.11 Using the current specifications, resurfacing a road will cost dollar 1.5M i
ID: 2757527 • Letter: #
Question
.11
Using the current specifications, resurfacing a road will cost dollar 1.5M initially, need dollar 120K in annual maintenance, and need to be resurfaced every 10 years. A proposed new specification is expected to be more resistant to wear. The resurfacing cost will be dollar 2.1M with dollar 90K in annual maintenance and resurfacing every 15 years. Develop a choice table for interest rates from 0 percentage to 25 percentage. If the highway department's interest rate is 6 percentage which specification is preferred?Explanation / Answer
Particulars
Interest Rate
Plan-A:
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23%
24%
25%
Maintenance Cost
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
Initial Cost Annuity=1,500,000/13.1808, FV=P*(1.06^10-1)/0.06 = 13.18
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
Total Cost
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
PV of Perpetuity=A/r
23380189.00
11690094.50
7793396.33
5845047.25
4676037.80
3896698.17
3340027.00
2922523.63
2597798.78
2338018.90
2125471.73
1948349.08
1798476.08
1670013.50
1558679.27
1461261.81
1375305.24
1298899.39
1230536.26
1169009.45
1113342.33
1062735.86
1016529.96
974174.54
935207.56
Particulars
Interest Rate
Plan-B:
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23%
24%
25%
Maintenance Cost
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
Initial Cost Annuity=2,100,000/23.276, FV=P*(1.06^15-1)/0.06 = 23.28
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
Total Cost
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
PV of Perpetuity=A/r
18022168.76
9011084.38
6007389.59
4505542.19
3604433.75
3003694.79
2574595.54
2252771.10
2002463.20
1802216.88
1638378.98
1501847.40
1386320.67
1287297.77
1201477.92
1126385.55
1060127.57
1001231.60
948535.20
901108.44
858198.51
819189.49
783572.55
750923.70
720886.75
A= Fixed periodic payment
r = Interest Rate or discount rate per compounding period
Based on the above tables Plan-A is a better option, in the both tables the Equal Annual Initial Cost has been calculated based on the life of the resurfacing and the rate of 6%.
Particulars
Interest Rate
Plan-A:
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23%
24%
25%
Maintenance Cost
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
$120,000
Initial Cost Annuity=1,500,000/13.1808, FV=P*(1.06^10-1)/0.06 = 13.18
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
113801.89
Total Cost
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
233801.89
PV of Perpetuity=A/r
23380189.00
11690094.50
7793396.33
5845047.25
4676037.80
3896698.17
3340027.00
2922523.63
2597798.78
2338018.90
2125471.73
1948349.08
1798476.08
1670013.50
1558679.27
1461261.81
1375305.24
1298899.39
1230536.26
1169009.45
1113342.33
1062735.86
1016529.96
974174.54
935207.56
Particulars
Interest Rate
Plan-B:
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23%
24%
25%
Maintenance Cost
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
$90,000
Initial Cost Annuity=2,100,000/23.276, FV=P*(1.06^15-1)/0.06 = 23.28
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
90221.69
Total Cost
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
180221.69
PV of Perpetuity=A/r
18022168.76
9011084.38
6007389.59
4505542.19
3604433.75
3003694.79
2574595.54
2252771.10
2002463.20
1802216.88
1638378.98
1501847.40
1386320.67
1287297.77
1201477.92
1126385.55
1060127.57
1001231.60
948535.20
901108.44
858198.51
819189.49
783572.55
750923.70
720886.75
A= Fixed periodic payment
r = Interest Rate or discount rate per compounding period
Based on the above tables Plan-A is a better option, in the both tables the Equal Annual Initial Cost has been calculated based on the life of the resurfacing and the rate of 6%.
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