# Forecasting size premium for small company valuation

Why should you consider forecasting size premium when valuing a small company? Consider this:

You can value just about any company using a number of income-based business valuation methods. These methods require that you provide two key inputs:

• Estimate of business earnings, usually in the form of cash flow
• A factor representing business risk such as the discount or capitalization rate

An example of business valuation based on income is the discounted cash flow method. To use this technique, you would project the business earnings over a number of years into the future. Then, you would need to provide an assessment of business risk by calculating or building up the discount rate.

## Company size matters – the size premium

One of the elements that make up the discount rate is the so-called company size premium. Larger firms tend to be less risky while smaller companies entail greater risk. So you can expect the discount rate for a smaller business to be a bigger number. Since the discount rate appears in the denominator in the valuation calculation, the value of a smaller company is lower for the same level of earnings compared to a larger competitor.

If you take a peek at the discount rate build-up formula, you will see the company size premium being included. How are these numbers determined? You can calculate the size premia from returns of publicly traded companies taken over a period of time, say a year.

## Smaller companies are higher risk

Smaller companies will tend to generate greater returns to compensate the investors for the higher risk. You can compile returns for a group of companies of a certain size, usually measured by market capitalization. The additional returns provided by a group of companies in a certain market cap range give you an idea of the company size premium.

This is in fact how the calculation of the company size premia is done. The data can be arranged in a table giving you a measure of additional size premium for a given company market capitalization.

So far so good. You can read off the company size premium and come up with a discount rate to use in your business valuation. But what if the company you are valuing is smaller than the smallest publicly traded companies?

## What about the really small private companies?

Since it is not easy to find reliable data on returns for very small private companies, you can try using the data you have to estimate the size premium for your target firm.

One way to do this is to use extrapolation. You base your estimate on the known numbers then use the so-called linear regression calculation, available in a typical spreadsheet program, to estimate the size premium for your size company.

For example, in Excel this calculation is performed using the Forecast formula. You specify the company market cap, presumably smaller than the range of capitalizations you have available from existing data. The desired number is calculated for you using the known values of company size premia and market capitalizations.

### Example – forecasting size premium for a small private firm

As an example, we would like to come up with a size premium to value a private company whose equity value is under \$10,000,000. Let’s pick a few starting numbers for our estimate first.

Company Market Cap, \$M Size Premium
150 8.94%
100 11.65%
50 14.35%

As you can see from the table, the lowest market cap number we have available is \$50M, much larger than our \$10M target firm. To get the estimate we need, we use the table data as the starting point and apply the Forecast model to get an estimate at a new market cap, namely \$10M. Here is the result:

16.52%

This is over two percentage points higher than the size premium measured for companies in the \$50M market cap range. How much difference can this make to your business valuation result? Consider the following scenario of future cash flows for the business over the next 5 years:

Year of Forecast Earnings
1 \$500,000
2 \$600,000
3 \$450,000
4 \$650,000
5 \$800,000

Let’s say that the company terminal value at the end of the forecast is \$10M. Using the 25% discount rate gives us the business value of \$4,819,584. If the discount rate is reduced by two percentage points to 23% the business value rises to \$5,165,073.

### Valuing a business by discounting its cash flow

See an example of how to value a company of any size by discounting its cash flow while forecasting size premium to properly account for business risk.

### Iuri Colares says:

The 2016 Valuation Handbook – Cost of Capital (Exhibit B-1), based on historical risk premium average since 1963 for a portfolio of average market value of \$148 million, calculated a Size Premium over CAPM of 11,24% and a Smoothed Size Premium over CAPM of 6,41%, data smoothing with regression analysis: Smoothed Size Premium = 11,780% – 2,476% * Log(Market Value).

Thus, the 2016 Valuation Handbook Smoothed Size Premium for a market value of \$150M is 6,39%, of \$100M is 6,83%, of \$50M is 7,57%, of \$10M is 9,30%, and of \$2M is 11,03%.

On the other hand, ValuAdder current Company Size Premium (Risk Assesment tab) for a market value up to \$150M is 9,67%, up to \$100M is 12,03%, up to \$50 million is 14,39%, extrapolated up to \$10 million is 16,28%, and extrapolated up to \$2 million is 16,66%.

What might be the explanation for this huge difference?

### Harry says:

You seem to be rather confused about the data analysis results. Consult the Valuation Handbook for details on the CRSP Deciles Size Premia study and note the market capitalization ranges for the deciles and the size premia indicated. I believe you will find that ValuAdder numbers are pretty close.

Also, the interpolation by linear regression across the entire range of market capitalization will get you in trouble as the relationship is highly nonlinear. You would need to resort to a piece wise interpolation to capture the actual relationship. This is especially true for the tiny companies within or below the 10th Decile sizes.

You should note that there are two distinct methodologies used to calculate the size risk premia:

• CRSP Deciles Size Premia study; and