Question

The City of San Antonio is considering various options for providing water in its 50-year plan, including desalting. One brackish aquifer is expected to yield desalted water that will generate revenue of $4.1 million per year for the first 5 years, after which less production will decrease revenue by 10% per year each year. If the aquifer will be totally depleted in 23 years, what is the present worth of the desalting option revenue at an interest rate of 5% per year?

The present worth of the desalting option revenue at an interest rate of 5% per year is determined to be $

Answer 1

As per the question City of San Antonio is considering various options for providing water in 50 year plan and opted for aquifer for desalting the water

The revenue generated in the year 1 to 5 from the aquifer =$4,100,000

From the 6^th year to 23^rd year the revenue decreases by 10% per year each year

So the revenue or cash flow (from 6^th year to 23^rd year) in current year = Cash flow of previous year –(Cash flow of previous year) x (10/100)

The effective life of the aquifer = 23 years

Rate of interest (r) = 5% =0.05

Present Value Factor (PVF) @5% = (1+ r)^-N = (1+ 0.05)^-N

Where ,    rate of interest (r) = 0.05 and N= number of years

Year(N)	Cash Flow in $	Present Value Factor (PVF) @5%	Present Value in $ =Cash flow X PVF
1	4100000	0.95238095	3904761.905
2	4100000	0.90702948	3718820.862
3	4100000	0.86383760	3541734.154
4	4100000	0.82270247	3373080.147
5	4100000	0.78352617	3212457.283
6	3690000	0.74621540	2753534.814
7	3321000	0.71068133	2360172.697
8	2988900	0.67683936	2023005.169
9	2690010	0.64460892	1734004.431
10	2421009	0.61391325	1486289.512
11	2178908.1	0.58467929	1273962.439
12	1961017.29	0.55683742	1091967.805
13	1764915.56	0.53032135	935972.4036
14	1588424	0.50506795	802262.0582
15	1429581.6	0.48101710	687653.1927
16	1286623.44	0.45811152	589417.0223
17	1157961.1	0.43629669	505214.5923
18	1042164.99	0.41552065	433041.0791
19	937948.49	0.39573396	371178.0674
20	844153.64	0.37688948	318152.6288
21	759738.28	0.35894236	272702.2547
22	683764.45	0.34184987	233744.7891
23	615388	0.32557131	200352.6747
Net present worth (NPW) =			$35823481.98

The present worth (NPW) of the revenue from the desalting aquifer option at an interest rate of 5% per year is $35823481.98