1. Real Options Chapter 8 A 4-Step Process for Valuing Real Options

2. 2 Assumptions MAD – Market Asset Disclaimer – use present value of underlying as if it were a market security Properly anticipated prices fluctuate randomly, regardless of cash flows a project is expected to have

3. A 4-step Process Step 1Step 2Step 3Step 4 StepCompute base case present value without flexibility using CDF valuation model Model the uncertainty using event trees Identify and incorporate managerial flexibilities creating a decision tree Conduct Real Options Analysis (ROA) ObjectivesCompute base case present value without flexibility at t=0 Understand how the present value develops over time Analyze the event tree to identify and incorporate managerial flexibility to respond to new information Value the total project using a simple algebraic methodology and an Excel spreadsheet CommentsTraditional present value without flexibility Still no flexibility; this value should equal the value form step 1. Estimate uncertainty using either historical data or management estimates as input Flexibility is incorporated into event trees, which transforms them into decision trees. The flexibility has altered the risk characteristics of the project; therefore, the cost of capital has changed. ROA will include the base case present value without flexibility plus the option (flexibility) value. Under high uncertainty and managerial flexibility, option value will be substantial.

4. Samuelson’s Proof Proved that properly anticipated prices fluctuate randomly Returns will not be cyclical on companies that have cyclical cash flows Means that multiple, correlated sources of uncertainty (some with mean reversion) can be combined into a single multiplicative binomial process.

5. Samuelson’s Proof (cont’d) Step 1: Assume spot price of asset follows stationary autoregressive scheme, perturbed by random error (zero-mean unit variance):

6. Samuelson’s Proof (cont’d) Progression of expected spot prices and their variances

7. Samuelson’s Proof (cont’d) Step 2: Show that expected prices of futures contracts do not change through time. Then we could prove that the value of a project, which is the sum of values of T futures contracts, will remain constant if we add back the value of the contract that expires this time period. If we add back dividends, value of a project through time will be a random walk, regardless of cash flows.

8. Samuelson’s Proof (cont’d)

9. The expected change in futures price is 0, so expected futures prices do not change over time.

10. Empirical Evidence for Samuelson’s Proof Examine steel, chemical, and paper industries. Ran statistical tests for cyclicality in cash flows and return on invested capital (ROIC) versus time, as well as total return to shareholders. If Samuelson’s proof is correct, there should be no cyclicality in total return even if there are cycles in cash flows and ROIC. Cash flows and ROIC has cycles, but not total return.

11. Common Mistakes Assume volatility of underlying = volatility of one of its components Overcomplicate analysis with too many variables or uncertainties. Use Black-Scholes formula for more general models – it assumes European option, single source of uncertainty, no dividends, constant exercise price. Use decision tree without final solving step of using the replicating portfolio to ensure no arbitrage opportunities.

12. Conclusion Sets of uncertainties can be reduced to one: value of a project through time. Then the 4-step process can be used to solve real options problem.

13. Conclusion (cont’d): 4-step Process Estimate value of underlying risky asset Monte Carlo to inject assumptions about causal uncertainties and produce value-based event tree Add decision nodes (including options) to event tree Value payoffs of tree by working backwards in time using replicating portfolio method.