Question 1: We are considering buying a parcel of land that has been zoned for multifamily housing. We have determined that the best use of this land is to build condominiums.1

Our first decision involves the scale of our investment. The size of the lot dictates that we can build three units per floor and our issue is whether to build a two-storey (2S) or three-storey (3S) building.

A two-storey building would have six units and would cost $160,000 per unit to build. A three-storey building would have nine units and would cost $180,000 per unit to build. Cost per unit increases as the building gets taller, largely because of additional foundation and elevator costs. We will assume that condo investors earn their entire return through capital gains (rather than keeping the condos and renting them out).

Our second decision involves timing. The current value of a condominium unit is $200,000, but the housing market is volatile. We assume that the price of a condominium in one year will be either $240,000 or $180,000.

The risk-free rate of interest is 14% and there are no taxes.

(a) What is the static NPV of immediate development of a two-storey building? Assume that the building will be built immediately and the condos sold immediately.

(b) What is the static NPV of immediate development of a three-storey building? Assume that the building will be built immediately and the condos sold immediately.

(c) If the choice between a two-storey building and a three-storey building were made today, which should we choose? What is the maximum amount we would be willing to pay for the parcel of land?