May-2015

statement.
When Yi ≠ 0 the fractional amount of i th item
T i
= D i
/ Y i
is called tainting or taint.
The error of the book balance and account is
The details of the samples audited are clubbed together
and the accepted monetary value of the each item after
auditing will be rerecorded in a table. The audited value
of all of the transactions audited is analyzed and they are
tabulated.
The first stage is to calculate the mean and standard
deviation of the audited sample, which is evaluated by
adopting the formula.
The total monetary value of the objections in the sample,
mean and standard deviation are to be tabulated.
Step 2 –Evaluation of the Precision Limit
The next step is to evaluate the Standard Error of the
entire population of the accounting balance. This could
be evaluated by the following formula
SE =SD/√ (n), where
Precision defines the maximum degree of misstatement,
which will be acceptable. It can be expressed as
monetary value or percentage. It is an estimate which
describes the range of values less and more than the point
estimate within which the true value is expected to fall.
The lower and upper bounds of this range are referred to
as precision limits.
Reliability is the probability that the precision interval
contains the true value. It express the proportion of cases
in which the precision intervals would contain the true
value if the same estimating procedures were employed a
large number of times. Precision is the degree of uncertainty
in the cost auditor’s estimate of error.
Cost auditor has to prescribe himself the reliability factors,
which are normally about 95 or 99 percentages. The
respective value for the reliability factor is 1.96 or 2.58
respectively.
Mathematically Precision is
A= Ur *SE* N √ (1-n/N) (4.3)
Step 3 –Estimation of misstatements
After evaluating the precision by the above formula the
next step is to estimate the book balance, which could
be estimated by adopting the various types of estimators.
The mean estimator Ẋ m
= N*x, could be adopted.
The mean estimator for each interval could also be
adopted and the overall book balance could be derived.
In this step, though there are many methods such as
Mean-per-unit estimator, Ratio estimator, Regression
Estimator, PPS estimator, Felix and Grimlund method,
Cox and Snell method, Multinomial-Dirichlet method,
Distribution-free method available the mean estimator
could also be adopted for its simplicity. However, there is
major scope for improving the results derived below by
adopting other methods stated above.
The entire accounting balance will be analyzed and the
frequency of the each interval is found and recorded in a
table containing mid of interval, frequency and monetary
value. By multiplying the amount in each interval with
the frequency and summing all it is possible to get the
estimated value of the accounting balance.
Step 4 – Deriving conclusions
From the estimated value of the accounting balance, decision
interval could be evaluated i.e. (BV+A, BV-A) and
finally cost auditor can conclude that Ur percent certain
that the true account balance will be EV and falls within
BV ±A. The chart on the next page explains the process
involved in the model.
Phase III Efficiency of the Audit Model
The audit model said to be efficient, if the cost auditor is
able to derive his conclusions more accurately and more
scientifically. It is always possible to derive the more precise
conclusions if sample size is more.
The precision (A) could be calculated by using the following
formula
A = Ur *SE* N √ (1-n/N)
The width of the precision interval is
(BV-A, BV+A) (4.4)
Width of the precision interval will be
(BV+A – (BV-A)) = 2A
Therefore, if the precision value A is smaller it is possible
to get very close interval so as to get more accuracy.
The precision level could be narrowed down by increasing
sample size.
In the above audit model, the cost auditor takes n1
samples initially and the precision in that case will be A1.
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MAY 2015 the MANAGEMENT ACCOUNTANT 59