Applies To:

·        Business Case Delivery

·        Investment Valuation

Summary

Objectives

·        Learn how to identify benefit risks

·        Learn how to identify cost risks

·        Learn how to identify project risks using Monte Carlo simulation

·        Learn how to interpret project risks using Monte Carlo simulations

Overview

General Guidance

·        Business Cases should be conservative in nature.  Always strive to overstate costs and understate benefits to achieve conservatism. 

·        Business Cases are high level ROI estimates.  They are not intended to be budget models.  Excessive detail in either costs or benefits tends to obscure and confuse identifying which assumptions are most important.

Summary of Steps

1.      Develop Base Case with Minimum and Maximum Cases

2.      Calculate mean and standard deviation of NPV using the three cases from Step 1.

3.      Generate 1000 random scenarios using the mean and standard deviation from Step 2.

4.      Create the histogram of the NPV outcomes.

5.      Calculate the required probabilities associated with the 1000 NPV scenarios; e.g. probability of a negative NPV.

Step 1: Develop Base Case with Minimum and Maximum Cases

The Base Case represents the expected value for costs and benefits.  The Maximum Case is calculated by increasing the present value of the Base Case benefits by a reasonable percentage and decreasing the present value of the Base Case costs by a separate percentage.  The example below shows this calculation.

Example calculation of Minimum and Maximum Cases:

Step 2: Calculate mean and standard deviation of the present value of Benefits and Costs using the three cases from Step 1.

Steps for calculating Standard Deviation:

1.      Calculate the mean of the data series

2.      Find the difference of each observation from the mean: Difference = X_i– Mean

3.      Square the differences

4.      Sum the squares

5.      Find the average of the sum of squares

6.      Find the square root of average of sum of squares.  This is the Standard Deviation

Step 3: Generate 1000 random NPV scenarios using the mean and standard deviation from Step 2.

The steps for generating one random scenario are:

1.      Calculate the value of Benefits as Benefit Mean + or – (a normally distributed random number) x Benefit Standard Deviations

2.      Calculate the value of Costs as Cost Mean + or – (a normally distributed random number) x Cost Standard Deviations

3.      Calculate NPV = Benefits – Costs

Example random scenario table:

There are two challenges with calculating 1000 random scenario:

1.      It is a very tedious process to accomplish by hand

2.      It is highly unlikely that you can think up normally distributed random numbers needed to multiply the Standard Deviations by

Fortunately, there are two Excel functions that can be used in this process.  They are:

RAND(): This function returns a random number greater than or equal to 0 and less than 1, evenly distributed.  The number that is returned changes each time the cell containing this function is recalculated.

NORMINV: This function returns the inverse of the normal cumulative distribution (see Additional Resources for normal cumulative distribution)

The functions are combined to create one scenario: =NORMINV(RAND(), Mean, Standard Deviation. 

This combined function is copied into 1000 rows of one column with reference to the mean and standard deviation of benefits, and into 1000 rows of a second column with reference to the mean and standard deviation of costs.  NPV is calculated in a third column for each row.  The table below shows what the first 10 rows of calculations for benefits, costs and NPV look like:

Step 4: Create the Histogram of the NPV outcomes.

A Histogram is a graphical representation of the tabulated frequencies of data over discrete intervals, called bins.   The steps for creating a histogram are:

1.      Determine the number and size of each bin.  The lowest bin value should include the lowest NPV scenario value.  The highest bin value should include the highest NPV scenario value.  Typically 15 to 20 bins are sufficient for a Histogram that is recognizable as a normal distribution.

2.      Count how many NPV values fall into each bin.  This is the frequency of NPVs by bin

3.      Plot the data as a Histogram

Example histogram:

The tabulated frequency of the data shown in the table above is:

Plotting the data in the frequency table reveals the Histogram.  As you can see, the data approximates a normal distribution.  This is due to the use of the NORMINV function in generating the scenarios.

(Note to advanced practitioners: You can choose other distribution functions that you consider more representative of IT investments; e.g. the binomial distribution, or BINOMDIST in Excel).

Step 5: Calculate the required probabilities associated with the 1000 NPV scenarios; e.g. probability of a negative NPV.

Use the Excel function NORMDIST to find the value of the normal cumulative distribution for the mean and standard deviation of NPV.

Example

=NORMDIST(0,MeanNPV,StdDevNPV,TRUE) returns the probability of NPV less than 0.  This probability is 9% for the Histogram shown above.

Next Steps

This How To describes the calculation methods for Monte Carlo simulation.  Fortunately, all of these steps are automatically completed if you use Business_Case_TEMPLATE_VRF4 located on ESP on a Pagehere.  Tab 7. NPV Variance Analysis of the template is the Monte Carlo simulation.