Section B Finance Theory II - Real Options

Real Options Real options ƒ Managers have many options to adapt and revise decisions in response to unexpected developments. ƒ Such flexibility is clearly valuable and should be accounted for in the valuation of a project or firm. 2 Real options, cont. Imbedded options ƒ Follow-up investments ƒ Option to abandon the project ƒ Option to wait before investing ƒ Option to expand / change production methods Key elements ƒ Information will arrive in the future ƒ Decisions can be made after receiving this information 3 Our plan Last class ƒ Real options: basic intuition ƒ Simple DCF analysis of real options (decision trees) Today ƒ Review of option pricing ¾ Why doesn’t simple DCF work quite well? ƒ ƒ Identifying real options Valuing real options using Black Scholes 4 1. Review of option pricing Real options and financial options Option Definition The right (but not the obligation), to buy/sell an underlying asset at a price (the exercise price) that may be different than the market price. Financial Options Options on stocks, stock indices, foreign exchange, gold, silver, wheat, etc. Vs. Real Options: Not traded on exchange. Underlying asset is something other than a security 6 Pricing of a call option on stock Stock Option (X = 110) S1 = 120 S0 = 100 10 ? S1 = 80 0 The challenge is to find the value of the call option today 7 Pricing of a call option on stock ƒ Consider the following strategy: ¾ Borrow money (or sell a bond with face value of B) ¾ Buy a N shares of stock ƒ Choose N and B so that the payoffs from the portfolio = option payoffs 10 = -B + N*120 B = 20 N = 0.25 ? 0 = -B + N*80 8 Pricing of a call option on stock ƒ Our stock / bond portfolio has exactly the same payoff as the option ¾ So, the option and the portfolio must have the same value today ¾ Otherwise: arbitrage opportunity ƒ What is the value of the portfolio today (assume risk-free rate =4%)? -B / (1+r) + N * S0 ƒ = -20 / 1.04 + 0.25 * 100 = 5.77 We just priced the option. Option value = $5.77. 9 Why standard DCF doesn’t work very well? ƒ Let’s value our option using standard DCF ¾ What discount rate should we use? ¾ Let’s try the required return on stock E[RS] p = 0.8 S1 = 120 E[S1] = 112 => E[RS] = 12% S0 = 100 p = 0.2 S1 = 80 10 Why standard DCF doesn’t work very well? ƒ DCF gives us the following option value: (0.8 * 10 + 0.2 * 0) / 1.12 = $7.14 ≠ $5.77 What’s wrong? ƒ Discount rate of 12% is too low => the option is riskier than the underlying stock Why? ƒ Option is a levered position in a stock. ¾ Recall the analogy with firms’ financial leverage: Higher financial leverage => higher equity betas and equity returns. 11 Option is a levered position in a stock ƒ Recall our replicating portfolio: Borrow B/(1+r) and buy N shares of stock ¾ Suppose that stock beta = 1 and market premium = 8% • Note that this works. CAPM: 12% = 4% + 1 * 8% ƒ What is option beta? βoption = wbond * β bond + wstock * β stock = 4.33 0 ƒ ƒ 25/5.77 * 1 So, the required return on the option is 38% = 4% + 4.33 * 8% And the option value is again: $5.77 = 8 / 1.38 12 How about multiple periods? ƒ In principle, we can value the option the same way as before ¾ Start at time T=2 and move backwards ƒ But several things change at each node: ¾ Replicating portfolio, option beta, discount rate T=0 T=1 T=2 144 120 96 100 80 ƒ ƒ 64 This can become quite tedious That’s where option pricing models such as Black-Scholes come in. 13 Options valuation techniques ƒ “Dynamic” DCF (decision trees) ¾ Recall our “Handheld PC” and “Copper Mine” examples ¾ Approximation used for real-options problems ¾ Not an exact answer because of problems with discounting ƒ Binomial model ¾ Similar to our one-period example from today’s class ¾ Requires more computations than Black-Scholes ¾ Can be useful when Black-Scholes doesn’t work very well ƒ Black-Scholes ¾ We will focus on this model from now on 14 Black-Scholes formula ƒ Black-Scholes formula relies on the same valuation principles as the binomial model (replicating portfolios, no