Question 21.2: The discounted payback method Newland City Council has inves...
The discounted payback method
Newland City Council has investigated the possibility of investing in a new project, and the following information has been obtained:
The discounted payback method
Newland City Council has investigated the possibility of investing in a new project, and the following information has been obtained:
| £000 | £000 | |
| Total cost of project | 500 | |
| Expected net cash flows: | ||
| Year 1 | 20 | |
| 2 | 50 | |
| 3 | 100 | |
| 4 | 200 | |
| 5 | 300 | |
| 6 | \underline{30} | \underline{700} |
| Net return | \underline{\underline{200}} |
Required:
Assuming a rate of interest of 8%, calculate the project’s overall return using the following methods:
(a) payback; and
(b) discounted payback.
(a) Payback method
| Year | Net cash flow | Cumulative net cash flow |
| £000 | £000 | |
| 0 | (500) | (500) |
| 1 | 20 | (480) |
| 2 | 50 | (430) |
| 3 | 100 | (330) |
| 4 | 200 | (130) |
| 5 | 300 | 170 |
| 6 | 30 | 200 |
Calculation
By the end of the fifth year, the original investment of £500 000 will have been covered. Assuming that the net cash flows accrue evenly throughout the year, therefore, the payback period is about 4 years 5 months. After 4 years the total cash flows received = £370 000 (£20 000 + 50 000 + 100 000 + 200 000). The £130 000 still necessary to equal the original cost of the investment (£500 000 – 370 000) will
be met part way through Year 5, i.e. (£130 000 ÷ 300 000) × 12 months = 5.2 months. The payback period is, therefore, about 4 years and 5 months (41 months)
(b) Discounted payback
| Year | Net cash flow | Discount factors | Present value | Cumulative |
| at 8% | present value | |||
| [Column (2) × Column (3)] | ||||
| (1) | (2) | (3) | (4) | (5) |
| £000 | £000 | £000 | ||
| 0 | (500) | 1.0 | (500) | (500) |
| 1 | 20 | 0.9259 | 19 | (481) |
| 2 | 50 | 0.8573 | 43 | (438) |
| 3 | 100 | 0.7938 | 79 | (3590) |
| 4 | 200 | 0.735 | 147 | (212) |
| 5 | 300 | 0.6806 | 204 | (8) |
| 6 | 30 | 0.6302 | 19 | 11 |
Calculation
Using the discounted payback method, the project would recover all of its original cost during Year 6. Assuming that the net cash flows accrue evenly, this would be about the end of the fifth month because (£8000 ÷ 19 000) × 12 months = 5.1 months. Hence the discounted payback period is about 5 years 5 months (65 months).