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 $1\mathrm{.}2$ million gallons of CTL gasoline in each of the next twenty$-$five years, and they can sell the gasoline for $$2\mathrm{.}25$ per gallon. The capital cost of indirect CTL is $$10\mathrm{.}5$ million and operating costs for indirect CTL $($labor$,$ fuel, and maintenance$)$ are $$600,000$ per year. The capital cost of direct CTL is $$16$ million and operating costs for direct CTL are $$280,000$ per year.

Question $(50$ points$)$: Assume capital cost for both technologies can be depreciated using the straight line with a depreciation lifetime of $15$ years, starting from year $1$ to year $15.$ There is no salvage value so capital cost is $100\%$ depreciated. Consider tax rate of $21\%$ for the taxable income and a discount rate of $7\mathrm{.}5\%$ for all costs and revenues. Calculate the following metrics for before tax cash flow $($BTCF$)$ and after tax cash flow $($ATCF$)$ and conclude which technology Charvon should choose.

NPV

IRR

B$/$C

PVR

Assume that the capital costs are incurred entirely in Year $0,$ and the operating costs and annual revenues are collected beginning at the end of Year $1.($In other words, capital costs are not discounted but all other annual costs and revenues are discounted.$)$