Question

The current static NPV of a construction project is $500. The risk-free rate is 5% per year and the volatility of the project is 20% per year. In four years, there is an opportunity to expand the project by 40% at a cost of $150. You may also abandon the project for $300 (salvage value) in four years.

a) Construct a two-step binomial tree for the construction project and use the real option valuation approach to compute the value of the expansion option connected to this project. Assume continuous time discounting.
b) Use the two-step binomial tree constructed in a) and use the real options valuation approach to compute the value of the option to abandon connected to this project. Assume continuous time discounting.
c) What is the value of a chooser option connected to the above real investment project.

Answer 1

The value of the expansion option can be calculated using a two-step binomial tree. The same approach can be used to calculate the value of the option to abandon. The value of a chooser option can be determined by considering the value of the expansion option and the option to abandon.

Step-by-step explanation:

To calculate the value of the expansion option, we can construct a two-step binomial tree. In the first step, the project can either stay the same or expand. In the second step, the project can either stay the same or abandon. The value of the expansion option at the end of the second step is the maximum of the difference in the NPV of the expanded project and the cost of expansion. The value of the expansion option at the end of the first step is the discounted value of the value at the end of the second step.

To calculate the value of the option to abandon, we can use a similar approach. At the end of the second step, the value of the option to abandon is the salvage value. At the end of the first step, the value of the option to abandon is the discounted value of the value at the end of the second step.

The value of a chooser option connected to the project can be calculated by considering the value of the expansion option and the option to abandon. The chooser option allows the decision maker to choose between the two options at the end of the first step.