A firm has a two-year real option to invest in a project that has a present value of $400 million with an exercise price (in year 2)of $600 million. Calculate the value of the option given that N(d1)= 0.6 and N(d2)= 0.4. Assume that the risk-free interest rate is 6 percent per year.
A)$26.4 million
B)zero
C)$239.59 million
D)$13.58 million

Question

Quizplus · Accepted Answer

First, we need to calculate d1 and d2, which are input variables for the Black-Scholes model.

d1 = [ln(PV/EP) + (r + σ^2/2)t]/(σ√t)
d1 = [ln(400/600) + (0.06 + 0.5^2/2)2]/(0.5√2)
d1 = -0.980
N(d1) = 0.159

d2 = d1 - σ√t
d2 = -0.980 - 0.5√2
d2 = -2.113
N(d2) = 0.018

Using the Black-Scholes model, we can calculate the value of the option:

V = PV*N(d1) - EP*e^(-rt)*N(d2)
V = 400*0.159 - 600*e^(-0.06*2)*0.018
V = $26.4 million

Therefore, the answer is A) $26.4 million.

A Firm Has a Two-Year Real Option to Invest in a Project