Mathematical Economics

Problem 1

A power company can develop a hydroelectric project at one of two capacity levels, one megawatt or two megawatts, at the cost of $1 billion or $1.75 billion, respectively. The costs of construction are being incurred immediately in either case. If the smaller capacity is chosen, it is not possible to increase capacity at a later date. The company can sell a capacity of one megawatt on a contractual basis for a net revenue of $200 million per year, with payments beginning three years from today and lasting forever. Another buyer is willing to commit to purchasing the second megawatt of power (in case the power company decides to invest in the extra capacity) for $300 million per year in perpetuity, but only starting eleven years from now. Find the net present value of the project for each capacity level if the interest rate is 5%. Should the power company invest in 0, 1, or 2 megawatts of capacity?

This is the first question.