1) A business is introducing a new product and wants to forecast net profit, which depends on uncertain variables like sales volume, price, and costs. 2) Monte Carlo simulation is used to model uncertainty, introducing random market conditions that impact volume and price. 3) The simulation calculates net profit 1,000 times to generate a probability distribution, showing most likely outcomes and risks of loss.

1. Financial Forecast
Based on market conditions – A Monte Carlo Simulation

2. Case : Financial Forecast of good’s sale based on market conditions
Application used : Frontline Solver(trial version) Number of simulations run : 1000
Product name : P1 Average Sales and Cost Scenarios of product P1
Interpretation : When the market condition is hot more units are sold at a lesser price.
A view of the Frontline Solver
Market condition
1 -Hot
2 - Ok
3 - Slow
Parameter Average
Volume 75000
Selling Price(in dollars) 9.67
Unit Cost Price (in dollars) 6.50
Price (in dollars)
8
10
11
Points to note
The average model does not give a correct forecast
To convert this model into a risk analysis model uncertainty
needs to be introduced for future predictions which
oscillates between hot and slow.
An uncertain variable needs to be introduced which can
generate the values randomly associated with market
conditions
Generation of such numbers happen using Integer
uniform probability distribution of Frontline Solver

3. Function Descriptions
PsIntUniform :PsiIntUniform (a, b,...)
PsiIntUniform (a,b) is a discrete distribution with equal probability at each integer value between the
lower and upper bounds (a and b). This distribution gives valid result only when the probability of
occurrence for each of these are equally likely. The values can be as follows : (a,a+1,a+2……b-2,b-
1,b).The mean and the median is a+b/2 and the probability mass function is 1/(b-a) + 1 and a <=
b <= c
PsiTriangular :PsiTriangular (a,c,b,...)
PsiTriangular (a,c,b) is a distribution with lower bound a, upper bound b, and most likely value c. This
model works when practically no data is available. If the parameter c = b, then the distribution is also
known as a Right Triangular distribution else if c = a, then the distribution is also known as a Left
Triangular distribution. If X1 and X2 are independent uniform (0,1) random variables, then (X1+X2)/2
has a Triangular (0,0.5,1) distribution.
PsiMean :PsiMean (cell,simulation)
PsiMean returns the mean value for the specified uncertain function cell. The mean or average value is
the 1st moment of the distribution of trials and is computed as:

4. Problem Statement
A Business Planning Example using Monte Carlo Simulation
A firm is planning to introduce a new product and net profit for that product is computed based on the following :
• Sales volume in units
• Selling Price per unit
• Unit cost
• Fixed costs
Net profit will be calculated as Net Profit = Sales Volume* (Selling Price – Cost Price ) - Fixed costs.
Fixed costs are as follows : overheads , advertising etc. amounts to 1,20,000 $.
Apart from fixed cost all other costs have variability or uncertainty and all variables under consideration have potential to depict
randomness leading to uncertainty.
Assumptions
• Sales volume (in units) can depend on local market
• The selling price per unit will depend on competitor actions.
• Unit costs will also vary depending on vendor prices and production experience.
• With equal probability of market being Slow, Ok or Hot as per research
50,000 units at an average selling price of $11.00 per unit are slow under slow scenario
75,000 units, with a lower selling price of $10.00 per unit.
100,000 units sold at the average selling price to $8.00 per unit.
Using the concept of averages, the average sales volume = (50000+75000+100000/3) = 75000
Average Selling price per unit = (8+10+11/3) = 9.67
Cost price per unit = (5.5 + 6.5 + 7.5/3) = 6.59 (assuming cost price oscillates between 5.5$ and 7.5$.
Net Profit is again an uncertain as calculated above is again an uncertain function under consideration

5. Focus on uncertain market condition – Introduction of Integer Probability Distribution
Financial Forecast of Product P1
The representation of the problem in Excel
Sales and Cost Data Cost Scenarios Uncertain
Sales
scenarios Volume
Price in
dollars
Sales
scenario Average
Unit
cost J4 value K4 value/volume L4 value/price
1 –Hot 100000 8 Volume 75000 1 5.5 3 50000 11
2 – Ok 75000 10 Price 9.67 2 6.5
3 – Slow 50000 11 Unit cost 6.5949284 3 7.5
Fixed Cost 120000 Net Profit -49746.4
Average
Profit(Uncertain) -7545.28
The application of the discrete distribution function to forecast sales based on equal probability of occurrence of market conditions - hot, ok
and slow which affects the sales of product P1

