CHAPTER 12 Real Options
What is a real option?
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What are some types of real options?
Types of real options (Continued)
Five Procedures for Valuing Real Options
Analysis of a Real Option: Basic Project
Approach 1: DCF Analysis
Investment Timing Option
Investment Timing (Continued)
Procedure 2: Qualitative Assessment
Procedure 3: Decision Tree Analysis (Implement only if demand is not low.)
Use these scenarios, with their given probabilities, to find the project’s expected NPV if we wait.
Decision Tree with Option to Wait vs. Original DCF Analysis
The Option to Wait Changes Risk
Procedure 4: Use the existing model of a financial option.
Inputs to Black-Scholes Model for Option to Wait
Estimate of P
Step 1: Find the PV of future CFs at option’s exercise year.
Step 2: Find the expected PV at the current date, Year 0.
The Input for P in the Black-Scholes Model
Estimating s2 for the Black-Scholes Model
Three Ways to Estimate s2
Estimating s2 with Judgment
Estimating s2 with the Direct Approach
Find Returns from the Present until the Option Expires
Use these scenarios, with their given probabilities, to find the expected return and variance of return.
Estimating s2 with the Indirect Approach
The Indirect Approach (Cont.)
Indirect Estimate of 2
From earlier slides, we know the value of the project for each scenario at the expiration date.
Use these scenarios, with their given probabilities, to find the project’s expected PV and PV.
Find the project’s expected coefficient of variation, CVPV, at the time the option expires.
Now use the formula to estimate 2.
The Estimate of 2
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Step 5: Use financial engineering techniques.
Other Factors to Consider When Deciding When to Invest
A New Situation: Cost is $75 Million, No Option to Wait
Expected NPV of New Situation
Growth Option: You can replicate the original project after it ends in 3 years.
Decision Tree Analysis
Expected NPV of Decision Tree
Financial Option Analysis: Inputs
Estimating P: First, find the value of future CFs at exercise year.
Now find the expected PV at the current date, Year 0.
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Estimating s2: Find Returns from the Present until the Option Expires
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Why is s2 so much lower than in the investment timing example?
Estimating s2 with the Indirect Method
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Now use the indirect formula to estimate 2.
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Total Value of Project with Growth Opportunity
Sensitivity Analysis on the Impact of Risk (using the Black-Scholes model)