The total discounted benefits are divided by the total discounted costs. Projects with a benefit-cost ratio greater than 1 have greater benefits than costs; hence they have positive net benefits. The higher the ratio, the greater the benefits relative to the costs. Note that simple benefit-cost ratio is insensitive to the magnitude of net benefits and therefore may favor projects with small costs and benefits over those with higher net benefits. (This problem can be eliminated by the use of the incremental benefit-cost ratio or the net present value.)
n+1 = the number of years over which benefits and costs are analyzed
First, discount the costs and benefits in future years.
The discounted benefits of the project in year i are equal to Bi/(1+d)i
The discounted costs of the project in year i are equal to Ci/(1+d)i
Then, sum both the discounted benefits and the discounted costs over all years (0 though n) and divide the sum of the discounted benefits by the sum of the discounted costs:
Σ(Bi/(1+d)i)/Σ (Ci/(1+d)i), summed over i = 0 to n.
This method is applicable if there are two or more alternative projects to compare to the base case. It is also known as the "Challenger-Defender Method."
Bk = the total discounted benefits of an alternative k, calculated as above
First, discount all future costs and benefits to obtain Ck and Bk for each alternative and for the base case.
This procedure is mathematically equivalent to Net Present Value, and it always gives the same result, but use of this procedure may provide greater insights into the relationships between costs and benefits of the different projects.
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