Unit 03 — How to Solve Anything
Four topics on depreciation. All five faculty problems are worked in full, year by year, with the machinery account laid out the way the examiner wants to see it — plus the textbook's illustrations, its entire 16-statement True/False bank, its MCQs, all eight descriptive questions and five interview questions, and extra problems on top.
◆ The routine that solves every depreciation numerical
1 FIND THE COST invoice + carriage + installation + erection
+ reconditioning ← NOT just the invoice
2 IDENTIFY THE METHOD "original cost" / "fixed installment" → SLM
"diminishing balance" / "WDV" → WDV
3 BUILD A TIMELINE one row per machine, one column per year
mark the months owned in each year
4 DEPRECIATE EACH MACHINE SLM: Cost × Rate × n/12 (base never changes)
SEPARATELY WDV: Opening BV × Rate × n/12 (base shrinks)
5 ON A SALE cost of the portion − accumulated dep to the
DATE OF SALE = WDV; proceeds − WDV = profit/loss
6 PRESENT Machinery A/c year by year + working notes below
Step 3 is the one people skip and the one that saves them. Draw the grid before you compute anything. Every faculty problem here has two or three machines bought and sold on different dates, and the whole difficulty is bookkeeping, not arithmetic.
Topic 1 of 4 · Textbook §7.1–7.7 · pp. 155–160 · 28 questions
Concepts, Factors and Methods — the Theory Bank
Depreciation carries more examinable theory than any other numerical topic, because the textbook prints a 16-statement True/False bank, an MCQ set, eight descriptive questions and five interview questions. All of them are here.
How to know a question belongs to this topic
It asks you to
Define, explain, compare or choose — never compute.
Give-away words
what is the meaning ofstate the objectives
merits and demeritswhich method is used for
can a firm changediscuss the statement
The five sentences worth memorising verbatim
1. "Depreciation is the diminution in the value of the fixed assets because of their use, wear and tear, efflux of time, depletion etc."
2. "Depreciation is required to be provided on fixed assets. Question of depreciation does not arise on current assets."
3. "Depreciation is a mere book entry… there is no actual cash outgo of funds from the firm."
4. "Diminishing Balance Method is also known as Written Down Value Method."
5. "A change in the existing method of depreciation is treated as a change in an accounting policy."
2. "Depreciation is required to be provided on fixed assets. Question of depreciation does not arise on current assets."
3. "Depreciation is a mere book entry… there is no actual cash outgo of funds from the firm."
4. "Diminishing Balance Method is also known as Written Down Value Method."
5. "A change in the existing method of depreciation is treated as a change in an accounting policy."
Structure of a full answer
Definition → reason → a named example. Examiners reward the example; most students give only the first two.
Textbook True/False bank — all 16 statementspp. 173–174 · with the reasoning, not just the answer
Q. State whether each is True or False.
Solution — all sixteen with reasoning
| # | Statement | Ans | Why |
|---|---|---|---|
| 1 | Depreciation is the diminution in the value of fixed assets because of use, wear and tear, efflux of time, depletion etc. | True | The textbook's own definition. |
| 2 | Depreciation amount is the same every year both in SLM and Diminishing Balance. | False | Only in SLM. In WDV the base shrinks each year, so the amount falls. |
| 3 | Depreciation Fund Method provides readily available cash for replacement. | True | The money is invested outside the business in saleable securities. This is its single advantage. |
| 4 | Depreciation does not involve any outgo of cash from the firm. | True | A book entry. The only expense in your syllabus with no cash flow. |
| 5 | Depreciation amount goes on reducing in Straight Line Method year after year. | False | It is constant in SLM. This is the WDV property, misattributed. |
| 6 | Depreciation is invested outside the business in Diminishing Balance method so replacement does not disturb liquidity. | False | That is the Sinking Fund method. WDV leaves the money inside the business, which is one of its demerits. |
| 7 | If a fixed asset is not used, depreciation need not be provided. | False | Use can be passive. "If a brand new car is kept in a garage, though not used, car would depreciate, perhaps more than its actual use." |
| 8 | Depreciation is necessary on fixed assets, not on current assets. | True | The single most-quoted line of the chapter. |
| 9 | Depreciation can be credited to the fixed asset account or to a 'provision for depreciation' account. | True | The two methods of §7.8. |
| 10 | Provision for depreciation account always shows a debit balance. | False | Credit. It accumulates against the asset — a contra-asset. It is deducted from the asset on the Balance Sheet. |
