Question

An electronics company estimated the investment cost for equipment for producing replacement CCTV will be $800,000. The operating and maintenance cost is expected to be $500,000 per year with an annual revenues estimated at $650,000. :Considering MARR of 15% per year, find The simple payback period=.......years The discounted payback period=......years

Answer 1

pay back period is the time period within which the initial cash outflow is covered in form of cash inflows.

we will find net cash flow per year = $650,000-$500,000

=$150,000

(1) simple pay back period = initial cash flow/ cash flow per year

=$800,000/$150,000

=5.33 years

(2) discounted pay back period

for this we will have to first find out discounted cash flow

years	cash flow	PV factor at 15%	discounted cash flow	cumulative cash flow
1	$150,000	0.8696[1/1.15]1	$130,440[150,000*0,8696]	$130,440
2	$150,000	0.7561[1/1.15]2	$113,415[150,000*0.7561]	$243,855[130,440+113,415]
3	$150,000	0.6575[1/1.15]3	$98,625[150,000*0.6575]	$342,480
4	$150,000	0.5717[1/1.15]4	$85,755[150,000*0.5717]	$428,235
5	$150,000	0.4972 [1/1.15]5	$74,580[150,000*0.4972]	$502,815
6	$150,000	0.4323[1/1.15]6	$64,845[150,000*0.4323]	$567,660
7	$150,000	0.3759[1/1.15]7	$56,385[150,000*0.3759]	$624,045
8	$150,000	0.3269[1/1.15]8	$49,035[150,000*0.3269]	$673,080
9	$150,000	0.2843	$42,645[150,000*0.2843]	$715,725[673,080+42,645]
10	$150,000	0.2472	$37,080	$752,805
11	$150,000	0.2149	$32,235	$785,040
12	$150,000	0.1869	$28,035	$813,075

discounted payback period have uneven cash flows each year so we will use following formula

= year before full recovery + unrecovered amount/ cash flow in next year

=11 + [($800,000-$785,040)/$28,035]

=11+($14,960/$28,035)

=11+0.534

=11.53 years

the years increases in discounted payback because of time value of money.

as the time increases value of money decreases $1 today is worth more than $1 after 1 year because of interest factor.