A progressive government is considering selling the right to develop a new toll road to interested private consortiums. The consortiums would have 1 year from the time of acquiring the right to develop the toll road until they must start development activities. Their estimates indicate that: (a) the total cost to develop the project is $100 million, (b) the expected value of the toll roads revenue is $75 million, and (c) the value of the toll roads revenue could be as high as $150 million but it could also be as low as $50 million.

a) Provide a written definition of call and put options. (5)

b) Draw general diagrams showing the payoff from a call and a put option. (5)

c) Approximate the value of the option using the risk-neutral approach; in other words, what price might the government ask for granting the development right? Assume r_f = 5% and t = 1 yr. (10)