XYZ Company purchased a new machine on January 1, 2011 and assigned it an 8-year

Question

XYZ Company purchased a new machine on January 1, 2011 and assigned it an 8-year life with a residual value (note the amount of the residual value is intentionally omitted from the problem). Using the straight-line depreciation method, the book value of the machine at December 31, 2013 was $47,250. Had XYZ Company used double-declining balance depreciation, the depreciation expense recorded on the machine in 2012 would have been $13,500.
Calculate the residual value assigned to the machine. Do not use decimals in your answer

Explanation / Answer

Straight-line depreciation rate = 1/8 = 0.125 or 12.5%

Therefore,

Double-declining balance depreciation rate = 12.5% x 2 = 25%

Double-declining balance depreciation for year 2 = $13,500

Therefore,

Book value of the machine at the end of year 1 = $13,500 x 100/25 = $54,000

The book value at the end of year 1 = Cost - 1st year's depreciation = Cost x ( 1 - 25%)

Or,

$54,000 = Cost x (1-0.25)

Or,

Cost = $54,000 / 0.75 = $72,000

Now, book value of the machine on December 31, 2013, under straight-line depreciation is $47,250.

Therefore,

Annual depreciation under straight-line method = ($72,000 - $47,250) / 3 = $8,250

Or,

$8,250 = [ cost - residual value ] / 8

Or,

$72,000 - residual value = $66,000

Therefore,

Residual value = $6,000

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