When analyzing business valuation multiples—such as price-to-revenue (P/R) or price-to-EBITDA—choosing the right type of average is essential to avoid misleading conclusions. While many professionals default to the arithmetic mean (a simple average), a more accurate and meaningful metric for ratios is the harmonic mean. This article explains why, using real-world examples and straightforward explanations for financial professionals, with a focus on applications in SBA 7(a) lending and business valuations.

Understanding Averages in Financial Contexts

There are three common types of averages:

• Arithmetic Mean: The sum of the numbers divided by the count (the standard average).
• Median: The middle number when values are arranged in order.
• Harmonic Mean: The reciprocal of the average of reciprocals, especially useful for rates and ratios.

Each has its place. The arithmetic mean works well for raw values like total revenues or enterprise values. The median is useful for datasets with extreme outliers. But when it comes to ratios, such as price-to-earnings (P/E), price-to-revenue (P/R), or price-to-EBITDA multiples, the harmonic mean is generally the superior choice.

Why Harmonic Mean Works Better for Ratios

Financial ratios are inverted in nature—expressing a price per unit of revenue or earnings. When averaging inverted values, the harmonic mean correctly accounts for the impact of scale and weighting. It prevents large outliers from skewing the results and provides a more representative benchmark.

Consider an example of price-to-revenue multiples for three companies in the same industry:

• Company A: Revenue = $10M, Enterprise Value (EV) = $20M, P/R = 2.0x
• Company B: Revenue = $5M, EV = $25M, P/R = 5.0x
• Company C: Revenue = $2M, EV = $40M, P/R = 20.0x

Arithmetic Mean:
(2 + 5 + 20) / 3 = 9.0x

Harmonic Mean:
3 / (1/2 + 1/5 + 1/20) = 3 / (0.5 + 0.2 + 0.05) = 3 / 0.75 = 4.0x

Which multiple better reflects the group? The arithmetic mean (9.0x) is heavily distorted by Company C’s 20.0x outlier, which arises from its low revenue base and high price. The harmonic mean (4.0x) provides a more balanced estimate, better reflecting the relative contribution of each company’s revenue to the overall valuation multiple.

This distinction is critical in business valuations, especially for SBA 7(a) lending, where overstated multiples can inflate fair market value estimates, leading to undercollateralized loans or increased default risk.

When to Use Harmonic Mean

Use the harmonic mean when averaging:

• Price-to-revenue multiples
• Price-to-EBITDA multiples
• Price-to-earnings (P/E) multiples
• Any rate or ratio where the denominator varies significantly across companies

Avoid using it for:

• Raw financial data like revenue or profit
• Data with many zero or negative values (harmonic mean is undefined in those cases)

Practical Challenges in Applying the Harmonic Mean

Valuation professionals and bankers face several challenges when using the harmonic mean for financial ratios:

• Outlier Identification: Extreme ratios (e.g., due to low denominators) require careful scrutiny to determine if they’re valid or should be excluded, as they can still influence the harmonic mean.
• Stakeholder Familiarity: Many clients or lenders are accustomed to arithmetic means and may question the use of the harmonic mean, requiring clear explanation.

Real-World Implications

Using the arithmetic mean for financial ratios can lead to significant valuation errors. In the example above, applying a 9.0x P/R multiple to a target company with $1M in revenue would yield an enterprise value of $9M. Using the harmonic mean’s 4.0x multiple, the value drops to $4M—a 55% difference. For SBA 7(a) lending, such an overvaluation could result in approving a loan with insufficient collateral, increasing default risk and potentially jeopardizing the SBA guaranty.

The harmonic mean’s approach aligns with best practices outlined by many valuation practitioners. It ensures valuations reflect market realities, particularly in the context of closely held businesses where revenue and earnings variability is common.

Conclusion

Understanding and applying the harmonic mean helps bankers and analysts produce more reliable, risk-aware valuations. It prevents distortions caused by outliers and aligns with best practices in professional valuation work. Whether evaluating a comparable set of private companies or reviewing M&A data, using the harmonic mean for financial multiples ensures conclusions rest on solid statistical ground, enhancing the credibility of SBA 7(a) valuations and supporting sound lending decisions.