arbitrage) Option value = N(d1) * S – N(d2) * PV(X) ƒ Note the similarities to the one-period binomial model Option value = N * S – PV(B) N(d): Cumulative normal probability density function d1 = ln[S/PV(X)] / (σT1/2) + (σT1/2)/2 d2 = d1 - (σT1/2) S = Current stock price X = Exercise price r = Risk-free interest rate T = Time to maturity in years. σ = Standard deviation of stock return 15 Recall “Handheld PC” example Model B NPV (t=3) = 16,557 D go for it Model A turns out well => good news for Model B Model B value at t=0 Model B value in t=0 ? "Static" NPV [(16,557 - 21,148)/2]/1.123 "Dynamic" NPV [(16,557 + 0)/2]/1.123 5,892 Option pricing [(16,557 + 0)/2]/???3 ??? -1,634 Model A turns out badly => bad news for Model B Model B NPV (t=3) = -21,148 D drop it 16 2. Identifying Real Options Two Issues with Real Options Identification ƒ Are there real options imbedded in this project? ƒ What type of options? Valuation ƒ How do we value options? ƒ How do we value different types of options? ƒ Can’t we just use NPV? 18 Identifying Real Options ƒ It is important to identify the options imbedded in a project. ƒ There are options imbedded in all but the most trivial projects. ƒ All the art consists in: ¾ Identifying those that are “significant”, if any ¾ Ignoring those that are not ƒ Identifying real options takes practice, and sometimes “vision”. 19 Identifying Real Options (cont.) ƒ Look for clues in the project’s description: “Phases”, “Strategic investment”, “Scenarios”, … ƒ Examine the pattern of cash flows and expenditures over time. For instance, large expenditures are likely to be discretionary. ƒ Taxonomy of frequently encountered options : ¾ ¾ ¾ ¾ ¾ Growth option Abandonment option Option to expand or contract scale Timing Option to switch (inputs, outputs, processes, etc.) 20 Is There An Option? ƒ Two conditions: (1) News will possibly arrive in the future; (2) When it arrives, the news may affect decisions. ƒ Search for the uncertainty that managers face: ¾ What is the main thing that managers will learn over time? ¾ How will they exploit that information? 21 Oz Toys’ Expansion Program ƒ Oz Toys’ management is considering building a new plant to exploit innovations in process technology. ƒ About three years out, the plant’s capacity may be expanded to allow Oz Toys’ entry into two new markets. 2000 EBIT * (1-t) Depreciation CAPX ∆ NWC FCF TV NPV (WACC=12%) 120.0 25.0 -145.0 2001 2.2 19.0 8.1 4.1 9.0 2002 4.0 21.0 9.5 5.5 10.0 2003 -10.0 21.0 307.0 75.0 -371.0 2004 11.5 46.3 16.0 7.1 34.7 2005 13.7 48.1 16.3 8.0 37.5 2006 17.4 50.0 17.0 9.7 40.7 610.5 -19.8 22 Oz Toys: Is There An Option? (1) Oz Toys might learn (or not) about: ƒ The demand for the current and/or new products ƒ The possibility of rivals entering the market ƒ Etc. (2) The information might affect (or not) Oz Toys’ decision: ƒ Whether or not to undertake expansion phase 1 at all ƒ Whether to undertake phase 2 (or even phase 3,…) ƒ Whether to push one new product or the other ƒ Etc. 23 Oz Toys: Identifying the Option ƒ Project’s description refers to two distinct phases ¾ Phase 1: New plant ¾ Phase 2: Expansion FCF FCF 100 0 -100 2000 2001 2002 2003 2004 2005 2006 - 200 - 300 - 400 ƒ Spike in spending: Probably discretionary CAPX Change in NWC 350 300 ƒ Possibly, an imbedded growth option 250 200 150 100 50 0 2000 2001 2002 2003 2004 2005 2006 24 Practical Issue #1: Simplifications ƒ Real projects, especially long-horizon ones, are complex: ¾ They often combine assets-in-place and options. ¾ Options are nested. ƒ Simplifying assumptions are needed: ¾ To allow the technical valuation analysis ¾ To keep the model flexible ¾ To keep the model understandable to you and others (especially others involved in the decision process) 25 Practical Issue #1: Simplifications (cont.) ƒ Cut the project into pieces corresponding to simple options. ƒ Search for the primary uncertainty that managers face ƒ A simplified model that dominates (is dominated) by the project gives an upper (a lower) bound for the project’s value, e.g.,: ¾ Using