2 Adrian is considering selling his house and renting a flat.
Adrian still owes \(\pounds 150000\) on his house. He has a mortgage for this, for which he has to pay \(\pounds 4800\) annual interest. If he sells he will pay off the \(\pounds 150000\) and invest the remainder of the proceeds at an interest rate of \(2.5 \%\) per annum. He will use the interest to help to pay his rent.
His estate agent estimates that there is a \(30 \%\) chance that the house will sell for \(\pounds 225000\), a \(50 \%\) chance that it will sell for \(\pounds 250000\), and a \(20 \%\) chance that it will sell for \(\pounds 275000\).
A flat will cost him \(\pounds 7500\) per annum to rent.
- Draw a decision tree to help Adrian to decide whether to keep his house, or to sell it and rent a flat. Compare the EMVs of Adrian's annual outgoings, and ignore the costs of selling.
- Would the analysis point to a different course of action if Adrian were to use a square root utility function, instead of EMVs?
Adrian's circumstances change so that he has to decide now whether to sell or not in one year's time. Economic conditions might then be less favourable for the housing market, the same, or more favourable, these occurring with probabilities \(0.3,0.3\) and 0.4 respectively. The possible selling prices and their probabilities are shown in the table.
| Economic conditions and probabilities | Selling prices ( £) and probabilities |
| less favourable | 0.3 | 200000 | 0.2 | 225000 | 0.3 | 250000 | 0.5 |
| unchanged | 0.3 | 225000 | 0.3 | 250000 | 0.5 | 275000 | 0.2 |
| more favourable | 0.4 | 250000 | 0.3 | 300000 | 0.5 | 350000 | 0.2 |
- Draw a decision tree to help Adrian to decide what to do. Compare the EMVs of Adrian's annual outgoings. Assume that he will still owe \(\pounds 150000\) in one year's time, and that the cost of renting and interest rates do not change.