| 11 | Replacement of fixed asset creates a liquidity problem unless planned properly. | True | Exactly the problem the Sinking Fund method exists to solve. |
| 12 | Depreciation is a mere accounting entry which does not affect the operational results of the firm. | False | Half-true and therefore false. It is a book entry with no cash movement — but it very much reduces profit. "If not provided, operational results would be overstated." |
| 13 | Fixed assets are not meant for sale in the ordinary course of business. | True | The definition of a fixed asset. This is why a fall in market price is ignored. |
| 14 | Even if the fixed asset is purchased in the middle of the year, depreciation is provided for the whole year. | False | Pro rata for the actual period of holding. This is the rule that decides half the marks in every faculty problem. |
| 15 | A change in the method of depreciation is treated as a change in an accounting policy. | True | And must be quantified in Notes to Accounts. |
| 16 | When a Provision for depreciation account is maintained, the balance sheet shows the fixed asset at original cost with provision as a deduction. | True | Cost in the inner column, provision deducted, net in the outer column. |
The pattern in the six false onesFive of the six false statements (2, 5, 6, 10, 14) work by attributing one method's property to another, or by generalising a rule past its boundary. Whenever a statement of this type appears, ask: is this true of SLM, of WDV, or of the Sinking Fund — and is the statement naming the right one? Statement 12 is the odd one out: it is false because it is incomplete, not because it is misattributed.
Textbook MCQ bank + extrasp. 174 · 12 questions
Q. Pick the most appropriate answer.
Solution
| # | Question | Answer | The pairing to remember |
|---|---|---|---|
| 1 | A firm in the business of livestock uses which method? | Revaluation Method | Livestock / loose tools → Revaluation. Too many items to account for singly; a valuer prices the lot each year. |
| 2 | For calculating extraction from mines and quarries: | Depletion Method | Mines / quarries / oil wells → Depletion. Per unit extracted. |
| 3 | Change in method of depreciation is … for a limited company: | Permitted in all cases, but change and impact of change are to be stated in Notes to Accounts | Not simply "permitted" — the disclosure half is what makes the option correct. |
| 4 | Burden on the P&L in the form of depreciation and interest would be … in the annuity method compared to SLM and WDV: | More | Annuity → heavier burden, because interest is charged on top of depreciation. |
| 5 | The greatest advantage of this method is ready funds for replacement, as the amount is invested outside the business: | Sinking Fund Method | Ready funds → Sinking Fund. The only method that solves the liquidity problem. |
| 6 | Which method is accepted by Indian income-tax authorities? | Diminishing Balance (WDV) | And therefore the method most firms actually use. |
| 7 | Under which method does the asset never reach zero? | WDV | A percentage of a shrinking base approaches zero but never arrives. |
| 8 | Which asset is not depreciated? | Land | No finite useful life. |
| 9 | Depreciation is charged to give effect to which accounting concept? | Matching Concept | Cost matched to the revenue it helped earn. |
| 10 | Installation charges on a new machine are: | Capitalised — added to the cost of the asset | §7.7(A). Depreciation is then computed on the total. |
| 11 | Depreciation for a machine bought on 1 October, books closing 31 March, is charged for: | 6 months | Pro rata to the actual period of holding. |
| 12 | Under the Provision method, the asset appears in the Balance Sheet at: | Original cost, with the provision shown as a deduction | Contrast with Method A, where the asset itself shows the WDV. |
The five pairings, in one line eachLivestock → Revaluation · Mines → Depletion · Ready funds → Sinking Fund · Heavier burden → Annuity · Income tax → WDV. Four of the twelve questions above are just these pairings reworded. Learn them and you have four marks before you read the paper.
Descriptive questions — all eight from the textbookpp. 174–175 · model answers
D1Discuss the statementTextbook Q1 (§7.1)
Q. "Depreciation is to be provided on fixed assets as well as current assets" — Discuss.
Solution
AnswerThe statement is incorrect. Depreciation is provided on fixed assets only. The textbook states it flatly: "Depreciation is required to be provided on fixed assets. Question of depreciation does not arise on current assets." p. 156
Why fixed assets: they are used in the business to earn profits over several accounting periods and are not meant for sale. At the end of their useful life there is no realisable value except a negligible scrap value. To match the cost against the revenue it helped generate, a portion of that cost must be charged each year.
