Relative Valuation
Aswath Damodaran
What is relative valuation?
In relative valuation, the value of an asset is compared to the values assessed by the market for similar or comparable assets.
To do relative valuation then,
we need to identify comparable assets and obtain market values for these assets
convert these market values into standardized values, since the absolute prices cannot be compared This process of standardizing creates price multiples.
compare the standardized value or multiple for the asset being analyzed to the standardized values for comparable asset, controlling for any differences between the firms that might affect the multiple, to judge whether the asset is under or over valued
Relative valuation is pervasive…
Most valuations on Wall Street are relative valuations.
Almost 85% of equity research reports are based upon a multiple and comparables.
More than 50% of all acquisition valuations are based upon multiples
Rules of thumb based on multiples are not only common but are often the basis for final valuation judgments.
While there are more discounted cashflow valuations in consulting and corporate finance, they are often relative valuations masquerading as discounted cash flow valuations.
The objective in many discounted cashflow valuations is to back into a number that has been obtained by using a multiple.
The terminal value in a significant number of discounted cashflow valuations is estimated using a multiple.
Why relative valuation?
“If you think I’m crazy, you should see the guy who lives across the hall”
Jerry Seinfeld talking about Kramer in a Seinfeld episode
“ A little inaccuracy sometimes saves tons of explanation”
. Munro
“ If you are going to screw up, make sure that you have lots of company”
Ex-portfolio manager
So, you believe only in intrinsic value? Here is why you should still care about relative value
Even if you are a true believer in discounted cashflow valuation, presenting your findings on a relative valuation basis will make it more likely that your findings/recommendations will reach a receptive audience.
In some cases, relative valuation can help find weak spots in discounted cash flow valuations and fix them.
The problem with multiples is not in their use but in their abuse. If we can find ways to frame multiples right, we should be able to use them better.
Standardizing Value
You can standardize either the equity value of an asset or the value of the asset itself, which goes in the numerator.
You can standardize by dividing by the
Earnings of the asset
Price/Earnings Ratio (PE) and variants (PEG and Relative PE)
Value/EBIT
Value/EBITDA
Value/Cash Flow
Book value of the asset
Price/Book Value(of Equity) (PBV)
Value/ Book Value of Assets
Value/Replacement Cost (Tobin’s Q)
Revenues generated by the asset
Price/Sales per Share (PS)
Value/Sales
Asset or Industry Specific Variable (Price/kwh, Price per ton of steel ....)
The Four Steps to Understanding Multiples
Define the multiple
In use, the same multiple can be defined in different ways by different users. When comparing and using multiples, estimated by someone else, it is critical that we understand how the multiples have been estimated
Describe the multiple
Too many people who use a multiple have no idea what its cross sectional distribution is. If you do not know what the cross sectional distribution of a multiple is, it is difficult to look at a number and pass judgment on whether it is too high or low.
Analyze the multiple
It is critical that we understand the fundamentals that drive each multiple, and the nature of the relationship between the multiple and each variable.
Apply the multiple
Defining the comparable universe and controlling for differences is far more difficult in practice than it is in theory.
Definitional Tests
Is the multiple consistently defined?
Proposition 1: Both the value (the numerator) and the standardizing variable ( the denominator) should be to the same claimholders in the firm. In other words, the value of equity should be divided by equity earnings or equity book value, and firm value should be divided by firm earnings or book value.
Is the multiple uniformly estimated?
The variables used in defining the multiple should be estimated uniformly across assets in the “comparable firm” list.
If earnings-based multiples are used, the accounting rules to measure earnings should be applied consistently across assets. The same rule applies with book-value based multiples.
Descriptive Tests
What is the average and standard deviation for this multiple, across the universe (market)?
What is the median for this multiple?
The median for this multiple is often a more reliable comparison point.
How large are the outliers to the distribution, and how do we deal with the outliers?
Throwing out the outliers may seem like an obvious solution, but if the outliers all lie on one side of the distribution (they usually are large positive numbers), this can lead to a biased estimate.
Are there cases where the multiple cannot be estimated? Will ignoring these cases lead to a biased estimate of the multiple?
How has this multiple changed over time?
Analytical Tests
What are the fundamentals that determine and drive these multiples?
Proposition 2: Embedded in every multiple are all of the variables that drive every discounted cash flow valuation - growth, risk and cash flow patterns.
In fact, using a simple discounted cash flow model and basic algebra should yield the fundamentals that drive a multiple
How do changes in these fundamentals change the multiple?
The relationship between a fundamental (like growth) and a multiple (such as PE) is seldom linear. For example, if firm A has twice the growth rate of firm B, it will generally not trade at twice its PE ratio
Proposition 3: It is impossible to properly compare firms on a multiple, if we do not know the nature of the relationship between fundamentals and the multiple.
Application Tests
Given the firm that we are valuing, what is a “comparable” firm?
While traditional analysis is built on the premise that firms in the same sector are comparable firms, valuation theory would suggest that a comparable firm is one which is similar to the one being analyzed in terms of fundamentals.
Proposition 4: There is no reason why a firm cannot be compared with another firm in a very different business, if the two firms have the same risk, growth and cash flow characteristics.
Given the comparable firms, how do we adjust for differences across firms on the fundamentals?
Proposition 5: It is impossible to find an exactly identical firm to the one you are valuing.
Price Earnings Ratio: Definition
PE = Market Price per Share / Earnings per Share
There are a number of variants on the basic PE ratio in use. They are based upon how the price and the earnings are defined.
Price: is usually the current price
is sometimes the average price for the year
EPS: earnings per share in most recent financial year
earnings per share in trailing 12 months (Trailing PE)
forecasted earnings per share next year (Forward PE)
forecasted earnings per share in future year
Looking at the distribution…
PE: Deciphering the Distribution
Comparing PE Ratios: US, Europe, Japan and Emerging Markets - January 2005
Median PE
Japan =
US =
Europe =
Em. Mkts =
PE Ratios in Brazil - January 2006
PE Ratio: Understanding the Fundamentals
To understand the fundamentals, start with a basic equity discounted cash flow model.
With the dividend discount model,
Dividing both sides by the earnings per share,
If this had been a FCFE Model,
PE Ratio and Fundamentals
Proposition: Other things held equal, higher growth firms will have higher PE ratios than lower growth firms.
Proposition: Other things held equal, higher risk firms will have lower PE ratios than lower risk firms
Proposition: Other things held equal, firms with lower reinvestment needs will have higher PE ratios than firms with higher reinvestment rates.
Of course, other things are difficult to hold equal since high growth firms, tend to have risk and high reinvestment rats.
Using the Fundamental Model to Estimate PE For a High Growth Firm
The price-earnings ratio for a high growth firm can also be related to fundamentals. In the special case of the two-stage dividend discount model, this relationship can be made explicit fairly simply:
For a firm that does not pay what it can afford to in dividends, substitute FCFE/Earnings for the payout ratio.
Dividing both sides by the earnings per share:
Expanding the Model
In this model, the PE ratio for a high growth firm is a function of growth, risk and payout, exactly the same variables that it was a function of for the stable growth firm.
The only difference is that these inputs have to be estimated for two phases - the high growth phase and the stable growth phase.
Expanding to more than two phases, say the three stage model, will mean that risk, growth and cash flow patterns in each stage.
