Question 5.12: Kernow Cleaning Services Ltd provides street-cleaning servic...
Kernow Cleaning Services Ltd provides street-cleaning services for local councils in the far south-west of England. 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 | 80,000 160,000 200,000 |
0.3 0.5 0.2 |
| Year 2 | 140,000 220,000 250,000 |
0.4 0.4 0.2 |
| Year 3 | 140,000 200,000 230,000 |
0.4 0.3 0.3 |
| Year 4 | 100,000 170,000 200,000 |
0.3 0.6 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 expected net present value (ENPV) of the street-cleaning machines.
(b) Calculate the net present value (NPV) of the worst possible outcome and the prob-ability 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 | \underline{40,000} | £250,000 × 0.2 | \underline{50,000} | |
| \underline{144,000} | \underline{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 | \underline{ 69,000} | £200,000 × 0.1 | \underline{20,000} | |
| \underline{185,000} | \underline{152,000} |
The expected net present value (ENPV) can now be calculated as follows:
| Year | Expected cash flow £ |
Discount rate 10% |
Expected PV £ |
| 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 | \underline{103,816} |
| ENPV \underline{(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 10% |
PV £ |
| 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 | \underline{ 68,300 } |
| NPV \underline{(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.