Interpolation and Extrapolation

Interpolation and extrapolation both are used to estimate hypothetical value for variables based on observation. Interpolation estimates value within the parameter of observation whereas extrapolation estimates value which is outside the parameter of observation.

In finance and management interpolation/extrapolation is mostly used to predict rate of return. Commonly used examples include IRR (Internal Rate of Return), Cost of irredeemable debt (to company or to investor).

Here we see how interpolation/extrapolation is used to calculate IRR manually.

Ø  Calculate Net Present Value (NPV) using a discount rate that gives a whole number.

Ø  Calculate a second NPV using another discount rate. If the first NPV was positive, use the rate that is higher than the first rate; if it was negative , use a rate that is lower than the first rate.

Note,

 where both first and second NPV are positive or negative then you use extrapolation and

 where NPV are in set of positive and negative whole numbers we use interpolation.

Basically same formula works for interpolation and extrapolation.

Ø  Use the two NPVS to calculate the IRR. The formula to apply is:

REQUIRED RATE OF RETURN (Where in this case is IRR)

IRR = a +((NPVa/(NPVa-NPVb))(b-a))%

Where, 

a	the lower of the two rates of return used
b	The higher of the two rates of return used
NPVa	The NPV obtained using rate a
NPVb	The NPV obtained using rate b

Between interpolation and extrapolation, interpolation is preferred. This is because using interpolation increases the likelihood of obtaining valid estimate. Using extrapolation means making assumption that are outside the range of observed trend.

However, for exam purpose without looking for exact two sets of positive and negative NPV it will be easier and time saving to tackle from two selected rates of return as the same formula works for interpolation and extrapolation.