Why not current assets: current assets — stock, debtors, cash — are held for conversion within the operating cycle, not for long-term use. They change form constantly. Stock is valued (at cost or market price, whichever is lower — Conservatism), and debtors are provided against (provision for doubtful debts), but neither process is depreciation.
The one qualification worth adding: a fall in market prices is a genuine cause of value reduction, but the textbook explicitly excludes it for fixed assets — "in case of fixed assets, a fall in price for depreciation is ignored. Only current assets are affected by this factor." Land is the one fixed asset not depreciated, having no finite life.
Why fixed assets: they are used in the business to earn profits over several accounting periods and are not meant for sale. At the end of their useful life there is no realisable value except a negligible scrap value. To match the cost against the revenue it helped generate, a portion of that cost must be charged each year.
Why not current assets: current assets — stock, debtors, cash — are held for conversion within the operating cycle, not for long-term use. They change form constantly. Stock is valued (at cost or market price, whichever is lower — Conservatism), and debtors are provided against (provision for doubtful debts), but neither process is depreciation.
The one qualification worth adding: a fall in market prices is a genuine cause of value reduction, but the textbook explicitly excludes it for fixed assets — "in case of fixed assets, a fall in price for depreciation is ignored. Only current assets are affected by this factor." Land is the one fixed asset not depreciated, having no finite life.
D2Meaning and needTextbook Q2 (§7.2, 7.3)
Q. What is the meaning of 'Depreciation'? Explain the need for providing depreciation.
Solution
MeaningDepreciation is the permanent, continuing and gradual shrinkage in the book value of a fixed asset, caused by use, wear and tear, efflux of time or depletion. Pickles defines it as "the permanent and continuing diminution in the quality, quantity or value of an asset."
Need — the five factors, §7.3
(A) Use of the asset — active or passive. Even an unused car in a garage depreciates. Depreciation runs from the date of acquisition or from when the asset is put to use.
(B) Efflux of time — a leased asset has a definite life; on expiry it ceases to exist. Time alone erodes value.
(C) Obsolescence — a better machine arrives and the existing one, though physically capable, must be written off. Most visible in computers.
(D) Accidents — when repairs exceed realisable value the asset is discarded.
(E) A fall in prices — ignored for fixed assets, since they are not held for sale.
The examinable distinction: only (A) and (B) are routinely used to compute depreciation. (C) and (D) are considered when they happen — they do not happen to all assets. (E) is excluded altogether.
(B) Efflux of time — a leased asset has a definite life; on expiry it ceases to exist. Time alone erodes value.
(C) Obsolescence — a better machine arrives and the existing one, though physically capable, must be written off. Most visible in computers.
(D) Accidents — when repairs exceed realisable value the asset is discarded.
(E) A fall in prices — ignored for fixed assets, since they are not held for sale.
The examinable distinction: only (A) and (B) are routinely used to compute depreciation. (C) and (D) are considered when they happen — they do not happen to all assets. (E) is excluded altogether.
D3ObjectivesTextbook Q3 (§7.2, 7.4)
Q. What are the objectives for providing depreciation?
Solution
Depreciation is an expense, and under the mercantile basis all expenses are recorded whether paid or not.
1. Calculation of correct net income. When an asset is used to earn income, the reduction in its value should be charged against that income. "If not provided, operational results would be overstated."
The balance sheet must exhibit a true financial position.
2. Presentation of fixed assets at proper value. Without depreciation, assets are overstated. Showing an asset at cost when its value has fallen is "similar to painting a better financial picture than it is."
Charging depreciation retains that amount inside the business rather than distributing it.
3. Replacement of the asset. If depreciation is not provided, profits are inflated and dividend would be distributed out of unearned profits — so no funds remain when the asset must be replaced.
Add this line for the extra mark"Depreciation is a mere book entry. Though depreciation is an expense, there is no actual cash outgo of funds from the firm. However, provision of depreciation reduces profits." It shows you understand objective 1 and objective 3 are not in conflict.
