Question

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.

Short answer

IRR of Project A equals 8.14% and of Project B equals 14.43%. Project B is acceptable because the internal rate of return for this project is higher than the minimum required rate of return.

Step-by-step solution

Definition of Internal Rate of Return

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.

Calculation of IRR of each project and its analysis

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.