Real Options Valuation and Dynamic NPV

Posted in CFA, finance by qmarks on April 9, 2011

There are different methodologies to value a project, payback, discounted payback, npv are namely a few. The DCF (discounted cash flow) is the widely used for any kind of valuation. However there are some drawbacks in it. For example in DCF the cash flows in each year is a static number. In many instances depending on the type of the project, each cash flow can deviate from the expected value. Even though there are some sensitivity applications to estimate the value range, in an excel spreadsheet we can only calculate the each input in bundles due to the structure of spreadsheet (2×2 matrix).  But what if we can forecast each input with a distribution function, (standard normal, log normal, uniform, discrete) with a mean, variance, maximum, minimum etc. variables? Wouldn’t that give us a better valuation range? Thanks to @Risk, we ( , a substitute for Oracle’s crystal ball) we can have dynamic NPV valuation range.

However, not all projects are finish on time. Take a pharmaceutical company as an example. There are several clinic trials to get the FDA approval, for every trial there are chances to continue or stop the project. Or at any time, you can be acquired by a giant, i.e. Pfizer, so you should also know your exit option value. Same applies to mining, or oil and gas companies. Their resource life is limited, for any moment, they need to acquire new resources, expand, or if things get messy they need may need to delay the project. How a DCF method can capture those options embedded in to the project?

At this point even the dynamic DCF cannot estimate the real value of the project. Therefore one needs to add these option values into the valuation. Thanks to Black-Scholes option pricing, we can estimate the value of those options. Under same rationale, we can justify the Black Scholes model through binomial method, or Monte Carlo simulation.

Here is a classic case for the Real Options, the Dragon Beer case. In this project, the CEO of a US based beer companies decides whether to enter into Chinese beer market in 2002. By using the static NPV method an executive can decide to reject the entry proposal into Chinese beer market. But adding the expansion and exit options into the valuation, the dynamic NPV (which is static NPV+ Real Options Value) justifies the investment decision. Here is my spreadsheet which estimates the option value. Real Option Spreadsheet (if a new window does not open, copy/paste this link: )

For 2 different option valuation, we used Black Scholes, Binomial and Monte Carlo simulation to estimate call and put option values. Our approach to value the volatility was the blended volatility of two comparable companies in China, in order to capture different capital structures in project cash flow volatility. We excluded the index volatility due to the elimination of unsystematic risk.

For the expansion option, the expansion CAPEX plus PV of maintenance CAPEX is assumed to be the Strike Price.

the discounted incremental cash flow is our Spot Price

risk free rate is the 30 year US government bond yield

volatility is our blended volatility of two comparables

time is the period between now and the beginning of expansion year.

The result is given in the spreadsheet.

For the exit option, the Right to exit is Strike Price

The PV of the  base line project cash flow is the Spot Price

the rest of the assumptions are the same as above. Result is also in the spreadsheet.

For any project valuation, it is better to know your Value at Risk, instead of blindly estimating the simple linear DCF method.


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