1. ACCT 742: Advanced Auditing
Chapter 6
Dollar Unit or Monetary Unit Sampling

2. 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.

3. 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.

4. 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
A/R , ,000
Inventory 50, ,000
P/E , ,000
Total Assets $100,000
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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)

5. First 10 Vouchers in a Population
Balance
Cumulative Balance 1
$100 2
150
250 3 40
290 4
200
490 5 10
500 6
790 7 50
840 8
190
1030 9 20
1050 19
180
1230
Suppose you want to select three vouchers to audit: Select three random
Numbers between 1 and 1230, say 237, 579, and 978. Select the vouchers
to be audited. (Voucher Nos. 2, 6, 8). These random numbers work like a
fish hook in picking the accounts to be audited.

6. PPS Sampling Technique
Probability of selecting a sample item is proportional to the size of the sample item. Two approaches:
Random Sampling
Systematic 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)
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, ...

7. Poisson Distribution = 0.05  l = 3.0 (See Table 6.1)
- r is the number of errors
 is the reliability factor or
Upper Misstatement Limit
(UML)
For r=0, P(r=0|l) = e-l,
ARIA = P(r=0|l) = e-l
= 0.05  l = 3.0
(See Table 6.1)

8. 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

9. Sample Size for E*  0 (Skip this part)
Determine or Estimate:
Total BV
ARIA (b-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).

10. 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

11. 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)