Question

A new machine will provide the following net annual cash inflows. If the cost of the machine is $12,000, what is the payback period? What is the discounted payback period if the discount rate is 10%?

Year    Cash Inflow

1 $ 1,345

2. 2,605

3 4,509

4 5,219

5 4,481

6 3,823

7 3,500

Answer 1

Payback Period = 3.68 years

Discounted Payback Period = 4.60 Years

Notes:

Payback Period= = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 3+(3541/5219)

= 3.68 years

Year	Investment	Cash Inflow	Net Cash Flow
0	-12,000.00	-	-12,000	(Investment + Cash Inflow)
1	-	1,345.00	-10,655	(Net Cash Flow + Cash Inflow)
2	-	2,605.00	-8,050	(Net Cash Flow + Cash Inflow)
3	-	4,509.00	-3,541	(Net Cash Flow + Cash Inflow)
4	-	5,219.00	1,678	(Net Cash Flow + Cash Inflow)
5	-	4,481.00	6,159	(Net Cash Flow + Cash Inflow)
6	-	3,823.00	9,982	(Net Cash Flow + Cash Inflow)
7	-	3,500.00	13,482	(Net Cash Flow + Cash Inflow)

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 4+ (1,672.054504473740 / 2,782.348448628070 )

= 4.60 Years

	Cash Flow	Discounting Factor ( 10%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-12,000	1	-12,000.000000000000	-12,000.00
1	1,345	0.9091	1,222.727272727270	-10,777.272727272700
2	2,605	0.8264	2,152.892561983470	-8,624.380165289260
3	4,509	0.7513	3,387.678437265210	-5,236.701728024050
4	5,219	0.6830	3,564.647223550300	-1,672.054504473740
5	4,481	0.6209	2,782.348448628070	1,110.293944154330
6	3,823	0.5645	2,157.983834595590	3,268.277778749920
7	3,500	0.5132	1,796.053413807470	5,064.331192557390