Linear interpolation
A straight-line estimation method for determining an intermediate value.
Example 1
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.
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
Using the data above, the estimated net present value at 7%, using extrapolation:
= -$4m - $8m
= -$12m.
