Valuation The Big Picture Aswath Damodaran

Valuation The Big Picture

• Aswath Damodaran

• http://www.damodaran.com

DCF Choices: Equity Valuation versus Firm Valuation

Equity Valuation

Firm Valuation

I. The Cost of Capital

The Cost of Capital is central to both corporate finance and valuation

• In corporate finance, the cost of capital is important because

• It operates as the hurdle rate when considering new investments
• It is the metric that allows firms to choose their optimal capital structure

• In valuation, it is the discount rate that we use to value the operating assets of the firm.

I. The Cost of Equity

A Simple Test

• You are valuing Ambev in U.S. dollars and are attempting to estimate a risk free rate to use in the analysis. The risk free rate that you should use is

• The interest rate on a nominal real denominated Brazilian government bond

• The interest rate on an inflation-indexed Brazilian government bond

• The interest rate on a dollar denominated Brazilian government bond (11.20%)

• The interest rate on a U.S. treasury bond (4.70%)

Everyone uses historical premiums, but..

• The historical premium is the premium that stocks have historically earned over riskless securities.

• Practitioners never seem to agree on the premium; it is sensitive to

• How far back you go in history…
• Whether you use T.bill rates or T.Bond rates
• Whether you use geometric or arithmetic averages.

• For instance, looking at the US:

• Arithmetic average Geometric Average

• Stocks - Stocks - Stocks - Stocks -

• Historical Period T.Bills T.Bonds T.Bills T.Bonds

• 1928-2004 7.92% 6.53% 6.02% 4.84%

• 1964-2004 5.82% 4.34% 4.59% 3.47%

• 1994-2004 8.60% 5.82% 6.85% 4.51%

Two Ways of Estimating Country Risk Premiums… September 2003

• Default spread on Country Bond: In this approach, the country risk premium is based upon the default spread of the bond issued by the country (but only if it is denominated in a currency where a default free entity exists.

• Brazil was rated B2 by Moody’s and the default spread on the Brazilian dollar denominated C.Bond at the end of September 2003 was 6.01%. (10.18%-4.17%)

• Relative Equity Market approach: The country risk premium is based upon the volatility of the market in question relative to U.S market.

• Country risk premium = Risk PremiumUS* Country Equity / US Equity
• Using a 4.53% premium for the US, this approach would yield:
• Total risk premium for Brazil = 4.53% (33.37%/18.59%) = 8.13%
• Country risk premium for Brazil = 8.13% - 4.53% = 3.60%
• (The standard deviation in weekly returns from 2001 to 2003 for the Bovespa was 33.37% whereas the standard deviation in the S&P 500 was 18.59%)

And a third approach

• Country ratings measure default risk. While default risk premiums and equity risk premiums are highly correlated, one would expect equity spreads to be higher than debt spreads.

• Another is to multiply the bond default spread by the relative volatility of stock and bond prices in that market. In this approach:

• Country risk premium = Default spread on country bond* Country Equity / Country Bond
• Standard Deviation in Bovespa (Equity) = 33.37%
• Standard Deviation in Brazil C-Bond = 26.15%
• Default spread on C-Bond = 6.01%
• Country Risk Premium for Brazil = 6.01% (33.37%/26.15%) = 7.67%

Can country risk premiums change? Updating Brazil in January 2005

• Brazil’s financial standing and country rating improved dramatically towards the end of 2004. Its rating improved to B1. In January 2005, the interest rate on the Brazilian C-Bond dropped to 7.73%. The US treasury bond rate that day was 4.22%, yielding a default spread of 3.51% for Brazil.

• Standard Deviation in Bovespa (Equity) = 25.09%
• Standard Deviation in Brazil C-Bond = 15.12%
• Default spread on C-Bond = 3.51%
• Country Risk Premium for Brazil = 3.51% (25.09%/15.12%) = 5.82%

From Country Spreads to Corporate Risk premiums

• Approach 1: Assume that every company in the country is equally exposed to country risk. In this case,

• E(Return) = Riskfree Rate + Country Spread + Beta (US premium)

• Implicitly, this is what you are assuming when you use the local Government’s dollar borrowing rate as your riskfree rate.

• Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk.

• E(Return) = Riskfree Rate + Beta (US premium + Country Spread)

• Approach 3: 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 Spread)

Estimating Company Exposure to Country Risk: Determinants

• Source of revenues: Other things remaining equal, a company should be more exposed to risk in a country if it generates more of its revenues from that country. A Brazilian firm that generates the bulk of its revenues in Brazil should be more exposed to country risk than one that generates a smaller percent of its business within Brazil.

• Manufacturing facilities: Other things remaining equal, a firm that has all of its production facilities in Brazil should be more exposed to country risk than one which has production facilities spread over multiple countries. The problem will be accented for companies that cannot move their production facilities (mining and petroleum companies, for instance).

• Use of risk management products: Companies can use both options/futures markets and insurance to hedge some or a significant portion of country risk.

Estimating Lambdas: The Revenue Approach

• 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, for instance, Embraer and Embratel, both of which are incorporated and traded in Brazil. Embraer gets 3% of its revenues from Brazil whereas Embratel gets almost all of its revenues in Brazil. The average Brazilian company gets about 77% of its revenues in Brazil:

• LambdaEmbraer = 3%/ 77% = .04
• LambdaEmbratel = 100%/77% = 1.30

• There are two implications

• A company’s 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

Estimating Lambdas: Earnings Approach

Estimating Lambdas: Stock Returns versus C-Bond Returns

Estimating a US Dollar Cost of Equity for Embraer - September 2003

• Assume that the beta for Embraer is 1.07, and that the riskfree rate used is 4.17%. The historical risk premium from 1928-2002 for the US is 4.53% and the country risk premium for Brazil is 7.67%.

• Approach 1: Assume that every company in the country is equally exposed to country risk. In this case,

• E(Return) = 4.17% + 1.07 (4.53%) + 7.67% = 16.69%

• Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other market risk.

• E(Return) = 4.17 % + 1.07 (4.53%+ 7.67%) = 17.22%

• Approach 3: 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)= 4.17% + (4.53%) + %) = 11.09%

Implied Equity Premiums

• We can use the information in stock prices to back out how risk averse the market is and how much of a risk premium it is demanding.

• If you pay the current level of the index, you can expect to make a return of 7.87% on stocks (which is obtained by solving for r in the following equation)

• Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 7.87% - 4.22% = 3.65%

Implied Premiums in the US

An Intermediate Solution

• The historical risk premium of 4.84% for the United States is too high a premium to use in valuation. It is much higher than the actual implied equity risk premium in the market

• The current implied equity risk premium requires us to assume that the market is correctly priced today. (If I were required to be market neutral, this is the premium I would use)

• The average implied equity risk premium between 1960-2004 in the United States is about 4%. We will use this as the premium for a mature equity market.

Implied Premium for Brazil: June 2005

• Level of the Index = 26196

• Dividends on the Index = 6.19% of 16889

• Other parameters (all in US dollars)

• Riskfree Rate = 4.08%
• Expected Growth (in dollars)
• Next 5 years = 8% (Used expected growth rate in Earnings)
• After year 5 = 4.08%

• Solving for the expected return:

• Expected return on Equity = 11.66%
• Implied Equity premium = 11.66% - 4.08% = 7.58%
• Implied Equity premium for US on same day = 3.70%
• Implied country premium for Brazil = 7.58% - 3.70% = 3.88%

Estimating Beta

• The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) -

• Rj = a + b Rm

• where a is the intercept and b is the slope of the regression.

• The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock.

• This beta has three problems:

• It has high standard error
• It reflects the firm’s business mix over the period of the regression, not the current mix
• It reflects the firm’s average financial leverage over the period rather than the current leverage.

