Final answer:
The book value of the combine after 2 years, using the double declining balance method of depreciation with a 5-year lifetime and a $5,000 salvage value, is closest to $22,000, which is option C.
Step-by-step explanation:
The subject of your question revolves around calculating the book value of an asset using the double declining balance method of depreciation. This method is a form of accelerated depreciation where the book value of the asset depreciates faster in the early years of its life. Here we need to calculate the book value of a combine after 2 years.
First, we calculate the annual depreciation rate using the formula: (100% / useful life) × 2. For a 5-year useful life, this results in a rate of 40% per year. The combine originally cost $50,000, and subtracting the $5,000 salvage value gives us a depreciable base of $45,000.
- Year 1 depreciation: $45,000 × 40% = $18,000.
- Book value at the end of Year 1: $50,000 - $18,000 = $32,000.
- Year 2 depreciation: $32,000 - $5,000 salvage value = $27,000 depreciable base.
$27,000 × 40% = $10,800. - Book value at the end of Year 2: $32,000 - $10,800 = $21,200.
The closest answer to $21,200 is $22,000, which corresponds to option C.