# Payback Period

Sometimes, people are interested in knowing how long it would take for the cumulative discounted benefits to become equal to the cumulative discounted costs. This is known as the payback period.

### Calculating the Payback Period

This is easily done with a spreadsheet. Two columns can be added, one for cumulative discounted costs and one for cumulative discounted benefits.

n+1 = the number of years over which benefits and costs are analyzed

B_{i} = the benefits of the project in year i, i=0 to n

C_{i} = the costs of the project in year i

d = the discount rate

First, discount the costs and benefits in future years.

The discounted benefits of the project in year i are equal to B_{i}/(1+d)^{i}

The discounted costs of the project in year i are equal to C_{i}/(1+d)^{i}

Then calculate the cumulative discounted costs and cumulative discounted benefits for each year. The first year in which the cumulative discounted benefits exceed the cumulative discounted costs is the payback period. This type of analysis assumes that in years after the payback period the benefits will exceed the costs.