The equity part three topics will build the previous two sessions and discuss commonly used models for valuing stocks.  There are a number of formulas covered, but none of them are terribly complex and many candidates will have likely seen at least a few of them before either in an academic or professional capacity.  Flashcards are a great tool for learning the formulas.  Keep in mind, candidates are also expected to understand the strengths and weaknesses of the different models, as well as the situations where one model may be more appropriate than others.

One thing that keen candidates should pick up on is the strong influence that the <a title="Gordon Growth Model (GGM)" href="https://financetrain.com/gordon-growth-model-ggm/">Gordon Growth Model </a>and its variants have across the valuation spectrum.  Several of the multiples presented can be derived from a “GGM like” model.

This tutorial aligns with Study Session 11 material in the Level II CFA Program Curriculum ©.

<strong>Notes</strong>

r<sub>ce</sub> = common notation for required return on common equity (or required return on equity for short).

r<sub>rf</sub> = common notation for return on a risk free asset; the standard risk free asset is government debt, such as U.S. Treasuries

b = common notation for a company’s earnings retention ratio

k = common notation for a company’s dividend payout ratio (= 1 – b).

β = beta; used in applications involving the Capital Asset Pricing Model

Subscript <sub>0</sub> vs. Subscript <sub>1</sub>: a “0” in the subscript represents the current period/time, while a “1” in the subscript indicates the value reflects the next future period.

BVE = Book Value of Equity; candidates much pay attention to the context in which this is applied (i.e. on a total basis or a per share basis); if the company has preferred stock, then the valuation may only want to include the Book Value of Common Equity (BVCE).

Multi-time period discounting vs. <a title="Multi-Stage Dividend Discount Models" href="https://financetrain.com/multi-stage-dividend-discount-models/">Multi-stage modeling</a>: multi-time period discounting applies discounting future values over multiple time periods (year 1, year 2, …, year n); multi-stage modeling (which incorporates multi-time period discounting) is the valuation of a company that is anticipated to go through more than one growth stage (ex. high growth, then mature growth).

<strong>Material</strong>

I.          Free Cash Flow Valuation

II.        Market Based Valuation

III.       Residual Income Valuation

IV.       Private Company Valuation

Equity Analysis Part 3 - Introduction

<h3>FCFF vs. FCFE Definitions</h3>
<strong>FCFF:</strong> Free Cash Flows to the Firm are available to both suppliers of equity and debt capital; return of these cash flows to stock and bond investors does not threaten the company’s existence as a going concern.

<strong>WACC &amp; FCFF: </strong>When performing a company valuation using discounted FCFFs, the discount rate applied should be the <a title="Weighted Average Cost of Capital (WACC)" href="https://financetrain.com/weighted-average-cost-of-capital-wacc/">weighted average cost of capital</a> (based on the target capital structure), to reflect both the cost of equity and cost of debt.
<div class="formula1">

Value<sub>0 </sub>= Σ  FCFF<sub>t</sub> / (1+WACC)<sup>t</sup>

Equity Value = Calculated Firm Value – Market Value of Debt

</div>
This can be converted to a share price by dividing the Equity Value by the number of shares outstanding.

