Determining the value of an asset is at the heart of analysts professional activities and skill in valuation is a very important element of success in investing
Valuation is the estimation of an asset's value based on:
Variables perceived to be related to future investment returns
Or, on comparisons with similar assets
Or, on estimates of immediate liquidation proceeds
Intrinsic value is the value of the asset given a hypothetically complete understanding完全掌握资产的所有信息下的估值 of the asset's investment characteristics
Sources of Perceived Mispricing
There are two sources of perceived mispricing(V_E-P)
E(IV)-P=(IV-P)+(E(IV)-IV)
IV-P: true mispricing
E(IV)-IV: estimation error
The difference between the true (real) but unobservable intrinsic value and the observed market price contributes to the abnormal return or alpha which is the concern of active investment managers
Other Definitions of Value / Price
Fair market value (price) is the price at which a willing, informed, and able seller would trade an asset to a willing, informed, and able buyer
Investment value is the value to a specific buyer taking account of potential synergies and based on the investor's requirements and expectations
Intrinsic value is most relevant to public company valuation
Going-Concern and Liquidation
Going-concern value
The value under a going-concern持续经营 assumption that the company will continue its business activities into the foreseeable future
Liquidation value
The value if the company is dissolved and its assets sold individually
Orderly liquidation value assumes adequate time to realize liquidation value
Going-concern value > Liquidation value
Valuation Model Selecting
Valuation Models
Absolute valuation models
Models that specify an asset's intrinsic value which is in order to be compared with the asset's market price
It does not need consider about the value of other firms
Relative valuation models
Models that derive values from relative comparison to similar assets,based on law of one price
It is typically implemented using price multiples
For examples P/E_{stock} \lt P/E_{market} → stock is relatively undervalued
Models Selection
Consistent with characteristics of company
Understand the company and how its assets create value
Based on quality and availability of data
DDM problematic when no dividends
P/E problematic with highly volatile earnings
Consistent with purpose of analysis
Free cash flow vs. dividends for controlling interest
Common Adjustments for Valuation
The value of a stock investment that would give an investor a controlling position will generally reflect a control premium
The value of non-publicly traded stocks generally reflects a lack of marketability discount
Among publicly traded(i.e., marketable) stocks, the prices of shares with less depth to their markets (less liquidity) often reflect an illiquidity discount
The price that could be realized for that block of shares would generally be lower than the market price for a smaller amount of stock, a so-called blockage factor
Sum-of-the-Parts Value
Sum-of-the-parts value (breakup value, private market value) is the value for a company as a whole obtained by adding up the values of individual parts of the firm
Useful when valuing a company with segments in different industries that have different valuation characteristics
Frequently used to evaluate the value that might be unlocked in a restructuring through a spinoff, split-off, or equity (IPO) carve-out
Conglomerate Discount
Conglomerate discount多元化经营折价 refers to the concept that the market applies a discount to the stock of a company operating in multiple, unrelated businesses compared to the stock of companies with narrower focuses
Possible explanations for the conglomerate discount include:
Inefficiency of internal capital markets
Companies' allocation of investment capital among divisions does not maximize overall shareholder value
Endogenous factors
Poorly performing companies tend to expand by making acquisitions in unrelated businesses
Research measurement errors
Process of Valuation
Steps of Valuation Process
Understanding the business
Industry and competitive analysis
Analysis of financial reports
Considerations in using accounting information
Forecasting company performance
A top-down forecasting approach moves from international and national macroeconomic forecasts to industry forecasts and then to individual company and asset forecasts
A bottom-up forecasting approach aggregates forecasts at a micro level to larger scale forecasts
Selecting the appropriate valuation model
Converting forecasts to a valuation
Applying the valuation conclusion
