imported>Doug Williamson |
imported>Doug Williamson |
| Line 1: |
Line 1: |
| ''Investment and funding appraisal.''
| | 1. |
|
| |
|
| (IRR). | | To sell the assets of a company (or other entity) in order to pay off debts, commonly involving the winding up of the entity. |
|
| |
|
|
| |
|
| == Overview of internal rate of return (IRR) ==
| | 2. |
|
| |
|
| IRR is an accounting method for calculating the return forecast to be achieved on a (potential) investment by equating the net present value (NPV) of its cash outflows and inflows over time to zero.
| | To close a market position, for example by selling an asset for cash. |
|
| |
|
|
| |
|
| IRR is a percentage summary of the cash flows of a project, for example, an IRR of 10%.
| | 3. |
|
| |
|
| The IRR summarises the ''timing'', as well as the ''amounts'', of the cashflows.
| | To turn any other asset - including the proceeds of crime - into cash. |
|
| |
|
|
| |
|
| For an investor, the IRR of an investment proposal represents their expected rate of [[return]] on their investment in the project.
| | :<span style="color:#4B0082">'''''Frauds made easier by technology'''''</span> |
|
| |
|
| A greater IRR is normally more attractive for an investor.
| | :"The frauds in Romania and the UK were both... made easier by technology (electronic payments can be liquidated more quickly and easily than cheques)." |
|
| |
|
| | :''The Treasurer magazine, March 2017, p39 - Lesley Meall, freelance journalist specialising in technology and finance.'' |
|
| |
|
| The IRR is driven by the expected future cash flows from the project.
| |
|
| |
|
| |
| The IRR 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 0.
| |
|
| |
|
| |
| <span style="color:#4B0082">'''Example 1: IRR - single period 10%'''</span>
| |
|
| |
| A project requires an investment today of $100m, with $110m being receivable one year from now.
| |
|
| |
| The IRR of this project is 10%, because that is the cost of capital which results in an NPV of $0, as follows:
| |
|
| |
|
| |
| [[PV]] of Time 0 outflow $100m
| |
|
| |
| = $(100m)
| |
|
| |
|
| |
| PV of Time 1 inflow $110m
| |
|
| |
| = $110m x 1.10<sup>-1</sup>
| |
|
| |
| = $100m
| |
|
| |
|
| |
| NPV = - $100m + $100m
| |
|
| |
| = '''$0'''.
| |
|
| |
|
| |
| <span style="color:#4B0082">'''Example 2: IRR - single period 5%'''</span>
| |
|
| |
| A project requires an investment today of $100m, with $105m being receivable one year from now.
| |
|
| |
| The IRR of this project is 5%, because that is the cost of capital which results in an NPV of $0, as follows:
| |
|
| |
|
| |
| [[PV]] of Time 0 outflow $100m
| |
|
| |
| = $(100m)
| |
|
| |
|
| |
| PV of Time 1 inflow $105m
| |
|
| |
| = $105m x 1.05<sup>-1</sup>
| |
|
| |
| = $100m
| |
|
| |
|
| |
| NPV = - $100m + $100m
| |
|
| |
| = '''$0'''.
| |
|
| |
|
| |
| <span style="color:#4B0082">'''Example 3: IRR - two periods 5%'''</span>
| |
|
| |
| A project requires an investment today of $100m, with $5m being receivable one year from now, and $105m two years from now.
| |
|
| |
| The IRR of this project is 5%, because that is the cost of capital which results in an NPV of $0, as follows:
| |
|
| |
|
| |
| [[PV]] of Time 0 outflow $100m
| |
|
| |
| = $(100m)
| |
|
| |
|
| |
| PV of Time 1 inflow $5m
| |
|
| |
| = $5m x 1.05<sup>-1</sup>
| |
|
| |
| = $4.76m
| |
|
| |
|
| |
| PV of Time 2 inflow $105m
| |
|
| |
| = $105m x 1.05<sup>-2</sup>
| |
|
| |
| = $95.24m
| |
|
| |
|
| |
| NPV = - $100m + $4.76m + $95.24m
| |
|
| |
| = '''$0'''.
| |
|
| |
|
| |
| <span style="color:#4B0082">'''Example 4: IRR - three periods 5%'''</span>
| |
|
| |
| 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.
| |
|
| |
| The IRR of this project is 5%, because that is the cost of capital which results in an NPV of $0, as follows:
| |
|
| |
|
| |
| [[PV]] of Time 0 outflow $100m
| |
|
| |
| = $(100m)
| |
|
| |
|
| |
| PV of Time 1 inflow $5m
| |
|
| |
| = $5m x 1.05<sup>-1</sup>
| |
|
| |
| = $4.76m
| |
|
| |
|
| |
| PV of Time 2 inflow $5m
| |
|
| |
| = $5m x 1.05<sup>-2</sup>
| |
|
| |
| = $4.54m
| |
|
| |
|
| |
| PV of Time 3 inflow $105m
| |
|
| |
| = $105m x 1.05<sup>-3</sup>
| |
|
| |
| = $90.70m
| |
|
| |
|
| |
| NPV = - $100m + $4.76m + $4.54m + $90.70m
| |
|
| |
| = '''$0'''.
