###### Cost of Equity Capital

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The net present value (NPV) and the internal rate of return (IRR) are techniques that can both be used by financial institutions or individuals when making major investment decisions. Each method has its own strengths and weaknesses. However, the net present value method comes out on top, and here’s why:

When dealing with independent projects, both NPV and IRR will yield the same investment decisions. Independent, in this context means that the decision to invest in one project does not rule out or affect investment in another project.

Even then, a challenge would arise when the projects are mutually exclusive. If two or more projects are mutually exclusive, the decision to invest in one project precludes investment in all the others. With such projects, the IRR method may provide misleading results if used in isolation.

There are some problems associated with the IRR method:

- the method assumes that all proceeds from a project are immediately reinvested in projects offering a rate of return equal to the IRR – this is very difficult in practice;
- it gives different rankings when the projects under comparison have different scales; and
- sometimes, the method may not provide a unique solution, especially when a project has a mixture of positive and negative cash flows during its productive life.

QuestionSuppose you have three independent projects – X, Y, and Z. Assume that the hurdle rate is 12% for all the three projects. Their NPVs and IRRs are as shown below.

$$ \begin{array}{|c|c|c|c|}

{} & { \textbf {Project X}} & {\textbf {Project Y}} & {\textbf {Project Z}} \\ \hline

{\text {NPV}} & {$20,000} & {$21,400} & {$23,000} \\

{\text {IRR} } & {20\%} & {32\%} & {18\%} \\

\end{array} $$Assuming the projects are mutually exclusive, which of the following is the

mosteconomically feasible project?

- Z
- X
- Y

SolutionThe correct answer is

A.$$ \begin{array}{c|c|c|c}

{} & { \textbf {Project X}} & {\textbf {Project Y}} & {\textbf {Project Z}} \\ \hline

{\text {NPV}} & {$20,000} & {$21,400} & {$23,000} \\

{\text {IRR} } & {20\%} & {32\%} & {18\%} \\

{\text {Decision}} & {\text{Accept}} & {\text{Accept}} &{\text{Accept}} \\

\end{array} $$If the IRR criteria is used, all the three projects would be accepted because they would all increase shareholders’ wealth. Their NPVs are all positive, and again, the three are all acceptable.

However, if the projects are mutually exclusive, then only one project would be chosen. If one were to pick one project based on internal rates of return of the projects, then one would go for Y. This is because its IRR is the highest compared to the other projects.

This decision would be wrong when we consider the sizes of the NPVs of the projects. While Y has the highest IRR, its NPV is lower than that of Z. The best decision would be to go for the project with the highest NPV, and that is project Z. Therefore, if projects are mutually exclusive, the NPV method should be applied.