Business valuation discount rate – what’s the arbitrage pricing model?

If you are valuing a business, assessing the company’s earning capacity and risk should sound familiar. Risk estimation gives you the all-important discount rate to plug into your business valuation. As a result, you can then use it with the discounted cash flow method.

Business appraisers use a number of ways to calculate the discount rates. And they usually prefer the Build-Up model and the capital asset pricing model or CAPM for short.

But wait, there is more. In the world of corporate finance, the relatively new kid on the block is the arbitrage pricing model, abbreviated as APT. This model appeared originally in the academic sources in the 1970’s. Importantly, the arbitrage pricing model offers you a powerful yet elegant way to estimate the cost of capital for any business.

Take a look at the standard CAPM formula. You will certainly spot that it depends on just a single risk factor, namely the systematic risk compared to the broad market as a whole. The risk is called systematic because you cannot diversify away from it.

Every business faces the market headwinds and must contend with the risks the market imposes. Your company may be more or less risky, but a degree of risk is always present.

The APT model extends the CAPM framework by introducing a number of risk factors. They affect what a given business is worth. In the formal language of finance, the APT is a multivariate model letting you assess the effect of each risk factor explicitly, rather than lumping everything in just the single beta. APT tells us that business risk varies according to how sensitive your business investment is to each of the risk factors.

In business valuation, appraisers usually see the APT risk factors in the macroeconomic context, including these:

Interest rate fluctuation

You would typically measure this as the difference between the short term and long term yields, e.g. those for the US Treasurys.

Yield spread

This is the difference between the yields on the higher and lower quality bonds.  This shows what the investors think of economic prospects going forward.

Risk of inflation

Expected rates of inflation represent a risk factor affecting all companies.

Business economic outlook

If your earnings forecast is out of line with the gross domestic product growth rates, you may be missing this risk factor in your analysis. Back to the drawing board!

You may wonder: if APT is so flexible and powerful, why is it not used more often in business valuation? The reason is the lack of consensus as to which risk factors should be included. Also, calculating the weights for each risk factor is challenging. This differs from the beta estimation, or building up the discount rates from well known risk premia. If you are valuing smaller businesses, you may hard put to see the connection between some macroeconomic factors and a niche player operating in a local or regional market place.

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