A highway needs to be reconstructed. Two alternatives are being considered, a co

Question

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 years. 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? Alternativee Annual Construction Maintenance Resurfacin Maintenance Rehabilitation Initial & Overla A-Concrete Year 15 Year 30 B- Asphalt Year 8 Year 15 Year 23 Year 30 Year 38 $7,000,000$18,000 $900,000 $4,200,000$30,000 $300,000 $300,000 $300,000 $400,000 $750,000

Explanation / Answer

Alternative A - Concrete pavement

Calculate the present worth -

PW = -$7,000,000 - $18,000(P/A, 4%, 45) - $500,000(P/F, 4%, 15) - $900,000(P/F, 4%, 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

PW = -$7,928,080

The Present Worth of Alternative A is -$7,928,080.

Alternative B - Asphalt pavement

Calculate the Present Worth -

PW = -$4,200,000 -$30,000(P/A, 4%, 45) - $300,000(P/F, 4%, 8) - $400,000(P/F, 4%, 15) - $300,000(P/F, 4%, 23) - $750,000(P/F, 4%, 30) - $300,000(P/F, 4%, 38)

PW = -$4,200,000 - ($30,000 * 20.7200) - ($300,000 * 0.7307) - ($400,000 * 0.5553) - ($300,000 * 0.4057) - ($750,000 * 0.3083) - ($300,000 * 0.2253)

PW = -$4,200,000 - $621,600 - $219,210 - $222,120 - $121,710 - $231,225 - $67,590

PW = -$5,683,455

The Present worth of Alternative B is -$5,683,455.

The present worth of Alternative B is numerically higher.

So, it is the most cost-effecttive option.

Thus, Alternative B (Asphalt pavement) is the most cost-effective pavement option.

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