European rather than American options ¾ Ignoring some of the options ¾ Ignoring some adverse effects of waiting (e.g. possible entry) 26 Oz Toys: Simplifications ƒ Value phase 1 and phase 2 separately. ƒ Focus on the option to undertake expansion phase 2 or not. ¾ Assume all other options are “negligible” ƒ Assume that phase 2 is to be undertaken in 2003 or never. D European Call option 27 3. Valuing Real Options Valuation of Real Options ƒ Tools developed to value financial options can be useful to estimate the value of real options embedded in some projects. ƒ Real options are much more complex than financial options. ƒ The aim here is to develop numerical techniques to “keep score” and assist in the decision-making process, not provide a recipe to replace sound business sense. 29 Options vs. DCF ƒ The real options approach is often presented as an alternative to DCF. ƒ In fact, the real options’ approach does not contradict DCF: It is a particular form that DCF takes for certain types of investments. ƒ Recall that option valuation techniques were developed because discounting is difficult ¾ I.e., due to the option, one should not use the same discount rate (e.g. WACC) for all cash flows. 30 Options vs. DCF (cont.) ƒ DCF method: ¾ “expected scenario” of cash flows, ¾ discount the expected cash flows ƒ This is perfectly fine as long as: ¾ expected cash flows are estimated properly ¾ discount rates are estimated properly ƒ Precisely, it is complex to account for options in estimating: ¾ expected cash flow ¾ discount rates 31 Start with the “static” DCF Analysis ƒ Begin by valuing the project as if there was no option involved ¾ Pretend that the investment decision must be taken immediately. ƒ This benchmark constitute a lower bound for the project’s value. ¾ NPV<0 does not mean that you will never want to undertake the investment. ¾ NPV>0 does not mean that you should go ahead immediately with the invest (nor that you will definitely invest in the future). 32 Oz Toys: DCF Analysis ƒ Disentangling the two phases. ƒ Requires making judgments about: ¾ Which expenses are discretionary vs. non-discretionary ¾ Which cash inflows/outflows are associated with each phase ƒ Note: Sometimes, simply retrieve disaggregated data used to construct the summary DCF analysis. 33 Oz Toys: Valuing Phases 1 and 2 2000 Phase 1 Cash flow Investment TV (5% growing perpetuity) NPV (WACC=12%) Phase 2 Cash flow Investment TV (5% growing perpetuity) NPV (WACC=12%) Total Cash flow Investment TV NPV (WACC=12%) 2001 2002 2003 2004 2005 2006 9.0 10.0 11.0 11.6 12.1 12.7 145.0 191.0 -3.7 23.2 25.4 28.0 382.0 419.5 -16.1 9.0 145.0 10.0 11.0 382.0 34.7 37.5 40.7 610.5 -19.8 34 Oz Toys: DCF Analysis (cont.) ƒ Both phases have negative NPV ƒ Phase 2’s NPV is probably largely overstated: ¾ Investment ($382M) is likely to be less risky than cash flows. ¾ Using the three-year risk-free rate of 5.5% DCF Analysis of Phase 2 Discounting the Investment at 5.5% 2000 2001 2002 2003 2004 2005 Phase 2 Cash flow Investment TV (5% growing perpetuity) NPV (WACC=12%) 23.2 25.4 2006 28.0 382.0 419.5 -69.5 35 Valuing the Option ƒ The strategy is to map the project into a simple option and use financial valuation tools to price the option: Black-Scholes formula. ƒ Oftentimes, this involves making somewhat heroic assumptions about the project. 36 Mapping: Project Æ Call Option Project Call Option Expenditure required to acquire the assets X Exercise price Value of the operating assets to be acquired S Stock price (price of the underlying asset) Length of time the decision may be deferred T Time to expiration Riskiness of the operating assets σ2 Variance of stock return r Risk-free rate of return Time value of money 37 Oz Toys: The 5 Variables X Investment needed in 2003 to obtain the phase 2 assets. $382M S PV of phase 2’s cash flows. $255.8 T It seems that phase 2 can be deferred for 3 years (Check with managers). 