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

A benefit cost ratio (BCR) is an indicator used in cost-benefit analysis, to show the relationship between the costs and benefits of a proposed project, in monetary or qualitative terms.

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## BREAKING DOWN 'Benefit Cost Ratio - BCR'

Benefit cost ratios (BCRs) are most often used in capital budgeting, to analyze the overall value for money of undertaking a new project. However, the cost-benefit analyses for large projects can be hard to get right, because there are so many assumptions and uncertainties that are hard to quantify. This is why there are usually a wide range of potential BCR outcomes.

The BCR also does not provide any sense of how much economic value will be created. So, the BCR is usually used to get a rough idea about the viability of a project, and how much the internal rate of return(IRR) exceeds the discount rate, which is the company’s weighted average cost of capital (WACC) — the opportunity cost of that capital.

## Benefit Cost Ratio Calculation

The BCR is calculated by dividing the proposed total cash benefits of a project by the proposed total cash costs of the project. Prior to dividing the numbers, the net present value (NPV) of the respective cash flows over the proposed lifetime of the project — taking into account the terminal values, including salvage/remediation costs — are calculated.

To calculate the net present values, we use the (NPV) formula, in which the values are divided by the sum of 1 and the discount rate raised to the number of periods:

NPV =

Ct = net cash inflow during the period t

Co = total initial investment costs

r = discount rate, and

t = number of time 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 it. 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 of BCR

If a project has a BCR that is greater than 1, the project will deliver a positive NPV and will have an internal rate of return (IRR) above the discount rate used in the DCF calculations. This suggests that the NPV of the project’s cash flows outweighs the NPV of the costs, and the project should be considered. 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.

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