The town of Glenforest needs an additional supply of water f

The town of Glenforest needs an additional supply of water from a river. The town engine s selected two plans for comparison. a. Gravity plan: Divert water from upstream and carry the water through s pipeline to the b. Pumping plan: Pump water from the river closer to the town. This plan is built in two town stages, the first stage installed initially and the second stage installed ten years after Assume a 10% painterest rate and a 30 year life with no salvage value. The cost of each alternative is as follows , Alt X Alt Y Initial investment Additional investment in the 10h year Operation & maintenance cost Power cost Gravity plan $2,800K S10K per year 1,400K $200K $25K per year S50K per year Determine the more economical plan based on Present worth method

Solution

A)

Cash Flow Diagram

Alternative X (Gravity Plan)

Alternative Y (Pumping Plan)

Initial Investment

$                            2,800,000.00

$                                1,400,000.00

Additional Investment in 10th Year

$                                                  -  

$                                   200,000.00

Operation and Maintenance Cost for 30 Years

$                                300,000.00

$                                   750,000.00

Power Cost for 30 Years

$                                                  -  

$                                1,500,000.00

Total Cost for 30 Years

$                            3,100,000.00

$                                3,850,000.00

B)

Calculations

Alternative X (Gravity Plan)

Alternative Y (Pumping Plan)

Operation and Maintenance Cost per Year

$                                  10,000.00

$                                      25,000.00

Power Cost Per Year

$                                                  -  

$                                      50,000.00

Cost per year except Additional investment and initial Investment

$                                  10,000.00

$                                      75,000.00

Annuity Factor for 30 Years at 10% Discount Rate

9.427

9.427

Discounted Cash Flows for 30 Years

$                                  94,269.14

$                                   707,018.59

Add: Discounted Cash Flow at 10th Year for Additional Investment (200000*0.385)

$                                                  -  

$                                      77,108.60

Add: Initial Cash Outflow

$                            2,800,000.00

$                                1,400,000.00

Total Discounted Cash Flow

$                            2,894,269.14

$                                2,184,127.19

C)

Analysis

Alternative X (Gravity Plan)

Alternative Y (Pumping Plan)

Total Discounted Cost

$                            2,894,269.14

$                                2,184,127.19

D)

Selection will be done on the basis of Cost of each alternative. The alternative which has lowest Net Present Value will be selected.

E)

Decision: Alternative Y(Pumping Plan) is better because it has Least NPV Over the Period of 30 Years.

Working note 1

Year

Value of $ 1 discounted at 10%

1

0.909

2

0.826

3

0.751

4

0.683

5

0.621

6

0.564

7

0.513

8

0.467

9

0.424

10

0.386

11

0.350

12

0.319

13

0.290

14

0.263

15

0.239

16

0.218

17

0.198

18

0.180

19

0.164

20

0.149

21

0.135

22

0.123

23

0.112

24

0.102

25

0.092

26

0.084

27

0.076

28

0.069

29

0.063

30

0.057

Total

9.427

Working note 2 – Initial Cash flow will not be discounted as it will have to be incurred at the start of the year ie Year 0.

A)	Cash Flow Diagram
		Alternative X (Gravity Plan)	Alternative Y (Pumping Plan)
	Initial Investment	$                            2,800,000.00	$                                1,400,000.00
	Additional Investment in 10th Year	$                                                  -	$                                   200,000.00
	Operation and Maintenance Cost for 30 Years	$                                300,000.00	$                                   750,000.00
	Power Cost for 30 Years	$                                                  -	$                                1,500,000.00
	Total Cost for 30 Years	$                            3,100,000.00	$                                3,850,000.00