D4Methods, merits and demeritsTextbook Q4 (§7.5)
Q. Name the different methods of providing depreciation and state their merits and demerits.
Solution
| Method | How it works | Merits | Demerits |
|---|---|---|---|
| 1. Straight Line | (Cost − Scrap) ÷ Life. Constant amount. | Simple. Works well for assets with a fixed life, e.g. a lease. Reaches scrap value exactly. | Charge to P&L is not equal because repairs rise with age. Not recognised by Indian income-tax authorities. No ready funds for replacement. |
| 2. Diminishing Balance (WDV) | Fixed rate on the opening balance. Falling amount. | Depreciation falls as repairs rise, so the total burden is roughly uniform. Recognised for income tax in India. | Tedious calculations on addition or sale. No replacement fund. Never reaches zero. |
| 3. Annuity | Treats the asset as an investment; charges interest on it; write-off from an annuity table. | Recognises the interest lost on the capital tied up — which SLM and WDV both ignore. | Heavier burden on the P&L (depreciation + interest). Complex. |
| 4. Depreciation Fund (Sinking Fund) | The amount is invested outside the business in government securities; sold on replacement. | Ready cash for replacement without disturbing operations. Eliminates the liquidity handicap of methods 1–3. | Funds tied up outside the business earn only a low, safe return. |
| 5. Depletion | Per unit extracted. Mine ₹5,00,000 ÷ 5,000 tons = ₹100/ton. | Directly tracks consumption of the asset. | Only applicable to wasting assets. |
| 6. Revaluation | (Opening + purchases) − closing valuation. | Practical where items are too numerous to track singly. | Depends on a valuer's subjective judgment. |
| 7. Machine Hour Rate | Cost ÷ total life-hours × hours run this year. | Matches wear to actual usage. | Requires accurate hour records. |
If the question is only worth 5 marksGive SLM and WDV in full (they are the two your syllabus names) and the other five as one line each. The single sentence that earns the comparison mark: in SLM the total charge to the P&L rises with age because repairs rise while depreciation stays flat; in WDV the two move in opposite directions and roughly cancel.
D5Sale and scrapping procedureTextbook Q5 (§7.9)
Q. State the accounting procedure in respect of sale of an asset and discarding machinery as scrap.
Solution
Answer — §7.9, five steps
1. Open a separate Machinery Disposal A/c for the asset sold.
2. Transfer the book value out of the asset account:
Machinery Disposal A/c Dr. / To Machinery A/c
If a Provision for Depreciation A/c is maintained, transfer the original cost from Machinery and the applicable accumulated depreciation from the Provision:
Machinery Disposal A/c Dr. / To Machinery A/c / To Provision for Depreciation A/c
3. Credit the sale proceeds or scrap proceeds to the Disposal account:
Cash / Bank A/c Dr. / To Machinery Disposal A/c
4. Close the Disposal account; the balance is the profit or loss.
5. Transfer it to the P&L:
If profit: Machinery Disposal A/c Dr. / To Profit and Loss A/c
If loss: Profit and Loss A/c Dr. / To Machinery Disposal A/c
Discarding as scrap is the same procedure with the scrap proceeds — often negligible or nil — as the credit in step 3. If nothing is realised, the whole written-down value becomes the loss.
Do not forget: before any of this, charge depreciation on the asset up to the date of sale. The written-down value transferred in step 2 must be the value on the day it left, not on the previous balance-sheet date.
2. Transfer the book value out of the asset account:
Machinery Disposal A/c Dr. / To Machinery A/c
If a Provision for Depreciation A/c is maintained, transfer the original cost from Machinery and the applicable accumulated depreciation from the Provision:
Machinery Disposal A/c Dr. / To Machinery A/c / To Provision for Depreciation A/c
3. Credit the sale proceeds or scrap proceeds to the Disposal account:
Cash / Bank A/c Dr. / To Machinery Disposal A/c
4. Close the Disposal account; the balance is the profit or loss.
5. Transfer it to the P&L:
If profit: Machinery Disposal A/c Dr. / To Profit and Loss A/c
If loss: Profit and Loss A/c Dr. / To Machinery Disposal A/c
Discarding as scrap is the same procedure with the scrap proceeds — often negligible or nil — as the credit in step 3. If nothing is realised, the whole written-down value becomes the loss.
Do not forget: before any of this, charge depreciation on the asset up to the date of sale. The written-down value transferred in step 2 must be the value on the day it left, not on the previous balance-sheet date.
D6Changing the methodTextbook Q6 (§7.6)
Q. Is it possible for a firm to change the method of depreciation? If so, what is the procedure to be followed?
Solution
AnswerYes. The method must be consistent from year to year — the Consistency convention — but a firm may change it, subject to requirements.
