Question

Find the discounted payback period at 15% if a machine cost $20,000 in year 0. The annual operating expenses are $1000 and the annual revenue is $6000

		Between 6 and 7 years
		Between 4 and 5 years
		between 5 and 6 years
		between 3 and 4 years

Answer 1

Year	PV of Cash inflow	Cumulative PV	Break-even?
1	5,000 / 1.15 = $4347.83	4347.83	No
2	$5,000 / (1.15)^2 = $3780.72	8128.55	No
3	$5,000 / (1.15)^3 = $3287.58	11416.13	No
4	$5,000 / (1.15)^4 = $2858.77	14274.9	No
5	$5,000 / (1.15)^5 = $2485.88	16760.78	No
6	$5,000 / (1.15)^6 = $2161.64	18922.42	No
7	$5,000 / (1.15)^7 = $1879.69	20802.11	Yes

Initial outflow = $20,000

Annual net inflows = 6,000 - 1,000 = $5,000

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Between Year 6 and Year 7, net inflow rises from $18922.42 to $20802.11

This takes about 0.57th of an year, between Year 6 and 7. This is found by:

(20,000 - 18922.42 / 20802.11 - 18922.42)

The payback period is 6.57 years.

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From the table and calculations above, the correct answer is:

Answer) Between 6 and 7 years