Determining asset cost, preparing depreciation schedules (3 methods), and identifying depreciation results that meet management objectives On January 3, 2018, Rapid Delivery Service purchased a truck at a cost of $100,000. Before placing the truck in service, Rapid spent $3,000 painting it, $600 replacing tires, and $10,400 overhauling the engine. The truck should remain in service for five years and have a residual value of $12,000. The truck’s annual mileage is expected to be 32,000 miles in each of the first four years and 8,000 miles in the fifth year—136,000 miles in total. In deciding which depreciation method to use, Andy Sargeant, the general manager, requests a depreciation schedule for each of the depreciation methods (straight-line, units-of-production, and double-declining-balance).
Requirements
Prepare a depreciation schedule for each depreciation method, showing asset cost, depreciation expense, accumulated depreciation, and asset book value.
Rapid prepares financial statements using the depreciation method that reports the highest net income in the early years of asset use, Consider the first year that Rapid uses the truck. Identify the depreciation method that meets the company’s objectives.

total cost = $100,000 + $3,000 + $600 + $10,400 = $114,000

straight line depreciation expense = ($114,000 - $12,000) x 1/5 = $20,400

year       depreciation expense        book value

1                   $20,400                         $93,600

2                  $20,400                         $73,200

3                  $20,400                         $52,800

4                  $20,400                         $32,400

5                  $20,400                         $12,000

RESULTS IN HIGHER INCOME DURING THE FIRST YEAR.

units of production deprecation = ($114,000 - $12,000) / 136,000 = $0.75 per mile

year       depreciation expense        book value

1                   $24,000                         $90,000

2                  $24,000                         $66,000

3                  $24,000                         $42,000

4                  $24,000                         $18,000

5                  $6,000                           $12,000

double-declining-balance depreciation:

depreciation year 1 = $114,000 x 2/5 = $45,600

depreciation year 2 = $68,400 x 2/5 = $27,360

depreciation year 3 = $41,040 x 2/5 = $16,416

depreciation year 4 = $24,624 x 2/5 = $9,850

depreciation year 5 = $14,774 - $12,000 = $2,774

year       depreciation expense        book value

1                   $45,600                         $68,400

2                  $27,360                         $41,040

3                  $16,416                           $24,624

4                  $9,850                           $14,774

5                  $2,774                            $12,000

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20