Buchan Enterprises is considering investing in a new machine. The machine will be purchased on 1 January in Year 1 at a cost of £50,000. It is estimated that it will last for five years, and it will then be sold at the end of the year for £2000 in cash.
The respective net cash flows estimated to be received by the company as a result of purchasing the machine during each year of its life are as follows:

Question

Year	£
1	8000	(excluding the initial cost)
2	16000
3	40000
4	45000
5	35000	(exclusive of the project’s sale proceeds)

The company’s cost of capital is 12 per cent.

Required:
Calculate:
(a) the payback period for the project
(b) its discounted payback period.

Accepted Answer

Payback for Buchan Enterprises:

(a) Payback period:

Year	Investment outlay	Cash inflow	Net cash flow	Cumulative cash flow
	£	£	£	£
1	(50000)	8000	(42000)	(42000)
2	–	16000	16000	(26000)
3	–	40000	40000	14000
4	–	45000	45000	59000
5	–	37000	37000	96000

Net cash flow becomes positive in Year 3. Assuming the net cash flow accrues evenly, it becomes positive during August: (26/40 × 12) = 7.8 months. The payback period, therefore, is about 2 years 8 months.

(b) Discounted payback period:

Year	Net cash flow	Discount factor @ 12%	Discounted net cash flow	Cumulative net cash flow
	£	£	£	£
0	(50000)	1.0000	(50000)	(50000)
1	8000	0.8929	7143	(42857)
2	16000	0.7929	12686	(30171)
3	40000	0.7118	28472	(1699)
4	45000	0.6355	28598	26899
5	37000	0.5674	20994	47893

Discounted net cash flow becomes positive in Year 4. Assuming the net cash flow accrues evenly throughout the year, it becomes positive in January of Year 4 (1699/28,598 × 12 = 0.7). Discounted payback period therefore equals 3 years 1 month. This value is in contrast with the payback method, where the net cash flow becomes positive in August of Year 3 (i.e. 2 years 8 months)

Question 19.TQ.5 : Buchan Enterprises is considering investing in a new machine...

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