Option Pricing Theory and Applications

Aswath Damodaran www.damodaran.com Aswath Damodaran Some Initial Thoughts " One hundred thousand lemmings cannot be wrong" Graffiti Aswath Damodaran Misconceptions about Valuation Myth 1: A valuation is an objective search for true value Myth 2.: A good valuation provides a precise estimate of value Truth 1.1: All valuations are biased. The only questions are how much and in which

direction. Truth 1.2: The direction and magnitude of the bias in your valuation is directly proportional to who pays you and how much you are paid. Truth 2.1: There are no precise valuations Truth 2.2: The payoff to valuation is greatest when valuation is least precise. Myth 3: . The more quantitative a model, the better the valuation Aswath Damodaran Truth 3.1: Ones understanding of a valuation model is inversely proportional to the number of inputs required for the model. Truth 3.2: Simpler valuation models do much better than complex ones. Approaches to Valuation Discounted cashflow valuation, relates the value of an asset to the present value of expected future cashflows on that asset. Relative valuation, estimates the value of an asset by looking at the pricing of 'comparable' assets relative to a common variable like

earnings, cashflows, book value or sales. Contingent claim valuation, uses option pricing models to measure the value of assets that share option characteristics. Aswath Damodaran Discounted Cash Flow Valuation What is it: In discounted cash flow valuation, the value of an asset is the present value of the expected cash flows on the asset. Philosophical Basis: Every asset has an intrinsic value that can be estimated, based upon its characteristics in terms of cash flows, growth and risk. Information Needed: To use discounted cash flow valuation, you need to estimate the life of the asset to estimate the cash flows during the life of the asset

to estimate the discount rate to apply to these cash flows to get present value Market Inefficiency: Markets are assumed to make mistakes in pricing assets across time, and are assumed to correct themselves over time, as new information comes out about assets. Aswath Damodaran DCF Choices: Equity Valuation versus Firm Valuation Firm Valuation: Value the entire business A ssets E x is tin g In v e s tm e n ts G e n e ra te c a s h flo w s to d a y In c lu d e s lo n g liv e d (fix e d ) a n d s h o rt-liv e d (w o rk in g c a p ita l) a s s e ts E x p e c te d V a lu e th a t w ill b e c re a te d b y fu tu re in v e s tm e n ts L ia b ilities A s s e ts in P la c e D ebt G ro w th A s s e ts E q u ity

F ix e d C la im o n c a s h flo w s L ittle o r N o ro le in m a n a g e m e n t F i x e d M a tu r i ty T a x D e d u c ti b l e R e s id u a l C la im o n c a s h flo w s S ig n ific a n t R o le in m a n a g e m e n t P e r p e tu a l L i v e s Equity valuation: Value just the equity claim in the business Aswath Damodaran The Drivers of Value Growth fromnew investments Growth created by making new investments; function of amount and quality of investments Effi ciency Growth Growth generated by using existing assets better

Terminal Value of firm (equity) Current Cashflows These are the cash flows from existing investment,s, net of any reinvestment needed to sustain future growth. They can be computed before debt cashflows (to the firm) or after debt cashflows (to equity investors). Expected Growth during high growth period Length of the high growth period Since value creating growth requires excess returns, this is a function of - Magnitude of competitive advantages - Sustainability of competitive advantages Cost of financing (debt or capital) to apply to discounting cashflows Determined by - Operating risk of the company - Default risk of the company - Mix of debt and equity used in financing Aswath Damodaran

Stable growth firm, with no or very limited excess returns Aswath Damodaran Aswath Damodaran Aswath Damodaran 1 Aswath Damodaran 1 Aswath Damodaran 1 Aswath Damodaran 1 I. Measure earnings right..

Aswath Damodaran 1 Operating Leases at Amgen in 2007 Amgen has lease commitments and its cost of debt (based on its A rating) is 5.63%. Year 1 2 3 4 5 6-12 Debt Value of leases = Commitment $96.00 $95.00 $102.00 $98.00

$87.00 $107.43 Present Value $90.88 $85.14 $86.54 $78.72 $66.16 $462.10 ($752 million prorated) $869.55 Debt outstanding at Amgen = $7,402 + $ 870 = $8,272 million Adjusted Operating Income = Stated OI + Lease exp this year - Depreciation = 5,071 m + 69 m - 870/12 = $5,068 million (12 year life for assets) Approximate Operating income= $5,071 m + 870 m (.0563) = $ 5,120 million Aswath Damodaran 1 Capitalizing R&D Expenses: Amgen R & D was assumed to have a 10-year life. Year R&D Expense Unamortized portion Amortization this year

