SPREADSHEET SIMULATION IN ACCOUNTING WITHOUT ADD-INS
V. Reddy Dondeti, Ph.D.
Professor
Norfolk State University
700 Park Avenue
Norfolk, VA 23504
E-mail: rdondeti@nsu.edu
Johnnie A. Mapp, Ph.D.
Professor
Norfolk State University
700 Park Avenue
Norfolk, VA 23504
E-mail: jmapp@nsu.edu
Jim Chen*, Ph.D.
Professor
Norfolk State University
700 Park Avenue
Norfolk, VA 23504
E-mail: jchen@nsu.edu
*Corresponding Author
SPREADSHEET SIMULATION IN ACCOUNTING WITHOUT ADD-INS
ABSTRACT
Simulation is widely used in both accounting practice and auditing practice for a variety
of types of problems. It is also utilized extensively in accounting education. Addressing the
functional competencies in the AICPA Core Competency Framework for Entry into the
Accounting Profession, AICPA states that individuals entering the accounting profession must be
able to build appropriate models and simulations using electronic spreadsheets and other
software. Developing and experimenting a simulation model on an electronic spreadsheet not
only eliminates the need for learning a programming language and simplifies the model building
process but also eases the experiments for different values of the parameters. This paper is
organized as follows. At first, it provides a discussion of random number generators in the
electronic spreadsheet environment. Next, it demonstrates the use of Microsoft Excel to develop
two working simulation models without third-party add-ins.
INTRODUCTION
Simulation is widely used in accounting practice to analyze risk. It is employed in
managerial accounting practice for (1) financial forecasting and budgeting, (2) replacement and
maintenance of machinery/equipment, (3) analyzing capital investment, (4) make or buy
decisions, (5) planning and controlling the budgetary process, (6) planning and implementing
revisions in accounting systems, (7) inventory analysis and control, (8) production planning and
control, and (9) strategic enterprise management (O’Leary, 1983; Kramer et al, 2008). It is also
heavily used in auditing practice. For example, parallel simulation is used frequently for controls
testing and substantive testing (Turney and Watne, 2003). Simulation is widely utilized in
accounting education as well to introduce uncertainty modeling, risk analysis, financial fraud
detection, unique accounting needs of smaller businesses, and strategic enterprise management to
students, and to develop students’ critical thinking skills (Blankley et al, 2004; Jabbour and Liu,
2005; Rich and Cascini, 2006; Cascini and Rich, 2007; Ragan et al, 2008; Schiff and Smith,
2008; Togo, 2007 & 2008).
Addressing the functional competencies in the AICPA Core Competency Framework for
Entry into the Accounting Profession, AICPA states that individuals entering the accounting
profession must be able to build appropriate models and simulations using electronic
spreadsheets and other software (AICPA, 2009). Though user-friendly simulation software
packages (e.g. Arena, ProcessModel and ProModel) are available, developing a simulation
model on an electronic spreadsheet has several advantages: (1) the elimination of the need for
learning a programming language, (2) the wide spread availability of and familiarity with
spreadsheet software, (3) the availability of many built-in statistical functions for generating
random numbers and data summarization, (4) the capability of displaying information in detail
and in easy-to-read format, not just the final results, (5) the ease of experiments for different
values of the parameters, (6) the capability of developing simulation models without add-ins
such as Crystal Ball and @RISK, and (7) a better understanding of the basic concepts behind the
simulation models.
This paper is organized as follows. At first, it provides a discussion of random number
generators in the electronic spreadsheet environment. Next, it demonstrates the use of Microsoft
Excel to develop two working simulation models without third-party add-ins.
RANDOM NUMBER GENERATORS
One of the requirements of almost any simulation model is some facility for generating
random numbers. Microsoft Excel provides two uniform random number generators in the form
of functions: RAND() and RANDBETWEEN(a,b). However, other theoretical distributions –
such as normal, exponential, gamma, and Poisson distributions – are encountered more
frequently than is the uniform distribution. In many cases, an empirical distribution is used. The
inverse transformation method is a general method for transforming a standard uniform deviate
into any other distribution, especially, when the distribution is an empirical one. In this section,
we briefly discuss procedures for generating random numbers from empirical and frequently
used theoretical distributions based on the inverse transformation method. Our emphasis is on
procedures that can be coded in a single statement. The procedures for generating random
numbers are well discussed in many simulation books. We refer the interested readers to
Random Number Generation and Monte Carlo Methods by James Gentle (Gentle, 2004).
