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 3 years, after which less production will decrease revenue by 10% per year each year. If the aquifer will be totally depleted in 20 years, what is the present worth of the desalting option revenue at an interest rate of 6% per year?
The present worth of the desalting option revenue at an interest rate of 6% per year is determined to be
Revenue for the 1st 3 years = 4,100,000
Then it decreases by 10% per year
Life = 20 years
Calculate the PW at interest rate of 6%
First calculate the PW of the 1st two years of revenues by putting the uniform cash flow factor.
4,100,000 (P/A, 6%, 2)
4,100,000 (1.8334) = 7,516,940
Let the cash flow of 3rd year is 4,100,000 (A1)
Calculate the PW of the geometric gradient series cash flow at the end of 2nd year.
P = A1 [1 – (1+g) N (1+i) –N ÷ i-g], where g = 10% and i=6%
P = 4,100,000 [1 – (1+0.10) 18 (1+0.06) –18 ÷ 0.06-0.10], where g = 10% and i=6%
P = 4,100,000 (23.69706)
P = 97,157,957
Now calculate the present value of the above amount at the 0th year
Present Worth at 0th year
PW = F (1+i) -n
PW = 97,157,957 (1.06) -2
PW = 86,470,236
Total PW = 86,470,236 + 7,516,940 = 93,987,176
The present worth of the desalting option revenue at an interest rate of 6% per year is $93,987,176
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