ACCT 742: Advanced Auditing

Chapter 6Dollar Unit or Monetary

Unit Sampling

Probability Proportional-to-size Sampling (Dollar Unit Sampling)

DOLLAR (Monetary) UNIT SAMPLING (DUS, CAV, MUS) It gives higher chances of picking higher dollar

amount accounts. It is easier to use. It can combine several different accounts. It is efficient compared to classical variable sampling

if no or few misstatements are expected. It does not depend on the sampling distribution being

closely approximated by the normal distribution. It provides an alternative to using variable sampling

to stratify a population.

Problems with DUS (MUS)

It requires that the amount of misstatement in each physical unit of the population not to exceed the book value of the unit.

Items with zero value or negative balance are not selected.

Highly understated accounts are less likely to be selected. As the number of misstatement increases, sample size

increases, and the sample size may be larger than the sample size calculated under a classical variable sampling application.

It may overstate the allowance for sampling risk when misstatements are found and cause the auditor to reject a correct client book value.

Dollar Unit Sampling: An Example

Each unit of dollar is considered to be a sampling unit It is based on a well tested recipe

CASH $10,000 10,000 A/R 20,000 30,000 Inventory 50,000 80,000 P/E 20,000 100,000

-----------Total Assets $100,000

====== How many total sample items or units we have in the

above example? (100,000 units) How many units or sample items we have in Cash

account? (10,000)If we select one item or unit from the above population, which account it is more likely that the unit will come from?

(Inventory account because there are more units)

First 10 Vouchers in a Population

Voucher # BalanceCumulative

Balance

1 $100 $100

2 150 250

3 40 290

4 200 490

5 10 500

6 290 790

7 50 840

8 190 1030

9 20 1050

19 180 1230

Suppose you want to select three vouchers to audit: Select three randomNumbers between 1 and 1230, say 237, 579, and 978. Select the vouchersto be audited. (Voucher Nos. 2, 6, 8). These random numbers work like afish hook in picking the accounts to be audited.

PPS Sampling Technique

Probability of selecting a sample item is proportional to the size of the sample item. Two approaches: Random Sampling Systematic Sampling

Random Sampling Select n random numbers between 0 and BV. Prepare a cumulative sum of account balances Select those accounts whose cumulative sums

contain the random numbers (RNs)

Systematic Sampling Determine the sampling interval: I = BV/n Select a random number (RN) between 0 and I Dollar units selected would be: RN, RN + I, RN + 2I,

...

Poisson Distribution

Poisson Distribution

0.00

0.05

0.10

0.15

0.20

0.25

1 2 3 4 5 6 7 8 9 10 11

No of Errors

Prob

abili

ty o

f Err

ors

0 1 2 3 4 5 6 7 8 9 10

r

P(r| ) = er!

- r is the number of errors is the reliability factor or Upper Misstatement Limit (UML)

For r=0, P(r=0|) = e,ARIA = P(r=0|) = e

(See Table 6.1)

Sample Size (No misstatement expected in the population, E* = 0)

n = BV*UML0/TM

UML0 = Upper Misstatement Limit (It is the same as Reliability Factor in Poisson Distribution, see Table 6.1)

TM = Tolerable Misstatement

ARIA = 5% UML0 = 3.0

TM = $6,000, BV = $100,000

Assume each unit is in error by $1

n = BV*UML0/TM = $100,000* 3.0/$6,000 = 50

Sample Size for E* 0 (Skip this part)

Determine or Estimate: Total BV ARIA (-Risk) TM (Tolerable misstatement) Expected misstatement in the population (E*) Determine RF (Reliability factor, Table 6.1 or Table 3.6)

(Use the first row in the table for RF) EF (Expansion Factor) from AICPA tables (Tables 6.2).

n = (Total BV) *(Reliability Factor)

TM - (Expected Misstatement) *(Expansion Factor)

Steps for Determining Error Bounds

Separate the overstatements from understatements Determine individual tainting for over- and under-statements

tainting = t = (Error in the account)/(BV of the account) Rank order tainting for overstatements and understatements

separately Determine unadjusted Error Bounds (EB) for overstatements

and understatements separately Determine Most Likely Misstatement (MLM) for both

overstatements and understatements

MLM = (Total BV)*(Sum of tainting/n) Adjust the Error Bounds by subtracting the opposite MLM

Error Bounds

Net Mmaxo/s = Mmaxo/s - MLMu

Net Mmaxu/s = Mmaxu/s- MLMo

Mmaxo/s=(Total BV/n)*[UML0*$1+{UML1-UML0}*(tO1)+{UML2–UML1}*(tO2)+ ...]

Mmaxu/s=(Total BV/n)*[UML0*$1+{UML1-UML0}*(tu1)+{UML2–UML1}*(tu2)+ ...]

Basic bound = (Total BV/n)* UML0*$1

First addition to basic bound:

(Total BV/n)*{UML1-UML0}*(tO1)