Benefit-Cost Ratio

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.)

Calculating the Simple Benefit-Cost Ratio

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 though n) and divide the sum of the discounted benefits by the sum of the discounted costs:

Σ(B_i/(1+d)ⁱ)/Σ (C_i/(1+d)ⁱ), summed over i = 0 to n.

Calculating the Incremental Benefit-Cost Ratio

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."

B_k = the total discounted benefits of an alternative k, calculated as above

C_k = the total discounted costs of an alternative k, calculated as above

First, discount all future costs and benefits to obtain C_k and B_k for each alternative and for the base case.

Then start by identifying the base case as the defender, represented by the subscript "f."

Pick the alternative with the least value of total discounted costs as the challenger "c."

Calculate the incremental benefit-cost ratio to compare the challenger and defender: (B_f-B_d)/(C_f-C_d)

If the incremental B/C ratio is greater than 1, the challenger becomes the defender. Otherwise, the defender remains. In either case, the next alternative in order or increasing value of C_k is picked as the new challenger.

Continue to compare challenger to defender following the above logic until all alternatives have been considered. The surviving defender is the economically preferred alternative.

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.