There are many ways (or criteria) in economics that can be used to assess the “profitability” of a project or decision that involves an up-front investment before profits are generated over time. Payback periods are one of the simplest, both in terms of concept, and of practical implementation.
The core idea is to measure how long it takes (in time) for the initial investment amount to be repaid (with a project that has a shorter payback to be preferred over one with a longer payback, if all other factors were equal or not relevant). One can consider to basic forms:
An example of each of these simple breakeven measures is given below.
The examples use the following profile of revenues and costs (and where we treat profit and cash as identical items for ease of presentation here) with profits or cash flow calculated as the difference between these:
The time-to-breakeven is 3 years (or between 2 and 3 years), as highlighted with green-shading in the following image:
The payback period or time-to-cumulative-breakeven is six years. This requires one to calculate the cumulated profit as a new line item:
Especially in models whose time periods are annual, one may wish to estimate more precisely the exact timing of breakeven, rather than having a whole year figure only. An interpolation in time can be done to estimate more precisely the time point at which breakeven is reached.
The simplest approaches are:
(In general, if such accuracy is required it is better to considering building a more granular model, such as one with a quarterly time axis, but obviously such issues should be identified before the model is built, not as a brand new modelling activity that would need to start almost from the beginning).
To implement these, one calculates the weighting factors that apply in each period (discounting factors), use these to calculate the weighted cash flows for each period, and then cumulate these before finding the time to cumulative breakeven for the weighted cash flows.
For example, with a discount rate of 12% per year, the weighting factor for the first year is 1/1.12 (approximately 0.89), and for the second year it is the square of this (approximately 0.80), and so on. The weighted profit in year 1 is then approximately -67 (i.e. -75 times 0.89) and so on. The cumulated (time-weighted or discounted) payback time is 7 years:
The concepts of net present value (NPV) and internal-rate-of-return (IRR) are discussed in detail in later chapters of this course. Readers who are already familiar with these concepts can for the moment simply note that the cumulative time weighted cash flow used above is simply the same as the net present value of the cash flows (cumulated to the same point).
Similarly if a periodic discount rate of 28% p.a. were used for the weighting, (so that the weighting in the first period is 1/1.28), then the sum of the cash flows over the 10 years is zero. That is, the internal-rate-of-return (IRR) over a 10 year horizon is 28% p.a.
(The concept of discounting and the use of functions such as NPV is discussed in much more detail later in this course. It is introduced here only to highlight the link to the non-weighted approaches to payback periods).