Free Cash Flow, Market-Based, Residual Income & Private Company Valuation (R31, R32, R33, R34)

Leading Dividend Yield

Leading dividend yield = Next year's dividend / CURRENT price per share *Do not use expected market price to calculated leading dividend yield.

Valuing Private Companies

"I'MA gonna value a private company": I → Income Based Approaches (FCF, CCF, EEM) M → Market Based Approaches (GPCM, GTM, PTM) A → Asset Based Approach Generally speaking: - Private companies are owned and operated by the same people so agency issues are less of a problem than in public companies. (This has a positive impact on the private company's valuation) - Private companies are less‐likely to be able to attract highly‐skilled managers. - Private company ownership tends to be concentrated in a few hands, which can lead to perquisites and other benefits to owners at the expense of other shareholders. - Net income multiples are more commonly used to value smaller private companies, where EBIT & EBITDA multiplies are popular for large and mature private company valuation. - The Asset Based Valuation approach generally yields the lowest value

Standardized Unexpected Earnings (SUE)

(SUE) Unexpected earnings per share divided by the standard deviation of unexpected earnings per share over a specified prior time period. SUE = (Actual EPS - Mean Expected EPS) / Standard Deviation of Past Unexpected Earnings The numerator is the unexpected earnings at time t and the denominator is the standard deviation of past unexpected earnings over some period prior to time t

Clean Surplus Accounting

**NEED TO ADD DETAIL HERE**

Equity Valuation Using Residual Income Model

A significant proportion of the total intrinsic value of a stock comes from its current book value when using the RI model. When using the RI model to value equity, the analyst should include both separately identifiable intangible assets and goodwill resulting from an acquisition in the calculation of book value of equity. RI models use accounting data and are applicable to companies that do not pay any dividends and to those that have negative free cash flows.

Free Cash Flow to Equity (FCFE): The 'Uses' Approach

An analyst can back into FCFE through the 'uses' approach as follows: FCFE = (Cash & Equivalents₁ - Cash & Equivalents₀) + Cash Dividends paid + Share Repurchases - New Equity Issuance

Free Cash Flow To The Firm (FCFF): The 'Uses' Approach

An analyst can back into FCFF through the 'uses' approach as follows: FCFF = Increases in cash balances + After-tax interest expense + Repayment of principal − New borrowings + Cash dividends paid + Share repurchases − New equity issues

Price to Earnings Ratio (P/E Ratio)

An increase in the growth rate of dividends would result in a higher P‐E. An increase in systematic risk and/or an increase in the equity risk premium would be expected to lower the stock's P‐E.

Free Cash Flow Forecasting: Two Approaches

Approaches to forecasting Free Cash Flow (FCFF & FCFE): 1) calculate the CURRENT level of free cash flow and apply a constant growth rate to project FCF into the future: FCF₁ = FCF₀ (1+g) 2) forecast the individual components of FCF (e.g. after-tax operating income, non-cash charges, and investments in fixed and working capital) (see individual flash cards for forecasting these components)

Book Value Per Share

Book Value Per Share is calculated using Common Shareholders Equity divided by the number of Common Shares outstanding. Common Shareholders Equity = Total Shareholders Equity - Total Value of Preferred Stock

FCFF vs FCFE

Both the direct and the indirect methods of valuing equity should theoretically yield same estimates for the value of a firm's equity. However, there are instances when analysts might prefer one over the other: FCFE is preferred if: - A company's capital structure is relatively stable (leverage ratios are not expected to change) FCFF is preferred if: - An analyst is valuing a levered company with negative FCFE - An analyst is valuing a levered company with a changing capital structure because a) growth in FCFF may reflect a company's fundamentals more accurately than growth in FCFE, which would be affected by fluctuating amounts of net borrowing, and/or b) going forward, the required return on equity would probably be more sensitive to changes in financial leverage than the WACC.

