Historical estimates

forward-looking (ex-ante) estimates

macroeconomic model estimates

survey estimates

Beta = Cov_(s,m) / Var_mkt

Beta = Correlation * (SD_stock / SD_mkt)

Beta is equal to the covariance divided by the market portfolio variance, or the product of the correlation and the ratio of the stock standard deviation to the market standard deviation. 

If a risk-free asset is part of the investment opportunity set, then the efficient frontier is a:

active asset selection

A statistical factor model

The market price of risk, or return per unit of standard deviation risk, is determined as follows:

(E(r_mkt) − RFR) / SD_mkt

(Study Session 18, LOS 54.d)

=[(W_A)²(S_A)² + (W_B)²(S_B)² + 2(W_A)(W_B)(S_A)(S_B)(Corr_A,B)]^0.5

Covariance(A,B) formula

Rule out portfolios with higher standard deviations a/o lower returns

Wilson must perform some calculations to see if stock B is more efficient than the S&P 500. Wilson would first determine the portfolio weights that can make the expected return of the stock B and T-bill portfolio equal to the S&P 500 portfolio. By setting up:

E(R_Benchmark) = w × E(R_StockA) + (1 − w) × E(R_Treas) and solving for w. (w = Weight_Stock)

The standard deviation of that portfolio is (0.75 × 35%) = 26.25% > 24% which is the standard deviation of the S&P 500. Thus, the portfolio using Stock B and Treasury bills is not more efficient than the S&P 500. (Study Session 18, LOS 54.b)

With regard to the capital allocation line (CAL), moving along the CAL above the point of the tangency portfolio represents:

borrowing at the risk-free rate to be invested in more than 100% of the tangency portfolio. The CAL becomes the efficient frontier when the risk free asset is available to invest in.

The slope of the CML =

(E(r_market) − RFR) / SD of returns on mkt portfolio

Because the CML is a straight line, it implies that all the portfolios on the CML are perfectly positively correlated.

The Prudent Man Rule has been construed as a directive to (2 things): 

preserve capital and avoid risk

Adjusted beta was developed to compensate for:

drift; the beta instability problem, or the tendency of historical betas to generate inaccurate forecasts

An adjusted beta is a weighted average of the estimated beta and either 1.0 (the average for all stocks) or a peer mean (the beta of similar firms). The objective of an adjusted beta measure is to compensate for beta drift, or the tendency of beta to revert to 1.0 (or the industry average).

Calculate P/S given EPS, Sales/Sh, P/E, RR, g, ROE

Calculate profit margin: E₀ / S₀ (EPS / SPS)

P₀ / S₀ = [(E₀ / S₀)(1 − b)(1 + g)] / (r − g)

b = retention ratio

Companies with low dividends will attract a clientele of investors with high marginal tax rates and low desires for current income. 

Year 0 FCFE = Earnings per share − [(Capital Expenditures − Depreciation)(1 − Debt Ratio)] − [Change in working capital x (1 − Debt Ratio)]

WACC/k_e = RFR + equity risk premium + small stock premium + company-specific risk premium + industry risk premium

Note that the risk-free rate is the Treasury yield, not the returns for bonds in general. 

Then plug new k_e into WACC formula using given tax rate, debt/capital ratio, cost of debt, etc

The equity risk premium is the difference between:

the required equity return and the risk-free return.

The two-stage DDM has the limitation that a sudden decrease to the lower growth rate in the second stage may not be realistic. Further, the model has the difficulty in trying to estimate the length of the high-growth stage.

What method should you use to value a company in a country with rapidly changing inflation rates?

(build-up, multifactor, bond-yield plus risk-premium)

Free cash flow to the firm (FCFF)

(1) from NI

(2) from EBIT

(3) from EBITDA

(4) from CFO

Assume Depreciation only NCC

(1) FCFF = NI + Dep + Int*(1 – tax rate) – FCInv – WCInv.

