Depreciation methods and interest on investment Which of the listed depreciation methods explicitly accounts for the time value of money (interest on investment) in its annual depreciation calculation?

Introduction / Context:
Depreciation schedules allocate cost for accounting; financial evaluation methods incorporate the time value of money. It is essential to distinguish a book method of depreciation from economic analyses that include interest.

Given Data / Assumptions:

• Straight-line and declining-balance are book depreciation methods.
• Interest on investment refers to time value of money, not interest expense as a separate line item.
• We are asked which depreciation method itself embeds interest in the calculation of annual depreciation charges.

Concept / Approach:
Straight-line yields a constant annual charge equal to (P − S)/n without discounting. Declining-balance applies a rate to book value; again, it does not discount future charges to present worth. Methods that explicitly include interest are evaluation tools (e.g., sinking fund planning, present-worth and capital recovery factors), not the two book methods listed. Therefore, neither straight-line nor declining-balance includes interest within the depreciation formula.

Step-by-Step Solution:
Write SL formula: (P − S)/n → no i (interest) term.Write DB concept: Dep(r) = rate * book_value(r−1) → no discounting.Conclude that neither method embeds interest.

Verification / Alternative check:
Plant economics texts separate book depreciation schedules from discounted cash flow analyses where interest appears in NPV/IRR or capital recovery factor.

Why Other Options Are Wrong:

• Straight-line or declining-balance alone do not feature an interest rate variable.
• Choosing both would be incorrect for the same reason.

Common Pitfalls:

• Confusing the use of interest in cash-flow evaluations with its absence in standard book depreciation methods.

Final Answer:
Neither (a) nor (b)