Current 3366.00 1.00 3366.00 -1 2314.00 0.90 2082.60 $231.40 -2 2028.00 0.80 1622.40 $202.80 -3 1655.00 0.70 1158.50 $165.50 -4 1117.00 0.60 670.20 $111.70 -5 865.00 0.50

432.50 $86.50 -6 845.00 0.40 338.00 $84.50 -7 823.00 0.30 246.90 $82.30 -8 663.00 0.20 132.60 $66.30 -9 631.00 0.10 63.10 $63.10 -10 558.00 0.00 0.00 $55.80

Value of Research Asset = $10,112.80 $1,149.90 Adjusted Operating Income = $5,120 + 3,366 - 1,150 = $7,336 million Aswath Damodaran 1 II. Get the big picture (not the accounting one) when it comes to cap ex and working capital Capital expenditures should include Research and development expenses, once they have been re-categorized as capital expenses. Acquisitions of other firms, whether paid for with cash or stock. Working capital should be defined not as the difference between

current assets and current liabilities but as the difference between noncash current assets and non-debt current liabilities. On both items, start with what the company did in the most recent year but do look at the companys history and at industry averages. Aswath Damodaran 1 Amgens Net Capital Expenditures If we define capital expenditures broadly to include R&D and acquisitions: Accounting Capital Expenditures = - Accounting Depreciation = Accounting Net Cap Ex = Net R&D Cap Ex = (3366-1150) = Acquisitions in 2006 = Total Net Capital Expenditures = $1,218 million $ 963 million $ 255 million $2,216 million $3,975 million

$ 6,443 million Acquisitions have been a volatile item. Amgen was quiet on the acquisition front in 2004 and 2005 and had a significant acquisition in 2003. Aswath Damodaran 1 III. Betas do not come from regressions Aswath Damodaran 1 Carry much noise Aswath Damodaran 2 Look better for some companies, but looks can be deceptive Aswath Damodaran

2 Bottom-up Betas Aswath Damodaran 2 Two examples Amgen Tata Motors The unlevered beta for pharmaceutical firms is 1.59. Using Amgens debt to equity ratio of 11%, the bottom up beta for Amgen is Bottom-up Beta = 1.59 (1+ (1-.35)(.11)) = 1.73 The unlevered beta for automobile firms is 0.98. Using Tata Motors debt to equity

ratio of 33.87%, the bottom up beta for Tata Motors is Bottom-up Beta = 0.98 (1+ (1-.3399)(.3387)) = 1.20 A Question to ponder: Tata Motors recently made two big investments. Tata Nano: Promoted as the cheapest car in the world, Tata Motors hopes that volume (especially in Asia) will make up for tight margins. Jaguar/Land Rover: Tata acquired both firms, catering to luxury markets. What effect will these investments have on Tata Motors beta? Aswath Damodaran 2 B. The Historical Risk Premium Evidence from the United States 1928-2011 1962-2011 2002-2011 Arithmetic Average Geometric Average Stocks - T. Bills Stocks - T. Bonds Stocks - T. Bills Stocks - T. Bonds 7.55% 5.79%

5.62% 4.10% 2.22% 2.36% 5.38% 3.36% 4.02% 2.35% 2.39% 2.68% 3.12% -1.92% 1.08% -3.61% 6.46% 8.94% What is the right premium? Go back as far as you can. Otherwise, the standard error in the estimate will be large. Std Error in estimate = Annualized Std deviation in Stock prices ) Number of years of historical data

Be consistent in your use of a riskfree rate. Use arithmetic premiums for one-year estimates of costs of equity and geometric premiums for estimates of long term costs of equity. Aswath Damodaran 2 IV. And the past is not always a good indicator of the future It is standard practice to use historical premiums as forward looking premiums. : 1928-2011 1962-2011 2002-2011 Arithmetic Average Geometric Average Stocks - T. Bills Stocks - T. Bonds Stocks - T. Bills Stocks - T. Bonds 7.55% 5.79% 5.62%

4.10% 2.22% 2.36% 5.38% 3.36% 4.02% 2.35% 2.39% 2.68% 3.12% -1.92% 1.08% -3.61% 6.46% 8.94% An alternative is to back out the premium from market prices: Aswath Damodaran 2 Implied Premiums in the US: 1960-2010 Aswath Damodaran 2

