Question

A construction company wants to buy or lease some new office equipment. The office equipment could be purchased for $8500 now and pay a monthly maintenance fee of $75 per month. The second option would be leasing the equipment for $800 per month with no maintenance fee. The company uses a 15%/year hurdle rate (MARR) compounded monthly.

a) What is the breakeven in number of months between the two options?

b) If the study period for the analysis is 1 year, which option should I choose?

Please do not use excel.

Answer 1

a]	The breakeven number of months would make
	the PV of the cash flows of the two options
	equal. The monthly interest rate = 15%/12 = 1.25%.
	So,
	8500+75*PVIFA(1.25,n) = 800*PVIFA(1.25,n)
	8500 = 725*PVIFA(1.25,n)
	PVIFA(1.25,n) = 8500/725 =	11.7241
	PVIFA for r = 1.25% and n = 13 = 11.9302
	PVIFA for r = 1.25% and n = 12 = 11.0793
	So, breakeven n = 12+(11.7241-11.0793)/(11.9302-11.0793) =	12.76
	Breakeven months = 12.76 months
b]	PV of the buy option = -8500-75*(1.0125^12-1)/(0.0125*1.0125^12) =	$         -9,331
	PV of the lease option = -800*(1.0125^12-1)/(0.0125*1.0125^12) =	$         -8,863
	As the PV of cash outflows for lease option is lower, leasing should be chosen.