Question

When originally purchased, a vehicle costing $23,000 had an estimated useful life of 8 years and an estimated salvage value of $3,000. after 4 years of straight-line depreciation, the asset's total estimated useful life was revised from 8 years to 6 years and there was no change in the estimated salvage value. the depreciation expense in year 5 equals:?

Answer 1

For the initial case: the annual straight-line depreciation would be (23,000 - 3,000) / 8 = $2,500/yr. After 4 years, the value would be lower by $2500*4 = $10000, so 23,000 - 10,000 = $13,000 book value.
Revising the estimated life down to 6 years means that only 2 years remain, so the new straight-line depreciation is (13,000 - 3,000) / 2 = $5,000/yr
Therefore, the depreciation expense in year 5 is $5,000.

Answer 2

The correct answer is:

$5,000.

Explanation:

When it is first purchased, the depreciation expense is calculated using the formula:

$\text{Depreciation expense}=\frac{\text{Cost}-\text{Salvage Value}}{\text{Useful Life}}$

The cost was $23,000; the salvage value was $3,000; and the useful life was 8 years:

$\text{Depreciation Expense}=\frac{23000-3000}{8}=\frac{20000}{8}= \ 2500$

This means the value of the vehicle depreciates $2500 per year.

After 4 years, the vehicle would depreciate 2500(4) = $10,000.

This makes the new value $23000-$10000 = $13000.

Reevaluating the depreciation expense at this point, we use $13000 for the "cost" (current value), $3000 is still the salvage value, and now the total useful life was 6; we take 4 off of this, since it has already been 4 years:

$\text{Depreciation Expense}=\frac{13000-3000}{6-4}=\frac{10000}{2}= \ 5000$

The depreciation expense in year 5 is $5,000.