Sell-side analysts associated with investment firms' brokerage operations are perhaps the most visible group of analysts offering valuation judgments
Buy-side analysts works in investment management firms,trusts and bank trust departments, and similar institutions, an analyst may report valuation judgments to a portfolio manager or to an investment committee as input to an investment decision
Applications of Equity Valuation
Selecting stocks
Inferring (extracting) market expectations
Evaluating corporate events
Rendering fairness opinions
Evaluating business strategies and models
Communicating with analysts and shareholders
Appraising private businesses
Share-based payment (compensation)
Contents of a Research Report
Contain timely information
Be written in clear, incisive language
Be objective and well researched, with key assumptions clearly identified
Distinguish clearly between facts and opinions
Present sufficient information to allow a reader to critique the valuation
State the key risk factors involved in an investment in the company
Disclose any potential conflicts of interests faced by the analyst
Discounted Dividend Valuation
Framework of Model
Models
DCF Model
{V}_0=\sum_{{i}=1}^{+\infty} \frac{{CF}_{{i}}}{(1+{r})^{{i}}}
An asset's intrinsic value is the present value of its expected future'cash flows'
DDM Model
V_0=\sum_{i=1}^{+\infty} \frac{D_i}{\left(1+r_e\right)^i}
DDM shows the intrinsic value to the investor is the present value of all future dividends discounted at required return of equity
DDM is from the perspective of non-controlling investors'judgment of stock's intrinsic value
Advantages and disadvantages of DDM
Infinite Stream
Forecast the stock price at a certain point in the future
V_0=\sum\frac{D_i}{(1+r)^i}+\frac{P_n}{(1+r)^n}
Future dividends can be forecast by assuming one of several stylized growth patterns
Constant growth forever(Gordon growth model)
Two distinct stages of growth
Three (or more) distinct stages of growth
A finite number of dividends can be forecast individually up to a terminal point, then the terminal value is estimated
Forecasted value at beginning of the final mature growth phase
The terminal value is then discounted back, and added to the present value of prior stage dividends
Two methods are often used
Apply a price multiple to a projected terminal value of a fundamental such as P/E, P/B
Gordon growth model
Gordon Growth Model
Basic Concepts of GGM
Gordon Growth Mode
V_0=\frac{D_1}{r_e-g}
Assumptions of Gordon Growth Model
Dividends grow at constant rate (g) forever
Growth rate is less than required return (r_e \gt g)
Considerations of Using Gordon Growth Model
The GGM should reflect long-term growth expectations: GDP growth, industry life cycle stages and the impact of the five force model
The model's intrinsic values V_0 are very sensitive to the input variables for r_e and g Sensitivity analysis may be required to obtain a range of values rather than a specific point estimate of value
Gordon growth model can accurately value companies that are repurchasing shares when the analyst can appropriately adjust the dividend growth rate for the impact of share repurchases
Sustainable Growth Rate
SGR(g) is the sustainable growth rate in earnings and dividends if we assume:
Growth from internally generated sources (No new equity issued)
Some key financial ratios remain unchanged
SGR(g)= ROE × retention rate(b)
ROE is calculated using beginning-of-period shareholders' equity
The lower the earnings retention ratio, the lower the growth rate(dividend displacement of earnings)
PRAT model: SGR = Net Profit Margin × Total Asset Turnover × Financial Leverage × retention rate
Applications of GGM
Valuation of Preferred Stock
V_0=\frac{D_p}{r_p}
The discount rate or capitalization rate is often at a positive spread over the firms junior ranking debt yield
Justified P/E Ratio
The Gordon model can also be used to calculate a "justified (or fundamental)"price multiple
Justified leading P/E Ratio
\text{Justified leading P/E}=\frac{V_0}{E_1}=\frac{\frac{D_1}{r-g}}{E_1}=\frac{\frac{D_1}{E_1}}{r-g}=\frac{1-b}{r-g}
High growth followed by linearly declining followed by perpetual growth
Strengths
Ability to model many growth patterns
Solve for V, implied g, and implied r
Weaknesses
Require high-quality inputs (GIGO)
Model must be fully understood
Value estimates are sensitive to g and r
Model suitability is very important
Spreadsheet Modeling
In practice we can use spreadsheets to model any pattern of dividend growth
It can involve a great deal of information and can project different growth rates for differing periods
The reason for this is the inherent flexibility and computational accuracy of spreadsheet modeling.