A Simple Example
Assume that you have been asked to estimate the PE ratio for a firm which has the following characteristics:
Variable High Growth Phase Stable Growth Phase
Expected Growth Rate 25% 8%
Payout Ratio 20% 50%
Beta
Number of years 5 years Forever after year 5
Riskfree rate = Rate = 6%
Required rate of return = 6% + 1(%)= %
PE and Growth: Firm grows at x% for 5 years, 8% thereafter
PE Ratios and Length of High Growth: 25% growth for n years; 8% thereafter
PE and Risk: Effects of Changing Betas on PE Ratio:
Firm with x% growth for 5 years; 8% thereafter
PE and Payout
I. Comparisons of PE across time: PE Ratio for the S&P 500
Is low (high) PE cheap (expensive)?
A market strategist argues that stocks are over priced because the PE ratio today is too high relative to the average PE ratio across time. Do you agree?
Yes
No
If you do not agree, what factors might explain the higher PE ratio today?
E/P Ratios , Rates and Term Structure
Regression Results
There is a strong positive relationship between E/P ratios and rates, as evidenced by the correlation of between the two variables.,
In addition, there is evidence that the term structure also affects the PE ratio.
In the following regression, using 1960-2005 data, we regress E/P ratios against the level of rates and a term structure variable ( - rate)
E/P = % + Rate - ( Rate) () () ()
R squared = %
II. Comparing PE Ratios across a Sector
PE, Growth and Risk
Dependent variable is: PE
R squared = % R squared (adjusted) = %
Variable Coefficient SE t-ratio prob
Constant
Growth rate ≤
Emerging Market
Emerging Market is a dummy: 1 if emerging market
0 if not
Is Telebras under valued?
Predicted PE = + (.075) - (1) =
At an actual price to earnings ratio of , Telebras is slightly overvalued.
Given the R-squared on the regression, though, a more precise statistical statement would be that the predicated PE for Telebras will fall within a range. In this case, the range would be as follows:
Upper end of the range:
Lower end of the range:
As a general rule, the higher the R-squared the narrower the range for the predicted values. The range will also tend to be tighter for firms that fall close to the average and become wider for extreme values.
Using the entire crosssection: A regression approach
In contrast to the 'comparable firm' approach, the information in the entire cross-section of firms can be used to predict PE ratios.
The simplest way of summarizing this information is with a multiple regression, with the PE ratio as the dependent variable, and proxies for risk, growth and payout forming the independent variables.
PE versus Growth
PE Ratio: Standard Regression for US stocks - January 2006
Problems with the regression methodology
The basic regression assumes a linear relationship between PE ratios and the financial proxies, and that might not be appropriate.
The basic relationship between PE ratios and financial variables itself might not be stable, and if it shifts from year to year, the predictions from the model may not be reliable.
The independent variables are correlated with each other. For example, high growth firms tend to have high risk. This multi-collinearity makes the coefficients of the regressions unreliable and may explain the large changes in these coefficients from period to period.
The Multicollinearity Problem
Using the PE ratio regression
Assume that you were given the following information for Dell. The firm has an expected growth rate of 10%, a beta of and pays no dividends. Based upon the regression, estimate the predicted PE ratio for Dell.
Predicted PE =
Dell is actually trading at 22 times earnings. What does the predicted PE tell you?
The value of growth
Time Period Value of extra 1% of growth Equity Risk Premium
January 2006 %
January 2005 %
January 2004 %
July 2003 %
January 2003 %
July 2002 %
January 2002 %
July 2001 %
January 2001 %
July 2000 %
January 2000 %
Brazil: Cross Sectional Regression
January 2006
Value/Earnings and Value/Cashflow Ratios
While Price earnings ratios look at the market value of equity relative to earnings to equity investors, Value earnings ratios look at the market value of the firm relative to operating earnings. Value to cash flow ratios modify the earnings number to make it a cash flow number.
The form of value to cash flow ratios that has the closest parallels in DCF valuation is the value to Free Cash Flow to the Firm, which is defined as:
Value/FCFF = (Market Value of Equity + Market Value of Debt-Cash)
EBIT (1-t) - (Cap Ex - Deprecn) - Chg in WC
Consistency Tests:
If the numerator is net of cash (or if net debt is used, then the interest income from the cash should not be in denominator
The interest expenses added back to get to EBIT should correspond to the debt in the numerator. If only long term debt is considered, only long term interest should be added back.
Value of Firm/FCFF: Determinants
Reverting back to a two-stage FCFF DCF model, we get:
V0 = Value of the firm (today)
FCFF0 = Free Cashflow to the firm in current year
g = Expected growth rate in FCFF in extraordinary growth period (first n years)
WACC = Weighted average cost of capital
gn = Expected growth rate in FCFF in stable growth period (after n years)
Value Multiples
Dividing both sides by the FCFF yields,
The value/FCFF multiples is a function of
the cost of capital
the expected growth
Value/FCFF Multiples and the Alternatives
Assume that you have computed the value of a firm, using discounted cash flow models. Rank the following multiples in the order of magnitude from lowest to highest?
Value/EBIT
Value/EBIT(1-t)
Value/FCFF
Value/EBITDA
What assumption(s) would you need to make for the Value/EBIT(1-t) ratio to be equal to the Value/FCFF multiple?
Illustration: Using Value/FCFF Approaches to value a firm: MCI Communications
MCI Communications had earnings before interest and taxes of $3356 million in 1994 (Its net income after taxes was $855 million).
It had capital expenditures of $2500 million in 1994 and depreciation of $1100 million; Working capital increased by $250 million.
It expects free cashflows to the firm to grow 15% a year for the next five years and 5% a year after that.
The cost of capital is % for the next five years and 10% after that.
The company faces a tax rate of 36%.
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Multiple Magic
In this case of MCI there is a big difference between the FCFF and short cut measures. For instance the following table illustrates the appropriate multiple using short cut measures, and the amount you would overpay by if you used the FCFF multiple.
Free Cash Flow to the Firm
= EBIT (1-t) - Net Cap Ex - Change in Working Capital
= 3356 (1 - ) + 1100 - 2500 - 250 = $ 498 million
$ Value Correct Multiple
FCFF $498
EBIT (1-t) $2,148
EBIT $ 3,356
EBITDA $4,456
Reasons for Increased Use of Value/EBITDA
1. The multiple can be computed even for firms that are reporting net losses, since earnings before interest, taxes and depreciation are usually positive.
2. For firms in certain industries, such as cellular, which require a substantial investment in infrastructure and long gestation periods, this multiple seems to be more appropriate than the price/earnings ratio.
3. In leveraged buyouts, where the key factor is cash generated by the firm prior to all discretionary expenditures, the EBITDA is the measure of cash flows from operations that can be used to support debt payment at least in the short term.
4. By looking at cashflows prior to capital expenditures, it may provide a better estimate of “optimal value”, especially if the capital expenditures are unwise or earn substandard returns.
5. By looking at the value of the firm and cashflows to the firm it allows for comparisons across firms with different financial leverage.
Value/EBITDA Multiple
The Classic Definition
The No-Cash Version
When cash and marketable securities are netted out of value, none of the income from the cash and securities should be reflected in the denominator.
Enterprise Value/EBITDA Distribution - US
EV/EBITDA Multiple: Brazil in January 2006
The Determinants of Value/EBITDA Multiples: Linkage to DCF Valuation
Firm value can be written as:
The numerator can be written as follows:
FCFF = EBIT (1-t) - (Cex - Depr) - Working Capital
= (EBITDA - Depr) (1-t) - (Cex - Depr) - Working Capital
= EBITDA (1-t) + Depr (t) - Cex - Working Capital
From Firm Value to EBITDA Multiples
Now the Value of the firm can be rewritten as,
Dividing both sides of the equation by EBITDA,
A Simple Example
Consider a firm with the following characteristics:
Tax Rate = 36%
Capital Expenditures/EBITDA = 30%
Depreciation/EBITDA = 20%
Cost of Capital = 10%
The firm has no working capital requirements
The firm is in stable growth and is expected to grow 5% a year forever.
