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

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

View Profile on Experts.com.

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:

Click here to view the entire article in PDF format.

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.

©Copyright 2002 - All Rights Reserved

DO NOT REPRODUCE WITHOUT WRITTEN PERMISSION BY AUTHOR.

### Related articles

9/13/2016· Accounting

By: Sidney Blum

Royalty auditing is a niche service that has exploded in popularity over the last 20 years. The primary purpose of a royalty audit is to test whether a licensee has complied with a license agreement or statutory requirement. The royalty auditor is hired by an intellectual property owner (aka, licensor) or minerals owner to inspect the books and records of a licensee primarily to determine if usage-based monetary amounts have been paid as contractually required. In addition to monetary damage calculations, most royalty audits examine for breach of contract in a wide variety of areas, such as intellectual property protection, record keeping, distribution channels, and permitted usage.

8/12/2015· Accounting

By: David Nolte

The US Court of Appeals for the Ninth Circuit has opened the door significantly wider for those who wish to pursue qui tam False Claims Act suits by reversing a dismissal of two such matters. Ruling en banc in United States ex rel. Hartpence v. Kinetic Concepts, Inc., the Ninth Circuit has removed a prior restriction that any prior public disclosure must have originated from the whistleblower as well.

10/6/2017· Accounting

When a client voiced strong suspicions that her soon-to-be ex-husband was hiding assets, her attorney investigated the claim but found nothing amiss. However, he hired a forensic accounting expert to help ensure his client would receive an equitable share of the marital estate. The expert turned up a trunkload of hidden treasure - undeclared cash income and property "stashed" under the names of the husband's mother and siblings.

;