91Ó°ÊÓ

For refurbishing the current Machine

$\begin{array}{c}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{1}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{2}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{3}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{4}\mathbf{+}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{5}\\ \mathbf{=}\mathbf{\$}\mathbf{350}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{340}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{200}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{40}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\mathbf{=}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\frac{\mathbf{\$}\mathbf{40}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{130}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{31}\\ \mathbf{=}\mathbf{4}\mathbf{.}\mathbf{31}\mathbf{Y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}{\mathbf{N}\mathbf{o}\mathbf{.}\mathbf{o}\mathbf{f}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{680}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}{\mathbf{8}}\\ \mathbf{=}\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}{\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}{\mathbf{2}}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{600}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{o}\mathbf{r}\mathbf{10}\mathbf{\%}\end{array}$

$\begin{array}{c}\mathbf{N}\mathbf{P}\mathbf{V}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{219}\mathbf{,}\mathbf{810}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{19}\mathbf{,}\mathbf{810}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{t}\mathbf{a}\mathbf{b}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}\mathbf{=}\frac{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}}{\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{219}\mathbf{,}\mathbf{810}}{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{200}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{017}\end{array}$

For purchasing new Machine

$\begin{array}{c}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{1}\mathbf{+}\mathbf{C}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{2}\mathbf{+}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{i}\mathbf{n}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{3}\\ \mathbf{=}\mathbf{\$}\mathbf{3}\mathbf{,}\mathbf{780}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{510}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{310}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{P}\mathbf{e}\mathbf{r}\mathbf{i}\mathbf{o}\mathbf{d}\mathbf{=}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{p}\mathbf{a}\mathbf{r}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{c}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\frac{\mathbf{\$}\mathbf{310}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{440}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{+}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{705}\\ \mathbf{=}\mathbf{2}\mathbf{.}\mathbf{7}\mathbf{Y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}{\mathbf{N}\mathbf{o}\mathbf{.}\mathbf{o}\mathbf{f}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{900}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}}{\mathbf{10}}\\ \mathbf{=}\mathbf{\$}\mathbf{230}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{O}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{I}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{230}\mathbf{,}\mathbf{000}}{\frac{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}}{\mathbf{2}}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{230}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{300}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{o}\mathbf{r}\mathbf{10}\mathbf{\%}\end{array}$

$\begin{array}{c}\mathbf{N}\mathbf{P}\mathbf{V}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{332}\mathbf{,}\mathbf{930}\mathbf{-}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{600}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{732}\mathbf{,}\mathbf{930}\end{array}$

Based on the above analysis, the payback period for refurbishing the current machine is higher than for purchasing a new machine. Furthermore, the NPV is also lower for refurbishing g current machine than for purchasing a new machine.

So the recommended option would be to purchase the new machine.