The Anatomy of a Crisis: Implied ERP from September 12, 2008 to January 1, 2009 Aswath Damodaran 2 Implied Premium for India using the Sensex: April 2010 Level of the Index = 17559 FCFE on the Index = 3.5% (Estimated FCFE for companies in index as % of market value of equity) Other parameters Riskfree Rate = 5% (Rupee) Expected Growth (in Rupee) Next 5 years = 20% (Used expected growth rate in Earnings) After year 5 = 5%

Solving for the expected return: Aswath Damodaran Expected return on Equity = 11.72% Implied Equity premium for India =11.72% - 5% = 6.72% 2 V. There is a downside to globalization Emerging markets offer growth opportunities but they are also riskier. If we want to count the growth, we have to also consider the risk. Two ways of estimating the country risk premium: Default spread on Country Bond: In this approach, the country equity risk premium is set equal to the default spread of the bond issued by the country. Equity Risk Premium for mature market = 4.5% Equity Risk Premium for India = 4.5% + 3% = 7.5%

Adjusted for equity risk: The country equity risk premium is based upon the volatility of the equity market relative to the government bond rate. Country risk premium= Default Spread* Country Equity / Country Bond Standard Deviation in Sensex = 30% Standard Deviation in Indian government bond= 20% Default spread on Indian Bond= 3% Total equity risk premium for India = 4.5% + 3% (30/20) = 9% Aswath Damodaran 2 Country Risk Premiums January 2012 Canada United States of America Argentina Belize Bolivia Brazil Chile Colombia Costa Rica Ecuador El Salvador

Guatemala Honduras Mexico Nicaragua Panama Paraguay Peru Uruguay Venezuela Aswath Damodaran 6.00% 6.00% 15.00% 15.00% 12.00% 8.63% 7.05% 9.00% 9.00% 18.75% 10.13% 9.60% 13.50% 8.25%

15.00% 9.00% 12.00% 9.00% 9.60% 12.00% Austria [1] Belgium [1] Cyprus [1] Denmark Finland [1] France [1] Germany [1] Greece [1] Iceland Ireland [1] Italy [1] Malta [1] Netherlands [1] Norway Portugal [1] Spain [1] Sweden Switzerland United Kingdom

Angola Botswana Egypt Mauritius Morocco Namibia South Africa Tunisia 6.00% 7.05% 9.00% 6.00% 6.00% 6.00% 6.00% 9.00% 9.00% 9.60% 7.50% 7.50% 6.00% 6.00% 10.13% 7.28% 6.00% 6.00%

6.00% 10.88% 7.50% 13.50% 8.63% 9.60% 9.00% 7.73% 9.00% Albania Armenia Azerbaijan Belarus Bosnia and Herzegovina Bulgaria Croatia Czech Republic Estonia Georgia Hungary Kazakhstan Latvia Lithuania Moldova

Montenegro Poland Romania Russia Slovakia Slovenia [1] Ukraine Bahrain Israel Jordan Kuwait Lebanon Oman Qatar Saudi Arabia Senegal United Arab Emirates 12.00% 10.13% 9.60% 15.00% 13.50% 8.63% 9.00% 7.28% 7.28%

10.88% 9.60% 8.63% 9.00% 8.25% 15.00% 10.88% 7.50% 9.00% 8.25% 7.28% 7.28% 13.50% 8.25% 7.28% 10.13% 6.75% 12.00% 7.28% 6.75% 7.05% 12.00% 6.75% Bangladesh Cambodia China

Fiji Islands Hong Kong India Indonesia Japan Korea Macao Malaysia Mongolia Pakistan Papua New Guinea Philippines Singapore Sri Lanka Taiwan Thailand Turkey Vietnam Australia New Zealand 10.88% 13.50% 7.05% 12.00% 6.38%

9.00% 9.60% 7.05% 7.28% 7.05% 7.73% 12.00% 15.00% 12.00% 10.13% 6.00% 12.00% 7.05% 8.25% 10.13% 12.00% 6.00% 6.00% 3 VI. And it is not just emerging market companies that are exposed to this risk.. If we treat country risk as a separate risk factor and allow firms to have different exposures to country risk (perhaps based upon the proportion of

their revenues come from non-domestic sales) E(Return)=Riskfree Rate+ (US premium) + Country ERP) The easiest and most accessible data is on revenues. Most companies break their revenues down by region. One simplistic solution would be to do the following: % of revenues domesticallyfirm/ % of revenues domesticallyavg firm Consider two firms Tata Motors and Tata Consulting Services. In 2008-09, Tata Motors got about 91.37% of its revenues in India and TCS got 7.62%. The average Indian firm gets about 80% of its revenues in India: Tata Motors = 91%/80% = 1.14 TCS = 7.62%/80% = 0.09 There are two implications A companys risk exposure is determined by where it does business and not by where it is located Firms might be able to actively manage their country risk exposures Aswath Damodaran 3 Estimating lambdas: Tata Motors versus TCS

