GEOMETRIC ESCALATION OF OPERATING COST

Chicago USA

When values vary by a constant percentage from period to period instead of by a constant dollar amount, a geometric gradient series is generated instead of an arithmetic gradient series. The following development generates a factor that permits calculation of the future value, F, or the equivalent uniform series of equal values, A´, for a gometric gradient series of values that has de first term in the gradient represented by A and each subsequent term increasing or decreasing by a geometric ratio, r, which is one plus or minus the constant percent change from period to period.
Example: Project operating costs are estimated to be $200.000 in year 1 and to increase 10% per year in each subsequent year. If i * = 15%, what uniform equivalent annual cost can be used in lieu of the geometric gradient series of costs?


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