Reference no: EM133057649
This question is based on the following seminal paper on real options: Titman, Sheridan, 1985, "Urban Land Prices Under Uncertainty", American Economic Review, volume 75, number 2, pages 505 - 513.
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 static NPV of immediate development of a two-story 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-story building? Assume that the building will be built immediately and the condos sold immediately.
c. If the choice between a two-story building and a three-story building were made today, which should we choose?
d. If the choice between a two-story building and a three-story building were made today, what is the maximum amount we would be willing to pay for the parcel of land?
From this point forward (i.e. when answering parts e. through m.), assume that we will wait one year and that we will make our decision after observing condominium prices at t = 1.
e. What is the net year-1 value of the two-story building, if condominium prices rise? 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.
f. What is the net year-1 value of the three-story building, if condominium prices rise? 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.
g. What is the optimal choice if condominium prices rise? (Hint: make your choice based on your answers to parts e. and f.)
h. 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.
i. 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.
j. What is the optimal choice if condominium prices decline? (Hint: make your choice based on your answers to parts h. and i.)
k. 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).
Hint: You can check your work by solving the binomial option problem using both available methods: the replicating portfolio approach and the risk-neutral probability approach. If your solutions are correct, the two results should be equal.
l. If the choice between a two-story building and a three-story building will be made in one year (i.e. at t = 1), what is the maximum amount we would be willing to pay for the parcel of land?
m. It is optimal to delay the construction of the condominiums by one year and make our decision at t = 1 instead of deciding today.