Real Options. Bernt Arne Ødegaard. 23 November 2017

Transcription

1 Real Options Bernt Arne Ødegaard 23 November Real Options - intro Real options concerns using option pricing like thinking in situations where one looks at investments in real assets. This is really a matter of creative thinking, playing the game of spot the option. Well known examples are The deferral option, the option to delay a project before starting it. an american call option The option to abandon projects an american put option When specified carefully, can use standard option theory to price the options, and calculate correct project present values. 2 Motivating example Exercise 1. On 11/10/97, MCI s management announced an agreement with WorldCom. Roughly, MCI shares would be exchanged for the equivalent of $51 in WorldCom stock. At the time, the deal was not a sure thing. The justice department might balk at the monopolizing. It would take about five months for the takeover to be finalized. Today s price of MCI stock is P now = The five-month T-bill rate was roughly 5% (p.a.). Before any of the takeover news hit the market, MCI was selling for $30 a share. 1. Infer the state price probability of the deal going through. 2. Use the inferred probability to find the price of a a 4/98 call option on MCI with a $40 strike price. 3. As a matter of fact, at the close of 11/10 an MCI 4/98-$40 call was selling for 4 5/8. The discrepancy can (maybe) be explained by the fact that in addition to WorlCom, GTE had offered $40 cash per share of MCI, and there was a claim in the Wall Street Journal that GTE was considering an offer of $45. Let us plausibly posit that by January, we will know whether the Worldcom - MCI deal goes through. If the deal fails, there is still GTE, who is prepared to offer $40 $45 a share. As a reasonable estimate of the final bid from GTE, let us take the midpoint of the GTE offers, $42.5. So, by April, we have the following three possible outcomes: $51, $42.5 or $30. The first occurs for sure if it is known by January that the WorldCom takeover gets an OK. The second or third outcomes are assumed to occur randomly if the deal is called off by January. Graphically, this is what we have in mind: 1

2 P OK january P notok january In addition to knowing the November price of MCI stock, $41 1/2, we also know the price of a January MCI call option with strike $42 1/2. This option closed on 11/10 at $1 3/4. Can we use this information to confirm the correctness of the price for the 4/98 option? 4. At the same time, show that the current value of MCI stock is consistent with your numbers. 5. What was the markets implied probability of the MCI-WorldCom deal going through? 3 Real options Two characteristics Assets derive their value from the value of other assets Cash flows are contingent on the occurrence of specific events These are option-like characteristics Applying present value of expected cash flows, systematically underestimates the value of such assets. Call option, right to buy Profit Buying a call option. 0 K S T Put option, right to sell 2

3 Profit Buying a put option. 0 K S T Determinants of option value Call Put Current value of underlying + - Variance of underlying + + Dividends/payout from the underlying - + Strike price of the option - + Time to expiration + + Risk free interest rate + - Option pricing models Binomial model: Replicating portfolio argument. Determinants of option value: Current price of underlying how it moves Continous time limit - Black Scholes Extension of option pricing not just simple puts and calls Caps, barrier options Compount options Rainbow option (two or more sources of uncertainty) 3.1 The option of delaying a project Traditional investment analysis: Only accept project with higher returns than the hurdle rate. Problems: Do not consider the option built into many investment projects: Wait one period and then redo investment evaluation. Examples: Undeveloped land (real estate investor) Patent (exclusive right to develop) Natural resource company undeveloped reserves. Option to delay a project Payoff of option to delay X: Initial investment. V : Value of project (NPV of future cashflows) This value is random, affected by uncertanty which will be resolved in the future. 3

4 NPV decision for the firm V X Negative NPV Positive NPV Inputs: Value of underlying asset PV of future cashflows starting project now. Variance in the value of the asset Exercise price of the option initial investment cost Expiration of option Riskless rate (matching maturity) Cost of delay like dividend yield in option price Cost of delay = Cash flows next period/present value now If cashflows flow proportianally, 1/no years in project If these inputs are present: Charge ahead, price option The calculated option price some issues Necessary assumptions to replicate the option (when pricing) trading possibilities of underlying asset. This is problematic for the kind of investments we are looking at with real option models Does this invalidate the approach? Well, think about it this way: This is how the markets should work if they applies this is still relevant as a benchmark value. problems in valuing the option to delay: How well is the project approximated by the typical assumptions used in option pricing. (continous process etc) Implications in valuing the option to delay. NPV may be negative now, but may become positive. NPV may already be positive, but may still want to delay Added uncertainty may make options-like projects more valuable. Option-pricing models: Black Scholes easier to apply, but restrictive assumptions. Binomial option pricing model: Allow for early exercise, typical for real options Allow for modelling underlying uncertainty more generally How to implement? use variance input of Black Scholes Exercise 2. You are interested in aquiring the exclusive rights to market a new product that will make it easier for people to access their on the road. If you do aquire the rights to the product, you estimate it will cost you $50 mill up front to set up the infrastructure needed to provide the service. Based on your current projections, you believe that the service will generate only $10 mill in after-tax cashflows each year. In addition, you expect to operate without serious competition for the next five years. 4

