The opportunity to invest in a project can be thought of as a two year option on an asset which is worth $400 million (PV of the cash flows from the project) with an exercise price of
$600 million (investment needed). Calculate the value of the option given that N(d1) = 0.6 and
N(d2) = 0.4 and interest rate is 6%.
A) $26.4 million
B) Zero
C) $200 million.
D) None of the above.

Question

Quizplus · Accepted Answer

The value of the option can be calculated using the Black-Scholes formula for a two year option on a non-dividend paying asset. The formula is:

C = S*N(d1) - X*e^(-rT)*N(d2)

Where:
C = value of the option
S = current value of the asset (PV of cash flows)
X = exercise price (investment needed)
r = interest rate
T = time to expiration (2 years)

Plugging in the given values and solving, we get:

C = 400*0.6 - 600*e^(-0.06*2)*0.4
C = 240 - 400*0.4
C = $26.4 million

Therefore, the option is worth $26.4 million and the best choice is A).

The Opportunity to Invest in a Project Can Be Thought