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# How to calculate cost benefit ratio

### 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."

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

Ck = the total discounted costs 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.

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:  (Bf -Bd )/(Cf -Cd )

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 Ck 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.

Source: bca.transportationeconomics.org
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