(2) FCFF = EBIT*(1 – tax rate) + Dep – FCInv – WCInv

(3) FCFF = [EBITDA*(1-t)] + (Dep*t) - FCInv - WCInv

(4) FCFF = CFO + [Int x (1-t)] - FCInv

A constant payout approach means:

(1) dividend stream

(2) stability of dividends

(3) risk assessment of equity

(1) dividends will vary in proportion with earnings

(2) volatile dividends

(3) higher risk premium

Bond-yield plus risk premium method (formula)

Required return = YTM on long-term bonds (20yr) + equity risk premium (over its bonds)

Build-up method of determining ROE:

takes into account a company’s size and is usually applied to closely held companies for which beta is not available

The Pastor-Stambaugh method for determining ROE

is a modified version of the Fama-French factor model that considers liquidity

Residual income (formula) and discount rate to use when determining project NPV

Residual income = Net income – equity charge

RI = NI – k_eBV_equity

where:
equity charge = required return on equity × beginning book value of equity. 

The residual income method concentrates on returns to equity holders. As such, the proper discount rate to use when determining the project NPV is the required return on equity.

V₀ = B₀ + [((ROE-r)*B₀) / (r - g)]

B = book value

r = required return on equity

The method of forecasted fundamentals is based on the rationale that:

stock values differ due to differences in the expected values of fundamentals such as sales, earnings, or related growth rates

A stable dividend policy:

means that a company’s dividend payout is aligned with company’s long-term growth rate such that there is stability in the rate of increase for the dividend

Bird-in-in-the-hand theory states that:

investors prefer the certainty of dividends now to uncertain capital gains in the future

Modigliani and Miller proposed that dividend policy:

has no impact on the price of a firm’s stock

FCF = NOPLAT + depreciation – change in net working capital – CAPEX

Unlevered Net Income = NI + Net Interest (after tax)

NOPLAT = Unlevered NI + Change in deferred taxes

(NOPLAT = Net Operating Profit Less Adjusted Taxes)

The price-to-earnings (P/E) multiple of a cyclical firm normally ______ at the depths of recession and ______ at the peak of economic boom.

peaks at the depths of recession

bottoms out at the peak of economic boom

Use appropriate beta for target company's leverage.

Real Cost of Equity =

[(1 + Nominal cost of equity) / (1 + inflation rate)] - 1

where nominal cost of equity = CAPM

PVGO = PV_Growth - PV_{No Growth}

 (V₀ = whatever period in future)

PV_{No Grow} = V₀ = (Expected E_t) / k_e

PV_Grow = D₁ / (r - g) = EPS1*(Payout ratio) / (r - g)

(1) Threat of new entrants (entry barriers)

(2) Threat of substitutes

(3) Bargaining power of buyers

(4) Bargaining power of suppliers

(5) Rivalry among existing companies

[D₀ * (1+g_L)]/ (r-g_L) + [D₀*H*(g_S - g_L)]/ (r - g_L)

where H = t/2

FCFF Valuation: (check on use of debt)

FCFE Valuation (same)

FCFF: V₀ = FCFF₁ / (WACC - g)

FCFE: V₀ = FCFE₁ / (r-g)

Leading P/E:

(1-b) / (1-g)

Trailing P/E:

[(1-b)(1+g)]/(r-g)

ROE = (NI/Sales)(Sales/Assets)(Assets/Equity)

(Profit Margin)*(Asset Turnover)*(Fin Leverage)

=NOPAT - $WACC

NOPAT = EBIT*(1-t)

Discount for Lack of Control (DLOC) formula

Total discount formula

1 - [1 / (1+Control Premium)]

1 - [(1-DLOC)(1-DLOM)]

Free Cash flow to Equity (FCFE) from:

(1) FCFF

(2) NI

(3) CFO

(4) Target debt ratio

(1) FCFF - [Interest*(1-t)] + Net borrowing

(2) NI + Dep - FCInv - WCInv + NB

(3) CFO - FCInv + NB

(4) NI - [(1-DR)*(FCInv-Dep)] - [(1-DR)*WCInv]

Equity risk premium=

[(1+Exp. Infl)*(1+Exp. growth in real EPS)*(1+Exp. Growth in P/E)] - 1] + Exp. Income component - Expected LT government bond yield

Find unlevered beta of comparable:

Beta of comparable (UL) = Current Beta / [1+(D/E)]

Our new beta = Beta of comparable (UL) * [1+(D/E)]