Question

XYZ Company purchased a new piece of equipment on January 1, 2022. The
following information relates to the equipment purchased:

Purchase price ..............     ?
Residual value ..............     ?
Life ........................   8 years

Using the straight-line depreciation method, the equipment's book value
at December 31, 2025 would be $82,700.

Using the double-declining balance depreciation method, the depreciation
expense recorded on the equipment in 2023 would be $30,000.

Calculate the residual value assigned to this piece of equipment.

Answer 1

a)Double declining depreciation rate = 2 /useful life

                                            = 2/8

                                             = .25 or 25%

We have to make reverse working under double declining depreciation method to compute cost /Book value at purchase date.Let the purchase cost /book value at beginning of 2022 be"X" so depreciation expense for 2022 = X *.25 =.25X

Purchase cost -Depreciation expense for 2022 = Book value at end of 2022

X -.25X = 120000

.75X =120000

X =120000/.75

= 160000

Year	Depreciation expense	Book value at beginning/purchase cost
2023	30000	30000/.25 = 120000
2022	160000*.25=40000	160000

Purchase price = 160000

b)Under straight line method:

Book value at end of Dec 31,2025 =Cost - Accumulated depreciation over 4 years       [1Jan2022-31Dec 2025]

   82700 = 160000- Accumulated depreciation over 4 years     

Accumulated depreciation over 4 years      = 160000-82700

                                  = 77300

or depreciation expense per year = 77300/4 = 19325

Depreciation expense per year =[cost -residual value /useful life

19325= [160000-residual value]/8

19325*8 = [160000-residual value]

[160000-residual value] = 154600

Residual value =160000-154600

                = 5400