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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
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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
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estimating required return
single factor: CAPM - required return = rf + beta*(equity premium - rf)
multifactor: return = rf + sensitivity1*premium1 + sens2*prem2 + ...
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multifactor models:
fama-french
pastor-stambaugh
BIRR
- fama-french
- return = (market index - rf)*sensitivity + (small - big)returns*sens + (high B/M - low B/M)*sens
- pastor-stambaugh
- return = same as fama-french + liquidity premium*sensitivity
- BIRR
- aka arbitrage pricing model. could give any of five premiums*sensitivity
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build-up method
return = rf + equity risk premium + size premium + company specific premium
does NOT USE BETAS!!
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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*(
)
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WACC
WACC =
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How to discount FCFF and FCFE
- discount FCFF at WACC
- discount FCFE at return on equity
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Market value way to find equity value
Equity value = firm value - market value of debt
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Porter's five forces
- threat of new entrants
- threat of substitutes
- bargaining power of buyers
- bargaining power of suppliers
- rivalry among competitors
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control vs minority perspective in using dividends or FCF
- control use FCF
- minority (just buying 1 share) use dividends
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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:

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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
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Calculate sustainable growth rate
g = b*ROE where b = plowback ratio
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What financial statement data is used for DuPont analysis
Use current IS data and beginning of period BS data (do NOT average BS data)
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FCFF, FCFE calculation from:
NI
CFO
EBIT
EBITDA
FCFE = FCFF + net borrowing - interest*(1-tax)
NI: FCFF = NI + Non Cash Charges - change in working capital + interest*(1-tax) - FCInv
CFO: FCFF = CFO + interest*(1-tax) - FCInv
EBIT: FCFF = EBIT*(1-tax) + NCC - change in working capital - FCInv
EBITDA: FCFF = EBITDA*(1-tax) + NCC*tax - change in WC - FCInv
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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
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Calculate working capital
(Current assets - cash) - (Current liabilities - current portion of notes payable)
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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
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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 non-recurring 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 = (1-b)*(1+g)/(r-g)
- leading = (1-b)/(r-g)
PEG: PEG = P/E/g where g is not stated as a decimal
terminal value = trailing P/E*earnings in time t
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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)
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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 =

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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*(1-tax)
- EBITDA - better to use EV/EBITDA, not P/EBITDA
- FCFE
- calculation of justified ratio: two steps
- 1. get value - Vo = FCFEo*(1+g)/(r-g)
- 2. P/CF = V/CF
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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 = (r-g)/(1+g)
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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 =
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Calculate residual income
RI = NI - beginning book value of equity*required return on equity
RI = (ROE - required return on equity)*BVequity
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Private equity terms:
carried interest
ratchet
hurdle rate
target fund size
vintage
- management fee: GP management fee calculated based on paid-in capital
- carried interest: GP's share of profits. first payment calculated as carried interest*(NAV - committed capital). note committed capital may be more than paid-in 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 2-3 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.
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Private equity performance terms:
Paid-in 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.
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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
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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
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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
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calculate pre and post money valuations and ownerships for multiple financing rounds
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compute discount rate for VC adjusted for risk
adjusted discount rate =  -1
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Calculate value using single stage RI
Value =
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Calculate Multistage RI using different Continuing RI using:
earnings persistence
decline to mature industry level
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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, avail-for-sale securities, etc.). This makes RI not applicable in the real world.
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