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# The Bias in Annual (Versus Monthly) Discounting is Immaterial

By: Jay Abrams, ASA, CPA, MBA
Tel: 818-505-6008
Email Mr. Abrams

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Abstract

This article presents a discussion of the validity of using the mid-year convention from a different point of view than the March 2002 BVR article by Michael Dobner.1 Although our conclusions are similar, we develop exact formulas for annuity discount factors with growth for both monthly and daily cash flows. These can be useful tools for the valuation community when precision is important.

In Robert Trout's recent article,2 he stated that midyear discounting of annual cash flows creates a bias in the present values vis-á-vis monthly discounting. This is incorrect. The flaw is that, given compound interest, the monthly interest rate is not equal to the annual discount rate divided by 12. Dr. Trout used 12% annual interest and assumed that 1% monthly interest is equivalent. However it is not.

Using i as the periodic interest rate (monthly for equations [1] - [8], and daily for equations [9] - [10]) and r as the annual rate, we begin in equation [1] with the statement that 12 months of compounding at the equivalent monthly rate will yield the same result as the annual rate, or:

Jay Abrams, ASA, CPA, MBA, founder and head of Abrams Valuation Group (AVG), is one of those rare individuals who integrates theory and practice. He has valued businesses and consulted on mergers and acquisitions in a wide range of industries, provided valuations and discounts for fractional interests and restricted stock, and conducted independent statistical and mathematical research regarding problems facing businesses. During his 25 years of accounting and valuation experience, he has made, and continues to make, significant contributions to the science of valuing businesses. Mr. Abrams' book, Quantitative Business Valuation: A Mathematical Approach For Today's Professionals (McGraw-Hill, 2001) shows how to integrate advanced scientific methods into real-world valuation analysis.

DO NOT REPRODUCE WITHOUT WRITTEN PERMISSION BY AUTHOR.

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