Net Borrowing and Capital Expenditures

Capital Expenditures have two components: 1) Maintenance: expenditures necessary to maintain existing capacity (known as fixed capital replacement) which are based on the CURRENT level of sales, and 2) Growth: expenditures necessary to support expansion which are based on FORECASTS of sales growth. Using a balance sheet to calculate Net Borrowing: = (current long term + short term debt) - (previous year long term + short term debt)

Forecasting EBIT

EBIT forecasting involves forecasting SALES and the EBIT MARGIN based on historical data and on the future outlook for the company.

Normalized EPS

EPS can be normalized based on historical averages or based on average ROE. Normalized EPS = Current Book Value Per Share × Average ROE Normalized EPS = Average of historical EPS over the course of an entire business cycle (so as to capture and smooth the ups and downs)

Environmental, Social and Governance: Impact on FCFF/FCFE

ESG factors can affect a company's value in both quantitative and qualitative ways. Quantitative ESG impact can be included in cash flow forecasts (i.e. environmental fines) Qualitative ESG impact must be included in FCF valuation by adjusting the cost of equity (adding a risk premium) for the ESG risk.

Enterprise Value Multiple: EV/EBITDA

EV/EBITDA is more useful than P/E when comparing companies with different levels of financial leverage. EBITDA is the most commonly used enterprise value multiple, but FCFF may be a better measure because EBITDA may not capture required CapEx. EBITDA = NI + taxes + Dep + Int Exp EV/EBITDA↑ when growth (g) of FCFF↑ EV/EBITDA↑ when ROIC↑ EV/EBITDA↑ when WACC↓

Earnings Surprise & Scaled Earnings Surprise

Earnings Surprise = Reported Earnings - Mean Expected Earnings Scaled Earnings Surprise = (Reported Earnings - Mean Expected Earnings) / Standard Deviation of Earnings

Economic Value Added (EVA)

Economic value added (EVA) = NOPAT − (C% × Total capital) NOPAT = EBIT* (1 − t) C% → cost of capital (WACC) Total Capital → all interest bearing debt (LT & ST) plus all equity *In order to compute EVA, - R&D costs that have been expensed must be added back to EBIT - expenses associated with amortization of goodwill are added back to EBIT - accumulated amortization is added back to TOTAL CAPITAL - LIFO reserve is added to TOTAL CAPITAL - non-recurring items are adjusted

Enterprise Value Multiples

Enterprise Value (EV) Multiples: EV/FCFF EV/EBITDA EV/EBITA EV/EBIT EV/Sales

Enterprise Value (EV)

Enterprise Value = Market value of common equity + Market value of preferred stock + + Market value of Non-Controlling Interests + Market value of debt + Non-controlling interest − Cash and short-term investments Enterprise Value ratios (ie. EV/EBITDA; EV/sales; EV/FCF; etc) are more reliable than other ratios when there are issues with debt or when comparing emerging markets (accounting differences might exist).

Dividends & Share Repurchases: Affect on FCFF & FCFE

FCFF = NI + NCC + Int(1-t) - FCInv - WCInv FCFE = NI + NCC - FCInv - WCInv + Net Borrowing **Dividends, share repurchases, and share issuances do not show up in the FCFF and FCFE formulas. Therefore, they have no impact on FCFF or FCFE.**

Free Cash Flow To The Firm (FCFF)

FCFF: = EBIT (1 − Tax rate) + Depreciation − FCInv − WCInv = Net Income + Impairment Charges on Intangible Assets + Restructuring Expenses - Amortization of Bond Premium

Firm Value Using FCFF

Firm Value Using FCFF = ∑[FCFF / (1+WACC)] Sum of all forecasted FCFFs, discounted by the firm's weighted average cost of capital, determines the value of the firm today.