The procedure:
1. The change is treated as a change in an accounting policy — not as the correction of an error.
2. The fact of the change must be stated in the financial statements.
3. The impact of the change, duly quantified, must be disclosed in "Notes to Accounts". Impact means the increase or decrease in profit or loss caused by the change.
The reason to give: "the reader of the financial statements should be apprised of the change and impact of change on the financial results." Without it, a reader comparing this year with last would wrongly attribute a change in profit to trading performance. This is the Full Disclosure convention overriding pure Consistency — and it is why the MCQ answer is not simply "permitted" but "permitted, with the change and its impact stated in Notes to Accounts."
The procedure:
1. The change is treated as a change in an accounting policy — not as the correction of an error.
2. The fact of the change must be stated in the financial statements.
3. The impact of the change, duly quantified, must be disclosed in "Notes to Accounts". Impact means the increase or decrease in profit or loss caused by the change.
The reason to give: "the reader of the financial statements should be apprised of the change and impact of change on the financial results." Without it, a reader comparing this year with last would wrongly attribute a change in profit to trading performance. This is the Full Disclosure convention overriding pure Consistency — and it is why the MCQ answer is not simply "permitted" but "permitted, with the change and its impact stated in Notes to Accounts."
D7Factors for calculationTextbook Q7 (§7.3, 7.7)
Q. If the value of a fixed asset falls, is it necessary to provide depreciation? What are the basic factors for calculation of depreciation?
Solution
Part 1 — the market-value questionA fall in market price is not a reason to provide depreciation on a fixed asset. Fixed assets are not held for sale, so their market price is irrelevant to the accounts — the Cost Concept keeps them at cost less accumulated depreciation. "In case of fixed assets, a fall in price for depreciation is ignored. Only current assets are affected by this factor."
Depreciation is provided because the asset is being used up in earning revenue, not because its resale value moved.
Depreciation is provided because the asset is being used up in earning revenue, not because its resale value moved.
Part 2 — the three factors, §7.7
(A) Cost. Not necessarily the purchase price. Add erection expenses (new asset) and reconditioning expenses (second-hand asset), plus carriage and installation, wherever the spending brings the asset into working condition or improves its capacity or life. Depreciation is computed on this total.
(B) Estimated life. Must be estimated; the asset is written off totally over it, except for scrap value.
(C) Scrap / residual value. Deducted before the cost is spread (in SLM).
Plus the rule that governs every numerical — period of holding: depreciation is calculated pro rata to the actual period the asset was held. Bought mid-year → from the date of purchase. Sold mid-year → up to the date of sale.
(B) Estimated life. Must be estimated; the asset is written off totally over it, except for scrap value.
(C) Scrap / residual value. Deducted before the cost is spread (in SLM).
Plus the rule that governs every numerical — period of holding: depreciation is calculated pro rata to the actual period the asset was held. Bought mid-year → from the date of purchase. Sold mid-year → up to the date of sale.
D8Recommend a methodTextbook Q8 (§7.2, 7.5(iv))
Q. A firm does not want to disturb its business operations for replacing a fixed asset. Discuss the method of depreciation that is recommended.
Solution
AnswerThe Depreciation Fund Method — also called the Sinking Fund Method.
The problem it solves. Under SLM, WDV and Annuity, the depreciation amount stays inside the business and gets absorbed into current assets and other fixed assets. When replacement day arrives, heavy cash is needed and none is available in liquid form. The firm must then borrow, or sell something, or postpone the replacement — all of which disturb operations. The textbook calls this "the greatest handicap in respect of all the above methods."
How the Sinking Fund works. Each year the depreciation amount is invested outside the business in readily saleable securities — preferably government securities, because they are secure and their price fluctuations are almost negligible. When the asset's life expires, the securities are sold and the proceeds buy the replacement.
A second advantage: the securities earn interest throughout, so the full depreciation total is not needed to buy the new asset — "interest amount would take care of the increased price of the asset, if any, for replacement."
Conclusion to write: "The greatest advantage of the Sinking Fund Method is its ready availability of cash for replacement of the asset, without disturbing the business operations. The liquidity problem often experienced by management does not arise."
