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Real Options I

Real Options I. The First example of Real Options is the option to delay investment, or Wait. Undertaking any project destroys the option of undertaking that project in the future. Key element of investment: Irreversibility. Destructive element: First Mover Advantage. Waiting.

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Real Options I

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  1. Real Options I The First example of Real Options is the option to delay investment, or Wait. Undertaking any project destroys the option of undertaking that project in the future. Key element of investment: Irreversibility. Destructive element: First Mover Advantage.

  2. Waiting • Do not use NPV rule. • NPV averages over future states of nature. • Ignores your role as optimal decision-maker. • Akin to American Call on Dividend-Paying Stock. • You lose a dividend • But gain time • Normative & Positive Implications.

  3. Waiting Positive Implications: • Hurdle rates that are much higher than wacc. • Vacant Land in high-rent areas. • Undeveloped profitable opportunities.

  4. Waiting - Example Consider an investment that is irreversible. Once undertaken it generates a cash flow each year into perpetuity. The cash flow is random, and can be characterized as a Random Walk, or Geometric Brownian Motion with no drift. The option to undertake this exists for 6 years.

  5. Waiting vs NPV

  6. Several Things to Note (Graph produced by Dixit1.xls) Even when project has negative NPV, value is positive. (Value of flexibility.) Where NPV > Option Value, the option is not defined. Trigger Value increases in sigma.

  7. Waiting - Example 2 Even if the cash flows from a project are perfectly predictable (i.e., riskless), option analysis may be appropriate (& yield different decision rules from the NPV rule) if interest rates are variable. See the ingross.xls spreadsheet for an example of this.

  8. Review the 3 Themes Distr’n: Geometric Brownian Motion implies log-normal terminal distr’n. & Truncation is handled by the Max functions throughout the tree. Dynamic Optimization: Value depends on doing what is optimal Solve recursively

  9. Expectations and Discounting: This project is not a traded asset - let alone the option on it. But, we use option pricing theory, as if it were. Corporate Finance generally invokes the fiction of a twin security. 3rd Theme (cont’d.)

  10. 3rd Theme (cont’d.) Note that both next year’s cash flow (R) and the project value move through time. Since the value is always R/r, the cash flow provides a rate of return equal to the risk-free rate. In the risk-neutral world the project’s expected rate of return is the risk-free rate. This implies that the expected capital gain must be 0.

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