2.3 Using Scaling Factors
Scaling factors can be used in order to be able to run sensitivity analysis where the items to be varied have a profile that is not easy to describe using simple formulas, and where one wishes to varying the entire profile of values in the same way. Scaling factors are used to vary the entire original profile, and are generally used in either of two ways:
- Multiplicative Scaling, in which the scaling factor (s) has a base value of 1.0 (or 100%), and is used to multiply each of the original growth rates: The sensitivity analysis is then conducted by varying s, for example using the values 80%, 100% and 120%.
- Additive Scaling, in which the scaling factor has a base value of 0 (or 0%) and the sensitivity analysis is conducted by varying s, using the values -2%, 0%, 2%, for example.
As an example, let us assume that the base case growth rate assumptions for a five-year period are: 10%, 5%, -2%, 3%, 4%. That is, the growth is expected to be robust initially (in the first two periods), followed by a year of contraction (or recession), which is followed by a slight increase and stabilisation phase. The following image shows the use of a multiplicative scaling approach. That is, the original profile is used to create a new profile with the values s*10%, s*5%, ,,,,, s*4% (where s is the value of cell E6):
Sensitivity analysis is then condicted by varying s (for example using the values 80%, 100% and 120%); the following image shows the creation of a DataTable to do so:
… yielding the results:
Of course, if the “additive scaling” approach were used, then, the corresponding formulas (in row 6) would be of the form s+10%, s+5%, …, s+4%, and the sensitivity analysis is conducted by varying s, using the values -2%, 0%, 2% (for example).