A machine bought today will help earn profit for years. Charging its whole cost to the year of purchase would overstate that year’s expense and flatter every later year. Depreciation spreads the cost over the years of use.
This topic defines depreciation and its terms, shows the entries and how the carrying amount builds up, explains why depreciation is an application of the accruals concept, and sets out the straight-line and reducing balance methods, with the other methods the examiner uses and the requirements of International Accounting Standard (IAS) 16.
Depreciation is the biggest single topic in the area on transactions in the financial statements. A full question or a large part of one appeared in 8 of the 20 diets reviewed, with one or two Section A items almost every year. Read the topic on the cost of property, plant and equipment first. The next topic covers disposal and revaluation.
In 30 seconds
Depreciation is the systematic allocation of the Depreciable amount (cost less residual value) over the asset’s Useful life. The entry is Dr Depreciation expense, Cr Accumulated depreciation. Carrying amount = cost − accumulated depreciation. Straight-line charges (cost − residual value) ÷ life each year. Reducing balance charges a fixed percentage of the carrying amount at the start of the year, so the charge falls each year.
Land is not depreciated. Depreciation starts when the asset is available for use. It applies the accruals (matching) concept.
What depreciation is
Depreciation spreads the depreciable amount of a non-current asset over its expected useful life so that a fair share of the cost is charged in each period. The terms come from IAS 16 (paragraph 6).
| Term | Meaning |
|---|---|
| Depreciation | The systematic allocation of the depreciable amount of an asset over its useful life |
| Depreciable amount | The cost of an asset, or its revalued amount, less its residual value |
| Residual value | The expected disposal value of the asset, after deducting disposal costs, at the end of its useful life |
| Useful life | The period over which the asset is expected to be available for use by the entity |
An item of equipment costing ₦300,000 with a residual value of ₦50,000 after four years has a depreciable amount of ₦250,000, allocated over the four years. Depreciation is charged as an expense in each year of the asset’s life and Starts when the asset is available for use (IAS 16, paragraph 55). Most non-current assets are depreciated, but not Land, which has an indefinite useful life (IAS 16, paragraph 58).
When property is bought, the land element and the building are separated, and only the building is depreciated.
Accounting for depreciation
Each category of non-current asset has two ledger accounts, one for the asset at cost and one for accumulated depreciation, so each category can be shown separately in the statements. The entry for the year is:
Dr Depreciation expense, Cr Accumulated depreciation
The balance on the depreciation expense account is taken to the statement of profit or loss for the period. The accumulated depreciation account holds all the depreciation to date, as a credit balance carried forward, and is deducted from cost in the statement of financial position. The figure that results is the carrying amount, also called net book value.
For example, an asset is bought for ₦90,000 and depreciated at ₦15,000 a year.
| Year | Cost | Accumulated depreciation | Carrying amount |
|---|---|---|---|
| 1 | 90,000 | 15,000 | 75,000 |
| 2 | 90,000 | 30,000 | 60,000 |
The asset account stays at ₦90,000. Only the accumulated depreciation changes, and the carrying amount falls by the same amount.
The purpose of depreciation
Depreciation applies the accruals or matching concept. An asset is capitalised at cost. But it is used to earn profit, so some of its cost must be charged to profit or loss each period to match the consumption of its cost with the income it helps generate. The charge is the depreciation.
The straight-line method
The straight-line method charges the depreciable amount in equal amounts to each period of the expected useful life.
Annual charge = (cost − expected residual value) ÷ expected useful life in years
It is the most common method and the easiest to calculate.
Example. A machine costs ₦250,000. It has a life of five years and a residual value of ₦50,000.
- Find the depreciable amount. Cost less residual value is the part of the cost the machine will use up.
250,000 − 50,000 = 200,000 - Divide by the useful life. Equal amounts go to each year.
200,000 ÷ 5 = 40,000 a year
As a percentage of cost. Divide 100%, less any residual value, by the life.
| Case | Working | Rate |
|---|---|---|
| Ten-year life, no residual value | 100% ÷ 10 | 10% |
| Six-year life, residual value 10% of cost | (100% − 10%) ÷ 6 | 15% |
An exam question may say that a Full year’s depreciation is charged in the year of acquisition, even if the asset was bought late in the year. If it says nothing, charge depreciation for the months of ownership.
Example. A machine costs ₦250,000, with a five-year life and no residual value. It is bought on 1 September. The year end is 31 December.
- Find the annual charge.
