# Benefit-Cost Ratio (Bcr): Definition, Formula, And Example

## Key Takeaway:

The benefit-cost ratio (BCR) is a financial metric used to determine the feasibility and profitability of a proposed project or investment.The BCR formula involves dividing the total expected benefits of the project by the total expected costs. A BCR of 1 or higher indicates that the project is expected to be profitable.An example of calculating the BCR involves estimating the expected benefits and costs of a new manufacturing plant. By comparing the BCR to the threshold set by the organization, they can determine whether the project should be approved or not.

Are you interested in calculating the value of your investments? Knowing how to calculate the Benefit-Cost Ratio (BCR) can help you make informed decisions. This article will explain the definition, formula, and example of the BCR.

## Benefit-Cost Ratio (BCR): Definition

A **Benefit-Cost Ratio (BCR)** is a financial metric used to assess whether the benefits of a project outweigh its costs. It is calculated by dividing the total present value of benefits by the total present value of costs. The resulting ratio indicates the amount of benefit gained for every unit of cost incurred. BCR is a widely used tool in project evaluation and is particularly useful when comparing multiple projects with different costs and benefits. By comparing BCR values for different projects, analysts can determine which project provides the most value for money. However, it is important to note that BCR should not be the sole factor when assessing a project's feasibility.

**Pro Tip:** While calculating BCR, consider allocating weights to the benefits and costs based on their significance to the project's goals. This can help prioritize the importance of each item and provide a more accurate assessment of the project's feasibility.

## The Formula for Calculating the Benefit-Cost Ratio

**Benefit-Cost Ratio (BCR)** is the measure of the profitability of an investment, comparing the benefits to be derived from the investment with the costs associated with it. Here, we will discuss the formula for calculating the Benefit-Cost Ratio.

To calculate the Benefit-Cost Ratio, first, we need to calculate the present value of all the benefits and costs. The formula for the Benefit-Cost Ratio (BCR) is:

**BCR = PV (Benefits) / PV (Costs)**

Where PV refers to the present value of the benefits or costs.

To illustrate the formula, let's consider the following example: Suppose you are considering investing in a project that costs $10,000 and is expected to generate a benefit of $15,000 after two years. The discount rate is 5%.

To calculate the present value of benefits and costs, we need to use the discounted cash flow method.

**PV (Costs)** = $10,000

**PV (Benefits)** = $15,000 / (1 + 5%) = $13,375.23

Therefore, the Benefit-Cost Ratio (BCR) is:

**BCR** = $13,375.23 / $10,000 = 1.34

Thus, the **BCR of the project is 1.34 which is greater than 1**, indicating that the project is profitable.

It is important to note that the higher the BCR, the more profitable the investment is. However, the BCR should not be used as the sole decision-making criterion, and other factors such as risk should also be considered.

To improve the BCR, one could consider reducing the cost component of the project or increasing the benefit component. For instance, reducing the cost by negotiating a better deal with suppliers or enhancing the benefits by increasing the revenue generated from the project.

## Example of Benefit-Cost Ratio Calculation

To illustrate how **Benefit-Cost Ratio (BCR)** is calculated, here is an informative example. The ratio is calculated by dividing the present value of benefits by the present value of costs.

YearProject Costs ($)Benefits ($)1500,000100,0002200,000300,0003100,000500,000

Let's assume that the discount rate is 10%. To calculate the sum of Present Values (PV) of costs and benefits, we need to use the formula `PV = FV / (1+r)^n`

, where FV is the future value, r is the discount rate, and n is the time period.

