Question 1
Consider a property purchased in year 0, and sold in year 4. In years 1, 2, 3, and 4, NOI is
equal to $500,000, including capital reserve expenses of $20,000 a year. The property is bought
for $5,000,000 in year 0, and will sell for $6,000,000 in year 4.
Depreciation is straight line to zero, and takes place over a period of 27.5 years. The assessed
land value in year 0 is $1,500,000. The property is purchased with a CPM of $2,000,000, with
maturity of 30 years, annual payments, and interest rate of 6%. There is an initial CAPEX in
year 0 of $500,000, which is then depreciated over a period of 10 years, and a CAPEX in year
4, before selling the property, which is paid with the capital reserve.
The marginal income tax rate of the equity investor is 37%. Assume that the investor will
be able to conduct a 1031 exchange transaction when selling the building, and so will not have
to pay capital gain taxes at sale. Also, assume that the investors can benefit from interest rate
tax shields.
a Construct the EATCFs for years 1 to 4. What is the Equity IRR?
b How would the equity IRR change if new legislation in the US removed interest rate tax
shields from investment assets, and abolished 1031 exchanges? Assume that capital gains
taxes are 20%. For simplicity, assume that both the depreciation piece and the actual
capital gain piece of the gain are taxed at the same rate.
Question 2
Go back to the EATCF calculations in Question 1, assuming that there are tax shields and that
the investor will do a 1031 exchange at sale. Say that the required rate of return on this asset
is 8%. What is the NPV of the investment?
Question 3
You are discussing the purchase of a parcel of land located very close to a small, local, and
un-towered airport, which is being petitioned to be closed within 1 year. The airport is not
used by residents, and generates a fair amount of noise, which especially affects the nearby
parcels of land. The land you are evaluating is currently being used as a recreational sports
field. Revenues from this usage imply a present value of only $100,000; assume that, if the use
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remains the same, the land value will be the same in 1 year. However, the land is suitable (and
zoneable) for apartments. The key source of uncertainty in deciding whether to develop the
land is whether or not the airport will actually be closed.
If the airport closes, then the land will be developed into an apartment building; the value
of land is then expected to be $1,600,000 (one year from now, if the airport closes). However,
if the airport stays, the land will continue to be used in its current capacity.
You, as a savvy Business graduate, know that there is substantial option value in the land.
However, so do its current owners. Both you and the owners agree on the relevant scenarios,
and you also agree on the NPV from apartment development. However, you and the owners
disagree on how likely it is that the airport will be closed, and that development will take place.
Perhaps unsurprisingly, the owners claim that it is nearly certain that the airport will close,
while you are more skeptical.
a. Several conversations have failed to reach a consensus. The owners are determined to
charge something close to $1,600,000 for the land, which is effectively pricing 100% certainty of
the airport closing. You have an idea that will perhaps shed some light on the situation. On
Zillow.com, you noticed that a nearby neighborhood has houses for sale close to your plot of
land. Your goal is to use the information in these prices to value the land option. Over lunch,
you explain to the owners your methodology. First, you draw a simple diagram that makes
clear what the source of uncertainty is, and the problem you face. The picture describes an
“up” state, in which the airport closes, and a “down” state in which it does not. Each state
should also show what the land will be worth if it is utilized in its highest and best use in each
state. Draw such a tree.
b. The owners agree with the graph, but to reiterate, neither of you know the probabilities.
Here’s the tricky part. You pull out for-sale fliers of several nearby neighborhood houses. You
show that the average price for these properties is currently $400,000. The owners agree that
these buildings have “priced in” the benefit of the airport being closed down in the near future,
because similar buildings (same builder, size, etc.) located close to another small local airport
a few miles away, with the same noise issues, are selling for less ($375,000). You come to an
agreement that if the airport is closed, the houses close to your land that currently sell for
$400,000 will jump in value to $450,000, but that if the airport stays, they will revert to the
value of their comparables, equal to $375,000. At this point, you know that because agreement
of this final point has been reached, your work is done. You leave lunch, and back at your office,
start scratching down a replicating portfolio consisting of nearby houses and loans with an 8%
rate that will price the land option. Determine the value of the land, finding the replicating
portfolio.
c. You take your estimate back to the retired couple, and understandably, they are not
pleased: “You seem to have made a present value calculation while taking into account nothing
about the probabilities of the medical complex expanding, or the risk associated with that
uncertainty. This makes zero sense to me.” In a few sentences or less, explain to Bill and
Shirley the rationale behind your calculations.
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