i.
Choice Table for interest Rates from 0% to 25%.
Answer to Problem 11P
Choice table for both specification plan has been made.
Explanation of Solution
Given:
Cost of resurfacing a road = $1.5 M
Annual Maintenance = $120K
Time period = 10 years.
Calculation:
Current Specification:
Current Plan | Maintenance Cost | Initial Cost Annuity = 1500000/13.1808 | FV = A×(1.06^10)/0.6 | Total Cost | PV of Perpetuity = A/i | |
13.181 | ||||||
0.01 | 120000 | 113802 | 233802 | 23380200 | ||
0.02 | 120000 | 113802 | 233802 | 11690100 | ||
0.03 | 120000 | 113802 | 233802 | 7793400 | ||
0.04 | 120000 | 113802 | 233802 | 5845050 | ||
0.05 | 120000 | 113802 | 233802 | 4676040 | ||
0.06 | 120000 | 113802 | 233802 | 3896700 | ||
0.07 | 120000 | 113802 | 233802 | 3340029 | ||
0.08 | 120000 | 113802 | 233802 | 2922525 | ||
0.09 | 120000 | 113802 | 233802 | 2597800 | ||
0.1 | 120000 | 113802 | 233802 | 2338020 | ||
0.11 | 120000 | 113802 | 233802 | 2125473 | ||
0.12 | 120000 | 113802 | 233802 | 1948350 | ||
0.13 | 120000 | 113802 | 233802 | 1798477 | ||
0.14 | 120000 | 113802 | 233802 | 1670014 | ||
0.15 | 120000 | 113802 | 233802 | 1558680 | ||
0.16 | 120000 | 113802 | 233802 | 1461263 | ||
0.17 | 120000 | 113802 | 233802 | 1375306 | ||
0.18 | 120000 | 113802 | 233802 | 1298900 | ||
0.19 | 120000 | 113802 | 233802 | 1230537 | ||
0.2 | 120000 | 113802 | 233802 | 1169010 | ||
0.21 | 120000 | 113802 | 233802 | 1113343 | ||
0.22 | 120000 | 113802 | 233802 | 1062736 | ||
0.23 | 120000 | 113802 | 233802 | 1016530 | ||
0.24 | 120000 | 113802 | 233802 | 974175 | ||
0.25 | 120000 | 113802 | 233802 | 935208 |
Proposed Plan
Proposed Plan | Maintenance Cost | Initial Cost Annuity = 2100000/23.276 | FV = A×(1.06^15-1)/0.6 | Total Cost | PV of Perpetuity = A/i |
23.276 | |||||
0.01 | 90000 | 90221.68758 | 180221.7 | 18022168.76 | |
0.02 | 90000 | 90221.68758 | 180221.7 | 9011084.38 | |
0.03 | 90000 | 90221.68758 | 180221.7 | 6007389.587 | |
0.04 | 90000 | 90221.68758 | 180221.7 | 4505542.19 | |
0.05 | 90000 | 90221.68758 | 180221.7 | 3604433.752 | |
0.06 | 90000 | 90221.68758 | 180221.7 | 3003694.793 | |
0.07 | 90000 | 90221.68758 | 180221.7 | 2574595.537 | |
0.08 | 90000 | 90221.68758 | 180221.7 | 2252771.095 | |
0.09 | 90000 | 90221.68758 | 180221.7 | 2002463.196 | |
0.1 | 90000 | 90221.68758 | 180221.7 | 1802216.876 | |
0.11 | 90000 | 90221.68758 | 180221.7 | 1638378.978 | |
0.12 | 90000 | 90221.68758 | 180221.7 | 1501847.397 | |
0.13 | 90000 | 90221.68758 | 180221.7 | 1386320.674 | |
0.14 | 90000 | 90221.68758 | 180221.7 | 1287297.769 | |
0.15 | 90000 | 90221.68758 | 180221.7 | 1201477.917 | |
0.16 | 90000 | 90221.68758 | 180221.7 | 1126385.548 | |
0.17 | 90000 | 90221.68758 | 180221.7 | 1060127.574 | |
0.18 | 90000 | 90221.68758 | 180221.7 | 1001231.598 | |
0.19 | 90000 | 90221.68758 | 180221.7 | 948535.1979 | |
0.2 | 90000 | 90221.68758 | 180221.7 | 901108.438 | |
0.21 | 90000 | 90221.68758 | 180221.7 | 858198.5124 | |
0.22 | 90000 | 90221.68758 | 180221.7 | 819189.4891 | |
0.23 | 90000 | 90221.68758 | 180221.7 | 783572.5548 | |
0.24 | 90000 | 90221.68758 | 180221.7 | 750923.6983 | |
0.25 | 90000 | 90221.68758 | 180221.7 | 720886.7504 |
Conclusion:
Choice table for both specification plan has been made.
ii.
