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A new highway is to be constructed. Design A calls for a concrete pavement costing $95 per foot with a 16-year life; three paved ditches costing $4 per foot each; and two box culverts every mile, each costing $8,000 and having a 16-year life. Annual maintenance will cost $1,700 per mile; the culverts must be cleaned every four years at a cost of $350 each per mile. Design B calls for a bituminous pavement costing $55 per foot with a 8-year life; three sodded ditches costing $1.55 per foot each; and four pipe culverts every mile, each costing $2,250 and having a 8-year life. The replacement culverts will cost $2,450 each. Annual maintenance will cost $2,700 per mile; the culverts must be cleaned yearly at a cost of $215 each per mile; and the annual ditch maintenance will cost $1.60 per foot per ditch. Compare the two designs on the basis of equivalent worth per mile for a 16-year period. Find the most economical design on the basis of AW and PW if the MARR is 12% per year. N 1 2 3 4 Discrete Compounding; i = 12% Single Payment Uniform Series Compound Compound Sinking Amount Present Amount Present Fund Factor Worth Factor Factor Worth Factor Factor To Find F To Find P To Find F To Find P To Find A Given P Given F Given A Given A Given F FIP PIF FIA PIA AIF 1.1200 0.8929 1.0000 0.8929 1.0000 1.2544 0.7972 2.1200 1.6901 0.4717 1.4049 0.7118 3.3744 2.4018 0.2963 1.5735 0.6355 4.7793 3.0373 0.2092 1.7623 0.5674 6.3528 3.6048 0.1574 1.9738 0.5066 8.1152 4.1114 0.1232 2.2107 0.4523 10.0890 4.5638 0.0991 2.4760 0.4039 12.2997 4.9676 0.0813 2.7731 0.3606 14.7757 5.3282 0.0677 3.1058 0.3220 17.5487 5.6502 0.0570 3.4785 0.2875 20.6546 5.9377 0.0484 3.8960 0.2567 24.1331 6.1944 0.0414 4.3635 0.2292 28.0291 6.4235 0.0357 4.8871 0.2046 32.3926 6.6282 0.0309 5.4736 0.1827 37.2797 6.8109 0.0268 6.1304 0.1631 42.7533 6.9740 0.0234 6.8660 0.1456 48.8837 7.1196 0.0205 6 Capital Recovery Factor To Find A Given P AIP 1.1200 0.5917 0.4163 0.3292 0.2774 0.2432 0.2191 0.2013 0.1877 0.1770 0.1684 0.1614 0.1557 0.1509 0.1468 0.1434 0.1405 7 8 9 10 11 12 13 14 15 16 17 The AW value for Design A is $ - 85,200 /mi. (Round to the nearest hundreds.) The PW value for Design A is $ - 593,800 /mi. (Round to the nearest hundreds.) The AW value for Design B is $ - 94,200 /mi. (Round to the nearest hundreds.) The PW value for Design B is $ - 656,700 /mi. (Round to the nearest hundreds.) The most economical design on the basis of AW and PW is A new highway is to be constructed. Design A calls for a concrete pavement costing $95 per foot with a 16-year life; three paved ditches costing $4 per foot each; and two box culverts every mile, each costing $8,000 and having a 16-year life. Annual maintenance will cost $1,700 per mile; the culverts must be cleaned every four years at a cost of $350 each per mile. Design B calls for a bituminous pavement costing $55 per foot with a 8-year life; three sodded ditches costing $1.55 per foot each; and four pipe culverts every mile, each costing $2,250 and having a 8-year life. The replacement culverts will cost $2,450 each. Annual maintenance will cost $2,700 per mile; the culverts must be cleaned yearly at a cost of $215 each per mile; and the annual ditch maintenance will cost $1.60 per foot per ditch. Compare the two designs on the basis of equivalent worth per mile for a 16-year period. Find the most economical design on the basis of AW and PW if the MARR is 12% per year. N 1 2 3 4 Discrete Compounding; i = 12% Single Payment Uniform Series Compound Compound Sinking Amount Present Amount Present Fund Factor Worth Factor Factor Worth Factor Factor To Find F To Find P To Find F To Find P To Find A Given P Given F Given A Given A Given F FIP PIF FIA PIA AIF 1.1200 0.8929 1.0000 0.8929 1.0000 1.2544 0.7972 2.1200 1.6901 0.4717 1.4049 0.7118 3.3744 2.4018 0.2963 1.5735 0.6355 4.7793 3.0373 0.2092 1.7623 0.5674 6.3528 3.6048 0.1574 1.9738 0.5066 8.1152 4.1114 0.1232 2.2107 0.4523 10.0890 4.5638 0.0991 2.4760 0.4039 12.2997 4.9676 0.0813 2.7731 0.3606 14.7757 5.3282 0.0677 3.1058 0.3220 17.5487 5.6502 0.0570 3.4785 0.2875 20.6546 5.9377 0.0484 3.8960 0.2567 24.1331 6.1944 0.0414 4.3635 0.2292 28.0291 6.4235 0.0357 4.8871 0.2046 32.3926 6.6282 0.0309 5.4736 0.1827 37.2797 6.8109 0.0268 6.1304 0.1631 42.7533 6.9740 0.0234 6.8660 0.1456 48.8837 7.1196 0.0205 6 Capital Recovery Factor To Find A Given P AIP 1.1200 0.5917 0.4163 0.3292 0.2774 0.2432 0.2191 0.2013 0.1877 0.1770 0.1684 0.1614 0.1557 0.1509 0.1468 0.1434 0.1405 7 8 9 10 11 12 13 14 15 16 17 The AW value for Design A is $ - 85,200 /mi. (Round to the nearest hundreds.) The PW value for Design A is $ - 593,800 /mi. (Round to the nearest hundreds.) The AW value for Design B is $ - 94,200 /mi. (Round to the nearest hundreds.) The PW value for Design B is $ - 656,700 /mi. (Round to the nearest hundreds.) The most economical design on the basis of AW and PW is
