imported>Doug Williamson |
imported>Doug Williamson |
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| ''Investment and funding appraisal.''
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| (IRR). | | One unit of the UK pound sterling (GBP). |
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| | For most of the historical period up the early 19th century, it could - in theory - be exchanged for one pound (weight) of silver. |
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| == Overview of internal rate of return (IRR) ==
| | Thereafter the pound was generally backed by gold (the 'gold standard'). |
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| IRR is a percentage summary of the cash flows of a project, for example, an IRR of 10%.
| | Since 1931, the pound sterling has been a fiat currency. |
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| The IRR summarises the ''timing'', as well as the ''amounts'', of the cashflows.
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| For an investor, the IRR of an investment proposal represents their expected rate of [[return]] on their investment in the project.
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| A greater IRR is normally more attractive for an investor. | | A pound is also one unit of a number of other currencies including those of Egypt (EGP), Lebanon (LBP), Sudan (SDG) and Syria (SYP). |
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| The IRR is driven by the expected future cash flows from the project.
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| The IRR of a set of cash flows is:
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| :the [[cost of capital]] which,
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| :when applied to discount all of the cash flows,
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| :including any initial investment outflow at Time 0,
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| :results in a [[net present value]] (NPV) of 0.
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| <span style="color:#4B0082">'''Example 1: IRR - single period 10%'''</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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| <span style="color:#4B0082">'''Example 2: IRR - single period 5%'''</span>
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| A project requires an investment today of $100m, with $105m being receivable one year from now.
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| The IRR of this project is 5%, 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 $105m
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| = $105m x 1.05<sup>-1</sup>
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| = $100m
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| NPV = - $100m + $100m
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| = '''$0'''.
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| <span style="color:#4B0082">'''Example 3: IRR - two periods 5%'''</span>
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| A project requires an investment today of $100m, with $5m being receivable one year from now, and $105m two years from now.
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| The IRR of this project is 5%, 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 $5m
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| = $5m x 1.05<sup>-1</sup>
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| = $4.76m
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| PV of Time 2 inflow $105m
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| = $105m x 1.05<sup>-2</sup>
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| = $95.24m
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| NPV = - $100m + $4.76m + $95.24m
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| = '''$0'''.
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| <span style="color:#4B0082">'''Example 4: IRR - three periods 5%'''</span>
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| A project requires an investment today of $100m, with $5m being receivable one year from now, a further $5m two years from now, and $105m three years from now.
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| The IRR of this project is 5%, 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 $5m
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| = $5m x 1.05<sup>-1</sup>
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| = $4.76m
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| PV of Time 2 inflow $5m
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| = $5m x 1.05<sup>-2</sup>
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| = $4.54m
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| PV of Time 3 inflow $105m
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| = $105m x 1.05<sup>-3</sup>
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| = $90.70m
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| NPV = - $100m + $4.76m + $4.54m + $90.70m
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| = '''$0'''.
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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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| == Excel's =IRR() function ==
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| Excel's =IRR() function returns the IRR for a block of cells within a single row or column, specified as a range.
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| <span style="color:#4B0082">'''Example 5: =IRR() function'''</span>
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| Cell A1 contains -100.
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| Cell A2 contains 110.
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| =IRR(A1:A2)
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| will return '''10%'''.
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| (This is the result we saw in Example 1 above.)
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| == Determining IRR manually ==
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| Unless the pattern of cash flows is very simple, it is normally only possible to determine IRR manually by trial and error (iterative) methods.
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| <span style="color:#4B0082">'''Example 6: 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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| == See also == | | == See also == |
| * [[Cost of capital]] | | * [[Egypt]] |
| * [[Discount rate]] | | * [[Fiat currency]] |
| * [[Discounted cash flow]] | | * [[FKP]] |
| * [[Effective interest rate]] | | * [[GBP]] |
| * [[Funding]] | | * [[GIP]] |
| * [[Hurdle rate]] | | * [[Gold standard]] |
| * [[IBR]] | | * [[Libra]] |
| * [[Implied rate of interest]] | | * [[Lira]] |
| * [[Interpolation]] | | * [[SHP]] |
| * [[Investment appraisal]] | | * [[SSP]] |
| * [[IRI]] | | * [[Sterling]] |
| * [[Iteration]] | | * [[United Kingdom]] |
| * [[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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| * [[Return on investment]]
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| * [[Shareholder value]]
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| * [[Time value of money]]
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| * [[Weighted average cost of capital]]
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| * [[Yield to maturity]]
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| [[Category:The_business_context]] | | [[Category:The_business_context]] |
| [[Category:Corporate_finance]]
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| [[Category:Investment]]
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| [[Category:Long_term_funding]]
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| [[Category:Cash_management]]
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| [[Category:Financial_products_and_markets]] | | [[Category:Financial_products_and_markets]] |
| [[Category:Liquidity_management]]
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| [[Category:Trade_finance]]
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