| |
|
| |
|
| |
| == Project decision making with IRR ==
| |
|
| |
|
| |
| Target or required IRRs for ''investment'' are set based on the investor's [[weighted average cost of capital]], appropriately adjusted for the risk of the proposal under review.
| |
|
| |
| In very simple IRR investment project analysis the decision rule would be that:
| |
|
| |
| (1) All opportunities with above the required IRR should be accepted.
| |
|
| |
| (2) All other opportunities should be rejected.
| |
|
| |
|
| |
| However this assumes the unlimited availability of further capital with no increase in the cost of capital.
| |
|
| |
|
| |
| A more refined decision rule is that:
| |
|
| |
| (1) All opportunities with IRRs BELOW the required IRR should still be REJECTED; while
| |
|
| |
| (2) All other opportunities remain eligible for further consideration (rather than automatically being accepted).
| |
|
| |
|
| |
| For ''borrowing'' or ''funding'' opportunities, the appropriate comparator rate is the organisation's cost of borrowing, for borrowings of comparable risk.
| |
|
| |
| The IRR decision rule for evaluating borrowing opportunties is the opposite of that for investments, as described above.
| |
|
| |
| For borrowing opportunties, a ''lower'' IRR indicates a potentially more cost-effective borrowing, that warrants further consideration.
| |
|
| |
|
| |
| == Excel's =IRR() function ==
| |
|
| |
| Excel's =IRR() function returns the IRR for a block of cells within a single row or column, specified as a range.
| |
|
| |
|
| |
| <span style="color:#4B0082">'''Example 5: =IRR() function'''</span>
| |
|
| |
| Cell A1 contains -100.
| |
|
| |
| Cell A2 contains 110.
| |
|
| |
| =IRR(A1:A2)
| |
|
| |
| will return '''10%'''.
| |
|
| |
| (This is the result we saw in Example 1 above.)
| |
|
| |
|
| |
| == Determining IRR manually ==
| |
|
| |
| Unless the pattern of cash flows is very simple, it is normally only possible to determine IRR manually by trial and error (iterative) methods.
| |
|
| |
|
| |
| <span style="color:#4B0082">'''Example 6: Straight line interpolation'''</span>
| |
|
| |
| Using straight line interpolation and the following data:
| |
|
| |
| First estimated rate of return 5%, positive NPV = $+4m.
| |
|
| |
| Second estimated rate of return 6%, negative NPV = $-4m.
| |
|
| |
| The straight-line-interpolated estimated IRR is the mid-point between 5% and 6%.
| |
|
| |
| This is '''5.5%'''.
| |
|
| |
|
| |
| Using iteration, the straight-line estimation process could then be repeated, using the value of 5.5% to recalculate the NPV, and so on.
| |
|
| |
| The IRR function in Excel uses a similar trial and error method.
| |
|
| |
|
|
| |
|
| == See also == | | == See also == |
| * [[Compound Annual Growth Rate]] | | * [[Forced sale]] |
| * [[Cost of capital]] | | * [[Liquid]] |
| * [[Cost of debt]] | | * [[Liquidation]] |
| * [[Discount]] | | * [[Liquidity]] |
| * [[Discount rate]] | | * [[Side pocket]] |
| * [[Discounted cash flow]] | | * [[Winding-up]] |
| * [[Effective interest rate]]
| |
| * [[Funding]]
| |
| * [[Hurdle rate]]
| |
| * [[IBR]]
| |
| * [[Implied rate of interest]]
| |
| * [[Interpolation]]
| |
| * [[Investment appraisal]]
| |
| * [[IRI]]
| |
| * [[Iteration]]
| |
| * [[Linear interpolation]]
| |
| * [[Market yield]]
| |
| * [[Net present value]]
| |
| * [[Opportunity cost]]
| |
| * [[Present value]]
| |
| * [[Return on investment]]
| |
| * [[Shareholder value]]
| |
| * [[Time value of money]]
| |
| * [[Total shareholder return]] (TSR)
| |
| * [[Weighted average cost of capital]]
| |
| * [[Yield]]
| |
| * [[Yield to maturity]]
| |
|
| |
|
| [[Category:The_business_context]] | | [[Category:The_business_context]] |
| [[Category:Corporate_finance]] | | [[Category:Identify_and_assess_risks]] |
| [[Category:Investment]] | | [[Category:Manage_risks]] |
| [[Category:Long_term_funding]] | | [[Category:Risk_frameworks]] |
| | [[Category:Risk_reporting]] |
| [[Category:Cash_management]] | | [[Category:Cash_management]] |
| [[Category:Financial_products_and_markets]] | | [[Category:Financial_products_and_markets]] |
| [[Category:Liquidity_management]] | | [[Category:Liquidity_management]] |
| [[Category:Trade_finance]]
| |
