# Net Present Value

The sum of discounted costs are subtracted from the sum of discounted benefits. Projects with positive net present value should be considered; the greater the net present value, the more justifiable the project. However, a large project could have a higher net present value than a smaller project, even if it has a lower benefit-cost ratio. This relationship is illustrated in graphs found in the Graphical Representation section.

### Calculating the Net Present Value

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, sum both the discounted benefits and the discounted costs over all years (0 through n) and subtract the sum of the discounted costs from the sum of the discounted benefits:

Σ (B_{i}/(1+d)^{i}) - Σ (C_{i}/(1+d)^{i}) summed over i = 0 to n.