Free Cash Flow vs Dividend Discount Model

Free Cash Flow (FCFF or FCFE) would be preferred over DDM for valuing a firm if: - The firm has very low, or no, cash dividends - The firm's dividends are at the discretion of the board of directors - The firm being analyzed is a takeover target. Once the takeover is complete, the new owners would have discretion over use of free cash flow - The ownership perspective is a CONTROLLING INTEREST DDM is preferred over FCF for valuing a firm if: - The ownership perspective is a MINORITY INTEREST ** A difference between firm value using FCF and firm value using DDM could exist if the controlling interest is valued as a premium (i.e. controlling interest is worth more than minority interest)

Free Cash Flow to Equity (FCFE)

Free cash flow to equity (FCFE)* may be more volatile than cash flow from operations (CFO). FCFE = CFO - FCInv + Net Borrowing FCFE = FCFF - Int(1-t) + Net Borrowing FCFE = EBIT(1-t) - Int(1-t) + Dep - FCInv - WCInv + Net Borrowing FCFE = EBITDA(1-t) - Int(1-t) + Dep(t) - FCInv - WCInv + Net Borrowing *This is the most suitable definition for 'free cash flow'

Valuing Private Companies - Market Based Approach: Guideline Public Company Method (GPCM)

GPCM uses multiples from comparable PUBLIC companies and adjusts the multiple for the target company's specific risk and growth factors. It also requires the addition of a CONTROL PREMIUM, but ONLY on the EQUITY PORTION of the target company. Multiple = X Multiple adjustment for risk and growth = Y New Multiple = X × (1 +/- Y) Multiple Adjustment for CONTROL PREMIUM: Equity % × Control Premium = Control Premium applied to multiplier Final Multiple = [X × (1 +/- Y)] × (1 + Control Premium applied to multiplier)

Private Company Valuation: Impact on Private Company Value

Generally speaking: - Private companies are owned and operated by the same people so agency issues are less of a problem than in public companies. (POSITIVE TO VALUE) - Private companies are less-likely to be able to attract highly-skilled managers. (NEGATIVE TO VALUE) - Private company ownership tends to be concentrated in a few hands, which can lead to perquisites and other benefits to owners at the expense of other shareholders. (NEGATIVE TO VALUE)

Growth Rate

Growth Rate = Retention Rate × ROE

Justified Forward P/E after Inflation

If a company's entire growth comes from inflation, then the Justified Forward P/E after Inflation = 1 / [p + (1-λ)(% inflation)] p → real rate of return required by equity λ → % inflation costs that company can pass through to revenue

Stock Valuation Determination

If the FCF Value of Equity < Market Price (MV) of Equity → stock is OVERVALUED (will plot BELOW the Security Market Line (SML) and Required Return on Equity (re) > Actual Return on Equity (ROE)) FCF Value of Equity > MV Equity → stock is UNDERVALUED (will plot ABOVE the SML and re < ROE) FCF Value of Equity = MV Equity → stock is FAIRLY valued (will plot ON the SML and re = ROE)

Firm Value and Non-Operating Assets

If there are significant non-operating assets (e.g. cash, marketable securities, land held for investment purposes, etc.) then the total firm value must be estimated as the sum of the value determined through the FCF valuation PLUS the *market* value of the non-operating assets: Value of Firm = FCF Value (aka value of operating assets) + Market Value of Non-Operating Assets

Implied Growth Rate

If we assume that the market price of a stock is exactly equal to it's intrinsic value, then growth (g) of residual income can be estimated as: g = r - [(ROE - r) × B₀/(V₀ - B₀) V₀ → intrinsic value (market price, in this case) B₀ → book value

Other Private Company Equity Valuation Discounts

In addition to the lack of control discount and the lack of marketability discount, the following discounts may apply when valuing an equity interest in a private company: - key person discount - portfolio discount - discount for non-voting shares

Forecasting Net Borrowing: Target Debt Ratio (DR)

In order to forecast FCFE it can be assumed that the company finances net new investment in fixed capital (new fixed capital less depreciation) and investment in working capital based on the TARGET DEBT RATIO (DR). Net Borrowing = DR(FCInv - Dep) + DR(WCInv) FCFE = NI - (1-DR)(FCInv - Dep) - (1-DR)(WCInv)

International Firm Valuation using FCF

In order to remove the affects of high and/or volatile inflation, the value of equity for a firm can be calculated using real (inflation-adjusted) values. To estimate real discount rate: Start with the REAL required rate of return on stocks for a particular country (country return) Adjust for Industry Risk; Size Risk; Leverage Risk The real growth rate will be determined using the expected real growth rate for the relevant country.

