Special to the Legal
In my last blog, I discussed assessment of risk in the context of business valuation. I stated, “In valuing a privately owned company, where public markets do not assess the risk, the assessment is determined by the valuation analyst. This assessment is one of the most significant and subjective aspects of business valuation.”
Risk is quantified by the development of the cost of equity. Key elements of the cost of equity include:
- Market risk premium
- Small stock risk premium
- Company specific risk premium
Once these specific risk premiums are quantified, they are added to a risk-free rate of return to arrive at the cost of equity. This process is called the “build-up approach.” In this post, I expand on the technical aspects of the development of the small stock risk premium.
Small Stock Risk Premium
To measure the small stock risk premium element of cost of equity, we use data from the portfolio created by the Center for Research in Security Prices, University of Chicago Graduate School of Business. This portfolio is widely used by business valuators and represents data accumulated from 1926 through 2011. The portfolio is separated into 10 deciles, with decile 1 representative of the largest companies and decile 10 the smallest companies. The deciles are assigned based upon the market capitalizations of the companies. It compares the average return on investment and risk increase in deciles 8 to 10 (smallest companies) to the deciles 1 to 3 (largest companies). The companies contained in the portfolio are all public companies, listed on public stock exchanges. Decile 1 and 2 companies generally are characterized as large cap, deciles 3 to 5 as mid-cap, deciles 6 to 8 as small cap and deciles 9 and 10 as micro-cap. Decile 10 (smallest companies) is further split into four groupings designated as 10 w, x, y and z, with “w” companies the largest and “z” companies the smallest. Deciles 1 to 5 are assigned size premia in the range of (0.38) to 1.74 percent. At decile 9, the size premia is 2.8 percent, jumping to 6.10 percent for decile 10. The w, x, y and z subgroups of decile 10 are assigned size premia in the range of 4.34 percent to 11.77 percent. As can be seen, the smaller the company, the greater the size premia. There is a relationship between the size of a company and its return on investment, and this relationship is amplified for smaller companies.
The portfolio of companies utilizes a formula to mathematically convert a range of data points into a size premia, which becomes a component of cost of equity. The data points include the beta, the arithmetic mean return, the actual return in excess of the riskless rate and, finally, the Capital Asset Pricing Model return in excess of the riskless rate.
Once the small stock risk premium is determined, it is included as a component of the build-up approach to arrive at the cost of equity.
Terry Silver is a certified public accountant, certified valuation analyst and certified in financial forensics for Citrin Cooperman, an accounting, tax and business consulting firm in Philadelphia, where he is a partner with more than 33 years of experience as an accountant and auditor. He focuses his practice on business valuation and financial forensic services, expert testimony and matrimonial actions. He can be reached at email@example.com or 215-545-4800.