In a design, you have the choice of purchasing one of the following batch reactors:

$\backslash$table$[[,$A$,$B$,$C$],[$Material of construction,Carbon steel,Stainless steel,Hastalloy$],[$Installed Cost $($$$),15,000,25,000,40,000],[$Equipment Life $(y),3,5,7],[$Yearly Maintenance Cost $(\frac{\text{\$}}{y}),4,000,3,000,2,000]]$

If the internal rate of return for such comparisons is $9\%$ p$.$a$.,$ which of the alternatives is least costly$?$

$2.$ Sooner Manufacturing is considering updating the lighting in its factory to more energy$-$efficient LED fixtures. After extensive research, two alternatives remain. The first one costs $$20,000$ and will save the company $$4,000$ per year in electricity costs; the second one costs $$25,000$ and will save the company $$6,000$ per year in electricity costs. The company estimates that these fixtures will last for $10$ years. If the company's discount rate is $8\%,$ which option should they choose? $($Note: you may consider yearly savings as positive cash flow for this analysis.$)$