Question

Two alternative pumps are being compared. Pump A costs $4000, will save $1200 per year in operating and maintenance expenses, and is expected to last for 6 years. Pump B costs $4800, will save $1400 per year, and is also expected to last for 6 years. If the cost of capital is 16%, which has the better discounted payback period?

Answer 1

	Pump A	Pump B
Initial Cost	-4000	-4800
Annual Savings	1200	1400

Life = 6 years (of both)

Interest rate = 16%

Calculate discounted payback period

Discounted Payback Period of Pump – A

Year	CF	PV Factor	DCF	CCF
0	($4,000)	1	($4,000)	-$4,000
1	$1,200	0.86	$1,034.48	-$2,965.52
2	$1,200	0.74	$891.80	-$2,073.72
3	$1,200	0.64	$768.79	-$1,304.93
4	$1,200	0.55	$662.75	-$642.18
5	$1,200	0.48	$571.34	-$70.85
6	$1,200	0.41	$492.53	$421.68

Using interpolation

Discounted Payback Period = 5 + [-$70.85 – 0 ÷ -$70.85 – ($421.68)]*1 = 5.14 years

Discounted Payback Period of Pump – B

Year	CF	PV Factor	DCF	CCF
0	($4,800)	1	($4,800)	-$4,800
1	$1,400	0.86	$1,206.90	-$3,593.10
2	$1,400	0.74	$1,040.43	-$2,552.68
3	$1,400	0.64	$896.92	-$1,655.75
4	$1,400	0.55	$773.21	-$882.55
5	$1,400	0.48	$666.56	-$215.99
6	$1,400	0.41	$574.62	$358.63

Using interpolation

Discounted Payback Period = 5 + [-$215.99 – 0 ÷ -$215.99 – ($358.63)]*1 = 5.38 years

Decision

Pump – A has a better payback period.