Software as a service (Saas) is a common subscription based business model which relies on charging periodic subscriptions to a customer base.

Time value of money calculations can be used to estimate the number of customers at the end of any particular accounting period for the saas business model financial projection.

To carry out the calculations we use the future value of an annuity formula.

FV = Pmt x ( (1 + i)^{n}- 1 ) / i

**Variables used in the formula**

FV = Future Value

Pmt = Periodic payment

i = Discount rate

n = Number of periods

Assuming the number of new customers added each period in the Saas model is constant, and the rate at which customers leave (the churn rate), is constant, then the future value of an annuity formula can be used to calculate the number of customers at the end of any period.

If we treat the future value (FV) as the number of customers at the end of period n, the periodic payment (Pmt) as the constant addition to customers each period, and the discount rate (i) as the customer churn rate per period, then the variables in the formula above can be restated as follows:

FV = Pmt x ( (1 + i)^{n}- 1 ) / i

**Variables used in the formula**

FV = Number of customers at the end of period n

Pmt = Periodic addition to customers

i = Churn rate

n = Number of periods

## SaaS Model Customer Numbers Example

Suppose for example, a Saas business adds 200 customers per period (Pmt), and has a churn rate of 5% per period (i), then the number of customers it will have at the end of period 24 is given as follows:

n = 24 periods i = -5% (rate is negative as customers are leaving) Pmt = 200 customers added per period FV = Customers = Pmt x ( (1 + i)^{n}- 1 ) / i FV = Customers = 200 x ( (1 - 5%)^{24}- 1 ) / -5% FV = Customers = 2,832

The time value of money calculations show that, assuming a constant addition of 200 customers per period and a churn rate of 5%, at the end of period 24 the subscription based business will have 2,832 customers,

## Peak Value for the Number of Customers in a Saas Model

As the number of periods (n) gets higher, and since the discount rate (churn) is negative, the term in (1 + i)^{n} in the formula above gets very small and can be treated as zero. The formula then simplifies as follows to the value of a perpetuity formula:

FV = Customers = Pmt x ( (1 + i)^{n}- 1 ) / i FV = Customers = Pmt x ( 0 - 1 ) / i FV = Customers = - Pmt / i FV = Customers = -200 / -5% = 4,000

As this is independent of n it must represent the peak value of the number of customers in the Saas model. For this particular business, the number of customers will eventually grow to 4,000 and then remain constant as the new additions (200) match the customers leaving (4,000 x 5% = 200).

The time value of money calculations can be used to provide an estimate of the number of customers in a Saas business model financial projection providing the number of customer additions per period, and the churn rate per period remain constant.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.