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 demand for office hisdoud coss land in Sacramento over the next year. This building would cost $42 milion 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.) Building value

Answer 1

All the financials below are in $ mn

Compare this with a stock on which there is a call option.

S₀ = Current stock price = 41.5

S_u = Price in the up state = 42.7

S_d = Price in the down state = 41

risk free rate, r = 2.5%

Time to maturity, t = 1 years

Strike Price, K = 42

Value of the right to construct = value of the call option = C

u = S_u / S₀ = 42.7 / 41.5 =  1.0289

d = S_d / S₀ = 41 / 41.5 =   0.9880

Risk neutral probability, p = [(1 + r)^t - d] / (u - d) = [(1 + 2.5%)¹ - 0.9880] / (1.0289 - 0.9880) =  0.9044

Payoff from call option at the end of year 1:

In up state: C_u = max (S_u - K, 0) = max ( 42.7 - 42, 0) = 0.7

In down state: C_d = max (S_d - K, 0) = max ( 41 - 42, 0) = 0

Hence, Value of the call option, C = [ p x C_u + (1 - p) x C_d] / (1 + r)^t] = [0.9044 x 0.7 + (1 - 0.9044) x 0] / (1 + 2.5%)¹ =  0.6176 mn = $  617,647.06

Hence, please enter your answer as $  617,647.06