Chapter 8, Problem 11P

To determine

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.

To determine

ii.

Specification to be preferred when interest rate is 6%.

Answer to Problem 11P

As the Present value of cash outflow is less in current specification, the current specification will be selected.

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.

To determine

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.

To determine

iv.

Impact on environment due to road surfacing.

Answer to Problem 11P

1. Alteration of landscape which leads to negative impact on wildlife in a number of deleterious ways.
2. Mortality of wildlife due to destruction of their habitats.
3. The debris from the tires of vehicles results to land pollution.
4. 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:

1. Alteration of landscape which leads to negative impact on wildlife in a number of deleterious ways.
2. Mortality of wildlife due to destruction of their habitats.
3. The debris from the tires of vehicles results to land pollution.
4. Road noise affects birds negatively. Bird population declines due to proximity of road areas.

Conclusion:

1. Alteration of landscape which leads to negative impact on wildlife in a number of deleterious ways.
2. Mortality of wildlife due to destruction of their habitats.
3. The debris from the tires of vehicles results to land pollution.
4. Road noise affects birds negatively. Bird population declines due to proximity of road areas.