250,000 ÷ 5 = 50,000 - Count the months owned. September, October, November and December make four months.
4 months - Charge the part year. Take four twelfths of the annual charge.
50,000 × 4/12 = 16,667
The reducing balance method
The reducing balance method charges a fixed percentage of the carrying amount at the start of each year. The charge is highest in Year 1 and lowest in the last year. For an asset costing ₦100,000 at 30%:
| Year | Carrying amount at start ₦ | Charge at 30% ₦ | Carrying amount at end ₦ |
|---|---|---|---|
| 1 | 100,000 | 30,000 | 70,000 |
| 2 | 70,000 | 21,000 | 49,000 |
| 3 | 49,000 | 14,700 | 34,300 |
| 4 | 34,300 | 10,290 | 24,010 |
When the rate is not given, find it from the cost, the residual value and the life.
Formula: rate = 1 − (residual value ÷ cost)1/n, where n is the life in years.
Example. An asset costs ₦10,000 with a residual value of ₦2,000 and a life of five years.
- Divide the residual value by the cost.
2,000 ÷ 10,000 = 0.2 - Take the fifth root. The life is five years, so n = 5.
0.21/5 = 0.7248 - Subtract from 1.
Rate = 1 − 0.7248 = 0.2752 = 27.5% - Work out the charges. Apply the rate to the carrying amount at the start of each year.
| Year | Carrying amount at start ₦ | Charge at 27.5% ₦ | Carrying amount at end ₦ |
|---|---|---|---|
| 1 | 10,000 | 2,750 | 7,250 |
| 2 | 7,250 | 1,994 | 5,256 |
| 3 | 5,256 | 1,445 | 3,811 |
| 4 | 3,811 | 1,048 | 2,763 |
| 5 | 2,763 | 763 | 2,000 |
The last charge is 763, not 27.5% of 2,763 (about 760). It is set so that the asset ends at its residual value of 2,000. The difference of 3 is rounding.
Other methods and rules the examiner uses
Background. Two methods are the core, but past papers set others, and IAS 16 allows methods that reflect the pattern in which the asset’s benefits are used (IAS 16, paragraphs 60 and 62).
Units of production
The charge follows output. Formula: (cost − residual value) × units produced in the year ÷ total expected units. The cost includes installation (November 2018 Question 5).
Example. A machine costs ₦3,000,000 including installation and has a residual value of ₦300,000. It is expected to make 900,000 units in its life and made 135,000 this year.
- Find the depreciable amount.
3,000,000 − 300,000 = 2,700,000 - Find the share of output used this year. Machines wear out with use, so output is the measure.
135,000 ÷ 900,000 = 15% - Apply that share.
2,700,000 × 15% = ₦405,000
Sum-of-the-years-digits
This method charges more in the early years. Formula: (cost − residual value) × remaining years ÷ the sum of the years’ digits. For a life of n years the sum of the digits is n(n + 1) ÷ 2.
Example. An asset costs ₦2,400,000 and has a residual value of ₦150,000. Its life is five years.
- Find the depreciable amount.
2,400,000 − 150,000 = 2,250,000 - Add the years’ digits. Count the life down from five to one.
5 + 4 + 3 + 2 + 1 = 15 - Charge each year. Year 1 uses the full five years remaining, so its fraction is 5/15. Each later year uses one fewer.
Year 1: 5/15 × 2,250,000 = 750,000
| Year | Years remaining | Fraction | Charge ₦ |
|---|---|---|---|
| 1 | 5 | 5/15 | 750,000 |
| 2 | 4 | 4/15 | 600,000 |
| 3 | 3 | 3/15 | 450,000 |
| 4 | 2 | 2/15 | 300,000 |
| 5 | 1 | 1/15 | 150,000 |
| Total | 15/15 | 2,250,000 |
The five charges add up to the depreciable amount, which is the check that the method is right.
Loose tools
Small tools are usually valued by the Revaluation method: depreciation = opening value + purchases − closing valuation.
Change of estimate
If the useful life or residual value is revised, the remaining carrying amount less the new residual value is spread over the remaining life. It is not restated back (IAS 16, paragraph 51; IAS 8).
IAS 16 requirements on depreciation
May 2022 asked for four requirements.
They are:
- each part of an item with a significant cost is depreciated separately (paragraph 43)
- the depreciable amount is allocated on a systematic basis over the useful life (paragraph 50)
- the residual value, useful life and method are reviewed at least at each year end, with changes treated as changes in estimate (paragraph 51)
- depreciation begins when the asset is available for use and continues until it is derecognised, even if idle (paragraph 55)
- land is not depreciated (paragraph 58)
- the method must reflect the pattern in which the benefits are consumed (paragraph 60)
The ideas in more depth
Depreciation is not a valuation. It allocates cost. The carrying amount need not match the market value. Depreciation and cash. No cash leaves when depreciation is charged. The cash left when the asset was bought. Why the asset account stays at cost. The accumulated depreciation account records what has been used up, so the cost stays visible. Which method. Straight-line suits assets used evenly.
Reducing balance suits assets that lose more value early. The method must reflect the pattern of use.
Sources: IAS 16 Property, Plant and Equipment: paragraph 6 (definitions), paragraphs 43, 50, 51, 55, 58, 60 and 62.
Worked example: Bauchi Plastics
Scenario. Bauchi Plastics has a 31 December year end. It buys a machine on 1 March Year 1 for ₦2,600,000, with a residual value of ₦200,000 and a life of eight years, depreciated straight-line by months. It buys a van on 1 January Year 1 for ₦5,000,000 depreciated at 20% reducing balance. Required: the charges, the accumulated depreciation and the carrying amounts at the end of Year 2.
- Machine: annual charge. The depreciable amount is cost less residual value, spread over the life.
(2,600,000 − 200,000) ÷ 8 = 300,000 - Machine: Year 1. It was bought on 1 March, so it was owned for ten months, March to December.
300,000 × 10/12 = 250,000
Dr Depreciation 250,000, Cr Accumulated depreciation 250,000 - Machine: Year 2. A full year.
Charge = 300,000
Accumulated depreciation = 250,000 + 300,000 = 550,000
Carrying amount = 2,600,000 − 550,000 = 2,050,000 - Van: Year 1. Reducing balance applies the rate to the carrying amount at the start of the year. In Year 1 that is the cost.
20% × 5,000,000 = 1,000,000
Carrying amount = 4,000,000 - Van: Year 2. Now apply the rate to the lower carrying amount.
20% × 4,000,000 = 800,000
Accumulated depreciation = 1,000,000 + 800,000 = 1,800,000
Carrying amount = 5,000,000 − 1,800,000 = 3,200,000 - Total charge for Year 2. Add the two assets. It is an expense in profit or loss.
300,000 + 800,000 = 1,100,000
Statement of financial position at the end of Year 2. Show each asset at cost, less accumulated depreciation.
| Asset | Cost ₦ | Accumulated depreciation ₦ | Carrying amount ₦ |
|---|---|---|---|
| Machine | 2,600,000 | 550,000 | 2,050,000 |
| Van | 5,000,000 | 1,800,000 | 3,200,000 |
| Total | 7,600,000 | 2,350,000 | 5,250,000 |
Finding a reducing balance rate. A different asset costs ₦6,000,000, has a residual value of ₦1,200,000 and a four-year life.
- Divide the residual value by the cost.
1,200,000 ÷ 6,000,000 = 0.2 - Take the fourth root. The life is four years.
0.21/4 = 0.6687 - Subtract from 1.
Rate = 1 − 0.6687 = 33.1%
Common mistakes in the exam
- Depreciating cost and forgetting to deduct the residual value in the straight-line method.
- Applying the reducing balance percentage to cost every year. It applies to the carrying amount.
- Depreciating land.
- Charging a full year when the question says to charge by months, or the reverse.
- Reducing the asset account instead of crediting accumulated depreciation.
- Mixing up the charge for the year with the accumulated depreciation.
- Confusing the carrying amount with market value.
Quick revision
- Depreciable amount = cost − residual value. Entry: Dr Depreciation expense, Cr Accumulated depreciation.
- Carrying amount = cost − accumulated depreciation.
- Straight-line: (cost − residual) ÷ life. Reducing balance: rate × opening carrying amount.
- Rate = 1 − (residual ÷ cost)1/n. Units of production: (cost − residual) × units ÷ total units.
- Land is not depreciated. Depreciation starts when available for use. Depreciation applies the accruals concept.
Practice questions
These are original questions in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one first.
