1. Three-way choice Option Price Option Value Real Options Calls & Puts Endogenous/Exogenous Option Price Option Value Real Options Calls & Puts Endogenous/Exogenous

2. Histogram of realized net benefits

3. REAL OPTIONS The basic idea expressed in this course is that, if benefits are greater than costs, do it. Hence, investments appear to resolve to a simple matter of maximizing NPV. When firms are faced with risky choices (i.e., actions or investments that have uncertain outcomes) they often use hurdle rates to evaluate alternatives that greatly exceed anything that can be justified by CAPM -- or any other portfolio model for that matter. 1.Asymmetric, weird distributions means that expected value may underestimate actual risk. High hurdle rates can offset this bias. 2.Project selection bias (i.e., where outcomes are risky, the likelihood is that project selection will be biased in favor of projects for which costs have been underestimated and benefits over estimated). High hurdle rates can offset this bias. 3.There is another possible reason: as we have seen, experience, history, time can reduce uncertainty and therefore project risk. We know that information has a measurable value. If time will provide information, it follows that delay can have value as well. It is a mistake to ignore the value of delay in analysis. High hurdle rates can be a proxy for the cost of not delaying, although not a very good one. A new approach to the evaluation of risky choices - the theory of real options. This theory provides an evaluative method that is conceptually and practically superior to the alternative of ignoring project risk or subjecting all risky projects to evaluation using very high hurdle rates. The basic idea expressed in this course is that, if benefits are greater than costs, do it. Hence, investments appear to resolve to a simple matter of maximizing NPV. When firms are faced with risky choices (i.e., actions or investments that have uncertain outcomes) they often use hurdle rates to evaluate alternatives that greatly exceed anything that can be justified by CAPM -- or any other portfolio model for that matter. 1.Asymmetric, weird distributions means that expected value may underestimate actual risk. High hurdle rates can offset this bias. 2.Project selection bias (i.e., where outcomes are risky, the likelihood is that project selection will be biased in favor of projects for which costs have been underestimated and benefits over estimated). High hurdle rates can offset this bias. 3.There is another possible reason: as we have seen, experience, history, time can reduce uncertainty and therefore project risk. We know that information has a measurable value. If time will provide information, it follows that delay can have value as well. It is a mistake to ignore the value of delay in analysis. High hurdle rates can be a proxy for the cost of not delaying, although not a very good one. A new approach to the evaluation of risky choices - the theory of real options. This theory provides an evaluative method that is conceptually and practically superior to the alternative of ignoring project risk or subjecting all risky projects to evaluation using very high hurdle rates.

4. Option Price Maximum an individual would pay for an option (right to participate in a lottery) prior to the event (drawing), given the ex ante probabilities of each of the SONs that might occur. Option Price is the certainty equivalent of the lottery (price you pay is certain, payoff uncertain) Where the option reduces risk, this is a premium; where it increases risk, a discount. The following diagrams reflect both cases using the examples of a dam and a bridge Maximum an individual would pay for an option (right to participate in a lottery) prior to the event (drawing), given the ex ante probabilities of each of the SONs that might occur. Option Price is the certainty equivalent of the lottery (price you pay is certain, payoff uncertain) Where the option reduces risk, this is a premium; where it increases risk, a discount. The following diagrams reflect both cases using the examples of a dam and a bridge

5. A Risk Reducing Project

6. Payoff and option value of risk reducing investment

7. Same project: expected surplus and option price

8. An Uncertainty Increasing Project

9. Risk increasing project: expected surplus and option price

10. Option price and max EV of WTP

11. SOME UNSTATED ASSUMPTIONS of ENPV The commitment is fully reversible (i.e., there are no sunk costs -- if benefits are less than anticipated or costs turn out to be higher, the commitment can be undone and costs fully recovered) OR If the investment is irreversible, it is a now or never proposition (i.e., it cannot be delayed without a substantial loss) The commitment is fully reversible (i.e., there are no sunk costs -- if benefits are less than anticipated or costs turn out to be higher, the commitment can be undone and costs fully recovered) OR If the investment is irreversible, it is a now or never proposition (i.e., it cannot be delayed without a substantial loss)

12. THE ABILITY TO DELAY AN IRREVERSIBLE INVESTMENT UNDERMINES THE SIMPLE NPV RULE WHY? Holding an investment opportunity that can be postponed is analogous to holding a call option; it gives you the right but not the obligation to exercise it at a future time. When an entity makes an irreversible investment, it "kills" its option to invest. That means that it sacrifices the possibility that waiting would provide information that would affect the desirability or timing of the investment. This "opportunity cost" (lost option value) should be included as part of the cost of the investment. WHY? Holding an investment opportunity that can be postponed is analogous to holding a call option; it gives you the right but not the obligation to exercise it at a future time. When an entity makes an irreversible investment, it "kills" its option to invest. That means that it sacrifices the possibility that waiting would provide information that would affect the desirability or timing of the investment. This "opportunity cost" (lost option value) should be included as part of the cost of the investment.