5 What is the present value of the project, assuming an interest rate of 15%? The biggest source of uncertainty about this project is the number of people who will be interested in the product. While current market tests indicate that you will capture a relatively small number of business travellers as your customers, they also indicate the possibility that the potential market could be much larger. In fact, a simulation of the projects cash flows yield a standard deviation of 42% in the present value of the cash flows, Value this project as an option. The current risk free interest rate is 5%. Instead of using the Black Scholes formula, calculate the option price using a binomial framework, using one year for each step in the binomial tree, allowing for early exercise. Valuing a patent Right to market and develop a product. ie. option Valuing a firm with many patents Sum of exercised options (value of commercial prediction) options (patents) currently alive potential for developing more patents (cost of developing new patents) Natural Resource Options Initial value of starting production X Undeveloped Reserves as options Present value of production schedule starting now V Value max (X,V) Inputs for valuation: Available quantities of the resource, estimated value if extracted today. 3.2 The options to expand and abandon Similar to the investment timing option at future date, pay a cost (investment) Two step procedure First step: Low/negative NPV project Second step: Possibility to expand depending on uncertainty resolved during the first project. The second project provides the option, what one needs inputs to. 3.3 Valuing equity in distressed firms. In distressed firms, equity is an option held by equityholders, to pay off debtholders and assume control of the firm. Value of firm Face value debt Value of equity 5

6 This framework can be used to value the firm directly. Exercise 3. You are valuing the equity in a firm whose assets are currently valued at 100 million. The standard deviation in this asset value is 40%. The face value of debt is 80 million (it is zero coupon debt with 10 years left to maturity). The Treasure 10 year bond rate is 10%. Use this information to value the equity and the debt of the firm. What is the implicit interest rate on the debt? Suppose the value of the firm falls to 50. What is then the value of the equity in the firm? What about the implicit interest rate on the firm s debt? Implications of viewing equity as an option: equity may have value even if value of the firm is currently below bond promised payment. Note also that this can be used to figure out properties of the bonds of the firm, such as implicit probabilities interest rates, or alternatively, implicit probabilities of default. 4 Another perspective on real options A call option is the right to pay a strike price to receive the present value of a stream of future cash flows (represented by the price of the underlying asset). An investment project is the right to pay an investment cost to receive the present value of a stream of future cash flows (represented by the present value of the project Note the similarities: Investment project Call option Investment cost Strike price Present value of project Price of underlying asset The correct use of NPV 1. Compute NPV by discounting expected cash flows at the opportunity cost of capital. 2. Accept a project if and only if its NPV is positive and it exceeds the NPV of all mutually exclusive alternative projects Option-like features in investment decisions. Decision of whether and when to invest. [Call option] Ability to shut down, restart, abandon projects. [Put option] Ability to be flexible about choice of inputs, outputs, production technologies [Flexibility options] Ability to invest in projects that may give rise to new options. [Strategic options] Exercise 4. Suppose you own a tract of land, and you find oil in the ground. The current oil price is 15/barrel. Suppose this is a small find, with a small number of barrels of oil. What is the nature of the decision problem? Specifically, suppose that the find is one barrel of oil. This barrel can be extracted by paying X = The effective annual risk free rate is r = 5%. The oil forward curve is such that the effective annual lease rate, δ, is 4% (constant over time). What can you currently sell the land for? What uncertainties will affect the decision problem? 6

7 Suppose this is a large find, you expect to be able to extract oil from it in the indefinite future. What is the nature of the decision problem? Initial investment trigger Restart trigger Shutdown trigger Start Stop Restart Exercise 5. A project costs 100 to initiate. The project produces an infinite stream of cashflows starting 1 year after investment. The cashflows are expected to increase by 3% thereafter. The risk free rate is 7%, the project beta is 1.33 and the market risk premium is 6%. 1. Suppose the project cashflow next year is expected to be 18. Value the project. 2. Suppose the project does not have to be initiated immediately, it can be delayed for one or two years, but if it is not initiated by year 2 it is no longer possible to start it. Also suppose that there is uncertainty about the initial cash flows from the project, they are lognormally distributed with volatility 50%. Value the project. Exercise 6. Consider a gold mine with an estimated inventory of one million ounces and a capacity output rate of 30,000 ounces per year. The price of gold is expected to grow 3% a year. The firm owns the right to this mine for the next 20 years. The cost of opening the mine is $100 million, and the average production cost is $250 per ounce. Once initiated, the production cost is expected to grow 5% a year. The standard deviation in gold price is 20%, and the current price of gold is $375 per ounce. The riskless rate is 6%. 5 Summary Real Options Analysis: Using tools from option pricing in real investment decision. Look for: Contingent choice Ask: What is the observable contractible important 7

8 exogenous factor relevant for profitability of investment project References 8