3. In a particular locality of a state, the vehicle users take a roundabout rout

Question

3. In a particular locality of a state, the vehicle users take a roundabout route to reach certain places because of the presence of a river. This results in excessive travel time and increased fuel cost. So, the state government is planning to construct a bridge across the river. The estimated initial investment for constructing the bridge is 4,000,000. The estimated life of the bridge is 15 years. The annual operation and maintenance cost is $150,000. The value of fuel savings due to the construction of the bridge is $600,000 in the first year and it increases by $50,000 every year thereafter till the end of the life of the bridge. Check whether the project is justified

Explanation / Answer

Year

Initial Investment

Maintenance cost

Benefit(Fuel Saving)

P.V of Maintenace cost

P.V of benefit

0

4000000

1

150000

600000

1,36,363.6

5,45,454.5

2

150000

650000

1,23,966.9

5,37,190.1

3

150000

700000

1,12,697.2

5,25,920.4

4

150000

750000

1,02,452.0

5,12,260.1

5

150000

800000

93,138.2

4,96,737.1

6

150000

850000

84,671.1

4,79,802.8

7

150000

900000

76,973.7

4,61,842.3

8

150000

950000

69,976.1

4,43,182.0

9

150000

1000000

63,614.6

4,24,097.6

10

150000

1050000

57,831.5

4,04,820.5

11

150000

1100000

52,574.1

3,85,543.3

12

150000

1150000

47,794.6

3,66,425.4

13

150000

1200000

43,449.7

3,47,597.3

14

150000

1250000

39,499.7

3,29,164.1

15

150000

1300000

35,908.8

3,11,209.7

Net Present value

11,40,911.9

65,71,247.1

Total Benefit= P>.V of Benefit= 65,71,247

Total cost=Initial investment + P.V of Maintenance cost

Total cost= 11,40,911+ 40,00,000=51,40,911.9

Total Benefit/Total cost=6571247/5104911=1.2872403

Since B/C ratio (Total Benefit/Total cost) is greater than 1, the project is justified

Year

Initial Investment

Maintenance cost

Benefit(Fuel Saving)

P.V of Maintenace cost

P.V of benefit

0

4000000

1

150000

600000

1,36,363.6

5,45,454.5

2

150000

650000

1,23,966.9

5,37,190.1

3

150000

700000

1,12,697.2

5,25,920.4

4

150000

750000

1,02,452.0

5,12,260.1

5

150000

800000

93,138.2

4,96,737.1

6

150000

850000

84,671.1

4,79,802.8

7

150000

900000

76,973.7

4,61,842.3

8

150000

950000

69,976.1

4,43,182.0

9

150000

1000000

63,614.6

4,24,097.6

10

150000

1050000

57,831.5

4,04,820.5

11

150000

1100000

52,574.1

3,85,543.3

12

150000

1150000

47,794.6

3,66,425.4

13

150000

1200000

43,449.7

3,47,597.3

14

150000

1250000

39,499.7

3,29,164.1

15

150000

1300000

35,908.8

3,11,209.7

Net Present value

11,40,911.9

65,71,247.1

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