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REAL OPTIONS AND EVALUATION OF REAL OPTIONS TURKISH CAPITAL MARKET BOARD PROGRAM NAMIK K. AYENGIN 04.18.2003 A NEW KIND OF OPERATIVE INSTRUMENT:REAL OPTIONS • In very competitive market environment, managers of the firms have to do their best efforts to satisfy their shareholders. So the managers have used new financial and operative instruments like derivatives, takeovers and real options. Real options actually are operative instruments rather than financial instruments, dealing with actual investment decisions and giving the managers more flexibility MAJOR CHARACTERISTIC OF INVESTMENT • Irreversiblity: Investments partially or completely irreversible that means the initial cost of investment partially sunk at least. • Uncertainty : Because of the uncertainties and risks in the economic environment, the outcomes of investments can not be estimated in the initial stages. • Timing: Some timing considerations also come with the investment decisions, management may prefer maximize to information about uncertain conditions as much as they can do. The Real Option Approach • The main idea is keeping ways open and having high flexibility. • Superior of NPV approach. • Deal with uncertainty and risk. WHAT IS AN OPTION? A REAL OPTION? OPTIONS ANALYSIS? • • • • Options In general, Options are rights to exercise but not an obligation The main element of an option is that the cost of exercising the option Because of giving flexibility, an option has value. In the financial markets, options are mostly standard contracts. In their basic form, they specify the price at which the holder of the option can buy or sell some asset, such as a stock, some commodity, or foreign exchange. Real Options • “Real options deal with physical things rather than financial contracts. They provide “rights, not obligations” to to control and manage uncertain economic environment. In general it could be said that all elements of a structure providing flexibility is considered as “real options”. SOME EXAMPLES OF REAL OPTIONS • • • • R&D in production and marketing Increase or decrease in scale of operations Timing to invest Switching to a different production technology or market • Temporary shut-down • Abandonment SOME EXAMPLES APPLICATIONMEANING • Setting up a power plant that allow to use 2 kind of fuel . So dual-fuel power plant that can use either oil or gas give the operators to use the more economic fuel as a input , although this kind of facility is much more costly for investment . • Using updatable computer systems so limited cost of new technologies. • Research and development efforts give the management some proper ways to go in the future, for example having the patents of products that are not attractive now but in the future. That is why some companies have been interested in new patents even though they are not using them in production. Options Analysis • Options analysis have the methods for calculating the value of of “real options” that provide flexibility. They estimate the expected value of the asymmetrical distribution of possible outcomes associated with options. The result of an options analysis is a value for a particular option or element of a system. Real Option Approach Has At Least Three Basic Distinct Phases: • Discovery, in this phase, managers identify the areas where the most attractive opportunities of uncertainty are and which of them may potentially offer the greatest rewards from options; • Selection, In this phase, managers evaluate how to reach the possible means of providing flexibility to applications, and decide on which of these options should be implemented; and • Monitoring, In the last phase, the managers should focus on the uncertainties that are weather in consistent with predictions or not. So that the decision makers will know when to implement or abandon the options that were built into the system. VALUE –ADDED BY REAL OPTIONS Real options analysis gives to managers the power of estimation of the value of operation flexibility. Because of not availability of flexibility evaluation, the manager have not been able to think about the value of flexibility. So improvements in management science managers can easily discover much greater value in: • Development activities, and • Flexibility in timing.Subject to enforcement action PURPOSE OF USING REAL OPTION ANALYSIS Using real