3 years r 3-year risk-free rate (Check yield curve). σ2 5.5% Variance per year on phase 2 assets. Can’t get it from DCF spreadsheet. Phase 2 Cash flow TV PV (WACC=12%) 2000 2001 2002 2003 2004 23.2 Say 40% 2005 25.4 2006 28.0 419.5 255.8 38 Practical Issue #2: What Volatility? ƒ Volatility (σ) cannot be looked up in a table or newspaper. ¾ Note: Even a rough estimate of σ can be useful, e.g., to decide whether to even bother considering the option value. 1. Take an informed guess: ƒ Systematic and total risks are correlated: High β projects tend to have a higher σ. ƒ The volatility of a diversified portfolio within that class of assets is a lower bound. ƒ 20-30% per year is not remarkably high for a single project. 39 Practical Issue #2: What Volatility? (cont.) 2. Data: ƒ For some industries, historical data on investment returns. ƒ Implied volatilities can be computed from quoted option prices for many traded stocks ¾ Note: These data need adjustment because equity returns being levered, they are more volatile than the underlying assets. 40 Practical Issue #2: What Volatility? (cont.) 3. Simulation: ƒ Step 1: Build a spread-sheet based (simplified) model of the project’s future cash flows ¾ Model how CFs depend on specific items (e.g. commodity prices, interest and exchange rates, etc.) ƒ Step 2: Use Monte Carlo simulation to simulate a probability distribution for the project’s returns and infer σ. 41 Black-Scholes Formula ƒ Two numbers suffice: S × (1 + r)T A= X ƒ B=σ× T and A table that gives the Black-Scholes’ call option value as a fraction of the stock price S (see handout) Black-Scholes Formula: 0.50 0.55 0.60 0.65 0.70 0.75 0.60 5.1 6.6 8.3 10.0 11.9 13.7 0.65 6.6 8.3 10.1 11.9 13.8 15.8 Columns: A 0.70 8.2 10.0 11.9 13.8 15.8 17.8 0.75 10.0 11.9 13.8 15.8 17.8 19.8 Lines: B 0.80 11.8 13.8 15.8 17.8 19.8 21.8 0.86 14.2 16.1 18.1 20.1 22.1 24.1 42 Black-Scholes Formula (cont.) ƒ The number A captures phase 2’s value if the decision could not be delayed (but investment and cash flows still began in 2003). ƒ Indeed, in that case, A would be phase 2’s Profitability Index: PI = PV(cf) S = =A PV(inv.) ⎛ X ⎞ ⎜⎜ ⎟ T⎟ ⎝ (1 + r) ⎠ and A > 1 ⇔ NPV > 0 ƒ The option’s value increases with A (as shown in the table). 43 Black-Scholes Formula (cont.) ƒ The number B, Cumulative Volatility, is a measure of “how much S can change” between now and the decision time T. ƒ Intuitively, S can change more: ¾ when S has more variance per year, i.e., σ is large ¾ when there is more time for S to change, i.e., T is large ƒ B captures the value of being able to delay the decision. Note: When B=0, only the project’s NPV matters (whether A>1) because either the decision has to be taken now (T=0) or it might just as well be taken now as no news will arrive (σ =0). 44 Oz Toys: Valuation S ⋅ (1 + r ) T 255.8 ⋅ (1.055)3 = = 0.786 A= X 382 Black-Scholes Formula: 0.50 0.55 0.60 0.65 0.70 0.75 0.60 5.1 6.6 8.3 10.0 11.9 13.7 0.65 6.6 8.3 10.1 11.9 13.8 15.8 and B = σ ⋅ T = 0.4 ⋅ 3 = 0.693 Columns: A 0.70 8.2 10.0 11.9 13.8 15.8 17.8 0.75 10.0 11.9 13.8 15.8 17.8 19.8 Lines: B 0.80 11.8 13.8 15.8 17.8 19.8 21.8 0.86 14.2 16.1 18.1 20.1 22.1 24.1 ƒ The value of phase 2 is (roughly): V2 = 19% * S = .19 * 255.8 = $48.6M ƒ The value of the expansion program is: V1 + V2 = -3.7 + 48.6 = $44.9M 45 Practical Issue #3: Checking the Model ƒ Formal option pricing models make distributional assumptions. ƒ Approach 1: Try and find a model that is close to your idea of the real distribution (More and more are available). ƒ Approach 2: Determine the direction in which the model biases the analysis, and use the result as an upper or lower bound. ƒ Approach 3: Simulate the project as a complex decision tree and solve by brute force with a computer (i.e., not analytically). 46 Practical Issue #4: Interpretation ƒ Since we use simplified models, the results need to be taken with a grain of salt and interpreted. ƒ Put complexity back into the model with: ¾ Sensitivity analysis ¾ Conditioning and qualifying of inferences ƒ Iterative process. ƒ Helps you identify the main levers of the project, and where you need to gather more data or fine tune the analysis. 47