On January 3, 2014, Trusty Delivery Service purchased a truck at a cost of $90,000. Before placing the truck in service, Trusty spent $3,000 painting it, $1,500 replacing tires, and $4,500 overhauling the engine. The truck should remain in service for five years and have a residual value of $9,000. The truck's annual mileage is expected to be 22,500 miles in each of the first four years and 10,000 miles in the fifth year - 100,000 miles in total.

In deciding which depreciation method to use, Mikail Johnson, the general manager, requests a depreciation schedule for each of the depreciation methods (straight-line, units-of-production, and double-declining-balance).

Accumulated depreciation for Years 1 - 5 under:

Explanation:

The total cost of the asset is $90,000 + $3,000 + $1,500 + $4,500 = $99,000, since all the other costs were directly attributable cost and were necessary to bring the asset to usable form.

Under straight-line method, depreciation expense is (cost - residual value) / No of years = ($99,000 - $9,000) / 5 years = $18,000 yearly depreciation expense.

Accumulated depreciation for Years 1 to 5 is $18,000 x 5 years $90,000.

The unit-of-production method is used when the asset value closely relates to the units of output it is able to produce. It is expressed with the formula below:

(Original Cost - Salvage value) / Estimated production capacity x Units/year

At Year 1, depreciation expense (DE) is: ($99,000 - $9,000) / 100,000 miles x 22,500 miles = $20,250/year

Accumulated depreciation for the first four years is $20,250 x 4 years = $81,000.

At Year 5, depreciation = $90,000 / 100,000 miles x 10,000 miles = $9,000

Note that this depreciation method results in higher depreciation charge when the asset is heavily used, at this time, it was in Years 1 - 4.

Accumulated depreciation expense for Years 1 to 5, under this method, is $90,000 (addition of first four years and the Year 5).

The double-declining method is otherwise known as the reducing balance method and is given by the formula below:

Double declining method = 2 X SLDP X BV

SLDP = straight-line depreciation percentage

BV = Book value

SLDP is 100%/5years = 20%, then 20% multiplied by 2 to give 40%

At Year 1, 40% X $99,000 = $39,600

At Year 2, 40% X $59,400 ($99,000 - $39,600) = $23,760

At Year 3, 40% X $35,640 ($59,400 - $23,760) = $14,256

At Year 4, 40% X $21,384 ($35,640 - $14,256) = $8,554 approximately (the depreciation expense would stop at this stage since the amount falls below the residual value).

Accumulated depreciation expense for Years 1 to 4, under this method, is $86,170 (addition of all the yearly depreciation).

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