Question

You are evaluating the purchase of a vehicle for your business. You've decided that the best choice is a car that will cost you $35,000, but you're uncertain how long you should plan on holding the car before you replace it. The table below lists the running costs and salvage value of the vehicle for each year.

	1	2	3	4	5
Running Costs	-3000	-3500	-4000	-4500	-5000
Salvage Value	25000	20000	15000	10000	5000

What is the annual equivalent cost of replacing the vehicle every 5 years? Assume your cost of capital is 16.1%. Enter your answer to the nearest cent. Ignore taxes.

(Your answer will be a cost, and therefore a negative number. Don't forget the minus sign.)

Answer 1

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P
2
3
4		Equivalent annual cost should be such that the present value annual cost should be equal to the NPV of the cashflows.
5
6		Cash Flow for a vehicle with 5 year life will be as follows:
7		Year	0	1	2	3	4	5
8		Initial investment	-35000
9		Running Costs		-3000	-3500	-4000	-4500	-5000
10		Salvage						5000
11		Net Cash Flow	-35000	-3000	-3500	-4000	-4500	0
12
13		Cash flow of replacing the vehicle every 5 year will be as follows:
14		Year	0	1	2	3	4	5	6	7	8	9	10	…
15		1st Vehicle	-35000	-3000	-3500	-4000	-4500	0
16		2nd Vehicle						-35000	-3000	-3500	-4000	-4500	0
17		3rd Vehicle											-35000	…
18		…
19		Net Cash Flow	-35000	-3000	-3500	-4000	-4500	-35000	-3000	-3500	-4000	-4500	-35000	…
20
21		Cost of cpaital	16.10%
22
23		NPV of replacing vehicle every 5 years is X then after 5 years also NPV replacing vehicle every 5 years will be X.
24		Thus NPV of all the cash flow can be found as follows:
25
26		Year	0	1	2	3	4	5
27		Net Cash Flow	-35000	-3000	-3500	-4000	-4500	X
28		MARR (i)	16.10%
29		(P/F,i,n) for each year	1.00	0.86	0.74	0.64	0.55	0.47	=1/((1+$D28)^I26)
30		Present Value of cash flows = FCF*(P/F,i,n)	($35,000.00)	($2,583.98)	($2,596.59)	($2,556.01)	($2,476.76)	0.47X
31
32		Since NPV is X therefore
33		X = -35000-2583.98-2596.59-2556.01-2476.76+0.47X
34		Solving the above equation,
35		X	($85,967.73)	=SUM(D30:H30)/(1-I29)
36
37		Hence NPV of cash flow of replacing vehicle every 5 Year	($85,967.73)
38
39		Since term of project is infinite therefore equivalent annual cost term will also be infinite.
40		Assuming Equivalent annual cost is A and Cost of Capital is i, then
41		Present Value of Cash Flows will be	=A/i
42
43		Present value annual cost should be equal to the NPV of the cash flows i.e.
44		A/i	($85,967.73)
45		or
46		A	($13,840.80)	=D44*D21
47
48		Hence Equivalent annual cost is	($13,840.80)
49