The Charvon oil company is planning to make a large investment in coal-to-liquids (CTL) gasoline. The end product will be a perfect substitute for gasoline made from petroleum, but the feedstock will be coal instead of oil. Two technologies are available to the Charvon company. The first is called indirect CTL, where the coal is gasified prior to being liquefied. The second is called direct CTL, where the coal is dissolved in a solvent, and the resulting liquid is processed into gasoline. The Charvon company has hired you as a consultant to help them decide which technology they should choose. Charvon expects to produce one million gallons of CTL gasoline for five years following construction of the plant, and they can sell the gasoline for $3 per gallon. The capital cost of indirect CTL is $9 million and operating costs for indirect CTL (labor, fuel, and maintenance) are $600,000 per year. The capital cost of direct CTL is $9.45 million and operating costs for direct CTL are $500,000 per year.

In this question we will perform a sensitivity analysis on the timing of the CO2 tax. Calculate the NPV of each type of plant assuming that the $10 per ton CO2 tax is implmented at the beginning of years one, two, three, four and five. (You should thus have five different NPVs for each type of CTL plant, corresponding to the five different implementation dates.) Plot the NPV of each type of plant as a function of the year that the tax is implemented. Find (approximately) the threshold year of implementation under which the Charvon company would be indifferent between the direct and indirect CTL plants.