Question

4. 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 Blue Pencil Publishing:

Consider the following case:

Blue Pencil Publishing is evaluating a proposed capital budgeting project (project Sigma) that will requ ire an initial investment of $800,000.

Blue Pencil Publishing 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. Blue Pencil Publishing’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:

1)            36.58%

2)            34.54%

3)            38.61%

4)            40.64%

Year Year 1	Cash Flow $375,000
Year 2	$500,000
Year 3 Year 4	$425,000 $500,000

Which of the following is the correct calculation of project IRR?

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

If mutually exclusive projects are proposed that both have an IRR greater than the necessary WACC, the IRR method states that the firm should accept:

1) The project with the greatest IRR, assuming that both projects have the same risk as the firm's average project

2) The project that requires the lowest initial investment, assuming that both projects have the same risk   as the

firm 's average project

3) The project with the greater future cash inflows, assuming tha t both projects have the same risk as the firm's average project

Answer 1

Cash flow for year 1, C1 = $375,000

Cash flow for year 2, C2 = $500,000

Cash flow for year 3, C3 = $425,000

Cash flow for year 4, C4 = $500,000

Initial investment , I = $800,000

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

[ (C1/(1+IRR)¹) + (C2/(1+IRR)²) + (C3/(1+IRR)³) + (C4/(1+IRR)⁴) ] = I

[ (375,000/(1+IRR)¹) + (500,000/(1+IRR)²) + (425,000/(1+IRR)³) + (500,000/(1+IRR)⁴) ] = 800,000

We have to find IRR by trial and error method

by assuming any value and substituting the assumed value in the above equation

we want IRR such that

Leht Hand side of equation(LHS) = Right hand side of equation (RHS) = 800,000

by following this method we find that for IRR = 40.64028%

LHS = RHS

hence IRR = 40.64028% or 40.64% ( rounding off to two decimal places)

hence , correct option is 4) 40.64%

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

If mutually exclusive projects are proposed that both have an IRR greater than the necessary WACC, the IRR method states that the firm should accept:

1) The project with the greatest IRR, assuming that both projects have the same risk as the firm's average project