest*(1tax)  FCInv
EBIT: FCFF = EBIT*(1tax) + NCC  change in working capital  FCInv
EBITDA: FCFF = EBITDA*(1tax) + NCC*tax  change in WC  FCInv

Calculate non cash charges for CFO from indirect method
 NI
 + Depreciation and amortization
  Gain on sale
 + Loss on sale
 +/ Restructuring expense/income
 + increase in deferred tax liability if not expected to reverse
 + amortization of bonds issued at discount
  amortization of bonds issued at premium

Calculate working capital
(Current assets  cash)  (Current liabilities  current portion of notes payable)

Calculate FCInv using gross and net PPE
FCInv = change in gross PPE  gain on sale
FCInv = ending net PPE  beg net PPE + depreciation expense  gain on sale

P/E:
rationale for using
drawbacks
calculation of actual ratio
calculation of justified ratio
PEG
terminal value
rationale: key to investment value, most widely used by Wall Street, proxy for risk and growth
drawbacks: negative or very low earnings make P/E useless, volatile, easily distorted
 calculation of actual ratio: trailing = Po/Eo
 leading = Po/E1
 Back out nonrecurring items (gain/loss sale, impairments, accounting estimates)
 must normalize earnings for business cycle  either average recent EPS or **average recent ROE and multiply by most recent BVPS**
 calculation of justified ratio:
 trailing = (1b)*(1+g)/(rg)
 leading = (1b)/(rg)
PEG: PEG = P/E/g where g is not stated as a decimal
terminal value = trailing P/E*earnings in time t

P/B:
rationale for using
drawbacks
calculation of actual ratio
calculation of justified ratio
rationale: BV usually positive, good for liquid asset firms
drawbacks: human capital not reflected, size distortion, accounting conventions create distortion, inflation and technology change can create large difference in market value and book value
calculation of actual: market price/book value of equity
calculation of justified: Po/Bo = (ROE  g)/(r  g)

P/S:
rationale for using
drawbacks
calculation of actual ratio
calculation of justified ratio
rationale: distressed firms bc sales never negative
drawbacks: does not account for cost structure, some revenue recognition potential distortion
calculation of actual: price/sales per share
 calculation of justified:
 Po/So =

P/CF:
rationale for using
drawbacks
calculation of actual ratio
calculation of justified ratio
rationale: difficult to manipulate
drawbacks: FCFE better than CFO, can be negative and difficult to compute
 calculation of actual: can use different definitions of cash flow 
 Traditional CF = NI + NCC
 CFO
 Adjusted CFO = CFO + interest*(1tax)
 EBITDA  better to use EV/EBITDA, not P/EBITDA
 FCFE
 calculation of justified ratio: two steps
 1. get value  Vo = FCFEo*(1+g)/(rg)
 2. P/CF = V/CF

P/EBITDA
justified dividend yield
 Use EV/EBITDA
 EV = market value of debt + market value of equity + market value of preferred stock  cash (and cash like securities)
justified dividend yield: Do/Po = (rg)/(1+g)

harmonic mean
weighted harmonic mean
 ex. one share has E = 1 and P = 10, second has E = 2, P = 16
 harmonic mean =
weighted harmonic mean =

Calculate residual income
RI = NI  beginning book value of equity*required return on equity
RI = (ROE  required return on equity)*BVequity

Private equity terms:
carried interest
ratchet
hurdle rate
target fund size
vintage
 management fee: GP management fee calculated based on paidin capital
 carried interest: GP's share of profits. first payment calculated as carried interest*(NAV  committed capital). note committed capital may be more than paidin capital. subsequent payments calculated as carried interest*(new NAV  old NAV).
 ratchet: allocation of portfolio company equity between shareholders and managers
 hurdle rate: IRR target before GP earns carried interest
 target fund size: signal's GP's ability to raise funds. GP not being able to reach target size is interpreted as a negative signal
 vintage: year fund was started. J curve (VCs)  at 23 years bad ideas have cost but good ones havent paid, so expect to see loss of value. 10 years, expect to see gain of value.

Private equity performance terms:
Paidin capital (PIC)
Distributed to PIC (DPI)
Residual value to PIC (RVPI)
Total value to PIC (TVPI)
 PIC: % of capital used by GP. ie how much of the target fund size has been received. = PIC/committed capital
 DPI: multiple that shows return that has actually been paid to LP. Note no time component. = cumulative distributions/PIC
 RVPI: multiple that shows return on unrealized gains for LP. = NAV after distributions/PIC
 TVPI: multiple that shows total value of LP's investment. sum of DPI and RVPI.

calculate NAV for private equity fund before and after distributions
before: NAV = previous NAV + capital called down  management fee + operating results
after: NAV before  carried interest  distributions to LP

NPV valuation of VC: calculate pre and post money valuation for VC company, required fractional ownership
post money: PV of the total terminal value of fund
pre money: post money  VC investment
fractional ownership: VC investment/post money value

IRR valuation of VC: calculate investor's future wealth (W), required fractional ownership
investor's future wealth (W): FV of investment using discount rate
fractional ownership: investor's future wealth/FV of firm

calculate pre and post money valuations and ownerships for multiple financing rounds

compute discount rate for VC adjusted for risk
adjusted discount rate = 1

Calculate value using single stage RI
Value =

Calculate Multistage RI using different Continuing RI using:
earnings persistence
decline to mature industry level

Define clean surplus relationship
usually does not hold true due to many comprehensive items (off balance sheet items, currency change from consolidation of foreign subsidiaries, availforsale securities, etc.). This makes RI not applicable in the real world.