Beta Estimation : The Index Effect

Determinants of Betas

The Solution: Bottom-up Betas

Bottom-up Betas: Embraer, Ambev, Vale and Petrobras

Gross Debt versus Net Debt Approaches: Embraer in September 2003

• Net Debt Ratio for Embraer = (Debt - Cash)/ Market value of Equity

• = (1953-2320)/ 11,042 = -3.32%

• Levered Beta for Embraer = 0.95 (1 + (1-.34) (-.0332)) = 0.93

• The cost of Equity using net debt levered beta for Embraer will be much lower than with the gross debt approach. The cost of capital for Embraer, though, will even out since the debt ratio used in the cost of capital equation will now be a net debt ratio rather than a gross debt ratio.

From Cost of Equity to Cost of Capital

Estimating Synthetic Ratings

• The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio

• Interest Coverage Ratio = EBIT / Interest Expenses

• For Embraer’s interest coverage ratio, we used the interest expenses and EBIT from 2002.

• Interest Coverage Ratio = 2166/ 222 = 9.74

• For Ambev’s interest coverage ratio, we used the interest expenses and EBIT from 2003.

• Interest Coverage Ratio = 2213/ 570 = 3.88

• For Vale’s interest coverage ratio, we used the interest expenses and EBIT from 2003 also

• Interest Coverage Ratio = 6371/1989 = 3.20

Interest Coverage Ratios, Ratings and Default Spreads

• If Interest Coverage Ratio is Estimated Bond Rating Default Spread(2003) Default Spread(2004)
• > 8.50 (>12.50) AAA 0.75% 0.35%
• 6.50 - 8.50 (9.5-12.5) AA 1.00% 0.50%
• 5.50 - 6.50 (7.5-9.5) A+ 1.50% 0.70%
• 4.25 - 5.50 (6-7.5) A 1.80% 0.85%
• 3.00 - 4.25 (4.5-6) A– 2.00% 1.00%
• 2.50 - 3.00 (4-4.5) BBB 2.25% 1.50%
• 2.25- 2.50 (3.5-4) BB+ 2.75% 2.00%
• 2.00 - 2.25 ((3-3.5) BB 3.50% 2.50%
• 1.75 - 2.00 (2.5-3) B+ 4.75% 3.25%
• 1.50 - 1.75 (2-2.5) B 6.50% 4.00%
• 1.25 - 1.50 (1.5-2) B – 8.00% 6.00%
• 0.80 - 1.25 (1.25-1.5) CCC 10.00% 8.00%
• 0.65 - 0.80 (0.8-1.25) CC 11.50% 10.00%
• 0.20 - 0.65 (0.5-0.8) C 12.70% 12.00%
• < 0.20 (<0.5) D 15.00% 20.00%
• The first number under interest coverage ratios is for larger market cap companies and the second in brackets is for smaller market cap companies. For Embraer and Ambev , I used the interest coverage ratio table for smaller/riskier firms (the numbers in brackets) which yields a lower rating for the same interest coverage ratio.

Estimating the cost of debt

• Company EBIT Interest Interest Rating Company Country Cost of

• Expense Coverage Spread Spread Debt($)

• Embraer (2003) 2166 222 9.76 AA 1.00% 4% 9.17%

• Ambev 2213 570 3.88 BB+ 2.00% 4% 10.70%

• Vale 6371 1989 3.20 BB 2.50% 4% 11.20%

• Petrobras 14974 3195 4.69 A- 1% 4% 9.70%

• Riskfree Rate = 4.17% for Embraer in 2003, 4.70% for all other firms

• Cost of debt ($) = Riskfree Rate + Company Spread + Country Spread

• (I have assumed that all of these companies will have to bear only a portion of the total country default spread of Brazil which is 4.50%)

Weights for the Cost of Capital Computation

• The weights used to compute the cost of capital should be the market value weights for debt and equity.

• There is an element of circularity that is introduced into every valuation by doing this, since the values that we attach to the firm and equity at the end of the analysis are different from the values we gave them at the beginning.

• As a general rule, the debt that you should subtract from firm value to arrive at the value of equity should be the same debt that you used to compute the cost of capital.

