<h2><strong>Valuation: Relative vs. Intrinsic</strong></h2>
<strong>Relative valuation</strong> is an approach where an asset’s price attractiveness is evaluated in comparison to the valuation of like securities.

For example, an analyst may calculate the justified P/E ratios for stocks in a specific industry to determine which companies are relatively “cheap” and which are relatively “expensive” based on the industry average.

<strong>Intrinsic valuation</strong> is an approach whereby an estimation of future returns for an asset is calculated in order to derive the asset’s fair price; the derived price can then be compared to the current market price to see if the asset is over-priced or under-priced by the market.

For example, an analyst may estimate a stock’s future dividend payments and its share price appreciation to determine a fair current price.
<h2><strong>Going Concern Valuation vs. Liquidation Valuation</strong></h2>
In performing a going concern valuation, the analyst will assume that the corporation in question will exist and generate profits in perpetuity.

A liquidation valuation essentially looks at the value of a company in the event that its assets are quickly sold.
<h2><strong>Other Considerations when Valuing Equity</strong></h2>
The valuation approach an analyst takes should be congruent with the nature of the ownership perspective that would be assumed.

<strong>Control</strong>

When valuing a company from a takeover/acquisition perspective, the valuation should adjust for a control premium as controlling interest gives the owner the ability to dictate how cash flow will be used (compared to say an individual shareholder who has limited to almost no ability to influence the amount or timing of dividend payments, for example.

While the Gordon Growth Model may be appropriate for an individual investor, this valuation method would not readily reflect the ownership nature of a controlling position investment.

<strong>Marketability and Liquidity</strong>

Companies that do not trade publicly require higher returns from investors.

Stock values for a non-publicly traded company should be discounted for their lack of marketability (i.e., a marketability discount).

Additionally, publicly traded stocks that trade thinly should have a liquidity discount applied to their valuations.
<h2><strong>Applications for Equity Valuation</strong></h2>
<ul>
	<li>Stock selection</li>
	<li>Market expectations analysis</li>
	<li>Fairness opinions</li>
	<li>Shareholder communication</li>
	<li>Corporate event interpretation</li>
	<li>Private equity</li>
	<li>Business strategy assessment</li>
</ul>
<h2><strong>Alpha</strong></h2>
Alpha is the attainment of excess risk adjusted returns above an appropriate benchmark.

<strong>Ex-Ante Alpha:</strong> based on expectations of the future.

Expected(Holding Period Return) = ((Price <sub>1</sub> - Price <sub>0</sub>) + Expected Dividend)/P <sub>0</sub>

Ex-Ante Alpha = E(HPR) – Expected Theoretical Return

The expected theoretical return can be based on an acceptable theoretical valuation technique, such as the Capital Asset Pricing Model.

<strong>Ex-Post Alpha:</strong> analyzes actual returns.

α = HPR – Return generated by similar securities.
<h2><strong>Equity Valuation Steps</strong></h2>
<ol>
	<li>Study the company’s business and industry.</li>
	<li>Forecast the company’s future financial performance.</li>
	<li>Determine the valuation method (intrinsic/absolute or relative) and incorporate any special considerations.</li>
	<li>Calculate the company’s value.</li>
	<li>Make a clear investment recommendation on the company.</li>
</ol>

The Process of Valuing Equity

<strong>Holding Period Return (HPR)</strong>
<div class="formula1">r = ((Dividend + Share Price Change)/Share Price Paid)-1</div>
<strong>Expected vs. Realized Holding Period Return</strong>

Expected HPR is based on investor expectations for share price appreciation and dividend payments; different investors may have different expectations for the same stock and would therefore have different expected HPRs.

Realized HPR is based on historical fact, as share price change and dividend payment are known values.

<strong>Required Return</strong>

This value is the minimum return that an investor demands for a specific asset based on its riskiness.

Required return reflects the opportunity cost of forgoing the next best investment.
<div class="formula1">

Expected Alpha = expected return – required return

Realized Alpha = actual HPR – comparable asset return

</div>
<strong>Discount Rate</strong>

The discount rate is used to calculate the present value of future cash flows.

Generally, a single discount rate is used for all future period cash flows.

When calculating the intrinsic value of a stock, the investor will apply a discount rate that is based on the risk free rate of return plus some equity risk premium.

<strong>Internal Rate of Return (IRR)</strong>

IRR is the case of a discount rate that equalizes the present value of cash inflows with present value of cash outflows.

Within the context of a net present value analysis, when the cash inflows and outflows are known, IRR will be the rate that causes the NPV to equal zero.

<strong>Convergence to Intrinsic Value</strong>

When calculating the intrinsic value of a stock, an analyst may discover that his/her calculated value differs from the current market value.

If the investor’s calculated intrinsic value is more accurate than the current market price, then a special investment opportunity may be present.

When the market value shifts to the calculated intrinsic value over time, then convergence is taking place.

Despite a perceived mispricing, convergence may not occur over the investor’s time horizon.  Quoting the legendary economist John Maynard Keynes “the market can stay irrational longer than you can stay solvent.”

 

Equity Return Measures

The ERP is the amount of return required by an investor above and beyond the risk free rate, where the risk free rate is commonly the rate of return from a sovereign government bond with a maturity comparable to the investor’s time horizon.

<strong>Historical Estimates for ERP</strong>: this approach calculates the ERP based on historical returns of a stock market index above government bond returns over a sample period of time.

Analysts may adjust a historical ERP to remove biases that could be present in the sample.

<strong>Forward Estimates for ERP</strong>: this is an ex-ante approach where the ERP is based on current data about expected future returns.

