Linear interpolation: Difference between revisions
imported>Doug Williamson (Colour change of example headers) |
imported>Doug Williamson (Standardise headings with examples) |
||
| Line 2: | Line 2: | ||
<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: | ||
| Line 15: | Line 15: | ||
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. | ||
| Line 29: | Line 29: | ||
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. | ||
| Line 35: | Line 37: | ||
<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: | ||
| Line 41: | Line 43: | ||
= -$4m - $8m | = -$4m - $8m | ||
= -$12m. | = -$'''12m'''. | ||
Revision as of 14:34, 2 December 2015
A straight-line estimation method for determining an intermediate value.
Example 1: Linear interpolation
Consider a set of cashflows which has:
Net present value (NPV) of +$4m at a yield of 5%.
Net present value (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:
5% + ( +4 / ( +4 - -4 = +8 ) ) x ( 6 - 5 )%
= 5.5%.
5.5% is the estimated internal rate of return (IRR) of the cashflows.
Interpolation and 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.
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.
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.
Example 2: Extrapolation
Using the data above, the estimated net present value at 7%, using extrapolation:
= -$4m - $8m
= -$12m.
