Economies of Scale in Audit Fee Studies: Is the Log Transformation the Best Fit for All Fair Value Assets?

• In Event: Audit Complexity, Audit Efficiency, and Audit Fees

Abstract

Log transformations of total assets and audit fee have long been used in modeling audit fees in literature (e.g., Simunic 1980; Craswell et al. 1995; Francis et al. 2005). As assets increase, the audit fee increases, but at a diminishing rate for larger client sizes, reflecting the economies of scale that arise when auditing larger clients. In this paper, we challenge the log transformation as the best fit for all types of assets, particularly in auditing fair value assets using different levels of valuation inputs. We examine different mathematical transformations of assets to determine more appropriate transformations for different valuations of fair value assets. Taking advantage of the unique setting offered by closed-end mutual funds in which virtually all assets are reported at fair value, we study the association between audit fees and the assets using level 1, level 2, and level 3 fair value inputs. Our results show that the log transformation still provides the best fit for level 1 assets in an audit fee model, suggesting that there are large economies of scale for these assets. However, for level 2 and 3 assets, the original dollar value and the cube root transformation respectively provide a better explanation for variation in audit fees, suggesting lower economies of scale for these types of assets. Our findings indicate that different economies of scale exist for different types of assets, providing helpful insight in assessing audit fees.

Authors

• Charles P Cullinan, Bryant University

• Hui Du, University of Houston–Clear Lake

• Xiaochuan Zheng, Bryant University