91Ó°ÊÓ

The metric used in capital budgeting to determine the project’s profitability is the internal rate of return. IRR is calculated using the same formula as used for NPV. Under calculation of IRR net present value is considered as 0.

Project A:

$\begin{array}{rcl}\mathit{N}\mathit{P}\mathit{V}& \mathbf{=}& \underset{\mathbf{t}\mathbf{=}\mathbf{0}}{\overset{\mathbf{T}}{\mathbf{∑}}}\frac{{\mathbf{C}}_{\mathbf{t}}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{t}}}\\ \mathbf{0}& \mathbf{=}& \mathbf{\left(}\begin{array}{c}\frac{\mathbf{-}\mathbf{288}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{0}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{1}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{2}}}\mathbf{+}\\ \frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{3}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{4}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{5}}}\mathbf{+}\\ \frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{7}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{6}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{7}}}\end{array}\mathbf{\right)}\\ \mathit{I}\mathit{R}\mathit{R}& \mathbf{=}& \mathbf{8}\mathbf{.}\mathbf{14}\mathbf{\%}\end{array}$

Project B:

$\begin{array}{rcl}\mathit{N}\mathit{P}\mathit{V}& \mathbf{=}& \underset{\mathbf{t}\mathbf{=}\mathbf{0}}{\overset{\mathbf{T}}{\mathbf{∑}}}\frac{{\mathbf{C}}_{\mathbf{t}}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{t}}}\\ \mathbf{0}& \mathbf{=}& \mathbf{\left(}\begin{array}{c}\frac{\mathbf{-}\mathbf{395}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{0}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{1}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{2}}}\mathbf{+}\\ \frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{3}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{4}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{5}}}\mathbf{+}\\ \frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{7}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{6}}}\mathbf{+}\frac{\mathbf{\$}\mathbf{77}\mathbf{,}\mathbf{000}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{IRR}\mathbf{)}}^{\mathbf{7}}}\end{array}\mathbf{\right)}\\ \mathit{I}\mathit{R}\mathit{R}& \mathbf{=}& \mathbf{14}\mathbf{.}\mathbf{43}\mathbf{\%}\end{array}$

Project A will not be accepted because the internal rate of return is lower than the minimum required rate of return.