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 4 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?

Answer 1

Cash Flow from Year 1 to year 4 =4100000
Rate =6%
Fall in revenue from year 5 to year 20 =10%
PV of Desalting option =4100000/(1+6%)+4100000/(1+6%)^2+4100000/(1+6%)^3+4100000/(1+6%)^4+4100000*(1-10%)/(1+6%)^5+4100000*(1-10%)^2/(1+6%)^6+4100000*(1-10%)^3/(1+6%)^7+4100000*(1-10%)^4/(1+6%)^8+4100000*(1-10%)^5/(1+6%)^9+4100000*(1-10%)^6/(1+6%)^10+4100000*(1-10%)^7/(1+6%)^11+4100000*(1-10%)^8/(1+6%)^12+4100000*(1-10%)^9/(1+6%)^13+4100000*(1-10%)^10/(1+6%)^14+4100000*(1-10%)^11/(1+6%)^15+4100000*(1-10%)^12/(1+6%)^16+4100000*(1-10%)^13/(1+6%)^17+4100000*(1-10%)^14/(1+6%)^18+4100000*(1-10%)^15/(1+6%)^19+4100000*(1-10%)^16/(1+6%)^20=31142086.95