The problem it solves. Under SLM, WDV and Annuity, the depreciation amount stays inside the business and gets absorbed into current assets and other fixed assets. When replacement day arrives, heavy cash is needed and none is available in liquid form. The firm must then borrow, or sell something, or postpone the replacement — all of which disturb operations. The textbook calls this "the greatest handicap in respect of all the above methods."
How the Sinking Fund works. Each year the depreciation amount is invested outside the business in readily saleable securities — preferably government securities, because they are secure and their price fluctuations are almost negligible. When the asset's life expires, the securities are sold and the proceeds buy the replacement.
A second advantage: the securities earn interest throughout, so the full depreciation total is not needed to buy the new asset — "interest amount would take care of the increased price of the asset, if any, for replacement."
Conclusion to write: "The greatest advantage of the Sinking Fund Method is its ready availability of cash for replacement of the asset, without disturbing the business operations. The liquidity problem often experienced by management does not arise."
Interview questions — all fivepp. 175–176 · short-answer format
Q. (1) What is depreciation? (2) Why must it be provided while finalising accounts? (3) Which method is mostly adopted and why? (4) What is the special advantage of the sinking fund method? (5) Can a firm change from SLM to WDV?
Solution
| 1 | Reduction or diminution in the value of an asset caused by wear and tear or efflux of time. It occurs whether the asset is used actively or passively — even an unused asset depreciates with the passage of time. |
| 2 | To calculate correct operating results and exhibit a proper financial position. Depreciation is an expense like any other; every fixed asset has a finite life, so its cost must be charged against the income it helps earn. Once provided, the asset appears at a reduced value and the balance sheet shows a true and fair position. |
| 3 | Diminishing Balance Method. Two reasons: (i) depreciation falls year after year while repairs rise, so "the total burden on the income in the form of depreciation and repairs over the life of the asset would be uniform"; (ii) it is the accepted method for income-tax purposes in India. |
| 4 | Normally depreciation is reinvested in the business and locked up in current and other fixed assets, so no ready cash exists when replacement is due. Under the sinking fund method the amount is invested separately in safe, liquid securities such as government securities, which can be sold without disturbing operations. |
| 5 | Yes. The firm must state the change in the financial statements and disclose the change and its quantified impact on profit or loss in "Notes to Accounts." |
Topic 2 of 4 · Faculty sheet Q1 & Q4 · Textbook Illustration 1 · 10 questions
Straight Line Method — Computation
SLM is the easy half of the syllabus provided you get the cost right and the months right. Both faculty SLM problems turn on exactly those two things.
How to know a question belongs to this topic
Give-away words
Straight Line MethodOriginal Cost Method
fixed installmentby equal installments
estimated residual valueuseful life of N years
The formula
With a life: \((\text{Cost} - \text{Scrap}) \div \text{Life}\). With a rate: \(\text{Cost} \times \text{Rate}\% \times n/12\). The base is the ORIGINAL cost, every single year.
The two places marks are lost
1. Depreciating the invoice price instead of cost + carriage + installation + erection + reconditioning.
2. Charging a full year on an asset bought or sold mid-year. Count the months.
2. Charging a full year on an asset bought or sold mid-year. Count the months.
Layout that earns marks
A Machinery Account in T-form, one block per year, with working notes below showing each machine's depreciation separately. Never present a bare final figure.
Faculty Depreciation sheet — Q1Second-hand machine · residual value · sheet p. 1
Q. On 1st January 2020 ZEE Ltd purchased a second-hand machine for ₹96,000, spent ₹24,000 on its cartage, repairs and installation; estimated useful life of machine 4 years; estimated residual value ₹72,000. Compute depreciation to be charged for FY 2020-21, 2021-22 and 2022-23 under SLM. Financial year ending is 31st March every year.
Solution
Why this question exists: to see whether you capitalise the ₹24,000 and whether you notice the financial year does not start on the purchase date.
Why this stepWhat to write
§7.7(A): expenses on a second-hand asset are reconditioning in nature, not repairs, and are capitalised. So is cartage, and so is installation. All ₹24,000 joins the asset.
Cost of machine \(= 96{,}000 + 24{,}000\)
\(= \)₹1,20,000
\(= \)₹1,20,000
SLM deducts the residual value before spreading the rest over the life.
Depreciable amount \(= 1{,}20{,}000 - 72{,}000 = ₹48{,}000\)
Spread evenly over the estimated useful life of 4 years.
