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.