The discounted cash flow model

The most intellectually robust form of valuation is the discounting of future cash flows, provided that the valuer is blessed with some relatively reliable forecasts.

When valuing a business using discounted cash flow techniques, there is clearly a need for management to make explicit assumptions with regards to the growth of the business in the years for which there are specific forecasts. These assumptions will include the anticipated inflation in revenues and costs and there is then a secondary assumption required, relating to growth in perpetuity. This is part of calculating the terminal value at the end of the period of discrete cash flow forecasting, using the Gordon Growth Model, also known as the dividend discount model (DDM).

Alternative valuation approaches

Alternatively, the valuation may be undertaken using a multiplier of some description, Earnings Before Interest & Tax (EBIT) multiplier and a multiplier of post-tax earnings. Such approaches are often used when there is a dearth of reliable forecast data. Although the growth assumption is no longer explicit in such calculations as it is buried within the multiplier, it cannot be ignored.

It is also important for all valuers to recognise that a multiple of a single profit figure can be unpacked into the components of growth and return. It is nothing more and nothing less than a form of terminal value calculation assuming constant performance in the future.

Growth assumptions

The upper limit

It is generally accepted that the upper boundary for a long term growth assumption is the rate of growth in the economy in which the business operates. This is on the basis that any assumption higher than this will mean that the enterprise will become larger than its host economy over the long term.

There may be sectors of the economy which are likely to grow relatively fast in comparison to the overall economy. An example of such a sector in the UK is healthcare arising from the powerful combination of an ageing population and medical advances. However such a trend can only occur for a finite period. Economists will remind us that if something cannot continue indefinitely, then it will not.

In such a situation, a period of growth above the rate of increase in the Gross Domestic Product (GDP) can be forecast, but only for a finite period. After a period of more rapid growth the assumptions will need to revert to an equilibrium level.

The lower limit

There is no lower limit for the long term growth assumption. If a business is operating in a declining market and there are no intentions to develop into new markets, then a negative growth rate could be an entirely reasonable assumption.

This is a relatively unusual state of affairs as most management would be expected to react to changes in markets, in order that the business could remain in being. However no economic axiom is broken by assuming that a business will dwindle away to nothing over the long term.

The steady state

The figures that are normally provided with regards to changes in GDP are quarterly figures and the figures reported are real, rather than nominal. In other words, changes in GDP are expressed after the impact of inflation.

Until the Great Recession of 2008 the UK economy had been growing steadily at a remarkably stable annual rate of 5% nominal. Therefore with background inflation of 3.0% to 3.5%, the real growth in GDP was 1.5% to 2.0% a year. These were the figures that were headlined.

Another source for long term growth is given by Dimson, Marsh and Staunton. They examined the 19 major world stock markets for the period from 1900 to 2010. For the UK listed company market the real growth in dividends was 0.46% a year over that 111 year period. For the USA the figure was a growth of 1.37% a year on average. However, even such a lengthy period as 111 years cannot be seen as homogenous.

In the UK, the period from 1900 to 1950 delivered rather disappointing returns to investors. It was the period from 1951 to 1991 which was the engine room of much of that long term average growth. This tale of two halves is scarcely surprising when we consider the savage effects of two world wars on the UK economy.

The macroeconomic view

We must assume that small businesses will form a constant proportion of UK GDP over the very long term. This is the only safe assumption that can be made. On this basis, the starting point for considering the growth of a smaller company is the growth in GDP.

However, it is strongly arguable that this is the starting point. It then needs to be modified so there are two moderating factors to consider, population growth and business failure.

Population growth

Growth in GDP per head is likely to be a better measure of the average growth in the small business sector, rather than growth in GDP. This is based on the simple truth that the number of small businesses might be expected to rise in line with the increase in the population;

• More streets and therefore corners, means a higher number of corner shops.
• More mouths equates both to additional dentists and restaurants.
• More heads equals an increase in hairdressers.

As the UK population has been growing steadily the growth in GDP per head is constantly somewhat less than the growth in absolute GDP. Although the total output of small businesses must be assumed to grow in line with GDP, we should presume that the number of those businesses at any time retains the same proportion to the population.

The growth in GDP can therefore be broken down into the GDP growth per head and the net birth rate of new businesses. This is a net rate as small businesses are born, but they also die.

Business birth and death

Viewed from the present at any future point, the total small business universe will include new businesses which are set up and existing businesses which have survived. This has a very material impact on growth assumptions, if using macroeconomic arguments.

In an excellent article in “Business Valuation Update” in September 2013 by Dohmeyer, Butler and Burkert, the aggregate growth assumption for smaller entities is examined. The authors sorted 10,000 companies from Pratt’s Stats (a commonly used database of smaller businesses in the USA). These entities were sorted by business age.

The authors sought to establish the growth rate of companies aged from 5 to 25 and they computed that the average real growth rate was a surprisingly impressive 4.8% a year. However, they recognised that the sorted data only included surviving companies, which produced a very material statistical survivorship bias.

They then looked at the data on net business formation in the USA. This data indicated that this bias equated to growth of 5% a year. This was due to the fact that there were business failures every year, and the impact of these failures needed to be factored into their model.

Once they had adjusted for this statistical bias they concluded that the real rate of growth for a starting sample of small businesses was 0%. They therefore assumed for their model that the nominal growth rate equated to the rate of inflation.

The authors concluded that the average growth rate of the surviving companies cannot be lovingly applied by the valuer without recognising that he or she is thereby ignoring the survivorship bias. 

Refining the growth in GDP

To reflect the effect of business churn, a further refinement is needed. For the small business sector as a whole, the growth in GDP will be represented by:

• growth in those companies existing at any point in time that continue to survive into the future; 
• less the turnover of those businesses which fail and;
• the growth of new businesses which are created.

Conclusions

The output of smaller businesses must be assumed to grow in line with GDP.

• The rate of growth of GDP per head is likely to be a better measure for a surviving individual company than growth in absolute GDP and is historically a lower level.
• A further reduction is required to recognise that there will be some business failures in any population of small businesses.

The work by Dohmeyer, Butler and Burkert indicates that for the US market at least, real growth of nil and nominal growth equal to inflation, is a suitable assumption for an individual small business.

Andrew Strickland, Corporate Partner, Scrutton Bland
Valuation Group, March 2014