How To Calculate Benefit-Cost Ratio (BCR): With Examples

By Indeed Editorial Team

Updated February 4, 2022 | Published March 15, 2021

Updated February 4, 2022

Published March 15, 2021

A benefit-cost ratio formula is a tool professionals use to measure the total cost of a potential project against its expected profit. By accounting for all related expenses, the formula can help determine whether a project will be profitable. In this article, we define the benefit-cost ratio formula, explain why it's helpful and how to use it, and include an example to guide you in your own calculations.

What is the benefit-cost ratio formula?

The benefit-cost ratio formula, or BCR, is a financial metric that professionals use to assess the costs and benefits of a project to determine its viability. Companies analyze a proposed project with the BCR to see the relationship between the costs to complete the project and the expected benefits over time.

You can express BCR values either as monetary or qualitative. When a project has a BCR value higher than one, a firm and its investors can expect the project to deliver a positive net present value and an internal rate of return above the discount rate. This means that the cash flow from the project is more than the cost of the project, so the project is a good financial consideration.

When a project has a BCR value lower than one, the cash flow benefits are less than the cost, meaning the project costs more than it will return financially.

You can write the BCR formula as the present value of all the benefits you expect from a project divided by the present value of all the costs you expect to incur. When writing the benefit-cost ratio formula mathematically, it looks like this:

BCR = PV of expected benefits / PV of expected costs

Where:

PV = Present value

Related: NPV and IRR: Definition and Examples

When to use the benefit-cost ratio formula

The most common use for the BCR is when analyzing the overall fiscal value of a new project in capital budgeting. Since capital budgeting often includes projects where you assumptions and where quantitative data may be uncertain, there is often a large variety of potential BCR outcomes. The BCR can provide a rough idea for the viability of a project, its internal rate of return, whether it exceeds the discount rate and the weighted-average cost of capital.

Related: Capital Budgeting: Definition, Importance and Different Methods

Benefits of using the benefit-cost ratio formula

While it's advisable to use multiple indicators and measures when assessing project viability, the BCR is special because of its ability to show absolute amounts of cost and benefits. The BCR formula helps compare project alternatives or difference investments. It can help investors to determine the risk involved in a project by forecasting whether there is a small profit margin with a higher risk or a larger profit margin with a lower risk. Since you can calculate time periods as part of the BCR, you can also use the formula to identify cash flow in relation to time.

Related: The Importance of Project Management

How to calculate the benefit-cost ratio

You can calculate the BCR formula using the following steps:

1. Find the present value of expected benefits

You can find the present value (PV) of expected benefits in a period by determining all the cash inflows and monetary benefits you expect from the project, such as incremental revenue, sales, cost savings, increased value of assets or received interest payments.

For example:

PV of expected benefits = $1,000

2. Find the present value of expected costs

Locate the present value (PV) of expected costs in a period by determining all the cash outflows you expect from the project, such as initial investments, administrative costs, disposal costs, production expenses and any other costs to for completing the project.

For example:

PV of expected costs = $500

3. Find the discounting rate

Based on the opportunity cost or the available market information, determine the discounting rate or interest rate. This can represent the target return rate, the capital cost rate or the risk adjusted market interest rate. When there are multiple periods, each period will use the discount rate to the power of the period.

For example:

Discounting rate = 2% or 0.02

Number of periods = 3

4. Input the numbers into the formula

Input the values list above into the BCR formula. Remember that when there are multiple periods, each period will use the discount rate to the power of the period.

BCR = PV of expected benefits / PV of expected costs to the power of each period

When using the example numbers above, the formula looks like this:

BCR = ($1,000 / (1 + 0.02)1) + ($1,000 / (1 + 0.02)2) + ($1,00 / (1 + 0.02)3) / $500

5. Compute the formula

Solve for the PV of expected benefits using basic mathematical rules.

BCR = ($1,000 / (1 + 0.02)1) + ($1,000 / (1 + 0.02)2) + ($1,00 / (1 + 0.02)3) / $500

BCR = ($980.40) + ($961.20) + ($942.30) / $500

BCR = $2,883.90 / $500

BCR = $5.77

6. Evaluate the BCR

Since the BCR value is above one in this example, the cash flow from the project is more than the cost of the project, so the project is a good financial consideration. For every $1 the project costs, there should be $5.77 in benefits.

Relate**d: [What Is Cost of Capital? Examples and How To Calculate**](https://www.indeed.com/career-advice/career-development/what-is-cost-of-capital)

Example of a benefit-cost ratio formula

Here is an example of an organization using the BCR formula:

Villa Homes wants to assess the profitability of a new project in which it builds a community center inside a growing neighborhood. Assume that the company leases the equipment it needs for $100,000, that the inflation rate is 4% and that the company expects to see a $200,000 annual profit increase over the next three years. Villa Homes can use the BCR formula to calculate the overall value of this new project.

Villa Homes first inputs the above values into the BCR formula for all three years like this:

($200,000 / (1 + 0.04)1) + ($200,000 / (1 + 0.04)2) + ($200,00 / (1 + 0.04)3) / $100,000

Next, it solves for the PV of expected benefits:

($200,000 / (1 + 0.04)1) + ($200,000 / (1 + 0.04)2) + ($200,00 / (1 + 0.04)3) = $555,118

Finally, Villa Homes divides by the PV of expected costs:

$555,018 / $100,000 = $5.55

Villa Homes considers this project a good financial decision because the BCR is above one. This BCR tells Villa Homes that for every $1 it spends to build the new community center, it can expect to see $5.55 in benefits, meaning the cash flow from the project is more than the cost of the project.

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