Empirical Distribution
Using the inverse transformation method for a general discrete distribution is essentially a
table lookup. To generate random numbers from an empirical distribution, we can use either the
LOOKUP, VLOOKUP, or HLOOKUP functions provided by Excel. The vector form of
LOOKUP function is discussed here. The syntax of the vector form is
=LOOKUP(lookup_value, lookup_vector, result_vector)
The values in the lookup vector must be in ascending order. LOOKUP compares the
lookup_value to each cell in the lookup_vector until it finds a cell larger than the lookup_value.
It then moves up one cell and returns the content of the corresponding cell in the result_vector as
the answer. For example, assume the relative frequency of sales in unit per month for laser
printers is as shown in Table 1.
Table 1
Unit Sales of Laser Printers
Unit Sales Per Month
Relative Frequency
350
0.1
450
0.1
550
0.5
650
0.3
To generate monthly unit sales, say, for six months in cells E2 through E7 from the above
empirical distribution, at first, convert Table 1 into a cumulative-relative-frequency table as
shown in Columns A and B of Table 2. Then, type =LOOKUP(RAND(),$B$2:$B$5,
$A$2:$A$5) in cell E2. Finally, position the mouse pointer over the fill handle and drag it to cell
E7 to extend the LOOKUP function from cell E2 to the range E3:E7. Suppose the numbers
generated by RAND() are 0.22, 0.04, 0.39, 0.78, 0.23, and 0.16, the unit sales generated will be
550, 350, 550, 650, 550, and 450, respectively.
Table 2
Illustration of Empirical Random Number Generation
Triangular Distribution
The cumulative distribution function (CDF) of a triangular distribution with lower limit a,
mode c and upper limit b is
The inverse of F is then
Thus, a triangular-distributed random number can be generated by the Excel formula
=IF(r<=(c-a)/(b-a), a+SQRT(r*(b-a)*(c-a)),b-SQRT((1-r)*(b-a)*(b-c))
where r can be generated by the RAND() function. Storing the value from the RAND() function
in the variable r is important because the RAND() function returns a new value each time it is
called.
The Triangular Distribution may be used when the knowledge about a population is
limited but the minimum, maximum and mode are known.
Exponential Distribution
The CDF of an exponentially distributed random variable is
F(x) = 1 – e-βx for x > 0
where 1/β equals the mean of the exponential random variable. The inverse of F is then
F-1(r) = -ln(1-r)/β
Therefore, the Excel formula for generating an exponentially distributed random number is
simply
= -LN(1-RAND())/beta
Because RAND() is uniformly distributed, 1-RAND() is also uniformly distributed, and the
above Excel formula can be further simplified as
= -LN(RAND())/beta
The distribution of time that elapses before the occurrence of some event often follows an
exponential distribution.
Normal Distribution
The closed-form functional representation of the inverse of the CDF for the normal
distribution does not exist. Fortunately, Excel has a built-in function
NORMINV(probability,mean,std_dev) which returns the inverse of the normal cumulative
distribution for the specified mean and standard deviation. So, to generate a normal random
number in Excel, we can use the simple formula
= NORMINV(RAND(), mean, std_dev)
Gamma Distribution
There are two ways of writing (parameterizing) the gamma distribution that are common
in the literature. EXCEL uses
Excel provides a built-in function GAMMAINV(probability,alpha,beta) which returns the
inverse of the gamma cumulative distribution. Thus, we can use the following formula to
generate a gamma distributed random number in Excel.
=GAMMAINV(RAND(),alpha,beta)
Because an exponential distribution with parameter beta is the same as a gamma
distribution with parameters alpha and beta where alpha = 1, the GAMMAINV function can also
be used to generate an exponentially distributed random variable.
