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## Real Options

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**Real Options**Mehmet Bozbay Hoksung Yau Laura Goadrich Ping Fong Hsieh Sirisha Sumanth March 8, 2004**Objectives**• Overview • Terminology • Real options in the Real world • Overvaluing options (Agouron) • Exploring options (Cisco) • Case study (Nole) • Summary**Issues in Real Options**• Advantages: • Successfully explains valuation of multiple companies believed to have substantial real options • Explain some of the difference in markets not accounted by traditional techniques • Disadvantage: • Real Options can be miscaluculated/misused and misvalue a company • Provides a method to exemplify market outcomes using nontraditional techniques**Overview: Real Options**• Helps investors determine whether a company’s stock is over- or undervalued • Real options considers impact of: • Risk • New technology • New market • … • Real-World Examples: Agouron Pharmaceuticals, Cisco, Nole**Terminology**• Scope-up options • Opportunities to increase variability in product lines • Eg. IBM expanding to create graphic cards • Scale-up options • Opportunities to expand capacity • Eg. Power Packaging took over one plant of General Mills • Learning options • Opportunities to acquire companies with the goal of entering into new businesses • Eg. GE taking over Datex-Ohmeda • Equity Stakes • Purchasing equity in start-up companies**Real-World Example: Agouron Pharmaceuticals**• Kellogg & Charnes (2000) Financial Analysts Journal • Illustrates the problem of valuing a company with real options and how that valuation can differ from the market’s valuation • Background: biotechnology companies known for having high values when their products are in development (no positive cash flow)**Real-World Example: Agouron Pharmaceuticals**• Types of real options available • Growth option • Expand production if favorable in the market • Abandonment option (why choose?) • Viable reasons for abandonment • inhibit share holder loss • scrap failing projects • …**Real World Example:Agouron Pharmaceuticals**• Valuations of Agouron based on real options differed from the actual market values of the company’s stock as a particular drug progressed through the development process • Discovery • Preclinical • Clinical trial- phase I • Clinical trial- phase II • Clinical trial- phase III • FDA filing and review • Once the drug hit the market, the drug can vary in quality from Breakthrough - Above Average - Average - Below Average - Dog**Real World Example:Agouron Pharmaceuticals**• Root cause of differences: • The abandonment of a drug is rarely announced • Only one drug made it to phase II and III • Potential projects were included in the valuation when they were not part of the product pipeline • Investors were making different assumptions • Political pressure for FDA to approve drugs for HIV-positive patients • Assumed need less than eight years from phase II to launch, but only took two years • Sales were four times expectations in the first year • Lesson: real options were not overlooked by the market, but may have been overvalued**Real-World Example:Cisco Basics**• Sell: Networking supplies • Scale-up options • Supply network equipment for Internet connectivity • Scope-up options • Supplies businesses and individuals • Learning options • Integrating voice, video and data in their network**Real-World Example: Cisco Example**• Traditional discounted cash flow example • Market Value (FY 2000): $445.1 billion • Assumptions: • Earnings will grow at a rate of 10% annually after 2005 • The risk-free rate is 5% • The market risk premium is 6% • There is no adjustment for earnings after 5 years**Real-World Example: Cisco Evaluation**CostOfCapital = riskFreeRateOfInterest + riskPremiumOfMarket * Volatility = 5% + (6% * 1.45) = 13.7%**Real-World Example: Cisco Sensitivity Analysis**• DCF = $266.565billion vs. Market Value= $445.1billion • Difference: $178.535billion • SensitivityAnalysis • Vary constant growth rate of 10% to 11% • DCF – MarketValue = $91.061million • Vary cost of capital from 13.7% to 16% • Difference: $284.873million • Lesson: Not considering options poorly represents the actual market value.**Real-World Example: Nole Background**• Example illustrating valuing an option. • Initial start-up costs • capital expenditures $500million • investment in working capital $50million • Depreciation & capital expenditures $100million/year • Option 1: Not expand • Revenues Y1 $1billion Y2 $1.2billion Y3 $1.44billion Y4 $1.526billion Y5 $1.617billion Y6 $1.715billion**Real-World Example: Nole Choices**• Option 2: Expand in year 3 with $2billion • Annual depreciation $200million • Expenditures • Annual capital expenditures year 4, 5, 6 each $100million • No additional capital expenditures • Revenues Y1 $1billion Y2 $1.2billion Y3 $1.44billion Y4 $1.9billion Y5 $2.47billion Y6 $3.211billion**Real-World Example: Nole Expanding Black-Scholes**Value of option= P x N(d1) – X x e –r x t x N(d2) = $1,231 x 0.4678 – $2,300 x e-6% x 3 x 0.1718 = $245million Value of Expansion Option using DCF = -$31million**Real-World Example: Nole Variability of Volatility**Increasing volatility increases cost of capital decreases value of underlying decreases value of option**Summary**• Agouron showed a large difference between real world valuations and traditional methods. • Cisco illustrated the positive impact of using options. • Nole compared the valuation traditional verses options and clearly expressed the need for options to describe the marketplace.**Complication from Internal and External Interactions**Interaction between option holders and underlying asset’s value can complicate the analysis of real option.**Inability to Explain Absurd Valuation**The options a company has are usually not independent with each other. Their values are not additive. It’s questionable whether the presence of real options can explain the absurd price that were witnessed in recent years for many Internet stock.