A firm has a three-year real option to invest in a project that has a present value of $500 million with an exercise price (in year 3)of $800 million.Calculate the value of the option given that N(d₁)= 0.3 and N(d₂)= 0.15.Assume that the risk-free interest rate is 6% per year. A)$30.00 million B)$49.25 million C)zero D)$7.08 million

Question

Quizplus · Accepted Answer

To calculate the value of the option, we need to use the Black-Scholes option pricing model. The formula for a call option is:

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

where:
S = present value of the project = $500 million
X = exercise price = $800 million
r = risk-free interest rate = 6%
t = time to maturity = 3 years
d1 = (ln(S/X) + (r + σ^2/2)*t) / (σ*sqrt(t))
d2 = d1 - σ*sqrt(t)

To calculate d1 and d2, we need to estimate the volatility (σ) of the project's returns. Let's assume that the volatility is 30%.

d1 = (ln(500/800) + (0.06 + 0.3^2/2)*3) / (0.3*sqrt(3)) = -0.7584
d2 = -0.7584 - 0.3*sqrt(3) = -1.7361

Using a standard normal distribution table, we can find that N(d1) = 0.2236 and N(d2) = 0.0421.

Therefore, the value of the option is:

C = 500 * 0.2236 - 800 * e^(-0.06*3) * 0.0421 = $49.25 million

So, the best choice is B, as it correctly calculates the value of the option using the Black-Scholes option pricing model.

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