6. Functions – Triangular and Mean
Triangular function takes into consideration the lower, upper and the most likely unit cost.
Mean on the other hand is the moment of distribution of trials

7. Introduction of uncertainty variable –J4(Using Intuniform discrete distribution)
Steps to note
Click on Distribution
Select Discrete Distribution
Select IntUniform
Set lower limit based on the least value taken from
the market condition in this case it is 1
Set upper limit to the maximum limit. In this case it
is 3
Save the parameters and return to value contained
below the J4 cell which depicts the uncertainty
Repeat click on the cell will help re-calculate and
oscillate between values 1 and 3 based on market
conditions
The probability distribution function shows a 5
pc chance of the market condition that is slow and
hot and 90 pc chance that a market condition is Ok.

8. Correlation establishment- Market condition to volume and price of a product that are used as
uncertain variables
Description Computation
Using the values associated with market
condition in J4 the cells in K4 and L4(refer slide
3) represent Sales Volume and Selling Price and
bear correlations to each other.
With cell K4 selected, we enter the formula:
(Sales Volume): =CHOOSE(J4,B4,B5,B6)
With cell L4 selected, we enter the formula: (Sales Price): =CHOOSE(J4,C4,C5,C6)

9. Finding the unit cost using Triangular function that uses continuous distribution
Points to note
The triangular distribution is a continuous distribution that
helps extract any unit cost value in the range : - min,likely
and max
The unit cost as found to be most likely was 6.033 for the
current trial as represented in the above excel and 6.52 is
the unit cost having a probability of occurrence of 90 pc. The
rest of the values fall in the 10 pc range as shown from the
probability distribution function.

10. Finding the unit cost using Triangular function that uses continuous distribution - Cumulative
Distribution Function
Points to note
The cumulative distribution function denotes that the unit cost ranging from 5.5 $ to 7.5 $ can have 5 pc chances of
occurring in the range of 5.6 to 5.8 and 7.2 to 7.5 and 90 pc of the time remains in the range of 5.9 to 7.1 with high
occurrences of 6.52

11. Statistics and Percentiles - Finding the Net Profit – Cumulative Distribution Function - (Unit cost
and its impact on Net Profit)
Point to Note
The marker 2 shows net loss of 71000 dollars probability of which is 5 pc or below whereas the loss of 49000
has a probability and frequency of less than 25 pc and loss of 2000 dollar has a probability nearing 60 pc and
higher is the frequency of occurence. Marker 5 shows that a net profit around 48000 dollar ,the probability of
occurence and frequency hovers around 80 pc whereas marker 1 indicates that receiving a profit of 78000 dollar
has less than 20 pc probability of occurence.

12. Statistics – The Frequency Distribution Function - Graph representation (Unit cost and its impact
on Net Profit)
Points to note
The frequency chart denotes that net profit greater than 0 happens for 38.6 pc of the time where as less than 0 i.e.
probability of occurrence of loss is 61 pc. Minimum and Maximum net profit are as follows : -92528 and 119772
The Value at Risk 95% statistic shows that we have a 5% chance of making $68395 or more, and the Conditional
Value at Risk 95% statistic shows that the average of all the observed Net Profit values below the VaR 95% level is -
$12864.

13. Sensitivity Analysis
Points to note
The unit cost and market condition have a negative correlation with the net profit. Higher Unit Costs leads to lower
Net Profits. The state of the market is not in direct control. Net Profit suffers in a hot market as there is a narrow
margin between Selling Price and the Unit Cost, for which situation can be improved
Risk management: The model used to determine how to reduce the chances of a loss and increase the
chance of a (larger) profit.
The Sensitivity tab displays a Tornado chart that shows the Net Profit that changes with a change in the
uncertain variables

14. Interactive Simulation
Interactive simulation offers the following benefits :
• Check the scenarios instantly by changing the unit
costs
• The impact of the change on Net Profit and answer
the whatiffs
• Click the Frequency tab in the Uncertain Function
to re-display the frequency chart of outcomes for
cell computing Net Profit.
• Change the number in cell that displays unit
cost,sales volume,selling price etc
• Trials cumulating to thousand are performed, and
the chart is updated. checking the Statistics Bar -
we have expected loss of only -$22,632 and
expected gain of $14744.

15. Source :https://www.solver.com/monte-carlo-simulation
Dr. Chandrani Singh
Thank You