please show methods of calculation, and fomulas and methods for solving the equation for price please.

11.15 Economic rents Thanks to acquisition of a key patent, your company now has exclusive production rights for barkelgassers (BGs) in North America. Production facilities for 200,000 BGs per year will require a $25 million immediate capital expenditure. Production costs are estimated at $65 per BG. The BG marketing manager is confident that all 200,000 units can be sold for $100 per unit (in real terms) until the patent runs out five years hence. After that the marketing manager hasn't a clue about what the selling price will be. What is the NPV of the BG project? Assume the real cost of capital is 9%. To keep things simple, also make the following assumption: - The technology for making BGs will not change. Capital and production costs will stay the same in real terms. - Competitors know the technology and can enter as soon as the patent expires, that is, they can construct new plants in 5 years and start selling BGs in year 6 . - If your company invests immediately, full production begins after 12 months, that is, in year 1. - There are no taxes. - BG production facilities last 12 years. They have no salvage value at the end of their useful life. First, consider the sequence of events: - At t=0, the investment of $25 million is made. - At t=1, production begins, so the first year of revenue and expenses is recorded at t=2. - At t=6, the patent expires and competition may enter. Since it takes one year to achieve full production, competition is not a factor until t=7. (This assumes the competition does not begin construction until the patent expires.) - After t=7, full competition will exist and thus any new entrant into the market for BGs will earn the 9 percent cost of capital