Question

In which of the following methods the depreciation for any year is taken as a constant percentage of the remaining value at the beginning of that year?

• A. Straight line method
• B. Declining balance method
• C. Estimated value method
• D. Sum-of-the-years-digits method

Hint:

To easily identify the method:
- "Constant amount of value lost" $\rightarrow$ Straight Line Method.
- "Constant percentage of remaining value lost" $\rightarrow$ Declining Balance Method.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Depreciation represents the gradual decline in the economic value of an asset (such as farm machinery) due to wear, tear, age, and obsolescence.
Different accounting methods distribute this loss of value over the asset's useful life.
Key Formula or Approach:
In the Declining Balance Method, the annual depreciation (\(D_t\)) for year \(t\) is calculated as: \[ D_t = V_{t-1} \times x \] where:
- \(V_{t-1}\) is the book value (remaining value) of the asset at the beginning of year \(t\).
- \(x\) is a constant depreciation rate (expressed as a decimal).

Step 2: Detailed Explanation:
Let us analyze the distinct depreciation methods:
- Straight Line Method: This method assumes the asset loses an equal amount of value every year.
The annual depreciation is constant throughout the useful life: \[ D = \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Useful Life}} \] - Declining Balance Method: Also called the reducing balance method, this approach applies a constant percentage rate to the remaining book value at the start of each year.
As the book value decreases over time, the actual depreciation amount also declines each year, resulting in higher depreciation expenses in the early years.
This aligns with the question's definition.
- Sum-of-the-years-digits Method: This is an accelerated method where a changing fraction is applied to a constant depreciable base.
The fraction's denominator is the sum of the years of useful life, and the numerator decreases each year.
- Estimated Value Method: This method relies on periodic physical appraisals to determine the asset's current market value, without using a fixed annual mathematical formula.

Step 3: Final Answer:
The declining balance method calculates depreciation as a constant percentage of the asset's remaining value at the start of the year.