Please type clearly and show steps. Will rate for the answer! Thanks. A highway
ID: 1117961 • Letter: P
Question
Please type clearly and show steps. Will rate for the answer! Thanks.
A highway needs to be reconstructed. Two alternatives are being considered, a concrete pavement and an asphalt pavement. Both options have a service life of 45 vears. The treatments expected during the life of each pavement are shown in the table below. Assume an interest of 4%. Which is the most cost-effective pavement option, based on present worth? Alternative Initial Maintenance Rehabilitation Annual Construction Maintenance| Resurfacin & Overla $7,000,000$18,000 A-Concrete Year 15 Year 30 B Asphalt Year 8 Year 15 Year 23 Year 30 Year 38 $500,000 $900,000 $4,200,000$30,000 $300,000 $300,000 $300,000 $400,000 $750,000Explanation / Answer
Time = 45 years
Interest rate = 4%
For A-Concrete:
Present worth of the alternative = Present value of initial cost + Present value of annual maintenance cost + Present value of maintenance surfacing + Present value of rehabilitation and overlay cost
PW = -$7,000,000 - $18,000(P/A, 4%, 45) - $500,000(P/F, 4%, 15) - $900,000(P/F, 4%, 30)
Present worth of the alternative = 7000000 + 18000*(1-1/(1+4%)^45)/.04 + 0 + 500000/1.04^15 + 900000/1.04^30
PW = -$7,000,000 - ($18,000 * 20.7200) - ($500,000 * 0.5553) - ($900,000 * 0.3083)
PW = -$7,000,000 - $372,960 - $277,650 - $277,470
Present worth of the alternative = $7928080
For B-Asphalt:
Present worth of the alternative = Present value of initial cost + Present value of annual maintenance cost + Present value of maintenance surfacing + Present value of rehabilitation and overlay cost
Present worth of the alternative = 4200000 + 30000*(1-1/(1+4%)^45)/.04 + 300000/1.04^8 + 300000/1.04^23 + 300000/1.04^38 + 400000/1.04^15 + 750000/1.04^30
Present worth of the alternative = $5683457
Since, the present worth of all the cost is lower in case of alternative B Asphalt, then this alternative should be selected. Here, alternative B Asphalt is the most cost effective payment option.