13. The right decision rule Where commitments are both irreversible and postponable, the NPV rule should be amended to read: PROJECT BENEFITS MUST EXCEED COSTS BY AN AMOUNT EQUAL TO THE BENEFIT OF KEEPING THE INVESTMENT OPTION ALIVE OR YOU SHOULDN’T DO IT Where commitments are both irreversible and postponable, the NPV rule should be amended to read: PROJECT BENEFITS MUST EXCEED COSTS BY AN AMOUNT EQUAL TO THE BENEFIT OF KEEPING THE INVESTMENT OPTION ALIVE OR YOU SHOULDN’T DO IT

14. Examples of projects that call for 3-way analysis

15. A Practical Example 1 LET'S SAY WE HAVE TO DECIDE WHETHER OR NOT WE WANT TO BUY 1000 F-35s @ $200M PER ($200B) Givens: They would replace existing planes, consequently this decision would have no effect on operating and maintenance costs). Buying F-35s will only have a payoff (assumed to be $500B in PV terms -- i=.05) if the air combat environment becomes significantly more challenging (q) and the threat of air combat does not change The probability of q =.5 LET'S SAY WE HAVE TO DECIDE WHETHER OR NOT WE WANT TO BUY 1000 F-35s @ $200M PER ($200B) Givens: They would replace existing planes, consequently this decision would have no effect on operating and maintenance costs). Buying F-35s will only have a payoff (assumed to be $500B in PV terms -- i=.05) if the air combat environment becomes significantly more challenging (q) and the threat of air combat does not change The probability of q =.5

16. A Practical Example 2 If we buy now we get an NPV of $50 B

17. A Practical Example 3 If we delay for ten years it would cost $400B in current dollars to buy the equivalent of 200 F- 35s (@ $200 M/PER), hence the PV cost = $246 M However, in ten years we would buy the F-35 only if the more dangerous SON eventuates. Hence, EV =.5 (0) +.5 (500 -246) = $127 B The value of the option to wait is, in this case, = $127B - $50B = $77 B. If we delay for ten years it would cost $400B in current dollars to buy the equivalent of 200 F- 35s (@ $200 M/PER), hence the PV cost = $246 M However, in ten years we would buy the F-35 only if the more dangerous SON eventuates. Hence, EV =.5 (0) +.5 (500 -246) = $127 B The value of the option to wait is, in this case, = $127B - $50B = $77 B.

18. Exogenous learning

19. A Practical Example 5 Another way of putting it: HOW HIGH WOULD PRICES HAVE TO GROW ON THE 200 F-35s BETWEEN NOW AND THEN TO JUSTIFY BUYING NOW? An amount equal to the PV of buying now ($50B) = $651.5 = PV 651 = 400;.5 (0) +.5 (500 - 400) = $50 B. IN OTHER WORDS, BUYING 200 F-35s NOW AND ONLY NOW AT A COST OF $200 B IS THE SAME AS BUY LATER AT A COST OF $651 BILLION IF NEEDED. Another way of putting it: HOW HIGH WOULD PRICES HAVE TO GROW ON THE 200 F-35s BETWEEN NOW AND THEN TO JUSTIFY BUYING NOW? An amount equal to the PV of buying now ($50B) = $651.5 = PV 651 = 400;.5 (0) +.5 (500 - 400) = $50 B. IN OTHER WORDS, BUYING 200 F-35s NOW AND ONLY NOW AT A COST OF $200 B IS THE SAME AS BUY LATER AT A COST OF $651 BILLION IF NEEDED.

20. A practical example: endogenous learning

21. Results of project learning

22. Expected project cash flows

23. Anticipated phase 3 values if project sold (in millions $)

24. Expected cash flow with phase three sale (in millions $)