Estimating Cost of Capital: Embraer

• Equity

• Cost of Equity = 4.17% + 1.07 (4%) + 0.27 (7.67%) = 10.52%
• Market Value of Equity =11,042 million BR ($ 3,781 million)

• Debt

• Cost of debt = 4.17% + 4.00% +1.00%= 9.17%
• Market Value of Debt = 2,093 million BR ($717 million)

• Cost of Capital

• Cost of Capital = 10.52 % (.84) + 9.17% (1- .34) (0.16)) = 9.81%

• The book value of equity at Embraer is 3,350 million BR.

• The book value of debt at Embraer is 1,953 million BR; Interest expense is 222 mil; Average maturity of debt = 4 years

• Estimated market value of debt = 222 million (PV of annuity, 4 years, 9.17%) + $1,953 million/1.09174 = 2,093 million BR

Estimating Cost of Capital: Ambev

• Equity

• Cost of Equity = 4.7% + 0.87 (4%) + 0.41 (7.87%) = 11.41%
• Market Value of Equity = 29,886 million BR ($ 9,508 million)

• Debt

• Cost of debt = 4.7% + 4.00% +2.00%= 10.70%
• Market Value of Debt = 5,808 million BR ($1,848 million)

• Cost of Capital

• Cost of Capital = 11.41 % (.837) + 10.7% (1- .34) (0.163)) = 10.70%

• The book value of equity at Ambev is 4,209 million BR.

• The book value of debt at Ambev is 5,980 million BR; Interest expense is 570 mil; Average maturity of debt = 3 years

• Estimated market value of debt = 570 million (PV of annuity, 3 years, 10.7%) + $5,980 million/1.1073 = 5,808 million BR

Estimating Cost of Capital: Vale

• Equity

• Cost of Equity = 4.7% + 1.04 (4%) + 0.37 (7.87%) = 11.77%
• Market Value of Equity = 56,442 million BR ($ 17,958 million)

• Debt

• Cost of debt = 4.7% + 4.00% +2.50%= 11.20%
• Market Value of Debt = 14,484 million BR ($ 4,612 million)

• Cost of Capital

• Cost of Capital = 11.77 % (.796) + 11.2% (1- .34) (0.204)) = 10.88%

• The book value of equity at Vale is 15,937 million BR.

• The book value of debt at Vale is 13,709 million BR; Interest expense is 1,989 mil; Average maturity of debt = 2 years

• Estimated market value of debt = 1,989 million (PV of annuity, 2 years, 11.2%) + 13,709 million/1.1122 = 14,484 million BR

Estimating Cost of Capital: Petrobras

• Equity

• Cost of Equity = 4.70% + 0.79 (4%) + 0.66(7.87%) = 12.58%
• Market Value of Equity = 85,218 million BR ($ 27,114 million)

• Debt

• Cost of debt = 4.7% + 4.00% + 1.00%= 9.70%
• Market Value of Debt = 39,367 million BR ($ 12,537 million)

• Cost of Capital

• Cost of Capital = 12.58 % (.684) + 9.7% (1- .34) (0.316)) = 10.63%

• The book value of equity at Petrobras is 50.987 million BR.

• The book value of debt at Petrobras is 42,248 million BR; Interest expense is 1,989 mil; Average maturity of debt = 4 years

• Estimated market value of debt = 3,195 million (PV of annuity, 4 years, 9.7%) + 42,248 million/1.0974 = 39,367 million BR

If you had to do it….Converting a Dollar Cost of Capital to a Nominal Real Cost of Capital - Ambev

• Approach 1: Use a BR riskfree rate in all of the calculations above. For instance, if the BR riskfree rate was 12%, the cost of capital would be computed as follows:

• Cost of Equity = 12% + (4%) + %) = 18.71%
• Cost of Debt = 12% + 2% = 14%
• (This assumes the riskfree rate has no country risk premium embedded in it.)

• Approach 2: Use the differential inflation rate to estimate the cost of capital. For instance, if the inflation rate in BR is 8% and the inflation rate in the U.S. is 2%

• Cost of capital=

• = 1.107 (1.08/1.02)-1 = 17.21%

II. Valuing Control and Synergy Acquisition Valuation

• It is not what you buy but what you pay for it….

