You own a one-year call option to buy one acre of Los Angeles real estate. The e

Question

You own a one-year call option to buy one acre of Los Angeles real estate. The exercise price is $2.04 million, and the current, appraised market value of the land is $1.74 million. The land is currently used as a parking lot, generating just enough money to cover real estate taxes. The annual standard deviation is 14% and the interest rate 10%. Suppose the land is occupied by a warehouse generating rents of $170,000 after real estate taxes and all other out-of-pocket costs. The present value of the land plus warehouse is again $1.74 million. You have a European call option. What is it worth of the European call option? (Enter your answer in millions. Do not round intermediate calculations. Round your answer to 4 decimal places.)

Call value $

Explanation / Answer

Formula for European call option = SN(d1) + XN(d2)e-rt

here, S = Current price = $1.74million, X = exercise price is $2.04 million,
N= cumulative standard normal probability distribution
t = maturity period = 1year and sd = standard deviation = 14%
d1 = log ( S/K)+ ( r+sd2 / 2)t / sd*squareroot t

=log (1.74 / 2.4) +{10% + (1.74)2 / 2} / 14% * 1

=log (0.725) + (1.665) / 0.14

= -0.32158 + 1.665 / 0.14

= 1.3434 / 0.14 = 9.5958

d2 = d1 -  sd*squareroot t

= 9.5958 - 0.14 = 9.45583

Therefore, call option value= 1.7N(9.5958) + 2.4N(9.45583) e-10% * 1

e-10% * 1 = e -0.1 = 0.90484

call option value= 1.7N(9.5958) + 2.4N(9.45583) 0.90484

= 0.0066 is the value of the call option

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