Question

J&R Construction 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 $42 million to construct. Due to low demand for office space in the downtown area, such a building is worth approximately $41.5 million today. If demand increases, the building would be worth $42.7 million a year from today. If demand decreases, the same office building would be worth only $41 million in a year. The company can borrow and lend at the risk-free annual effective rate of 2.5 percent. A local competitor in the real estate business has recently offered $483,000 for the right to build an office building on the land.

What is the value of the office building today? Use the two-state model to value the real option. (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.)

Answer 1

Value of the office building today = $41.5 million

Here, u = $42.7 million/ $41.5 million = 1.02891

d= $41 million/$41.5 million = 0.987951807

Risk neutral probability p = (1.025- 0.987951807)/(1.02891-0.87951807) = 0.9044

K = $42 million ,

Value of option if price goes up to $42.7 million = $0.7 million

Value of option if price goes down to $41 million = $0

So, value of the real option = (p*value of option if price moves up + (1-p)*value of option when price moves down)/1.025

=(0.9044*$0.7 million + 0.0956*0)/1.025

=$617647.06