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and the best mathematical models for Discounts for Lack of Marketability (DLOM) are......? (PART 1)

Updated: Feb 1, 2023

Today's post is by Andrew Strickland of Scrutton Bland, Chartered Accountants. Andrew specialises in corporate finance and business valuation. Andrew is a member of the Valuation Committee of the ICAEW and its subject matter expert. Andrew has undertaken a large number of business valuation assignments in respect of shareholder disputes and also in respect of divorce. He also works on fiscal valuations for a variety of tax purposes.

Business valuers struggle with the impact of liquidity. This affects the valuations of both whole businesses and also fractional interests in businesses.The most popular current mathematical models being used by practitioners are not the ones that we should be using – as they do not behave as we might expect.

There are better alternative models that should be at centre stage.

The best materials are those held by Business Valuation Resources in Portland Oregon. If you want to deepen your understanding in this area, their resources are highly recommended.

Before we get too deeply immersed in the detail, what do we mean by a Discount for Lack of Marketability. What is it that is lacking? There are five common attributes to liquidity: the ability to sell a financial instrument:

quickly; - for a known price; - without the transaction moving the price; - with a minimal bid ask spread; - and with modest dealing costs.

What does it mean?

Based on the above, the most liquid market is generally thought to be that for US Treasury Bills. Against that yardstick, other financial instruments all suffer from reduced liquidity.

However, when applying a DLOM we are normally considering a discount from guideline public companies – so we are thinking of a relative loss of liquidity: the guideline public company stock is likely to be less liquid than a Treasury bill but it is far more liquid than the stock we are valuing.We are considering mathematical models for calculating a DLOM. These models mainly deal with one aspect only of liquidity – that of the time factor -the inability to deal in a liquid stock for a lockout period. They do not address other aspects of illiquidity such as the extra dealing costs.

Which model is the most popular?

The most popular model with practitioners appears to be the Finnerty Average Strike 2012 model. The Chaffe protective put option model and the Longstaff lookback option are apparently in second and third places.

These three models have problems with them when considering a lack of liquidity for longer periods. There are other models that do not have such problems. Therefore it is surprising that these other models do not take centre-stage. It could be that practitioners prefer to use what they know.

We need to consider what we expect a mathematical model to do.

For this purpose I am ignoring dividends. Dividends create problems with all of these models. The impact of dividends on the DLOM is a subject all of its own. We expect greater periods of illiquidity to increase the DLOM – so it needs to relate to change over time. We are not expecting a flatlining graph untroubled by the number of years of illiquidity.

If there is an immediate liquidity event within the qualities of the stock, we expect a minimal DLOM. If there is no liquidity event for an eternity, then the present value of future cash flows is nil. The DLOM is therefore 100%. We therefore expect the model to increase towards 100% but not to exceed it, over extended time periods. We then expect a curve rather than a straight line – this is because we expect the rate of increase of the DLOM to diminish over time. The difference between 0 and 10 years illiquidity we expect to be substantial. We expect the difference between 50 years and 60 years of illiquidity to be modest. None of the three current favourite models comply with the above expectations: the Chaffe model is the earliest model; it is also the one that comes closest to meeting the above expectations.

In my next post, I will look at some of the models and the ways that they behave.


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