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There is ongoing controversy in the business valuation literature regarding the preferability of the arithmetic mean or the harmonic mean when estimating ratios for use in valuation. This research conducts a simulation using data reported from actual market transactions. Successive random samples were taken from data on valuation multiples and alternative measures of central tendency were calculated, accumulating more than 3.7 million data points. The measures (arithmetic mean, median, harmonic mean, geometric mean) were compared using hold-out sampling to identify which measure provided the closest approximation to actual results, evaluated in terms of least squares differences. Results indicated the harmonic mean delivered superior predictions to the other measures of central tendency, with less overstatement. Further, differences in sample size from 5 to 50 observations were evaluated to assess their impact on predictive performance. Results showed substantial improvements up to sample sizes of 20 or 25, with diminished improvements thereafter.


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  • Subject
    • Business

  • Department
    • Department of Accounting & Law, Mike Cottrell College of Business

  • Institution
    • Gainesville

  • Event date
    • 15 November 2019

  • Date submitted

    19 July 2022

  • Keywords
  • Additional information
    • Author Biography:

      William Black, CPA, CMA, ABAR, CFE, CVA is a forensic accountant and accounting educator with a strong interest in business ethics. After several decades of independent practice, including expert witness testimony on intellectual property, breach of contract damages, and business valuation matters, he returned to school and earned his PhD in Accounting from the University of Mississippi. He now teaches financial and managerial accounting, financial statement analysis, accounting theory, and accounting information systems at the University of North Georgia, and still consults on interesting and challenging business valuation and forensic accounting assignments. He is President of the Georgia Association of Accounting Educators, Membership Chair of the Georgia chapter of the Association of Certified Fraud Examiners, and Senior Editor of the Accounting Historians Journal.