Valuation is something usually done only when selling or buying a company (see: probability of gain and loss). However it is a versatile tool in assessing issues as risk and strategies both in operations and finance.
The risk and strategy element is often not evident unless the valuation is executed as a Monte Carlo simulation giving the probability distribution for equity value (or the value of entity). We will in a new series of posts take a look at how this distribution can be used.
By strategy we will in the following mean a plan of action designed to achieve a particular goal. The plan may involve issues across finance and operation of the company; debt, equity, taxes, currency, markets, sales, production etc. The goal usually is to move the value distribution to the right (increasing value), but it may well be to shorten the left tail – reducing risk – or increasing the upside by lengthening the right tail.
There are a variety of definitions of risk. In general, risk can be described as; “uncertainty of loss” (Denenberg, 1964); “uncertainty about loss” (Mehr &Cammack, 1961); or “uncertainty concerning loss” (Rabel, 1968). Greene defines financial risk as the “uncertainty as to the occurrence of an economic loss” (Greene, 1962).
Risk can also be described as “measurable uncertainty” when the probability of an outcome is possible to calculate (is knowable), and uncertainty, when the probability of an outcome is not possible to determine (is unknowable) (Knight, 1921). Thus risk can be calculated, but uncertainty only reduced.
In our context some uncertainty is objectively measurable like down time, error rates, operating rates, production time, seat factor, turnaround time etc. For others like sales, interest rates, inflation rates, etc. the uncertainty can only subjectively be measured.
“[Under uncertainty] there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability waiting to be summed.” (John Maynard Keynes, 1937)
On this basis we will proceed, using managers best guess about the range of possible values and most likely value for production related variables and market consensus etc. for possible outcomes for variables like inflation, interest etc. We will use this to generate appropriate distributions (log-normal) for sales, prices etc. For investments we will use triangular distributions to avoid long tails. Where, most likely values are hard to guesstimate or does not exist, we will use rectangular distributions.
Benoit Mandelbrot (Mandelbrot, 2004) and Taleb Nasim (Nasim, 2007) have rightly criticized the economic profession for “over use” of the normal distribution – the bell curve. The argument is that it has too thin and short tails. It will thus underestimate the possibility of far out extremes – that is, low probability events with high impact (Black Swan’s).
Since we use Monte Carlo simulation we can use any distribution to represent possible outcomes of a variable. So using the normal distribution for it’s statistically nicety is not necessary. We can even construct distributions that have the features we look for, without having to describe it mathematically.
However using normal distributions for some variables and log-normal for others etc. in a value simulation will not give you a normal or log-normal distributed equity value. A number of things can happen in the forecast period; adverse sales, interest or currency rates, incurred losses, new equity called etc. Together with tax, legal and IFRS rules etc. the system will not be linear and much more complex to calculate then mere additions, subtraction or multiplication of probability distributions.
We will in the following adhere to uncertainty and loss, where loss is an event where calculated equity value is less than book value of equity or in the case of M&A, less than the price paid.
Assume that we have calculated the value distribution (cumulative) for two different strategies. The distribution for current operations (blue curve) have a shape showing considerable downside risk (left tail) and a limited upside potential; give a mean equity value of $92M with a minimum of $-28M and a maximum of $150M. This, the span of possible outcomes and the fact that it can be negative compelled the board to look for new strategies reducing downside risk.
They come up with strategy #1 (green curve) which to a risk-averse board is a good proposition: reducing downward risk by substantially shortening the left tail, increasing expected value of equity by moving the distribution to the right and reducing the overall uncertainty by producing a more vertical curve. In numbers; the minimum value was reduced to $68M, the mean value of equity was increased to $112M and the coefficient of variation was reduced from 30% to 14%. The upside potential increased somewhat but not much.
To a risk-seeking board strategy#2 (red curve) would be a better proposition: the right tail has been stretched out giving a maximum value of $241M, however so have the left tail giving a minimum value to $-163M, increasing the event space and the coefficient of variation to 57%. The mean value of equity has been slightly reduced to $106M.
So how could the strategies have been brought about? Strategy #1 could involve introduction of long term energy contracts taking advantage of today’s low energy cost. Strategy #2 introduces a new product with high initial investments and considerable uncertainties about market acceptance.
As we now can see the shape of the value distribution gives a lot of information about the company’s risk and opportunities. And given the boards risk appetite it should be fairly simple to select between strategies just looking at the curves. But what if it is not obvious which the best is? We will return later in this series to answer that question and how the company’s risk and opportunities can be calculated.
References
Denenberg, H., et al. (1964). Risk and insurance. Englewood Cliffs, NJ: PrenticeHall,Inc.
Greene, M. R. (1962). Risk and insurance. Cincinnati, OH: South-Western Publishing Co.
Keynes, John Maynard. (1937). General Theory of Employment. Quarterly Journal of Economics.
Knight, F. H. (1921). Risk, uncertainty and profit. Boston, MA: Houghton Mifflin Co.
Mandelbrot, B., & Hudson, R. (2006). The (Mis) Behavior of Markets. Cambridge: Perseus Books Group.
Mehr, R. I. and Cammack, E. (1961). Principles of insurance, 3. Edition. Richard D. Irwin, Inc.
Rable, W. H. (1968). Further comment. Journal of Risk and Insurance, 35 (4): 611-612.
Taleb, N., (2007). The Black Swan. New York: Random House.
