# Useful time series models – Growth of sales over time up to a maximum as a function of marketing effort

An example of a **Monte Carlo simulation risk analysis model** for **forecasting**

**Technical difficulty**: 1

# Model description

Sometimes we might find it easier to estimate what our annual sales will be when stabilized, but be unsure of how quickly we will be able to achieve that stability. In this sort of situation it can be easier to model a theoretical maximum sales and match it to some ramping function. A typical form of such a ramping function r(t) is:

which will produce a curve that starts at 0 for t = 0 and asymptotically reaches 1 at an infinite value of t, but reaches 0.5 at t_{1/2}. Consider the following problem: you expect a final sales rate of PERT(1800,2300,3600) and expect to achieve half that in the next PERT(3.5,4,5) years. Produce a sales forecast for the next 10 years.

The example model below provides a solution:

# Download model

Click on the button below to download the Excel model. ModelRisk needs to be installed in order for the model to work.