Forward ERP estimates can be based on a Gordon Growth Model, macroeconomic statistical models, or a survey of experts.  Each technique has its own strengths and weaknesses.
<h2>Required Return on Equity</h2>
An investor’s required return on equity (or common equity as it is sometimes stated) is the total amount of return that an investor will demand in order to make the stock investment that is under consideration.  Generically, this amount reflects the risk free rate plus the appropriate equity risk premium.

Several methods for calculating the required return on equity will now be described.
<h3>Capital Asset Pricing Model (CAPM) and Beta</h3>
The <a title="The Capital Asset Pricing Model" href="https://financetrain.com/the-capital-asset-pricing-model/">CAPM model</a> applies the risk free rate and a broad market equity risk premium, but goes on to make a security specific adjustment to the market ERP, called beta, based on the individual security’s sensitivity to broad market equity risk premium.
<div class="formula1">CAPM r <sub>common equity</sub> = r <sub>risk free</sub> + β * (ERP<sub>market</sub>)</div>
Under CAPM, ERP is the broad market return minus the risk free rate of return.

When a stock is described as “high beta” this means the stock has a heightened sensitivity to changes in the value of the broader market.

A stock with a beta equal to one has returns that move in lock step with the broad stock market.

<a title="How to Calculate Stock Beta in Excel" href="https://financetrain.com/how-to-calculate-stock-beta-in-excel/">Beta</a> (β) is commonly calculated from a least squares regression of the individual stock’s returns on the broad market index’s returns. CAPM is a form of a single factor regression model.

In valuing stocks an analyst is looking to the future; in respect for this the historical beta is often adjusted when determining the required return on equity.
<div class="formula1">Adjusted beta = 2/3 historical beta + ((1/3)*(1.0))</div>
Beta for a non-public company

1) Un-lever the beta of a publicly traded peer company
<div class="formula1">β <sub>U peer</sub> = (1/(1+(Debt to Equity Ratio <sub>peer</sub>))) * β <sub>peer</sub></div>
2) Calculate the non-public company’s beta with the unlevered peer beta
<div class="formula1">β non-public company = (1 + D/E <sub>non-public co.</sub>) * β <sub>U peer</sub></div>
<h3>Multifactor Models</h3>
Some analysts might feel that the single variable relationship of an individual company to a broad market index is insufficient in calculating a required return for equity.  Other models and theories, such as arbitrage pricing theory will use multiple variables to calculate return.

<strong>Fama-French Multifactor (FFM) Model</strong>

FFM is a three factor model.
<div class="formula1">r <sub>ce</sub> = r <sub>f</sub> + (β <sub>mkt</sub> * ERP) + (β <sub>size</sub> * SMB) + (β <sub>value</sub> * HML)</div>
<strong>ERP:</strong> market factor.  Similar to basic CAPM, this is the equity return premium of the broad market over the risk free rate of return; also noted as RMRF (return of market minus return of risk free rate).

<strong>SMB:</strong> size factor.  It represents the average returns of three small cap stock portfolios minus the average return of three large cap portfolios.  SMB is the small cap return premium.

<strong>HML:</strong> value factor.  It represents the average return from two high book value to market value portfolios minus the return of two low book value to market value portfolios.  HML is a value premium.

<strong>Pastor-Stambaugh Model</strong>

PSM is a four factor model that adds one additional factor to FFM, a liquidity factor.  The liquidity factor incorporates the excess returns to a portfolio by shorting high liquidity stocks to invest the proceeds in low liquidity stocks.

<strong>Macroeconomic Multifactor Models</strong>

Such models apply macroeconomic variables to derive a required rate of return (or cash flow discounting rate) for a stock.

One example is the BIRR Five Factor model, which applies the following five factors on top of the risk free rate: confidence risk, time horizon risk, inflation risk, business cycle risk, and market timing risk.

<strong>Build-up Method</strong>

The build-up method can be used for privately held companies.

In calculating the required return, this approach starts with the risk free rate and equity risk premium, and then adds one or more additional premiums or discounts without adjusting these premiums for beta.
<h2>International Issues for Required Return on Equity</h2>
When investing in foreign stocks, the domestic investor introduces currency risk to the portfolio, as exchange rate movements will impact returns.

Emerging market investing presents complications beyond currency movements, as stock ownership can be highly concentrated and volatility can be extreme and persistent.

Two approaches for estimating emerging market returns:

1) <strong>Country Spread Model</strong> = ERP <sub>developed market</sub> + country premium

2) <strong>Country Risk Rating Model</strong>: This approach uses a regression model to determine the relationship between developed market equity returns and semi-annual risk ratings for the country in question.
<h2>Weighted Average Cost of Capital (WACC)</h2>
<a title="Weighted Average Cost of Capital (WACC)" href="https://financetrain.com/weighted-average-cost-of-capital-wacc/">WACC</a> is the weighted average costs of a firm’s debt and equity financing.

WACC is relevant when considering total firm value (not just equity value) and can be used as a discount rate for cash flows to all suppliers of capital.

WACC = (Market Value of Debt / (MVD + Market Value of Common Equity)* r <sub>debt</sub> * (1- tax rate))) + (MVCE / (MVD+MVCE) * r <sub>ce</sub>)))

In selecting an appropriate discount rate, the analyst must consider the cash flow.  If the cash flow has been adjusted for interest payments, then an equity return rate would be appropriate.  If the cash flow is available to all capital holders, then WACC would be appropriate.

Equity Risk Premium (ERP) and Required Return on Equity

Equity Analysis Part 1

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Equity Analysis Part 1

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