Advancing Valuation Theory and
Putting That Theory to Work for You
Jay B. Abrams, founder and leader of AVGI, wrote Quantitative Business Valuation: A Mathematical Approach for Today's Professionals (2001), the most advanced quantitative book yet published about the valuation of private businesses. The following is a partial list of models, formulas, and other significant discoveries that appear in the book:
- The invention of the Log Size Model for calculating discount rates, including the use of Newton's Method of Iterations for automatic calculation. The model quantifies the relationship of stock-market returns with the logarithm of firm size.
- First calculation of 95% confidence intervals around the valuation estimate.
- Formulas to measure the impact of valuation errors in absolute and percentage terms for errors in forecasting cash flows, discount rates, and growth rates for large firms and small firms.
- Invention of models for calculating the Discount for Lack of Marketability.
- Complex present-value formulas, as part of the Economic Components Model, for periodic-transaction cost differentials for both the buyer and seller.
- Multiple Regression Equation for calculating restricted stock discounts.
- A new model for calculating control premiums based on voting-rights premiums.
- Several Annuity Discount Factors (ADFs) for valuing finite cash flows with growth, with or without stub periods, as well as an ADF for monthly cash flows, both mid-month and end-of-month.
- The Periodic Perpetuity Factor (PPF), a formula and technique that simplifies valuations where large periodic expenditures make a traditional 5- or 10-year forecast inadequate (such as in manufacturing, when replacing buildings and extremely expensive equipment may occur every 20 to 50 years). In addition, the PPF is the only accurate method to make new-versus-used decisions in buying extremely expensive capital equipment, such as ships, airplanes, CT scans, MRIs, or fleets of trucks and taxicabs.
- Formulas to quantify the net present value of interest and principal of loans, including formulas for the present value of the principal when the discount rate and nominal rates are different.
- A decision-tree model for valuing startup firms.
- Valuation formulas for both the firm and the Employee Stock Ownership Plan (ESOP), both pre- and post-transaction, as well as formulas for the dilution in value after sale to the ESOP.
- The first empirical test of an entire valuation theory, reconciling the models developed with public company data to sales of small private firms in the transactional database of the Institute of Business Appraisers.
- An exponential sales-decay model for forecasting sales.
The following formulas and inventions, which represent significant discoveries, have appeared in other publications:
- Mr. Abrams developed a mathematical solution to pinpoint the source of an accounting transposition error, which is the solution to a 500-year-old problem.* He accompanied the discovery with a spreadsheet to provide the solution automatically.
- Mr. Abrams developed a mathematical expression of the present value of cash flows of a hybrid corporation that begins as an S corporation and switches to a C corporation; he also calculated the first and second partial derivatives that explain Duffy and Johnson's** results from computer modeling.
* "How to Quickly Find & Fix Transposition Errors," by Jay B. Abrams, The Practical Accountant, June 1992, p. 76.
** "Valuation of S Corporations Revisited: The Impact of the Life of an "S" Election Under Varying Growth and Discount Rates," by Robert E. Duffy and George L. Johnson, Business Valuation Review, December 1993, p. 155.