Tata Motors % of production/operations in India % of revenues in India Lambda Flexibility in moving operations Aswath Damodaran TCS High High 91.37% (in 2009) Estimated 70% (in 2010) 7.62% 0.80 0.20

Low. Significant physical assets. High. Human capital is mobile. 3 VII. Discount rates can (and often should) change over time The inputs into the cost of capital - the cost of equity (beta), the cost of debt (default risk) and the debt ratio - can change over time. For younger firms, they should change over time. At the minimum, they should change when you get to your terminal year to inputs that better reflect a mature firm. Aswath Damodaran 3 VIII. Growth has to be earned (not endowed or estimated)

Aswath Damodaran 3 IX. All good things come to an end..And the terminal value is not an ATM Aswath Damodaran 3 Terminal Value and Growth Aswath Damodaran 3 X. The loose ends matter Aswath Damodaran 3 1. The Value of Cash An Exercise in Cash Valuation Enterprise Value

Cash Return on Capital Cost of Capital Trades in Company A $ 1 billion $ 100 mil 10% 10% US Company B $ 1 billion $ 100 mil 5% 10% US Company C $ 1 billion $ 100 mil 22% 12% Argentina In which of these companies is cash most likely to trade at face value, at a

discount and at a premium? Aswath Damodaran 3 Cash: Discount or Premium? Aswath Damodaran 3 2. Dealing with Holdings in Other firms Holdings in other firms can be categorized into Minority passive holdings, in which case only the dividend from the holdings is shown in the balance sheet Minority active holdings, in which case the share of equity income is shown in the income statements Majority active holdings, in which case the financial statements are consolidated.

We tend to be sloppy in practice in dealing with cross holdings. After valuing the operating assets of a firm, using consolidated statements, it is common to add on the balance sheet value of minority holdings (which are in book value terms) and subtract out the minority interests (again in book value terms), representing the portion of the consolidated company that does not belong to the parent company. Aswath Damodaran 4 How to value holdings in other firms.. In a perfect world.. In a perfect world, we would strip the parent company from its subsidiaries and value each one separately. The value of the combined firm will be Value of parent company + Proportion of value of each subsidiary To do this right, you will need to be provided detailed information on each subsidiary to estimated cash flows and discount rates.

Aswath Damodaran 4 Two compromise solutions The market value solution: When the subsidiaries are publicly traded, you could use their traded market capitalizations to estimate the values of the cross holdings. You do risk carrying into your valuation any mistakes that the market may be making in valuation. The relative value solution: When there are too many cross holdings to value separately or when there is insufficient information provided on cross holdings, you can convert the book values of holdings that you have on the balance sheet (for both minority holdings and minority interests in majority holdings) by using the average price to book value ratio of the sector in which the subsidiaries operate. Aswath Damodaran 4 Tata Motors Cross Holdings

Aswath Damodaran 4 3. Other Assets that have not been counted yet.. Unutilized assets: If you have assets or property that are not being utilized (vacant land, for example), you have not valued it yet. You can assess a market value for these assets and add them on to the value of the firm. Overfunded pension plans: If you have a defined benefit plan and your assets exceed your expected liabilities, you could consider the over funding with two caveats: Collective bargaining agreements may prevent you from laying claim to these excess assets. There are tax consequences. Often, withdrawals from pension plans get taxed at much higher rates. Do not double count an asset. If you count the income from an asset in your cashflows, you cannot count the market value of the asset in your value. Aswath Damodaran 4

4. A Discount for Complexity: An Experiment Company A Company B Operating Income $ 1 billion $ 1 billion Tax rate 40% 40% ROIC 10% 10% Expected Growth 5% 5% Cost of capital 8% 8% Business Mix Single Business Multiple Businesses Holdings Simple Complex Accounting Transparent Opaque

Which firm would you value more highly? Aswath Damodaran 4 Measuring Complexity: Volume of Data in Financial Statements Company General Electric Microsoft Wal-mart Exxon Mobil Pfizer Citigroup Intel AIG Johnson & Johnson IBM Aswath Damodaran Number of pages in last 10Q 65 63 38

86 171 252 69 164 63 85 Number of pages in last 10K 410 218 244 332 460 1026 215 720 218 353 4 Item Operating Income Measuring Complexity: A Complexity Score

