Often, Monte Carlo simulation can come in handy to calculate risk or evaluate investments in projects. This is a simple demonstration.
The following provides the breakdown of profit made by a business unit. All metrics are measured in daily basis.
Profit = Income - Expenses Income = Sales (S) * Profit Margin per Sale (M) M assumes an uniform dist. from $350 to $400 S = Number of Leads (L) * Conversion Rate (R) L assumes an uniform dist. with from 3000 to 4000 R assumes a normal dist. with mean of 4% and sd of 0.5% Expenses = Fixed Overhead (H) + Total Cost of the Leads (C) C = Cost Per Lead (Cpl) * Number of Leads (L) Cpl assumes an uniform dist. from $8 to $10 H assumes a constant of $20000
Profit = Leads * Conversion Rate * Profit Margin per Sale - (Cost per Lead * Leads + Fixed Overhead)
Profit Forecast Model
An oversimplified daily profit forecast model,
If we set a profitability goal of $100,000 a month, what is the probability that we achieve that? How about the probability that we lose money?
##  "Probability of hitting goal is 4.70%"
##  "Probability of incurring losses is 17.5%"
We can also plot the cumulative probability for clearer visualization.
What if we further assume that cost per lead and conversion rate are correlated?
##  "Probability of hitting goal is 23.1%"
##  "Probability of incurring losses is 37.8%"
What if we are offered an option to increase our leads at the cost of fixed overheads increase?
##  "Probability of hitting goal is 16.8%"
##  "Probability of incurring losses is 54.0%"
What is the maximum cost per lead we can accept if we wish to cover our probability of losses at X%?
##  "Maximum cost per lead allowed to reduce risk down to 0.05 is $9.4"