Question

Depreciation for Partial Periods

Malone Delivery Company purchased a new delivery truck for $36,000 on April 1, 2019. The truck is expected to have a service life of 5 years or 90,000 miles and a residual value of $3,000. The truck was driven 8,000 miles in 2019 and 20,000 miles in 2020. Malone computes depreciation expense to the nearest whole month.

Required:

1. Compute depreciation expense for 2019 and 2020 using the following methods: (Round your answers to the nearest dollar.)
   1. Straight-line method

      2019	$
      2020	$

   2. Sum-of-the-years'-digits method

      2019	$
      2020	$

   3. Double-declining-balance method

      2019	$
      2020	$

   4. Activity method

      2019	$
      2020	$

2. For each method, what is the book value of the machine at the end of 2019? At the end of 2020? (Round your answers to the nearest dollar.)
   1. Straight-line method

      2019	$
      2020	$

   2. Sum-of-the-years'-digits method

      2019	$
      2020	$

   3. Double-declining-balance method

      2019	$
      2020	$

   4. Activity method

      2019	$
      2020	$

Answer 1

Answer to Part 1.

Straight Line Method:
Straight Line Depreciation per year = (Cost – Residual Value) / Useful Life
Straight Line Depreciation per year = ($36,000 - $3,000) / 5
Straight Line Depreciation per year = $6,600

Depreciation Expense for 2019 = $6,600 * 9/12
Depreciation Expense for 2019 = $4,950

Depreciation Expense for 2020 = $6,600

Sum of the years’ digit Method:
Sum of the years’ digit = n (n + 1) / 2
Sum of the years’ digit = 5 * (5 + 1) / 2 = 15

Depreciable Expense = Remaining Useful Life of the asset / Sum of the years’ digit * Depreciable Cost
Depreciable Cost = Cost – Residual Value
Depreciable Cost = $36,000 - $3,000 = $33,000

Depreciation Expense for 2019 = $33,000 * 5/15 * 9/12
Depreciation Expense for 2019 = $8,250

Depreciation Expense for 2020 = ($33,000 * 5/15 * 3/12) + ($33,000 * 4/15 * 9/12)
Depreciation Expense for 2020 = $9,350

Double Declining Balance Method:
Double Declining Depreciation Ratio = 2 * Straight Line Depreciation Rate
Straight Line Depreciation Rate = 1 / Useful Life
Straight Line Depreciation Rate = 1 / 5 = 20%
Double Declining Depreciation Ratio = 2 *20% = 40%

Depreciation Expense for 2019 = $36,000 * 40%
Depreciation Expense for 2019 = $14,400

Depreciation Expense for 2020 = ($36,000 - $14,400) * 40%
Depreciation Expense for 2020 = $8,640

Activity Method:
Depreciation per mile driven = (Cost – Residual Value) / Expected Miles driven
Depreciation per mile driven = ($36,000 - $3,000) / 90,00
Depreciation per mile driven = $0.3667

Depreciation Expense for 2019 = 8,000 * $0.3667
Depreciation Expense for 2019 = $2,933

Depreciation Expense for 2020 = 20,000 * $0.3667
Depreciation Expense for 2020 = $7,334

Answer to Part 2.

Straight Line Method:
Book Value at the end of year 2019 = Cost – Depreciation Expense for the year
Book Value at the end of year 2019 = $36,000 - $4,950
Book Value at the end of year 2019 = $31,050

Book Value at the end of year 2020 = Book Value at the year end 2019 - Depreciation Expense for the year
Book Value at the end of year 2020 = $31,050 - $6,600
Book Value at the end of year 2020 = $24,450

Sum of the years’ digit Method:
Book Value at the end of year 2019 = Cost – Depreciation Expense for the year
Book Value at the end of year 2019 = $36,000 - $8,250
Book Value at the end of year 2019 = $27,750

Book Value at the end of year 2020 = Book Value at the year end 2019 - Depreciation Expense for the year
Book Value at the end of year 2020 = $27,750 - $9,350
Book Value at the end of year 2020 = $18,400

Double Declining Balance Method:
Book Value at the end of year 2019 = Cost – Depreciation Expense for the year
Book Value at the end of year 2019 = $36,000 - $14,400
Book Value at the end of year 2019 = $21,600

Book Value at the end of year 2020 = Book Value at the year end 2019 - Depreciation Expense for the year
Book Value at the end of year 2020 = $21,600 - $8,640
Book Value at the end of year 2020 = $12,960

Activity Method:
Book Value at the end of year 2019 = Cost – Depreciation Expense for the year
Book Value at the end of year 2019 = $36,000 - $2,933
Book Value at the end of year 2019 = $33,067

Book Value at the end of year 2020 = Book Value at the year end 2019 - Depreciation Expense for the year
Book Value at the end of year 2020 = $33,067 - $7,334
Book Value at the end of year 2020 = $25,733