\(\text{Annual depreciation} = \dfrac{48{,}000}{4} = \)₹12,000
The machine was bought 1 Jan 2020, but the three years asked for all begin on or after 1 April 2020 — by which time it has been owned for a full year already. Each of the three is a complete year of ownership.
FY 2020-21 ₹12,000
FY 2021-22 ₹12,000
FY 2022-23 ₹12,000
FY 2021-22 ₹12,000
FY 2022-23 ₹12,000
The part-year the question skipsThe stub period 1 Jan 2020 – 31 Mar 2020 is three months and would carry \(12{,}000 \times \tfrac{3}{12} = ₹3{,}000\) of depreciation in FY 2019-20. The question does not ask for it, but write it as a note — it proves you applied the pro-rata rule rather than missing it.
The trap most students fall into: computing \(\tfrac{96{,}000 - 72{,}000}{4} = ₹6{,}000\) per year, exactly half the right answer, by forgetting to capitalise the ₹24,000. The word "repairs" in the question is what misleads — but repairs on a second-hand asset bought to bring it into working condition are capital, not revenue. p. 160
The trap most students fall into: computing \(\tfrac{96{,}000 - 72{,}000}{4} = ₹6{,}000\) per year, exactly half the right answer, by forgetting to capitalise the ₹24,000. The word "repairs" in the question is what misleads — but repairs on a second-hand asset bought to bring it into working condition are capital, not revenue. p. 160
Book value check: after 4 years of ₹12,000, accumulated depreciation is ₹48,000 and the book value is ₹1,20,000 − ₹48,000 = ₹72,000 — exactly the estimated residual value. Under SLM the asset always lands precisely on its scrap value. If yours does not, you have made an error.
Faculty Depreciation sheet — Q4SLM · two machines · one sold mid-year · sheet p. 1
Q. Sharma & Co., whose books are closed on 31st March, purchased machinery for ₹1,50,000 on 1st April 2015. Additional machinery was acquired for ₹50,000 on 1st October 2015. Certain machinery which was purchased for ₹50,000 on 1st October 2015 was sold for ₹40,000 on 30th September 2017. Compute depreciation for all the years up to the year ended 31st March 2018. Depreciation is charged @ 10% p.a. on Straight Line Method.
Solution
Step 3 first — the grid. Two machines, three financial years. Mark the months each machine is owned in each year, and the rest is arithmetic.
| Machine | Cost | Full-year dep. @10% SLM | FY 2015-16 | FY 2016-17 | FY 2017-18 |
|---|---|---|---|---|---|
| A — bought 1 Apr 2015 | ₹1,50,000 | ₹15,000 | 12 months | 12 months | 12 months |
| B — bought 1 Oct 2015 sold 30 Sep 2017 | ₹50,000 | ₹5,000 | 6 months (Oct–Mar) | 12 months | 6 months (Apr–Sep) |
Why this stepWhat to write
Machine A: bought on the first day of the financial year, so every year is complete. SLM base never changes.
\(1{,}50{,}000 \times 10\% = \)₹15,000 in each of the three years.
Machine B, FY 2015-16: bought 1 Oct, year ends 31 Mar → Oct, Nov, Dec, Jan, Feb, Mar = 6 months.
\(50{,}000 \times 10\% \times \tfrac{6}{12} = \)₹2,500
Machine B, FY 2016-17: owned throughout.
\(50{,}000 \times 10\% = \)₹5,000
Machine B, FY 2017-18: sold 30 Sep → owned Apr to Sep = 6 months. Depreciation must be charged up to the date of sale before computing the WDV.
\(50{,}000 \times 10\% \times \tfrac{6}{12} = \)₹2,500
Add the two machines in each year.
FY 2015-16: \(15{,}000 + 2{,}500 = ₹17{,}500\)
FY 2016-17: \(15{,}000 + 5{,}000 = ₹20{,}000\)
FY 2017-18: \(15{,}000 + 2{,}500 = ₹17{,}500\)
FY 2016-17: \(15{,}000 + 5{,}000 = ₹20{,}000\)
FY 2017-18: \(15{,}000 + 2{,}500 = ₹17{,}500\)
Profit or loss on the sale of Machine B
Sum every year's depreciation on Machine B, including the six-month stub in the year of sale.
Accumulated dep. \(= 2{,}500 + 5{,}000 + 2{,}500 = ₹10{,}000\)
WDV on the day it left the business.
