Question 5.A.16: Kernow Ltd provides street-cleaning services for a small tow...
Kernow Ltd provides street-cleaning services for a small town. The work is currently labour intensive and few machines are employed. However, the business has recently been considering the purchase of a fleet of street-cleaning vehicles at a total cost of £540,000. The vehicles have a life of four years and are likely to result in a considerable saving of labour costs. Estimates of the likely labour savings and their probability of occurrence are set out below:
| Estimated savings £ |
Probability of occurrence | |
| Year 1 | 80,000 | 0.3 |
| 160,000 | 0.5 | |
| 200,000 | 0.2 | |
| Year 2 | 140,000 | 0.4 |
| 220,000 | 0.4 | |
| 250,000 | 0.2 | |
| Year 3 | 140,000 | 0.4 |
| 200,000 | 0.3 | |
| 230,000 | 0.3 | |
| Year 4 | 100,000 | 0.3 |
| 170,000 | 0.6 | |
| 200,000 | 0.1 |
Estimates for each year are independent of other years. The business has a cost of capital of 10 per cent.
(a) Calculate the ENPV of the street-cleaning machines.
(b) Calculate the NPV of the worst possible outcome and the probability of its occurrence.
(a) The first step is to calculate the expected annual cash flows:
| Year 1 | £ | Year 2 | £ |
| £80,000 × 0.3 | 24,000 | £140,000 × 0.4 | 56,000 |
| £160,000 × 0.5 | 80,000 | £220,000 × 0.4 | 88,000 |
| £200,000 × 0.2 | 40,000 | £250,000 × 0.2 | 50,000 |
| 144,000 | 194,000 | ||
| Year 3 | £ | Year 4 | £ |
| £140,000 × 0.4 | 56,000 | £100,000 × 0.3 | 30,000 |
| £200,000 × 0.3 | 60,000 | £170,000 × 0.6 | 102,000 |
| £230,000 × 0.3 | 69,000 | £200,000 × 0.1 | 20,000 |
| 185,000 | 152,000 |
The ENPV can now be calculated as follows:
| Year | Expected cash flow | Discount rate | Expected PV |
| £ | 10% | £ | |
| 0 | (540,000) | 1.000 | (540,000) |
| 1 | 144,000 | 0.909 | 130,896 |
| 2 | 194,000 | 0.826 | 160,244 |
| 3 | 185,000 | 0.751 | 138,935 |
| 4 | 152,000 | 0.683 | 103,816 |
| ENPV (6,109) | |||
(b) The worst possible outcome can be calculated by taking the lowest values of savings each year, as follows:
| Year | cash flow | Discount rate | PV |
| £ | 10% | £ | |
| 0 | (540,000) | 1.000 | (540,000) |
| 1 | 80,000 | 0.909 | 72,720 |
| 2 | 140,000 | 0.826 | 115,640 |
| 3 | 140,000 | 0.751 | 105,140 |
| 4 | 100,000 | 0.683 | 68,300 |
| ENPV (178,200) | |||
The probability of occurrence can be obtained by multiplying together the probability of each of the worst outcomes above, that is, (0.3 × 0.4 × 0.4 × 0.3) = 0.014 (or 1.4 per cent).
Thus, the probability of occurrence is 1.4 per cent, which is very low.