Forecasting Investments in Fixed and Working Capital

Investment in Fixed Capital in excess of Depreciation (FCInv - Dep) and Investment in Working Capital (WCInv) can be forecasted as linked to increases in SALES. IF depreciation is the ONLY non-cash charge, the FCFE equation can be simplified as: FCFE = NI - (FCInv - Dep) - WCInv + Net Borrowing

Justified Dividend Yield

Justified Dividend Yield = (r − g) / (1 + g) Dividend yield is POSITIVELY related to the required return on equity (r) and NEGATIVELY related to the expected growth (g) in dividends. **this is the only multiple that is positively related to the required return on equity** If the stock's justified dividend yield is higher than its current dividend yield, it is overvalued (i.e. investors want more dividend for the risk they are taking on)

Justified Leading P/E

Justified Leading P/E = (1-b)/(r-g) Justified Leading P/E = (D₁/E₁)/(r-g) Justified Leading P/E = P₀/E₁ (1 - b) → payout ratio (1 minus retention rate) Remember that growth (g) is a function of ROE and retention rate: g = ROE × b If earnings (E) are expected to grow by a factor of g then the leading P/E (P/E₁) will be LOWER than the trailing P/E (P/E₀) by a factor of g.

Justified P/B

Justified P/B = (ROE-g)/(r-g) Key driver of P/B is the spread between ROE and required return on equity (r). The greater the spread between ROE and r, the greater the P/B. The difference (spread) between ROE and r is excess return (alpha) for the shareholders.

Justified Price to Sales (Justified P/S)

Justified P/S = P₀/S₀ Justified P/S = [Net Profit Margin × Payout Ratio × (1+g)]/ (r-g) Justified P/S = [(E₀/S₀)(1-b)(1+g)]/(r-g) P/S↑ when E/S↑ and when g↑ If P/S multiple based on market price is lower than the justified P/S multiple, the stock is undervalued.

Justified Trailing P/E

Justified Trailing P/E = [(1-b)(1+g)]/(r-g) Justified Trailing P/E = [D₀(1+g)/E₀]/(r-g) Justified Trailing P/E = (D₁/E₀)/(r-g) Justified Trailing P/E = P₀/E₀

Leading P/E Ratio

Leading P/E = CURRENT STOCK PRICE / EXPECTED EARNINGS OVER THE NEXT FOUR QUARTERS Can also use expected 12 months earnings, expected fiscal year earnings, etc. Leading P/E should be used if the company's business has changed fundamentally (due to an acquisition, divestiture, etc) such that use of trailing P/E would not be appropriate.

Leverage Changes: Affect on FCFF & FCFE

Leverage changes DO have an impact on FCFE. When leverage is unstable it is preferrable to use FCFF instead of FCFE. Short term: in the current period, an INCREASE in debt financing will INCREASE FCFE Long term: going forward, an INCREASE in debt financing will result in after-tax interest expense that reduces NI and REDUCES FCFE

Market Value Added (MVA)

MVA: the difference between the market values of the company's debt and equity and the book values of debt and equity (aka invested capital) Market value added = Market value of the company − Accounting book value of total capital Market value of company = MARKET value of debt + MARKET value of equity

Net Income and EBITDA

Net income and EBITDA are poor proxies for cash flows when using the FCFE and FCFF models.