options analysis, managers can now calculate the value of such actions, compare them to their cost and compare to a firm rationale for justifying or rejecting them. HISTORY OF REAL OPTIONS • In the last decade many of leading global technological companies have been beginning to use real options to improve proper strategies about technology management, innovation and system development. The Binomial Option Pricing Model Let us say we have an option to purchase land next year at a price of $50 per hectare, which is also the current price of the land. However, next year the price may go up to $60 a hectare with an 85% probability, or may fall to $40 per hectare with a 15% probability. The riskless rate of return is 10%. Land 60 50 40 110 Bond (rF=10%) 100 110 Call Option (X=50) 10 C 0 • The expected rate of return on the land is 14%, and the standard deviation of returns is also 14% • If we discounted the expected cash flows of the call at 14%, we would get a price of $7.46, and a standard deviation of returns of 48%. Because it is riskier, the call should intuitively have a higher rate of return. We should thus have a lower price and higher expected return for the call. Solution by replicating the option Suppose we buy 1/2 hectare of land, and borrow $18.18. The net cost today is 25-18.18=$6.82 The debt repayment next year is 18.18(1.1)=$20 Our 1/2 hectare of land will be worth either 30 or 20, so the total payoff will be either $10 or $0 10 6.82 0 Since the payoff is identical to the payoff on the call option, we conclude C=6.82 N60 – B(1+0.1) = 10 N40 – B(1+0.1) = 0 => N = ½ => B = 18.18 Observe that the expected return on the call is now 24.6%, which is higher than the expected return on the stock due to the greater risk. Note that we did not use the probabilities of the up and down state at all in calculating the price. Solve by risk-neutral probabilities • Conceptual leap: instead of thinking of a world where people require compensation for risk through higher discount rates, we think of everyone using the risk-free rate of return to value all cash flows. To compensate for this monumental assumption, we revise the “subjective” (true) probabilities of the up and the down states to come up with “risk-neutral” probabilities for the up and the down state. • The risk-neutral probabilities are the revised probabilities for the up and the down state that exactly compensate for risk. We will see that they revise the probability of the up state downward, and the probability of the down state upward. • Let q = the risk-neutral probability of the up-state. • P(stock) = 50 = [q*60 + (1-q)*40]/1.1 • q=.75 • We can now value the option directly by using the risk-neutral probabilities: • • P(call)=[.75*10+.25*0]/1.1 • P(call)=6.82 • Note that this is the same answer we previously derived by arbitrage. Example: • You bought a 100-share call contract three weeks ago. It expires five weeks from today. On that date, the price will either be $120 or $95. The two states are equally likely to occur. Currently, P(stock)=$96. X=$112. You can borrow money at 10% annually. What is the value of the call contract? Standard method • Replicate the cash flows of the call contract with a portfolio of stock and borrowing. • Payoff(Call contract) = 100(120-112) = 800 if up • = 100*0 if down • Now calculate the payoffs of a portfolio of N stocks and borrowing B dollars. • Use an interest rate of (1.1)5/52-1=.921%: • Payoff(portfolio)= N*120-B*(1.00921) if up • = N*95-B*(1.00921) if down • Solve for N & B that replicate the payoffs: • 25*N=800 N=32 • 32*95-B*1.00921=0 B=3012.26 • Now calculate the cost of this portfolio=32*96-3012.26=$59.74. Since the call contract has the same payoffs, it must also have the same price. Method 2: Risk-Neutral Pricing • Calculate the risk-neutral probabilities that satisfy risk-neutral pricing for the stock: • 96 = [q*120 + (1-q)*95]/1.00921 • 1.884 = 25*q q = .07536 • Now price the call contract using the risk neutral probabilities • P(call contract)=[.07536*800 + (1-.07536)*0]/1.00921 • =$59.74 • We get the same answer. Real Option Example NSP Power is contemplating three choices for constructing a power plant. • Build a 24 megawatt (MW) plant for $4000. • For an extra $75, this power plant can be made expandable to 44 MW, but this will require an extra $1100 in costs at the time of expansion. • For $4500, the power plant can be made so that it is costless to expand to 44 MW. • Assume that all output can be sold at the current market price. The current market price of $30/MW will move for two years, and then be constant in perpetuity. The price path below has been constructed so that price increases by 36% after an upward move (75% probability) or decreases by 26% after a downward move (25% probability). This gives an expected price increase of 20% and a standard deviation of returns of 26%. 