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Benefit-Cost Ratio

A benefit-cost ratio greater than 1.0 usually indicates an economically acceptable investment.

$$BCR=\frac{\text{Present worth of benefits}}{\text{Present worth of costs}}$$

Problem: CE Board May 2015

If the benefit-cost ratio is 1.8, how much should be spent on a project that provides annual benefits of P120,000 for 5 years at 12%?

$$PW\ of\ benefits=120000(P/A,12\%,5)=432,573$$
$$Cost=\frac{432,573}{1.8}=240,318$$

Final answer: P240,318.

Problem: CE Board May 2016

A small entrepreneur invests P80,000 and expects gross income P25,000 with operating cost P6,000 annually for 10 years at 12%. Compute BCR.

$$A=25,000-6,000=19,000$$
$$PW=19000(P/A,12\%,10)=107,354.24$$
$$BCR=\frac{107,354.24}{80,000}=1.34$$

Final answer: 1.34.

Problem: Benefit-Cost Ratio

A public project has present benefits P9.5M and present costs P7.8M. Find B/C.

$$B/C=\frac{9.5}{7.8}=1.22$$

Answer: The benefit-cost ratio is 1.22.

Problem: Benefit-Cost Ratio with Disbenefit

Present benefits are P12M, disbenefits are P1.5M, and costs are P8M. Find modified B/C.

$$B/C=\frac{B-D}{C}=\frac{12-1.5}{8}=1.31$$

Answer: The modified B/C ratio is 1.31.

Problem: B/C Decision

A project has B/C = 0.96. State the decision using the usual public-project criterion.

A project is acceptable when B/C is at least 1.00.

Answer: Reject the project by the B/C criterion.

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