# Benefit-Cost Ratio (BCR): Formula, Calculation, and Example Explained

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## What Is the Benefit-Cost Ratio (BRC)?

The Benefit-Cost Ratio (BCR) is a crucial metric in cost-benefit analysis, providing insights into project viability by comparing expected benefits to total costs. A BCR over 1.0 suggests profitability, making it a key factor in investment decisions. This article explains how to calculate the BCR, its significance, and how it aids in making informed financial choices.  

### Key Takeaways

*   The Benefit-Cost Ratio compares a project's expected cash benefits to its total cash costs to assess project viability.
*   A BCR greater than 1.0 implies that a project is likely profitable and beneficial, while a BCR below 1.0 suggests more costs than benefits.
*   The BCR is calculated by dividing the net present value (NPV) of expected cash benefits by the NPV of project costs.
*   BCRs should be used alongside other financial metrics, as they simplify complex project evaluations and do not account for all variables.
*   A practical example illustrates how a BCR of 5.77, as calculated for Company ABC, indicates significant expected benefits relative to costs.

## How Do Benefit-Cost Ratios (BCRs) Work?

BCRs are often used in [capital budgeting](https://www.investopedia.com/terms/c/capitalbudgeting.asp) to determine if a new project is worth the cost. But analyzing large projects can be difficult due to many assumptions and uncertainties that are hard to quantify. 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 leads to a wide range of potential BCR outcomes.

BCRs offer a rough idea of project viability but don't detail economic value creation. BCRs also help assess how much the internal rate of return (IRR) exceeds the discount rate or WACC.

The BCR is calculated by dividing the proposed total cash benefit of a project by the proposed total cash cost of the project. Before dividing, calculate the net present value (NPV) of cash flows over the project's life, including [terminal values](https://www.investopedia.com/terms/t/terminalvalue.asp) and any salvage or remediation costs.

## How to Interpret BCR Results for Project Success

A project with a BCR over 1.0 is expected to deliver positive NPV and an IRR above the discount rate. This means the project's cash flow NPV is greater than the costs, making it a viable choice.  

A BCR of 1.0 means NPV of profits equals costs. If BCR is under 1.0, costs outweigh benefits, and the project may not be viable.

## Example: Applying the Benefit-Cost Ratio (BCR)

As an example, assume Company ABC wishes to assess the profitability of a project that involves renovating an apartment building over the next year. The company decides to lease the equipment needed for the project for $50,000 rather than purchase it. The inflation rate is 2%, and the renovations are expected to increase the company’s annual [profit](https://www.investopedia.com/terms/p/profit.asp) 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 upfront. 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.

 In this example, a BCR of 5.77 shows the project's estimated benefits far outweigh its costs.

## Understanding the Limitations of Benefit-Cost Ratios (BCRs)

The main limitation of BCR is its simplification of a project's outcomes to a single number, ignoring many factors and unforeseen events. Relying on BCR as a rule where over 1.0 signals success can be misleading and offer false security.

Use BCR alongside other analyses to make informed decisions.

## What Is the Benefit-Cost Ratio (BRC) Used for?

The BRC is used in cost-benefit analysis to describe the connection between the costs and benefits of a potential project.

## How Do You Calculate the Benefit-Cost Ratio?

The benefit-cost ratio is determined by dividing the proposed total cash benefit of a project by the proposed total cash cost of the project.

## What Does a Benefit-Cost Ratio Over 1.0 Suggest?

A reading over 1.0 suggests that on a broad level, a project should be financially successful; a reading of 1.0 suggests that the benefits equal the costs; and a reading below 1.0 suggests that the costs trump the benefits.

## The Bottom Line

In a cost-benefit analysis, the Benefit-Cost Ratio effectively summarizes the relationship between a project's expected benefits and costs. A BCR greater than 1.0 indicates that a project should have a positive net present value, making it financially viable. However, reliance solely on the BCR can be misleading due to potential assumptions and uncertainties. It is important to use BCR alongside other metrics like the internal rate of return and weighted average cost of capital for more informed decision-making.