The payback period is the time it takes for a project to recover its investment expenditures. For example, a set of solar panels may be essentially free from month to month to operate, but the initial cost is high. It may take years or even decades to recover the initial cost.
Determine the costs of the project, above what you would otherwise be expending if you hadn't done the project at all during the time of construction. Denote this total with the letter C.
For example, if you installed solar panels, you'll need to add up not only the cost of the panels and the labour of installation but also the cost of additional electricity used above normal monthly levels in order to work the construction equipment to install them.
Determine the difference between monthly expenditures after completion of the project and monthly expenditures if you hadn't done the project at all. Denote this monthly difference with the letter D.
Continuing with the above example, suppose the cost of maintaining the solar panels is £0 (though unlikely) and the cost of electricity after installing them is -$10 per month because you're selling energy back to the grid. Suppose that you were paying £78 in electrical before the project. Then D is 120 - (-10) = £84.
Solve the equation C-nD=0 to determine how many months, n, must pass to break even. This is the payback period.
Suppose in the above example that C is £6,500. Then n is C/D = 10000/130 = 76.9 months or 6.4 years.
Introduce the time value of money by making future savings increasingly less valuable. The time value of money accounts for the greater desire of having a dollar now than later. Therefore, a dollar in the future is worth less in the future than it's worth now.
Continuing with the above example, suppose an annual cost of money of 2%, which works out to (1.02)^(1/12) - 1 = 0.00165. This is the monthly depreciation rate of money. The formula that you therefore want to solve is C = D [1 - 1/(1+i)^n]/i, where i is 0.00165 and n is the unknown number of months. (Here, the caret ^ indicates exponentiation.) If you use a financial calculator enter C as present value PV, D as monthly payment PMT, i as the periodic rate and then compute n. The same result can be found by using logarithms. For this example, n is 84.8 months, or 7.1 years, somewhat longer than the initial estimate.