Question

The property appraisal district for Marin County has just installed new software to track residential market values for property tax computations. The manager wants to know the total equivalent cost of all future costs incurred when the three county judges agreed to purchase the software system. If the new system will be used for the indefinite future, find the equivalent value (a) now and (b) for each year hereafter. The system has an installed cost of $174515 and an additional cost of $74515 at year 17. The annual software maintenance contract cost is $4515 for the first 7 years, $6772.5 for the second 6 years, $9030 for the third 4 years, and $17,776 thereafter. In addition, there is expected to be a recurring major upgrade cost of $17451 every 14 years. Assume that i= 7% per year for county funds.

Answer 1

	A	Present Value of installed Cost	$174,515
	B	Present Value of additional cost in year17	$23,590	(74515/(1.07^17)
		Annual software maintenance costs:
	Pmt	Annual Cost from Year 1 to 7	$4,515
	Rate	Discount Rate	7%
	Nper	Number of Years	7
	PV	Present Value of 7 years annual cost $4515	$24,332.64
		(Using PV function of excel)
	C	Present Value annual from year 1 to 7	$24,333
		Annual Cost of$6772.5 from year8 to 13
	Pmt	Annual Cost from Year 8 to 13	$6,772.50
	Rate	Discount Rate	7%
	Nper	Number of Years	6
	PV	Present Value of 6 years cost at end of year7	$32,281.39
		(Using PV function of excel)
	D	Present Value now of annual cost from year 8 to 13	$20,103.23	(32281.39/(1.07^7)
		Annual Cost of$9030 from year14 to 17
	Pmt	Annual Cost from Year 14to 17	$9,030.00
	Rate	Discount Rate	7%
	Nper	Number of Years	4
	PV	Present Value of 4 years cost at end of year13	$30,586.52
		(Using PV function of excel)
	E	Present Value now of annual cost from year 14 to 17	$12,692.32	(30586.52/(1.07^13)
		Annual Cost of $17776 from year 18 to perpetuity
		Value of annual cost at end of year17=17776/0.07	$253,942.86
	F	Present Value now of annual cost from year 18 forever	$80,391.81	(253942.86/(1.07^17)
		Cost of Recurring Major Upgrades:
		Discount Rate for 14 years=(1.07^14)-1=	1.57853415
		Recurring Major upgrade cost every 14 years	$17,451
	G	Present Valueof Recurring Major Upgrade Cost=	$11,055.19	(17451/1.5783415)
	(a)	Equivalent Cost Now=A+B+C+D+E+F+G	$346,679.73
	(b)	Equivalent Cost for each year hereafter=346679.73*0.07=	$24,267.58