The PV of Project Costs is:

**PV of Year 1 Project Cost**= 100,000 / ( 1 + 0.1 ) ^ 1 = 90,909**PV of Year 2 Project Cost**= 300,000 / ( 1 + 0.1 ) ^ 2 = 247,934**PV of Year 3 Project Cost**= 500,000 / ( 1 + 0.1 ) ^ 3 = 413,223**Total PV of Project Costs**= 90,909 + 247,934 + 413,223 = 752,066

The PV of Project Benefits is:

**PV of Year 1 Project Benefits**= 100,000 / ( 1 + 0.1 ) ^ 1 = 90,909**PV of Year 2 Project Benefits**= 300,000 / ( 1 + 0.1 ) ^ 2 = 247,934**PV of Year 3 Project Benefits**= 500,000 / ( 1 + 0.1 ) ^ 3 = 413,223**Total PV of Project Benefits**= 90,909 + 247,934 + 413,223 = 752,066

Now, BCR can be calculated by dividing the PV of Benefits by the PV of Costs.

**BCR = 752,066 / 752,066 = 1**

In summary, the BCR for this project is 1, which indicates that the present value of the benefits and costs are equal. This means that the project is neither profitable nor unprofitable and is expected to have a neutral impact on the organization's profitability.

According to a study by the University of Pennsylvania Law School, Benefit-Cost Analysis is commonly used in decision-making processes undertaken by government agencies.

### Some Facts About Benefit-Cost Ratio (BCR): Definition, Formula, and Example:

**✅ Benefit-Cost Ratio (BCR) is a financial metric used to determine the profitability of a project.** *(Source: Investopedia)*

**✅ The BCR formula involves dividing the total discounted benefits by the total discounted costs of a project.** *(Source: WallStreetMojo)*

**✅ A BCR of greater than 1 indicates that a project is profitable, while a BCR of less than 1 means that the project is not profitable.** *(Source: My Accounting Course)*

**✅ BCR can be used to compare the profitability of different projects and determine which one to invest in.** *(Source: Corporate Finance Institute)*

**✅ BCR can be influenced by factors such as discount rate, project timeline, and project risk, among others.*** (Source: ProjectEngineer)*

## FAQs about Benefit-Cost Ratio (Bcr): Definition, Formula, And Example

### What is the Benefit-Cost Ratio (BCR) and why is it important?

The Benefit-Cost Ratio (BCR) is a financial metric that compares the benefits of a project or investment to its costs. It is calculated by dividing the total expected benefits of a project by its total expected costs. BCR is important because it provides a quantitative measure of the potential economic value of a project and helps decision-makers evaluate whether a proposed investment will be profitable.

### What is the formula for calculating the Benefit-Cost Ratio?

The formula for calculating the Benefit-Cost Ratio (BCR) is simple. It is calculated by dividing the total expected benefits of a project by its total expected costs. BCR = Total Expected Benefits / Total Expected Costs.

### Can the Benefit-Cost Ratio be greater than 1?

Yes, the Benefit-Cost Ratio (BCR) can be greater than 1. In fact, a BCR of greater than 1 is a sign that the benefits of a project are expected to outweigh its costs. A BCR of less than 1 indicates that a project may not be profitable and its costs may exceed its benefits.

### What is an example of calculating the Benefit-Cost Ratio?

An example of calculating the Benefit-Cost Ratio (BCR) is as follows: A proposed investment requires an initial cost of $100,000 but is expected to generate $200,000 in benefits over the next five years. BCR = $200,000 / $100,000, which equals 2. This means that for every dollar spent on the investment, there will be a return of $2 in benefits.

### Can the Benefit-Cost Ratio be negative?

Yes, the Benefit-Cost Ratio (BCR) can be negative. In cases where the total expected costs are greater than the total expected benefits, the BCR will be less than 1 and may even be negative. This suggests that the project is not economically viable and may not be worth pursuing.

### What are the limitations of using the Benefit-Cost Ratio?

While the Benefit-Cost Ratio (BCR) is a useful financial metric for evaluating project profitability, it has some limitations. For example, it does not take into account non-monetary benefits or social costs, which can have a significant impact on project value. Additionally, it assumes that future benefits and costs can be accurately predicted, which may not always be the case.