**Model Risk**The risk associated with the use of an incorrect model or incorrect inputs Example : • American put option on a stock priced $100 • The exercise price is $100 • Risk-free is 5 % • One year to expiration • Volatility is 32 % The correct model (binomial model) gives the price value $16.41 Incorrect model ( Black-Scholes) gives the price value $15.48 Error 5.7%**Failure to meet Assumption**Major Assumptions Lognormality Randomness Known and constant volatility Minor Assumptions Known and constant risk-free rate No taxes and transaction costs American-style option**Major Assumptions**Lognormality The rate of return on the underlying asset is lognormally distribution. Example: A non-dividend –paying stock sells for $100 and moves up to $110 after one year. The logarithmic return is ln(1.10) = 9.53% The model typically assume the logarithmic return follows a normal distribution, which means the return itself follows a lognormality distribution Randomness Prices are randomness to assure that markets are competitiveness that allows pricing models to work. No one participant can dominate all the others. Known and constant volatility The volatility in standard option-pricing models is not directly observe and easy to obtain. Also, the models are sensitive to the volatility.**Minor Assumptions**• Known and constant risk-free rate Option-pricing models generally assume a known and constant risk-free rate. • No taxes and transaction costs It facilitates the capture of most essential elements of the economic process being modeled. • American-style option The option is the one that can be exercised before expiration. It offers more flexibility.**Difficulty of Estimating Inputs**• Market Value of the Underlying Asset Sometimes, the estimating for appropriate discount rate, the life of a project may be difficult. • Exercise Price The amount of money can be received or paid in the future are difficult to determine. • Time to Expiration A company can’t know how long it can keep a project before abandoning it to claim a salvage value. • Volatility The option prices are very sensitive to the estimate of volatility. But it is very difficult to observe in financial option-pricing application.**Risk-Free Rate**The value of an option is not so sensitive to estimate of the risk-free rate. It is acceptable to obtain an estimate of the risk-free rate by estimating the rate on a default-free zero-coupon security. Example A real option expires in 275 days Let the bid and ask discount rates on US government zero-coupon bonds (Treasury Bills) for maturity be 4.52% and 4.54% We spilt the difference and assume a rate of 4.53%**Example**The price of one year bill If the T-bill price is $96.54 per $100 par, the annual rate is The continuous compounded rate is (in order to use in Black-Schole Model)**Nontradability of the Underlying Asset**• Assumption in the area of real options analysis: underlying asset can be bought and sold in a liquid market. • When using binomial approach, the ability to trade the asset and the option in such a manner that no arbitrage opportunity exists is the glue that binds the models together.**Assumptions of Hedging, Tradability, and Risk Neutral**Valuation • r: Risk-free rate (5%) • u: Holding period return on the stock if it goes up ($150) • d: Holding period return on the stock if it goes down ($50) • Stock price: $100**Risk-adjusted discount rate and probability of outcomes**• If the probability of up move is 0.6, then Risk-adjusted discount rate k = 0.1. • If k = 0.12, then q=0.62.**Risk-adjusted discount rate and probability of outcomes**(cont.) • If k is risk-free rate, then • q plays the same role as p in the option-valuation problem. Option-pricing models are often said to use risk neutral valuation.**Consistency of All Approaches**• No one assume investors are risk neutral. Rather, risk neutral valuation is simple and imposes only light demands. • Risk neutral valuation is not a different approach that obtains different numbers from a standard risk-adjusted approach.(Feinstein 1999)**Example**• Invest $9 in a project • If the outcome is good, invest $18 and begin to generate $10 a year forever. • If the outcome is bad, invest $18 and begin to generate $3 a year forever. • Probability of good outcome is 0.6 and bad outcome is 0.4 • Discount rate is 25%**Example (cont.)**• The market value of the project is: • The market value of the project at time 1 is:**Example (cont.)**• The value of the project at time 0 is: • NPV is • Up factor: • Down factor: • The risk neutral probability is**Example (cont.)**• Option value $11.28 • According to Feinstein’s approach, the overall discount rate is a blend of 25% and 5%. So the weighted discounted rate is: • The correct project value is $11.28**Summary**• One source of difficulty in applying real options valuation is the assumption may or may not be appropriate in the case of real options (lognormality distribution of the value of the underlying asset, randomness of prices) • The estimation of inputs, such as the volatility of the value of the underlying asset, the exercise price, the time to expiration, is more challenging for real options than for fincial options.**Chapter 6: Empirical Evidence on the Use and Accuracy of**Real Options Valuation**Paddock, Siegel, and Smith (1988) – Option Valuation of**Claims on Real Assets: The Case of Offshore Petroleum Leases • Real options model for valuing offshore oil and gas leases in a federal sale of 21 tracts in the Gulf of Mexico. • Real options were not able to explain the bids as well as one might have hoped. • Real options theory was not very well-known in 1988. • Data provided by the government were not too good to carry out analysis. • Winner’s curse – tendency for the highest bidder to pay more than fair**Quigg (1993) – Empirical Testing of Real Option-Pricing**Models • Market prices of 2,700 land transactions in Seattle during 1976-1979. • Market prices reflect a premium for the option to wait to invest (optimal development) that has a mean value of 6% of the land value. • Supports the belief that investors either use real options models or trade in such a manner that their valuations are consistent with those of real options models.**Berger, Ofek, and Swary (1996)– Investor Valuation of the**Abandonment Option • Whether investors price the option to abandon a firm at its exit value. • This option is priced as an American put, whose value increases with exit value. • Significant relationship between a company’s market value and its estimated exit value, suggesting that investors take the option to exit into account when valuing companies. • The more likely the option will be exercised, the more valuable is the option.