A light truck is purchased on January 1 at a cost of $19,000. It is expected to serve for five years and have a salvage value of $1,000. Calculate the depreciation expense for the first and third years of the truck's life using the following methods:

Depreciation Expense
Year 1 Year 3
1.Straight-line 3600 3600
2.Double-declining-balance $ $
3.Sum-of-the-years'-digits $ $

I have tried the examples in my book but I am not getting the correct solution. I want to understand what I am doing from start to finish because I have a whole chapter on depreciation. Please help.

To calculate the depreciation expense for the first and third years of the truck's life using different methods, let's go through each method step by step.

1. Straight-line depreciation:
This method evenly spreads the depreciation expense over the useful life of the asset. To calculate the annual depreciation expense, you need to subtract the salvage value from the initial cost and divide it by the useful life.

Depreciation expense = (Initial cost - Salvage value) / Useful life

In this case, the initial cost of the truck is $19,000, the salvage value is $1,000, and the useful life is 5 years.

For year 1:
Depreciation expense = ($19,000 - $1,000) / 5 = $18,000 / 5 = $3,600

For year 3, you will use the same formula:
Depreciation expense = ($19,000 - $1,000) / 5 = $18,000 / 5 = $3,600

2. Double-declining-balance depreciation:
This method assumes that the asset depreciates faster in the early years and slows down over time. To calculate the annual depreciation expense, you start with the initial cost and multiply it by a fixed rate, which is usually double the straight-line rate.

Depreciation expense = (Net Book Value at the beginning of the period) * (Double the straight-line rate)

To find the net book value at the beginning of each year, you subtract the accumulated depreciation from the initial cost.

For year 1:
Depreciation rate = Double the straight-line rate = 2 * (1 / Useful life) = 2 * (1 / 5) = 0.4 or 40%
Depreciation expense = ($19,000 - $1,000) * 0.4 = $18,000 * 0.4 = $7,200

For year 3:
Depreciation rate remains the same: 0.4 or 40%
Depreciation expense = ($19,000 - accumulated depreciation at the end of year 2) * 0.4
To find accumulated depreciation at the end of year 2, multiply the depreciation rate by the net book value at the beginning of year 2.

Net book value at the beginning of year 2 = initial cost - accumulated depreciation at the end of year 1
= $19,000 - ($19,000 * 0.4) = $19,000 - $7,600 = $11,400

Depreciation expense for year 3 = ($19,000 - $11,400) * 0.4 = $7,600 * 0.4 = $3,040

3. Sum-of-the-years'-digits depreciation:
This method also assumes that the asset depreciates faster in the early years. To calculate the annual depreciation expense, you determine the sum of the digits of the useful life and then calculate the fraction of the sum that represents the current year.

Depreciation expense = (Remaining life / Sum of the years' digits) * (Initial cost - Salvage value)

Sum of the years' digits = (Useful life * (Useful life + 1)) / 2

For year 1:
Remaining life = Useful life - 0 = 5
Sum of the years' digits = (5 * (5 + 1)) / 2 = 15

Depreciation expense = (5 / 15) * ($19,000 - $1,000) = (1 / 3) * $18,000 = $6,000 / 3 = $2,000

For year 3:
Remaining life = Useful life - 2 = 5 - 2 = 3
Sum of the years' digits = (3 * (3 + 1)) / 2 = 6

Depreciation expense = (3 / 6) * ($19,000 - $1,000) = (1 / 2) * $18,000 = $9,000 / 2 = $4,500

By following these calculations, you should be able to determine the correct depreciation expenses for the first and third years using the provided methods.

To calculate the depreciation expense for the first and third years using different depreciation methods, let's start with the information provided:

Cost of the truck: $19,000
Salvage value: $1,000
Expected service life: 5 years

1. Straight-Line Method:
The straight-line method assumes an equal depreciation amount each year over the useful life of the asset.

To calculate the annual depreciation expense using the straight-line method, you can use the following formula:
Depreciation Expense = (Cost - Salvage Value) / Useful Life

For Year 1:
Depreciation Expense = ($19,000 - $1,000) / 5 = $3,600

For Year 3, the calculation remains the same as the depreciation expense remains constant each year:
Depreciation Expense = ($19,000 - $1,000) / 5 = $3,600

2. Double-Declining-Balance Method:
The double-declining-balance method assumes a higher depreciation expense in the earlier years, which gradually decreases over time.

To calculate the annual depreciation expense using the double-declining-balance method, you can use the following formula:
Depreciation Expense = Book Value at the Beginning of the Year * (2 / Useful Life)

For Year 1:
Book Value at the Beginning of the Year = Cost = $19,000
Depreciation Expense = $19,000 * (2 / 5) = $7,600

For Year 3, you need to calculate the Book Value at the Beginning of the Year first:
Book Value at the Beginning of Year 3 = Cost - Total Depreciation Expense until Year 2
Total Depreciation Expense until Year 2 = Depreciation Expense Year 1 + Depreciation Expense Year 2
Total Depreciation Expense until Year 2 = $7,600 + $7,600 = $15,200
Book Value at the Beginning of Year 3 = $19,000 - $15,200 = $3,800
Depreciation Expense = $3,800 * (2 / 5) = $1,520

3. Sum-of-the-Years'-Digits Method:
The sum-of-the-years'-digits method assumes a higher depreciation expense in the earlier years, which gradually decreases over time. The formula considers the ratio of remaining useful life to the sum of the digits.

To calculate the annual depreciation expense using the sum-of-the-years'-digits method, you can use the following formula:
Depreciation Expense = (Remaining Useful Life / Sum of the Years' Digits) * Depreciable Amount

Depreciable Amount = Cost - Salvage Value
Sum of the Years' Digits = 1 + 2 + 3 + 4 + 5 = 15

For Year 1:
Depreciable Amount = $19,000 - $1,000 = $18,000
Depreciation Expense = (5 / 15) * $18,000 = $6,000

For Year 3, you need to calculate the Remaining Useful Life first:
Remaining Useful Life = Useful Life - Number of Years Passed
Remaining Useful Life = 5 - 3 = 2
Depreciation Expense = (2 / 15) * $18,000 = $2,400

So, the depreciation expense for the first and third years using the different methods would be:

1. Straight-Line: Year 1: $3,600, Year 3: $3,600
2. Double-Declining-Balance: Year 1: $7,600, Year 3: $1,520
3. Sum-of-the-Years'-Digits: Year 1: $6,000, Year 3: $2,400