S. Saluja (Property Developers) Ltd intends to bid at an auction, to be held today, for a large town house that has fallen into disrepair. The auctioneer believes that the house will be sold for about £450,000. The business wishes to renovate the property and divide it into studio apartments 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 studio apartments 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 apartments 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 town house is acquired. There is, however, some uncertainty over the remaining key variables. 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 town 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 studio apartments that would cause the project to have a zero NPV? (Each apartment will be sold for the same price: £150,000.)

(c) Comment on the calculations carried out in answering (b) above.