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 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

Answer 1

Revenue for the 1^st 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 1^st 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 3^rd year is 4,100,000 (A1)

Calculate the PW of the geometric gradient series cash flow at the end of 2^nd 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 0^th year

Present Worth at 0^th 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