Depreciation – Diminishing balance method: Under the diminishing (declining) balance method, the depreciation in year n is computed by applying a fixed rate N% to which amount?

Introduction / Context:Depreciation allocation affects taxable income, performance metrics, and economic evaluations of chemical plants. The diminishing balance method accelerates depreciation by applying a fixed percentage to the remaining book value each year.

Given Data / Assumptions:

• Diminishing (declining) balance method is used.
• Fixed depreciation rate N is specified.
• Book value evolves year by year as cost minus accumulated depreciation.

Concept / Approach:In the diminishing balance method, annual depreciation is proportional to the opening book value for that year. Thus, the expense declines over time as the base (book value) declines.

Step-by-Step Solution:Let BV(n−1) be the book value at the end of year (n − 1).Annual depreciation in year n = (N/100) * BV(n−1).Book value at the end of year n = BV(n−1) − depreciation(n).This repeats until salvage or replacement.

Verification / Alternative check:Contrast with straight-line depreciation where a constant charge is applied each year to allocate from initial cost minus salvage over economic life.

Why Other Options Are Wrong:

• Initial cost (a): used in straight-line, not in declining balance for the annual base.
• Prior year’s depreciation (c): not the base; the base is the book value.
• Difference between initial cost and salvage (d): straight-line would use this spread, not the declining balance base.

Common Pitfalls:Confusing book value with historical cost; ignoring that the rate applies to the beginning-of-year book value each period.

Final Answer:The book value at the end of year (n − 1).