Question

A new highway is to be constructed. Design A calls for a concrete pavement costing $90 per foot with a 20- year life; two paved ditches costing $3 per foot each; and three box culverts every mile, each costing $9,000 and having a 20- year life. Annual maintenance will cost $1,800 per mil e; the culverts must be cleaned every five years at a cost of $450 each per mile.
Design B calls for a bituminous pavement costing $45 per foot with a 10- year life; two sodded ditches costing $1.50 per foot each; and three pipe culverts every mile, each costing $2,250 and having a 10 -year life. The replacement culverts will cost $2,400 each. Annual maintenance will cost $2,700 per mile; the culverts must be cleaned yearly at a cost of $225 each per mile; and the annual ditch maintenance will cost $1.50 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. (Note: assuming cleaning also occurs at the end of the life time)

note ;

1:comparision is based on 1 mile.

2:1 mile = 5280feet

for this problem:

a: Develop the cash flow table for each design

b:set up the cash flow equation but do not perform the numerical computations.

Answer 1

Answer:

Cost for concerete pavement = $ 90 X 5280

Cost for concerete pavement = $ 475,200

cost for each paved ditch = $ 3 X 5280

cost for each paved ditch = $ 15,840

cost for 2 paved ditch = $ 31,680

cost of three box culverts every mile = $ 9000 X 3

cost of three box culverts every mile = $ 27,000

Total cost for concrete pavement in year 0 = $ 475,200 + $ 31,680 + $ 27,000

Total cost for concrete pavement in year 0 = $ 533,880

Annual maintenance = $ 1800

Annula maitenance in year 5 = $ 1,800 + $ 450 ( $ 2,250)

The cash flow table for design A

Design A

year Cash outflows

0 $533,880

1 $1,800

2 $1,800

3 $1,800

4 $1,800

5 $2,250

6 $1,800

7 $1,800

8 $1,800

9 $1,800

10 $2,250

11 $1,800

12 $1,800

13 $1,800

14 $1,800

15 $2,250

16 $1,800

17 $1,800

18 $1,800

19 $1,800

20 $1,800

============================================================================

Design B

Cost of pavement for design B = $ 45 X 5280

Cost of pavement for design B = $ 237,600

cost of sodded ditches = $ 1.50 X 5280

cost of sodded ditches = $ 7,920

cost of two sodded ditches = $ 15,840

Cost of three pipe culverts = $ 2,250 X 3

Cost of three pipe culverts = $ 6,750

Cost of replacement culverts = $ 2400 X 3

Cost of replacement culverts = $ 7,200

annual maintenance = $ 2,700

cost of cleaning culverts = $ 225 X 3

cost of cleaning culverts = $ 675

annual ditch maintenance = $ 1.50 X 5280

annual ditch maintenance = $ 7,920

Initial cost of bituminous pavement = $ 237,600 + $ 7,920 + $ 6,750

Initial cost of bituminous pavement = $ 252,270

Annual cost of maintenance = $ 2700 + $ 225 + $ 1.50 X 5280

Annual cost of maintenance = $ 10,845

Year 11 cost = $ 237,600 + $ 7,920 + $ 2400 x 3 ( cost of replacement culverts)

Year 11 cost = $ 252,720

Cash flow table for design B

Design B

year Cash outflows

0 $252,270

1 $10,845

2 $10,845

3 $10,845

4 $10,845

5 $10,845

6 $10,845

7 $10,845

8 $10,845

9 $10,845

10 $10,845

11 $252,720

12 $10,845

13 $10,845

14 $10,845

15 $10,845

16 $10,845

17 $10,845

18 $10,845

19 $10,845

20 $10,845

========================================================================

b) cash flow equation for design A equivalent wortth = $ 533,880 ( A/P , 6% , 20 years) + $ 1800 + $ 2,250 ( P/A , 6% , 20 years )

Cash flow equation for design B equivalent wortth = $ 252,270 ( A/P , 6% , 20 years) + $ 10,845 + $ 252,720 ( P/A , 6% , 20 years )

Explanation: