Question

A company is considering the purchase of new equipment for its production area. The equipment has an initial cost of $ 3,000 with operation and maintenance costs, as well as the market liquidation value as shown in the following table:

Year	Costs of operation	Rescue value
1	$1,000	$1,500
2	$1,700	$1,000
3	$2,400	$500
4	$3,100	$0

Determine the Optimal Economic Life of this investment, if the MARR of the company is 12%

Answer 1

-	Particulars	Cahflow	PVF @ 12%	1 Year	2 Years	3 Years	4 Years
A	Initial Cost (Year 0)	$        3,000	1	$        3,000	$        3,000	$        3,000	$        3,000
B	PV of Cost of Operation
.	Year 1	$        1,000	0.8929	$      892.86	$      892.86	$      892.86	$      892.86
.	Year 2	$        1,700	0.7972		$ 1,355.23	$ 1,355.23	$ 1,355.23
.	Year 3	$        2,400	0.7118			$ 1,708.27	$ 1,708.27
.	Year 4	$        3,100	0.6355				$ 1,970.11
.	PV of Cost of Operation		$      892.86	$ 2,248.09	$ 3,956.36	$ 5,926.47
C	PV of Salvage Value
.	Year 1	$        1,500	0.8929	$ 1,339.29
.	Year 2	$        1,000	0.7972		$      797.19
.	Year 3	$            500	0.7118			$      355.89
.	Year 4	$               -	0.6355				$             -
.	PV of Salvage Value		$ 1,339.29	$      797.19	$      355.89	$               -
D	PV of Cost for the given Life	A+B-C		$ 2,553.57	$ 4,450.89	$ 6,600.47	$ 8,926.47
E	PVAF @ 12%				1.6900	2.4017	3.0375
F	Equivalent Annual Cost		$ 2,553.57	$ 2,633.66	$ 2,748.29	$ 2,938.75

As Equivalent annual Cost is Less in case of Machine Used for 1 Year, Optimal Economic Life of the Investment is 1 Year.

Computation of PVAF:

Year(n)	r	1+r	(1+r)^-n	1- [(1+r)^-n]	[1- [(1+r)^-n]] /r
2	12.00%	1.1200	0.7972	0.2028	1.6900
3	12.00%	1.1200	0.7118	0.2882	2.4017
4	12.00%	1.1200	0.6355	0.3645	3.0375