Question 5.7: A business has the opportunity to invest £12 million immedia...
A business has the opportunity to invest £12 million immediately in new plant and equipment in order to produce a new product. The product will sell at £80 per unit and it is estimated that 200,000 units of the product can be sold in each of the next four years. Variable costs are £56 a unit and additional fixed costs (excluding depreciation) are £1.0 million in total. The residual value of the plant and machinery at the end of the life of the product is estimated to be £1.6 million.
The business has a cost of capital of 12 per cent.
(a) Calculate the NPV of the investment proposal.
(b) Carry out separate sensitivity analysis to indicate by how much the following factors would have to change in order to produce an NPV of zero:
(i) initial outlay on plant and machinery
(ii) discount rate
(iii) residual value of the plant and machinery.
(a) Annual operating cash flows are as follows:
| £m | £m | |
| Sales (200,000 × £80) Less |
16 | |
| Variable costs (200,000 × £56) | 11.2 | |
| Fixed costs | \underline{ 1.0} | \underline{ 12.2} |
| \underline{ 3.8} |
Estimated cash flows are as follows:
| Year 0 £m |
Year 1 £m |
Year 2 £m |
Year 3 £m |
Year 4 £m |
|
| Plant and equipment | (12.0) | 1.6 | |||
| Operating cash flows | \underline{ } | \underline{ 3.8 } | \underline{ 3.8 } | \underline{ 3.8 } | \underline{ 3.8 } |
| (\underline{ 12.0 }) | \underline{ 3.8 } | \underline{ 3.8 } | \underline{ 3.8 } | \underline{ 5.4 } | |
| The NPV of the project is: | |||||
| Year 0 £m |
Year 1 £m |
Year 2 £m |
Year 3 £m |
Year 4 £m |
|
| Cash flows | (12.0) | 3.8 | 3.8 | 3.8 | 5.4 |
| Discount rate (12%) | 1.0 | 0.89 | 0.80 | 0.71 | 0.64 |
| Present value | (12.0) | 3.38 | 3.04 | 2.70 | 3.46 |
| NPV (\underline{ 0.58 }) | |||||
(b) (i) The increase required in the initial outlay on plant and equipment to achieve an NPV of zero will be £0.58 million (as the plant and equipment are already expressed in present value terms). This represents a 4.8 per cent increase on the current estimated figure of £12 million ((0.58/12) x 100).
(ii) Using a discount rate of 14 per cent, the NPV of the project is:
| Year 0 £m |
Year 1 £m |
Year 2 £m |
Year 3 £m |
Year 4 £m |
|
| Cash flows | (12.0) | 3.8 | 3.8 | 3.8 | 5.4 |
| Discount rate (14%) | 1.0 | 0.88 | 0.77 | 0.68 | 0.59 |
| Present value | (12.0) | 3.34 | 2.93 | 2.58 | 3.19 |
| NPV (\underline{ 0.04}) |
This is very close to an NPV of zero and so 14 per cent is the approximate figure. It is 16.7 per cent higher than the cost of capital ((14 − 12)/12) × 100).
(iii) The fall in the residual value of the plant and equipment (R) that will lead to a zero NPV is:
(R × discount factor at the end of four years) − NPV of the project = 0
By rearranging this equation, we have
(R × discount factor at the end of four years) = NPV of the project
R × 0.64 = £0.58 million
R = £0.58 million/0.64
= (\underline{£0.9 million})
This represents a 43.8 per cent decrease in the current estimated residual value (((1.6 − 0.9)/1.6) × 100).