Audit Sampling for Tests of
Details of Balances
1. Understand the differences between sampling for tests of transactions and sampling for tests
of details of balances.
2. Apply non-statistical sampling to tests of details of balances.
Be able to compute sample sizes and project errors using non-statistical sampling.
Know the actions available to the auditor when projected error exceeds tolerable
Projecting errors to the population was previously discussed
in Ch. 9. The objective is to estimate the potential amount of
misstatement in year-end balances.
2. Evidence Decisions - As usual, we can start with our four
A. Which procedures - This issue is easy. The procedure
for year-end A/R to which sampling applies is
confirmation (which primarily satisfies the existence and
accuracy (valuation) objectives).
Consult the test of details of balances audit program in
Table 16-5 on p. 541. Do you see any other TODB for
A/R for which sampling is likely to apply?
Note that in other areas (particularly inventory),
sampling often applies to multiple audit procedures.
B. Sample size - Based on auditor judgment, considering
risk model, results of TOT and analytical procedures.
Auditor judgment is quantified in Monetary Unit
Sampling (MUS) and other statistical methods, but the
inputs still involve considerable judgment.
C. Which items - Also based on auditor judgment. As
discussed in Chapter 16, the emphasis is on large
amounts and old amounts. We will be more specific as
to how this is accomplished for statistical and
D. When - As discussed in Ch. 16, confirmations are often
sent 1-3 months prior to year-end to facilitate timely
completion of the audit.
E. Evaluation of Results
1. Identify errors - need to separate true errors from
valid timing differences (see Prob. 16-31).
2. Project errors to population (including
consideration of sampling risk).
3. Evaluate acceptability of population (decision
options if the population is not acceptable are
discussed on p. 143-144 of the notes).
Discussion of Bill DeBurger Case
3. Sample Size and Selection
A. Sample size - The key factors affecting sample size are:
Population size (note that population size generally
has no effect in transaction sampling).
Tolerable misstatement (materiality)
Desired assurance from test (depends on several
factors, including inherent risk and control risk)
B. AICPA formula - The AICPA Audit Sampling Guide
(1999) provides a simplified formula based on monetary
unit sampling. Steps in process:
1. Select items to be examined 100% (usually all
accounts greater than tolerable misstatement).
2. Compute sample for remaining dollars using this
formula (the population value excludes the items
tested 100% in step 1):
Population amount X Assurance Factor = Sample
Tolerable misstatement Size
3. Assurance factor
Assessment of Inherent Risk That Other Substantive Procedures Will
and Control Risk Fail to Detect a Material Misstatement
Maximum Maximum Moderate Low
Maximum 3.0 2.7 2.3 2.0
Slightly below maximum 2.7 2.4 2.0 1.6
Moderate 2.3 2.1 1.6 1.2
Low 2.0 1.6 1.2 1.0
The level of assurance depends upon the effectiveness of
controls, audit risk, and the results of other tests.
4. Allocate sample - the sample is then allocated to
strata of the accounts receivable population,
considering the relative materiality of each strata.
4. Sample Size Example (modification of Prob.17-29)
Book value 1,975,000
Tolerable misstatement 50,000
Assurance factor (moderate risk, no 2.3
assurance from other tests)
Total of accounts in excess of 875,000
tolerable misstatement (3 accts)
1,100,000 X 2.3 = 51 51
1,975,000 - 875,000)
Total sample size (51 + 3 accounts 54
larger than tol. mistmt.)
Effect of changes in variables on sample size
Change in Sample Comment
Population Increase Larger population will
increase require more evidence
Tolerable Decrease Greater materiality, less
Assurance Increase More assurance from test
increase requires more evidence
Multiple Choice 17-25 (c)
Accounts receivable contains a few unusually large balances. The
1. Eliminate any large balances from the sample.
2. Continue to draw samples until no large balances appear in the
3. Stratify the population so the large balances are reviewed separately.
4. Increase the sample size to lessen the impact of the large balances.
5. Error Projection - Errors are projected within strata, then
combined to compute an overall projected error.
Example - p. 565 of text
(1) (2) (3)=(2)/(1) (4)
Sample Errors and Sample Population (5)=(4)X(3)
Size in Untested Error Book Value Projected
Stratum Dollars Amts.(a) Rate by Stratum Error
1 88,955 (2,740) (.0308) 88,955 (2,740)(b)
2 43,955 971 .0221 71,235 1,572
3 13,105 2,158 .1647 47,105 7,757
Totals 146,055 389 207,295 6,589
(a) Amounts may be audited by confirmation or alternative procedures. Sample items not
tested should be treated as errors.
