If a given budget is available, the discounted benefits that can be achieved with that budget can be compared for alternative projects. On the other hand, if a given benefit is desired, the discounted costs required to achieve that benefit can be compared for alternative projects. This approach can be used even if the benefits cannot be monetized; an example would be cost per new transit rider.
### Calculating the Cost-Effectiveness of Achieving a Given Benefit
n+1 = the number of years over which costs are analyzed B = the given benefit (the benefit need not be expressed in monetary terms) C_{i} = the costs of the project in year i, i=0 to n d = the discount rate
First, discount the costs in future years. The discounted costs of the project in year i are equal to C_{i}/(1+d)^{i} Then, sum the discounted costs over all years (0 through n)
Σ (C_{i}/(1+d)^{i}), summed over i = 0 to n, is the cost to achieve benefit B. Compare to the cost of alternative projects.
### Calculating the Cost-Effectiveness of Different Uses of a Given Amount of Funding
n = 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 (need not be expressed in monetary terms) C = the given amount of funding d = the discount rate
First, discount the monetary benefits in future years. The discounted monetary benefits of the project in year i = B_{i}/(1+d)^{i} Then, sum the discounted benefits costs over all years (0 though n)
Σ (B_{i}/(1+d)^{i}), summed over i = 0 to n, is the benefit that can be achieved with funding C. Compare to alternative projects. |