Question

Depreciation for Partial Periods

Bar Delivery Company purchased a new delivery truck for $52,200 on April 1, 2016. The truck is expected to have a service life of 10 years or 144,000 miles and a residual value of $1,920. The truck was driven 9,200 miles in 2016 and 11,300 miles in 2017. Bar computes depreciation to the nearest whole month.

Required:

Compute depreciation expense for 2016 and 2017 using the
For interim computations, carry amounts out to two decimal places. Round your final answer to the nearest dollar.
Straight-line method

2016: $____
2017: $____

Sum-of-the-years'-digits method

2016: $____
2017: $____

Double-declining-balance method

2016: $____
2017: $____

Activity method

2016: $____
2017: $____

For each method, what is the book value of the machine at the end of 2016? At the end of 2017?
(Round your answers to the nearest dollar.)
Straight-line method

2016: $____
2017: $____

Sum-of-the-years'-digits method

2016: $____
2017: $____

Double-declining-balance method

2016: $____
2017: $____

Activity method

2016: $____
2017: $____

The book value of the asset in the early years of the asset's service will be (about the same/higher/lower) under an accelerated method as compared to the straight-line method. The (activity/double-declining balance/straight-line/sum-of-the-years-digits) method is appropriate when the service life of the asset is affected primarily by the amount the asset is used.

Answer 1

Annual depreciation expense:

	Straight-line depreciation
2016	$ 3,771
2017	$ 5,028
	Sum-of-the-years'-digits
2016	$ 6,856
2017	$ 8,456
	Double-declining-balance
2016	$ 7,830
2017	$ 8,874
	Activity method
2016	$ 3,212
2017	$ 3,946

Year end book value:

	Straight-line depreciation
2016	$ 48,429
2017	$ 43,401
	Sum-of-the-years'-digits
2016	$ 45,344
2017	$ 36,887
	Double-declining-balance
2016	$ 44,370
2017	$ 35,496
	Activity method
2016	$ 48,988
2017	$ 48,254

Explanation:

Straight-line depreciation method:

Annual straight-line depreciation = Depreciable amount /Useful life

                                                            = ($ 52,200 - $ 1,920)/10 = $ 50,280/10 = $ 5,028

Depreciation in 2016 = Depreciation expense x No. of months/12

                                       = $ 5,028 x 9/12 = $ 5,028 x 0.75 = $ 3,771

Depreciation in 2017 = $ 5,028

Book value at the end of 2016 = $ 52,200 - $ 5,028 = $ 48,429

Book value at the end of 2017 = $ 48,429 - $ 5,028 = $ 43,401

Sum-of-the-years'-digits method:

Sum-of-the-years'-digits depreciation = Depreciable Base x Remaining useful life/Sum of year’s Digit

Sum-of-the-years'-digits depreciation in 1^st year = $ 50,280 x 10/ [10 x (10+1)/2]

                                                                                         = $ 50,280 x 10/ [(10 x 11)/2)]

                                                                                          = $ 50,280 x 10/ (110/2)

                                                                                          = $ 50,280 x 10/55 = $ 50,280 x 0.181818182

                                                                                          = $ 9,141.818182 or $ 9,141.82

Sum-of-the-years'-digits depreciation in 2^nd year = $ 50,280 x 9/ 55

                                                                                        = $ 50,280 x 0.163636364

                                                                                         = $ 8,227.636364 or $ 8,227.64

Depreciation expense in year 2016 = 9 x $ 9,141.82/12 = 9 x 761.8181818 = $ 6,856.36

Depreciation expense in year 2017 = 9 x $ 9,141.82/12 = 3 x $ 9,141.82/12 + 9 x $ 8,227.64/12

                                                               = 3 x $ 761.8181818 + 9 x $ 685.6363636

                                                               = $ 2,285.4545 + $ 6,170.727 = $ 8,456.18

Book value at the end of 2016 = $ 52,200 - $ 6,856.36 = $ 45,343.64

Book value at the end of 2017 = $ 45,343.64 - $ 8,456.18 = $ 36,887.45

Double-declining-balance method:

Double-declining depreciation = 2 × Straight-line depreciation rate × Book value at the beginning of the year

Depreciation expense in 2016 = 2 x 10 % x $ 52,200 x 9/12

                                                          = 20 % x $ 52,200 x 9/12

                                                         = $ 7,830

Book value at the end of year 2016 = $ 52,200 - $ 7,830 = $ 44,370

Depreciation expense in year 2017 = 20 % x $ 44,370

                                                          = $ 8,874

Book value at the end year 2017 = $ 44,370 - $ 8,874 = $ 35,496

Activity method:

Depreciation expense = (Cost – salvage value) x Actual activity performed during the period/total estimated time activity of the asset

Depreciation expense in 2016 = $ 50,280 x 9,200/144,000

                                                      = $ 50,280 x 0.063888889 = $ 3,212.3333 or $ 3,212

Book value at the end of year 2016 = $ 52,200 - $ 3,212 = $ 48,988

Depreciation expense in 2016 = $ 50,280 x 11,300/144,000

                                                      = $ 50,280 x 0.078472 = $ 3,945.583 or $ 3,946

Book value at the end of year 2017 = $ 52,200 - $ 3,946 = $ 48,254