Quantifying the value of uncertainty and optionality in M&A, market entry, and R&D projects; and the business case for real-scale, real-world decision trees

OLYMPUS DIGITAL CAMERA(Disclosure: This blog post is based on an actual client engagement.  The blog post has to some extent been anonymized / obfuscated, and has been approved by the client in question.)

According to garbage can theory, as formulated by Michael D. Cohen, James G. March, and Johan P. Olsen back in 1972, organizational choices can often be seen as the outcome of seemingly unrelated problems, solutions and decision makers coming together in a fairly random way.  This blog post, which is about valuing high-tech start-ups facing massive uncertainty and optionality through the use of decision trees, is a case in point:  A windsurfing friend of mine was in the process of developing his high-tech start-up, I was in the process of starting up a quantitative practice as part of my strategy advisory firm, and the two of us were already working on another joint project, completely unrelated to start-ups, high-tech, quantitative methods, and valuation.

My friend, let us call him Andrew, is electrical engineer by training, with long background from the oil and gas industry, the last few years on contract with a control system provider.  Andrew has an entrepreneurial  mind, and has ongoing investments in real estate organized as a holding company, say ABI.  However, one day he told me that he had formed a small subsidiary of ABI, let us call it Subsidiary, to commercialize a specific invention of his in the area of predictive algorithms for condition-based maintenance.   Early technical tests based on real data provided robust, but probably not statistical significant evidence that the technology worked.  He had already received a Norwegian patent for the technology and an international patent was in process.  Furthermore, he had received some funding from a governmental scheme and from an individual with professional background from commercial air transport.  I, with a doctoral degree in engineering and 10 years + of experience from similar industries, could clearly see the technical credibility and commercial potential of this invention.

Andrew was now facing some serious decisions: whether or not to invest in the case, on what market to focus, whether to partner with what company, whether to seek additional funding from new investors and in case what type of investors, and generally how to go all in or not.  He was also facing serious some major uncertainties, including what was the probability of technical success, what was the market, and what was the size of the addressable market.

Ultimately, he also wanted to know what his share in Subsidiary was actually worth, with or without an industrial investor.  I suggested at that point that we could apply decision trees for valuating his share, as such trees explicitly models the uncertainty, the optionality, and the complexity inherent in the sequence of decisions and uncertainties that aggregate to form a commercialization process for a high-tech start-up.

Using decision trees for valuing staged investments with uncertainty and optionality is of course nothing new; I learned about decision trees whilst I got my MS in Management at MIT in the early nineties.  Furthermore, most MBAs today with a specialization in decision theory or corporate finance have learned about them at university, as they are described in most intermediate-level text books.  However, fact is that with some exceptions (typically companies doing oil exploration or multi-stage R&D) very few individuals in Norway can use them effectively for real-size problems.

There are of course a number of alternative approaches to valuing such project, typically based on deterministic discounted free cash flow (DFCF), various types of multiples, or in the extreme, real options theory.  None of them provided the capability for modelling the complex sequence of decisions and uncertainties that Andrew and Subsidiary faced.

Equipped with DPL Professional from Syncopation Software, Andrew and I produced a full decision tree for the situation at hand during two half-day workshops plus some individual work on my side.  The fully expanded tree had around 8-9m end nodes, each of them with a different evaluation function.  The software automatically calculates the optimal decision at any point in the tree, that is, the decision that maximizes expected future DFCF from Subsidiary for ABI.  Unlike in a spreadsheet analysis, the optimum decision depends on history.  The optimization process starts in the future and works backwards towards the current.

outcome distributionFigure to left: Distribution of ABI’s share of DFCF from Subsidiary, red = go for it; green = sell IP as is.  One can see the founder’s dilemma, either go all in and either lose significant money (= the left part of the red curve)  or make it big (= the long red tail to the right), or just sell the IP as is and get a small, but unknown amount of money for it (= the green curve just on the positive side).

