Build Up Model

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Build Up Model

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The build up model uses the sum of various risk factors to create a discount or capitalization rate. ValuSource valuation applications use the following model to determine the discount rate:

 

Risk Free Rate

+

Large Company Equity Risk Premium

+

Small Company Equity Risk Premium

+

Company Specific Risk Premium

=

Total Risk

Company Specific Risk is also referred to as Unsystematic Risk or Specific Industry and Company Risk.

The risk free rate of return comes from the Long Term Government Bond Yield. The Large Company Risk Premium is calculated by taking the arithmetic mean of Large Company Stock Total Returns and subtracting the arithmetic mean of Long Term Government Bond Income return. Thus, the Large Company Equity Risk Premium represents the component of risk related to owning equities.

The Large Company Equity Risk Premium calculation is as follows:

 

Large Company Risk Premium

Long Term Government Bond Income Return

=

Large Company Equity Risk Premium

There are two approaches to determining the Small Company Risk Premium. The first is to use the arithmetic mean from the Long Term Returns as a basis to determine the Small Stock Equity Risk Premium. SBBI breaks down all the combined companies from the NYSE, AMEX and NASDAQ exchanges into deciles based on market capitalization. The following table calculates the Small Stock Equity Risk Premium for the 10th decile:

 

10th Decile Arithmetic Return

Large Company Total Return

=

10th Decile Small Stock Equity Risk Premium

This was an approach Ibbotson used to recommend, but they now recommend the CAPM approach. See below for details.

When you use the simple difference between the mean of the Small Company Total Return and the Large Company Total Return, rather then the beta adjusted approach, you assume the company you are measuring has the same risk as the average company in the size category you selected (i.e. 10, 10a, 10b, Micro-cap, etc.). A more appropriate approach, and the one Ibbotson recommends, is to use the risk or beta adjusted approach. This means using the numbers from the Size Premium, Return in Excess of CAPM column instead of the numbers from the Arithmetic Mean column.

Ibbotson feels that adding a company specific risk premium to a Small Stock Equity Premium based on the arithmetic mean increases the chance of adding a component of company specific risk that is already accounted for in the average risk. Using the beta adjusted approach isolates size differences in relationship to average companies in the size category selected (i.e. 10th, 10a, 10b, Micro-cap, etc.). This makes it more difficult to double count components of company specific risk. It's very difficult to determine exactly what is and is not accounted for in the "average" risk, so double counting is more likely using risk rates based on the arithmetic means.

What you add for company specific risk should vary based on whether you use the arithmetic mean or return in excess of CAPM approach. Using the CAPM approach accounts for size only differences in return, making it easier to isolate the non-size factors that need to be added to the company specific premium. If you use this method to build up a discount rate, you will need to add company specific risk and potentially industry specific risk as well. You may also need to add a size component to the company specific premia based on the difference in size between the target company and the average capitalization of the small stock equity premia that you selected. This number is very difficult to quantify and there are no empirical studies to quantify this amount.

For a detailed discussion of cost of capital in relation to business valuation, we recommend that you read Cost of Capital, Estimation and Application by Shannon Pratt, published by John Wiley & Sons, Inc.