Plant economics — when are annual depreciation charges non-constant? Annual depreciation cost is not constant under which depreciation calculation method commonly used in chemical engineering economics?

Introduction / Context:
Depreciation spreads the depreciable value of equipment over its useful life for accounting, taxes, and project evaluation. Different methods alter cash flows and profitability projections. A frequent exam point is identifying which methods yield constant year-to-year charges and which do not.

Given Data / Assumptions:

• We compare common methods: straight-line, sinking fund, present worth (time-value analysis approach), and declining balance.
• Annual depreciation cost here means the booked depreciation expense each year, not accumulated depreciation.
• No special salvage timing effects are assumed beyond the usual definitions.

Concept / Approach:
In the straight-line method, the annual charge equals (P − S)/n, which is constant. In the declining-balance method, a fixed percentage is applied to the book value, so the first year is largest and charges reduce each year. The sinking-fund framework explicitly incorporates interest earnings on the fund and yields increasing annual deposits rather than a constant depreciation expense. Present-worth analysis discounts cash flows for comparison but is not itself an annual depreciation schedule. Of the listed choices, the hallmark non-constant pattern identified in cost accounting questions is the declining balance method.

Step-by-Step Solution:
State what is constant in straight-line: Dep = (P − S)/n each year (constant).Recall declining balance: Dep(r) = rate * book_value(r−1) → decreases annually.Recognize sinking fund: annual deposit typically escalates with interest assumptions; not a constant charge.Conclude the widely accepted non-constant schedule among standard accounting methods is the declining balance method.

Verification / Alternative check:
Example tables in plant economics texts show declining-balance charges descending year by year, while straight-line remains flat.

Why Other Options Are Wrong:

• Straight-line method: produces a constant annual charge.
• Sinking fund method: focuses on building a fund; not the typical depreciation expense schedule used in this context.
• Present worth method: an evaluation technique, not an annual depreciation formula.

Common Pitfalls:

• Confusing time-value evaluation methods (present worth) with depreciation schedules.
• Assuming all methods yield constant yearly expenses.

Final Answer:
Declining balance (diminishing balance) method