I examine how an internal auditor, called the firm, designs a control system for a strategic employee who conditions his thefts on the amount and types of controls. Society sets minimum testing amounts and fines for detected theft, whereas the firm determines the employee's wages and the amount of monitoring above the minimum. The results fall into three separate cases. When society's minimum testing standards and fines are sufficiently high, the employee never steals in any period. In this case, the firm performs the minimum amount of testing and pays the lowest feasible wage. In the remaining two cases, the testing standard and fines are too low to prevent theft by themselves. In these two cases the firm's control system determines whether there will be theft in the first period. I show that if the firm chooses to prevent all first‐period theft, then it uses only one type of control. She offers a wage premium and monitors the minimum amount. The wage premium substitutes for a tine large enough to prevent all theft. If the firm designs controls that do not prevent all theft, then the firm also uses only one control. In contrast to the no‐theft case, the firm pays the lowest feasible wage and monitors above the minimum. This choice reflects the increasing returns to scale of monitoring in preventing theft.

One of the most common decisions facing an internal auditor is choosing which line items to investigate. An extensive literature (Dworin and Grimlund 1984; Leslie et al. 1980; Menz& fricke 1984; Teitlebaum and Robinson 1975) deals with the statistical and decision-theoretic aspects of his choice. This paper expands on previous work by adding a strategic source of errors: dishonest employees. It addresses the question of how the presence of strategic errors affects the relationship between the auditor's testing strategy and item value. I show that incorporating strategic errors can lead to audit strategies similar to Physical Units and Dollar Units Sampling. I highlight the assumptions driving the results by contrasting a firm's (or internal auditor's) use of an optional test in four stylized models of accounts receivable. The first model examines the firm's behavior when faced with nonstrategic (statistical) billing errors. In this model the accounting system generates random errors that result in over- or underbilling customers. The firm can use a costly, imperfect test to remove errors before the bills are sent out. In this nonstrategic model the firm randomizes and tests an item if and only if the benefit is greater than the cost. Because the amount of billing error is unrelated to the item value, there is no clear link between the firm's testing decision and the value of the line item. The second billing model adds the possible existence of dishonest employees who can steal from line items. A dishonest employee makes two decisions. He decides whether to steal from the line item, and, if he steals, he chooses the amount of the theft. A dishonest employee would steal the entire item if he were certain that the firm would never test that item. The dishonest employee's behavior forces the firm to consider the value of the item in determining the region of untested items. Specifically, low value items are never tested. As in many strategic models, the interaction with dishonest employees may lead to randomization. In particular, the randomized testing strategy can look like Stratified Physical Units Attributes Sampling (Leslie et alt 1980). The firm sorts items into different groups and each item in a group has the same probability of being tested. The third model contains only the statistical errors of incorrectly adding or deleting a sales discount, a percentage of the item value. Since the testing gain is directly related to the value of the line item, the firm's strategy depends on an item's value. The firm always tests high value items, and never tests low value items. The fourth model adds potentially dishonest employees who can pros vide unearned sales discounts to their confederates. In this model the firm stratifies items into three groups. It never investigates small items, always investigates large items, and randomizes over intermediate value items with probabilities roughly proportionate to the value of the item. This procedure is similar to a common audit procedure, Dollar Unit Cell Width Sampling (Leslie et al. 1980).

