Question

You are looking to purchase a new vehicle for $24,500. This vehicle gets 21 mpg and you average driving 15,000 miles per year. You expect that gasoline will average $2.40 per gallon for the first year and will increase 15% per year but it will never get above $5 per gallon because of government controls. Maintenance is included for the first two years but after that you think that maintenance will cost $1,000 and increase by 10% per year after that. The vehicle will lose 30% of its value the first year but the salvage value will only decrease by 10% per year after that. For an interest rate of 6%, what is the economic life of the vehicle?

Answer 1

						Present value(PV) of Cash flow=(Cash flow)/((1+i)^N)
						i=Interest rate=6%=0.06
						N=Year of cash flow
						Expenses on gasoline in year1	$                1,714	(15000/21)*$2.4
						Expenses on gasoline in year2	$                1,971	(1714*1.15)
						Maximum expenses on gasoline	$                3,571	(15000/21)*$5
						Expenses on gasoline in year (N+1)=Expenses on gasoline in Year(N)*1.15, subject to maximum $3571
						Maintenance cost in year2	$                1,100	(1000*1.1)
						Maintenance cost in year (N+1)=Maintenace cost in year (N)*1.1
						Salvage Value at the end of year1	$17,150		(1-0.3)*24500)
						Salvage value at the end of year2	$15,435	(17150*(1-0.1)
						Salvage value at the end of Year N=17150*(1-0.1)^(N-1)
					N	Year	0	1	2	3	4	5	6	7	8
					A	Initial cost	$24,500
					B	Expenses on gasoline		$      1,714	$        1,971	$     2,267	$     2,607	$      2,998	$     3,448	$     3,571	$          3,571
					C	Maintenance cost		$0	$0	$1,000	$1,100	$1,210	$1,331	$1,464	$1,611
					D=A+B+C	Total Cost	$24,500	$      1,714	$        1,971	$     3,267	$     3,707	$      4,208	$     4,779	$     5,036	$          5,182
					PV=D/(1.06^N)	Present Value of costs	$24,500	$      1,617	$        1,755	$     2,743	$     2,936	$      3,145	$     3,369	$     3,349	$          3,251
					CPV	Cumulative present value of costs	$24,500	$    26,117	$      27,872	$   30,615	$   33,551	$    36,696	$   40,065	$   43,414	$        46,665
					S	Salvage Value		$17,150	$15,435	$13,892	$12,502	$11,252	$10,127	$9,114	$8,203
					NPV=CPV-S	Net Present Value of costs		$      8,967	$      12,437	$   16,723	$   21,049	$    25,444	$   29,938	$   34,300	$        38,462
Using PMT function of Excel with Rate=6%,Nper=N,PV=-NPV						Equivalent Annual Cost		$9,505.29	$6,783.50	$6,256.41	$6,074.59	$6,040.31	$6,088.32	$6,144.30	$6,193.84
						ECONOMIC LIFE OF THE VEHICLE	5 YEARS	(The Equivalent Annual Cost is minimum ($6040) at 5 years
							Year	Equivalent annual cost
							1	$9,505.29
							2	$6,783.50
							3	$6,256.41
							4	$6,074.59
							5	$6,040.31
							6	$6,088.32
							7	$6,144.30
							8	$6,193.84