Strategy

Valuation of real options, revisited, based on a McKinsey Quarterly 1997 reprint

McKinsey Quarterly / McKinsey Insights are interesting sources of business insight and ideas for any business professional.  I enjoy in particular reading reprints of old articles, to see how old strategy ideas survive the test of time.  Some days ago I came across a reprint of a McKinsey Quarterly article* from 1997 by Keith Leslie and Max Michaels titled “The real power of real options”.

The article is about “Chang[ing] the way you create value: The case for applying options thinking to any strategic situation.”  It is fairly easily accessible, though it makes extensive reference to the Black-Scholes formula for valuing European call options, and how it can be used to value real options.

Being skeptical about Black-Scholes for valuation of real options, I thought it might be interesting to try to replicate Leslie and Michaels’ numerical results** using decision tree methodology / Monte Carlo simulation with DPL software from Syncopation Software.  I will in this blog post share with my readers key insights into this primarily academic exercise.

Note first that I will restrict myself to real options here; financial options have often a simpler structure that makes them more amenable for analytical approaches or numerical methods.

Note then that Black-Scholes is just a typical example of an analytical approach to modelling real options.  In addition to analytical approaches, we see other approaches in use for valuing real options, including numerical methods (stochastic dynamic programming and partial differential equations), and decision trees (as already indicated) (plus, in practice, DCF).

Note furthermore that replicating another person’s work from a journal article is non-trivial.  (There were also a number of quality issues with the article, including implied non-realistic assumptions like what seem to be zero oil field development time, zero oil field lifetime, and discount factors of 1.  I have tried to convert to more realistic assumptions, but keep results comparable***.)  I apologize for any misunderstanding on my side.

Here is comparison of results:

Model

Value, USDm

DCF, USDm

Value of flexibility, USDm

Black-Scholes, as in article (European option) 100 -100 200
Decision tree (American option) 53 -108 161
DCF (for comparison) -100 -100 0

So, essentially same result: negative value if valued using DCF, positive value if including value of flexibility, waiting / decision deferral has flexibility value and is good.  This value is nicely illustrated by the following decision tree policy summery (ignore the LNP* nodes, they are uncertainty nodes):

policy summary

What is then new?  Here is new and why finance professionals should consider using a decision tree as an alternative to Black-Scholes or other approaches for modeling real options: i) hugely increased modelling flexibility, including multiple decisions / decision points, multiple sources / types of uncertainty, and Excel integration; ii) more natural parameterisations; iii) no need for draconian simplifications (justified or not justified); and iv) white box rather than black box (indeed, decision trees are generally perceived as good pedagogical devices by finance professionals and non-professionals alike, see policy summary above).

In essence, decision trees / Monte Carlo simulation are better able to capture the richness of the problem at hand for real options.  This is not about theoretical correctness / accuracy, but about being approximately right rather than exactly wrong.

But fact is, few finance professionals use decision trees in their daily work, even though most master level students in finance learn about them at university.  (I have some anecdotal evidence that their serious use in Norway is limited to 3-5 major energy companies plus some universities, 1-2 individuals per organization.)  Why is this?  Two words: discount rates.  In DCF one uses a discount rate that at least in theory has a theoretical basis (i.e., capital asset pricing model or weighted average cost of capital), though in practice it is fairly arbitrary, but accepted by finance professionals.  In Black-Scholes one uses risk-free rate.  There is no general acceptance among finance professionals regarding correct discount rate for a decision tree, except that it is somewhere in-between risk-free return and discount rate for a similar DCF model.  In addition, there is the more philosophical issue of how to interpret probability distributions of net present values …

Finally, and though there are quality issues with Leslie and Michaels’ article (but it was written more than 20 years ago), I believe their conclusions have stood the test of time:  “In an increasingly uncertain world, real options have broad application as a management tool. They will change the way you value opportunities. They will change the way you create value—both reactively and proactively. And they will change the way you think.”

By the way, I will this fall reduce my involvement in my strategy advisory firm Crisp Ideas to work on some other projects.  Thanks to my friends in Syncopation Software / the DPL guys, especially Nicki Franz and Tony Manzella, for interesting discussions about decision trees and how they can be used for valuation of what are essentially real options.

DISCLAIMER: I was long time ago a McKinsey consultant (like Leslie and Michaels) with McKinsey’s offices in Stockholm and Oslo.

Grim

*) Source: https://www.mckinsey.com/business-functions/strategy-and-corporate-finance/our-insights/the-real-power-of-real-options.

**) The case in question appears to have been compiled based on BP’s development of the Andrew field in the North Sea, probably with obfuscated numbers.

***) For reference, I have included the following parametric assumptions:

Parameter

Leslie and Michaels’ article

Decision tree

Comment
Option maintenance costs, per year

USDm 15

USDm 15

Development cost

USDm 600

USDm 600

Development time

NA

5 years

Field size

50m barrels

120m barrels

For decision tree, set so that NPV for field is USDm 500
Today’s oil price

USD 10

USD 10

Field lifetime

NA

15 years

Risk-free rate 5% 5%
Discount rate NA 7.5%

Field size was in my approach set as deterministic parameter.  Oil price was modeled as GBM, with sigma = 0.3 and no drift (i.e., same as in article).

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