Factors 1. Multiple Businesses 2. One-time income and expenses 3. Income from unspecified sources 4. Items in income statement that are volatile Tax Rate 1. Income from multiple locales 2. Different tax and reporting books 3. Headquarters in tax havens 4. Volatile effective tax rate Capital Expenditures 1. Volatile capital expenditures 2. Frequent and large acquisitions 3. Stock payment for acquisitions and investments Working capital 1. Unspecified current assets and current liabilities 2. Volatile working capital items Expected Growth rate 1. Off-balance sheet assets and liabilities (operating leases and R&D) 2. Substantial stock buybacks 3. Changing return on capital over time 4. Unsustainably high return Cost of capital

Follow-up Question Number of businesses (with more than 10% of revenues) = Percent of operating income = Percent of operating income = Gerdau Score GE Score 1 10% 0% 2.00 10.00 10.00 2 1 0 30 0.8 1.2 Percent of operating income =

Percent of revenues from non-domestic locales = Yes or No Yes or No Yes or No Yes or No Yes or No 15% 70% No No Yes Yes Yes 5.00 3.00 Yes=3 Yes=3 Yes=2 Yes=2 Yes=4 0.75 2.1 0 0

2 2 4 1 1.8 3 0 0 2 4 Yes or No No Yes=4 0 4 Yes or No Yes or No No Yes

Yes=3 Yes=2 0 2 0 2 Yes or No Yes or No Is your return on capital volatile? Is your firm's ROC much higher than industry average? Number of businesses (more than 10% of revenues) = Percent of revenues= Yes or No Yes or No No No Yes Yes=3 Yes=3 Yes=5

0 0 5 3 3 5 No 1 50% No Yes Yes=5 1.00 5.00 No=2 No=2 0 1 2.5 2 0

0 20 2.5 0 0 No 0% 63% Yes 0% Yes=5 20.00 20.00 Yes = 10 10.00 0 0 12.6 10 0 48.95 5 0.8

1.2 0 0.25 90.55 1. Multiple businesses 2. Operations in emerging markets 3. Is the debt market traded? 4. Does the company have a rating? 5. Does the company have off-balance sheet debt? Yes or No No-operating assets Minority holdings as percent of book assets Minority holdings as percent of book assets Firm to Equity value Consolidation of subsidiaries Minority interest as percent of book value of equity Per share value Shares with different voting rights Does the firm have shares with different voting rights? Equity options outstanding Options outstanding as percent of shares Complexity Score = Aswath Damodaran Answer Weighting factor 4

Dealing with Complexity In Discounted Cashflow Valuation The Aggressive Analyst: Trust the firm to tell the truth and value the firm based upon the firms statements about their value. The Conservative Analyst: Dont value what you cannot see. The Compromise: Adjust the value for complexity Adjust cash flows for complexity Adjust the discount rate for complexity Adjust the expected growth rate/ length of growth period Value the firm and then discount value for complexity In relative valuation In a relative valuation, you may be able to assess the price that the market is charging for complexity: With the hundred largest market cap firms, for instance: PBV = 0.65 + 15.31 ROE 0.55 Beta + 3.04 Expected growth rate 0.003 # Pages in 10K Aswath Damodaran

4 5. The Value of Synergy Aswath Damodaran 4 Valuing Synergy (1) the firms involved in the merger are valued independently, by discounting expected cash flows to each firm at the weighted average cost of capital for that firm. (2) the value of the combined firm, with no synergy, is obtained by adding the values obtained for each firm in the first step. (3) The effects of synergy are built into expected growth rates and cashflows, and the combined firm is re-valued with synergy. Value of Synergy = Value of the combined firm, with synergy - Value of the combined firm, without synergy Aswath Damodaran 5 Valuing Synergy: P&G + Gillette Free Cashflow to Equity Growth rate for first 5 years

Growth rate after five years Beta Cost of Equity Value of Equity Aswath Damodaran P&G Gillette Piglet: No Synergy Piglet: Synergy $5,864.74 $1,547.50 $7,412.24 $7,569.73 Annual operating expenses reduced by $250 million 12% 10% 11.58% 12.50% Slighly higher growth rate 4% 4% 4.00% 4.00% 0.90 0.80 0.88

0.88 7.90% 7.50% 7.81% 7.81% Value of synergy $221,292 $59,878 $281,170 $298,355 $17,185 5 6. Brand name, great management, superb product Are we short changing the intangibles? There is often a temptation to add on premiums for intangibles. Among them are