EXAM TIPS: FREE CASH FLOW VALUATION

ON THE EXAM: 1) Are they asking for the value of the FIRM or the value of the EQUITY? 2) Are they asking for the TOTAL VALUE or a PER SHARE VALUE? 3) Is the data provided related to FCFF or FCFE? 4) Is the discount rate data related to the WACC (used for FCFF) or the REQUIRED RETURN ON EQUITY (used for FCFE)? 5) Are you given REAL (inflation adjusted) or NOMINAL (including inflation) growth rates and discount rate? Do not mix real and nominal rates when calculating FCF value. **Be careful: when you are asked to find the value PER SHARE instead of the value of the firm you must use FCFF or FCFE PER SHARE. Example: if the question says "FCFE at the end of 2011 is $1.265mm, there are 600,000 shares and FCFE growth is 6%, required return is 12.7%. Find the value of the stock today." you must first calculate the FCFE per share ($1.265mm/600k = $2.11) then find FCFE₁ per share ([2.11(1.06)]/[.127-.06] = $33.38.

Price to Cash Flow Ratio (P/CF Ratio)

Observed P/CF (or P/FCFE) = CURRENT MARKET VALUE OF STOCK / CASH FLOW (as defined by question) If the P/CF multiple based on market price is greater than that based on fundamentals (the intrinsic value calculated by the analyst, using trailing FCFE, for example), the stock is overvalued.

Percentage Surprise

Percentage surprise is calculated as earnings surprise (difference between reported EPS and expected EPS) divided by expected EPS. Percentage Surprise = Earnings Surprise / Expected Earnings If the company makes a greater‐than‐expected loss, the earnings surprise would be negative and since expected EPS is also negative, the percentage surprise would be positive.

Valuation: Stock vs Firm Value

Price Multiples: ratios of a STOCK'S market price to a measure of fundamental value PER SHARE (e.g. earnings per share, bv per share, cf per share, sales per share, etc) Enterprise Value Multiples: ratios of the TOTAL MARKET VALUE of all of a company's sources of capital to a measure of fundamental value for THE ENTIRE COMPANY. (e.g. Firm Value = EBITDA × ?) Momentum Indicators: relate EITHER the stock price OR a fundamental to it's value in the past (trends or patterns)

Market Based Valuation: Comparables vs Forecasted Fundamentals

Price and Enterprise Multiples can be derived in two ways: 1) Method of Comparables → using multiples (BV per share, CF per share, Sales per share, P/E, etc) from similar companies (size; industry; growth potential; risk (financial); etc) to determine a justified price multiple for the target company. In this method we say that the company is "RELATIVELY" over/under/fairly valued. 2) Method of Forecasted Fundamentals → using multiples (leading and trailing P/E) derived from forecasts of the target company's own fundamentals (rather than comparing to other companies). In this method we say that the company is simply over/under/fairly valued (not 'relatively' because we aren't comparing it to another firm)

Residual Income Valuation: Strengths & Weaknesses

RI Model Strengths: - A significant proportion of the total intrinsic value of a stock comes from its current book value which is readily available - RI models use readily available accounting data - RI models are applicable to company's that do not pay dividends and those that have negative free cash flows - RI models are applicable to company's with unpredictable cash flows - RI models focus on ECONOMIC PROFITABILITY RI Model Weaknesses: - accounting data may be manipulated by mgmt - accounting data may need to be adjusted significantly to be used - RI model assumes that the 'clean-surplus relation' holds (see flashcard) - RI model assumes that interest expense appropriately reflects the cost of debt capital

Return on Invested Capital (ROIC)

ROIC (expected profitability) = Operating Profit after Tax / Total Invested Capital (TIC)

Residual Income

Residual Income = Net Income - Equity Charge Equity Charge = Cost of Equity Capital × Equity Capital Equity Capital = BV of assets × (1 - % of debt in capital structure)

Lack of Marketability Discount (DLOM)

Restricted Stock: A discount for lack of marketability based on values of unregistered shares would UNDERESTIMATE the true discount because these shares will enjoy ready marketability in the near term, while there is no such guarantee for private company shares. IPOs: Post-IPO prices tend to be higher than pre-IPO prices due to other factors besides just the greater marketability (e.g., due to lower risk and greater certainty regarding future cash flows). Therefore, a DLOM based on the differences between pre- and post-IPO prices would OVERESTIMATE the true discount. Put Options: Put option prices primarily reflect the cost of downside protection (not the price of attaining marketability). Using put option prices to estimate the DLOM would OVERESTIMATE the true discount.

