After studying the possible alternatives, management has requested that you perform an analysis of an investment opportunity. The investment opportunity entails investing in a new electricity generator to replace the old one currently in use. The new machine costs $$40$ million, is expected to have a four$-$year life, and is expected to save the company $$7\mathrm{.}25$ million in reduced energy costs per year due to its higher efficiency and electricity output $($relative to the old machine$).$ The new machine will also require a $$1$ million increase in net working capital. Assume that the investment in working capital will be recaptured at the end of the new machine$$s life. The old generator, which is anticipated to have an additional four years of life remaining, has a current book value of $$10$ million, and a market value of $$12$ million. Assume that neither project has any salvage value at the end of year four, and that the marginal tax rate is $35\%.$ If the discount rate $($risk$-$adjusted cost of capital$)$ is $9\%,$ should you purchase the new system? Be sure to calculate the NPV$,$ IRR, MIRR, payback, discounted payback, and BCR$.$ Utilize straight$-$line depreciation for both machines.