<strong>FCFE:</strong> Free Cash Flows to Equity are available to stock holders only; return of these cash flows to stock investors does not threaten the company’s existence as a going concern.
<div class="formula1">Value<sub>0 </sub>= Σ  FCFE<sub>t</sub> / (1 + r<sub>ce</sub>)<sup>t</sup></div>
The equity value derived from an FCFE analysis can then be divided by the number of shares outstanding to arrive at a share price.
<h3>Selecting FCFF or FCFE</h3>
The following situations can help an analyst decide which valuation approach is more appropriate:
<ul>
	<li>If the company has a consistent capital structure, then FCFE can be used in the valuation.</li>
	<li>If the company is highly leveraged and negative Free Cash Flows to Equity, then FCFF may be more appropriate.</li>
	<li>FCFF can be more appropriate when valuing a company that regularly changes its degree of financial leverage.</li>
</ul>
<h3>FCF Modeling vs. Dividend Discount Modeling (DDM)</h3>
Advantages and/or Appropriateness of FCF Valuation over DDM Valuation:
<ul>
	<li>FCF approaches can be applied companies that do not pay dividends.</li>
	<li>FCF approaches may be better for companies currently paying an unsustainable dividend.</li>
	<li>The FCFE model can be used when performing a valuation from a control perspective, as the majority owner will have discretion over how to use the equity cash flows; in contrast, DDM modeling may better reflect the view of a small shareholder who does not have control.</li>
</ul>
<h3>Calculating FCFF and FCFE</h3>
<strong>FCFF from Net Income</strong>
<div class="formula1"><strong>FCFF from Net Income</strong> = Net Income + Non-cash Charges + (Interest Expense * (1-tax rate)) – Fixed Capital Investment – Working Capital Investment</div>
<ul>
	<li>This approach is sometimes called the “add-back” method.</li>
	<li>The most common non-cash charge would be depreciation, but there are others.</li>
	<li>Non-cash gains would need to be subtracted from net income.</li>
</ul>
<strong>FCFF from Cash Flow from Operations</strong>
<div class="formula1"><strong>FCFF from Cash Flow from Operations</strong> = CFO + (Interest Expense * (1-tax rate)) – Fixed Capital Investment</div>
<ul>
	<li>The CFO approach should deliver the same results as the net income approach.</li>
	<li>When starting with CFO, analysts may still need to adjust for certain non-cash charges, such as restructuring charges.</li>
</ul>
<strong>FCFE from Net Income</strong>
<div class="formula1">

<strong>FCFE from Net Income</strong> = Net Income + Non-cash Charges  – Fixed Capital Investment – Working Capital Investment + Net Borrowing

Net Borrowing = New Debt – Principal Repayments

</div>
<strong>FCFE from Cash Flow from Operations</strong><strong> </strong>
<div class="formula1"><strong>FCFE from Cash Flow from Operations</strong> = CFO – Fixed Capital Investment + Net Borrowing</div>
<strong>Calculating FCFE from FCFF (and vice versa)</strong>
<div class="formula1">

FCFE = FCFF – (Interest Expense * (1-tax rate)) + Net Borrowing

FCFF = FCFE + (Interest Expense * (1-tax rate)) – Net Borrowing

</div>
<strong>FCFF from EBIT and EBITDA</strong>
<div class="formula1">

FCFF = (EBIT*(1-tax rate)) + Non-cash Charges – Fixed Capital Investment – Working Capital Investment

FCFF = (EBITDA*(1-tax rate)) + (Depreciation*(tax rate)) + Deferred Tax Increases – Fixed Capital Investment – Working Capital Investment

</div>
Once FCFF has been calculated, then it can be converted to FCFE, if the situation requires the FCFE value.
<h3>Reported Financials and the FCF Valuation Process</h3>
When deriving the working capital investment values for an FCF valuation, analysts should be mindful of the impacts of acquisitions, divestitures, and/or foreign subsidiary accounting as these items can complicate the relationship between the balance sheet and the statement of cash flows.
<h3>Other Cash Flow Issues for FCF Valuation</h3>
<strong>Share repurchases:</strong> Once a company performs a share repurchase, both FCFF and FCFE would decrease because those funds are not available to either debt or equity capital suppliers.

<strong>Issuing debt:</strong> Increases FCFE, but not FCFF

<strong>Issuing stock:</strong> Excluded from FCFF and FCFE
<h3>Erroneous FCF Proxies</h3>
<ul>
	<li>When performing valuations, analysts will sometimes inappropriately use net income, EBIT, or EBITDA as substitutes for cash flows.</li>
	<li>In an FCFF valuation, for example, EBITDA is problematic because it is pre-tax, it does not account for the tax shield of depreciation expense, and it does not account for fixed and working capital investments.</li>
	<li>In an FCFE valuation, EBITDA causes problems by ignoring net borrowing.</li>
</ul>
<h3>Preferred Stock Dividends</h3>
In the event that a company has issued preferred stock, the preferred dividends must be added back to FCFF; preferred dividends should not be added back for FCFE.