Issues in Acquisition Valuation

• Acquisition valuations are complex, because the valuation often involved issues like synergy and control, which go beyond just valuing a target firm. It is important on the right sequence, including

• When should you consider synergy?
• Where does the method of payment enter the process.

• Can synergy be valued, and if so, how?

• What is the value of control? How can you estimate the value?

The Value of Control

• Control has value because you think that you can run a firm better than the incumbent management.

• Value of Control = Value of firm, run optimally - Value of firm, status quo

• The value of control should be inversely proportional to the perceived quality of that management and its capacity to maximize firm value.

• Value of control will be much greater for a poorly managed firm that operates at below optimum capacity than it is for a well managed firm. It should be negligible or firms which are operating at or close to their optimal value

Price Enhancement versus Value Enhancement

The Paths to Value Creation

• Using the DCF framework, there are four basic ways in which the value of a firm can be enhanced:

• The cash flows from existing assets to the firm can be increased, by either
• increasing after-tax earnings from assets in place or
• reducing reinvestment needs (net capital expenditures or working capital)
• The expected growth rate in these cash flows can be increased by either
• Increasing the rate of reinvestment in the firm
• Improving the return on capital on those reinvestments
• The length of the high growth period can be extended to allow for more years of high growth.
• The cost of capital can be reduced by
• Reducing the operating risk in investments/assets
• Changing the financial mix
• Changing the financing composition

I. Ways of Increasing Cash Flows from Assets in Place

II. Value Enhancement through Growth

III. Building Competitive Advantages: Increase length of the growth period

Illustration: Valuing a brand name: Coca Cola

• Coca Cola Generic Cola Company

• AT Operating Margin 18.56% 7.50%

• Sales/BV of Capital 1.67 1.67

• ROC 31.02% 12.53%

• Reinvestment Rate 65.00% (19.35%) 65.00% (47.90%)

• Expected Growth 20.16% 8.15%

• Length 10 years 10 yea

• Cost of Equity 12.33% 12.33%

• E/(D+E) 97.65% 97.65%

• AT Cost of Debt 4.16% 4.16%

• D/(D+E) 2.35% 2.35%

• Cost of Capital 12.13% 12.13%

• Value $115 $13

Gauging Barriers to Entry

• Which of the following barriers to entry are most likely to work for Embraer?

• Brand Name

• Patents and Legal Protection

• Switching Costs

• Cost Advantages

• What about for Ambev?

• Brand Name

• Patents and Legal Protection

• Switching Costs

• Cost Advantages

Reducing Cost of Capital

Embraer : Optimal Capital Structure

Ambev: Optimal Capital Structure

Vale: Optimal Capital Structure

Value of stock in a publicly traded firm

• When a firm is badly managed, the market still assesses the probability that it will be run better in the future and attaches a value of control to the stock price today:

• With voting shares and non-voting shares, a disproportionate share of the value of control will go to the voting shares. In the extreme scenario where non-voting shares are completely unprotected:

Valuing Ambev voting and non-voting shares

• Status Quo Value = $5,304 million* 3.14 = 16,655 million BR

• Optimal Value = $6,277 million *3.14 = 19,710 million BR

• Number of shares

• Voting =15.735
• Non-voting =22.801
• Total = 38.536

• Value/ non-voting share = 16,655/38.536 = 433 BR/share

• Value/ voting share = 433 + (19710-16655)/15.735 = 626 BR/share

Sources of Synergy

A procedure for 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

J.P. Morgan’s estimate of annual operating synergies in Ambev/Labatt Merger

J.P. Morgan’s estimate of total synergies in Labatt/Ambev Merger

Evidence on Synergy

• A stronger test of synergy is to evaluate whether merged firms improve their performance (profitability and growth), relative to their competitors, after takeovers.

• McKinsey and Co. examined 58 acquisition programs between 1972 and 1983 for evidence on two questions -
• Did the return on the amount invested in the acquisitions exceed the cost of capital?
• Did the acquisitions help the parent companies outperform the competition?
• They concluded that 28 of the 58 programs failed both tests, and 6 failed at least one test.

