$3.$ The Fernandez Company is considering which of two machines it should buy to produce a product it will need for the foreseeable future. Machine A costs $$4$ million up$-$front and has pre$-$tax operating costs of $$1$ million per year for $4$ years. After $4$ years, the machine must be replaced and no salvage value is expected to be realized. Machine B costs $$5$ million up$-$front and has pre$-$tax operating costs of $$1\mathrm{.}2$ million per year, but it lasts for $8$ years, after which it must be replaced and will have no salvage value. Both machines fall into the MACRS $5-$year class, which implies recovery allowances of $20\%,32\%,19\%,12\%,11\%$ and $6\%$ in years $1-6,$ respectively. Assume that machine prices and operating costs are not expected to rise because inflation will be offset by other factors. The cost of capital is $8\%,$ and the firm$$s marginal tax rate is $25\%.$

a$.$ What are the after$-$tax cash flows associated with each machine?

b$.$ What are the net present values $($NPVs$)$ of the two machines?

c$.$ What are the equivalent annual costs $($EACs$)$ of the two machines? Assuming Fernandez must purchase one of the machines, which one should it purchase?