91Ó°ÊÓ

The profitability index is the metric that determines the attractiveness of the different available projects to make an investment decision. Under this metric, the present value of the cash flows generated from the investment is compared with the initial investment.

Project X profitability index:

$$\begin{gathered} \mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathit{a}\mathit{b}\mathit{i}\mathit{l}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{s}\mathbf{=}\frac{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}\mathbf{+}\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{088}}{\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{000}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{30} \end{gathered}$$

Project Y profitability index:

$$\begin{gathered} \mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathit{a}\mathit{b}\mathit{i}\mathit{l}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x}\mathbf{=}\frac{\mathbf{N}\mathbf{P}\mathbf{V}\mathbf{+}\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}}{\mathbf{P}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{c}\mathbf{a}\mathbf{s}\mathbf{h}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{f}\mathbf{l}\mathbf{o}\mathbf{w}\mathbf{s}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{459}\mathbf{+}\mathbf{\$}\mathbf{40}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{40}\mathbf{,}\mathbf{000}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{16} \end{gathered}$$

Investment Decision: The business entity must select project X because it has a higher profitability index than project Y. Even if the net present value of project X is lower, it must be selected because the investment values of both projects are different, and the business entity must decide based on the profitability index.