## Exercise: Sales Forecast using MCM

Apr 9, 2019## 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)
C = Cost Per Lead (Cpl) * Number of Leads (L)
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?

`## [1] "Probability of hitting goal is 4.70%"`

`## [1] "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?

`## [1] "Probability of hitting goal is 23.1%"`

`## [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?

`## [1] "Probability of hitting goal is 16.8%"`

`## [1] "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%?

`## [1] "Maximum cost per lead allowed to reduce risk down to 0.05 is $9.4"`