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    Size Variables in Audit Fee Models: An Examination of the...
    research summary posted August 31, 2016 by Jennifer M Mueller-Phillips, tagged 10.0 Engagement Management, 10.06 Audit Fees and Fee Negotiations 
    Size Variables in Audit Fee Models: An Examination of the Effects of Alternative Mathematical Transformations
    Practical Implications:

    The authors’ results indicate that the complexity associated with auditing more subjectively valued assets may affect audit fees in a manner that is not fully captured by the traditional log transformation. Based on their findings, the authors also suggest that future audit fee studies assess alternative mathematical transformations of client size variables.


    Cullinan, C. P., H. Du, and X. Cheng. 2016. Size Variables in Audit Fee Models: An Examination of the Effects of Alternative Mathematical Transformations. Auditing: A Journal of Practice and Theory. 35 (3): 169-181.

    audit fee, fair valued assets, closed-end mutual funds, and non-linear.
    Purpose of the Study:

    Company size, typically measured as total assets, is an important factor in audit fee models. The size measure is usually transformed by taking the natural logarithm of total assets. The log of assets and the log of audit fees are used when studying audit fees to control for the non-linear relationship between asset size and audit fees. For example, as the population size (the number of individual assets held) increases, the sample size necessary to audit the population is only minimally affected, creating a non-linear relationship. This method was born from necessity after the realization that there was no true way to determine the form of the function; however, when this method became widely used, fair value accounting was not commonly used. Now that fair value accounting has become the “norm” and there are different methods of measuring fair value, mathematical transformations should be revisited. ASC 820 requires the disclosure of whether fair values were determined based on directly observable inputs (Level 1), indirectly observable inputs (Level 2), or unobservable inputs (Level 3). The authors combine the two insights regarding fair valued assets and mathematical transformations to examine whether the log transformation of different types of fair valued assets provides the best fit in an audit fee model, or whether other mathematical transformations may better reflect the non-linear nature of the relationship between different types of fair valued assets and audit fees. 

    Design/Method/ Approach:

    The authors examine these issues in audit fee models among closed-end mutual funds and among a broad-based sample of publicly traded companies.

    • The authors find that for the closed-end audit fee model, the log transformation provides the best fit for Level 1 valued assets, while a square root transformation provides the best fit for assets valued using Level 2 inputs, and cube root best fits Level 3 valued assets.
    • The authors’ findings are consistent with the idea that auditing the fair value of assets valued using Level 2 and Level 3 inputs may be more costly for auditors because they have to assess management’s evaluation of indirectly observable inputs and/or management’s own estimates of future cash flows and discount rates.
    • The authors find that, for the broad-based sample, the audit fee model also indicates that the log transformation alone may not fully capture the non-linear relationship between assets of different levels of complexity and audit fees.
    • The authors find that, for both the closed-end and broad-based samples, the significance of the other variables in the audit fee models can differ when the transformations of the size variables are allowed to vary. This suggests that a more rigorous test of non-size variables can be performed when the size variables are permitted to follow a better-fitting mathematical transformation. 
    Engagement Management
    Audit Fees & Fee Negotiations