Initial value of an investment project in a binomial real option valuation model

How do you measure the initial value of a project in a binomial tree ROV? I'm not specifically working in the valuation scene, but sort of had an interest in how the models work logically. It's not NPV, since that can take a very low value. What's the first "S"?

• Essentially you’re asking what is $S_0$ in option pricing formulae. As far as theory is concerned, this number is given. You may not know what the future value of under underlying project is but you ought to have an idea about its current (market) value. There’s no formula but this estimate may rely on the opinions of experts, an asset’s replacement value, references to peer groups etc. – Kevin Apr 15 at 16:53
• I would argue that under a model, a project‘s PV is determined by its potential future cashflows, the hedging program and all (optimal) future decisions. Hence, today’s value is a function of the tree, not the starting point. Does that make sense? – Kermittfrog Apr 15 at 16:59
• @Kermittfrog I think (and perhaps James can clarify) we consider a situation where the market value of a project is an exogenous process (say geometric Brownian motion) which the firm observes and can decide when to optimally invest (pay some amount $I$ to acquire the production asset which then perpetually generates some random profits). In this sense, today’s value (the initial value of the underlying project) wouldn’t be determined endogenously in the model. The value of the firm’s real option would, of course, be a function of the parameters of the process governing the project’s value – Kevin Apr 15 at 17:19
• @Kevin interesting. I had no idea about any ways to calculate this. I was simply imagining an investment project as a mind experiment with two options to expand in the time frame of three years as a way to understand the model on a live example. To be honest, I still don't know how I would go about calculating the value of the underlying asset here. Classic models such as DCF present it rather simply. – James Apr 15 at 19:03
• @Kevin I read on the topic a bit, and it turns out that Copeland and Antikarov sort of came up with a viable algorithm of calculating the underlying asset value in their book "Real Options: A Practitioner's Guide". It starts with NPV calculation basically. – James Apr 16 at 16:21