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Multiple Internal Return of Return (IRR) for Mixture Project

Multiple Internal Return of Return (IRR) for Mixture Project

Internal rate of return (IRR) is the discount rate that makes Net Present Value (NPV) of investment zero.

NPV = initial cash flow – sum of present value of each cash outflow + sum of present value of each cash inflow

Mixture project has multiple IRRs. In theory, a cash flow stream with K changes in sign after initial cash flow can have up to positive K sensible interest rates of return.

Project Decision:

It is invalid IRRs for mixture project decision, but to avoid the multiple-IRR problem, we can solve this case with following methods:

  1. Use Modified IRR (MIRR): combining cash flows until only one change in sign remains.
  2. Build Net Present Value (NPV) graph/profile

Example:

Company has the following Project A for investment opportunity.

Project A
Dates: 0 1 2
Cash Flow -$100 $230 -$132

 

NPV= -100 + 230/(1+r)^1 – 132/(1+r)^2

IRR1= 10%

IRR 2 =20%

Required:

  1. Assume that required rate of return is 14%, using Modified Internal Rate of Return (MIRR) for project decision.
  2. Build graph or profile, and commend this project.

Solution:

  1. MIRR
  • For project A, Cash outflow at date 2 is -$132.
  • With a discount rate of 14 percent, so PV=-$132/(1+14%)= -$115.79
  • The adjusted cash flow at date 1 is $114.21(130-115.79). Thus, the MIRR approach produces the following two cash flows for the project: (-$100, $114.21)
  • Adjusted NPV=-100+114.21/(1+IRR)=> IRR=14.21%
  • Because of IRR=14.21%> 14%, so the project should be accepted if required rate of 14%.
  1. Graph or Profile

  • Project A has two changes of sign in its cash flows. It has an outflow at date 0 ,an inflow at date 1, and an outflow at date 2.
  • This project has given two IRRs: 10% and 20%, and its NPV is positively when discount rate between 10% and 20%.
  • According to graph, if required rates are between 10% and 20% (rates make positive NPVs), so the Project A will be accepted otherwise rejected.

Source:

  1. Phnom Penh HR
  2. Mcgraw-Hill – Fundamentals Of Corporate Finance

 

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