ABSTRACT: Management and auditors face increased responsibilities to evaluate internal control and assess the risk of fraud. This case provides the opportunity to evaluate internal controls and the possibility of fraud in a very small not-for-profit child care center, a setting that is easy to understand. The first goal of the case is to identify internal control weaknesses by applying the COSO internal control framework in an environment that lacks many aspects of internal control. Interactions among the five components of the COSO framework provide the basis for analyzing internal control. The case requires students to consider possible misappropriation of funds using the fraud triangle. A secondary goal of the case is to introduce financial reporting for a not-for-profit organization as a means of accountability.

Popcorn ash particles are fragments of sintered coal fly ash masses that resemble popcorn in low apparent density. They can travel with the flow in the furnace and settle on key places such as catalyst surfaces. Computational fluid dynamics (CFD) models are often used in the design process to prevent the carryover and settling of these particles on catalysts. Particle size, density, and drag coefficient are the most important aerodynamic parameters needed in CFD modeling of particle flow. The objective of this study was to experimentally determine particle size, shape, apparent density, and drag characteristics for popcorn ash particles from a coal-fired power plant. Particle size and shape were characterized by digital photography in three orthogonal directions and by computer image analysis. Particle apparent density was determined by volume and mass measurements. Particle terminal velocities in three directions were measured in water and each particle was also weighed in air and in water. The experimental data were analyzed and models were developed for equivalent sphere and equivalent ellipsoid with apparent density and drag coefficient distributions. The method developed in this study can be used to characterize the aerodynamic properties of popcorn-like particles.

Recently, Shafer and Srivastava [1], Srivastava and Shafer [2], Srivastava [3]–[4], and Van den Acker [5] have identified appealing features of belief function evidential networks. These networks can express the support that audit evidence provides for assertions, accounts and financial statements. These networks can also aggregate many pieces of evidence into an overall level of support for a particular assertion, account or an entire set of financial statements. There is little empirical evidence about the ability of practicing auditors to express their evaluations of the strength of audit evidence in terms of belief functions. Many traditional models assume the use of probabilities. These might be called the traditional type of subjective probabilities. They are additive by definition, i.e. P(a) + P(~a) = 1. Throughout the remainder of this paper they will simply be referred to as probabilities. This study examines the question of expressing the support provided by audit evidence empirically. Auditors are asked to express the level of support that evidence provides for or against an assertion or account and the ignorance that remains about the assertion or account after considering the evidence. Many auditors who use probabilities to measure risk express ignorance by giving equal weight to support for and support against the objective. Belief functions express ignorance by allocating mass to all elements of the frame (all possible outcomes), an alternative that is distinct from assigning equal mass to each element of the frame. Thus, belief functions show ignorance as an amount separate from the amounts of support for and against the objective. Forty-nine experienced auditors were asked to estimate the strength of the evidence provided in twenty-eight different audit situations. These auditors were given the opportunity to model their estimates of support and ignorance in ways that were consistent either with belief functions or with Probabilities. In this study, a statistically significant percentage of the auditors represented their estimates in ways that were consistent with belief functions and were inconsistent with probabilities. This suggests that future practitioner decision aids may include belief functions as a way of naturally expressing the ignorance and risk that persist in many audit engagements.