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 24 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 worth of desalting option is $28,238,084.2

Step-by-step explanation:

For this question we have to calculate the present value of the desalting option revenue for all the 24 years , where

for first 5 years the payment would remain $4.1 million, and after that it will keep on decreasing for the rest of the years .

The rate of interest here given is 9% and with this interest we will calculate the present value of the option, for which we will use the formula of present value factor.

PRESENT VALUE FACTOR = \frac{1}{ ( 1 + I )^{N} }

Where I is the interest rate and the N is the number of year, so

Year Payment Present value factor Present value of cash flow

(\frac{1}{ ( 1 + I )^{N} })

1 $ 4100000 .917 $ 3761468

2 $4100000 .842 $3450888

3 $ 4100000 .772 $3165952

4 $ 4100000 .708 $2904543

5 $4100000 .650 $2664719

6 $3690000 .596 $2200226

7 $ 3321000 .547 $1816701

8 $2988900 .502 $1500028

9 $2690010 .460 $1238555

10 $2421009 .422 $1022660

11 $2178908 .388 $844398.5

12 $1961017 .356 $ 697209.7

13 $1764916 .326 $575677.8

14 $1588424 .299 $475330.3

15 $1429582 .275 $392474.5

16 $1286623 .252 $324061.5

17 $1157961 .231 $267573.7

18 $1042165 .212 $220932.5

19 $937948.5 .194 $182421.3

20 $844153.6 .178 $150623.1

21 $759738.3 .164 $124367.7

22 $683764.5 .150 $102564.7

23 $615388 .138 $84923.5

24 $553849.2 .126 $69785

TOTAL PRESENT VALUE OF CASH FLOW = $28,238,084.2