Question 8.A.11: Calculate the pre-tax cost of loan capital for Lim Associate...
Calculate the pre-tax cost of loan capital for Lim Associates plc. (Hint: Start with a discount rate of 10 per cent.)
Using a discount rate of 10 per cent, the NPV is calculated as follows:
| Cash flows | Discount rate | PV of cash flows | |
| £m | 10% | £m | |
| Year 0 | 17.6 | 1.00 | 17.6 |
| Year 1 | (2.0) | 0.91 | (1.8) |
| Year 2 | (2.0) | 0.83 | (1.7) |
| Year 3 | (2.0) | 0.75 | (1.5) |
| Year 4 | (22.0) | 0.68 | (15.0) |
| NPV (2.4) |
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The discounted future cash outflows exceed the issue price of the loan capital and so the NPV is negative. This means that the discount rate is too low. Let us try 15 per cent.
| Cash flows | Discount rate | PV of cash flows | |
| £m | 15% | £m | |
| Year 0 | 17.6 | 1.00 | 17.6 |
| Year 1 | (2.0) | 0.87 | (1.7) |
| Year 2 | (2.0) | 0.76 | (1.5) |
| Year 3 | (2.0) | 0.66 | (1.3) |
| Year 4 | (22.0) | 0.57 | (12.5) |
| NPV (0.6) | |||
This discount rate is a little too high as the discounted cash outflows are less than the issue price of the loan capital. Thus, the appropriate rate lies somewhere between 10 per cent and 15 per cent.
| Trial | Discount factor | Net present value |
| £m | ||
| 1 | 10% | (2.4) |
| 2 | 15% | 0.6 |
| Difference | 5% | 3.0 |
The change in NPV for every 1 per cent change in the discount rate will be:
£3.0 m/5 = £0.6 m
Thus, the reduction in the 15 per cent discount rate required to achieve a zero NPV will be 1 per cent as a 15 per cent discount rate produced an NPV of £0.6 million. In other words, the discount rate is 14 per cent.