54.7 40.5 30 30 22.2 16.5 The variable costs of production are $21.25 per MW for the first 24 MW’s and $42.50 per MW for the next 20 MW’s. The riskless rate is 10%. After t=2, all uncertainty is resolved, and so cash flows beyond this point should be discounted at the risk-free rate. Which plant should NSP choose, and what is the NPV? Real Options Example: Solution, Part I • The first thing to solve for is the riskneutral probabilities of the up and the down state. Notice that the subjective (true) probabilities and returns are the same at all nodes, so we only have to solve • This gives p = 58% and 1-p = 42%. We can then work backward from t=2. We first analyze the problem for the 24 MW plant, and then address each of the two additional options. • • • • Valuation of 24 MW plant At t=2, the price is known forever, and we simply must decide whether to operate or shut down. Formally, the value at time 2 in each of the three states is Max[24*(54.7 – 21.25)*(1+1/0.1),0] = $8831 ==> operate Max[24*(30 – 21.25)*(1+1/0.1),0] = $2310 ==> operate Max[24*(16.5 – 21.25)*(1+1/0.1),0] = $0 ==> abandon The values at t=1 are then 0.58 * 8831 0.42 * 2310 Max[24 * (40.5 21.25),0] 5538 462 $6000 1.1 0.58 * 2310 0.42 * 0 Max[24 * (22.2 21.25),0] 1218 23 $1241 1.1 Working backwards we get a value at t=0 of 0.58 * 6000 0.42 * 1241 $3637 1.1 Note that if we had naively taken a present value, we would have obtained PV= .75 * 462 .25 * 23 .75 * .75 * 8831 2 * .75 * .25 * 2310 $4345 1.2 1.2 * 1.2 Valuation of the Option to Expand When expansion is costless, the value at time 2 of the option to expand in each state is • Max[20*(54.7 – 42.5)*(1+1/0.1),0] = $2684 ==> expand • Max[20*(30 – 42.5)*(1+1/0.1),0] = $0 ==> don’t expand • Max[20*(16.5 – 42.5)*(1+1/0.1),0] = $0 ==> don’t expand The values at t=1 are then 0.58 * 2684 0.42 * 0 Max[20 * (40.5 42.5),0] 1415 0 $1415 1.1 0.58 * 0 0.42 * 0 Max[20 * (22.2 42.5),0] $0 1.1 Working backwards we get a value at t=0 of 0.58 * 1415 0.42 * 0 $746 1.1 If we had naively taken a present value, we would have obtained PV= .75 * .75 * 2684 $1048 1.2 * 1.2 Valuation of the Option to Expand When Expansion is Costly If expansion costs $1100, then the option value of expansion is 2684 1100 * 746 $440 2684 The ordinary DCF value of expansion is then 2684 1100 * 1048 $618 2684 Summarizing the NPV’s of Alternatives • • • • 1. 24 MW Plant 2. Expandable at Cost of $1100 3. Expandable Plant Initial Cost $4000 Ordinary DCF 4345-4000 =$345 $4075 4963-4075 =$888 $4500 5393-4500 = $893 Option Valuation 3637-4000 = $-363 4077-4075 =$2 4383-4500 =$-117 The difference between ordinary DCF and real option evaluation method is clear here. In DCF method analysis the most attractive number 3 investment, but on the other hand, by using option valuation analysis, the most attractive is number 2 investment alternative. CONCLUSION • • • • The main concept is keeping open possibilities in management decision process has made manager think differently than before. This new methodology helps the managers to: Recognize that the value of the projects is integrally associated with the fluctuations of the market; Understand that uncertainly is not always a risk to be avoided, but also presents valuable opportunities that can be exploited; Adopt a proactive stance toward risk, looking not just to respond to it passively, but to manage it proactively through the use of real options; and Introduce far more flexibility, justified in terms of its option value, into the design of systems than has been the norm. Although real option is a new instrument, some primitive forms of real options have already been in used by Turkish companies. For example investment timing, when interest rates is relatively high, companies postpone investment decision under the expectation of decrease in the interest rates in the future. But, there are many areas with high potential for real option applications in scientific meaning.