Free Cash Flow Valuation

<h2>Single Stage FCFE and International Valuation</h2>

<ul>
  <li>This approach is a variation on the Gordon Growth Method.</li>
  <li>Real cash flows, the real growth rate, and the real required rate of return will be applied to minimize potential distortion caused by inflation and other international differences.</li>
  <div class="formula1">
	International Stock: V<sub>0</sub> = (FCFE<sub>0</sub> * (1 + growth rate <sub>real</sub>)) / (r <sub>real</sub> - g <sub>real</sub>)
  </div>
  <li>Be mindful of the situation, to know if the question requires a total valuation or a per share valuation.  If performing a per share valuation, then FCFE would need to be a per-share value to arrive at a stock price.</li>
</ul>

<h2>Two Stage Valuation</h2>

<ul>
  <li>General Two Stage FCFF Valuation</li>
	<div class="formula1">
	V<sub>firm</sub> = &Sigma; FCFF<sub>t</sub> / (1 + WACC)<sup>t</sup> + [(FCFF <sub>n+1</sub> / (WACC - g) &times; 1/(1+WACC)<sup>n</sup>]
	</div>
  <li>General Two Stage FCFE Valuation</li>
  <div class="formula1">
  V<sub>equity</sub> = &Sigma; FCFE<sub>t</sub> / (1 + r<sub>ce</sub>)<sup>t</sup> + [(FCFE <sub>n+1</sub> / (r<sub>ce</sub> - g) * 1/(1 + r<sub>ce</sub>)<sup>n</sup>]
  </div>
  <ul>
	<li>Either the FCFE or FCFF general two stage model may be applied for situations where a high growth phase is expected to shift to a mature growth phase (or where a mature growth phase is expected to shift to a decline phase).</li>
	<li>The first segment of the expression is the present value of the shares in the high growth phase.</li>
	<li><b>Terminal Value: </b>The second segment of the formula is terminal value of the company at maturity.  It is a Gordon Growth Model like valuation performed at the year that stable growth is reached, which is then discounted back to a present value.  Correctly calculating and then discounting the terminal value trips up many candidates either through misapplication or calculation errors.</li>
	<li>rce is commonly derived using CAPM for exam purposes.</li>
	<li>This model does not necessarily represent two years, but two stages.</li>
		<ul class="list2">
		<li>The first segment of the formula can be calculated for several years and then the terminal value is calculated at the end of the high growth phase.</li>
		</ul>
	<li>It is difficult to achieve full understanding of the two stage model without practice.  Candidates must walk through numerous practice problems to be exam ready (and CFAI loves to test this material).</li>
  </ul>

</ul>
<h2>Three Stage FCF Valuation</h2>

<ul>
  <li>As the name denotes, a three stage model can be applied to cover three phases of a company's growth life cycle (ex. high growth to slower growth to mature growth or high growth to mature growth to decline).</li>
  <li>Candidates are advised to spend time mastering problems for the two stage growth model before becoming overly concerned about the three stage growth model.</li>
  
</ul>

<h3>Sensitivity Analysis and FCF Valuation</h3>

Because the value calculated in an FCF model is highly sensitive to the inputs; analysts are well served by testing a range of values for assumptions like the discount rate and growth rate.


One, Two, and Three Stage FCF Calculations

<h2>Introduction</h2>

<ul>
	<li>Stock share price multiples often heavily factor into stock recommendations.</li>
	<li>Because of this key role that multiples play in equity analysis and investing, CFAI expects candidates to understand how a company's fundamentals and its accounting choices influence its share price multiples.</li>
	<li>Two share price multiple methods in equity valuation are:</li>
	<ol>
		<li>the method of comparables, and;</li>
		<li>the method of forecasted fundamentals.</li>
	</ol>
	
