MR JOHNSON'S DILEMMA

Mr Johnson owns a plot of land on which he intends to construct apartment units for sale. The number of apartments to be constructed may be either $10$ or $15.$ The total construction costs for these alternatives are estimated to be $$60m$ and $$102\mathrm{.}5m$ respectively. The current market price for each apartment if built now is $$8m.$ The market price after one year will depend on market conditions then: if the market is buoyant, each apartment will be sold for $$9\mathrm{.}1m$ and if it is sluggish, the sale price for each unit will be $$7\mathrm{.}5m.$ The yearly rental per apartment unit is $$0\mathrm{.}7m$ and the risk$-$free interest rate is $10\%$ p$.$a$.$

Draw and analyse a decision tree to enable Mr Johnson decide whether to start construction now or keep the land vacant for one year. Show all workings.

Assume:

a$.$ The construction cost will remain unchanged. Ignore construction time.

b$.$ There is equal probability of the market being either buoyant or sluggish

Hint:

$DCF=\frac{C{F}_n}{(1+r{)}^n}$

For Present Value of cash flow in I year's time, discount by factor $0\mathrm{.}909($interest rate $=10\%)$

At a decision node, you choose the highest payoff value. At a chance node you accept outcome and calculate the EMV of payoffs, applying probability of occurrence where applicable

Building now for sale after I year means rental for I year can be earned