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Internal rate of return (IRR) ?? ?? 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

Finance Dec 02, 2020

Internal rate of return (IRR) ?? ?? 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 Grey Fox Aviation Company: Consider the following case: Grey Fox Aviation Company is evaluating a proposed capital budgeting project (project Sigma) that will require an initial investment of $750,000. Grey Fox Aviation Company 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. Grey Fox Aviation Company's WACC is 10%, 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 Which of the following is the correct calculation of project Sigma's IRR? Year 1 Year 2 Cash Flow $325,000 $450,000 $400,000 $475,000 Year 3 O 30.73% O 38.41% O 34.57% O 32.65% Year 4 If this is an independent project, the IRR method states that the firm should reject project Sigma accept project Sigma If the project's cost of capital were to increase, how would that affect the IRR? O The IRR would increase. O The IRR would decrease. O The IRR would not change.

Expert Solution

IRR is the rate at which NPV is zero.

Lets compute NPV at 38% as shown below:

= - $ 750,000 + $ 325,000 / 1.38 + $ 450,000 / 1.382 + $ 400,000 / 1.383 + $ 475,000 / 1.384

= $ 4,976.613483

Lets compute NPV at 39% as shown below:

= - $ 750,000 + $ 325,000 / 1.39 + $ 450,000 / 1.392 + $ 400,000 / 1.393 + $ 475,000 / 1.394

= - $ 7,095.247425

It means the IRR lies between 38% and 39% since the initial investment of $ 750,000 is recovered between them and same is shown below:

= Lower rate + [ (Lower rate NPV / (Lower rate NPV - Higher rate NPV) ] x (Higher rate - lower rate)

= 38 + [ ($ 4,976.613483) / ($ 4,976.613483 - (- $ 7,095.247425) ] x (39 - 38)

= 38 + $ 4,976.613483 / $ 12,071.86091

= 38.41% Approximately

Since the IRR is more than WACC, hence the project shall be accepted.

Since the IRR is independent of the cost of capital, hence the IRR would not change.

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