Question

Benefit-Cost Analysis

Given Parameters:

Scenario One Benefit-Cost Ratio: 1.11

Scenario Two Benefit-Cost Ratio: 0.52

1. Did your benefit-cost analysis reach the same or different conclusions in the two scenarios analyzed? If different conclusions, why?
2. Assume that the proposal in fact “passed” the analysis with a benefit-cost ratio greater than 1. Does this imply that the proposed project is the optimal or best use for the $8.55 million to be invested in resource conservation? Explain.
3. In conducting benefit-cost analyses, do you think nonuse values should be considered? Why or why not?
4. Current models of climate change and cost-benefit analysis can rely heavily on the inclusion of extremely low probability but very high cost (catastrophic and irrevocable ecosystem changes, for example) events. Do inclusion of these events increase the validity of the analysis or do they bias the results?

Answer 1

What Is a Benefit-Cost Ratio (BRC)?

A benefit-cost ratio (BCR) is a ratio used in a cost-benefit analysis to summarize the overall relationship between the relative costs and benefits of a proposed project. BCR can be expressed in monetary or qualitative terms. If a project has a BCR greater than 1.0, the project is expected to deliver a positive net present value to a firm and its investors.

KEY TAKEAWAYS

• A benefit-cost ratio (BCR) is an indicator showing the relationship between the relative costs and benefits of a proposed project, expressed in monetary or qualitative terms.
• If a project has a BCR greater than 1.0, the project is expected to deliver a positive net present value to a firm and its investors.
• If a project's BCR is less than 1.0, the project's costs outweigh the benefits, and it should not be considered.

How Benefit-Cost Ratio Works

Benefit-cost ratios (BCRs) are most often used in capital budgeting to analyze the overall value for money of undertaking a new project. However, the cost-benefit analyses for large projects can be hard to get right, because there are so many assumptions and uncertainties that are hard to quantify. This is why there is usually a wide range of potential BCR outcomes.

The BCR also does not provide any sense of how much economic value will be created, and so the BCR is usually used to get a rough idea about the viability of a project and how much the internal rate of return (IRR) exceeds the discount rate, which is the company’s weighted-average cost of capital (WACC) – the opportunity cost of that capital.

The BCR is calculated by dividing the proposed total cash benefit of a project by the proposed total cash cost of the project. Prior to dividing the numbers, the net present value of the respective cash flows over the proposed lifetime of the project – taking into account the terminal values, including salvage/remediation costs – are calculated.

What Does the BCR Tell You?

If a project has a BCR that is greater than 1.0, the project is expected to deliver a positive net present value (NPV) and will have an internal rate of return (IRR) above the discount rate used in the DCF calculations. This suggests that the NPV of the project’s cash flows outweighs the NPV of the costs, and the project should be considered.

If the BCR is equal to 1.0, the ratio indicates that the NPV of expected profits equals the costs. If a project's BCR is less than 1.0, the project's costs outweigh the benefits, and it should not be considered.

Example of How to Use BCR

As an example, assume company ABC wishes to assess the profitability of a project that involves renovating an apartment building over the next year. The company decides to lease the equipment needed for the project for $50,000 rather than purchasing it. The inflation rate is 2%, and the renovations are expected to increase the company's annual profit by $100,000 for the next three years.

The NPV of the total cost of the lease does not need to be discounted, because the initial cost of $50,000 is paid up front. The NPV of the projected benefits is $288,388, or ($100,000 / (1 + 0.02)^1) + ($100,000 / (1 + 0.02)^2) + ($100,00 / (1 + 0.02)^3). Consequently, the BCR is 5.77, or $288,388 divided by $50,000.

In this example, our company has a BCR of 5.77, which indicates that the project's estimated benefits significantly outweigh its costs. Moreover, company ABC could expect $5.77 in benefits for each $1 of costs.

Limitations of BCR

The primary limitation of the BCR is that it reduces a project to a simple number when the success or failure of an investment or expansion relies on many factors and can be undermined by unforeseen events. Simply following a rule that above 1.0 means success and below 1.0 spells failure is misleading and can provide a false sense of comfort with a project. The BCR must be used as a tool in conjunction with other types of analysis to make a well-informed decision.

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Discounted cash flow (DCF) is a valuation method used to estimate the attractiveness of an investment opportunity.