A new highway is to be constructed Design A calls for a conc

A new highway is to be constructed. Design A calls for a concrete pavement costing S85 per foot with a 16-year life, three paved ditches costing $5 per foot each; and three box culverts every mile, each costing $10,000 and having a 16-year life. Annual maintenance will cost 51,800 per mile; the culverts must be cleaned every four years at a cost of S550 each per mile Design B calls for a bituminous pavement costing S35 per foot with a 8-year life, four sodded ditches costing $1.45 per foot each, and two pipe culverts every mile, each costing $2,150 and having a 8-year life. The replacement culverts will cost $2,500 each. Annual maintenance will cost $2,900 per mile; the culverts must be cleaned yearly at a cost of $215 each per mile; and the annual ditch maintenance will cost $1.45 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 10% per year Click the icon to view the interest and annuity table for discrete compounding when the MARR is 10% per year. The AW value for Design A is /mi. (Round to the nearest hundreds.) The PW value for Design A is S The AW value for Design B is Smi. (Round to the nearest hundreds.) The PW value for Design B is oud to the nearest hundreds.) The most economical design on the basis of AW and PW is Round to the nearest hundreds.)

Solution

Let determine the cash flows associated with the two options - Design A - Concrete Pavement - Concrete Pavement 85 per foot life 16 years 3 Paved Ditches 5 per foot Each 3 box culverts 10000 each life 16 years Annual maintainance cost 1800 per mile Cleaning cost for culverts 550 each per mile every 4 years Design B - Bituminous pavement - Bituminous pavement 35 per foot 8 year life 4 sodded ditches 1.45 per foot each 2 pipe culverts 2150 each every mile each 8 year life Replacement culverts 2500 each Annual maintainance cost 2900 per mile Cleaning cost for culverts 215 each per mile each year Annual ditch maintainance cost 1.45 per foot per ditch MARR 10% Life 16 years Total length - 1 mile = 5280 foot Concrete Pavement 85 x 5280 = 448800 3 Paved Ditches 3 x 5 x 5280 = 79200 3 box culverts 3 x 10000 30000 558000 Annual maintainance cost 1800 each year Cleaning cost for culverts 550 x 3 = 1650 every 4 years Year Cash flow PV facor @ 10% PV of cash flows 0 558000 1.000 558000 1 1800 0.909 1636 2 1800 0.826 1488 3 1800 0.751 1352 4 3450 0.683 2356 5 1800 0.621 1118 6 1800 0.564 1016 7 1800 0.513 924 8 3450 0.467 1609 9 1800 0.424 763 10 1800 0.386 694 11 1800 0.350 631 12 3450 0.319 1099 13 1800 0.290 521 14 1800 0.263 474 15 1800 0.239 431 16 3450 0.218 751 7.824 574864 (excluding 1 for t=0) PW = 574864 AW = PW/7.824 = 73477.2 Bituminous pavement 35 x 5280= 184800 Buy again after 8 years Replacement culverts 2500 x 2 5000 Buy again after 8 years 189800 4 sodded ditches 1.45 x 4 x 5280 = 30624 2 pipe culverts 2 x 2150 = 4300 224724 Annual maintainance cost 2900 each year Cleaning cost for culverts 215 x 2 430 each year Annual ditch maintainance cost 4 x 1.45 x 5280 = 30624 each year 33954 Year Cash flow PV facor @ 10% PV of cash flows 0 224724 1.000 224724 1 33954 0.909 30867 2 33954 0.826 28061 3 33954 0.751 25510 4 33954 0.683 23191 5 33954 0.621 21083 6 33954 0.564 19166 7 33954 0.513 17424 8 223754 0.467 104383 9 33954 0.424 14400 10 33954 0.386 13091 11 33954 0.350 11901 12 33954 0.319 10819 13 33954 0.290 9835 14 33954 0.263 8941 15 33954 0.239 8128 16 33954 0.218 7389 7.824 578913 (excluding 1 for t=0) PW = 578913 AW = PW/7.824 = 73994.74 PW AW Design A 574864.21 73477.20 Design B 578913.30 73994.74