Chapter 17 Real Options

1. Chapter 17 Real Options

2. Real options • The application of derivatives theory to the operation and valuation of real investment projects • A call option is the right to pay a strike price to receive the present value of a stream of future cash flows • An investment project is the right to pay an investment cost to receive the present value of a future cash flow stream Investment Project Call Option Investment Cost = Strike Price Present Value of Project = Price of Underlying Asset

3. Investment and the NPV rule • NPV rule: • Compute NPV by discounting expected cashflows at the opportunity cost of capital • Accept a project if and only if its NPV is positive and it exceeds the NPV of all mutually exclusive alternative projects. • Example under certainty: • Invest in a $10 machine, that will produce one widget/year forever at a cost of $0.90/widget. The widget will sell at $0.55 next year and the price will increase at 4% per year. Risk-free rate is 5% per year. The investment can occur anytime. Should it? If yes, when?

4. Investment and the NPV rule (cont.) • Example under certainty: (cont.) • Static NPV: NPVInvest today = $27 NPVWait five years = $30.49 NPVWait 23.82 years = $35.03

5. Investment and the NPV rule (cont.) • The project as an option: • The decision to invest is analogous to the decision to exercise an American option early • Exercise price ~ investment cost • Underlying asset ~ value of the project • Tradeoff between three factors: • Dividends foregone by not exercising: cashflows from selling widgets • Interest saved by deferring the payment of exercise price • Value of the insurance lost by by exercising (the implicit put option): since no uncertainty, there is no insurance value • S = $55 (=$0.55/(0.05-0.04)), K = $28 (=$10 + $0.90/0.05), r = 0.04879 (=ln1.05), s = 0, d = 0.0095669 (=ln1.05 – ln1.05) C = $35.03

6. Investment under uncertainty • Example: • A project requires an intial investment of $100, and is expected to generate a perpetual cashflow stream, with a first cash flow $18 in one year, expected to grow at 3% annually. Assume a discount rate of 15%. If the project can be delayed for up to two years, should the project be accepted? If yes, when? • Static NPV: $18/(0.15 – 0.03) – $100 = $50 • Trade-off between three factors: • Foregone initial cashflow: $18 • Interest savings: $7 (7% x $100) • Value of preserved insurance: Is it more than the loss due to delay? Loss of $11 if delayed

7. Investment under uncertainty (cont.) • Example: (cont.) • What is the value of the insurance? Need to know the volatility of cashflows:

8. Investment under uncertainty (cont.) • Example: (cont.) • S = $150, K = $100, r = 6.766% (=ln1.07), s = 0.5, t = 2 years, d = 0.1133 (=ln(1+($18/$50))), p* = 0.335C = $55.80 > $50

9. Real options in practice • The decision about whether and when to invest in a project ~ call option • The ability to shut down, restart, and permanently abandon a project ~ project + put option • Strategic options: The ability to invest in projects that may give rise to future options ~ compound option • Flexibility options: Ability to switch between inputs, outputs, or technologies ~ rainbow option

10. Static NPV Option Not to Operate Real options in practice (cont.) • Peak-load electricity generation • Plant idle when price of electricity is less than the cost of fuel • Plant online when electricity price spikes or fuel price declines • Similar to owning a strip of call options on electricity expiring daily, with a strike price of cost of variable inputs • Spark spread: Selec – H x Sgas, where H is plant efficiency measure • Profit = max(Selec – H x Sgas, 0), a European exchange option • By rewriting using put-call parity:

11. Real options in practice (cont.) • Research and development • Costs incurred to acquire technology to be used in future projects • Projects in the future only undertaken if they have positive NPV

12. Real options in practice (cont.)

13. Commodity extraction as an option • Incur the extraction costs to realize the value of the resource: defer investment and stop and start production • Example: Single-barrel extraction under certainty • A plot of land contains one barrel of oil that can be extracted by paying $13.60. Currently, oil sells for $15/barrel, effective annual lease rate d is 4%, and effective annual risk-free rate is 5% • How much is the land worth? • $1.40 (= $15 – $13.60) [no real options, immediate extraction] • $1.796 [considering real options, trigger price $16.918 at t = 12.575] • If the lease rate of an extractive commodity is zero, it is best to leave the commodity underground forever

14. Commodity extraction as an option (cont.) • Example: Single-barrel extraction under uncertainty • The same example as before, but oil price volatility is 15% • How much is the land worth? • $3.7856 [considering real options, trigger price $25.3388] • When uncertainty is introduced, the optimal exercise time is later, and the project value, and trigger price is higher

15. Commodity extraction as an option (cont.)

16. Commodity extraction as an option(cont.) • Example: Valuing an infinite oil reserve • Example 17.1: Suppose S0 = $15, r = 5%, d = 4%, c = $8, and the investment cost I is $180 • The value of the producing well is $15/0.04 – $8/0.05 = $215. • Per barrel extraction cost is d(c/r + I) = $13.60 • CallPerpetual [$15/0.04, $8/0.05 + 180, 0.000001, ln(1.05), ln(1.04)] = [$44.914, $422.956] • The value of the well is $422.956 • Extraction occurs when S = 0.04 x $422.956 = $16.918 • Example 17.2: Assumptions above + oil price volatility s = 0.15 • CallPerpetual [$15/0.04, $8/0.05 + 180, 0.15, ln(1.05), ln(1.04)] = [$94.639, $633.469]

17. Commodity extraction with the option to shut down and restart production

18. Commodity extraction with the option to shut down and restart production (cont.)

19. Commodity extraction with the option to shut down and restart production (cont.)