Depreciation Methods Questions and Answers

Answer: C

The geometric charge starts large and shrinks, so at some point a straight line write-off of the remaining book value over the remaining life gives more. Switching at that point maximises the present worth of the tax saving.

Answer: D

Correct answer: sum of the integers from one to n

The denominator is \( 1 + 2 + \cdots + n = n(n+1)/2 \), which for a five-year asset is 15. The numerator is the years of life remaining, so the fractions run 5/15, 4/15 and so on down to 1/15 - a charge that declines by equal steps and sums to exactly the depreciable base.

Answer: A

Correct answer: increases each year

The sinking fund method assumes a fund earning interest, so the amounts set aside early have longer to accumulate and less needs to be charged then; the charge rises year by year. It is the mirror image of the accelerated methods and is rarely used for tax, since it defers the deduction rather than advancing it.

Answer: B

Correct answer: the output actually produced

The units of production method treats the asset as having a total output rather than a total life, and charges each year in proportion to what it produced. It matches cost to use exactly, which is why it suits a machine whose work varies from year to year - and why an idle year attracts no charge at all.

Answer: C

It is driven by production rather than the calendar, so an asset standing idle for a whole year accrues no depreciation at all. The other three all charge something in every year regardless of whether the asset was used.

Answer: D

Correct answer: a taxable gain

Selling above book value means more depreciation was charged than the asset actually lost, so the excess is recaptured and taxed. Selling below book value gives a deductible loss for the same reason in reverse. Book value is not a valuation, so a gain or loss on disposal is the normal case rather than a sign of error.

Answer: A

Correct answer: natural resources that are consumed

Depletion applies to a wasting asset - a mine, an oil field, a quarry - whose value is consumed as the resource is removed rather than as equipment wears out. The parallel is exact in purpose and different in measure: depreciation follows time or use, depletion follows the quantity extracted.

Answer: B

Correct answer: units extracted against the total recoverable

Cost depletion divides the property’s cost by the estimated recoverable units to give a rate per unit, and charges that rate on the units taken each year. It is the depletion counterpart of the units of production method, and it depends on an estimate of the reserve that may itself be revised as extraction proceeds.

Answer: C

Correct answer: gross income from the property

Percentage depletion applies a statutory percentage to the gross income from the property, with no reference to what the property cost. It can therefore exceed the cost over the life, which is why it is a policy instrument rather than a cost allocation, and why it is limited by a proportion of taxable income.

Answer: D

Correct answer: a collection of similar assets treated as one account

Group depreciation pools assets of similar life and type into a single account and applies one rate to the whole, which avoids tracking each item separately. Retirements are charged against the accumulated depreciation of the pool rather than computed individually, so no gain or loss is recognised on an ordinary disposal.