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Benefit-Cost Ratio of a Road Project

Mediumbenefit-cost ratio
A road project costs $1,200,000 now. It produces user benefits of $150,000 per year and needs $30,000 per year of maintenance, both for 20 years. At 5%, the conventional benefit–cost ratio is most nearly:
  1. A1.19
  2. B1.25
  3. C1.56
  4. D1.67
Show solution

Answer: A. 1.19

Equation: conventional B/C = PW(benefits) / [first cost + PW(O&M)], with PW of a uniform series = A(P/A, i, n). Values: first cost $1,200,000; benefits $150,000/yr; O&M $30,000/yr; i = 5%, n = 20, so (P/A, 5%, 20) = 12.4622. Step 1: PW(benefits) = 150,000 × 12.4622 = $1,869,330. Step 2: PW(O&M) = 30,000 × 12.4622 = $373,866. Step 3: B/C = 1,869,330 / (1,200,000 + 373,866) = 1.19. 1.25 is the modified B/C (O&M subtracted from benefits); 1.67 ignores discounting; 1.56 leaves out maintenance.
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