Solution manual aswers auditing theory by cabrera chapter 19 ans

Risk of incorrect acceptance that likely misstatement could be less thantolerable misstatement even though the actual misstatement in the population is greater, or the b.. Risk of incorr

AUDIT SAMPLING FOR SUBSTANTIVE TESTS

I Review Questions

1 An incorrect acceptance decision directly impairs the effectiveness of an audit.

Auditors wrap up the work and the material misstatement appears in the financial statements

An incorrect rejection decision impairs the efficiency of an audit Further

investigation of the cause and amount of misstatement provides a chance to reverse the initial decision error

2 The two methods of projecting the known misstatement to the population are the

average difference method and the ratio method Refer to Chapter 19 for

formula expressions of each

3 The important thing is to audit all the sample units You cannot simply discard

one that is hard to audit in favor of adding to the sample a customer whose balance is easy to audit This action might bias the sample If considering the entire balance to be misstated will not alter your evaluation conclusion, then you

do not need to work on it any more Your evaluation conclusion might be to

accept the book value, as long as the account counted in error is not big enough

to change the conclusion Your evaluation conclusion might already be to reject the book value, and considering another account to be misstated just reinforces

the decision

If considering the entire balance to be misstated would change an acceptance evaluation to a rejection evaluation, you need to do something about it Since

the example seems to describe a dead end, you may need to select more accounts (expand the sample) and perform the procedures on them (excluding confirmation) and reevaluate the results

4 Two main reasons for stratifying a population when sampling for variables (peso) measurement:

a Some units may be individually significant (e.g., large) and taking sampling risk with respect to them is not a good idea

b Auditors may want to achieve audit coverage of a large proportion of pesos

in the balance by choosing the largest units (a protective sampling objective, which is closely related to avoiding sampling risk)

5 The tolerable misstatement (judged for the audit of a particular account balance) must be less than the monetary misstatement considered material to the overall

financial statements Also, the aggregation of multiple tolerable misstatement

amounts for several different balances under audit must be equal to or less than the amount of monetary misstatement considered material to the overall statements

6 The appropriate general set of objectives is the objective(s) of obtaining evidence about each of the client’s assertions in the financial balance In general, the assertions are about:

Existence (and cutoff)

Occurrence (and cutoff)

Completeness (and cutoff)

Rights and obligations (ownership, owership)

Valuation

Measurement

Presentation and disclosure

7 Influence on sample size:

Sample Size Relationships: Audit of Account Balances

Predetermined Sample Size Will Be:

Sample Size Influence

High Rate or Large Amount

Low Rate or Small Amount

Sample Size Relation

1 Risk of incorrect

2 Risk of incorrect

rejection

3 Tolerable

4 Expected

5 Population

variability

8 The three basic steps in quantitative evaluation are these:

1 Figure the total amount of actual misstatement found in the sample This

amount is called the known misstatement.

2 Project the known misstatement to the population The projected amount is called the likely misstatement.

3 Compare the likely misstatement (also called the projected misstatement) to

the tolerable misstatement for the account, and consider the

a Risk of incorrect acceptance that likely misstatement could be less than

tolerable misstatement even though the actual misstatement in the population is greater, or the

b Risk of incorrect acceptance that likely misstatement could be greater

than tolerable misstatement even though the actual misstatement in the population is smaller

9 Nonstatistical measurements described in Chapter 19 (page 718) leave only one avenue for “accounting for further misstatement”: Apply experience and professional judgment to decide if further misstatement could be large enough to prevent an acceptance decision If the projected likely misstatement is a great

deal less than the amount considered material, an auditor could judge that

further misstatement, if known, would not affect acceptance If projected likely misstatement is close to the amount considered material, maybe acceptance is not warranted

10 Account balances also can be audited, at least in part, at an interim date When account balance audit work is done before the company’s year-end date, auditors

must extend the interim-date audit conclusion to the balance-sheet date The process of extending the audit conclusion amounts to nothing more (and nothing

less) than performing substantive-purpose audit procedures on the transactions

in the remaining period and on the year-end balance to produce sufficient competent evidence for a decision about the year-end balance

Additional considerations include:

a If the company’s internal control over transactions that produce the balance under audit are not particularly strong, you should time the substantive detail work at year-end instead of at interim

b If control risk is high, then the substantive work on the remaining period will need to be extensive

c If rapidly changing business conditions might predispose managers to misstate the accounts (try to slip one by the auditors), the work should be

timed at year-end In most cases, careful scanning of transactions and analytical review comparisons should be performed on transactions that

occur after the interim date

As an example, accounts receivable confirmation can be done at an interim date Subsequently, efforts must be made to ascertain whether controls continue to be strong You must scan the transactions of the remaining period, audit any new large balances, and update work on collectibility, especially with analysis of cash received after the year-end

