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

(b) [1] What is the static NPV of immediate development of a three-story building? Assume that the building will be built immediately and the condos sold immediately.

(c) [1] If the choice between a two-story building and a three-story building were made today, which should we choose? What is the maximum amount we would be willing to pay for the parcel of land? But we can wait one year.

(d) [2] What is the net year-1 value of each of the two alternative developments, if condominium prices rise? Assume that construction costs will be the same in one year as they are today. What is the optimal choice?

(e) [2] What is the net year-1value of each of the two alternative developments, if condominium prices decline? Assume that construction costs will be the same in one year as they are today. What is the optimal choice?

(f) [5] What is the value today of the development with the flexibility to wait? To answer this question, use either the replicating portfolio approach or the risk-neutral probability approach. The underlying asset is the condominiums with V = $100,000, Vu = $150,000, and Vd = $90,000. Use a one-step binomial model.

(g) [1] What is the maximum amount we would be willing to pay for the parcel of land if we have the flexibility to wait?

(h) [0.5] Should we delay investment one year? YES or NO.