Calculating Value/EBITDA Multiple
In this case, the Value/EBITDA multiple for this firm can be estimated as follows:
Value/EBITDA Multiples and Taxes
Value/EBITDA and Net Cap Ex
Value/EBITDA Multiples and Return on Capital
Value/EBITDA Multiple: Trucking Companies
A Test on EBITDA
Ryder System looks very cheap on a Value/EBITDA multiple basis, relative to the rest of the sector. What explanation (other than misvaluation) might there be for this difference?
US Market: Cross Sectional Regression
January 2006
Price-Book Value Ratio: Definition
The price/book value ratio is the ratio of the market value of equity to the book value of equity, ., the measure of shareholders’ equity in the balance sheet.
Price/Book Value = Market Value of Equity
Book Value of Equity
Consistency Tests:
If the market value of equity refers to the market value of equity of common stock outstanding, the book value of common equity should be used in the denominator.
If there is more that one class of common stock outstanding, the market values of all classes (even the non-traded classes) needs to be factored in.
Book Value Multiples: US stocks
Book Value Multiples: Brazil
Price Book Value Ratio: Stable Growth Firm
Going back to a simple dividend discount model,
Defining the return on equity (ROE) = EPS0 / Book Value of Equity, the value of equity can be written as:
If the return on equity is based upon expected earnings in the next time period, this can be simplified to,
PBV/ROE: European Banks
PBV versus ROE regression
Regressing PBV ratios against ROE for banks yields the following regression:
PBV = + (ROE) R2 = 46%
For every 1% increase in ROE, the PBV ratio should increase by .
Under and Over Valued Banks?
Looking for undervalued securities - PBV Ratios and ROE : The Valuation Matrix
Price to Book vs ROE: US companies in January 2005
PBV Matrix: Telecom Companies
PBV, ROE and Risk: Large Cap US firms
PBV versus ROE: Brazilian companies in January 2006
IBM: The Rise and Fall and Rise Again
PBV Ratio Regression: US
January 2006
PBV Regression: Brazil in January 2006
Price Sales Ratio: Definition
The price/sales ratio is the ratio of the market value of equity to the sales.
Price/ Sales= Market Value of Equity
Total Revenues
Consistency Tests
The price/sales ratio is internally inconsistent, since the market value of equity is divided by the total revenues of the firm.
Revenue Multiples: US stocks
Revenue Multiples: Brazil
Price/Sales Ratio: Determinants
The price/sales ratio of a stable growth firm can be estimated beginning with a 2-stage equity valuation model:
Dividing both sides by the sales per share:
PS/Margins: European Retailers - September 2003
Regression Results: PS Ratios and Margins
Regressing PS ratios against net margins,
PS = + (Net Margin) R2 = %
Thus, a 1% increase in the margin results in an increase of in the price sales ratios.
The regression also allows us to get predicted PS ratios for these firms
Current versus Predicted Margins
One of the limitations of the analysis we did in these last few pages is the focus on current margins. Stocks are priced based upon expected margins rather than current margins.
For most firms, current margins and predicted margins are highly correlated, making the analysis still relevant.
For firms where current margins have little or no correlation with expected margins, regressions of price to sales ratios against current margins (or price to book against current return on equity) will not provide much explanatory power.
In these cases, it makes more sense to run the regression using either predicted margins or some proxy for predicted margins.
A Case Study: The Internet Stocks
PS Ratios and Margins are not highly correlated
Regressing PS ratios against current margins yields the following
PS = - (Net Margin) R2 =
()
This is not surprising. These firms are priced based upon expected margins, rather than current margins.
Solution 1: Use proxies for survival and growth: Amazon in early 2000
Hypothesizing that firms with higher revenue growth and higher cash balances should have a greater chance of surviving and becoming profitable, we ran the following regression: (The level of revenues was used to control for size)
PS = - ln(Rev) + (Rev Growth) + (Cash/Rev)
() () ()
R squared = %
Predicted PS = - () + () + (.3069) =
Actual PS =
Stock is undervalued, relative to other internet stocks.
Solution 2: Use forward multiples
Global Crossing lost $ billion in 2001 and is expected to continue to lose money for the next 3 years. In a discounted cashflow valuation (see notes on DCF valuation) of Global Crossing, we estimated an expected EBITDA for Global Crossing in five years of $ 1,371 million.
The average enterprise value/ EBITDA multiple for healthy telecomm firms is currently.
Applying this multiple to Global Crossing’s EBITDA in year 5, yields a value in year 5 of
Enterprise Value in year 5 = 1371 * = $9,871 million
Enterprise Value today = $ 9,871 million/ = $5,172 million
(The cost of capital for Global Crossing is %)
The probability that Global Crossing will not make it as a going concern is 77%.
Expected Enterprise value today = (5172) = $1,190 million
PS Regression: United States - January 2006
EV/Sales Regression: Brazil in January 2006
Choosing Between the Multiples
As presented in this section, there are dozens of multiples that can be potentially used to value an individual firm.
In addition, relative valuation can be relative to a sector (or comparable firms) or to the entire market (using the regressions, for instance)
Since there can be only one final estimate of value, there are three choices at this stage:
Use a simple average of the valuations obtained using a number of different multiples
Use a weighted average of the valuations obtained using a nmber of different multiples
Choose one of the multiples and base your valuation on that multiple
Picking one Multiple
This is usually the best way to approach this issue. While a range of values can be obtained from a number of multiples, the “best estimate” value is obtained using one multiple.
The multiple that is used can be chosen in one of two ways:
Use the multiple that best fits your objective. Thus, if you want the company to be undervalued, you pick the multiple that yields the highest value.
Use the multiple that has the highest R-squared in the sector when regressed against fundamentals. Thus, if you have tried PE, PBV, PS, etc. and run regressions of these multiples against fundamentals, use the multiple that works best at explaining differences across firms in that sector.
Use the multiple that seems to make the most sense for that sector, given how value is measured and created.
A More Intuitive Approach
Managers in every sector tend to focus on specific variables when analyzing strategy and performance. The multiple used will generally reflect this focus. Consider three examples.
In retailing: The focus is usually on same store sales (turnover) and profit margins. Not surprisingly, the revenue multiple is most common in this sector.
In financial services: The emphasis is usually on return on equity. Book Equity is often viewed as a scarce resource, since capital ratios are based upon it. Price to book ratios dominate.
In technology: Growth is usually the dominant theme. PEG ratios were invented in this sector.
