Question

The city of Waterbourne has made it a strategic goal to enhance livability in the city. The city has decided to undertake a project that will occur in two phases. During the first phase, the city will connect several of the parks with walking paths. During the second phase, the city will add water features or splash fountains to several of the parks.

The initial cost of the project will be $409250. Annual utilities for maintaining the walking paths and keeping them lit during the early evening are estimated to be $13520, with costs increasing by $157 each subsequent year. The paths will require repaving in year 9 at a cost of $49867 and again in year 19 at a cost of $65295.

The water features and splash fountains will be added to the parks at the end of year 11 at a cost of $222659. The water utilities are estimated to be $16643 per year, increasing by 12% each subsequent year. (The first payment for the water utilities will occur at the end of year 11.)

The city has secured a sponsorship from a local business to help pay for part of the project. The city will receive a grant from the business of $112755 per year, increasing by 7% each subsequent year. The city will receive the grant for 8 years. (The city will receive the first grant payment at the end of year 1.)

Using a nominal annual interest rate of 7% compounded annually and a lifespan of 28 years, what is the present worth of the entire project?

Answer 1

		Formula
Life (N)	28	U1*(P/A,I,N)	PV of U1	164,093.74
Interest rate (I)	7%	G*(P/G,I,N)	PV of G	17,776.55
Initial cost (C1)	409,250	PV(U1) + PV(G)	Total PV of annual utility cost (Pvau)	181,870.29
Annual utility cost (U1)	13,520	R9/(1+I)^9	PV of repaving in year 9 (PVr9)	27,124.34
Annual increase in utility cost (G)	157	R19/(1+I)^19	PV of repaving in year 19 (PVr19)	18,054.61
Repaving in year 9 (R9)	49,867	C11/(1+I)^11	PV of additional cost (Pvac)	105,783.69
Repaving in year 19 (R19)	65,295	[WU/(I-g)][1 - ((1+g)/(1+I))^N]	PV of water utility cost (Pvwu10) at year 10	424,457.55
Additional cost (C11)	222,659	PVwu10/(1+I)^10	PV of PVwu10 at year 0 (PVwu0)	215,772.69
Water utility cost (WU)	16,643	Since I = g, PV = AG*18/(1+I)	PV of grant (Pvag) at year 10	1,896,813.08
Annual increas in water utility cost (g)	12%	Pvag/(1+I)^10	PV of Pvag at year 0 (PVag0)	964,243.59
Annual grant (AG)	112,755	-C1-Pvau-PVr9 -PVr19-Pvac-PVwu0+PVag0	Present Worth (PW) of the project	6,387.96
Increase in annual grant (g1)	7%