</ul>

<h2>Method of Comparables</h2>

<ul>
<li>In economic theory, the "law of one price" indicates that the stock of two identical companies should sell for the same price in an efficient market.</li>
<li>Method of Comparables: allows analysts to evaluate a stock's valuation against its industry peers, size peers, and the broader market.</li>
<li>A challenge when employing the method of comparables is that it can be difficult to find two companies that are perfectly comparable.</li>
<li>A stock's price-to-earnings (P/E) ratio, for example, must be assessed against appropriate benchmark P/E ratios, including:</li>
	<ul>
		<li>The stock of the most comparable company; </li>
		<li>Stocks in the company's business unit peer group; </li>
		<li>Stocks in the company's broader industry peer group; </li>
		<li>The broad market P/E ratio; and </li>
		<li>The company's own historical P/E ratios.</li>
	</ul>

</ul>

<h2>Method of Forecasted Fundamentals</h2>

<ul>
<li>Forecasted Fundamentals: this methodology forecasts the fundamentals that a company needs in order to generate required cash flows; the cash flows are then discounted.</li>
<li>The forecasted fundamentals approach seeks to overcome the holes in relative view of the method of comparables by analyzing the relationship between a stock's price multiples and its core economic factors that drive the price multiples.</li>
</ul>
<h2>Justified Multiples</h2>
Either the comparables or forecasted fundamentals method can be used to determine a "justified" price multiple.
<ul>
<li>Method of Comparables example: an analyst may look at a stock's P/E relative to its industry average P/E ratio to determine if the company is relatively cheap or expensive; there may be good reasons for a company to trade above or below the average P/E ratio.</li>
<li>Method of Forecasted Fundamentals example: upon performing a discounted free cash flow valuation, an analyst can form an opinion about what a company's P/E ratio "should" be and then compare that to the P/E based on market price.</li>

</ul>



Share Price Multiple Methods in Equity Valuation

<ul>
	<li>In general, a company's P/E ratio is its price per share divided by earnings per share; however there are multiple versions of earnings (trailing twelve months, forecasted twelve months, etc.) and multiple ways to decompose the ratio for analysis purposes.</li>
	<div class="formula1">
		P/E = Price per share / Earnings per share
	</div>
	<li>CFAI focuses on leading P/E and trailing P/E, so follow those for exam purposes, as they are presented.</li>
	<li>The P/E ratio is useful because: it attempts to value a company based on its earnings power; the P/E ratio is easy to understand; it is widely followed; and it can assist in estimating investment returns.</li>
	<li>The P/E ratio can be criticized because: it does not work for a company with negative earnings; it can be misinterpreted for companies with inconsistent earnings; and it can easily be manipulated by company management through discretion allowed under accounting standards.</li>

</ul>

<h2>Trailing P/E Issues</h2>

<ul>
	<li><b>Non-recurring items:</b> Whenever looking at a company's trailing P/E ratio, analysts should revise earnings to exclude non-recurring items.</li>
	<li><b>Cyclical companies:</b> Whenever analyzing companies whose earnings are highly sensitive to the business cycle, analysts need to normalize (or smooth) earnings; this can be done with average ROE, for example.</li>
	<li><b>Accounting practices:</b> Analysts must be aware that a company's accounting may require revisions so that historical accrual based earnings reflect economic reality.</li>
	<li><b>Dilution:</b> A company's stock may have dilutive exposure and basic EPS might not reflect the actual EPS that investors would see in the future as the number of shares outstanding could grow through exercised options, convertible securities, etc.</li>

</ul>

<h2>Leading P/E and Earnings Yield</h2>

<h3>Leading P/E</h3>
This ratio will reflect a company's future earnings, possibly the next fiscal year or next four quarters (if a company is in the middle of a fiscal year).  A leading P/E can be in year as well, reflecting some portion of year to date earnings and forecasted earnings for the remainder of the year.
<br><br>
<h3>Earnings Yield</h3>
<div class="formula1">Earnings Yield = Earnings per share / Price per share</div>
<ul>
<li>This is the inverse of the P/E ratio.</li>
<li>Unlike the P/E ratio, it can be used when a company has negative earnings.</li>
</ul>

