Question 21.TQ.5: Buchan Enterprises is considering investing in a new machine...
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 would last for 5 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:
| 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%.
Required:
Calculate (a) the payback period for the project; and (b) its discounted payback period.
Payback for Buchan Enterprises
(a) Payback period:
| Year | Investment | Cash | Net | Cumulative |
| outlay | inflow | cash flow | 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 | Discounted | Cumulative |
| @ 12% | net cash flow | net cash flow | ||
| £ | £ | £ | ||
| 0 | (50000) | 1.0000 | (50000) | (50000) |
| 1 | 8000 | 0.8929 | 7143 | (42 857) |
| 2 | 16000 | 0.7929 | 12686 | (30 171) |
| 3 | 40000 | 0.7118 | 28472 | (1 699) |
| 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 (1 699/28 598 × 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).