Question

You purchase a car that has an initial cost of $25,000. Property tax on the car will be $500 when you purchase the car and will decrease by 5% per year because the county estimates that the tax value will depreciate. Fuel cost in the first year is $1,050 and is estimated to increase by $125 per year because of expected increases in fuel cost. The cost to insure this car with you as the driver is estimated to be $1,500 in the first year, and to decrease by 10% per year as the car loses value 2 and as you age into a less risky driver category. Maintenance and repair costs are expected to be $100 in the first year, and to increase by $150 per year. At the end of 10 years, you plan to sell the car and expect that you can get $5,000 as the salvage value. The interest rate is 7%, compounded annually.

e) What is the equivalent annual maintenance and repair cost ($/year)?

f) What is the equivalent annual salvage value ($/year)?

g) Suppose that the equivalent uniform annual cost is $7,000 per year (this is not the correct answer to a previous part), and the vehicle is driven 12,500 miles per year. What is the average cost per mile ($/mile)?

Answer 1

First, lets see the overall cashflows. These are shown in the table below. Also shown are the NPV and the Equalized Annaual Cost (EAC), which is same as UAC.

Year	Purchase Cost	Tax	Fuel Cost	Insurance Cost	Maintenance	Salvage	Net Cashflow
0	-25000	-500					-25500
1		-475	-1050	-1500	-100	0	-3125
2		-451	-1175	-1350	-250	0	-3226
3		-429	-1300	-1215	-400	0	-3344
4		-407	-1425	-1094	-550	0	-3476
5		-387	-1550	-984	-700	0	-3621
6		-368	-1675	-886	-850	0	-3778
7		-349	-1800	-797	-1000	0	-3946
8		-332	-1925	-717	-1150	0	-4124
9		-315	-2050	-646	-1300	0	-4311
10		-299	-2175	-581	-1450	5000	495
NPV					($4,859.69)	$2,541.75
EAC					($691.91)	$361.89

Find below the same table, but in formulas format for understanding.

D F Maintenance Tax Insurance Cost Salvage Purchase Cost -25000 -1500 | A 1 Year 20 3 1 4 2 5 3 64 75 8 6 9 7 10 8 11 9 12 10 13 NPV 14 EAC C Fuel Cost -500 =C2*0.95 -1050 =C3*0.95 =D3-125 =C4*0.95 =D4-125 =C5*0.95 =D5-125 =C6*0.95 =D6-125 =C7*0.95 =D7-125 =C8*0.95 =D8-125 =C9*0.95 =D9-125 =C10*0.95=D10-125 =C11*0.95=D11-125 =E3*0.9 =E4*0.9 =E5*0.9 =E6*0.9 =E7*0.9 =E8*0.9 =E9*0.9 =E10*0.9 =E11*0.9 -100 =F3-150 =F4-150 =F5-150 =F6-150 =F7-150 =F8-150 =F9-150 =F10-150 =F11-150 =NPV(7%,F3:F12) =-PMT(7%,10,F13) Η Net Cashflow =SUM(B2:G2) =SUM(B3:43) =SUM(B4:G4) =SUM(B5:G5) =SUM(B6:66) =SUM(B7:67) =SUM(B8:48) =SUM(B9:69) =SUM(B10:G10) =SUM(B11:G11) =SUM(B12:G12) O O 5000 =NPV(7%,G3:G12) --PMT(7%,10,413)

Now we can easily answer the questions.

F. EAC of maintenance is -691.91, as shown.

G. EAC of salvage is 361.89, as shown.

H. Average cost per mile=7000/12500=.56