Question 5.3: S. Saluja (Property Developers) Ltd intends to bid at an auc...
S. Saluja (Property Developers) Ltd intends to bid at an auction, to be held today, for a manor house that has fallen into disrepair. The auctioneer believes that the manor house will be sold for about £450,000. The business wishes to renovate the property and divide it into flats to be sold for £150,000 each. The renovation will be in two stages and will cover a two-year period. Stage 1 will cover the first year of the project. It will cost £500,000 and the six flats completed during this stage are expected to be sold for a total of £900,000 at the end of the first year. Stage 2 will cover the second year of the project. It will cost £300,000 and the three remaining flats are expected to be sold at the end of the second year for a total of £450,000.
The cost of renovation is subject to a binding agreement with local builders if the manor house is acquired. There is, however, some uncertainty over the remaining input values. The business estimates its cost of capital at 12 per cent a year.
(a) What is the NPV of the proposed project?
(b) Assuming none of the other inputs deviates from the best estimates provided:
(i) What auction price would have to be paid for the manor house to cause the project to have a zero NPV?
(ii) What cost of capital would cause the project to have a zero NPV?
(iii) What is the sale price of each of the flats that would cause the project to have a zero NPV? (Each flat will be sold for the same price: £150,000.)
(c) Comment on the calculations carried out in answering (b) above.
(a) The NPV of the proposed project is as follows:
| Cash flows | Discount factor | Present value | |
| £ | 12% | £ | |
| Year 1 (£900,000 − £500,000) | 400,000 | 0.893 | 357,200 |
| Year 2 (£450,000 − £300,000) | 150,000 | 0.797 | 119,550 |
| Less Initial outlay | \underline{(450,000)} | ||
| NPV \underline{ 26,750} |
(b) (i) To obtain a zero NPV, the auction price for the manor house would have to be £26,750 higher than the current estimate (that is, the amount of the estimated NPV). This would make a total price of £476,750, which is about 6 per cent above the current estimated price.
(ii) As there is a positive NPV, the cost of capital that would cause the project to have a zero NPV must be higher than 12 per cent. Let us try 20 per cent.
| Cash flows | Discount factor | Present value | |
| £ | 20% | £ | |
| Year 1 (£900,000 – £500,000) | 400,000 | 0.833 | 333,200 |
| Year 2 (£450,000 − £300,000) | 150,000 | 0.694 | 104,100 |
| Less Initial outlay | \underline{(450,000)} | ||
| NPV \underline{(12,700)} |
As the NPV, using a 20 per cent discount rate, is negative, the ‘break-even’ cost of capital must lie somewhere between 12 per cent and 20 per cent. A reasonable approximation is obtained as follows:
| Discount rate | NPV | |
| % | £ | |
| 12 | 26,750 | |
| \underline{20} | \underline{(12,700)} | |
| Difference | \underline{8} | Range \underline{39,450} |
The change in NPV for every 1 per cent change in the discount rate will be:
\frac{39,450}{8} =4,931
The reduction in the 20 per cent discount rate required to achieve a zero NPV would therefore be:
\frac{12,700}{4,931}=2.6\%
The cost of capital (that is, the discount rate) would therefore have to be 17.4 (20.0 – 2.6) per cent for the project to have a zero NPV.
This calculation is, of course, the same as that used in the previous chapter when calculating the IRR of the project. In other words, 17.4 per cent is the IRR of the project.
(iii) To obtain a zero NPV, the sale price of each flat must be reduced so that the NPV is reduced by £26,750. In Year 1, six flats are sold, and in Year 2, three flats are sold. The discount factor for Year 1 is 0.893 and for Year 2 it is 0.797. We can derive the fall in value per flat (Y) to give a zero NPV by using the equation:
(6Y × 0.893) + (3Y × 0.797) = £26,750
Y = £3,452
The sale price of each flat necessary to obtain a zero NPV is therefore:
£150,000 – £3,452 = £146,548
This represents a fall in the estimated price of 2.3 per cent.
(c) These calculations indicate that the auction price would have to be about 6 per cent above the estimated price before a zero NPV is obtained. The margin of safety is therefore not very high for this factor. In practice, this should not represent a real risk because the business could withdraw from the bidding if the price rises to an unacceptable level.
The other two factors represent more real risks. Only after the project is at a very late stage can the business be sure as to what actual price per flat will prevail. It would be unusual to be able to have fixed contracts for sale of all of the flats before the auction. The calculations reveal that the price of the flats would have to fall only by 2.3 per cent from the estimated price before the NPV is reduced to zero. Hence, the margin of safety for this factor is very small.
The cost of capital is less sensitive to changes and there would have to be an increase from 12 per cent to 17.4 per cent before the project produced a zero NPV.
It may be possible to raise finance for the project at a fixed rate before the auction of the house. However, even if the funding cost cannot be fixed in advance, the cost of capital does not seem to be a sensitive factor.
It appears from the calculations that the sale price of the flats is the key sensitive factor to consider. A careful re-examination of the market value of the flats seems appropriate before a final decision is made.