Question 19.2: 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:
| £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
(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:
After 4 years the total cash flows received = £370,000 (£20,000 + 50,000 + 100,000 + 200,000).
The £30,000 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. So the payback period is about 4 years and 5 months (41 months), assuming that the net cash flows accrue evenly throughout the year.
(b) Discounted payback
| Year | Net cash flow | Discount factors | Present value at 8% [Column (2) × Column (3)] |
Cumulative present value |
| (1) | (2) | (3) | (4) | (5) |
| £000 | £000 | £000 | ||
| 0 | (500) | 1.0000 | (500) | (500) |
| 1 | 20 | 0.9259 | 19 | (481) |
| 2 | 50 | 0.8573 | 43 | (438) |
| 3 | 100 | 0.7938 | 79 | (359) |
| 4 | 200 | 0.7350 | 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. The, therefore, discounted payback period is about 5 years 5 months (65 months).