Question

Company purchased a new plant asset on April 1, 2025, at a cost of $711,000. It was estimated to have a service life of 20 years and a salvage value of $60,000. Judds' accounting period is the calendar year. Instructions a. Compute the depreciation for this asset for 2025 and 2026 using the sum-of-the-years'-digits method. b. Compute the depreciation for this asset for 2025 and 2026 using the double-declining-balance method.

Answer 1

The depreciation for the asset in 2025 using the sum-of-the-years'-digits method is $66,857.14, and for 2026 it is $60,761.90. Using the double-declining-balance method, the depreciation for 2025 is $71,100, and for 2026 it is $63,990.

Step-by-step explanation:

Using the sum-of-the-years'-digits method:

1. Compute the total years of service life for the asset. In this case, it is 20 years.
2. Calculate the sum of the digits: 20 + 19 + 18 + ... + 1 = 210.
3. Calculate the depreciation expense for each year using the formula: (Total depreciation cost) x (Remaining service life / Sum of the digits).
4. For 2025, the depreciation would be: ($711,000 - $60,000) x (20 / 210) = $66,857.14.
5. For 2026, the depreciation would be: ($711,000 - $60,000) x (19 / 210) = $60,761.90.

Using the double-declining-balance method:

1. Calculate the straight-line depreciation rate: (1 / Service life) x 2. In this case, it is (1 / 20) x 2 = 0.10 or 10%.
2. Calculate the depreciation expense for each year using the formula: (Net book value at the beginning of the year) x (Depreciation rate).
3. For 2025, the depreciation would be: ($711,000 - $0) x 10% = $71,100.
4. For 2026, the depreciation would be: ($711,000 - $71,100) x 10% = $63,990.

Answer 2

Depreciation for a new plant asset with a 20-year life and salvage value is calculated for 2025 and 2026 using sum-of-the-years'-digits and double-declining-balance methods. First year's depreciation will be prorated for 9 months, and the base for these calculations is the asset's cost minus the salvage value.

Step-by-step explanation:

The student's question involves computing the depreciation of a plant asset using two different methods: the sum-of-the-years'-digits method and the double-declining-balance method. Depreciation for 2025 and 2026 must be calculated for a plant asset with a purchase date of April 1, 2025, a cost of $711,000, a service life of 20 years, and a salvage value of $60,000.

For the sum-of-the-years'-digits method in 2025, since the asset was purchased on April 1, you would only calculate depreciation for 9 months of the year. You must first calculate the total sum of the years' digits for a 20-year life span, which would be 210 (20 + 19 + 18 + ... + 1). The fraction to apply for the first year is 20/210, and for the second year, it is 19/210. The depreciable base is the cost minus the salvage value, which is $711,000 - $60,000 = $651,000.

For the double-declining-balance method, the annual depreciation rate is 2 × (1/20) = 10%. In the first year, depreciation is only for nine months, and in the second year, it is for the full 12 months, with the calculation based on the book value at the beginning of each year. The book value decreases each year after accounting for depreciation.