CFA II Equity

• 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

• 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

single factor: CAPM - required return = rf + beta*(equity premium - rf)

multifactor: return = rf + sensitivity1*premium1 + sens2*prem2 + ...

• 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

return = rf + equity risk premium + size premium + company specific premium

does NOT USE BETAS!!

• 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 = 

• discount FCFF at WACC
• discount FCFE at return on equity

Equity value = firm value - market value of debt

• threat of new entrants
• threat of substitutes
• bargaining power of buyers
• bargaining power of suppliers
• rivalry among competitors

• control use FCF
• minority (just buying 1 share) use dividends

• 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: 

P0 = E1/r + PVGO

PVGO/P0 = % of price attributed to future growth

Divide through by E1 for PVGO for P/E ratio

g = b*ROE where b = plowback ratio

Use current IS data and beginning of period BS data (do NOT average BS data)

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

• 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

(Current assets - cash) - (Current liabilities - current portion of notes payable)

FCInv = change in gross PPE - gain on sale

FCInv = ending net PPE - beg net PPE + depreciation expense - gain on sale

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

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)

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 = 

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

• 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)

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

weighted harmonic mean = 

RI = NI - beginning book value of equity*required return on equity

RI = (ROE - required return on equity)*BVequity

• 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.

• 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.

before: NAV = previous NAV + capital called down - management fee + operating results

after: NAV before - carried interest - distributions to LP

post money: PV of the total terminal value of fund

pre money: post money - VC investment

fractional ownership: VC investment/post money value

investor's future wealth (W): FV of investment using discount rate

fractional ownership: investor's future wealth/FV of firm

adjusted discount rate = -1

Value = 

earnings persistence:

 where  is persistence of RI

• decline to mature industry level:
•  
• or
• 

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.