An Economic Analysis on Overbilling Incentives and Auditing Programs

Abstract

An institutional auditing program typically consists of the following steps: a sample audit, the decision to move to the full audit, a settlement offer, and the full audit. Statistical sampling techniques are often used to estimate the overbilling percentage and amount. This paper discusses the optimal settlement offer, the net recovery through auditing, the condition for the auditors to move to the full audit, and how an auditing program can be truly cost-effective. This paper provides an evaluation for the statistical sampling techniques to an auditing program. The economic incentives of a contractor to overbill are also identified. Finally, it presents the key metrics and the managerial implications for auditing managers to design or enhance their auditing programs.

Appendix

Proof of Eq. (9):

$$ \begin{aligned} \pi(\rho, 1) &= \rho (p^{\rm H}-c^{\rm H}) + (1-\rho)(p^{\rm H}-c^{\rm L}) - \gamma (1-\rho) m p^{\rm H}\\ &\quad - (\bar{e} - z) (1-\gamma) p^{\rm H}\\ &= \rho (p^{\rm H}-c^{\rm H}) + (1-\rho)(p^{\rm H}-c^{\rm L}) - \gamma (1-\rho) m p^{\rm H}\\ &\quad- (1-\rho) (1-\gamma) m p^{\rm H} + z (1-\gamma) p^{\rm H} \\ \pi(1, 1)&= p^{\rm H}-c^{\rm H} \end{aligned} $$

When π(ρ, 1) > π(1, 1)

$$ \begin{aligned} &(\rho -1 )(p^{\rm H} - c^{\rm H}) + (1-\rho)(p^{\rm H} - c^{\rm L}) - \gamma (1-\rho) m p^{\rm H}\\ &\quad> (1- \rho) (1-\gamma) m p^{\rm H} - z (1-\gamma) p^{\rm H}\\ &(1-\rho) (c^{\rm H} - c^{\rm L}) > (1 -\rho) m p^{\rm H} - z (1-\gamma) p^{\rm H}\\ &(1-\rho) (c^{\rm H} - c^{\rm L}) > (1 -\rho) (p^{\rm H} - p^{\rm L}) - z (1-\gamma) p^{\rm H}\\ & c^{\rm H} - c^{\rm L} > p^{\rm H} - p^{\rm L} - z \frac{1-\gamma}{1 - \rho} p^{\rm H}. \end{aligned} $$

$\square$