What Is the Benefit-Cost Ratio (BCR)? Formula and Example

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The benefit-cost ratio (BCR), also called the cost-benefit ratio or B/C ratio, compares a project’s discounted benefits with its discounted costs. You find it by dividing the present value of expected benefits by the present value of expected costs. A BCR above 1.0 means the benefits are expected to exceed the costs in today’s money. A BCR below 1.0 means the costs are expected to be larger.

What the Benefit-Cost Ratio Measures

BCR is the summary figure of a cost-benefit analysis. It answers a narrow question: how many dollars of benefit (in present-value terms) does the project return for each dollar of cost? A BCR of 1.25 means $1.25 of discounted benefit for every $1.00 of discounted cost.

In corporate capital budgeting, benefits are usually incremental cash inflows such as added revenue or cost savings. In public-sector analysis, where the ratio is most widely used, benefits can include non-cash items given a monetary value, such as travel time saved by a new road or reduced health costs from cleaner water.

Benefit-Cost Ratio Formula

BCR = PV of benefits ÷ PV of costs

Each stream is discounted before dividing:

PV = Σ CFₜ ÷ (1 + r)ᵗ

Here CFₜ is the benefit or cost in year t, and r is the discount rate. For a company that rate is often its weighted average cost of capital or a project-specific hurdle rate. Both streams should cover the full project life. That includes upfront outlays, ongoing operating costs, terminal or salvage values and any end-of-life costs such as remediation or decommissioning.

Interpreting the result

• BCR > 1.0: discounted benefits exceed discounted costs. Net present value is positive, and for conventional cash flows (outflows first, inflows after) the IRR is above the discount rate.
• BCR = 1.0: benefits exactly cover costs. NPV is zero and IRR equals the discount rate.
• BCR < 1.0: the project destroys value at that discount rate.

Example of the Benefit-Cost Ratio

Hypothetical example. A company is considering new equipment with these assumptions:

• Upfront cost: $200,000, paid today, so it is not discounted.
• Maintenance: $10,000 at the end of each of years 1 to 3.
• Benefits: $90,000 in cost savings at the end of each of years 1 to 3.
• Discount rate: 8%. No salvage value.

The 8% discount factors are 0.9259, 0.8573 and 0.7938, which sum to about 2.5771.

• PV of benefits = $90,000 × 2.5771 ≈ $231,939
• PV of costs = $200,000 + ($10,000 × 2.5771) ≈ $225,771
• BCR = $231,939 ÷ $225,771 ≈ 1.03
• NPV = $231,939 − $225,771 ≈ $6,168

The project clears the bar, but only just. At a 10% discount rate (factors summing to about 2.4869), PV of benefits falls to roughly $223,817 and PV of costs to about $224,869, so the BCR drops to roughly 0.995. A two-point change in the discount rate turns the answer from yes to no, so the ratio is best tested across a range of rates.

How the BCR Is Used

• Screening projects: a quick pass/fail test on whether a proposal covers its costs at the required return.
• Ranking under a budget limit: when capital is constrained, a higher BCR identifies projects that deliver more benefit per dollar spent.
• Public investment decisions: governments and agencies use BCRs to compare infrastructure, environmental and social programs, often in standardized appraisal formats.
• Project selection: project management frameworks, including PMP material, list BCR among benefit measurement methods alongside NPV, IRR and payback period.

Limitations of the Benefit-Cost Ratio

It reduces a project to one number. Forecasts for large projects rest on many assumptions about demand, costs, timing and risk. Small changes can move the ratio a long way, and a figure above 1.0 can give false comfort. Organizations often want a cushion above 1.0 to allow for forecast error, and the size of that cushion is a policy choice, not a standard.

It ignores scale. A $10,000 project with a BCR of 2.0 creates $10,000 of NPV. A $5 million project with a BCR of 1.2 creates $1 million. If you can only do one of them, the lower ratio wins on total value.

Classification changes the ratio. Recurring costs can be added to the denominator or netted against benefits in the numerator. In the example above, netting maintenance against savings gives ($80,000 × 2.5771) ÷ $200,000 ≈ 1.03 again by rounding, but the exact figure is 1.031 versus 1.027. NPV is identical either way. With larger operating costs the gap widens, so BCRs are only comparable when they follow the same convention.

Valuing non-cash benefits is subjective. Public-sector BCRs depend on how analysts put a price on things like time, safety or environmental quality.

BCR vs. Related Metrics

• Net present value: the dollar difference between discounted benefits and costs. NPV shows how much value is created, while BCR shows how efficiently it is created. For a choice between mutually exclusive projects, NPV is generally the deciding measure.
• Internal rate of return: the discount rate at which NPV is zero, which is also where the BCR equals 1.0. IRR expresses the project as a percentage return rather than a ratio.
• Profitability index (PI): PV of future cash flows divided by the initial investment. It is the corporate-finance version of the same idea. It differs from BCR mainly in that ongoing costs are netted into the numerator instead of sitting in the denominator.
• ROI: usually an undiscounted gain divided by cost. Unlike BCR, it does not account for when the cash arrives.

FAQs

The Bottom Line

The ratio helps analysts, managers and public agencies screen proposals and rank projects when capital is limited. Because small changes in forecasts or the discount rate can push a marginal project across 1.0, test the ratio across a range of rates and treat a thin margin with caution. When choosing between mutually exclusive projects, NPV generally decides, since BCR measures efficiency rather than total value created.