Simple Harmonic Mean

Simple Harmonic Mean - simple harmonic mean inherently gives a lower weight to higher P/Es and higher weight to lower P/Es and will, therefore, be lower than arithmetic mean

Approaches to Determining Terminal Value

Terminal Value can be calculated as: 1) Free Cash Flow at time t / (discount rate - g) or 2) Based on Valuation Multiples (e.g. EPS × P/E) Terminal Value in Year n = Justified TRAILING P/E × Forecasted Earnings in Year n Terminal Value in Year n = Justifed LEADING P/E × Forecasted Earnings in Year n+1 *If given a TRAILING P/E multiple, use the current earnings to determine terminal value. If given a LEADING P/E multiple, use the forecasted earnings to determine terminal value. (see page 225 of Wiley Vol. 3)

Clean Surplus Relation: RI Model Assumption

The Clean Surplus Relation states that Ending Book Value = Beginning Book Value + Earnings - Dividends If there are charges that bypass the income statement and go direct to equity then the clean surplus relation WILL NOT HOLD.

Total Discount: DLOC and DLOM Relationship

The DLOM and DLOC are NOT ADDITIVE, they are compounded: Total Discount = 1 - [(1-DLOM)(1-DLOC)]

P/E: Payout Ratio

The P/E multiple can be derived as: P/E = Payout Ratio / (r - g) If given the dividend you can also use: P/E = [D₁ / (r-g)] / EPS

PEG Ratios

The PEG Ratio, P/E per percentage point of growth ratio, captures the IMPACT of growth (g) on P/E: PEG = (P/E) / g g → is a whole number here, not a percentage! The investment with the lowest PEG ratio is the most attractive. If P/E is relatively low and PEG is low that could mean that g (growth) is high and the stock should be purchased. A low PEG could also mean that the stock has a low P/E due to higher risk relatively speaking.

Predicted P/E

The Predicted P/E is estimated by regressing a company's historical P/Es on fundamentals (i.e. growth rate in earnings, payout ratio, beta) A regression can only be used for its target company and only expresses the relationship between price and fundamentals over the sample period used. This relationship could change over time. There are also issues with multicollinearity (correlations within the linear combinations of each of the independent variables). This makes interpreting individual regression coefficients difficult.

Price to Book Ratio (P/B Ratio)

The Price to Book (P/B) ratio is calculated as the current price per share divided by the current book value per share as determined by the value of common shareholders equity only. BV of common shareholders' equity = Total shareholders' equity − Total value of preferred stock BV per share = BV of common shareholders' equity / # common shares

Private Company Valuation: Asset-Based Approach

The asset-based approach determines the value of a business as the value of its net assets i.e., the fair value of its assets less the fair value of its liabilities. This is an absolute valuation model. A company IN THE EARLIEST STAGES of development should be valued using the asset-based approach as future cash flows might be too unpredictable and there is no guarantee that the company will be able to operate as a going concern for the foreseeable future. This is also the approach used for liquidation purposes (ch. 7 bankruptcy) and often results in the LOWEST value of all of the approaches.

Private Company Valuation: Income Approach

The income approach is similar to the discounted cash flow approach applied to public companies. It determines the value of an asset as the present value of its expected future income. This is an absolute valuation model. A company that has successfully negotiated the early development stage and is witnessing high growth should be valued using the income approach (based on discounted expected future cash flows).

Lack of Control Discount (DLOC)

The lack of control discount is a function of the control premium: DLOC = 1 − [1/(1 + Control Premium)]

Private Company Valuation: Market Approach

The market approach determines the value of an asset based on price and enterprise value multiples from comparable assets recently sold in the market. This is a relative valuation model. A stable, relatively mature company should be valued using the market approach. For large and mature private companies, EBITDA or EBIT multiples are quite popular. However, net income multiples are more commonly used for smaller private companies.

