Real Options The Webber Company is an international conglomerate with a real est
ID: 2799913 • Letter: R
Question
Real Options The Webber Company is an international conglomerate with a real estate division that owns the right to erect an office building on a parcel of land in downtown Sacramento over the next year. This building would cost $55 million to construct. Due to low demand for office space in the downtown area, such a building is worth approximately $53.2 million today. If demand increases, the building would be worth $57.9 million a year from today. If demand decreases, the same office building would be worth only $49.8 million in a year. The company can borrow and lend at the risk-free annual effective rate of 4.8 percent. A local competitor in the real estate business has recently offered $1.8 million for the right to build an office building on the land. Should the company accept this offer? Use a two-state model to value the real option.Explanation / Answer
This is similar to binomial option pricing model for real estate.
Cost of construction is $55 million (which is strike price to local competitor who would earn only if value of building after 1 year is more than $ 55 million).
Current Value of Building is $ 53.2 million.
Risk Free Rate = 4.8% p.a.
size of uptick (u) = 57.9/53.2 = 1.08835
size of downtick (d) = 49.8/53.2 = 0.93609
Calculating Risk Neutral Probabilities
probability of price going up (p) = [(1+Rf)-d] / [u-d] = [(1+0.048)-0.93609] / [1.08835-0.93609] = 0.735
probability of price going down (1-p) = 1 - 0.735 = 0.265
Value of option at expiry if price goes up = max(0, 57.9 - 55) = $ 2.9 mn
Value of option at expiry if price goes down = max(0, 49.8 - 55) = 0
Therefore, value of option at expiry = 2.9 x 0.735 + 0 x 0.265 = $ 2.13 million
Therefore, Prevent Value of Option = 2.13 / (1+0.048) = $ 2.03 million
Since, local competitor is offering $1.80 million for right (option) which is less then fare value of option of $2.03 million; company should not accept the offer.
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