ABRAMS VALUATION GROUP, INC. ADVANCES VALUATION THEORY AND PUTS THAT THEORY TO WORK FOR YOU

• Invention of the Log Size Model for calculating discount rates, including 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. This leads to the conclusions that errors in forecasting discount rates and growth cause much larger valuation errors than errors in forecasting initial cash flow. Additionally, the valuation impact of those errors are greater in percentage terms for large firms than for small firms.
  

• Demonstration of the empirical superiority of using the arithmetic mean over the geometric mean
  

• Invention of models for calculating the Discount For Lack of Marketability
  

• Economic Components Model. As part of this model, Abrams developed the complex present value formulas for periodic transactions cost differentials for both the buyer and seller. Abrams also developed an empirical relationship between transactions costs and the logarithm of firm size.

• Multiple Regression Equation for calculating restricted stock discounts

• Multiple Regression Equation for calculating secondary limited partnership market fractional interest discounts

• Model for calculating control premiums based on voting rights premia, having demonstrated that the traditional acquisition premiums are for synergies, not control.
  

• Several Annuity Discount Factors (ADFs) for valuing finite cash flows with growth, with or without stub periods. Also, proof that the ADF is the difference of two Gordon model multiples, while the Gordon model multiple is an ADF where n, the number of years, goes to infinity. Also, ADF for monthly cash flows, both mid-month and end-of-month. Developed the formula for the profession for the ratio of present values of monthly and daily cash flows compared to midyear annual cash flows, demonstrating that the latter is only 0.2% lower than the former for most business valuations, thus proving that annual cash flows are more than sufficiently accurate for business valuations.
  

• Periodic Perpetuity Factor (PPF). This formula and technique greatly simplifies valuations where large periodic expenditures make a traditional 5 or 10 year forecast inadequate. For example, in manufacturing replacing buildings and extremely expensive equipment may occur every 20 to 50 years, and ignoring these capital replacements can lead to disastrous errors in the valuation, while attempting to model them was too cumbersome. Additionally, the PPF is the only accurate method to make new-vs.-used decisions in buying extremely expensive capital equipment, e.g., ships, airplanes, CT scans, MRIs, fleets of trucks and taxicabs, etc.
  

• Formulas to quantify the net present value of interest and principal in loans, including formulas for the present value of the principal when the discount rate and nominal rates are different.

• Iterative methodology to find and enforce consistency in the underlying assumptions (the implicit values of debt and equity) and the valuation results using the Capital Asset Pricing Model (CAPM) for both Direct Equity and Invested Capital Approach.
  

• Decision tree model for valuing startup firms.

• Valuation formulas for both the firm and the ESOP, both pre- and post-transaction, as well as formulas for the dilution in value after sale to the ESOP. Also developed formula for sharing the dilution between the owner/seller and the ESOP to provide the financial engineering to enable the client to achieve his or her desired results, given the pre-transaction valuation.

• Algebraic derivation of the cash flow statement and the definition of free cash flow for valuation purposes.

• 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.

• Exponential sales decay model for forecasting sales

The following formulas and inventions do not appear in the book
but are significant discoveries:

• A mathematical solution to pinpoint the source of an accounting transposition error, which is the solution to a 500-year-old problem.* Developed a spreadsheet to provide the solution automatically.
  
  
• 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. Also calculated the first and second partial derivatives that explain Duffy and Johnson's** results from computer modeling.
  
  

At Abrams Valuation Group, Inc., we have a passion for excellence. As cutting-edge leaders in the field, we have the ability to provide custom analysis and insight that is difficult to find elsewhere. Our credo, "Uniquely Applying Original Valuation Theory," guides our very existence. Life is more complex than books. One who can recognize the differences between a client's factual situation and the assumptions of a standard model, and who has the ability to develop new models can most effectively serve his clients.

* "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.

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