Question

You consider buying a lot on which you will build a small apartment complex. The asking price for the lot is $500,000 and the estimated cost to build the apartment complex is $1,000,000 (construction should take one year). One year from the date you intend to purchase the lot the city is going to make an important decision regarding the use of the land just across from your lot. You believe that there is a 30% chance that the decision would be favorable to you and a 70% chance that it would be unfavorable. In case of a favorable or unfavorable outcome your complex should generate an NOI of $250,000 or $200,000 respectively. For simplicity, you may assume that at any time you can sell your complex for a 9% CAP and your required rate of return is 10%.

a. Calculate the value of the lot using the traditional approach.

b. Calculate the value of the lot using the real option approach.

c. Should you buy the lot?

d. In case that you decided to buy the lot, should you build the apartment complex right away or wait for the city to make its decision first?

Answer 1

Answer for (a): In a traditional approach, we take the expected return for all the calculations. So, the expected NOI would be : 70%*$200,000 + 30%*$250,000 = $215,000

NOI / Asset Value = Cap rate.

215,000 / X = 9%

X = 215,000 / 9% = $ 2,388,888.89

As the value of the asset is at the end of year 1 wherein the construction is completed, we will discount this by 10% (Expected return) to arrive at the value on day 0 as the outflow for lot and construction happens on day 0.

Value of asset on day 0 = $2,171,717.17

Value of LOT = Value of Asset - construction cost = $1,171,717.17

Answer for (b):

In a real options approach, we have an option to buy the LOT and wait for a year to know the decision of the city and then decide whether to invest $1,000,000 on construction or not. But to decide in which outcome (favourable vs non-favourable) we have to invest, we need to analyse the returns on each of the cases.

Favourable condition: Approach is similar to the above calculation:

Asset value = $ 250,000 / 9% = $ 2,777,778

Value of asset on Day 0 = $2,525,252.7; Value of LOT = $1,525,252.7

Non-favourable condition in similar approachwould be = $1,222,222.0

So, in both cases return on buying LOT is very high and the option to wait and decide does not make any sense as you would invest in either of the cases.

Answer to (c): Yes, considering teh analysis above

Answer to (d): Yes, you should build it right away as waiting for the city's decision does not impact your outcome as in both the cases, buying the LOT and building a complex is profitable.