11 Classical variables sampling estimates the value of a population by calculating

the mean and standard deviation of a sample and imputing the results to the

population Probability proportional to size sampling uses the results of

sampling to calculate an estimated upper error limit and compares this with a preset tolerable error limit Although used for substantive testing purposes, PPS sampling is actually a variation for attribute sampling

12 Detection (or beta) risk affects sample size inversely for substantive testing purposes That is, the higher the acceptable detection risk, the smaller the sample size; and the lower the acceptable detection risk, the larger the sample size

13 Precision is the range + – within which the true answer most likely falls It is

set by the auditor as a function of materiality and those levels of beta and alpha

risk deemed acceptable Reliability is the likelihood that the sample range

contains the true value Also referred to as the confidence level, reliability is set

by the auditor on the basis of overall audit risk

14 PPS sampling is restricted to populations for which the auditor suspects a few errors of overstatement only

15 Several statistical software packages are available to facilitate audit sampling applications In addition to calculating sample size and evaluating sample results, these packages can also assist in the following sampling areas:

a Stratify populations for sampling purposes;

b Generate random numbers to facilitate sample selection;

c Draw the sample, given computerized data bases

II Multiple Choice Questions

Supporting Computations:

1,200 x P4 = P4,800

P450,000 x 3.5% = P157,500

Audited Value 47,520

Book Value 48,000

490,000 x 0.99 = 485,100 490,000 – 485,100 = P4,900 P480

120

P 17,500

P500,000

III Comprehensive Cases

Case 1 a Alpha risk is the risk of rejecting a population that is essentially correct.

Beta risk is the risk of accepting a population that is materially incorrect.

Alpha risk affects audit efficiency because overauditing results from incorrectly rejecting a population Beta risk impacts audit effectiveness because underauditng results from incorrectly accepting a population

Collectively, alpha and beta risk comprise sampling risk, defined as the

probability that the auditor will draw erroneous conclusions about a population

b Attention to, and quantification of, alpha and beta risk assist the auditor in applying an audit risk approach to substantive testing During the audit planning stage, the auditor identifies areas of high audit risk and sets detection (beta) risk low for these areas The result is that more substantive testing is devoted to the high risk areas relative to the lower risk areas This approach enhances both audit efficiency and audit effectiveness

c Because it is closely related to the basis for the auditor’s opinion, alpha risk

is usually set equal to overall audit risk Beta risk is set on the basis of the auditor’s evaluation of inherent risk and control risk The greater these risk factors, as determined by the auditor during the audit planning stages, the lower the beta risk set by the auditor The lower the acceptable beta risk, the larger the sample sizes for substantive testing purposes Alpha and beta risk, therefore, provide the necessary link between audit risk analysis and substantive audit testing

Case 2 a (1) Mean-per-unit estimates the total value of a population by (1) using the

sample mean as an estimate of the true population mean, and (2) extending this estimated population mean by the number of items in the population The computations are as follows:

(1) Estimated population mean =

P582,000 / 200 lots = P2,910 per lot (2) Estimated total value =

P2,910 per lot x 2,000 lots = P5,820,000 (2) Ratio estimation estimates total population value by (1) using the ratio

of the sample audited values to book values as an estimate of the ratio

of population audited value to book value, and (2) applying the estimated ratio to the population book value The computations are as follows:

(1) Estimated ratio of audited to book value =

P582,000 / P600,000 = 97%

(2) Estimated total value =

97% x P5,900,000 = P5,723,000 (3) Difference estimation estimates total population values by (1) using the average difference between the audited and book values of sample items as an estimate of the average difference for all population items, (2) extending the estimated average difference by the number of items

in the population, and (3) using the resulting estimate of the total difference between audited and book value to compute the estimated total value The computations are as follows:

(1) Estimated average difference in audit and book values:

(P582,000 - P600,000) / 200 lots = - P90 per lot (2) Estimated total difference =

- P90 per lot x 2,000 lots = - P180,000 (3) Estimated total value =

P5,900,000 - P180,000 = P5,720,000

b The sample contains an element of sampling error with respect to the average peso value of production lots The mean book value of the population is P2,950 (P5,900,000 / 2,000 lots), while the mean book value

in the sample is P3,000 (P600,000 / 200 lots) Mean-per-unit estimation uses the mean value of the sample as the basis for estimating total value Thus, if the sample contains a disproportionate number of higher (or lower) priced items, this sampling error will affect the estimate of the total population value