<h2>Gordon Growth Model (GGM)</h2>


<h3>Gordon Growth Model (GGM) and Trailing P/E Ratio</h3>
<ul>
	<li>GGM can be used to show how variables influence trailing P/E.</li>
	<div class="formula1">
		P<sub>0</sub>/E<sub>0</sub> = (Dividend payout ratio &times; (1 + Growth rate)) / (r<sub>ce</sub> - g)
	</div>
</ul>
<h3>GGM and Leading P/E Ratio</h3>
<ul>
	<div class="formula1">
		P<sub>0</sub>/E<sub>1</sub> = (Dividend<sub>1</sub> / Earnings<sub>1</sub>) / (r<sub>ce</sub> - g)
	</div>
	<li>As the growth rate goes up a stock's justified P/E increases.</li>
	<li>As the required return on common equity goes up, the justified P/E decreases.</li>
</ul>

<h2>P/E to Growth Ratio (PEG Ratio)</h2>

<div class="formula1">
PEG = (Leading P/E) / g

<br><br>
NOTE: g = earnings growth rate and the calculation requires the percentage form and not the decimal form (leading P/E should be a whole number above 1).
</div>
		<ul>
			<li>Stocks with high PEG multiples are considered to be less desirably priced than stocks with low PEG multiples.</li>
			<li>The PEG ratio can be misapplied because: it assumes that the P/E ratio and the growth rate have a linear relationship; it does not account for multiple periods of different growth rates; and it does not reflect different levels of risk across different companies.</li>
		</ul>

<h2>Terminal Values and the P/E Ratio</h2>

<ul>
<li>When performing multi-stage dividend discount or discounted cash flow modeling, a benchmark P/E ratio can be applied to the firm's forecasted earnings upon reaching a stable growth period.</li>
<div class="formula1">
Trailing Terminal Value: V<sub>n</sub> = (Benchmark Trailing P/E) * Earnings<sub>n</sub>
<br><br>
Leading Terminal Value: V<sub>n</sub> = (Benchmark Trailing P/E) * Earnings<sub>n+1</sub>
</div>
<li>These approaches will generate the terminal share price value for the period n (if trailing P/E is used) or period n+1 (if leading P/E is used).</li>

</ul>


Price to Earnings (P/E) Ratio (Leading P/E and Trailing P/E)

<div class="formula1">
P/B = market price per share / book value per share

	<ul>
		<li>Book Value per Share = Common Equity / Common Shares Outstanding</li>
		<li>Common Equity = Total Equity - Preferred Equity</li>
	</ul>
</div>
<br>
<h3>Positives of P/B</h3>
<ul>
	<li>Book value is usually positive.</li>
	<li>Many financial services companies trade close to their book values.</li>
	<li>Book value is less volatile than earnings.</li>
	<li>Stock return trends can be analyzed within the context of differences in P/B values.</li>

</ul>
<h3>Limitations of P/B</h3>
<ul>
	<li>Industry differences and asset size differences can create comparability challenges for the P/B ratio metric.</li>
	<li>Differing accounting practices can create comparability challenges for the P/B ratio metric.</li>
	<li>P/B is often driven by historical asset values (less depreciation), which may not reflect market value.</li>
	<li>Book value does not always capture all factors that drive a company's value, such as a unique workforce skill set.</li>
</ul>

<h2>P/B Value for a Constant Growth Company</h2>

<div class="formula1">
	P<sub>0</sub>/BV<sub>0</sub> = (ROE<sub>1</sub> - g) / (r<sub>ce</sub> - g)
</div>
<br>
For justified P/B ratios:

<ul>
	<li>As ROE increases, the P/B ratio increases</li>
	<li>As r<sub>ce</sub> increases, the P/B ratio decreases</li>
</ul>
<h2>Adjusting Book Value</h2>
Common adjustments to book value include:
<ul>
<li><b>Intangible Assets:</b> When a company overpays for an acquisition, then book value should be reduced by the amount of goodwill recognized.</li>

<li><b>Assets and Liabilities:</b> Book value should be adjusted for assets at historical value (moving them to market value); off balance sheet financing vehicles may also require adjustments to book value.</li>
<li><b>Different Accounting Practices:</b> When comparing companies with different accounting practices, adjustments will need to be made so their P/B ratios are really comparable.</li>