In Practice…
As a general rule of thumb, the following table provides a way of picking a multiple for a sector
Sector Multiple Used Rationale
Cyclical Manufacturing PE, Relative PE Often with normalized earnings
High Tech, High Growth PEG Big differences in growth across firms
High Growth/No Earnings PS, VS Assume future margins will be good
Heavy Infrastructure VEBITDA Firms in sector have losses in early years and reported earnings can vary
depending on depreciation method
REITa P/CF Generally no cap ex investments
from equity earnings
Financial Services PBV Book value often marked to market
Retailing PS If leverage is similar across firms
VS If leverage is different
Reviewing: The Four Steps to Understanding Multiples
Define the multiple
Check for consistency
Make sure that they are estimated uniformly
Describe the multiple
Multiples have skewed distributions: The averages are seldom good indicators of typical multiples
Check for bias, if the multiple cannot be estimated
Analyze the multiple
Identify the companion variable that drives the multiple
Examine the nature of the relationship
Apply the multiple
Real Options: Fact and Fantasy
Aswath Damodaran
Underlying Theme: Searching for an Elusive Premium
Traditional discounted cashflow models under estimate the value of investments, where there are options embedded in the investments to
Delay or defer making the investment (delay)
Adjust or alter production schedules as price changes (flexibility)
Expand into new markets or products at later stages in the process, based upon observing favorable outcomes at the early stages (expansion)
Stop production or abandon investments if the outcomes are unfavorable at early stages (abandonment)
Put another way, real option advocates believe that you should be paying a premium on discounted cashflow value estimates.
A Real Option Premium
In the last few years, there are some who have argued that discounted cashflow valuations under valued some companies and that a real option premium should be tacked on to DCF valuations. To understanding its moorings, compare the two trees below:
A bad investment………………….. Becomes a good one..
1. Learn at relatively low cost
2. Make better decisions based on learning
Three Basic Questions
When is there a real option embedded in a decision or an asset?
When does that real option have significant economic value?
Can that value be estimated using an option pricing model?
When is there an option embedded in an action?
An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (called a strike price or an exercise price) at or before the expiration date of the option.
There has to be a clearly defined underlying asset whose value changes over time in unpredictable ways.
The payoffs on this asset (real option) have to be contingent on an specified event occurring within a finite period.
Payoff Diagram on a Call
Price of underlying asset
Strike
Price
Net Payoff
on Call
Example 1: Product Patent as an Option
Present Value of Expected
Cash Flows on Product
PV of Cash Flows
from Project
Initial Investment in
Project
Project has negative
NPV in this section
Project's NPV turns
positive in this section
Example 2: Undeveloped Oil Reserve as an option
Value of estimated reserve of natural resource
Net Payoff on
Extraction
Cost of Developing
Reserve
Example 3: Expansion of existing project as an option
Present Value of Expected
Cash Flows on Expansion
PV of Cash Flows
from Expansion
Additional Investment
to Expand
Firm will not expand in
this section
Expansion becomes
attractive in this section
When does the option have significant economic value?
For an option to have significant economic value, there has to be a restriction on competition in the event of the contingency. In a perfectly competitive product market, no contingency, no matter how positive, will generate positive net present value.
At the limit, real options are most valuable when you have exclusivity - you and only you can take advantage of the contingency. They become less valuable as the barriers to competition become less steep.
Exclusivity: Putting Real Options to the Test
Product Options: Patent on a drug
Patents restrict competitors from developing similar products
Patents do not restrict competitors from developing other products to treat the same disease.
Natural Resource options: An undeveloped oil reserve or gold mine.
Natural resource reserves are limited.
It takes time and resources to develop new reserves
Growth Options: Expansion into a new product or market
Barriers may range from strong (exclusive licenses granted by the government - as in telecom businesses) to weaker (brand name, knowledge of the market) to weakest (first mover).
Determinants of option value
Variables Relating to Underlying Asset
Value of Underlying Asset; as this value increases, the right to buy at a fixed price (calls) will become more valuable and the right to sell at a fixed price (puts) will become less valuable.
Variance in that value; as the variance increases, both calls and puts will become more valuable because all options have limited downside and depend upon price volatility for upside.
Expected dividends on the asset, which are likely to reduce the price appreciation component of the asset, reducing the value of calls and increasing the value of puts.
Variables Relating to Option
Strike Price of Options; the right to buy (sell) at a fixed price becomes more (less) valuable at a lower price.
Life of the Option; both calls and puts benefit from a longer life.
Level of Interest Rates; as rates increase, the right to buy (sell) at a fixed price in the future becomes more (less) valuable.
The Building Blocks for Option Pricing Models: Arbitrage and Replication
The objective in creating a replicating portfolio is to use a combination of riskfree borrowing/lending and the underlying asset to create the same cashflows as the option being valued.
Call = Borrowing + Buying D of the Underlying Stock
Put = Selling Short D on Underlying Asset + Lending
The number of shares bought or sold is called the option delta.
The principles of arbitrage then apply, and the value of the option has to be equal to the value of the replicating portfolio.
The Binomial Option Pricing Model
The Limiting Distributions….
As the time interval is shortened, the limiting distribution, as t -> 0, can take one of two forms.
If as t -> 0, price changes become smaller, the limiting distribution is the normal distribution and the price process is a continuous one.
If as t->0, price changes remain large, the limiting distribution is the poisson distribution, ., a distribution that allows for price jumps.
The Black-Scholes model applies when the limiting distribution is the normal distribution , and explicitly assumes that the price process is continuous and that there are no jumps in asset prices.
The Black Scholes Model
Value of call = S N (d1) - K e-rt N(d2)
where,
d2 = d1 - √t
The replicating portfolio is embedded in the Black-Scholes model. To replicate this call, you would need to
Buy N(d1) shares of stock; N(d1) is called the option delta
Borrow K e-rt N(d2)
The Normal Distribution
When can you use option pricing models to value real options?
The notion of a replicating portfolio that drives option pricing models makes them most suited for valuing real options where
The underlying asset is traded - this yield not only observable prices and volatility as inputs to option pricing models but allows for the possibility of creating replicating portfolios
An active marketplace exists for the option itself.
The cost of exercising the option is known with some degree of certainty.
When option pricing models are used to value real assets, we have to accept the fact that
The value estimates that emerge will be far more imprecise.
The value can deviate much more dramatically from market price because of the difficulty of arbitrage.
Valuing a Product Patent as an option: Avonex
Biogen, a bio-technology firm, has a patent on Avonex, a drug to treat multiple sclerosis, for the next 17 years, and it plans to produce and sell the drug by itself. The key inputs on the drug are as follows:
PV of Cash Flows from Introducing the Drug Now = S = $ billion
PV of Cost of Developing Drug for Commercial Use = K = $ billion
Patent Life = t = 17 years Riskless Rate = r = % (17-year rate)
Variance in Expected Present Values =s2 = (Industry average firm variance for bio-tech firms)
Expected Cost of Delay = y = 1/17 = %
d1 = N(d1) =
d2 = N(d2) =
Call Value= 3,422 exp()(17) () - 2,875 (exp()(17) ()= $ 907 million
Valuing an Oil Reserve
Consider an offshore oil property with an estimated oil reserve of 50 million barrels of oil, where the cost of developing the reserve is $ 600 million today.
The firm has the rights to exploit this reserve for the next twenty years and the marginal value per barrel of oil is $12 per barrel currently (Price per barrel - marginal cost per barrel). There is a 2 year lag between the decision to exploit the reserve and oil extraction.
Once developed, the net production revenue each year will be 5% of the value of the reserves.
The riskless rate is 8% and the variance in ln(oil prices) is .
Valuing an oil reserve as a real option
Current Value of the asset = S = Value of the developed reserve discounted back the length of the development lag at the dividend yield = $12 * 50 /()2 = $
(If development is started today, the oil will not be available for sale until two years from now. The estimated opportunity cost of this delay is the lost production revenue over the delay period. Hence, the discounting of the reserve back at the dividend yield)
Exercise Price = Present Value of development cost = $12 * 50 = $600 million
Time to expiration on the option = 20 years
Variance in the value of the underlying asset =
Riskless rate =8%
Dividend Yield = Net production revenue / Value of reserve = 5%
Valuing the Option
Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = N(d1) =
d2 = N(d2) =
Call Value= 544 .22 exp()(20) () -600 (exp()(20) ()= $ million
This oil reserve, though not viable at current prices, still is a valuable property because of its potential to create value if oil prices go up.
