"Paradox Of Punishment" In The Auditing Process Of The Public Company's Accounting Reports

In recent years, frauds in accounting information disclosing have been exposed frequently. The fraudulent public companies have been criticized, and the certified public accountants (CPA), which are in charge of auditing the accounting reports, have been oppugned also. The auditing of accounting reports is a game process between the CPA and the public company. Many scholars have researched this game process, but most of them ignored the influence of time, and failed to think over the side effect of punishment. This paper is a small thinking about the auditing game to make up the two foregoing shortages. We can divide the auditing process into three steps: firstly the public company operates for a year, and it will get a good achievement or a bad one. The company wants to get the good one, but it can't come true sometimes because of the economic environment and industry's character. We assume that the achievement the company gets is decided by nature (denoted by N), the probabilities of good and bad are 1/2 respectively. The company (denoted by C) knows well about its achievement. Secondly, the company makes its accounting report based on its achievement. The company will choose honest (h), when its achievement is good; and the company can choose honest or fraud (f), when its achievement is bad. In the third step, the CPA (denoted by A) audits the accounting report. Because he doesn't know the choose of nature and the company, he has no idea about his situation in the game tree. The CPA can take an attitude of trust or distrust, and different attitude takes different effort. When the CPA trusts the accounting report, he can't find the fraud; but when the CPA distrusts the report, he will work harder, and he will check out all frauds with higher auditing cost. Now we express the auditing process into a dynamic game process with imperfect information. When the pubic company achieves good profits, the earning of the public company is M; when the public company achieves bad profits, and it discloses this situation honestly, its earning is L; when the achievement is bad and the public company cheats, if the CPA trust its report, the public company earns the highest—H; but if the CPA distrust its report, exposes its fraud, the public company will be punished by the supervision department of government, and now its earning is the lowest—P. We can know: H﹥M﹥L﹥P﹥0 . We must notice that when the public company is honest, its earning is independent of the CPA's choice. Because when the accounting report is honest, no matter the CPA trusts it or not, the auditing result reflects the real condition of the company. The earning of CPA is certain—S in general; but if he distrusts the accounting report, he will check the accounts and voucher carefully, there will be additional auditing cost, and now his earning will fall to S-C; when the public company cheats and the CPA trusts it blindly, in case the supervision department detects, the CPA will be punished, his earning is F; when the public company cheats and the CPA distrusts it, the public company can change the CPA, then the CPA can't earn the whole payment, subtracting the additional auditing cost, the last gain is only T-C. We can know: S﹥S-C﹥T-C﹥F﹥0. Suppose the probability of the public company being honest is α, then the probability of fraud is 1-α.And suppose the probability of the CPA choosing distrust is β, then the probability of trust is 1-β.We can calculate the expected profits of the public company and the CPA: πC =1/2M+1/2{αL+(1-α)[(1-β)H+βP]} =1/2 (M+H-βH+βP)+1/2α(L-H+βH-βP) πA=1/2 (1-β)S+1/2β(S-C)+1/2{α[(1-β)S+β(S-C)]+(1-α)[(1-β)F+β(T-C)] =1/2 (S+αS+F-αF)+ β[1/2(F-T)α-1/2(F-T)-C] According to the profits maximization principle, we can get the equilibrium of the mixed strategy. In the dynamic game model, the probability of financial fraud of the public company lies on the earnings of the CPA, changing the strength of punishment to the public company can't influence the company's action. When the strength of punishing the fraudulent company is enhanced, the earnings of fraudulent company descend from P to P′, P′﹤P,then -P′﹥-P, β′= HH ?? PL'﹤HH ?? PL=β* We can find that enhance the strength of punishment to the fraudulent company can't change the probability of the company to choose fraud, but the probability of the CPA to choose distrust descends. Because enhancing the strength of punishment to the fraudulent company will reduce the company's expected profits of fraud, the public company is inclined to disclose the accounting information honestly in the short run. Nevertheless, the morehonest the public company chooses, the more trust the CPA chooses, according to the cost –efficiency principle. Then the strength and extent of auditing will reduce in the long run. It will increase the expected profits of fraudulent accounting report, so the probability of fraud will increase. Therefore, enhancing the punishment to the fraudulent company can only work in the short run. In the long run it can't restrain the accounting report fraud happening. The CPA will choose trust more after enhancing the punishment to the fraudulent company, the strength and extent of auditing will descend. It isn't the prefect result obviously. When the strength of punishment to the CPA for negligence of duty is enhanced, then F falls to F′, -F﹤-F′,then α′=1-T 2?C F' ﹥1-T 2?C F =α* We can find that enhancing the punishment to the CPA will increase the probability of honesty of the company. Enhancing the punishment to the breach of duty will descend the expected profits for the trust, so the CPA will work harder and choose distrust more. The public company, as a rational "economic man", can forecast the action of the CPA, so it can only reduce the fraud. Finally the probability of the financial fraud descends. According to the foregoing paradox, if we want to descend the probability of financial fraud, we can enhance the strength of the punishment to the neglecting CPA; contrarily it is impossible to descend the probability of financial fraud by enhancing the strength of punishment to the fraudulent company, if we did so, the strength of the CPA supervising would weaken. This conclusion can help us seize the principal contradiction and constitute the effective supervising policy. In the accounting information market, the purchaser and the demander of...