The formula for calculating the double-declining-balance method is
a. book value at beginning of the year less residual value x 2/ estimated service life.
b. historical cost less residual value x 2/estimated service life.
c. historical cost x 1/service life.
d. book value at beginning of year x 2/estimated service life
The Correct Answer and Explanation is:
The correct answer is d. book value at beginning of year x 2/estimated service life.
Explanation:
The double-declining-balance (DDB) method is one of the accelerated depreciation methods used in accounting to allocate the cost of an asset over its useful life. It is a method that depreciates an asset more heavily in the earlier years of its useful life and less in the later years. The formula for calculating depreciation using the double-declining-balance method is:
[
\text{Depreciation Expense} = \text{Book Value at Beginning of Year} \times \left(\frac{2}{\text{Estimated Service Life}}\right)
]
Here’s how it works:
- Book Value at Beginning of the Year: This is the asset’s remaining book value at the start of the current year, which is its historical cost minus any accumulated depreciation from prior years.
- Estimated Service Life: This refers to the estimated number of years the asset is expected to be useful for the company.
- The Double Factor (2): The “2” represents the factor by which the asset is depreciated. This is why it is called the double-declining-balance method—it uses twice the straight-line depreciation rate.
Steps to calculate DDB depreciation:
- Initial Year: In the first year, depreciation is calculated by applying the formula to the full book value of the asset (which is equal to its historical cost, since no depreciation has been recorded yet).
- Subsequent Years: In the following years, the depreciation expense is calculated using the book value at the beginning of each year (i.e., the remaining value after deducting depreciation from previous years).
- Residual Value: The depreciation continues until the asset’s book value equals its estimated residual (salvage) value. After this point, no further depreciation is recorded.
Why other answers are incorrect:
- a. Book value at the beginning of the year less residual value x 2/estimated service life: The formula does not subtract residual value in the DDB method before calculating depreciation. Residual value is considered at the end of the asset’s useful life, not for annual depreciation calculations.
- b. Historical cost less residual value x 2/estimated service life: This is incorrect because the DDB method uses the book value at the beginning of the year, not historical cost less residual value.
- c. Historical cost x 1/service life: This formula represents straight-line depreciation, not the double-declining-balance method.
Thus, d correctly reflects the double-declining-balance method’s approach.