Extending this concept, the value of an oil company can be written as the sum of three values:
Value of oil company = Value of developed reserves (DCF valuation)
+ Value of undeveloped reserves (Valued as option)
An Example of an Expansion Option
Ambev is considering introducing a soft drink to the . market. The drink will initially be introduced only in the metropolitan areas of the . and the cost of this “limited introduction” is $ 500 million.
A financial analysis of the cash flows from this investment suggests that the present value of the cash flows from this investment to Ambev will be only $ 400 million. Thus, by itself, the new investment has a negative NPV of $ 100 million.
If the initial introduction works out well, Ambev could go ahead with a full-scale introduction to the entire market with an additional investment of $ 1 billion any time over the next 5 years. While the current expectation is that the cash flows from having this investment is only $ 750 million, there is considerable uncertainty about both the potential for the drink, leading to significant variance in this estimate.
Valuing the Expansion Option
Value of the Underlying Asset (S) = PV of Cash Flows from Expansion to entire . market, if done now =$ 750 Million
Strike Price (K) = Cost of Expansion into entire market = $ 1000 Million
We estimate the standard deviation in the estimate of the project value by using the annualized standard deviation in firm value of publicly traded firms in the beverage markets, which is approximately %.
Standard Deviation in Underlying Asset’s Value = %
Time to expiration = Period for which expansion option applies = 5 years
Call Value= $ 234 Million
One final example: Equity as a Liquidatiion Option
Application to valuation: A simple example
Assume that you have a firm whose assets are currently valued at $100 million and that the standard deviation in this asset value is 40%.
Further, assume that the face value of debt is $80 million (It is zero coupon debt with 10 years left to maturity).
If the ten-year treasury bond rate is 10%,
how much is the equity worth?
What should the interest rate on debt be?
Valuing Equity as a Call Option
Inputs to option pricing model
Value of the underlying asset = S = Value of the firm = $ 100 million
Exercise price = K = Face Value of outstanding debt = $ 80 million
Life of the option = t = Life of zero-coupon debt = 10 years
Variance in the value of the underlying asset = 2 = Variance in firm value =
Riskless rate = r = Treasury bond rate corresponding to option life = 10%
Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = N(d1) =
d2 = N(d2) =
Value of the call = 100 () - 80 exp()(10) () = $ million
Value of the outstanding debt = $100 - $ = $ million
Interest rate on debt = ($ 80 / $)1/10 -1 = %
The Effect of Catastrophic Drops in Value
Assume now that a catastrophe wipes out half the value of this firm (the value drops to $ 50 million), while the face value of the debt remains at $ 80 million. What will happen to the equity value of this firm?
It will drop in value to $ million [ $ 50 million - market value of debt from previous page]
It will be worth nothing since debt outstanding > Firm Value
It will be worth more than $ million
Valuing Equity in the Troubled Firm
Value of the underlying asset = S = Value of the firm = $ 50 million
Exercise price = K = Face Value of outstanding debt = $ 80 million
Life of the option = t = Life of zero-coupon debt = 10 years
Variance in the value of the underlying asset = 2 = Variance in firm value =
Riskless rate = r = Treasury bond rate corresponding to option life = 10%
The Value of Equity as an Option
Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = N(d1) =
d2 = N(d2) =
Value of the call = 50 () - 80 exp()(10) () = $ million
Value of the bond= $50 - $ = $ million
The equity in this firm drops by, because of the option characteristics of equity.
This might explain why stock in firms, which are in Chapter 11 and essentially bankrupt, still has value.
Equity value persists ..
Obtaining option pricing inputs in the real worlds
Valuing Equity as an option - Eurotunnel in early 1998
Eurotunnel has been a financial disaster since its opening
In 1997, Eurotunnel had earnings before interest and taxes of -£56 million and net income of -£685 million
At the end of 1997, its book value of equity was -£117 million
It had £8,865 million in face value of debt outstanding
The weighted average duration of this debt was years
Debt Type Face Value Duration
Short term 935
10 year 2435
20 year 3555
Longer 1940
Total £8,865 mil years
The Basic DCF Valuation
The value of the firm estimated using projected cashflows to the firm, discounted at the weighted average cost of capital was £2,312 million.
This was based upon the following assumptions –
Revenues will grow 5% a year in perpetuity.
The COGS which is currently 85% of revenues will drop to 65% of revenues in yr 5 and stay at that level.
Capital spending and depreciation will grow 5% a year in perpetuity.
There are no working capital requirements.
The debt ratio, which is currently %, will drop to 70% after year 5. The cost of debt is 10% in high growth period and 8% after that.
The beta for the stock will be for the next five years, and drop to after the next 5 years.
The long term bond rate is 6%.
Other Inputs
The stock has been traded on the London Exchange, and the annualized std deviation based upon ln (prices) is 41%.
There are Eurotunnel bonds, that have been traded; the annualized std deviation in ln(price) for the bonds is 17%.
The correlation between stock price and bond price changes has been . The proportion of debt in the capital structure during the period (1992-1996) was 85%.
Annualized variance in firm value
= ()2 ()2 + ()2 ()2 + 2 () ()()()()=
The 15-year bond rate is 6%. (I used a bond with a duration of roughly 11 years to match the life of my option)
Valuing Eurotunnel Equity and Debt
Inputs to Model
Value of the underlying asset = S = Value of the firm = £2,312 million
Exercise price = K = Face Value of outstanding debt = £8,865 million
Life of the option = t = Weighted average duration of debt = years
Variance in the value of the underlying asset = 2 = Variance in firm value =
Riskless rate = r = Treasury bond rate corresponding to option life = 6%
Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = N(d1) =
d2 = N(d2) =
Value of the call = 2312 () - 8,865 exp()() () = £122 million
Appropriate interest rate on debt = (8865/2190)(1/)-1= %
Back to Lemmings...
These are the three ingredients you find in almost every equity research report - comparables, a multiple (or standardized price) and a story (which represents the attempt to control for differences).
Relative valuations are everywhere and most valuations are relative valuations.
Most valuations that you see are relative valuations. There are two reasons why relative valuations are so popular:
If your objective is to buy or sell something, not matter what the price, you can justify your decision using relative valuation. There will always be some other assets out there which are more underpriced or overpriced than the asset you are buying or selling.
In contrast to the detail and time needed for discounted cashflow valuation, relative valuation is quicker and seems to require fewer assumptions about the future. (This, we will argue, is really an illusion.)
Even if you believe that discounted cashflow valuation is the only way to go, learning the language of relative valuation can be useful.
The distinction between price (representing equity value) and value (representing the combined market value of equity and debt) and enterprise value (representing firm value - cash and marketable securities) should be noted.
The last set of multiples - industry specific multiples - will vary depending upon the sector you look at. With power companies, it can take the form of market value of the firm/ kwh of power produced. With new economy companies in the late 1990s, this was taken to whole new levels of detail - value per subscriber, value per web site visitor….
While we can rail about the fact that a valuation based upon multiples is not as detailed as a discounted cashflow valuation,, the reality is that analysts will continue to use multiples to value companies and that we will often have to use these valuations.
Given this reality, we have to think about how best to use multiples. These four steps represent a way in which we can deconstruct any multiple, understand how to use it well and discover when it is being misused.