The distribution of time that elapses before the alphath occurrence of some event often
follows a gamma distribution. Gamma distribution also provides the most common best fit to
lead-time demand for a variety of inventory items (Bagchi et al, 1986).
Binomial Distribution
To generate a binomially distributed random number with parameters n and p, we can
generate n standard uniform numbers and the number of these standard random numbers that are
less than or equal to p is the binomially distributed random number generated. This procedure is
useful when the value of n is not large. So, for small values of n, we can use the following
formula to generate a binomially distributed random number in Excel.
=IF(RAND()<=p,1,0)+IF(RAND()<=p,1,0)+IF(RAND()<=p,1,0)+. . . + IF(RAND()<=p,1,0)
where IF(RAND()<=p,1,0) appears n times. For large values of n, the normal approximation to
binomial may be used.
Poisson Distribution
The Poisson random number generator cannot be coded in a single expression. However,
we may use the POISSON function to construct a cumulative distribution table. Then the
LOOKUP function can be used to access the table to generate the Poisson random numbers in
our spreadsheet simulation model.
The syntax of the POISSON function is
= POISSON(x,mean,cumulative)
where x = the number of events, mean = the expected value, and cumulative = a logical value
that determines the probability returned. If cumulative is TRUE, POISSON returns the
cumulative probability that 0 ≤ X ≤ x; if FALSE, it returns the probability that X = x.
For example, to develop a cumulative distribution table for a Poisson random variable
with mean = 3 in columns A and B, we (1) enter the number of events in column A as shown in
Table 3, (2) enter 0 and =POISSON(A2,3,TRUE) to cells B2 and B3, respectively, and (3)
extend the POISSON function in cell B3 to the range B4:B14. The POISSON functions in
column B are in a cell higher than their corresponding number of events because of the way the
LOOKUP function works. After the Poisson distribution table is constructed, we can use
=LOOKUP(RAND(), B2:B14,A2:A14) to generate the random numbers.
Table 3
Illustration of Poisson Cumulative Distribution Table Generation
It is obvious that the table lookup technique may also be used to generate binomial random
numbers.
The Poisson distribution often serves as an appropriate probability distribution for random
variables representing the number of occurrences of some phenomenon during a fixed period of
time.
EXAMPLES OF SPREADSHEET SIMULATION
A Capital Budgeting Example
A simple capital budgeting problem is listed in Table 4. The net present value (NPV)
spreadsheet model for the capital budgeting problem is presented in Table 5. After the formulas
are entered into the cells C15, C16 and C17, the range C13:C17 can be copied to the columns on
the right to generate additional simulations. For example, to generate additional 50 simulations,
we can copy C13:C17 to D13:BA17. Statistics such as total, average, maximum, and minimum
can be obtained easily with SUM, AVERAGE, MAX, and MIN functions, respectively.
Additional runs for the same values of parameters can be carried out easily by simply pressing
the CALC NOW (F9) key. Experiments for different values of the parameters can also be
executed easily by entering their values into their respective cells.
Table 4
A Capital Budgeting Problem
Table 5
NPV Simulation Model
A Cost-Volume-Profit Analysis Example of Spreadsheet Simulation
A simple Cost-Volume-Profit Analysis Problem is given in Table 6 and its corresponding
simulation model is presented in Table 7. This example introduces conditional probability.
Conditional probability can be coded using either the IF function or a table lookup technique.
We used the IF function here. For ease of presentation, the formula in cell B11 is shown in two
lines. Again, the formulae in the range B8:B18 can be extended to generate additional
simulations and statistical functions can be used to obtain summary statistics.
Table 6
A Cost-Volume-Profit Analysis Problem
Table 7
Cost-Volume-Profit Analysis Simulation Model
CONCLUSION
Simulation is widely used in accounting practice to analyze risk for a variety of types of
problems. Developing and experimenting a simulation model on an electronic spreadsheet not
only eliminates the need for learning a programming language and simplifies the model building
process but also eases the experiments for different values of the parameters. This paper
discusses the procedures for generating random numbers in the electronic spreadsheet
environment and demonstrates the use of Microsoft Excel to develop two working simulation
models without third-party add-ins. It clearly shows that spreadsheet simulation is useful,
inexpensive, and easy to learn.
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