Question

A video-recording system was purchased 3 years ago at a cost of $38,000. A 5-year recovery period and DDB (Double Declining Balance) depreciation have been used to write off the basis. The system is to be replaced this year with a trade-in value of $6,500. What is the difference between the book value and the trade-in value? The difference between the book value and the trade-in value is $ ______.

Answer 1

The difference between the book value of the video-recording system after three years of DDB depreciation and the trade-in value is $1,708.

Step-by-step explanation:

The question involves calculating the difference between the book value and the trade-in value of a video-recording system using the Double Declining Balance (DDB) method of depreciation. The original cost of the system was $38,000, and it has been depreciated over 3 years of its 5-year recovery period.

Calculating the depreciation, we first take two times the straight-line depreciation rate. Since it's a 5-year period, the rate is 20% per annum, doubled to 40% for DDB. For the first year, the depreciation is 40% of $38,000, which is $15,200, leaving a book value of $22,800.

In the second year, we again apply 40% to the new book value, leading to $9,120 depreciation and a new book value of $13,680. In the third year, depreciation is 40% of $13,680 which is $5,472, leaving a book value of $8,208. The difference between this book value and the trade-in value of $6,500 is obtained by subtracting $6,500 from $8,208, which equals $1,708.