Question

The anna corporation buys equipment on september 1, year one, for $82,000 with a ten-year expected life and an estimated residual value of $10,000. the asset is depreciated using the double-declining balance method and the half-year convention. what is the net book value for this asset at the end of year three?

O $59,040
O $47,232
O $51,840
O $41,472

Answer 1

Using the double-declining balance method with a half-year convention, the equipment's initial cost is $82,000, and the residual value is $10,000. After calculating yearly depreciation, the net book value of the equipment at the end of year three would be $47,872, with $47,232 as the closest given option.

"The correct option is approximately option B"

Step-by-step explanation:

The subject is Business, specifically focused on depreciation calculations using the double-declining balance method with a half-year convention. To solve this, first, calculate the annual depreciation rate which is (1/10 life expectancy) * 2 = 20% doubled because it's the double-declining method. Then, apply the half-year convention for the first year by taking half of the annual depreciation. The equipment's initial cost is $82,000, the residual value is $10,000, and the depreciation for the first half-year would be calculated on the cost less residual value. For year one, the depreciation is $7,200 ([$82,000 - $10,000] * 20% * 0.5). This leaves a book value of $74,800 at the end of year one. For subsequent years, apply the full 20% on the new book value.

In year two, the depreciation is $14,960 ($74,800 * 20%), reducing the book value to $59,840. In year three, the depreciation expense is $11,968 ($59,840 * 20%), leaving an end-of-year three net book value of $47,872 ($59,840 - $11,968). Thus, the closest option given, $47,232, would be the net book value at the end of year three.