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 8% per year?

The present worth of the desalting option revenue at an interest rate of 8% per year is determined to be

Answer 1

The present value of revenue is $ 29,798,017

The explanation is as follows:

Year	Cash flows	PVF @8%	Present value
1	4,100,000	0.926	3796296
2	4,100,000	0.857	3515089
3	4,100,000	0.794	3254712
4	4,100,000	0.735	3013622
5	4,100,000	0.681	2790391
6	3690000	0.630	2325326
7	3321000	0.583	1937772
8	2988900	0.540	1614810
9	2690010	0.500	1345675
10	2421009	0.463	1121396
11	2178908	0.429	934496.3
12	1961017	0.397	778746.9
13	1764916	0.368	648955.8
14	1588424	0.340	540796.5
15	1429582	0.315	450663.7
16	1286623	0.292	375553.1
17	1157961	0.270	312960.9
18	1042165	0.250	260800.8
19	937948.5	0.232	217334
20	844153.6	0.215	181111.7
21	759738.3	0.199	150926.4
22	683764.4	0.184	125772
23	615388	0.170	104810
PRESENT VALUE OF CASH INFLOWS			29798017