Consistent definition:
Consider two widely used multiples that are consistently defined. In the price-earnings ratio (PE), the numerator is equity value per share and the denominator is equity earnings per share. In the enterprise value/ EBITDA multiple, the numerator is firm value and the denominator is a pre-tax cash flow to all claimholders in the firm. In contrast, the price to EBITDA multiple is inconsistent. Why is this a problem? If you are comparing firms with different debt ratios, the firms will more debt will look cheaper on a price to EBITDA basis.
Uniformally Estimated:
This is actually much more difficult than it looks. Even if accounting standards are the same across firms, you run into two problems:
The degree to which firms bend accounting rules for their own purposes varies across firms. Some firms are inherently more conservative in reporting earnings than others.
The financial year ends at different points for different firms. If the denominator is the earnings in the most recent financial year, the multiple may not be comparable if some firms have December year-ends and some have June year-ends.
Before you use a multiple and develop rules of thumb (8 times EBITDA is cheap), you need to get a sense of the cross-sectional distribution.
Multiples have skewed distributions. Because a multiple cannot be less than zero but can potentially be infinite, the averages for multiples will be much higher than their medians, and the difference will increase as the outliers become larger. Many services cap outliers to prevent them from altering the averages too much, results…
The PE ratio cannot be estimated when the earnings per share are negative. Thus, if you have a sample of 20 firms and 10 have negative earnings, you will be able to compute the PE ratio for only the 10 that have positive earnings and will throw out the remaining firms. This will induce a bias in your sample. One way to avoid this is to take the cumulative values for market capitalization and net income for all 20 firms, and compute a PE ratio based upon the cumulated values. The resulting PE ratio will generally be much higher….
Behind every multiple (PE of 22, Value to EBITDA of 9) are implicit assumptions about growth, risk and cash flows.. In fact, you make the same assumptions when you use multiples that you make in discounted cashflow valuation.. The difference is that your assumptions are explicit in the latter. The first step in understanding a multiple is determining its fundamental drives…
Not only is it important that you find the drivers for each multiple, but you need to understand how changes in these drivers change the multiple. For example, we all accept the intuition that a company with a 20% growth rate should have a higher PE than an otherwise similar company with a 10% growth rate, but how much higher? Twice as high (which would make the relationship linear), times as high, times as high…
In practice, we all too often define comparable as a firm in the same industry or business. This is too narrow a definition. You can have firms in different businesses that have similar cashflow, growth and risk characteristics. These firms can be viewed as comparable firms.
You will never find two identical firms, no matter how hard you search. You therefore have to always control for the residual differences when making comparisons.
This is only the tip of the iceberg. You can have EPS before and after extraordinary items, primary and diluted EPS..
When you are negotiating with someone else and you are both using PE ratios to make your case, the first step is to make sure that you are using the same PE ratio.
There is also the tendency on the part of analysts to pick the definition of pE that best fits their biases. For instance, bullish analysts in the 1990s almost always used forward PE whereas bearish analysts used trailing PE. Since earnings were rising the former were generally much lower than the latter.
This graph for all . firms with data available on the Value Line CD ROM (contains about 7200 firms in the overall sample). Notice that the distributions are skewed to the left and that we have capped the PE ratios at 100….
Four things to note…
Notice the number of firms that we have lost in the sample as we compute PE ratios.
You lose even more firms as you go to forward PE, because you need analyst estimates of expected earnings per share to compute this. Any firms not followed by analysts will not have a forward PE…
The means were computed without capping the PE ratios… the outliers (notice the maximum values for the ratios) push the average to almost twice the median.
The median forward PE is higher than the trailing PE which is higher than the current PE…
This compares the percentages of firms in each market that trade in each PE ratio class… Some interesting differences:
More emerging market companies trade at very low PE ratios (less than 8) than European or US companies
More emerging market companies also trade at very high multiples of earnings.
The median PE ratio is lowest in emerging markets, reflecting the effect of country risk on PE.
To get to the heart of equity multiples, we start with an equity DCF model. In this case, we consider the simplest equity valuation model - a stable growth dividend discount model. Restated in terms of the PE ratio, we find that the PE ratio fo a stable growth firm can be written in terms of three variables:
The expected growth rate in earnings per share
The riskiness of the equity, which determines the cost of equity
The efficiency with which the firm generates growth,which is measured by how much the firm can pay out or afford to pay out after reinvested to create the growth.
At first sight, the second proposition may seem counter intuitive. After all, riskiest firms often have the highest PE ratios. The answer lies, of course, in the reality that firms with high risk also tend to have high growth, and growth usually trumps risk….
The value of a stock in a two-stage dividend discount model is the sum of two present values:
The present value of dividends during the high growth phase - this is the first term in the equation above. It is the present value of a growing annuity. (There is no constraint on the growth rate. In fact, this equation will yield the present value of a growing annuity even if g>r… the denominator will become negative but so will the numerator)
The present value of the terminal price… this is the second term in the equation…
The PE ratio for a high growth firm is a function of the same three variables that determine the PE ratio for a stable growth firm, though you have to estimate the parameters twice, once for the high growth phase and once for the stable growth phase.
The PE ratio for a firm can be stated in terms of growth, risk and payout over each phase of a n-period model… there are no additional variables that show up.
For a firm with these characteristics, times earnings is a fair price to pay. In fact, if you valued this firm using a dividend discount model, you would get the identical value per share.
As expected growth in the high growth period increases, the PE ratio increases, but the change in PE ratio for a given change in the growth rate is much greater when interest rates are low than when they are high. The reason is simple. The value of growth is a present value… If interest rates rise, the present value of growth decreases.
If you consider that expected growth rates in earnings usually change as a result of an earnings surprise, this would suggest that a stock’s price and PE ratio will be most sensitive to earnings surprises when interest rates are low than when they are high.
As you lengthen the growth period, the PE ratio increases but it increases more when the expected growth rate during the period is a high number than when it is lower… The length of the growth period is a function of competitive advantages. This would indicate that you should be much more informed about a firm’s competitive position and aware of the potential slippage in this position when you are investing in a high growth company than when you are investing in a low growth company.
As risk increases, PE ratios fall, not matter what the expected growth rate. At very high risk (or perceived risk), the PE ratio becomes relatively insensitive to changes in the growth rate. A manager of a high-growth, high risk firm (say a growth rate of 20% and a beta of 2) will get a much bigger payoff to reducing risk than increasing growth.
Note that this assumes that growth is held constant. The only way you can increase payout, holding growth constant, is to increase the return on equity:
Growth rate = (1 - Payout ratio) ROE
Thus, this graph could have been drawn in terms of the ROE. Higher return on equity companies will have higher PE ratios than lower ROE companies with the same expected growth rate in earnings. Consider it the payoff to quality growth.
The graph of PE ratios for the S&P 500 show an increasing PE ratio over time… The PE ratio in 1999 was clearly much higher than PE ratios over the prior two decades…
Not necessarily. There are other possible explanations, that relate back to the fundamentals that determine PE:
Discount rate: The discount rate applied to earnings and cashflows may be lower - this can occur either because
interest rates were lower in 2003 than they were in the 1980s
Investors may have perceived that equities were less risky and demanded a lower risk premium (there are related stories including the influx of pension fund money into stocks)
b. Expected Growth: By 1999, higher-growth technology firms like Cisco and Microsoft were a much larger segment of the S&P 500. The expected growth rate in earnings for stocks in the index would therefore be higher.. In 2003, the explanation might have been that earnings growth is usually healthy as companies come out of a recession.
c. More Efficient Growth: . stocks did increase the returns on their investments during the 1990s. This would translate into the capacity to return more cash to stockholders while maintaining growth…
Graphs out the inverse of the PE ratios (the earnings to price ratio or the earnings yield), the 10-year treasury bond rate and the difference between the 10-year rate and the 6-month rate. Even without any statistical analysis, the earnings yield and interest rates are highly correlated.