[One of the most common decisions facing an internal auditor is choosing which line items to investigate. An extensive literature (Dworin and Grimlund 1984; Leslie et al. 1980; Menzefricke 1984; Teitlebaum and Robinson 1975) deals with the statistical and decision-theoretic aspects of his choice. This paper expands on previous work by adding a strategic source of errors: dishonest employees. It addresses the question of how the presence of strategic errors affects the relationship between the auditor's testing strategy and item value. I show that incorporating strategic errors can lead to audit strategies similar to Physical Units and Dollar Units Sampling. I highlight the assumptions driving the results by contrasting a firm's (or internal auditor's) use of an optional test in four stylized models of accounts receivable. The first model examines the firm's behavior when faced with non-strategic (statistical) billing errors. In this model the accounting system generates random errors that result in over- or underbilling customers. The firm can use a costly, imperfect test to remove errors before the bills are sent out. In this nonstrategic model the firm randomizes and tests an item if and only if the benefit is greater than the cost. Because the amount of billing error is unrelated to the item value, there is no clear link between the firm's testing decision and the value of the line item. The second billing model adds the possible existence of dishonest employees who can steal from line items. A dishonest employee makes two decisions. He decides whether to steal from the line item, and, if he steals, he chooses the amount of the theft. A dishonest employee would steal the entire item if he were certain that the firm would never test that item. The dishonest employee's behavior forces the firm to consider the value of the item in determining the region of untested items. Specifically, low value items are never tested. As in many strategic models, the interaction with dishonest employees may lead to randomization. In particular, the randomized testing strategy can look like Stratified Physical Units Attributes Sampling (Leslie et al. 1980). The firm sorts items into different groups and each item in a group has the same probability of being tested. The third model contains only the statistical errors of incorrectly adding or deleting a sales discount, a percentage of the item value. Since the testing gain is directly related to the value of the line item, the firm's strategy depends on an item's value. The firm always tests high value items, and never tests low value items. The fourth model adds potentially dishonest employees who can provide unearned sales discounts to their confederates. In this model the firm stratifies items into three groups. It never investigates small items, always investigates large items, and randomizes over intermediate value items with probabilities roughly proportionate to the value of the item. This procedure is similar to a common audit procedure, Dollar Unit Cell Width Sampling (Leslie et al. 1980).]

Accounting research contains two distinct approaches to the interaction between accounting management and the independent auditor. Game theory suggests that the auditor's testing strategy will affect the manager's reporting strategy and that the two strategies form an equilibrium. The game‐theoretic approach views the auditor as active, in that the auditor acknowledges the effect that his or her testing strategy has on the manager's reporting. In contrast, in the decision‐theoretic approach, the auditor tests reports, but ignores the effect that such testing might have on the manager's reporting behavior. Essentially, the decision‐theoretic approach views the auditor as passive, taking the reporting strategy as given when designing tests. We use United Kingdom data to estimate both models and test their validity using nested hypothesis tests. Our results demonstrate that the active, game‐theoretic model better describes the auditor‐manager interaction. This is the first empirical validation of the game‐theoretic model using archival accounting data.

Issues surrounding the allocation of sunk capacity costs to products are among the oldest in managerial accounting. On the one hand, such costs are generally deemed to be irrelevant, but on the other hand, actual accounting systems commonly make these allocations. This paper examines a decision maker who incurs costs to acquire capacity and then uses an opportunity cost to allocate that capacity among a sequence of product proposals. Under specified circumstances, the sunk cost of capacity is shown to approximate the optimal opportunity cost of capacity. As the number of product proposals grows, the expected opportunity loss from using a simple sunk cost based capacity allocation rule goes to zero. The model is extended to consider different types of products and a multiperiod setting. Résumé. Les questions qui entourent la répartition des coûts irrécupérables relatifs à la capacité entre les différents produits comptent parmi les plus vieux problèmes en comptabilité de gestion. D'une part, ces coûts sont généralement réputés n'être pas pertinents, tandis que d'autre part, en réalité, les systèmes de comptabilité assurent couramment ces répartitions. Les auteurs examinent le cas d'un décideur qui engage des frais pour acquérir une certaine capacité et utilise ensuite un coût d'option pour répartir cette capacité entre une série de projets de fabrication de produits. Dans des circonstances données, les auteurs démontrent que les coûts irrécupérables de la capacité acquise se rapprochent du coût d'option optimal de cette capacité. À mesure que croît le nombre de projets de fabrication de produits, la perte d'option prévue, si l'on utilise une règle de répartition simple de la capacité fondée sur les coûts irrécupérables, se rapproche de zéro. Le modèle est élargi de façon à englober différents types de produits et plusieurs périodes.