Key conclusions were: If the objective ABI is to maximize ABI’s share of DFCF from Subsidiary, Andrew should continue his endeavour to build up Subsidiary.  Subsidiary should also team up with an industrial partner, as getting a small bite of a big cake is better than a big bite of a very small cake (and Andrew neither has the financial muscles nor the professional experience to do this alone).  If at the end of 2017, Andrew has not been able to compellingly demonstrate the technical and commercial merits of his invention, he should consider selling the IP.  Furthermore, the value of ABI’s share of Subsidiary are NOK Xm, with an uncertainty range of NOK A-Bm.  Not only that, the option value of the investment = the value of the investment with flexibility – the value of the investment with a fixed / tied to the mast plan (= the base case) (= NOK YM) = NOK Zm.

NOK Xm was probably on the low side and I observed during the engagement that Andrew became somewhat disappointed.  Not only that, a separate valuation based on DFCF in Excel resulted in a value that was not far-off from NOK Xm, at least after some fiddling with the numbers.  Why was the engagement then assessed a success, and what did Andrew then learn from this engagement, beyond getting a theoretically sound and accurate valuation of ABI’s share of the DFCF from Subsidiary?

Not unsurprisingly, I think what really caught his attention during this engagement were matters only indirectly related to the exact value of ABI’s share of DFCF of Subsidiary:

  • How to price Subsidiary’s products?
  • To whom in the value chain (manufacturers, control system providers, asset owners, or service providers) to offer these products?
  • What is the addressable market, and how big is it?
  • Is this an incremental or disruptive innovation?
  • What will over time happen if an industrial investor gets a significant ownership share?

Could we have had discussions about the above issues without the use of decision trees?  My hypothesis is yes, but that our process for creating such decision tree and our subsequent discussions about it significantly sharpened our joint insight into what are critical decisions, uncertainties, and parametric sensitivities facing Andrew and Subsidiary.

Why was this a particularly interesting engagement for me as an advisor?  Because it nicely illustrated some key issues and benefits related to the use of real-scale, real-world decision trees for M&A, market entry, and R&D projects:

  • In principle, one could have done the decision tree in Excel. But with 8-9m terminal nodes and history-dependent optimal decisions (at any point the decision is the one that maximizes expected value of outcome, given what is already known), one is lead to conclude that any claim to be able to do this in Excel would be bogus.
  • It is theoretically justifiable to use a lower cost of capital in a decision tree, based on explicitly modelling uncertainty, than in a deterministic DFCF model, in which uncertainty or risk is taken into account through a somewhat arbitrary adjustment of hurdle rate.
  • For this particular case, the value of optionality (the Z referred to above) was not massive. In practice, optionality is significant only if there is room for scaling up, scaling down, abandon, or defer.
  • It would of course possible to get the correct value for EV and MV from a traditional DFCF analysis, by arbitrarily adjusting some numbers, say a hurdle rate or discount rate. Personally, I like the good feeling of calculating correctly based on a sound model.
  • Decision trees appear in practice to be the only way to correctly value such cases. Multiple-based methods are not relevant; deterministic DFCF models do not really capture optionality and uncertainty (except through discount rate); and real options theory is applicable only for the simplest problems.

To sum up: correct EV (from a decision tree) = EV (from deterministic DFCF model) + value of optionality + value of reduced risk adjustment of cost of capital – cost of uncertainty – value of unjustified optimism.  If no optionality and value of reduced risk adjustment of cost of capital = cost of uncertainty, then we are back to correct EV (from a decision tree) = EV (from deterministic DFCF) – value of unjustified optimism.

Which is why it is better to get the model correct from the start, with a decision theoretical approach, and which is why I wanted to share with you my insights related to this engagement.  Do not hesitate to contact me for a discussion about how decision trees can be applied to model complex decision, valuation, and investment situations in your organization, typically in the context of M&A, market entry, or R&D projects.



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