Question

An investor owns a lot that is suitable for either six or nine condominium units. The per unit construction costs of the building are $80,000 with six units and $90,000 with nine units. Construction costs are the same whether construction takes place this year or next. Current market price of existing comparable condos is $100,000 per unit. Their per year rental rate is $8,000 per unit (net of expenses). If market conditions are favorable next year, each condominium will sell for $120,000 If conditions are unfavorable, each will sell for only $90,000. The risk-free rate of interest is 12 percent per year. What is the value of the lot?

Answer 1

1.

Building 9 condominium units

Profit = ($100,000 – $90,000) x 9 = $90,000

Building 6 condominium units

Profit = ($100,000 – $80,000) x 6 = $120,000

Therefore, building 6-unit condominium is the best choice if building now

2.

If the investor waits

Build 9 unit in favorable state

= 9 x ($120,000 – $90,000) = $270,000

Build 6 unit in unfavorable state

= 6 x ($90,000 – $80,000) = $60,000

If the investor builds 6 unit in the favorable state, the profit is only $240,000

If the investor builds (9) unit in the unfavorable state, the profit is ($0)

Risk neutral probability X

Invest $100,000 in a condominium this year,in next year =

= $120,000 + $8,000 With prob X

and $ 90,000 + $8,000 With prob (1 -X)

Therefore,

$ 100,000 = [ X * $128000 + (1-X)* $98000] / 1.12

X = 7/15

so, 1-X = 1 -7/15 = 8/15

The value of vacant land in the next year = [$270,000 x 7/15 + $60,000 x 8/15] / 1.12

= $141,071 > $120,000

It is better to keep the land vacant till next year