Brand name Great management Loyal workforce Technological prowess There are two potential dangers: For some assets, the value may already be in your value and adding a premium will be double counting. For other assets, the value may be ignored but incorporating it will not be easy. Aswath Damodaran 5 Valuing Brand Name Current Revenues = Length of high-growth period Reinvestment Rate = Operating Margin (after-tax) Sales/Capital (Turnover ratio) Return on capital (after-tax) Growth rate during period (g) = Cost of Capital during period =

Stable Growth Period Growth rate in steady state = Return on capital = Reinvestment Rate = Cost of Capital = Value of Firm = Aswath Damodaran Coca Cola $21,962.00 10 50% 15.57% 1.34 20.84% 10.42% 7.65% With Cott Margins $21,962.00 10 50% 5.28% 1.34 7.06% 3.53%

7.65% 4.00% 7.65% 52.28% 7.65% $79,611.25 4.00% 7.65% 52.28% 7.65% $15,371.24 5 7. Be circumspect about defining debt for cost of capital purposes General Rule: Debt generally has the following characteristics:

Defined as such, debt should include Commitment to make fixed payments in the future The fixed payments are tax deductible Failure to make the payments can lead to either default or loss of control of the firm to the party to whom payments are due. All interest bearing liabilities, short term as well as long term All leases, operating as well as capital Debt should not include Aswath Damodaran Accounts payable or supplier credit 5 But should consider other potential liabilities when getting to equity value If you have under funded pension fund or health care plans, you

should consider the under funding at this stage in getting to the value of equity. If you do so, you should not double count by also including a cash flow line item reflecting cash you would need to set aside to meet the unfunded obligation. You should not be counting these items as debt in your cost of capital calculations. If you have contingent liabilities - for example, a potential liability from a lawsuit that has not been decided - you should consider the expected value of these contingent liabilities Aswath Damodaran Value of contingent liability = Probability that the liability will occur * Expected value of liability 5 8. The Value of Control

The value of the control premium that will be paid to acquire a block of equity will depend upon two factors Probability that control of firm will change: This refers to the probability that incumbent management will be replaced. this can be either through acquisition or through existing stockholders exercising their muscle. Value of Gaining Control of the Company: The value of gaining control of a company arises from two sources - the increase in value that can be wrought by changes in the way the company is managed and run, and the side benefits and perquisites of being in control Value of Gaining Control = Present Value (Value of Company with change in control Value of company without change in control) + Side Benefits of Control Aswath Damodaran 5 Aswath Damodaran 5 Aswath Damodaran 5 Aswath Damodaran 5

Value of Control and the Value of Voting Rights The value of control at Adris Grupa can be computed as the difference between the status quo value (5469) and the optimal value (5735). The value of a voting share derives entirely from the capacity you have to change the way the firm is run. In this case, we have two values for Adris Grupas Equity. Status Quo Value of Equity = 5,469 million HKR All shareholders, common and preferred, get an equal share of the status quo value. Value for a non-voting share = 5469/(9.616+6.748) = 334 HKR/share Optimal value of Equity = 5,735 million HKR Value of control at Adris Grupa = 5,735 5469 = 266 million HKR Only voting shares get a share of this value of control Value per voting share =334 HKR + 266/9.616 = 362 HKR Aswath Damodaran 6 9. Distress and the Going Concern Assumption

Traditional valuation techniques are built on the assumption of a going concern, i.e., a firm that has continuing operations and there is no significant threat to these operations. In discounted cashflow valuation, this going concern assumption finds its place most prominently in the terminal value calculation, which usually is based upon an infinite life and ever-growing cashflows. In relative valuation, this going concern assumption often shows up implicitly because a firm is valued based upon how other firms - most of which are healthy are priced by the market today. When there is a significant likelihood that a firm will not survive the immediate future (next few years), traditional valuation models may yield an over-optimistic estimate of value. Aswath Damodaran 6 9. Distress and the Going Concern Assumption Traditional valuation techniques are built on the assumption of a going

concern, i.e., a firm that has continuing operations and there is no significant threat to these operations. In discounted cashflow valuation, this going concern assumption finds its place most prominently in the terminal value calculation, which usually is based upon an infinite life and ever-growing cashflows. In relative valuation, this going concern assumption often shows up implicitly because a firm is valued based upon how other firms - most of which are healthy are priced by the market today. When there is a significant likelihood that a firm will not survive the immediate future (next few years), traditional valuation models may yield an over-optimistic estimate of value. Aswath Damodaran 6 Aswath Damodaran 6 The Distress Factor