• KPMG in a more recent study of global acquisitions concludes that most mergers (>80%) fail - the merged companies do worse than their peer group.

• Large number of acquisitions that are reversed within fairly short time periods. bout 20.2% of the acquisitions made between 1982 and 1986 were divested by 1988. In studies that have tracked acquisitions for longer time periods (ten years or more) the divestiture rate of acquisitions rises to almost 50%.

Labatt DCF valuation

• Labatt is the Canadian subsidiary of Interbrew and is a mature firm with sold brand names. It can be valued using a stable growth firm valuation model.

• Base Year inputs

• EBIT (1-t) = $411 million
• Expected Growth Rate = 3%
• Return on capital = 9%
• Cost of capital = 7%

• Valuation

• Reinvestment Rate = g/ ROC = 3/9= 33.33%
• Value of Labatt = 411 (1-.333)/ (.07-.03) = $6.85 billion

• Ambev is paying for Labatt with 23.3 billion shares (valued at about $5.8 billion) and is assuming $ 1.5 billion in debt, resulting in a value for the firm of about $ 7.3 billion.

Who gets the benefits of synergy?

III. Valuing Equity in Cyclical firms and firms with negative earnings : The Search for Normalcy

• Aswath Damodaran

• http://www.damodaran.com

Begin by analyzing why the earnings are not not normal

1. If the earnings decline or increase is temporary and will be quickly reversed… Normalize

• You can normalize earnings in three ways:

• Company’s history: Averaging earnings or operating margins over time and estimating a normalized earning for the base year
• Industry average: You can apply the average operating margin for the industry to the company’s revenues this year to get a normalized earnings.
• Normalized prices: If your company is a commodity company, you can normalize the price of the commodity across a cycle and apply it to the production in the current year.

Aracruz in 2001: The Effect of Commodity Prices

Normalizing Earnings

2. If the earnings are negative because the firm is early in its life cycle…

• When operating income is negative or margins are expected to change over time, we use a three step process to estimate growth:

• Estimate growth rates in revenues over time
• Use historical revenue growth to get estimates of revenue growth in the near future
• Decrease the growth rate as the firm becomes larger
• Keep track of absolute revenues to make sure that the growth is feasible
• Estimate expected operating margins each year
• Set a target margin that the firm will move towards
• Adjust the current margin towards the target margin
• Estimate the capital that needs to be invested to generate revenue growth and expected margins
• Estimate a sales to capital ratio that you will use to generate reinvestment needs each year.

3. If earnings are negative because the firm has structural/ leverage problems…

• Survival Scenario: The firm survives and solves its structural problem (brings down its financial leverage). In this scenario, margins improve and the debt ratio returns to a sustainable level.

• Failure Scenario: The firm does not solve its structural problems or fails to make debt payments, leading to default and liquidation.

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.

DCF Valuation + Distress Value

• A DCF valuation values a firm as a going concern. If there is a significant likelihood of the firm failing before it reaches stable growth and if the assets will then be sold for a value less than the present value of the expected cashflows (a distress sale value), DCF valuations will understate the value of the firm.

• Value of Equity= DCF value of equity (1 - Probability of distress) + Distress sale value of equity (Probability of distress)

Bond Price to estimate probability of distress

• Global Crossing has a 12% coupon bond with 8 years to maturity trading at $ 653. To estimate the probability of default (with a treasury bond rate of 5% used as the riskfree rate):

• Solving for the probability of bankruptcy, we get

• With a 10-year bond, it is a process of trial and error to estimate this value. The solver function in excel accomplishes the same in far less time.

