Linear interpolation - Revision history

imported>Doug Williamson: Add formula.

2022-01-05T23:12:08Z

Add formula.

← Older revision		Revision as of 23:12, 5 January 2022
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	Using linear interpolation, the estimated yield at which the cashflows have an NPV of $0 is given by:		Using linear interpolation, the estimated yield at which the cashflows have an NPV of $0 is given by:

	5% + ( +4 / ( +4 - -4) ) x (6 - 5)%		IRR estimate = a% + ( A / ( A - B) ) x (b - a)%

	~~5% + ( +4 / +8 ) x 1%~~		Where:

	5% + 0.5%		a% = first estimated yield = 5%

			b% = second estimated yield = 6%

			A = NPV of cash flows at yield of a% = +$4m

			B = NPV of cash flows at yield of b% = -$4m


			IRR estimate:

			= 5% + ( +4 / ( +4 - -4) ) x (6 - 5)%

			= 5% + ( +4 / +8 ) x 1%

			= 5% + 0.5%

	= '''5.5%'''.		= '''5.5%'''.

2018-02-21T11:44:52Z

Categorise.

← Older revision		Revision as of 11:44, 21 February 2018
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	* [[Linear]]		* [[Linear]]
	* [[Straight line]]		* [[Straight line]]

			[[Category:Corporate_financial_management]]
			[[Category:Cash_management]]

2016-11-16T14:04:49Z

Removed link

2016-05-21T10:49:07Z

Layout.

← Older revision		Revision as of 10:49, 21 May 2016
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	This iteration process can be repeated as often as required until the result converges on a sufficiently stable final figure.		This iteration process can be repeated as often as required until the result converges on a sufficiently stable final figure.


	==Extrapolation==		==Extrapolation==

2016-05-21T10:48:21Z

Layout.

← Older revision		Revision as of 10:48, 21 May 2016
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	Interpolation is often used in conjunction with Iteration.		Interpolation is often used in conjunction with Iteration.

	Using iteration the straight-line estimated IRR of 5.5% would then be used, in turn, to recalculate the NPV at the estimated IRR of 5.5%, producing a recalculated NPV even closer to $0.		Using iteration, the straight-line estimated IRR of 5.5% would then be used, in turn, to recalculate the NPV at the estimated IRR of 5.5%, producing a recalculated NPV even closer to $0.

	5.5% and the recalculated NPV would then be used with interpolation once again to further refine the estimate of the IRR.		5.5% and the recalculated NPV would then be used with interpolation once again to further refine the estimate of the IRR.

	This iteration process can be repeated as often as required until the result converges on a sufficiently stable final figure.		This iteration process can be repeated as often as required until the result converges on a sufficiently stable final figure.


	==Extrapolation==		==Extrapolation==

2016-01-15T20:07:24Z

Improve calculations.

← Older revision		Revision as of 20:07, 15 January 2016
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	Net present value (NPV) of +$4m at a yield of 5%.		Net present value (NPV) of +$4m at a yield of 5%.

	~~Net present value (~~NPV) of -$4m at a yield of 6%.		NPV of -$4m at a yield of 6%.


	Using linear interpolation, the estimated yield at which the cashflows have an NPV of $0 is given by:		Using linear interpolation, the estimated yield at which the cashflows have an NPV of $0 is given by:

	5% + ( +4 / ( +4 - -4 ~~= +8~~ ) ) x ( 6 - 5 )%		5% + ( +4 / ( +4 - -4) ) x (6 - 5)%

			5% + ( +4 / +8 ) x 1%

			5% + 0.5%

	= '''5.5%'''.		= '''5.5%'''.

2015-12-04T12:29:03Z

Add TOC

← Older revision		Revision as of 12:29, 4 December 2015
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	A straight-line estimation method for determining an intermediate value.		A straight-line estimation method for determining an intermediate value.


			__TOC__

2015-12-02T16:45:53Z

Add 'sample'.

← Older revision		Revision as of 16:45, 2 December 2015
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	Another closely related linear estimation technique is extrapolation.		Another closely related linear estimation technique is extrapolation.

	This involves the straight-line estimation of values outside the range of the data used to do the estimation with.		This involves the straight-line estimation of values outside the range of the sample data used to do the estimation with.

2015-12-02T16:44:47Z

Simplify example heading and expand Example 2.

@@ Line 2: / Line 2: @@
-<span style="color:#4B0082">'''Example 1: Linear interpolation'''</span>
+<span style="color:#4B0082">'''Example 1: Interpolation'''</span>
 Consider a set of cashflows which has:
@@ Line 39: / Line 39: @@
 <span style="color:#4B0082">'''Example 2: Extrapolation'''</span>
-Using the data above, the estimated net present value at 7%, using extrapolation:
+Using the following data to estimate net present value (NPV) at a yield of 7%, using extrapolation:
 = -$4m - $8m

2015-12-02T14:34:32Z

Standardise headings with examples

← Older revision		Revision as of 14:34, 2 December 2015
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	<span style="color:#4B0082">'''Example 1'''</span>		<span style="color:#4B0082">'''Example 1: Linear interpolation'''</span>

	Consider a set of cashflows which has:		Consider a set of cashflows which has:
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	5% + ( +4 / ( +4 - -4 = +8 ) ) x ( 6 - 5 )%		5% + ( +4 / ( +4 - -4 = +8 ) ) x ( 6 - 5 )%

	= 5.5%.		= '''5.5%'''.

	5.5% is the estimated internal rate of return (IRR) of the cashflows.		5.5% is the estimated internal rate of return (IRR) of the cashflows.
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	This iteration process can be repeated as often as required until the result converges on a sufficiently stable final figure.		This iteration process can be repeated as often as required until the result converges on a sufficiently stable final figure.


			==Extrapolation==

	Another closely related linear estimation technique is extrapolation.		Another closely related linear estimation technique is extrapolation.
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	<span style="color:#4B0082">'''Example 2'''</span>		<span style="color:#4B0082">'''Example 2: Extrapolation'''</span>

	Using the data above, the estimated net present value at 7%, using extrapolation:		Using the data above, the estimated net present value at 7%, using extrapolation:
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	= -$4m - $8m		= -$4m - $8m

	= -$12m.		= -$'''12m'''.