imported>Doug Williamson |
imported>Doug Williamson |
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| (IRR).
| | Sustainable and Responsible Investment. |
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| == Definition of IRR ==
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| The internal rate of return of a set of cash flows is the [[cost of capital]] which, when applied to discount all of the cash flows (including any initial investment outflow at Time 0) results in a [[net present value]] (NPV) of NIL.
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| For an investor, the IRR of an investment proposal therefore represents their expected rate of [[return]] on their investment in the project.
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| <span style="color:#4B0082">'''Example 1: IRR'''</span>
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| A project requires an investment today of $100m, with $110m being receivable one year from now.
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| The IRR of this project is 10%, because that is the cost of capital which results in an NPV of $0, as follows:
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| [[PV]] of Time 0 outflow $100m
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| = $(100m)
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| PV of Time 1 inflow $110m
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| = $110m x 1.10<sup>-1</sup>
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| = $100m
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| NPV = - $100m + $100m
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| = '''$0'''.
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| If the project had been funded by borrowing all the required money at the IRR of 10%, there would have been exactly the right amount of surplus from the project to repay the borrowing and interest, with neither a deficit nor a surplus.
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| This is another way to define the IRR.
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| == Determining IRR ==
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| Unless the pattern of cash flows is very simple, it is normally only possible to determine IRR by trial and error (iterative) methods.
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| <span style="color:#4B0082">'''Example 2: Straight line interpolation'''</span>
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| Using straight line interpolation and the following data:
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| First estimated rate of return 5%, positive NPV = $+4m.
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| Second estimated rate of return 6%, negative NPV = $-4m.
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| The straight-line-interpolated estimated IRR is the mid-point between 5% and 6%.
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| This is '''5.5%'''.
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| Using iteration, the straight-line estimation process could then be repeated, using the value of 5.5% to recalculate the NPV, and so on.
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| The IRR function in Excel uses a similar trial and error method.
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| == Project decision making with IRR ==
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| Target or required IRRs are set based on the investor's [[weighted average cost of capital]], appropriately adjusted for the risk of the proposal under review.
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| In very simple IRR project analysis the decision rule would be that:
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| (1) All opportunities with above the required IRR should be accepted.
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| (2) All other opportunities should be rejected.
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| However this assumes the unlimited availability of further capital with no increase in the cost of capital.
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| A more refined decision rule is that:
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| (1) All opportunities with IRRs BELOW the required IRR should still be REJECTED; while
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| (2) All other opportunities remain eligible for further consideration (rather than automatically being accepted).
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| == See also == | | == See also == |
| * [[CertFMM]] | | * [[Corporate social responsibility]] |
| * [[Effective interest rate]] | | * [[Sustainability]] |
| * [[Hurdle rate]]
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| * [[Implied rate of interest]]
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| * [[Interpolation]]
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| * [[Iteration]]
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| * [[Linear interpolation]]
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| * [[Market yield]]
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| * [[Net present value]]
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| * [[Present value]]
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| * [[Shareholder value]]
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| * [[Weighted average cost of capital]]
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| * [[Yield to maturity]]
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