(b) Strata tested 100%; projected error = actual error
Auditor should consider sampling risk, especially when the
projected error is close to tolerable misstatement.
6. Options if projected error exceeds tolerable misstatement
(Note: for simplicity, we will assume errors are material if
greater than tolerable misstatement, rather than sum errors in all
segments and compare with materiality.)
a. Adjust the account balance
b. Increase the sample size
c. Perform expanded tests in specific areas (isolate the
d. Request the client to correct the population
e. Do not issue an unqualified opinion
7. Discussion of options for unacceptable results
Typical response is to adjust for actual errors. The adjustment
lowers the projected error. Although the projected portion of
errors is not frequently recorded as an adjustment, it can be
recorded as an adjustment to an allowance account (such as the
allowance for doubtful accounts).
If accounts receivable are still not acceptable, i.e., the adjusted
projected error (projected error reduced by the adjustment for
actual errors) is still greater than tolerable misstatement),
increase sample size in attempt to lower projected error.
A. Adjust the account balance - Recording actual errors is not
a problem. But clients are unlikely to adjust for
unidentified errors based on error projection.
B. Increase sample size - issue is similar to attribute
sampling. We are likely to increase sample size if
population is still unacceptable after recording actual
adjustments for two reasons:
1. The alternative to more testing is probably qualification.
2. The potential population is smaller (there are less
ending accounts receivable balances than sales
C. Isolation of errors - great if you can determine that errors
are all of one type, and caused by a unique problem.
However, this decision not to project errors should be
made with caution. Isolation is potentially appropriate in
problem 17-29. Errors number 3 and 5 are cutoff errors,
which are unique to year-end; the auditor might expand
D. Request the client to correct the population - Also a great
alternative, if client is capable of identifying errors, and
they are pervasive. Auditor must then perform tests on
E. Qualify opinion - Usually the last resort. May occur if
client is unwilling to adjust for errors, or pay for additional
Simplified example of error adjustment:
A/R book value 2,000,000
A/R tested 400,000
Overstatement errors - actual 30,000
Projected error 150,000
Tolerable misstatement 100,000
After adjusting for actual errors, projected error still exceeds
tolerable error ([150,000 - 30,000] = 120,000 > 100,000).
The auditor could:
Record an additional adjustment of at least $20,000
(probably to the allowance account)
Increase testing (will lower projected error only if the error
rate in the additional sample is less than the error rate in
the initial sample).
Any projected errors that are not adjusted are normally placed
on the schedule of adjustments not made to determine whether
such errors are material when combined with other errors. This
is discussed in Chapter 24.
Discussion Case – Bill DeBurger
Sampling Problem on next two pages (Collected)
Sample Multiple Choice (text)
17-25 (a), (c)
Part A - Compute Sample Size
Use the AICPA sampling formula to select a sample size for testing accounts receivable based on
the information below. The company has two major customers that will be tested as a separate
Book value of accounts receivable 6,000,000
Tolerable misstatement 100,000
Individual material accounts (2 accts - 1,600,000
amount is combined balance of accounts)
Assurance factor (Low risk, no assurance from 2.0
Calculate sample size
Part B - Project Error
Regardless of your answer to part a., assume that a total sample of 100 was selected and allocated
Account # of Sample Sample Population
Stratum Description accounts Size Amount Value
1 > $50,000 2 2 1,600,000 1,600,000
2 10,000 - 49,999 120 40 1,000,000 3,200,000
3 < $10,000 700 58 200,000 1,200,000
Three differences were uncovered as described on the following page.
Continued on next page
Errors and untested amounts:
Stratum Acct # Balance Confirmed Explanation
2 2196 40,000 20,000 Duplicate shipment not ordered by customer
2 1347 35,000 25,000 Customer payment on 12/29, rec’d by client
3 3652 10,000 2,000 Sale recorded 12/29 for goods shipped 1/3
Compute the projected error using the format below, which is similar to page 139 of the notes.
Note: The above are individual errors. Compute the error rate for each stratum by dividing the
total error in each stratum by the total sample size for that stratum.
Sample Size Strata Strata Stratum Book Projected
Stratum in Dollars Errors Error Rate Value Error
Totals 2,800,000 6,000,000
Part C - Evaluate the acceptability of the population and possible courses of action.
(Describe the action(s) you would take for these circumstances, and explain why. Do
not just list the five possible courses of action.)