Law of One Price

The method of comparables is based on the the Law of One Price. The Law of One Price states that similar assets should be priced similarly (or trade at similar, not the same, multiples)

Sources of Error in FCF Valuations

There are two main sources of error in FCF valuations: 1) Errors in estimating the GROWTH RATES (FCFF, FCFE, sales, net profit margins, etc.) 2) Errors in estimating the BASE YEAR VALUES of FCFE and FCFF

Equity Value of the Firm: Direct Method

To determine the Equity Value of the Firm using the Direct Method: 1) Sum the present value of the firm's FCFE (Discounted by the required rate of return (r))

Equity Value of the Firm: Indirect Method

To determine the Equity Value of the Firm using the Indirect Method: 1) calculate Firm Value using FCFF (discounted by WACC) 2) subtract the MARKET VALUE of debt from the Firm Value Equity Value (Indirect Method) = Firm Value - Market Value of Debt

Justified P/CF (or P/FCFE)

To determine the Justified P/CF (or P/FCFE) of a stock, you must first calculate the intrinsic value of the stock: V₀ = [FCFE₀(1+g)]/(r-g) Then divide the intrinsic value (V₀) by the trailing cash flow (as defined by the question) to find Justified P/CF (or P/FCFE).

Total Invested Capital (TIC)

Total Invested Capital (TIC) = Market Value of Common Shares + Market Value of Preferred Shares + Market Value of Debt + Minority Interest

Trailing P/E Ratio

Trailing P/E = CURRENT STOCK PRICE / EARNINGS OVER THE LAST FOUR QUARTERS Trailing P/E should be used if the company's earnings going forward are expected to be volatile or cannot be forecasted accurately.

Trailing Dividend Yield

Trailing dividend yield = Dividend rate / Current price per share If the company makes quarterly dividend payments, the dividend rate is calculated on the basis of the most recent quarterly dividend. For example, if the Q4 dividend was $.52 then the dividend rate would be $.52 × 4 = $2.08 If the company makes semi-annual dividend payments then the last two dividend payments are divided by current share price to determine trailing dividend yield.

Deriving Free Cash Flow from CFO: FCFF and Dividends Paid

Under IFRS, dividends paid can be classified as CFO or CFF. *Only if they are classified as CFO* should they be added to CFO to compute FCFF. Under GAAP, dividends paid are classified as CFF and therefore no adjustment is needed.

Deriving Free Cash Flow from CFO: FCFF and Interest & Dividends Received

Under IFRS, interest & dividends received can be classified as CFO or CFI. *Only if they are classified as CFI* should they be added to CFO to compute FCFF. Under GAAP, interest and dividends received are classified as CFO and therefore no adjustment is needed.

Deriving Free Cash Flow from CFO: FCFF and Interest Paid

Under IFRS, interest paid can be classified as CFO or CFF. Under GAAP, interest paid is classified as CFO. *Only if it is classified as CFO* should after‐tax interest paid be added back to CFO to compute FCFF. FCFF = CFO* + Int(1-t) - FCInv *CFO = NI + NCC - WCInv

Single Stage Residual Income Model

Under the Single Stage Residual Income Model, the intrinsic value of a stock: V₀ = B₀ + [(ROE - r)/(r-g)](B₀) The 'single stage' model can be used to find the intrinsic value of a company with multiple stages of dividend growth so long as a LONG TERM ROE and LONG TERM GROWTH (g) can be found (or are given)

Single Stage FCF Valuation

Value of the Firm = FCFF₁ / (r-g)

Equity Valuation Using FCFE

V₀ = [FCFE₀ × (1 + g)] / (r − g) FCFE₀ → also called "trailing FCFE"

Weighted Harmonic Mean

Weighted Harmonic Mean - most precise measure for computing the average of a group of price multiples - for an equal weighted index, the simple harmonic mean and weighted harmonic mean are equal

Median vs Mean

When given the option, use the median. Median mitigates the effect of outliers.