Audit Risk Model Practice Problems

Audit risk model: Planned detection risk (PDR) = Acceptable audit risk (AAR) ÷ (Inherent risk (IR) × Control risk (CR)). Assess each risk as low, moderate, or high.

Problem 1: Planning, then change

At the start of planning, an auditor assesses acceptable audit risk (AAR) as high, inherent risk (IR) as low, and control risk (CR) as low for accounts receivable.

a. Determine planned detection risk (PDR) and the planned amount of substantive evidence.
PDR high, evidence low. High AAR, low IR, and low CR all point toward accepting more detection risk.
b. Tests of controls over sales find a deviation rate well above tolerable, so the auditor raises CR to high. What happens to PDR and to planned evidence?
PDR decreases (to moderate), evidence increases. Controls can’t be relied on, so substantive work carries more of the load.
c. Go back to the original facts. Instead, the client announces it will go public next year, and the auditor lowers AAR to low. What happens to PDR and to planned evidence?
PDR decreases (to moderate), evidence increases. More outside users will rely on the statements, so the auditor accepts less risk
d. Now suppose both (b) and (c) happen. Determine PDR and the planned amount of substantive evidence.
PDR low, evidence high. Low ARR and high CR both push PDR down. Expect larger samples, more effective procedures, and timing closer to year-end

Problem 2: Directional effects

Each situation is independent. For each one, name the risk affected (AAR, IR, or CR) and its direction. Then give the effect on PDR and on planned substantive evidence (increase, decrease, or no effect).

a. The client is close to violating its debt covenants, and cash flow has gotten worse.
- Risk affected and direction: AAR decreases and/or IR increases
  - Likely financial difficulty after the report is issued lowers AAR; pressure to stay within debt covenants gives management an incentive to misstate, which raises IR
- Effect on PDR: Decrease
- Effect on evidence: Increase
b. This is a repeat engagement. Last year’s inventory work found no misstatements, and the client’s operations haven’t changed.
- Risk affected and direction: IR decreases
- Effect on PDR: Increase
- Effect on evidence: Decrease
c. During the year the client began large, nonroutine transactions with an entity owned by the CEO’s brother.
- Risk affected and direction: IR increases
- Effect on PDR: Decrease
- Effect on evidence: Increase
d. Tests of controls over cash disbursements find almost no deviations.
- Risk affected and direction: CR decreases
- Effect on PDR: Increase
- Effect on evidence: Decrease
e. The client’s stock is closely held by three family members, and it has no significant debt.
- Risk affected and direction: AAR increases (few outside users)
- Effect on PDR: Increase
- Effect on evidence: Decrease
f. The client’s inventory is small, high-value electronics that are easy to carry off.
- Risk affected and direction: IR increases (easy to misappropriate)
- Effect on PDR: Decrease
- Effect on evidence: Increase

Problem 3: Multiple choice

Which of the following would most likely cause an auditor to decrease planned detection risk?

a. Assessed control risk is reduced after tests of controls go well.
Incorrect. Lower CR and higher AAR both raise PDR
b. The auditor decides acceptable audit risk can be higher because few outside users rely on the statements.
Incorrect. Lower CR and higher AAR both raise PDR
c. The auditor finds the client’s revenue recognition requires significant management judgment.
C is correct, Significant management judgment raises IR, and higher IR means lower PDR
d. The client has had stable earnings and low leverage for several years.
Incorrect. Stable earnings and low leverage make financial difficulty less likely, which supports a higher AAR and higher PDR

Problem 4: Risk matrix across accounts

AAR is assessed as moderate for every account. Using the assessments below, determine PDR (low, moderate, or high) and the planned amount of substantive evidence for each account.
(PDR and Evidence is the answer) Watch for: fixed assets. Low IR and High CR offset each other, so the answer is moderate, not low

Cash
- IR
  - Low
- CR
  - Low
- PDR
  - High
- Evidence
  - Low

Accounts receivable
- IR
  - High
- CR
  - Moderate
- PDR
  - Low
- Evidence
  - High

Inventory
- IR
  - High
- CR
  - High
- PDR
  - Low
- Evidence
  - High

Fixed assets
- IR
  - Low
- CR
  - High
- PDR
  - Moderate
- Evidence
  - Moderate

Accrued liabilities
- IR
  - Moderate
- CR
  - Moderate
- PDR
  - Moderate
- Evidence
  - Moderate

Problem 5: Short answer (risks revised during fieldwork)

The auditor planned the receivables audit assuming moderate IR and low CR, and set the confirmation sample to match. When confirmations come back, the misstatements found are much larger than expected.

a. Which risk assessments should the auditor revisit, and in which direction?
Revise IR upward. If controls didn’t prevent or detect the misstatements, revise CR upward too
b. What happens to PDR and to the amount of evidence needed?
PDR decreases, so the auditor expands substantive testing: larger samples, additional procedures, or both
c. A staff auditor suggests “just raising acceptable audit risk so the original sample still works.” Explain why that is wrong.
AAR depends on user reliance, the client’s financial condition, and management integrity, not on what the audit finds. Raising it would just be working backward to justify the original sample

Problem 6: True or False

Circle True or False. If false, explain why.

a. AAR and PDR move in the same direction. True / False
True: Lower AAR means lower PDR
b. An increase in inherent risk leads to an increase in planned detection risk. True / False
False: Higher IR means lower PDR
c. An auditor can reduce inherent risk by performing more substantive tests. True / False
False: IR exists independently of the audit. More substantive testing lowers detection risk, not IR
d. Acceptable audit risk is inversely related to the amount of evidence needed. True / False
True
e. If control risk is assessed below maximum, the auditor must perform tests of controls to support that assessment. True / False
True: the auditor can’t assume controls work without testing them
f. Under PCAOB standards, inherent risk and control risk together make up the risk of material misstatement. True / False
True: Under PCAOB standards, RMM combines IR and CR, and audit risk depends on RMM and detection risk