</ul>




Price to Book (P/B) Value Ratio and Equity Valuation

<div class="formula1">P/S = Market Price per Share / Sales per Share</div>
<br>
<h3>P/S Positives</h3>
<ul>
<li>Sales can be more difficult for management to manipulate than earnings or book value.</li>
<li>While earnings can be negative, sales are never negative.</li>
<li>Sales can be more consistent than earnings.</li>
<li>P/S can be useful for analyzing companies with no earnings, are cyclical, or have reached maturity.</li>
<li>Stock return trends can be analyzed within the context of differences in P/S values.</li>

</ul>

<h3>P/S Drawbacks</h3>

<ul>
<li>Unprofitable companies can still show sales growth.</li>
<li>P/S ratio does not reflect cost structure.</li>
<li>Different companies may have different revenue recognition policies.</li>
</ul>

<h2>Fundamental View of P/S Ratio</h2>

<div class="formula1">P<sub>0</sub>/S<sub>0</sub> = [(Earning<sub>0</sub>/Sales<sub>0</sub>) &times; (Payout ratio) &times; (1 + Growth rate)] / (r<sub>ce</sub> - g)</div>
<ul class="list2">
For a justified P/S ratio:
<ul>
	<li>The P/S ratio increases as profit margin and sales growth increases.</li>
	<li>The P/S ratio decreases as the required rate of return on common equity increases.</li>

</ul>
</ul>




Price to Sales (P/S) Ratio

<ul>
	<li>Analysts may choose to value stocks based on price to cash flow ratios.</li>
	<li>The cash flow applied could be: Net Income plus Non-cash Charges (which is not correct); Cash Flow from Operations; Adjusted CFO; or Free Cash Flow to Equity.</li>
	<li>Positives of Cash Flow Ratios:</li>
		<ul>
			<li>Cash flows are more objective than earnings.</li>
			<li>When earnings are volatile, cash flow ratios will be more stable than the P/E ratio.</li>
			<li>Stock return trends can be analyzed within the context of differences in price to cash flow values.</li>
		</ul>
	<li>Drawbacks of Cash Flow Ratios:</li>
		<ul>
			<li>If Free Cash Flow to Equity is negative, then the P/FCFE metric cannot be used to value a stock.</li>
			<li>FCFE can be volatile.</li>
			<li>Cash flow approximation metrics can be misapplied by the analyst.</li>
		</ul>
</ul>


Price to Cash Flow Ratios

<ul>
<li>Enterprise Value (EV) = the total market value (MV) of the firm.</li>
	<div class="formula1">
	EV = MV of debt + MV preferred equity + MV common equity - Cash and investments
	<br><br>
	Cash and investments are netted out because these items reduce the net cost of purchasing the company.
	</div>
<li>Enterprise value is a commonly used valuation perspective in M&A and investment banking transaction analysis.</li>
<li>EBITDA = earnings before interest, taxes, depreciation and amortization</li>
	<div class="formula1">
		EBITDA = Net Income + Taxes + Interest Expense + Depreciation + Amortization
		<br><br>
		EBITDA is commonly used to approximate operational cash flows that are available to suppliers of debt and equity capital
	</div>
<li>EV/EBITDA ratio is done on a total and not per share basis as it reflects value for all suppliers of capital.</li>
<li>Positives of EV/EBITDA</li>
	<ul>
		<li>Can be used when comparing firms with different degrees of financial leverage because the P/E ratio reflects value after interest has been paid.</li>
		<li>The ratio will help make companies with high, but varying degrees of depreciation and amortization more comparable.</li>
		<li>EBITDA is less likely to be negative than earnings.</li>
	</ul>
<li>Negatives of EV/EBITDA</li>
	<ul>
		<li>EBITDA can overstate operational cash flows in instances where working capital is growing.</li>
		<li>EBITDA will not reflect variances in revenue recognition practices across companies, and this impacts cash flow from operations.</li>
		<li>EBITDA is not as suitable for total firm valuation as Free Cash Flow to the Firm.</li>
	</ul>
<li>Justifiable EV/EBITDA ratio: as FCFF rises, the multiple will increase; as WACC rises, the multiple will decrease.</li>
</ul>


