Question

The city of Carlsbad in California is considering building a $300 million water-desalination plant. The facility would be the largest in the Western Hemisphere, producing 50 million gallons of drinking water a day – enough to supply about 100,000 homes. This plant, which uses improved membranes and pumping system to bring down the energy cost to $0.90 in electricity to produce 10,000 gallons of water. Suppose the desalination plant is fully operational and you expect to operate it continuously for 20 years, with an estimated salvage value of $20 million. The operating and maintenance costs (excluding energy cost) amount to $15 million the first year and will increase at a rate of 3% per year. If the city plans to sells the water for about $925 per acre-foot (an acre-foot is 325,851 gallons – enough water for four people per year.), can it recover the capital cost and other operating costs? Assume the city’s interest rate for this water project is known to be 6%

Answer 1

Answer:

Statement of Annual Cost and Present Value of Cash Outflows:

Year	Cost of Water-deslination Plant	Electricity Cost	Operating & Maintenance Cost	Total Cost	PVIF at 6% p.a.	Present Value of Cash Outflow
0	$300,000,000	0	0	$300,000,000	1	$300,000,000
1		$16,200,000	$15,000,000	$31,200,000	0.9434	$29,434,080
2		$16,200,000	$15,450,000	$31,650,000	0.8900	$28,168,500
3		$16,200,000	$15,913,500	$32,113,500	0.8396	$26,962,495
4		$16,200,000	$16,390,905	$32,590,905	0.7921	$25,815,256
5		$16,200,000	$16,882,632	$33,082,632	0.7473	$24,722,651
6		$16,200,000	$17,389,111	$33,589,111	0.7050	$23,680,323
7		$16,200,000	$17,910,784	$34,110,784	0.6651	$22,687,082
8		$16,200,000	$18,448,108	$34,648,108	0.6274	$21,738,223
9		$16,200,000	$19,001,551	$35,201,551	0.5919	$20,835,798
10		$16,200,000	$19,571,598	$35,771,598	0.5584	$19,974,860
11		$16,200,000	$20,158,746	$36,358,746	0.5268	$19,153,787
12		$16,200,000	$20,763,508	$36,963,508	0.4970	$18,370,863
13		$16,200,000	$21,386,413	$37,586,413	0.4688	$17,620,510
14		$16,200,000	$22,028,006	$38,228,006	0.4423	$16,908,247
15		$16,200,000	$22,688,846	$38,888,846	0.4173	$16,228,315
16		$16,200,000	$23,369,511	$39,569,511	0.3936	$15,574,560
17		$16,200,000	$24,070,597	$40,270,597	0.3714	$14,956,500
18		$16,200,000	$24,792,714	$40,992,714	0.3503	$14,359,748
19		$16,200,000	$25,536,496	$41,736,496	0.3305	$13,793,912
20	($20,000,000)	$16,200,000	$26,302,591	$42,502,591	0.3118	$13,252,308
	Salvage Value
			Present Value of Cash Outflow	$704,238,019

Calculation of Present Value of Cash Inflows

Annual Cash Inflows = $925 per acre-foot x 55,240 Acre-foot per year = $51,097,000

1 acre-foot = 325,851 gallons

50 Million gallons = 50,000,000 / 325,851 acre-foot = 153.44 acre-foot

Total Acre-foot per year = 153.44 acre-foot x 360 days in a year = 55,240 Acre-foot per year

Present Value of Cash Inflows for 20 years = Annual Cash Inflows x PVIFA (6%, 20) = $51,097,000 x 11.47 = $586,082,590

Net Present Value = Present Value of Cash Inflows – PV of Cash Outflows = $586,082,590 - $704,238,019= -$118,155,429(negative)

Since the NPV is negative, it is not advisable to consider building of water desalination plant.

Calcuation of Price per Acre-foot of the water required to breakeven:

Let Sale Price per acre-foot of the water = S

To breakeven,

PV of Cash Inflow must be equal to PV of Cash Outflow

S x 55,240 acre-foot per year x PVIFA (6%, 20) = $704,238,019

S x 55,240 x 11.47 = $704,238,019

S = $704,238,019 / 633,602.80 = $1,111.48

To breakeven the price per acre-foot of the water required to be $1,111.48 acre-foot