To automatically insert electronic components in printed circuit boards for a cell phone production line, a...

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Col 1	Col 2	Col 3	Col 4	Col 5
Year	Cash flows ($)	Present Value Factor (P/F, 10%, n)	Discounted Cash Flow Col 2 * Col 3	Cumulative Discounted cash flows($)
0	-500000	1.0000	-500000.00	-500000
1	92500	0.9091	84091.75	-415908.25
2	92500	0.8264	76442.00	-339466.25
3	92500	0.7513	69495.25	-269971.00
4	92500	0.6830	63177.50	-206793.50
5	92500	0.6209	57433.25	-149360.25
6	92500	0.5645	52216.25	-97144.00
7	92500	0.5132	47471.00	-49673.00
8	92500	0.4665	43151.25	-6521.75
9	92500	0.4241	39229.25	32707.50

The discounted payback period = 8 + |-6521.75 / 39229.25|

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 8 + (6521.75 / 39229.25)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 8 + 0.17

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 8.17 years

Thus, it will take 8.17 years for the new SMP machine to fully recover its initial cost.

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