# Real options: discount rate for the value of the underlying security

This is an example inspired by Chapter 3, sub-chapter "Combining decision trees with real options(DTRO)", sub-sub-chapter "Case 4 Part Two", of

Boer, F.P., 2004. Technology Valuation Solutions, 1. edizione. ed. John Wiley & Sons Inc, Hoboken, NJ.

in order to make it shorter.

Suppose we have a project made up by two stages.

The first stage is R&D, with a probability of success of 50%. It requires 1 year.

If R&D is successful, the second stage, which starts at year 2 and lasts 1 year, is deployment. To deploy the project we need to invest 5 M\$, and we can get 8 M\$ out of it.

But there is no obligation to engage in stage 2, and the 8 M\$of revenues are characterized by market risk (customers can buy more than that or less than that), so we can treat Stage 2 as a call option (at least that is what I understood to be the reason for it). By reading the chapter about real options of: Brealey, R.A., Myers, S.C., Allen, F., Edmans, A., 2022. Principles of corporate finance. Con Contenuto digitale per download e accesso on line, 14° edizione. ed. McGraw-Hill Education, New York, NY. I would think that: 1. The strike price of the option equals the 5 M\$, discounted 1 year at the WACC of the company.
2. The value of the underlying asset of the option would equal the 8 M\$revenues we can get out of it, discounted 1 year at the WACC of the company. Boer (the first book) agrees on the first point. But not on the second point. For Boer, the underlying value equals 8 M\$ - 5 M\$= 3 M\$ (i.e., the NPV of the project at year 2), discounted 1 year at the WACC of the company, plus the 5 M$, discounted 1 year at the risk-free rate. So the 5 M$ are basically subtracted and re-added back, but the first time they are discounted at the WACC of the company, while the second time they are discounted at the risk-free rate.

I did not understand the logic behind this calculation by Boer (and the author left this world, so asking him is not an option either).

Would someone explain it?