# How To Use the Cost Benefit Formula (With Example)

Updated February 3, 2023 A cost-benefit 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 is profitable. Understanding how to use the cost-benefit ratio formula can also assist you in making informed financial decisions.

In this article, we define the cost-benefit ratio formula, discuss why it's helpful, explain how to use it and provide an example to guide you when making your own calculations.

## What is the cost-benefit ratio formula?

The cost-benefit ratio formula is a financial metric that professionals use to assess the costs and benefits of a project to determine its viability. You can analyze a proposed project with the ratio to see the relationship between the costs to complete the project and the expected benefits over time. You can write the BCR formula as the present value (PV) 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 cost-benefit ratio formula mathematically, it looks like this:

BCR = PV of expected benefits / PV of expected costs

You can express the cost-benefit ratio values either as monetary or qualitative. When a project has a cost-benefit ratio 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 project's cost, so the project is a good financial consideration.

Related: Net Present Value (NPV) vs. Internal Rate of Return (IRR)

## When to use the cost-benefit ratio formula

The most common use for the cost-benefit ratio is when analyzing the overall financial value of a new project in capital budgeting. Since capital budgeting often includes projects where assumptions and quantitative data may be uncertain, there's often a large variety of potential cost-benefit ratio outcomes. The cost-benefit ratio can provide a rough idea of 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

## Advantages of using the cost-benefit ratio formula

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

Related: The Importance of Project Management

## How to calculate the cost-benefit ratio

Here are the steps to calculate the cost-benefit ratio:

### 1. Find the present value factor

The present value factor is the factor that you can use to indicate the present value of cash a company receives in the future. It's based on the time value of money, which states that the money a company currently has is more valuable than that same amount in the future. This is because the current money has the potential to grow if the company invests it or saves it and earns interest. This PV factor is a number that's always less than one. Here's the formula for calculating the PV factor:

P = [1 / (1 + r) n]

Where:

• r: This represents the interest rate.

• P: This represents the present value factor.

• n: This represents the number of periods over which the company made payments.

### 2. Find the present value of expected benefits

The present value of expected benefits refers to the current value of a project's future cash flows. To determine this value, add all future cash flows or monetary benefits you expect from the project. These cash flows and benefits may include incremental revenue, sales, cost savings, the increased value of assets or received interest payments. Here's the formula for calculating the present value of expected benefits:

Present value expected benefits = future benefits x present value factor

Related: Present Value vs. Net Present Value: Definitions and Differences

### 3. Find the present value of expected costs

The present value of expected costs refers to the current value of all cash outflows you expect from the project. These cash outflows may include initial investments, administrative costs, disposal costs, production expenses and any other costs for completing the project. Here's the formula for calculating the present value of expected costs:

Present value of future costs = future costs x present value factor

Related: Present Value vs. Net Present Value: Definitions and Differences

### 4. 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, capital cost or the risk-adjusted market interest rate. When there are multiple periods, each period can use the discount rate to the power of the period.

Related: Interest Rates: What They Are and How To Calculate Them

### 5. Input the numbers into the formula

Input the values into the cost-benefit formula. Remember that when there are multiple periods, each period can use the discount rate to the power of the period. For example, if the PV of expected benefits is \$1,000, PV of expected costs is \$500, the discounting rate is 2% or 0.02 and the number of periods is 3. Your cost-benefit ratio is \$5.77. The equation looks like this:

Cost-benefit ratio = [\$1,000 / (1 + 0.02)¹] + [\$1,000 / (1 + 0.02)²] + [\$1,000 / (1 + 0.02)³] / \$500

= \$980.40 + \$961.17 + \$942.32 / \$500

= \$2,883.89 / \$500

= \$5.77

### 6. Evaluate the cost-benefit ratio

Since the value of the cost-benefit ratio is over 1 in the example above, the cash flow from the project is more than the cost of the project. Thus, the project is a good financial consideration. For every \$1 the project costs, there's \$5.77 in benefits.

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

## Example of a benefit-cost ratio formula

Here's an example of an organization using the cost-benefit ratio 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 cost-benefit 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:

Cost-benefit ratio = [\$200,000 / (1 + 0.04)¹] + [\$200,000 / (1 + 0.04)²] + [\$200,000 / (1 + 0.04)³] / \$100,000

Next, it solves for the PV of expected benefits:

\$555,018.20 = 192,307.69 + 184,911.24 + 177,799.27

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

\$5.55 = \$555,018.20 / \$100,000

Villa Homes considers this project a good financial decision because the BCR is above 1. 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 project's cost.

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