 # What Is the Benefit Cost Ratio (BCR)? Definition, Formula, Example.

The Benefit Cost Ratio (BCR), also referred to as Benefit-to-Cost Ratio is an indicator that is typically used within a cost benefit analysis. In project management, the benefit cost ratio can support the cost-benefit analysis of a business case. The PMI Project Management Body of Knowledge lists the BCR under project success measures, next to the net present value and return on investment (source: PMBOK®, 6th ed., part 1, ch. 1.2.6.4, p. 34).

If you compare investment alternatives, assess different project options or prepare for your PMP exam, you will want to understand the meaning and calculation of the cost-to-benefit ratio. Read on to learn the definition of the BCR and how it is calculated.

## Definition and Meaning of Benefit Cost Ratio

The benefit cost ratio (or benefit-to-cost ratio) compares the present value of all benefits with that of the cost and investments of a project or investment. These benefits and costs are treated as monetary cash flows or their equivalents, e.g. for non-monetary benefits or company-internal costs.

Its meaning depends on the value it is indicating. For the interpretation, refer to the following 3 generic ranges of BCR values:

#### What Does a BCR < 1 Indicate?

The present value of the benefits in a series of cash flows is lower than the present value of the corresponding costs. The lower the BCR, the higher the excess of discounted costs compared to the discounted benefits.

In general, pursuing investments with a negative BCR is not recommended. The same holds basically true for different project options.

However, there are certain types of projects that need to be conducted even if they are not generating sufficient tangible or quantifiable benefits to cover the costs, e.g. the implementation of regulatory or legal requirements. In these cases, the option with the highest BCR (yet below 1) may be the least unprofitable implementation scenario.

#### What Is the Meaning of a BCR = 1?

The present value of benefits of a series of cash flows equals the likewise discounted costs. This situation is obviously more preferable than options with a BCR lower than 1. However, if there are alternatives with a benefit-to-cost ratio exceeding 1, they are likely to be favored.

#### How Is a BCR > 1 Interpreted?

This value range indicates that the discounted benefits exceed the present value of the costs and investments. The general rule is that the higher the BCR the greater the profit an investment option or project is expected to generate.

Apart from the benefit cost ratio, there are other important quantitative and qualitative considerations though – in reality, a project or investment decision is based on a number of different criteria rather than relying on the BCR only.

### Typical Uses of the Benefit Cost Ratio

The BCR is typically used for cost benefit analyses, along with other measures such as the net present value, return on investment, internal rate of return, etc. The consideration of absolute amounts of cost and benefits sets this ratio apart from many other indicators.

The result of the net present value (NPV) calculation is one single figure that represents the expected net value of all cost and benefit without giving an idea of the volume and the relation of the underlying gross cash flows. The BCR can be used to supplement this missing piece of information. Representing the ratio of discounted benefits to discounted costs, it is a relative measure of whether and to which extent the present value of the benefits exceeds that of the investments and cost.

For instance, a project manager could be working on a cost benefit analysis of different project options that may involve products or results with differences in their profit margins. While the NPV is based on the net amount of these margins only, the BCR would be greater for a project with lower investments and costs and higher benefits and revenues, regardless of the net amounts.

#### Pros

• The BCR translates the absolute amounts of benefits and costs into a ratio
• It facilitates the comparison of different investment or project alternatives
• The ratio helps interpret the ‘inherent riskiness’ of forecasted net cash flows and profitability, e.g. in cases where small profit margins are prone to a higher risk while large margins offer a buffer for price adjustments
• It considers the value of cash flows in relation to the time of their occurrence

#### Cons

• The BCR alone does not indicate the liquidity / funding aspects of the analyzed options, e.g. an option may require large investments and expenses in earlier periods while producing returns in far later stages (for qualitative aspects, check Wikipedia)
• It is subject to various assumptions for the discount rate, residual value and cash flow forecast. These assumptions can significantly impact the outcome of a benefit cost analysis without considering the inherent insecurities of these parameters (read the corresponding discussion of assumptions in this article on the NPV)

## How Is the Benefit Cost Ratio Calculated?

### The BCR Formula

The benefit cost ratio is calculated by dividing the present value of benefits by that of costs and investments.

This is the consolidated formula (source):

where:
BCR = Benefit Cost Ratio
PV = Present Value
CF = Cash Flow of a period (classified as benefit and cost, respectively)
i = Discount Rate or Interest Rate
N = Total Number of Periods
t = Period in which the Cash Flows occur

Note that in this formula, both present values need to be inserted with their absolute, non-negative amounts. If you have consistently used negative cash flows for either the cost or the benefit side, your result will be negative. You will then need to multiply it with (-1).

