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 $

The present worth of desalting option is $28,238,084.2

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