Question

Question 14 of 14 9 Points A road can be paved with either asphalt or concrete. Concrete costs $12.000/km and lasts for 20 years. To be more economical, what is the maximum amount that can be spent on asphalt, which lasts only 10 years? The annual maintenance costs are $500/km for both pavements. Assume a MARR of 12%. The maximum amount that can be spent on asphalt is $ Enter your answer in the box. Round your answer to the nearest whole number. Do not include the dollar sign ($) in your answer. Remember to scan your work and submit it after you've completed the exam.

Answer 1

Given,

MARR = 12%

Concrete pavement:

Initial cost = -$12,000 per km

Annual maintenance cost = -$500 per km

Useful life = 20 years

From the compound interest table, we obtain

(P/A, 12%, 20) = 7.469

Present worth of the concrete pavement per km = -$12,000 -$500(P/A, 12%, 20) = -$12,000 - $500*7.469 = -$15,734.5

Asphalt pavement;

Let the initial cost of laying Asphalt pavement be 'A' per km

Initial Cost = -$A per km

Annual maintenance cost = -$500 per km

Useful life = 10 years

From the compound interest table, we obtain

(P/A, 12%, 10) = 5.650

(P/F, 12%, 10) = 0.3220

Present worth of the Asphalt pavement per km for one cycle(10 years) = -$A - $500(P/A,12%, 10) = -$A - $500*5.650 = -$A -$2,825

Present worth of the Asphalt pavement per know for 20 years = (-$A - $2,825) + (-$A - $2,825)(P/F, 12%, 10) = -$A - $2,825 -$0.3220A - $909.65

= -$1.3220A -$3,734.65

The maximum amount that can be spent on Asphalt pavement is the value that makes the PW of both the alternatives equal

=> -$1.3220A -$3,734.65 = -$15,734.5

=> -$1,3220A = -$11,999.85

=> A = (-$11,999.85)/(-$1.3220)

=> A = $9,077.04

Ans: 9,077