Enterprise Value (EV) to EBITDA

<ul>
	<li>A classic metric for valuing a stock.</li>
	<div class="formula1">
		Dividend Yield = Annual Dividend per Share / Price per Share
		<br><br>
		Trailing Dividend Yield = (Recently quarterly dividend per share &times; 4) / Price per share

	</div>
	<li><strong>Leading Dividend Yield:</strong> Calculated in the same manner, but forecasted future year dividend payments would be used.</li>
	<li><strong>Dividend Yield positives:</strong></li>
		<ul>
			<li>Payments are a key component of a stock's total return.</li>
			<li>Can be expected with greater certainty than stock price appreciation.</li>
		</ul>
	<li><strong>Dividend Yield drawbacks:</strong></li>
		<ul>
			<li>Dividend yield fails to reflect share price appreciation when evaluating a stock's total return potential.</li>
			<li>Dividends paid in the current period reduce a company's capital available to invest in future growth.</li>	
			<li>The tradeoff between dividends and capital gains can be difficult to evaluate.</li>
			<li>Not all companies pay dividends.</li>
		</ul>
	<li><strong>Justifiable Dividend Yield breakdown:</strong></li>
		<ul>
			<div class="formula1">Div<sub>0</sub>/P<sub>0</sub> = (r<sub>ce</sub> - Growth rate of dividend payment) / (1 + g)</div>
			<li>The yield has a negative relationship with the dividend growth rate.</li>
			<li>The yield is positively related to the required return on common equity.</li>
		</ul>
</ul>




Dividend Yield for Valuing Equity

<h2>Introduction</h2>
<ul>
	<li>Residual income reflects net income minus a deduction for the required return on common equity.</li>
	<li>While a firm may show positive earnings, the company would not generate true economic profit in the event that its net profit margin is less than its cost of equity capital.</li>

	<div class="formula1">
		Basic RI<sub>t</sub> = Earnings<sub>t</sub> - (r<sub>ce</sub> * Book Value of Equity <sub>t-1</sub>)
		<br><br>
		Earnings is EPS when calculating a per share value for RI.
	</div>
</ul>

<h2>Economic Value Added and Market Value Added (MVA)</h2>

<ul>
	<li>Economic Value Added attempts to quantify the value management created for shareholders during a given period, usually one year.</li>
	<li>This concept was applied in Corporate Finance 1, under capital budgeting topics.</li>

	<div class="formula1">
		Economic Value Added = NOPAT - $WACC
		<ul class="list2">
			<li>NOPAT = [EBIT * (1 - tax rate)]</li>
			<li>$WACC = WACC * invested capital</li>
		</ul>
	</div>
	<li>When calculating Economic Value Added, the analyst would be expected to make standard adjustments to reported financials, as discussed in FRA part 3.</li>
	<li>MVA is the difference between the market value of a company's long-term debt and equity less the book value of capital supplied by investors.</li>
	<ul><li>MVA attempts to measure the value created by management since the company started.</li></ul>
	<div class="formula1">
		MVA = MV of debt and equity - book value of supplied capital
	</div>
</ul>

<h2>Basic RI Model</h2>


<div class="formula1">
Share Price<sub>0</sub> = BVCE/Share<sub>0</sub> + &Sigma; RI<sub>t</sub>  / (1 + r<sub>ce</sub>)<sup>t</sup>
</div>
<ul>
	<li>This approach starts with the current book value per share of equity today and discounts the expected value of future residual incomes.</li>
	<li>Companies with positive residual incomes should have market share prices that exceed the book value per share.</li>

</ul>
<h2>RI and Dividend Discount Modeling</h2>

<ul>
	<li>RI and DDM tend to produce a similar valuation, however there is a key difference - by starting with the current book value of equity, RI front loads value recognition in a multi-period model.</li>
	<li>Alternatively, a multi-stage DDM model will back load a large portion of value in the terminal value calculation (which is a much less certain value than the current book value).</li>
</ul>
<h2>Fundamental Determinants of RI and the P/B Ratio</h2>