Section A style: multiple choice
Question 1. Depreciation is the allocation of:
- The depreciable amount over the useful life
- Market value over time
- Profit over the years
- The residual value only
Show the answer
A. Depreciation allocates the depreciable amount (cost less residual value) over the useful life.
Question 2. The entry for depreciation is:
- Dr Accumulated depreciation, Cr Expense
- Dr Asset, Cr Depreciation
- Dr Depreciation expense, Cr Accumulated depreciation
- Dr Bank, Cr Depreciation
Show the answer
C. Depreciation is an expense, with the matching credit in accumulated depreciation.
Question 3. An asset costs ₦1,950,000, has a residual value of ₦150,000 and a six-year life. The straight-line charge is:
- ₦325,000
- ₦300,000
- ₦275,000
- ₦1,800,000
Show the answer
B. (1,950,000 − 150,000) ÷ 6 = 300,000.
Question 4. An asset costs ₦4,000,000 and is depreciated at 25% reducing balance. The Year 2 charge is:
- ₦750,000
- ₦1,000,000
- ₦562,500
- ₦250,000
Show the answer
A. Year 1 charge 1,000,000, so the carrying amount is 3,000,000, and 25% × 3,000,000 = 750,000.
Question 5. Which asset is not depreciated?
- A van
- A building
- Land
- A machine
Show the answer
C. Land has an indefinite useful life.
Question 6. The carrying amount is:
- Cost plus depreciation
- Market value
- Residual value
- Cost less accumulated depreciation
Show the answer
D. Carrying amount is cost less accumulated depreciation.
Question 7. Depreciation under IAS 16 begins when the asset is:
- Ordered
- Available for use
- Paid for
- Fully used
Show the answer
B. Under IAS 16 depreciation starts when the asset is available for use.
Question 8. A machine costing ₦600,000 with a five-year life and no residual value is bought on 1 October. The Year 1 straight-line charge (year end 31 December) is:
- ₦120,000
- ₦30,000
- ₦60,000
- ₦600,000
Show the answer
B. 600,000 ÷ 5 × 3/12 = 30,000.
Question 9. Depreciation applies which concept?
- Going concern
- Prudence only
- Business entity
- Accruals (matching)
Show the answer
D. Depreciation matches the cost of an asset to the periods that benefit from it, which is the accruals concept.
Question 10. Loose tools are usually depreciated by the:
- Annuity method
- Straight-line method
- Revaluation method
- Units of production
Show the answer
C. Loose tools are usually valued by the revaluation method: opening value plus additions less the closing valuation.
Section B style: written questions
Question 11 (10 marks). (a) Define depreciation, depreciable amount, residual value and useful life. (4 marks) (b) State the formulae for straight-line and reducing balance depreciation. (4 marks) (c) Explain why land is not depreciated. (2 marks)
Question 12 (20 marks). Equipment costing ₦3,600,000 with a residual value of ₦400,000 and a life of eight years is bought on 1 October Year 1 (year end 31 December) and depreciated straight-line by months. A vehicle costing ₦4,000,000 is depreciated at 25% reducing balance from 1 January Year 1. An office property costs ₦9,000,000, of which land is ₦3,600,000, with a building life of 40 years.
(a) Prepare the equipment, accumulated depreciation and depreciation accounts for Years 1 and 2 and state the carrying amounts. (8 marks) (b) Calculate the vehicle charge and carrying amount for Years 1 to 3. (6 marks) (c) Calculate the property charge and the carrying amount after two years. (4 marks) (d) State TWO IAS 16 requirements on depreciation. (2 marks)
A further written question
Question 13 (10 marks). An asset costing ₦1,950,000 has a residual value of ₦150,000 and a six-year life. (a) Calculate the annual straight-line charge. (3 marks) (b) Calculate the carrying amount after four years. (3 marks) (c) After four years the total life is revised to eight years with the same residual value. Calculate the new annual charge. (4 marks)
Model answers
Show the model answer to Question 11
(a) Depreciation: the systematic allocation of the depreciable amount over the useful life. Depreciable amount: cost less residual value. Residual value: the expected disposal value, net of disposal costs, at the end of the life. Useful life: the period over which the asset is expected to be available for use. (b) Straight-line: (cost − residual value) ÷ useful life.
Reducing balance: a fixed percentage × the carrying amount at the start of the year. (c) Land has an indefinite useful life, so there is nothing to allocate.
Show the model answer to Question 12
(a) Equipment.
- Annual charge.
(3,600,000 − 400,000) ÷ 8 = 400,000 - Year 1. Bought on 1 October, so three months.
400,000 × 3/12 = 100,000 - Year 2. A full year.
