Question 19.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 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:
| 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.
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)