Question

A state government is considering construction of a flood control dike having a life span of 21 years. History indicates that a flood occurs every 7 years and causes $750,000 in damages, on average. If the state uses a MARR of 10% per year and expects every public-works project have a B-C ratio of at least 1.0, what is the maximum investment that will be allowed for the dike? Assume that the flood occurs in the middle of each 7-year period. (Enter your answer as a number without the dollar $ sign.)

Answer 1

ANSWER:

I = 10%

N = 21 YEARS

damages = money needed = $750,000 every 7th year

pw of benefits = money needed in year 7(p/f,i,n) + money needed in year 14(p/f,i,n) + money needed in year 21(p/f,i,n)

pw of benefits = 750,000(p/f,10%,7) + 750,000(p/f,10%,14) + 750,000(p/f,10%,21)

pw of benefits = 750,000 * 0.5132 + 750,000 * 0.2633 + 750,000 * 0.1351

pw of benefits = 384,900 + 197,475 + 101,325

pw of benefits = 683,700

pw of costs = investment

b/c = pw of benefits / pw of costs

1 = 683,700 / investment

investment = 683,700

so the maximum investment will be $683,700.