Question

A new highway is to be constructed. Design A calls for a concrete pavement costing​$90 per foot with a 20​-year​  life;four paved ditches costing ​$5 per foot​ each; and four box culverts every​ mile, each costing ​$9,000 and having a 20​-year life. Annual maintenance will cost ​$1,700 per​ mile; the culverts must be cleaned every five years at a cost of​$350 each per mile. Design B calls for a bituminous pavement costing ​$45 per foot with a 10-year ​life;four sodded ditches costing ​$1.65 per foot​ each; and three pipe culverts every​ mile, each costing ​$2,100 and having a 10​-year life. The replacement culverts will cost ​$2,400 each. Annual maintenance will cost ​$2,600 per​ mile; the culverts must be cleaned yearly at a cost of ​$225 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 20​-year period. Find the most economical design on the basis of AW and PW if the MARR is 6​%per year.

Answer 1

1 mile=5280 feet

Design A

Total construction cost per mile=(90+5)*5280= $501600

Culvert Cost for each mile= 9000*4=$36000

Annual Maintenance Cost of highway= $1700 per mile for 20 year i.e. $19498.87 of Present Value.Calculation is given below:

The cleaning cost of culvert is $350 every five year. Present Value is $603.02

Year	Culvert Cleaning Cost	Present Value (i.e. Cost/1.06^year)
5	$                       350.00	$                                                261.54
10	$                       350.00	$                                                195.44
15	$                       350.00	$                                                146.04
	Total	$                                                603.02

So, Present Value for total cost of design A for 20 year per mile= 603.02+19498.87+501600+36000=$557701.9

Design B

Construction cost oh highway per mile=(45+1.65)*5280=$246312

Culvert making cost per mile=2100*3=$6300

Annual maintenance for highway and ditch per mile= 2600+1.45*5280=$10256

Annual Culvert cleaning cost per mile is= 225*3=$675

So, total annual maintenance cost for design B= (10256+675)=$10931 for each of the 10 year i.e. $80453.11

PMT	10931
rate	6%
nper	10
PV	($80,453.11)

Total present Value of cost for Design B per mile for 10 year= (246312+6300+80453.11)=$333065.1

Now, after 10 year you need another $33065.1 to last for another 10 year ignoring inflation

So, for 20 present value of 20 year equivalent cost for design B= 333065.1+333065.1/1.06^10=$519046.9

As the present value of 20 year equivalent cost for Design B is lower than design A, design B should be accepted.

The AW for Design A and Design B is $557701.9/20=$27885.1 and 519046/20=25952.35 respectively

Design B is most economical.