Question

What is the payback period for a project with the following characteristics, given a minimum attractive rate of return (MARR) of 12%?

First Cost $20,000

Annual Benefits $8,000

Annual Maintenance $2,000 in year 1, then increases by $500 per year

Salvage value $2,000

Useful Life 10 years

Answer 1

First Cost = $20,000

Annual Benefits = $8,000

Annual Maintenance = $2,000 in year 1 and then it increases by $500 per year

Salvage value = $2,000

Life = 10 years

Calculate the Pay-back Period.

Step 1 – Calculate the Annual Net Cash Flow

Annual Net Cash Flow = Annual Benefits – Annual Maintenance Costs

Year	Annual Benefits	Annual Maintenance	Net Benefits
1	8000	2000	6000
2	8000	2500	5500
3	8000	3000	5000
4	8000	3500	4500
5	8000	4000	4000
6	8000	4500	3500
7	8000	5000	3000
8	8000	5500	2500
9	8000	6000	2000
10	8000	6500	1500

Step 2 – Calculate the discounted Pay-back Period at MARR of 12%

Year	CF	PV Factor	DCF	CCF
0	$-20,000	1	$-20,000	$-20,000
1	$6,000	0.89	$5,357.14	$-14,642.86
2	$5,500	0.8	$4,384.57	$-10,258.29
3	$5,000	0.71	$3,558.9	$-6,699.39
4	$4,500	0.64	$2,859.83	$-3,839.56
5	$4,000	0.57	$2,269.71	$-1,569.85
6	$3,500	0.51	$1,773.21	$203.36

In between 5th and 6th year the initial cost is recovered. Using interpolation

Pay-Back Period = 5 + [$-1,569.85 – 0 ÷ $-1,569.85 – ($203.36)] * 1

Pay-Back Period = 5.89 years

The discounted pay-back period will be 5.89 years.

Note – The simple or conventional payback period will be

Year	CF	NCF
0	$-20,000	$-20,000
1	$6,000	$-14,000
2	$5,500	$-8,500
3	$5,000	$-3,500
4	$4,500	$1,000

Pay-Back Period = 3 + (3,500 ÷ 4,500) = 3.78 years.