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. 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- or three-story building. A two-story building would have six units and would cost $80,000 per unit to build. A three-story building would have nine units and would cost $90,000 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 fully rented condos just break even on a cash flow basis so that they earn their entire return through expected capital gains. Our second decision involves timing. The current value of a one-unit condominium is $100,000, but the housing market is volatile. We assume that, with equal likelihood, the price of a condominium in one year will be either $150,000 or $90,000. The risk-free rate of interest is 10% and TC = 0.

(A) What is the net year-1 value of the two-story building, if condominium prices decline? Assume that the building will be built and the condos will be sold exactly at t = 1 (one year from today) and that construction costs will be the same in one year as they are today.

(B) What is the net year-1 value of the three-story building, if condominium prices decline? Assume that the building will be built and the condos will be sold exactly at t = 1 (one year from today) and that construction costs will be the same in one year as they are today.

(C) What is the value today of the development if the decision between the two-story and the three-story building will be made in one year (i.e. at t = 1)? Use a one-step binomial model with one condominium as the underlying asset (V= $100,000, Vu = $150,000, and Vd = $90,000).