Assume that at the beginning of 2000, Quick Travel, a FedEx competitor purchased a used Boeing 737 aircraft at a cost of 60,000,000. Quick Travel expects the plane to remain useful for 5 years (5 million miles) and to have a residual value of 5,000,000. Quick Travel expects to fly the plane 775,000 miles the first year 1,200,000 miles each year 2 through 4 and 625,000 miles the last year.
Compute Quick Travels first year depreciation on the plane using the following methods: Straight-line, units of production, double declining balance. Show the airplanes book value at the end of the first year under each depreciation method.
Show the airplane book value at the end of the first year under each method.
To compute Quick Travel's first-year depreciation on the plane using different methods and determine the book value at the end of the first year, we need to understand the formulas and approaches for each method.
1. Straight-Line Depreciation Method:
The straight-line method allocates an equal amount of depreciation over the useful life of the asset. To calculate the annual depreciation expense, we take the difference between the initial cost and the residual value, and divide it by the useful life of the asset.
Annual Depreciation Expense = (Initial Cost - Residual Value) / Useful Life
In this case:
Initial Cost = $60,000,000
Residual Value = $5,000,000
Useful Life = 5 years
Annual Depreciation Expense = ($60,000,000 - $5,000,000) / 5 = $11,000,000
To find the book value at the end of the first year, we subtract the depreciation expense from the initial cost.
Book Value at the end of Year 1 = Initial Cost - Depreciation Expense
Book Value at the end of Year 1 = $60,000,000 - $11,000,000 = $49,000,000
2. Units of Production Depreciation Method:
The units of production method allocates depreciation based on the usage or production level of the asset. In this case, it will be based on the number of miles flown.
First, we calculate the depreciation rate per mile:
Depreciation Rate per Mile = (Initial Cost - Residual Value) / Total Miles
In this case:
Total Miles = Sum of miles flown in each year: 775,000 + 1,200,000 + 1,200,000 + 1,200,000 + 625,000 = 5,000,000
Depreciation Rate per Mile = ($60,000,000 - $5,000,000) / 5,000,000 = $11
To calculate the first-year depreciation expense, we multiply the depreciation rate per mile by the miles flown in the first year.
First-Year Depreciation Expense = Depreciation Rate per Mile * Miles Flown in Year 1
First-Year Depreciation Expense = $11 * 775,000 = $8,525,000
Book Value at the end of Year 1 = Initial Cost - Depreciation Expense
Book Value at the end of Year 1 = $60,000,000 - $8,525,000 = $51,475,000
3. Double Declining Balance Depreciation Method:
The double declining balance method applies a depreciation rate that is double the straight-line rate. It allocates a higher percentage of depreciation in the earlier years, resulting in a decreasing depreciation expense over time.
To calculate the double declining balance depreciation rate, we divide 100% by the useful life of the asset and multiply it by 2.
Double Declining Balance Rate = (100% / Useful Life) * 2
In this case:
Double Declining Balance Rate = (100% / 5) * 2 = 40%
To calculate the first-year depreciation expense, we multiply the double declining balance rate by the book value at the beginning of the year.
First-Year Depreciation Expense = Double Declining Balance Rate * Book Value at the beginning of Year 1
Book Value at the beginning of Year 1 = Initial Cost
First-Year Depreciation Expense = 40% * $60,000,000 = $24,000,000
Book Value at the end of Year 1 = Initial Cost - Depreciation Expense
Book Value at the end of Year 1 = $60,000,000 - $24,000,000 = $36,000,000
To summarize, the first-year depreciation and book value at the end of the first year under each method are as follows:
- Straight-Line Method:
First-Year Depreciation Expense: $11,000,000
Book Value at the end of Year 1: $49,000,000
- Units of Production Method:
First-Year Depreciation Expense: $8,525,000
Book Value at the end of Year 1: $51,475,000
- Double Declining Balance Method:
First-Year Depreciation Expense: $24,000,000
Book Value at the end of Year 1: $36,000,000