Difficulty: Intermediate | Prerequisites: Understanding of PP&E initial measurement (see companion notes). Comfort with basic algebra for depreciation calculations.
Once an asset is on the books, the next question is how to allocate its cost over its useful life. That allocation is depreciation for tangible assets and depletion for natural resources. This topic also covers what happens when an asset's value drops below its carrying amount (impairment) and how to handle changes in estimates like useful life or residual value. You will need to compute depreciation under multiple methods and know which method produces which pattern of expense. This is one of the most calculation-heavy sections on Exam 3.
Depreciation spreads an asset's cost (minus residual value) over its useful life. The four main methods, straight-line, sum-of-the-years'-digits, double-declining-balance, and units-of-production, produce different expense patterns. Depletion works the same way for natural resources. Impairment writes an asset down when its carrying amount is no longer recoverable, and changes in accounting estimates are applied prospectively.
Straight-Line Depreciation
Allocates equal depreciation expense to each year of the asset's useful life. Formula: (Cost - Residual Value) / Useful Life. Think of it as the simplest, most even spread.
Sum-of-the-Years'-Digits (SYD)
An accelerated method that front-loads depreciation expense. Each year's fraction uses the remaining years of life as the numerator and the sum of all years' digits as the denominator. Produces a declining pattern of expense.
Double-Declining-Balance (DDB)
An accelerated method that applies twice the straight-line rate to the asset's book value (ignoring residual value in the rate calculation). The asset is never depreciated below its residual value.
Units-of-Production
Depreciation is based on actual usage or output rather than the passage of time. This is the one method that does not necessarily produce a declining pattern, because expense depends on how much the asset is used each period.
Depletion
The allocation of the cost of a natural resource (oil, minerals, timber) to expense as the resource is extracted. Journal entry: Debit Depletion, Credit Natural Resource.
Impairment
A write-down that occurs when an asset's carrying amount exceeds its fair value and the carrying amount is not recoverable. Fair value is measured using discounted cash flows, market prices, or prices of similar assets, never undiscounted cash flows.
Change in Accounting Estimate
A revision to useful life, residual value, or depreciation method. Recorded prospectively, meaning it affects the current and future periods only, with no restatement of prior periods.
All four methods below use the same asset: a delivery van costing $40,000 with an expected service life of 8 years and a residual value of $4,000. Depreciable base = $40,000 - $4,000 = $36,000.
Annual depreciation = $36,000 / 8 = $4,500 per year. The same amount every year.
Sum of digits for 8 years = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36.
Year 1: (8/36) x $36,000 = $8,000
Year 2: (7/36) x $36,000 = $7,000
Year 3: (6/36) x $36,000 = $6,000
And so on, declining each year.
The second-year depreciation is $7,000.
Straight-line rate = 1/8 = 12.5%. Double rate = 25%. Applied to book value (not depreciable base).
Year 1: 25% x $40,000 = $10,000. Book value at end of Year 1 = $30,000.
Year 2: 25% x $30,000 = $7,500. Book value at end of Year 2 = $22,500.
The second-year depreciation is $7,500. Note: the residual value is not subtracted from the base, but the asset is never depreciated below the residual value.
Depreciation per unit = $36,000 / total estimated units of output. Annual expense depends on how many units are produced or how many miles are driven that year. This method does not necessarily produce a declining pattern because the expense tracks actual usage.
Depletion works like units-of-production applied to natural resources. The journal entry is:
Debit: Depletion xxx
Credit: Natural Resource xxx
When a company revises the useful life or residual value of an asset, the change is recorded in the current and future years only (prospective treatment). Prior periods are not restated.
An asset is tested for impairment when indicators suggest its carrying amount may not be recoverable. The recoverability test compares undiscounted future cash flows to the carrying amount. If the carrying amount exceeds undiscounted cash flows, the asset is impaired and written down to fair value.