### Components of the BCR Formula

The Formula for calculating the benefit cost ratio consists of three components: The present value of all benefits, the present value of all costs and, finally, the division of these present values. We will discuss them in this subsection.

#### 1. Present Value of Benefits

The present value of benefits is calculated as the sum of discounted benefits. To determine this sum, all inflows in a period (i.e. cash flows considered as benefits) need to be discounted with 1 plus the discount rate i to the power of the period. This calculation needs to be performed for every period.

#### 2. Present Value of Cost

The present value of costs is calculated analogously that of the benefits. The difference is that for this figure, the outflows are considered as representing costs, rather than the inflows.

#### 3. Ratio of Both Present Values

To calculate the BCR, the present value of benefits is divided by the present value of costs. Thereby, both amounts should be absolute, i.e. non-negative.

### Input Parameters and Assumptions

The calculation of the BCR requires 3 input parameters for each period:

• cash flows (benefits),
• cash flows (costs), and
• interest or discount rate.

#### Cash Flows (Benefits and Costs)

The cash flows used for calculating the benefit cost ratio are typically monetary values stemming from a business forecast. Where benefits do not materialize in the form of monetary cash flows, an equivalent should be used. Otherwise, this indicator is not applicable to the particular type of analysis.

Cash flows need to be estimated separately for benefits and costs. Benefits include but are not limited to revenue, sales, savings, increases of values of assets, interest payments received, etc.

Examples of cost cash flows are the initial investments, expenses for the creation of products or results, administrative costs, disposal costs, etc.

You might also consider a residual value at the end of the projection’s time horizon, which may be the expected market value (benefit), disposal cost (a cost cash flow) or the present value of a perpetuity, an infinite series of cash flows. If you use the latter, make sure you split the infinite cash flows into cost and benefits and discount each group of cash flows separately.

#### Discount Rate

Define the discount or interest rate of your BCR analysis. It can represent the capital cost or target return rates of your organization (often used for assessment of projects) or a risk-adjusted market interest rate.

If a detailed calculation is required, you may consider using different interest rates among the projection period or applying different risk-adjusted rates to certain types of costs and benefits.

For further details on these parameters and related considerations, read the respective section of our net present value introduction.

## Example

A project manager is performing the cost-benefit analysis of 3 different software options. The company expects a return rate of 12% which is reflected in a corresponding discount rate.

### Projected Cash Flows

The cash flow projection is as follows,

### Discounted Cash Flows and Calculated Benefit Cost Ratios

Once the cash flows are estimated, they are discounted to their present value. The sum of discounted benefits is consequently divided by the sum of discounted costs. Doing these steps leads to the following result tables:

Calculated Results for Option 1:

• Present Value of Costs:               12,009
• Present Value of Benefits:           13,424
• Benefit Cost Ratio:                       1.12

Calculated Results for Option 2:

• Present Value of Costs:               18,510
• Present Value of Benefits:           18,325
• Benefit Cost Ratio:                       0.99

Calculated Results for Option 3:

• Present Value of Costs:                 9,238
• Present Value of Benefits:           11,003
• Benefit Cost Ratio:                       1.19

### Interpretation of Results

If the 3 options are ranked by their BCR, Option 3 is the most promising alternative, followed by Option 1. Option 2 has a BCR lower than 1 which indicates that it is not profitable at all.

This table includes the NPV for reference (check the NPV sample calculation for the details). While it is common that the NPV and BCR produce a similar ranking of options, this is not necessarily always the case.

If there were an option with high investments and costs and a small relative profit margin, the NPV would present this option in a more favorable way as it discounts the absolute profitability amounts. As the BCR is focusing on the relative profitability, the larger divisor of the BCR (due to higher costs) would likely push this option behind other options.

Note that the numbers used in this example are consistent with the NPV example. Thus, you can easily compare the different mechanics and effects in the calculation of both indicators.

## Conclusion

The benefit cost ratio is a common indicator of the profitability of a potential investment or project. While it does not cover all aspects of a cost benefit analysis, it indicates whether an option is beneficial. As the BCR compares discounted benefits with discounted costs, it offers a good indication of how big a ‘buffer’ between benefits and costs is.

However, like all other indicators, the BCR should not be used as the only basis for project or investment decisions given that it only covers certain aspects of a project option.