Using IRR to make capital investment decisions

Refer to the data regarding Hawkins Products in Exercise E26-25. Compute the IRR of each project, and use this information to identify the better investment.

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:

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

Project B:

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

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