Free Cash Flow Valuation
Basic Concepts of FCFs
Introduction of Free Cash Flows
Dividends are the cash flows actually paid to stockholders
Free cash flows(FCF) are the cash flows available for distribution after:
Fulfilling all obligations (operating expenses and taxes)
Without impacting on the future growth plans of the company (incremental working capital and fixed capital)
Strengths of FCFs
Used with firms that have no dividends
Functional model for assessing alternative financing policies
Rich framework provides additional detailed insights into company
Other measures such as EBIT, EBITDA, and CFO either double count or omit important cash flows
Limitations of FCFs
FCF may be negative due to large capital demands
Requires detailed understanding of accounting and FSA
Information may be not readily available or published
Free Cash Flows vs. Dividends
The logics behind the general valuation models are the same for both DDM and FCF models, but the numerator is different
FCFE could be either greater or less than dividends, but the same economic forces that lead to low (high) dividends lead to low (high) FCFE
Ownership perspective is very different between DDM and FCF model
FCFE model takes a control perspective and can be used in control perspective
DDM takes a minority perspective and can be used in valuing minority position in publicly traded shares
FCFF and FCFE
FCFF is the cash available to shareholders and bondholders after taxes,capital investment, and WC investment, pre-levered cash flow
FCFE is the cash available to equity holders after payments to and inflows from bondholders, post-leveraged cash flow
The two FCF approaches, indirect and direct, for valuing equity should theoretically yield the same estimates, if all inputs reflect identical assumptions
An analyst may prefer to use one approach rather than the other because of the characteristics of the company being valued
If the company's capital structure is relatively stable, using FCFE to value equity is more direct and simpler
The FCFF model is often chosen in two other cases:
Alevered company with negative FCFE
Alevered company with a changing capital structure
Calculations of FCFs
Calculating FCFF
Basic Formula
FCFF=EBIT\times(1-t)+NCC-WCInv-FCInv
NCC is non-cash charges, which represent an adjustment for noncash decreases and increases in net income
FCInv is net fixed capital investment, which equals to capital expenditure less proceeds from sales
WCInv is working capital investment excluding cash and short-term debt (notes payable and current portion of long-term debt)
Expanding Formulas
FCFF= NI+NCC+Int\times(1-t)-WCInv-FCInv
FCFF=EBITDA\times(1-t)+NCC\times t-WCInv-FCInv
FCFF=CFO+Int\times(1-t)-FCInv
Calculating FCFE
Basic Formula
FCFE=FCFF-Int \times(1-t)+NB
NB is net borrowings, which is debt issued less debt repaid over the period for which one is calculating free cash flow
NI is a Poor Proxy for FCFE
NI is a cash flow concept
NI recognizes non-cash charges such as depreciation, amortization
NI fails to recognize the cash flow impact of investments in working capital and net fixed assets, and net borrowings
EBITDA is a Poor Proxy for FCFE
EBITDA does not reflect taxes paid
EBlTDA ignores effect of depreciation tax shield
EBITDA does not account for needed investments in working capital and net fixed assets for going concern viability
EBlTDA is a pre-levered figure so it is pre-interest and before net borrowings
More Details About the Parameters
Non-Cash Charges
Working Capital Investments
Net investment in working capital for the purpose of calculating FCF excludes
Changes in cash and cash equivalents
Notes payable
Current portion of L.T.debt
There is an inverse (direct) relationship between changes in current assets (current liabilities) and changes in free cash flows
Fixed Capital Investments
Fixed capital investment (FCInv) represent a cash out flow necessary to support the company's current and future operations
Expenditures can include acquisition of intangible items such as trademarks
