A machine is assumed to depreciate 40 % in value in the...

A machine is assumed to depreciate $40 \%$ in value in the first year, $25 \%$ in the second year and $10 \%$ per annum for the next 3 years, each percentage being calculated on the diminishing value. What is the average percentage depreciation, reckoned on the diminishing value, for the 5 years?

Key Concepts

Diminishing Value Depreciation

This is a method where depreciation is calculated as a fixed percentage of the asset’s current book value, rather than its original cost. Each period’s depreciation amount decreases over time because it is applied to a reducing base, reflecting the idea that the asset’s value falls at a declining rate relative to its remaining value.

Compound Percentage Change

When successive rates are applied to a value, the effects multiply rather than add up linearly. In a depreciation context using the diminishing value method, each year’s depreciation rate compounds on the reduced value from previous years, similar to how compound interest works, which is essential to understand when calculating the overall effect over multiple periods.

Effective Average Depreciation Rate

This concept involves finding a single constant rate that, if applied uniformly over all periods, would result in the same final value as the series of varying annual depreciation rates. It encapsulates the overall effect of a sequence of percentage reductions into one representative rate, making it easier to compare with other depreciation methods or assets.

Geometric Mean

The geometric mean is used to compute the equivalent constant rate that yields the same cumulative effect over multiple periods of compounding. In the context of depreciation, it helps to determine the effective average rate when different annual percentages are applied, as it accurately reflects the multiplicative process inherent in the diminishing value method.

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