Summary:
S-curve distributions are frequently utilized in projects with non-linear cash flows
Common s-curve financial model applications include real estate development and infrastructure
S-curve application allows for more precise cash flow modeling
Pro Forma Models prebuilds applicable models with triggers allowing for s-curve and straight-line expense distributions
Definition:
A Sigmoid Function (s-curve) is a mathematical function that distributes cumulative data over time in a non-linear fashion. The function is called an s-curve because the function forms an "s" shape when plotted.
Financial Model Application & Importance:
S-curve distributions are frequently utilized in project management, real estate development, and infrastructure investment projects where work completed (costs, completion, hours, etc.) start slow, grow exponentially over time, and then ramp back down meaning they do not follow a normal distribution. Said another way, in real life projects do not typically follow a linear path and result in non-linear cash outlays.
For example, a real estate project may start slowly as land is being zoned and prepared, ramp up to significant spend in the middle of the project as construction reaches maximum productivity, and then wind down as final punch items are remedied and certificates of occupancy are issued. S-curve's are a useful tool for financial modelers as it allows for more precise cash and financing forecasts rather than assuming straight-line methods of expense recognition.
Example Case Study:
Consider the following example of a $50MM construction project with an 18 month duration:
The early periods (month 1-6) of construction start slow with incremental 1.00%-6.00% completion increments. As the construction project ramps up (months 7-12), incremental 9.00%-18.00% completion increments occur. The construction project winds down (months 13-18) with 1.00%-3.00% completion increments. If you have worked on a real estate development or even a home renovation project, this type of ramp up and wind down process is most likely something you have observed. Plotting this data results in the following s-curve illustrating the non-linear nature of cash outlays in line with the ebbs and flows of the development completion.
Pro Forma Models integrates an s-curve distribution into all development models and includes triggers allowing users to allocate expenses using straight-line and s-curve methodology. Examples of models with s-curve distribution functionality include:
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