The regression yields the following conclusions:
Every 1% increase in the treasury bond rate increases the earnings yield by % (an increase in the earnings yield lowers the PE ratio). The effect on the PE ratio will therefore depend upon whether the rate is increasing from 4% to 5% (the effect will be much larger) or from 9% to 10%..
Every 1% increase in the difference between long term and short term rates decreases the earnings yield by % (and increases PE ratios). As the yield curve becomes more upward sloping, expectations of real economic growth generally increase. This variable may therefore be a proxy fore economic growth. Higher growth translates into higher PE ratios.
In this sample, note that some of the firms in the sample are emerging market firms any may be exposed to more risk (political risk, economic risk, inflation risk…)
Higher growth telecomm companies have higher PE ratios..
One way to read this regression: If you have two companies - one with a growth rate of 10% and one with a growth rate of 20%, the latter should have a PE that is higher..
If the firm happens to be an emerging market firm, though, you would expect its PE ratio to be lower than a firm with similar growth in a developed market.
With a % growth rate and being an emerging market company, Telebras is overvalued slightly, even though it has a low PE ratio.
There is information in how the market prices all firms that can be used to value any firm in that market.
The expected growth rate is the consensus estimate of growth in earnings per share over the next 5 years - this is available from services like Zacks and I/B/E/S.
The relationship between PE and expected growth is positive - the line fit through is the regression line - but it is noisy… The band represents one standard error from the regression line of PE versus growth…
This regression has about 2500 firms. While the low R-squared may be troubling, it should not be unexpected, given the scatter plot on the previous page.
The signs of the coefficients are consistent with our priors for growth and higher growth have higher PE ratios. With risk and payout, though, the sign on the coefficient is wrong. Higher risk and lower payout firms firms seems to have higher (instead of lower) PE ratios.
Three problems with the regression. Each is fixable to some degree or the other.
You can either transform the variables (use the natural log of growth rates) to make the relationship linear or run non-linear regressions.
You can update the regressions frequently to allow for the instability in the coefficients.
You can use statistical techniques to minimize the effect of multi-collinearity.
In a multiple regression, the independent variables should be uncorrelated with each other - the correlations should be zero between growth and beta, growth and payout, payout and beta… As the correlation matrix above indicates, this is not always the case.
Plugging into the regression on page 48, we get
Predicted PE for Dell = + (10) + () - (0) =
At 22 times earnings, Dell is slightly undervalued, given how the market is pricing other stocks and Dell’s fundamentals.
However, note that the prediction from the regression comes with a range (which will be large because of the low R-squared). In fact, the regression prediction with 95% confidence is that Dell’s true PE lies between 19 and 29…
The coefficient on the expected growth rate tells you something about how the market values growth and the scarcity of growth. Clearly, the value attached to growth decreased from January 2000 to July 2002. If you consider the implied equity risk premium as what you believe that the market charges for an extra unit of risk, you can see that a high growth, high risk firm will be valued very differently in July 2002 than in January 2000.
How would you explain the uptick in 2003? On one level, it may indicate that the slide in value for growth stocks has stopped. The other is that growth had become a scarcer resource (fewer companies have high expected growth rates) and the market is pricing it higher.
Confirms our priors, looking at the entire market in September 2002.. Higher growth and return on capital result in higher value to EBITDA multiples… A lower tax rate increases the EBITDA multiple as well…
In contrast to price multiples, you look at firm or enterprise value when you compute value multiples. Firm value is the market value of equity + market value of debt. Enterprise value = Firm value - cash. Why would you use one as opposed to the other? When we compute value to earnings multiples, the earnings that are used tend to be operating earnings (EBIT, EBITDA etc.). Since the income from cash and marketable securities is not included in operating income, we exclude it from the numerator as well.
The most logical denominator for enterprise value is the free cashflow to the firm, which is the cashflow prior to debt payments but after taxes and reinvestment needs.
To investigate the determinants of the value to FCFF, we go back to a firm valuation model (rather than an equity valuation model).
This is a two-stage FCFF model - the first term in the equation is the present value of FCFF during the high growth phase and the second term is the present value of the terminal value…
Dividing both sides by the FCFF, we obtain the determinants of the free cashflow to the firm. In summary, the value to FCFF multiple is determined by the cost of capital and expected growth in FCFF.
For most firms, the ranking should be as follows:
Value to EBITDA
Value to EBIT
Value to EBIT (1-t)
Value to FCFF
Only if net cap ex and working capital is zero will EBIT (1-t) = FCFF.
Based upon the estimates of expected growth (15% for next 5 years and 5% thereafter) and the cost of capital (% for next 5 years and 10% thereafter), times FCFF would have been a fair value for MCI… Odds are, though, that most potential buyers would have viewed that as too high a multiple to pay for a company like MCI…
A little sleight of hand can create magic… Here, we keep value fixed while altering the denominator. As we move from FCFF to EBIT(1-t) to EBIT to EBITDA, the multiple drops and the firm (irrational though it might seem) starts looking more and more attractive to buyers…
Why does this happen? It is because we do not have a frame of reference. We tend to have a frame of reference only on PE ratios - we tend to know what is high, low or average - and not on EBITDA multiples. When presented with EBITDA multiples,we tend to compare the value ( in this case) to PE ratios that we have seen before… Not surprisingly, firms often look cheap on an EBITDA multiple.
The use of EBITDA multiples is relatively new in acquisitions. It acquired a foothold in the mid-1980s with leveraged buyouts but has acquired a large number of adherents since. The growth of cable, cellular and telecommunications companies may explain some of this…
The problem with using firm value is that cash is included in the numerator but not in the denominator. That is why the enterprise value version makes more sense…
A broad problem is posed when firms have holdings in other firms. If such holdings are passive, Value to EBITDA multiples will be overstated, since the numerator will include the value of your holdings, while the EBITDA will not include any of the income from these holdings. If such holdings are majority active and consolidated, the value to EBITDA will be understated because the numerator will include only the portion of the equity you own in the subsidiary but the EBITDA will include all of the EBITDA in the subsidiary.
The safest thing to do (assuming you can do this) is to net out the market value of your holdings from the numerator (for both active and passive holdings) and the EBITDA of your holdings from the denominator ( for majority active holdings)
As with the other multiples, a heavily skewed distribution. Suggests that the rule of thumb that is often used by Wall Street (EBITDA multiple less than 8 is cheap) should be used with caution.
Distribution looks very similar to the distribution in the US…
To delve into the fundamentals that determine EBITDA multiples, we return to a FCFF valuation model. We keep things simple by using a stable growth model.
The enterprise value to EbITDA multiple is a function of
The tax rate: Higher tax rates -> Lower multiple
Net Capital Expenditures and reinvestment (for any given growth rate): Higher net cap ex and reinvestment -> Lower multiple
Cost of capital: Higher cost of capital -> Lower multiple
Growth: Lower growth -> Lower multiple
A hypothetical firm. Note that I am making assumptions about the reinvestment rate and growth rate. Implicitly, I am also making assumptions about the return on capital. In fact, I am assuming (whether I want to or not) that my return on capital will be %. Note that the return on capital implied in this growth rate can be calculated as follows:
g = ROC * Reinvestment Rate
.05 = ROC * Net Cap Ex/EBIT (1-t)
= ROC * (.)/[()()]
Solving for ROC, ROC = %
If this firm were fairly valued, it should trade at times EBITDA.
