Cost Effectiveness

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)
Ci = 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 Ci/(1+d)i
Then, sum the discounted costs over all years (0 through n)

Σ (Ci/(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
Bi = 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 = Bi/(1+d)i
Then, sum the discounted benefits costs over all years (0 though n)

Σ (Bi/(1+d)i), summed over i = 0 to n, is the benefit that can be achieved with funding C. Compare to alternative projects.