Question

Refer to Short Exercise S26-4. Continue to assume that the expansion has no residual value. What is the project’s IRR? Is the investment attractive? Why or why not?

Short answer

The investment is attractive because the internal rate of return is positive and equals 15.89%.

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

$\begin{array}{rcl}\mathit{N}\mathit{P}\mathit{V}& \mathbf{=}& \mathbf{\sum }_{\mathbf{t}\mathbf{=}\mathbf{0}}^{\mathbf{T}}\frac{{\mathbf{C}}_{\mathbf{t}}}{{\left(1+IRR\right)}^{\mathbf{t}}}\\ \mathbf{0}& \mathbf{=}& \left(\begin{array}{c}\frac{-11,000,000}{{\left(1+IRR\right)}^0}+\frac{\$2,714,756}{{\left(1+IRR\right)}^1}+\frac{\$2,714,756}{{\left(1+IRR\right)}^2}+\\ \frac{\$2,714,756}{{\left(1+IRR\right)}^3}+\frac{\$2,714,756}{{\left(1+IRR\right)}^4}+\frac{\$2,714,756}{{\left(1+IRR\right)}^5}+\\ \frac{\$2,714,756}{{\left(1+IRR\right)}^6}+\frac{\$2,714,756}{{\left(1+IRR\right)}^7}\end{array}\right)\\ \mathit{I}\mathit{R}\mathit{R}& \mathbf{=}& \mathbf{15}\mathbf{.}\mathbf{89}\mathbf{\%}\end{array}$