In February 2009, LVS was rated B+ by S&P. Historically, 28.25% of B+ rated bonds default within 10 years. LVS has a 6.375% bond, maturing in February 2015 (7 years), trading at $529. If we discount the expected cash flows on the bond at the riskfree rate, we can back out the probability of distress from the bond price: Solving for the probability of bankruptcy, we get: Distress = Annual probability of default = 13.54% If LVS is becomes distressed: Cumulative probability of surviving 10 years = (1 - .1354)10 = 23.34% Cumulative probability of distress over 10 years = 1 - .2334 = .7666 or 76.66% Expected distress sale proceeds = $2,769 million < Face value of debt Expected equity value/share = $0.00

Expected value per share = $8.12 (1 - .7666) + $0.00 (.7666) = $1.92 Aswath Damodaran 6 10. Analyzing the Effect of Illiquidity on Value Investments which are less liquid should trade for less than otherwise similar investments which are more liquid. The size of the illiquidity discount should vary across firms and also across time. The conventional practice of relying upon studies of restricted stocks or IPOs will fail sooner rather than later. Aswath Damodaran Restricted stock studies are based upon small samples of troubled firms The discounts observed in IPO studies are too large for these to be arms length transactions. They just do not make sense. 6

Illiquidity Discounts from Bid-Ask Spreads Using data from the end of 2000, for instance, we regressed the bid-ask spread against annual revenues, a dummy variable for positive earnings (DERN: 0 if negative and 1 if positive), cash as a percent of firm value and trading volume. Spread = 0.145 0.0022 ln (Annual Revenues) -0.015 (DERN) 0.016 (Cash/Firm Value) 0.11 ($ Monthly trading volume/ Firm Value) We could substitute in the revenues of Kristin Kandy ($5 million), the fact that it has positive earnings and the cash as a percent of revenues held by the firm (8%): Spread = 0.145 0.0022 ln (Annual Revenues) -0.015 (DERN) 0.016 (Cash/Firm Value) 0.11 ($ Monthly trading volume/ Firm Value) = 0.145 0.0022 ln (5) -0.015 (1) 0.016 (.08) 0.11 (0) = .12.52% Based on this approach, we would estimate an illiquidity discount of 12.52% for Kristin Kandy. Aswath Damodaran 6 Relative Valuation Aswath Damodaran Aswath Damodaran 6

Relative valuation is pervasive Most asset valuations are relative. Most equity 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. Aswath Damodaran 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. 6 The Reasons for the allure If you think Im 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 H.H. Munro If you are going to screw up, make sure that you have lots of company Ex-portfolio manager Aswath Damodaran 6 The Four Steps to Deconstructing Multiples Define the multiple 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 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 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 Aswath Damodaran Defining the comparable universe and controlling for differences is far more

difficult in practice than it is in theory. 7 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? Aswath Damodaran 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. 7 Example 1: 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 Aswath Damodaran 7

Example 2: Enterprise Value /EBITDA Multiple The enterprise value to EBITDA multiple is obtained by netting cash out against debt to arrive at enterprise value and dividing by EBITDA. Enterprise Value Market Value of Equity + Market Value of Debt - Cash EBITDA Earnings before Interest, Taxes and Depreciation Why do we net out cash from firm value? What happens if a firm has cross holdings which are categorized as: Aswath Damodaran Minority interests? Majority active interests? 7 Descriptive Tests

What is the average and standard deviation for this multiple, across the universe (market)? What is the median for this multiple? How large are the outliers to the distribution, and how do we deal with the outliers? The median for this multiple is often a more reliable comparison point. 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? Aswath Damodaran 7 Looking at the distribution of PE ratios US Stocks in January 2011 Aswath Damodaran 7 PE: Deciphering the Distribution Aswath Damodaran 7 Comparing PE Ratios: US, Europe, Japan and Emerging Markets Aswath Damodaran 7 And 6 times EBITDA may not be cheap

Aswath Damodaran 7 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? Aswath Damodaran 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. 7 PE Ratio: Understanding the Fundamentals To understand the fundamentals, start with a basic equity discounted cash flow model. With the dividend discount model, P0 DPS1 r - gn Dividing both sides by the current earnings per share, P0 Payout Ratio * (1 + g n ) PE =

EPS0 r-gn If this had been a FCFE Model, P0 FCFE1 r - gn P0 (FCFE/Earnings)* (1+ g n ) PE = EPS 0 r-g n Aswath Damodaran 8 The Determinants of Multiples Aswath Damodaran 8 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? Aswath Damodaran Proposition 5: It is impossible to find an exactly identical firm to the one you are valuing. 8