Care should be used with non-recurring large acquisitions in forecasts
Fixed capital investment is a net amount
It is equal to the difference between capital expenditures (investments in long-term fixed assets) and the proceeds from the sale of long-term assets
If there were no disposals of fixed assets
Given gross PP&E: FCInv= GV_{ending}-GV_{beginning}
Given net PP&E: FCInv = BV_{ending}- BV_{beginning} + \text{depreciation expense}
If there were disposals of fixed assets
Given gross PP&E: FCInv_{disposals}=FCInv +\text{AD of disposed assets}-\text{P/L from disposals}
Given net PP&E: FCInv_{disposals}=FCInv - \text{P/L from disposals}
Adjust FCFF if there were disposals of fixed assets
Calculate "FCInv = CAPEX - proceeds from disposal", Subtract P/L from disposals from NI
Net Borrowing
Net borrowings only affect FCFE, they do not affect FCFF
Notes payable
Increase in notes payable, add to FCFE
Decrease in notes payable, subtract from FCFE
Current portion of long-term debt
Increase in short-term debt, add to FCFE
Decrease in short-term debt, subtract from FCFE
Long-term debt
Add debt issuances to net income to arrive at FCFE
Subtract debt repurchases from net income to arrive at FCFE
Free Cash Flows with Preferred Stocks
For the most part, the discussion of FCFF and FCFE so far has assumed the company has a simple capital structure with two sources of capital, namely, debt and equity
Including preferred stock as a third source of capital requires the analyst to account for the dividends paid on preferred stock and for the issuance or repurchase of preferred shares
Usages of FCFs
Interesting Contrasts
Effects of Changing Leverage
An increase in leverage will not affect FCFF
Changing leverage (i.e. changing the amount of debt financing in the company's capital structure), does have some effects on FCFE particularly
An increase in leverage affects FCFE in two ways
In the year the debt is issued, it increases FCFE by the amount of debt issued
After the debt is issued, FCFE is then reduced by the after-tax interest expense
Estimations of FCFs
Approach one: forecast overall growth rate of FCFs
Calculate historical FCF
Estimate FCF for current period
Apply a constant growth rate to current FCF: FCF\times(1+g)^n
Usually, g_{FCFF}\ne g_{FCFE}
Approach two: forecast components of FCFs
Forecast each underlying component of FCFs
NI, NCC, FCInv and WCInv are tied to sales forecast
More realistic and flexible, but time consuming
Approach three: sales-based forecasting method
Investment in fixed capital in excess of depreciation (FCInv- Dep) and investment in working capital (WCInv) both bear a constant relationship to forecast increases in the size of the company as measured by increases in sales \frac{FCInv-Dep}{\Delta Sales} and \frac{WCInv}{\Delta Sales} will keep constant
Optimal capital structure represented by the debt ratio (DR) is constant DR=\frac{D}{D+E} will keep constant
Use FCFF when high or changing debt levels, negative FCFE
Single-stage, two or more stages?
Single-stage model for income stock(slow and constant growth)
More-stage models for whose competitive advantage will disappear over time
Total FCF or components of FCF?
Terminal value via GGM or Multiples?
Nominal or real?
International setting or volatile inflation rates: use real rates
Total value or value of the operating assets?
Free cash flow valuation focuses on the value of assets that generate operating cash flows
If a company has significant non-operating assets, such as excess cash, excess marketable securities, or land held for investment, then analysts often calculate the value of the firm as the value of its operating assets (as estimated by FCFF valuation) plus the value of its nonoperating assets
Sensitivity Analysis
Apply sensitivity to each of the following variables:
The base-year value for the FCFF or FCFE
Future growth rate
Risk factors: beta, risk free rate and ERP
Relationship between discount rate and the growth rate is critical In general
Most sensitive: Beta and growth rate of FCF
Less sensitive: r_f, and FCF.
