$5.$ Three alternative designs are being considered for a potential improvement project related to the operation of your engineering department. The prospective net cash flows for these alternatives are shown in the following table, and the MARR is $15\backslash \%$ per year. $\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|\}\backslash$hline $\backslash$multirow$\{2\}\{*\}\{$End of Year, k$\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$Alternative Net Cash Flows$\}\backslash \backslash \backslash$hline & A & B & C $\backslash \backslash \backslash$hline $0$ & $-\backslash$$$200,000$ & $-\backslash$$$230,000$ & $-\backslash$$$212,500\backslash \backslash \backslash$hline $1$ & $90,000$ & $108,000$ & $-\backslash$$$15,000\backslash \backslash \backslash$hline $2$ & $90,000$ & $108,000$ & $122,500\backslash \backslash \backslash$hline $3$ & $90,000$ & $108,000$ & $122,500\backslash \backslash \backslash$hline $4$ & $90,000$ & $108,000$ & $122,500\backslash \backslash \backslash$hline $5$ & $90,000$ & $108,000$ & $122,500\backslash \backslash \backslash$hline $6$ & $90,000$ & $108,000$ & $122,500\backslash \backslash \backslash$hline $\backslash$end$\{$tabular$\}$ Show that the same capital investment decision results from the IRR method and the PW method applied by using the incremental investment analysis procedure.