An Example: Comparing PE Ratios across a Sector: PE Aswath Damodaran 8 PE, Growth and Risk Dependent variable is: R squared = 66.2% PE R squared (adjusted) = 63.1% Variable Coefficient SE t-ratio Constant 13.1151 3.471 3.78 Growth rate 121.223 19.27 6.29 Emerging Market

-13.8531 3.606 -3.84 Emerging Market is a dummy: 1 if emerging market 0 if not Aswath Damodaran prob 0.0010 0.0001 0.0009 8 Is Telebras under valued? Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35 At an actual price to earnings ratio of 8.9, Telebras is slightly overvalued. Aswath Damodaran 8

Amgens Relative Value Company Name King Pharmac. Pfizer I nc. GlaxoSmithKline ADR Amgen Wyeth Novartis AG ADR Lilly (Eli) Merck & Co. Hospira I nc. Cephalon I nc. Forest Labs. Teva Pharmac. (ADR) Gilead Sciences Schering- Plough Novo Nordisk ADR Bristol-Myers Squibb Genentech I nc. Allergan I nc. Biogen I dec I nc. Celgene Corp. MedI mmune I nc. Aswath Damodaran Market Cao

$5,064 $190,923 $158,986 $66,847 $74,271 $133,805 $66,440 $110,731 $6,416 $5,183 $16,381 $29,272 $37,365 $46,814 $33,333 $58,636 $83,856 $18,595 $15,254 $23,683 $13,560 PE Ratio 12.64 12.74 15.63 15.99

17.35 18.58 19.21 20.09 20.72 21.17 24.56 27.30 32.17 34.63 35.87 36.99 39.69 41.15 70.13 343.23 797.62 Expected Growth -0.50% 2.00% 5.00% 15.00% 9.00% 7.50% 7.00% 7.00%

8.00% 14.00% 10.00% 14.50% 17.50% 29.50% 14.50% 7.00% 27.50% 15.00% 33.50% 59.00% 58.00% Beta 1.10 0.85 0.85 0.85 1.00 0.70 0.85 0.85 0.70 1.15 0.80 0.75

0.90 0.95 0.85 1.00 0.80 0.85 1.10 1.30 1.00 ROE 20.29% 21.07% 55.29% 22.05% 29.22% 17.52% 31.49% 31.40% 22.75% 18.69% 24.72% 17.75% 63.97% 20.89% 21.22% 13.65%

22.29% 14.38% 3.04% 3.49% 1.23% 8 The Drivers of PE Ratios Regressing PE ratios against growth, we get PE = 14.86 + 0.85 (Expected growth rate) R2 = 49% Plugging in Amgens expected growth rate of 15%, we get PE = 14.86 + 0.85 (15) = 27.61 At 16 times earnings, Amgen seems to be significantly undervalued by almost 40% relative to the rest of the pharmaceutical sector. Aswath Damodaran

8 Comparisons to the entire market: Why not? 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. Aswath Damodaran 8 PE Ratio: Standard Regression for US stocks - January 2011 Aswath Damodaran 8 Amgen valued relative to the market

Plugging in Amgens numbers into the January 2007 market regression: Expected growth rate = 15% Beta = 0.85 Payout ratio = 0% Predicted PE = 10.645 + 1.176 (15) - 2.621 (0.85) = 26.06 Again, at 16 times earnings, Amgen seems to be significantly undervalued, relative to how the market is pricing all other stocks. Aswath Damodaran 9 Fundamentals hold in every market: PE regressions across markets Region Regression January 2011

R squared Europe PE = 11.55 + 53.32 Expected Growth + 6.00 Payout -1.35 Beta 29.8% Japan PE = 16.60 + 17.24 Expected Growth + 14.68 Beta 19.6% Emerging Markets PE = 19.47+ 17.10 Expected Growth + 2.45 Payout 7.8% Aswath Damodaran 9

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: Aswath Damodaran 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 9

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 estimat e value is obtained using one multiple. The multiple that is used can be chosen in one of two ways: Aswath Damodaran 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. 9

Conventional usage Sector Multiple Used Rationale Cyclical Manufacturing PE, Relative PE Often with normalized earnings Growth firms PEG ratio Big differences in growth rates Young growth firms w/ losses Revenue Multiples

What choice do you have? Infrastructure EV/EBITDA Early losses, big DA REIT P/CFE (where CFE = Net income + Depreciation) Big depreciation charges on real estate Financial Services Price/ Book equity Marked to market? Retailing Revenue multiples Margins equalize sooner

or later Aswath Damodaran 9 Back to Lemmings... Aswath Damodaran 9

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