400,000
| Year | Charge ₦ | Accumulated depreciation ₦ | Carrying amount ₦ |
|---|---|---|---|
| 1 | 100,000 | 100,000 | 3,500,000 |
| 2 | 400,000 | 500,000 | 3,100,000 |
(b) Vehicle. Apply 25% to the carrying amount at the start of each year.
| Year | Carrying amount at start ₦ | Charge at 25% ₦ | Carrying amount at end ₦ |
|---|---|---|---|
| 1 | 4,000,000 | 1,000,000 | 3,000,000 |
| 2 | 3,000,000 | 750,000 | 2,250,000 |
| 3 | 2,250,000 | 562,500 | 1,687,500 |
(c) Property.
- Take out the land. Land is not depreciated, so only the building is.
9,000,000 − 3,600,000 = 5,400,000 - Annual charge.
5,400,000 ÷ 40 = 135,000 - After two years.
Accumulated depreciation = 2 × 135,000 = 270,000
Carrying amount = 9,000,000 − 270,000 = 8,730,000
(d) Any two:
- significant parts depreciated separately
- depreciation allocated systematically over the useful life
- residual value, life and method reviewed at least yearly
- it begins when the asset is available for use
- land is not depreciated
Show the model answer to Question 13
(a) Annual charge.
- Straight-line formula.
(cost − residual value) ÷ life - Calculate.
(1,950,000 − 150,000) ÷ 6 = ₦300,000
(b) Carrying amount after four years.
- Accumulated depreciation.
4 × 300,000 = 1,200,000 - Carrying amount. Cost less accumulated depreciation.
1,950,000 − 1,200,000 = ₦750,000
(c) New annual charge.
- Remaining depreciable amount. Take the residual value off the carrying amount.
750,000 − 150,000 = 600,000 - Remaining life. The total life is now eight years and four have passed.
8 − 4 = 4 years - New annual charge.
600,000 ÷ 4 = ₦150,000 a year
It applies from the date of the change. Prior years are not restated.
Pathfinder on Depreciation: straight-line, reducing balance and IAS 16 requirements
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
From the previous syllabus. Asks for the reducing balance rate for a vehicle with a four-year life and a residual value (2 marks), the charge for two years and the carrying amount (3 marks).
Revise first: The reducing balance method
From the previous syllabus. Asks you to define depreciation (2½ marks) and list five factors to consider in the charge (7½ marks). Part (c) asks for non-current asset and bank accounts.
Revise first: What depreciation is
From the previous syllabus. Asks for the annual depreciation of a machine with an initial cost, installation cost and estimated output in units for each of five years.
Revise first: Other methods and rules the examiner uses
From the previous syllabus. Asks you to define depreciation, depreciable amount, useful life and residual value (6 marks), and to calculate five years’ charges on a straight-line basis (2 marks) and on a diminishing balance at 54% (12 marks).
Revise first: What depreciation is
From the previous syllabus. Asks for four general requirements of IAS 16 on depreciation (4 marks), and for two years’ depreciation on a straight-line and on a reducing balance basis (8 marks).
Revise first: IAS 16 requirements on depreciation
Asks for depreciation of equipment costing ₦1,600,000 with a five-year life by the straight-line method (6 marks) and the reducing balance method (6 marks), and the statement of financial position extracts at the end of the third year (3 marks).
Revise first: The straight-line method
From the previous syllabus. Question 2 asks for the sum-of-the-years-digits charge of a vehicle in its second year. Question 11 asks for the appropriate method of depreciating loose tools.
Revise first: Other methods and rules the examiner uses
From the previous syllabus. Both ask for the journal entries or double entry that record depreciation.
Revise first: Accounting for depreciation
From the previous syllabus. These ask how depreciation differs from other expenses, what is not considered in the useful life, and when depreciation starts under IAS 16.
Revise first: IAS 16 requirements on depreciation
One or two items a diet ask for a charge by a stated method, the carrying amount, or the entry. Check Section A of every diet you practise.
Revise first: Accounting for depreciation
Source: ICAN Pathfinder, Financial Accounting. Diets covered: November Diet, 2014, May Diet, 2015, November Diet, 2015, November Diet, 2016, May Diet, 2017, November Diet, 2017, May Diet, 2018, November Diet, 2018, May Diet, 2019, May Diet, 2022, May Diet, 2023 and May Diet, 2024 (the later ones are not all on the previous syllabus). Diets before November 2014, and November Diet, 2024 onwards, are not covered here.
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