# Benefit Cost Ratio - BCR

## What is a 'Benefit Cost Ratio - BCR'

A benefit cost ratio (BCR) attempts to identify the relationship between the cost and benefits of a proposed project. Benefit cost ratios are most often used in corporate finance to detail the relationship between possible benefits and costs, both quantitative and qualitative, of undertaking new projects or replacing old ones.

## BREAKING DOWN 'Benefit Cost Ratio - BCR'

The ratio is used to measure both the quantitative and the qualitative factors, since sometimes the benefits and the costs cannot be measured exclusively in financial terms. When possible, the qualitative factors should be translated into quantitative terms for the results to be easily understandable and tangible.

## Benefit Cost Ratio Calculation

The BCR is calculated by dividing the total discounted value of the benefits by the total discounted value of the costs. To calculate the discounted values of each, use the net present value (NPV) formula, in which the values are divided by the sum of 1 and the discount rate raised to the number of periods.

For example, assume company ABC wishes to assess the profitability of a project that involves renovating an apartment building that the company owns, over the next year. The company decides to lease the equipment needed for the project for \$50,000, rather than purchasing the equipment. The inflation rate is 2%, and the renovations are expected to increase the company's annual profit by \$100,000 for the next three years.

The NPV of the total cost of the lease does not need to be discounted, because the initial cost of \$50,000 is paid up front. The NPV of the projected benefits is \$288,388, or (\$100,000 / (1 + 0.02)^1) + (\$100,000 / (1 + 0.02)^2) + (\$100,00 / (1 + 0.02)^3). Consequently, the BCR is 5.77, or \$288,388 divided by \$50,000.

## Interpretation

If a project has a BCR that is greater than 1, it indicates that the NPV of the project benefits outweigh the NPV of the costs. Therefore, the project should be considered if the value is significantly greater than 1. If the BCR is equal to 1, the ratio indicates that the NPV of expected profits equal the costs. If a project's BCR is less than 1, the project's costs outweigh the benefits and it should not be considered.

In the previous example, company ABC had a BCR of 5.77, which indicates that the project's benefits significantly outweigh its costs. Moreover, company ABC could expect \$5.77 in benefits for each \$1 of its cost.