As the tax rate increases, the value to EBITDA multiples drop. The implications are
When comparing firms across markets with different tax rates, you would expect companies in countries with lower tax rates to trade at higher multiples. Thus, Deutsche Telecom’s EBITDA multiple will be lower than that of other European telecomm firms because the German tax rate is higher.
A firm with a large net operating loss carry-forward should trade at a higher multiple of EBITDA than n otherwise similar firm without this carry-forward.
Note that this keeps growth fixed and changed reinvestment. Firms that reinvest more to get the same growth (. have less efficient growth) will trade at lower multiples of EBITDA.
If you increase reinvestment while keeping growth fixed, you are are assuming that the return on capital decreases. This graph essentially fills in the story begun by the previous one. The greater the return spread (ROC - Cost of capital) earned by a firm, the higher the EBITDA multiple.
Trucking companies have fleets that they replace every few years. Thus, the capital expenditures for these firms are often discontinuous, with a year of very heavy cap ex followed by a few years of almost no cap ex…
It could well be that Ryder Systems has the oldest fleet in this group. In that case, the firm may look cheap right now but it will soon have to make a large capital expenditure to replace the fleet.
(While cap ex is discontinuous, depreciation and amortization are smoothed out…)
Confirms our priors, looking at the entire market. Note that growth is defined as growth in revenues rather than growth in net income because we are looking at enterprise value and not equity value.
Your definitions of equity in the numerator and denominator should be consistent… this may require the breaking down of book equity if there are multiple classes of shares outstanding.
If you have a class of shares that is non-traded, you have two choices. You can ignore this in computing market equity and take out a proportional shares of the book equity. Alternatively, you can estimate a value for the non-traded shares and add them to the market value of traded shares to arrive at a total market value of equity. It is generally not a good idea to include preferred stock in either the numerator or denominator.
The median is about half the mean… You do lose some firms (those with negative book equity) but not as many as you do with earnings multiples.
A larger portion of stocks trade at below book value in Europe than do in the United States. An even large proportion trade at below book value in emerging markets, but there are also far more outliers with very high PBV ratios.
Following a familiar route.. The price to book ratio is an equity multiple and you go back to an equity valuation model…
The price to book ratio is determined by the three variables that determine the PE ratio (growth, payout and risk) and one variable that is unique to it (the return on equity)
Every multiple has one variable that can be considered its key determinant - its companion variable, so to speak. For PE, it was growth.. For Value/EBITDA, it was the reinvestment rate. For price to book, it is return on equity.
Presents the mismatches in a matrix. You want to buy stocks in lower right quadrant and sell the stocks in the upper left quadrant… A hedge fund?
Looks at the 100 largest market cap firms in the United States… Shows how strong the link is between price to book and return on equity. With a 90% confidence interval, a handful of stocks fall outside the range, but there may be good reasons for each:
The two stocks that fall below the undervalued line are MO (Altria or Philip Morris) and FNMA (because of recent accounting and management scandals.
Above the overvalued line are the high flyers - EBAY, Dell, SAP where presumable investors expect the return on equity to climb over time and high growth to continue…
The most undervalued firms are all emerging market telecomm firms.. The implicit assumption we make about companies all being equally risk may be inappropriate here.
You could create a three dimensional graph with risk on the third axis. An undervalued firm would then be one with low price to book, high return on equity and low risk.
Graphs out the largest US market cap firms on a three dimensional graph with risk being the third dimension…
You could also try growth as the third dimension…
Shows another way in which you can play the price to book/ ROE relationship. A company with a low (high) price to book and low (high) return on equity may be fairly valued at a point in time, but if the return on equity changes, the price to book ratio will change. If you can call these turnarounds well, you can ride the price to book ratio up ..Consider the payoff to buying IBM right after took over as CEO in 1991…
Again, we stick with the variables that determine price to book ratios.. ROE is by far the dominant variable explaining PBV ratios…
Also, note the jump in R-squared. This is to be expected since the book value of equity now shows up on both sides of the equation (in PBV and ROE)
Lower R squared should be expected since the companies in this sample are much more diverse with different degrees of country risk. ROE continues to be the dominant variable explaining differences in PBV across companies but the payoff to having a higher ROE is even lower than in Europe.
The problem with this ratio is that revenues belong to the entire firm rather than just the equity investors in the firm.
Perhaps the most skewed of all multiples….
Revenue multiples vary the most across firms. The distribution is skewed but has multiple peaks, reflecting the fact that the same revenue can deliver different values in different sectors.
The key determinant of the price to sales ratio is the net margin.. The other 3 determinants - payout, growth and cost of equity - are common to all equity multiples.
Eyeballing the data.. Lower price to sales ratio firms tend to have low net margins and higher price to sales ratio firms tend to have high margins..
The R-squared could be improved by adding other variables (growth and risk, for example) to this regression.
From March 2000… Little or no relationship between current margins and price to sales ratios.. Note that almost all of the firms have negative margins…
The lack of the relationship in the graph is borne out by the regression. Not only is the R-squared low, but the relationship between price to sales ratio and net margins is negative - the more negative the margin, the higher the price to sales ratio.
Internet firms with higher revenues, higher revenue growth and more cash holdings trade for higher price to sales ratios in March 2000.
If you plug the values for Amazon in March 2000 into this regression, you get a predicted value of , whereas the actual price to sales ratio for the firm is . Relative to other internet stocks, Amazon is slightly undervalued. (In the discounted cashflow valuation done at the same point in time, we came to the opposite conclusion. Amazon was overvalued based upon its fundamentals.)
The conclusions can vary though both approaches have some intuitive appeal. The one thing that you cannot do is to be inconsistent. You cannot apply a current multiple to future earnings and not discount…
A regression for the entire market…. Again, net margin is the dominant variable determining price to sales ratio. The R-squared of this regression is much higher than the earlier regressions using earnings and book value…
The coefficient on net margin is much lower in Europe….
When doing relative valuation, you can choose between potentially a dozen or more multiples. With each multiple, you will estimate a different value for your firm, leaving you with the unenviable task of reconciling these values.
This is my preferred approach. Pick one multiple, but which one will depend upon what you view your objective to be.
Relate the multiples to what managers in a sector think about and focus on the most..
Not a set of iron-clad rules, but more rules of thumb…
Reviews the four basic steps in relative valuation.
This looks at the option to delay a project, to which you have exclusive rights.
The initial investment in the project is what you would need to invest to convert this project from a right to a real project.
The present value of the cash flows will change over time.
If the perceived present value of the cash flows stays below the investment needed, the project should never be taken.
Here, the initial project gives you the option to invest an additional amount in the future which you will do only if the present value of the additional cash flows you will get by expanding are greater than the investment needed.
For this to work, you have to do the first project to be eligible for the option to expand.
This is a negative net present value project, but it gives Disney the option to expand later. Implicitly, we are also saying that if Disney does not make the initial project investment (with a NPV of - $ 20 million), it cannot expand later into the rest of Latin America.
This values the option, using the Black Scholes model.
The value from the model itself is affected not only by the assumptions made about volatility and value, but also by the asssumptions underlying the model.
The value itself is not the key output from the model. It is the fact that strategic options, such as this one, can be valued, and that they can make a significant difference to your decision.
