Cutter Enterprises purchased equipment for $54,000 on January 1, 2021. The equipment is expected to have a five-year life and a residual value of $8,400. Using the double-declining-balance method, depreciation for 2021 and the book value at December 31, 2021, would be:

Book  value at December 31, 2021 =$32,400

Explanation:

using double declining balance method

Depreciation expense = 2×Straight-line depreciation percent ×Book value

Given value of machine = $54,000

Residual value = $8,400

Expected life = 5 years

But

straight line depreciation percent = 100% /5years = 20%

Depreciation expense = 2×Straight-line depreciation percent ×Book value

= 2*20% x$54,000  = 40% x $54,000=$21,600

or

Depreciation expense by double declining  = depreciation rate x cost of equipment

but depreciation rate = 1/estimated useful life x 2= 1/5 x 2= 2/5 x100% =40%

= 40% x $54,000= $21,600

Book  value at December 31, 2021, = Purchase cost - depreciation expense

=$54,000 - $21,600=$32,400

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