Market-Based Valuation
Basic Concepts of Multiples
Introduction of Multiples
Price multiples are ratios of a stock's market price to some measure of fundamental value per share
The intuition is that investors evaluate the price of a stock by considering what a share buys in terms of per share earnings,net assets, cash flow, or some other measure of value
Enterprise value multiples relate the total market value of all sources of a company's capital to a measure of fundamental value for the entire company
Relative Valuation Method
The method of comparables (i.e. relative valuation method)involves using a multiple to evaluate whether an asset is relatively fairly valued, relatively undervalued, or relatively overvalued in relation to a benchmark value of the multiple
Choices for the benchmark include:
A closely matched individual stock
The average for peer group of companies or industry
Own history
The economic rationale for the methods of comparable is law of one price
Cross Border Valuation Differences
Comparing companies across borders frequently involves accounting method differences, cultural differences,economic differences, and resulting differences in risk and growth opportunities
For example, P/E ratios for individual companies in the same industry across borders have been found to vary widely
Justified Price Multiples
A justified price multiple (also called warranted price multiple or intrinsic price multiple) for the stock is the estimated fair value of multiples
Justified price multiples can be justified on the basis of 1) method of comparables or 2) method of forecasted fundamentals
Comparison
If actual price multiple = justified price multiple, then be properly valued
If actual price multiple < justified price multiple, then be undervalued
If actual price multiple > justified price multiple, then be overvalued
The method is based on forecasted fundamentals relates multiples to company fundamentals (growth, risk, payout) through DCF model, and may permit the analyst to explicitly examine how valuations differ across stocks and against a benchmark given different expectations for growth and risk
Price Multiples
PE ratio
Rationale and Drawbacks of PE ratio
Rationale for Using P/E Ratio
Earnings power is a chief driver of investment value
P/E ratio is widely recognized and used by investors
Differences in stock's P/Es may be related to differences in long-run average returns on investments in those stocks, according to empirical research
Potential Drawbacks of P/E Ratio
Negative and very low earnings make P/E useless
Volatile or transitory earnings make interpretation difficult
Management discretion on accounting choices can distort earnings
Solely using the ratio avoids addressing the fundamentals (growth, risk, and cash flows)
Trailing and Leading P/E Ratio
Trailing P/E_0 (a.k.a. current P/E), is stock's current market price divided by the last four quarters (or past 12 months) EPS
In such calculations, EPS is sometimes referred to as "trailing 12 month (TTM) EPS"
Leading P/E_1 (a.k.a. forward P/E or prospective P/E), is stock's current market price divided by next year's expected EPS
Analysts interpreted "next year's expected earnings" as expected EPS for:
next four quarters
next 12 months (NTM P/E)
next fiscal year
Problems with Trailing P/E Ratio
Transitory and non-recurring components of earnings are company-specific
Non-recurring earnings are needed to be removed because valuation focus on future cash flows, so we calculate underlying earnings (persistent earnings, continuing earnings, or core earnings)
Non-recurring items to remove include: Gains/losses on asset sales; Asset write-downs for impairment; Loss provisions; Changes in accounting estimates
Cyclicality components of earnings due to business or industry trends
The countercyclical property of P/E (Molodovsky Effect)
Analysts should calculate normalized EPS to remove cyclical component of earnings and capture mid-cycle earnings under normal market conditions
Differences in accounting methods
Potentialdilution of EPS
Normalized Earnings
Method 1: historical average EPS
Normalized EPS is the average EPS over the most recent full cycle
Method 2: average ROE
Normalized EPS is the average ROE from the most recent full cycle multiplied by current book value per share
Method 2 is preferred since it more accurately reflects the effect of growth in company size on EPS
Example
Justified P/E Ratio
Fundamental factors affecting justified P/E ratio
Justified P/E positively related to growth rate and payout ratio, "all else equal"
Justified P/E inversely related to required return (real rate, inflation and equity risk premium), "all else equal"
Terminal Value Estimation
Terminal value is the intrinsic value projected at end of estimation horizon
Using fundamentals: Requires estimates of g, r, and payout
Using comparables: Uses market data to calculate benchmark
Predicted P/E from Regression
The P/E ratios may be regressed against the stock and company characteristics
The estimated equation exhibits the relationship between P/E and stock's characteristics
Positive coefficient with growth rate and payout ratio
Negative coefficient with beta
Limitations of regression
The method captures valuation relationships only for the sample of stock over a particular time period, and the predictive power of the regression for a different stock and different time period is not know
The relationship between P/E and fundamentals may change over time
Multicollinearity(correlation within linear combinations of the independent variables)
P/E-to-Growth[PEG] Ratio
PEG ratio is calculated as the stock's P/E divided by the expected earnings growth rate (in percentage terms)
PEG ratio is a calculation of a stock's P/E per percentage point of expected growth
Stocks with lower PEGs are more attractive than stocks with higher PEGs, all else being equal
PEG is useful but must be used with care for several reasons
PEG assumes a linear relationship between P/E and growth rate
The model for P/E in terms of the DDM shows that, in theory, the relationship is not linear
PEG does not factor in differences in risk, an important determinant of P/E
= PEG does not account for differences in the duration of growth
For example, dividing P/Es by short-term growth forecasts may not capture differences in long-term growth prospects
Valuation Based on Comparables
Peer company multiples
The subject stock's P/E is compared with the median or mean P/E for the peer group to arrive at a relative valuation
Are observed differences between P/E ratios explained by underlying determinants of P/E?