The estimate of total value developed in ratio estimation is based upon the ratio of audited values to book values, rather than upon mean peso value If this ratio has no tendency to vary with the peso value of the lot, the estimate

of total value is not affected by the mean value of items in the sample However, sampling error may still be present if the sample lots are not

representative of the population with respect to the ratio of audited values

to book values

Case 3 The auditors would project the misstatement found in the sample to the

population using either the ratio or difference approach The ratio approach

would result in a projected misstatement of P65,500 This may be computed by first calculating the ratio of the audited to book value as 1.0131 [P23,100 / P22,800 (since there is a net understatement of P300, the audited value is P23,100)] and estimating the audited value of the population as:

1.0131 x P5,000,000 = P5,065,500 (rounded) The projected misstatement is thus P65,500 under the ratio method

The difference approach results in an average difference of P1.50 (P300 net

difference divided by 200 items) Multiplying by the 100,000 invoices indicates

a projected misstatement of P62,400 (P1.50 x 41,600)

Case 4 The audit risk (ultimate risk) of material misstatement in the financial statements

(AR) is the product of:

(1) Inherent risk (IR), the risk of material misstatement in an assertion,

assuming there were no related internal controls

(2) Control risks (CR), the risk of material misstatement occurring in an

assertion, and not being prevented or detected on a timely basis by the internal control structure

(3) Detection risk (DR), the risk that the auditors’ procedures will lead them to

conclude an assertion is not materially misstated, when in fact such misstatement does exist

In equation form, this relationship is expressed as follows:

AR = IR x CR x DR This equation may be restated to solve for the allowable detection risk as follows:

DR = AR / (CR x IR) Using the risk levels set forth in the problem, the allowable risk of reliance upon substantive tests is computed as illustrated below:

DR = 02 / (.2 x 5) = 20 Thus the risk of incorrect acceptance should be limited to 20 percent if the auditors are to achieve their objective of holding audit risk to 2 percent

Case 5 a (1) Required sample size is calculated as follows:

Sample size =

Note: The reliability factor is from the zero misstatements row of the PPS sampling table given in the case

(2) The sampling interval is calculated simply by dividing the book value

of receivables by the sample size, as follows:

Sampling interval = Recorded receivables / Sample size

= P500,000 / 69 = P7,246

b The results may be evaluated as follows:

(1) Projected misstatement =

Book Value d Value Audite Misstatemen

t

Tainting

% Samplin g

Interval

Projected Misstatemen t

P1,197

(2) Basic precision = Reliability factor x Sampling interval

(3) Incremental allowance =

Reliability Factor Incremen (Increment – 1) Misstatement Projected Incremental Allowance

3.00

Recorded amount of population

x Reliability factor Tolerable misstatement – (Expected misstatement x Expansion factor)

P500,000 x 3 P25,000 – (P2,000 x 1.6)

(4) Upper limit on misstatement = P1,197 + P21,738 + P525

= P23,460 NOTES:

Projected misstatement

(a) Tainting percentages are calculated as the difference between book and audited value divided by book value (e.g., (P50 – P47) / P50 = 6%)

(b) No tainting percentage is calculated for items in excess of the sample interval and the actual misstatement is extended to projected misstatement (as for the third error)

Basic precision is always the reliability factor for zero misstatements

multiplied times the sampling interval

Incremental allowance

(a) Reliability factors are read from the PPS sampling table given in the case, starting at zero misstatements

(b) “Increment – 1” is the difference in the two adjacent reliability factors minus 1 (e.g., 4.75 – 3.00 – 1.00 = 75)

(c) Misstatements in excess of the sampling interval are not considered in the incremental allowance This is because the nature of the process requires that all items in excess of the sampling interval be included in the sample – therefore no allowance for items not in the sample is necessary

c The results obtained in part b would indicate that the auditors may accept

the population as not containing a tolerable misstatement at the 5 percent level of risk of incorrect acceptance The auditors would also consider the results obtained in conjunction with other audit tests

Case 6 a The advantages of probability-proportional-to-size (PPS) sampling over

classical variables sampling are as follows:

 PPS sampling is generally easier to use than classical variables sampling

 The size of a PPS sample is not based on the estimated variation of audited amounts

 PPS sampling automatically results in a stratified sample

 Individually significant items are automatically identified

 If no misstatements are expected, PPS sampling will usually result

in a smaller sample size than classical variables sampling

 A PPS sample can be easily designed and sample selection can begin before the complete population is available

b Sampling interval = Recorded receivables / Sample size

c Projected misstatement =

Book Value d Value Audite Misstatemen

t

Tainting

% Samplin g

Interval

Projected Misstatemen t

P1,700