91Ó°ÊÓ

Computation of payback period

$\begin{array}{c}\mathbf{P}\mathbf{a}\mathbf{y}\mathbf{b}\mathbf{a}\mathbf{c}\mathbf{k}\mathbf{=}\frac{\mathbf{A}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}{\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{910}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{483}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{3}\mathbf{.}\mathbf{954}\mathbf{y}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{s}\end{array}$

Calculation of ARR

role="math" localid="1656049007785" $\begin{array}{c}\mathbf{AnnualDepreciation}\mathbf{=}\frac{\mathbf{Cost}\mathbf{-}\mathbf{ResidualValue}}{\mathbf{UsefulLife}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{910}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{0}}{\mathbf{8}}\\ \mathbf{=}\mathbf{\$}\mathbf{238}\mathbf{,}\mathbf{750}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{-}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{D}\mathbf{e}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{c}\mathbf{i}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\\ \mathbf{=}\mathbf{\$}\mathbf{483}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{238}\mathbf{,}\mathbf{750}\\ \mathbf{=}\mathbf{\$}\mathbf{244}\mathbf{,}\mathbf{250}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{=}\frac{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}{\mathbf{2}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{910}\mathbf{,}\mathbf{000}}{\mathbf{2}}\\ \mathbf{=}\mathbf{\$}\mathbf{955}\mathbf{,}\mathbf{000}\end{array}$

$\begin{array}{c}\mathbf{A}\mathbf{R}\mathbf{R}\mathbf{=}\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{o}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{a}\mathbf{m}\mathbf{o}\mathbf{u}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{e}\mathbf{d}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{244}\mathbf{,}\mathbf{250}}{\mathbf{\$}\mathbf{955}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{256}\mathbf{o}\mathbf{r}\mathbf{25}\mathbf{.}\mathbf{6}\mathbf{\%}\end{array}$

Computation of NPV

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{a}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{I}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{×}\left[\frac{1-\frac{1}{{\left(1+r\right)}^n}}{r}\right]\\ \mathbf{=}\mathbf{\$}\mathbf{483}\mathbf{,}\mathbf{000}\mathbf{×}\left[\frac{1-\frac{1}{{\left(1+0.1\right)}^8}}{0.1}\right]\\ \mathbf{=}\mathbf{\$}\mathbf{483}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{5}\mathbf{.}\mathbf{3349}\\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{576}\mathbf{,}\mathbf{757}\end{array}$

$\begin{array}{c}\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}\mathbf{-}\mathbf{C}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{576}\mathbf{,}\mathbf{757}\mathbf{-}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{910}\mathbf{,}\mathbf{000}\\ \mathbf{=}\mathbf{\$}\mathbf{666}\mathbf{,}\mathbf{757}\end{array}$

Computation of IRR

IRR is the rate at which Present value of cash inflow equals initial investment.

Let’s say IRR = R%

Then,

$\begin{array}{c}\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{=}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{V}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}\\ \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{910}\mathbf{,}\mathbf{000}\mathbf{=}\mathbf{A}\mathbf{n}\mathbf{n}\mathbf{u}\mathbf{a}\mathbf{l}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{I}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{×}\left[\frac{1-\frac{1}{{\left(1+r\right)}^n}}{r}\right]\\ \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{910}\mathbf{,}\mathbf{000}\mathbf{=}\mathbf{\$}\mathbf{483}\mathbf{,}\mathbf{000}\mathbf{×}\left[\frac{1-\frac{1}{{\left(1+R\right)}^8}}{R}\right]\\ \mathbf{3}\mathbf{.}\mathbf{9545}\mathbf{=}\left[\frac{1-\frac{1}{{\left(1+R\right)}^8}}{R}\right]\end{array}$

By hit and trial method if R is taken 19% for 8 years then,

$\begin{array}{c}\mathbf{3}\mathbf{.}\mathbf{9545}\mathbf{=}\left[\frac{1-\frac{1}{{\left(1+0.19\right)}^8}}{0.19}\right]\\ \mathbf{3}\mathbf{.}\mathbf{9545}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{9545}\end{array}$

So the IRR = 19%

Computation of profitability index

$\begin{array}{c}\mathbf{P}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{i}\mathbf{t}\mathbf{a}\mathbf{b}\mathbf{i}\mathbf{l}\mathbf{i}\mathbf{t}\mathbf{y}\mathbf{I}\mathbf{n}\mathbf{d}\mathbf{e}\mathbf{x}\mathbf{=}\frac{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{o}\mathbf{f}\mathbf{n}\mathbf{e}\mathbf{t}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{i}\mathbf{n}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}}{\mathbf{I}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{m}\mathbf{e}\mathbf{n}\mathbf{t}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{576}\mathbf{,}\mathbf{757}}{\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{910}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{35}\end{array}$

By looking at the above analysis it can be seen that the payback period of the investment is around 4 years having IRR greater than the required return. The profitability index of the investment project is also 135%. So the project is investable.