If not, asset may be mispriced
Industry and sector multiples
Using industry and sector data can help an analyst explore whether the peer-group comparison assets are themselves appropriately priced
Own historical P/E
Analyst shall be alert to the impact on P/E levels of changes in a company's business mix and leverage overtime
Changes in the interest rate environment and economic fundamentals over different time period can be another limitations
Overall Market Multiples
The question of whether the overall market is fairly priced has captured analyst interest throughout the entire history of investing
Fed Model
The stock market is to be overvalued when the stock market's current earnings yield is less than the 10-year Treasury bond (T-bond) yield
Fed Model uses expected earnings for the next 12 months in calculating the ratio
Yardeni Model
Yardeni obtained the following expression for the justified P/E on the market
\frac{P}{E}=\frac{1}{C B Y-b \times L T E G}
CBY is current Moody's Investors Service A-rated corporate bond yield LTEG is the consensus five-year earnings growth rate forecast for market index b measures the weight the market gives to five-year earnings projections
Higher current corporate bond yield imply a lower justified P/E
Higher expected long-term growth results in a higher justified P/E
Earnings Yield and Dividend Yield
Ranking Stocks by P/E Ratio
Stock selection disciplines that use P/E ratios often involve ranking stocks
The security with the lowest positive P/E has the lowest purchase cost per currency unit of earnings among the securities ranked
Zero earnings and negative earnings pose a problem if the analyst wishes to use P/E as the valuation metric
Because division by zero is undefined, P/Es cannot be calculated for zero earnings
A "negative P/E security" will rank below the lowest positive P/E security, but the negative earning security is actually the most costly in terms of earnings purchased
Earnings Yield
If the analyst is interested in a ranking, however, one solution is the use of reciprocal of the original ratio, which places"price" in the denominator
In the case of the P/E, the inverse price ratio is earnings yield
Ranked by earnings yield from highest to lowest, the securities are correctly ranked from cheapest to most costly
In addition to zero and negative earnings, extremely low earnings can pose problems when using P/Es, particularly for evaluating the distribution of P/Es of a group of stocks under review. In this case, inverse price ratios can be useful
An extremely high P/E (an outlier P/E) can overwhelm the effect of the other P/Es in the calculation of the mean P/E
Although the use of median P/Es and other techniques can mitigate the problem of skewness caused by outliers, the distribution of inverse price ratios (earnings yield) is inherently less susceptible to outlier-induced skewness
Dividend Yield
Rationales for using dividend yield(D/P)
Dividend yield is a component of total return
Dividends are a less risky component of total return than capital appreciation
Drawbacks for using dividend yield(D/P)
Dividend yield is just one component of total return
Dividends paid now displace earnings in all future periods (dividend displacement of earnings)
Trailing dividend yield and Leading dividend yield
Trailing dividend yield is the dividend rate (annualized amount of the most recent dividend) divided by the current market price
Leading dividend yield is the forecasted dividends over the next year divided by the current market price
Justified Dividend Yield
Justified leading dividend yield
\frac{D_1}{V_0}=\frac{D_1}{\frac{D_1}{r-g}}=r-g
