Which of the following statements about the Benefit-Cost Ratio (BCR) is TRUE?

Question

BlackTom AI · Accepted Answer

Benefit-Cost Ratio (BCR) equals the present value of benefits divided by the present value of costs, so it measures benefit per unit cost: BCR = PV(Benefits) / PV(Costs).

1) Relevant knowledge points and concepts
- BCR: ratio of discounted benefits to discounted costs. If BCR > 1, discounted benefits exceed discounted costs.
- Net Present Value (NPV): NPV = PV(Benefits) − PV(Costs). Projects with higher NPV add more total value.
- Mutual exclusivity and scale: BCR is a relative measure; NPV is an absolute measure. When projects differ in scale, BCR can favour small projects that give high benefits per dollar even though their total contribution (NPV) is small.
- Risk and timing: Both BCR and NPV use discounting to reflect timing; IRR has different reinvestment assumptions and multiple-IRR issues.

2) Step-by-step reasoning
- Calculate BCR and NPV for projects of different scale to see the effect.
- Example: Project A (small): PV benefits = 150, PV costs = 100.
  - BCR_A = 150 / 100 = 1.5
  - NPV_A = 150 − 100 = 50
- Example: Project B (large): PV benefits = 1,400, PV costs = 1,000.
  - BCR_B = 1,400 / 1,000 = 1.4
  - NPV_B = 1,400 − 1,000 = 400
- Although BCR_A (1.5) > BCR_B (1.4), Project B has a much larger NPV (400 > 50). If projects are mutually exclusive or the objective is to maximize total value subject to a budget, Project B is preferred despite the lower BCR.

3) Intermediate calculation steps shown above:
- BCR_A = 150/100 = 1.5; NPV_A = 150 − 100 = 50
- BCR_B = 1400/1000 = 1.4; NPV_B = 1400 − 1000 = 400

4) Why the correct answer is correct
- The statement “BCR can be misleading if project scale is not considered” is true because BCR ignores absolute magnitude; it normalizes benefits by costs and can make small high-efficiency projects look better than larger higher-value projects.

5) Why other options are incorrect
- “BCR always favours projects with the highest NPV”: false — as shown, BCR can rank a small high-ratio project above a larger higher-NPV project.
- “A BCR > 1 means a project must be selected”: false — BCR > 1 means benefits exceed costs, but selection depends on budget constraints, mutual exclusivity, and comparative NPVs.
- “BCR accounts for risk and timing better than IRR”: false — both IRR and BCR rely on discounted cash flows; IRR has different assumptions and neither inherently handles risk better — risk should be addressed via discount rates or sensitivity analysis.

6) Conclusion
The correct statement is: BCR can be misleading if project scale is not considered. This matches the provided answer.

Which of the following statements about the Benefit-Cost Ratio (BCR) is TRUE?单项选择题

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