## Background

Often, Monte Carlo simulation can come in handy to calculate risk or evaluate investments in projects. This is a simple demonstration.

## Exercise

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)

Cpl assumes an uniform dist. from \$8 to \$10

H assumes a constant of \$20000
``````

In summary,

``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. ## Update Model

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%"``

## Sensitivity Analysis

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%"``

## Finding Optimal

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"``