Specification to be preferred when interest rate is 6%.
Answer to Problem 11P
As the Present value of
Explanation of Solution
Given:
Cost of resurfacing a road = $1.5 M
Annual Maintenance = $120K
Time period = 10 years.
Calculation:
Current Specification | ||||
Figures in Million $ | ||||
Year | Particulars | Amount | P.V Factor @ 6% | Total |
0 | Resurface cost | 1.5 | 1 | 1.50 |
1 | Annual maintenance cost | 0.12 | 0.904159 | 0.11 |
2 | Annual maintenance cost | 0.12 | 0.85298 | 0.10 |
3 | Annual maintenance cost | 0.12 | 0.804698 | 0.10 |
4 | Annual maintenance cost | 0.12 | 0.759149 | 0.09 |
5 | Annual maintenance cost | 0.12 | 0.716179 | 0.09 |
6 | Annual maintenance cost | 0.12 | 0.67564 | 0.08 |
7 | Annual maintenance cost | 0.12 | 0.637397 | 0.08 |
8 | Annual maintenance cost | 0.12 | 0.601317 | 0.07 |
9 | Annual maintenance cost | 0.12 | 0.567281 | 0.07 |
10 | Annual maintenance cost | 0.12 | 0.53517 | 0.06 |
Total | 2.35 |
Proposed Specification | ||||
Figures in Million $ | ||||
Year | Particulars | Amount | P.V Factor @ 6% | Total |
0 | Resurface cost | 2.1 | 1 | 2.10 |
1 | Annual maintenance cost | 0.09 | 0.904159 | 0.08 |
2 | Annual maintenance cost | 0.09 | 0.85298 | 0.08 |
3 | Annual maintenance cost | 0.09 | 0.804698 | 0.07 |
4 | Annual maintenance cost | 0.09 | 0.759149 | 0.07 |
5 | Annual maintenance cost | 0.09 | 0.716179 | 0.06 |
6 | Annual maintenance cost | 0.09 | 0.67564 | 0.06 |
7 | Annual maintenance cost | 0.09 | 0.637397 | 0.06 |
8 | Annual maintenance cost | 0.09 | 0.601317 | 0.05 |
9 | Annual maintenance cost | 0.09 | 0.567281 | 0.05 |
10 | Annual maintenance cost | 0.09 | 0.53517 | 0.05 |
11 | Annual maintenance cost | 0.09 | 0.504878 | 0.05 |
12 | Annual maintenance cost | 0.09 | 0.4763 | 0.04 |
13 | Annual maintenance cost | 0.09 | 0.449339 | 0.04 |
14 | Annual maintenance cost | 0.09 | 0.423905 | 0.04 |
15 | Annual maintenance cost | 0.09 | 0.39991 | 0.04 |
Total | 2.94 |
Conclusion:
As the Present value of cash outflow is less in current specification, the current specification will be selected.
iii.
Economic Difference between both specifications.
Answer to Problem 11P
As Proposed Specification has High present Value compared to Current specification and there is relatively high difference between the Cost involvements in Current plan compared to proposed plan, so it leads to economic difference.
Explanation of Solution
Given:
Cost of resurfacing a road = $1.5 M
Annual Maintenance = $120K
Time period = 10 years.
Concept used:
As Proposed Specification has High present Value compared to Current specification and there is relatively high difference between the Cost involvements in Current plan compared to proposed plan, so it leads to economic difference.
Conclusion:
As Proposed Specification has High present Value compared to Current specification and there is relatively high difference between the Cost involvements in Current plan compared to proposed plan, so it leads to economic difference.
iv.
Impact on environment due to road surfacing.
Answer to Problem 11P
- Alteration of landscape which leads to negative impact on wildlife in a number of deleterious ways.
- Mortality of wildlife due to destruction of their habitats.
- The debris from the tires of vehicles results to land pollution.
- Road noise affects birds negatively. Bird population declines due to proximity of road areas.
Explanation of Solution
Given:
Cost of resurfacing a road = $1.5 M
Annual Maintenance = $120K
Time period = 10 years.
Concept used:
- Alteration of landscape which leads to negative impact on wildlife in a number of deleterious ways.
- Mortality of wildlife due to destruction of their habitats.
- The debris from the tires of vehicles results to land pollution.
- Road noise affects birds negatively. Bird population declines due to proximity of road areas.
Conclusion:
- Alteration of landscape which leads to negative impact on wildlife in a number of deleterious ways.
- Mortality of wildlife due to destruction of their habitats.
- The debris from the tires of vehicles results to land pollution.
- Road noise affects birds negatively. Bird population declines due to proximity of road areas.
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