Question 15.17: Evaluating the Cost of Pumping Sewage Greenacres is a rapidl...
Evaluating the Cost of Pumping Sewage
Greenacres is a rapidly growing suburb of Brownsky, a major Sunbelt city. Greenacres pays Brownsky to treat and dispose of its sewage. Greenacres must pump the sewage up 200 feet, from near the river level to the top of the bluff where Brownsky sits. The electrical cost this year (year 1) will be $1.25 million. Greenacres is expected to grow at 7%. The estimated inflation rate in the cost per kWh is 5%. The economy is inflating at 3%. Greenacre’s interest rate is 8%. What is the PW of the pumping cost for year 10?
The cost in year 10 occurs 9 years later than the $1.25M cost in year 1. Each year, a kilowatt-hour of electricity costs 5% more and each year 7% more kWhs are used. Thus, the nominal-dollar cost of the pumping is (1.25 · 10^{6}) · (1.05^{9}) · (1.07^{9}), which equals 3.57M nominal dollars. On the other hand, since f is 3%, the real value of that $3.57M is only 2.73M year-1 dollars (equals 3.57/1.03^{9}). Finally, the present worth of the year 10 pumping cost equals $1.27M year-1 dollars (equals 2.73/1.08^{10}).