The internal rate of return $($IRR$)$ refers to the compound annual rate of return that a project generates based on its up$-$front cost and subsequent cash flows. Consider the case of Purple Whale Foodstuffs Inc.:

Purple Whale Foodstuffs Inc. is evaluating a proposed capital budgeting project $($project Sigma$)$ that will require an initial investment of $$800,000.$

Purple Whale Foodstuffs Inc. has been basing capital budgeting decisions on a project$$s NPV; however, its new CFO wants to start using the IRR method for capital budgeting decisions. The CFO says that the IRR is a better method because returns in percentage form are easier to understand and compare to required returns. Purple Whale Foodstuffs Inc.$$s WACC is $7\%,$ and project Sigma has the same risk as the firm$$s average project.

The project is expected to generate the following net cash flows:

Year

Cash Flow

Year $1$ $$275,000$

Year $2$ $$400,000$

Year $3$ $$500,000$

Year $4$ $$400,000$

Which of the following is the correct calculation of project Sigma$$s IRR?

$31\mathrm{.}09\%$

$29\mathrm{.}54\%$

$32\mathrm{.}64\%$

$27\mathrm{.}98\%$

If this is an independent project, the IRR method states that the firm should $.$

If the project$$s cost of capital were to increase, how would that affect the IRR?

The IRR would not change.

The IRR would decrease.

The IRR would increase.