• Distress = Annual probability of default = 13.53%

• To estimate the cumulative probability of distress over 10 years:

• Cumulative probability of surviving 10 years = (1 - .1353)10 = 23.37%

• Cumulative probability of distress over 10 years = 1 - .2337 = .7663 or 76.63%

Valuing Global Crossing with Distress

• Probability of distress

• Cumulative probability of distress = 76.63%

• Distress sale value of equity

• Book value of capital = $14,531 million
• Distress sale value = 25% of book value = .25*14531 = $3,633 million
• Book value of debt = $7,647 million
• Distress sale value of equity = $ 0

• Distress adjusted value of equity

• Value of Global Crossing = $3.22 (1-.7663) + $0.00 (.7663) = $ 0.75

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.

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

Example 1: Product Patent as an Option

Example 2: Undeveloped Oil Reserve as an option

Example 3: Expansion of existing project as an option

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.

When can you use option pricing models to value real options?

• All option pricing models rest on two foundations.

• The first is the notion of a replicating portfolio where you combine the underlying asset and borrowing/lending to create a portfolio that has the same cashflows as the option.
• The second is arbitrage. Since both the option and the replicating portfolio have the same cashflows, they should trade at the same value.

• As a result, option pricing models work best when

• 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.

• When option pricing models are used to value real assets where neither replication nor arbitrage are usually feasible, 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.

Illustrating Replication: The Binomial Option Pricing Model

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

1. Obtaining Inputs for Patent Valuation

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 = $ 3.422 billion
• PV of Cost of Developing Drug for Commercial Use = K = $ 2.875 billion
• Patent Life = t = 17 years Riskless Rate = r = 6.7% (17-year T.Bond rate)
• Variance in Expected Present Values =2 = 0.224 (Industry average firm variance for bio-tech firms)
• Expected Cost of Delay = y = 1/17 = 5.89%
• d1 = 1.1362 N(d1) = 0.8720
• d2 = -0.8512 N(d2) = 0.2076

• Call Value= 3,422 exp(-0.0589)(17) (0.8720) - 2,875 (exp(-0.067)(17) (0.2076)= $ 907 million

2. Valuing an Oil Reserve

• Consider an offshore oil property with an estimated oil reserve of 50 million barrels of oil, where the present value of the development cost is $12 per barrel and the development lag is two years.

• 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).

• 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 0.03.

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 /(1.05)2 = $ 544.22

• (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 = 0.03

• Riskless rate =8%

• Dividend Yield = Net production revenue / Value of reserve = 5%

Valuing Undeveloped Reserves

• Inputs for valuing undeveloped reserves

• Value of underlying asset = Value of estimated reserves discounted back for period of development lag= 3038 * ($ 22.38 - $7) / 1.052 = $42,380.44
• Exercise price = Estimated development cost of reserves = 3038 * $10 = $30,380 million
• Time to expiration = Average length of relinquishment option = 12 years
• Variance in value of asset = Variance in oil prices = 0.03
• Riskless interest rate = 9%
• Dividend yield = Net production revenue/ Value of developed reserves = 5%

• Based upon these inputs, the Black-Scholes model provides the following value for the call:

• d1 = 1.6548 N(d1) = 0.9510
• d2 = 1.0548 N(d2) = 0.8542

• Call Value= 42,380.44 exp(-0.05)(12) (0.9510) -30,380 (exp(-0.09)(12) (0.8542)= $ 13,306 million

3. An Example of an Expansion Option

• Ambev is considering introducing a soft drink to the U.S. market. The drink will initially be introduced only in the metropolitan areas of the U.S. 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 U.S. market, if done now =$ 750 Million

• Strike Price (K) = Cost of Expansion into entire U.S 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 34.25%.

• Standard Deviation in Underlying Asset’s Value = 34.25%

• Time to expiration = Period for which expansion option applies = 5 years

• Call Value= $ 234 Million

Opportunities and not Options…

Key Tests for Real Options

• Is there an option embedded in this asset/ decision?

• Can you identify the underlying asset?
• Can you specify the contigency under which you will get payoff?

• Is there exclusivity?

• If yes, there is option value.
• If no, there is none.
• If in between, you have to scale value.

• Can you use an option pricing model to value the real option?

• Is the underlying asset traded?
• Can the option be bought and sold?
• Is the cost of exercising the option known and clear?