Fair value is measured by: prices of similar assets, the market price of the asset, or the sum of the discounted expected cash flows. The undiscounted cash flows cannot be used for this measurement step.
Straight-Line Depreciation = (Cost - Residual Value) / Useful Life
SYD Depreciation (Year n) = (Remaining Life / Sum of Years' Digits) x (Cost - Residual Value)
Sum of Years' Digits = n(n + 1) / 2, where n = useful life in years
DDB Depreciation (Year n) = (2 / Useful Life) x Book Value at Beginning of Year n
Units-of-Production Depreciation = (Cost - Residual Value) / Total Estimated Units x Units Produced in Period
Depletion Entry: Debit Depletion xxx, Credit Natural Resource xxx
Goodwill = Book Value - Fair Value (from the PP&E notes, repeated here for completeness)
Students often assume double-declining-balance subtracts the residual value before applying the rate. It does not. The double rate is applied to the full book value, but the asset cannot be depreciated below its residual value.
Students think all accelerated methods produce a strictly declining pattern. The units-of-production method does not necessarily decline, since it depends on actual usage, which can fluctuate.
Students confuse the recoverability test (undiscounted cash flows) with the fair value measurement (discounted cash flows or market-based approaches). The undiscounted figure is a screening test, not a valuation.
Students sometimes think a change in accounting estimate requires restating prior-year financial statements. It does not. Changes in estimates are applied prospectively.
⚠️ Be able to calculate Year 2 depreciation under SYD and DDB for any given cost, life, and residual value. These are high-probability exam calculations.
⚠️ Units-of-production is the method that does not necessarily produce a declining pattern. Expect a multiple-choice question testing this distinction.
⚠️ Depletion journal entry: know the accounts (Depletion expense, Natural Resource credit).
⚠️ Changes in estimates go forward (prospective), never backward. If the exam asks whether prior years are restated, the answer is no.
⚠️ Impairment: distinguish the recoverability test (undiscounted cash flows) from the fair value measurement (discounted cash flows or market prices).
A delivery van costs $40,000 with a residual value of $4,000 and a life of 8 years. What is Year 2 SYD depreciation? ($7,000)
Using the same van, what is Year 2 DDB depreciation? ($7,500)
True or False: The units-of-production method always produces a declining depreciation pattern. (False)
Fill in the blank: When a change in accounting estimate occurs, it is recorded in ______ and future years. (current)
True or False: The depletion journal entry credits the Natural Resource account. (True)
Q: A delivery van costs $40,000 with a useful life of 8 years and a residual value of $4,000. What is the depreciation for the second year using the sum-of-the-years'-digits method?
A: $7,000. Sum of digits = 36. Year 2 fraction = 7/36. Depreciation = 7/36 x $36,000 = $7,000.
Q: Using the same van, what is the depreciation for the second year using the double-declining-balance method?
A: $7,500. DDB rate = 25%. Year 1 depreciation = 25% x $40,000 = $10,000. Year 2 depreciation = 25% x $30,000 = $7,500.
Q: Which depreciation method does not necessarily produce a declining pattern over an asset's service life?
A: The units-of-production method. Expense depends on actual usage, which can vary from year to year.
Q: What is the journal entry for depletion of a natural resource?
A: Debit Depletion xxx, Credit Natural Resource xxx.
Q: What happens when a change in accounting estimate occurs?
A: The change is recorded in the current and future years only (prospective treatment). Prior periods are not restated.
Q: When determining the fair value of an impaired asset, which approach cannot be used?
A: The sum of the undiscounted cash flows. Fair value must be measured using discounted cash flows, market prices, or prices of similar assets.
Depreciation methods connect directly to the initial measurement of PP&E covered in the companion notes: if the capitalised cost is wrong, every year's depreciation is wrong. Impairment testing reappears in the goodwill and intangible assets material. The prospective treatment of estimate changes is a principle that also applies to changes in the estimated useful life of intangible assets and to revisions in depletion rates for natural resources.
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