<ul>
<li>In theory a stock's intrinsic value should exhibit a certain relationship among its ROE, its growth rate, and its cost of equity capital:</li>
<div class="formula1">
Value<sub>0</sub> = BVCE<sub>0</sub> + [((ROE - r<sub>ce</sub>)/(r<sub>ce</sub> - g)) &times; BVCE<sub>0</sub>] 

</div>
<li>This relationship can be used to derive the price to book ratio and firms that generate a positive residual income should be valued with a price to book ratio greater than 1.0.</li>
	<div class="formula1">
		P<sub>0</sub>/B<sub>0</sub> = (ROE - r<sub>ce</sub>)/(r<sub>ce</sub> - g)
	</div>

<li>Note that if the other variables are known, the implied growth rate of a company can be determined using the RI model.</li></ul>

<h2>RI and Accounting Issues</h2>

Because residual income valuation relies heavily on reported financial data, analysts must proceed with certain cautions in mind:
<ul>
	<li>Is the company in question applying aggressive accounting assumptions and estimates in order to drive an artificially high net income?</li>
	<li>Does the company violate a clean surplus relationship?</li>
		<ul>
			<li>Clean surplus refers to the allowance of certain items to bypass the income statement and move directly to equity.  In U.S. GAAP, this includes specific items related to pensions, foreign exchange translations, and the valuation of financial instruments (these are direct to equity adjustments that fall under Other Comprehensive Income).</li>
			<li>When clean surplus is violated the book value of equity may be accurate, net income is absent of certain value drivers; therefore adjustments are required.</li>
		</ul>
	<li>Does the analyst need to revalue certain balance sheet items to their current market value and/or add in off balance sheet items?</li>
	<li>Are intangible assets, such as goodwill, large enough that they require balance sheet and income statement adjustment?</li>
</ul>
<h2>Single Stage RI Model</h2>

<div class="formula1">
	Value<sub>0</sub> = BVE<sub>0</sub> + [((ROE - r<sub>ce</sub>)/(r<sub>ce</sub> - g)) &times; BVE<sub>0</sub>]
</div>
<ul>
	<li>Values would be on a per share basis.</li>
	<li>Keep in mind that the RI model (like the Gordon Growth Model) can be used to derive a growth rate, when current and expected share prices are given.</li>
</ul>
<h2>Multi-Stage RI Model</h2>

<ul>
	<li>Just as the dividend discount model and the free cash flow discounting models can have multiple stages, so can the residual income model.</li>
	<li>This requires calculation of a terminal value of the residual income at the end of the abnormal growth phase.</li>
	<ul>
		<li>In contrast to the terminal value in a multi-stage DDM, the terminal value in a multi-stage RI model will be much smaller, as it will only capture the terminal value of residual income following the high growth period and not the terminal value of the share price.</li>
		<ul>
			<li>In the RI model, much of the value is front-loaded because the model uses the book value of equity as a starting point.</li>
		</ul>
	</ul>
</ul>
<h2>Advantages, Disadvantages and Appropriateness of the RI Model</h2>
<ul>
	<li>Advantages of the RI Model</li>
		<ul>
			<li>Because terminal value is not as significant in the RI model when compared to other models, there may be greater certainty in the valuation.</li>
			<li>The model is driven by publicly available accounting data.</li>
			<li>The model does not require a dividend payment.</li>
			<li>The model is not impacted by near term negative or unpredictable cash flows.</li>
			<li>The model captures economic profit.</li>
		</ul>
	<li>Disadvantages of the RI Model</li>
		<ul>
			<li>The model is vulnerable to accounting manipulation by company management.</li>
			<li>The model requires that the analyst have sophisticated understanding of public financial reporting, as large adjustments to reported financials may be required.</li>
			<li>Similar to the previous point, the model requires a clean surplus relationship.</li>
		</ul>
	<li>Appropriateness of RI Model</li>
		<ul>
			<li>The RI model can be utilized when: the company does not pay dividends; free cash flows are expected to be negative; or when there exists a high level of uncertainty around the terminal value.</li>

		</ul>
</ul>



Residual Income (RI) Valuation Model

Equity Analysis Part 3

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Equity Analysis Part 3

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