\(50{,}000 - 10{,}000 = \)₹40,000
Compare with the proceeds.
\(40{,}000 - 40{,}000 = \)NIL — no profit, no loss
Why that clean answer is a signal, not a coincidenceThe question was designed so the sale price equals the written-down value exactly. If your figure is not nil, you have almost certainly made one of these two errors:
· Forgot the ₹2,500 for Apr–Sep 2017 → you would get a WDV of ₹42,500 and report a loss of ₹2,500.
· Charged a full year in 2015-16 → you would get a WDV of ₹37,500 and report a profit of ₹2,500.
Use the nil result as your own check. And note what a nil result means in accounting terms: the estimated life and rate turned out to be exactly right — the asset was carried at precisely what it was worth.
· Forgot the ₹2,500 for Apr–Sep 2017 → you would get a WDV of ₹42,500 and report a loss of ₹2,500.
· Charged a full year in 2015-16 → you would get a WDV of ₹37,500 and report a profit of ₹2,500.
Use the nil result as your own check. And note what a nil result means in accounting terms: the estimated life and rate turned out to be exactly right — the asset was carried at precisely what it was worth.
Machinery Account — FY 2017-18, the year of the sale
| Dr. | Cr. | ||
|---|---|---|---|
| 1 Apr 2017 To Balance b/d (A ₹1,20,000 + B ₹42,500) | 1,62,500 | 30 Sep 2017 By Depreciation A/c (on B) | 2,500 |
| 30 Sep 2017 By Bank A/c (sale of B) | 40,000 | ||
| 31 Mar 2018 By Depreciation A/c (on A) | 15,000 | ||
| 31 Mar 2018 By Balance c/d | 1,05,000 | ||
| 1,62,500 | 1,62,500 | ||
| 1 Apr 2018 To Balance b/d | 1,05,000 | ||
Reading the account: Machine A's book value at 31 Mar 2018 is ₹1,50,000 − ₹45,000 (three years at ₹15,000) = ₹1,05,000, which is exactly the closing balance — correct, since B has gone. No "loss on sale" line appears because there was none; the sale proceeds of ₹40,000 exactly extinguish B's remaining book value.
Faculty Depreciation sheet — Q5The four-year one · three machines · two sales · sheet p. 1
Q. Bhushan & Company purchased a machinery on 1st April 2015 for ₹54,000 and spent ₹6,000 on its installation. On 1st December 2016 it purchased another machine for ₹30,000. On 30th June 2017 the first machine (1 Apr 2015) is sold for ₹36,000 and on the same date it purchased a new machinery for ₹80,000. On 1st December 2018 the second machine (1 Dec 2016) was also sold for ₹26,000. Depreciation was provided @ 10% p.a. on Original Cost Method, annually on 31st March. Calculate depreciation for four years.
Solution
"Original Cost Method" = SLM. Three machines, four financial years (2015-16 to 2018-19). Build the grid before touching a calculator.
| Machine | Cost | Full-year dep. | 2015-16 | 2016-17 | 2017-18 | 2018-19 |
|---|---|---|---|---|---|---|
| M1 · bought 1 Apr 2015 sold 30 Jun 2017 | ₹60,000 54,000 + 6,000 installation | ₹6,000 | 12 mo | 12 mo | 3 mo Apr–Jun | — |
| M2 · bought 1 Dec 2016 sold 1 Dec 2018 | ₹30,000 | ₹3,000 | — | 4 mo Dec–Mar | 12 mo | 8 mo Apr–Nov |
| M3 · bought 30 Jun 2017 | ₹80,000 | ₹8,000 | — | — | 9 mo Jul–Mar | 12 mo |
Why this stepWhat to write
M1: installation is capitalised. Depreciate on ₹60,000, not ₹54,000.
\(60{,}000 \times 10\% = ₹6{,}000\) full year
2017-18 (3 months): \(6{,}000 \times \tfrac{3}{12} = ₹1{,}500\)
2017-18 (3 months): \(6{,}000 \times \tfrac{3}{12} = ₹1{,}500\)
M2: bought 1 Dec 2016 → Dec, Jan, Feb, Mar = 4 months. Sold 1 Dec 2018 → Apr to Nov = 8 months.
\(30{,}000 \times 10\% = ₹3{,}000\) full year
2016-17: \(3{,}000 \times \tfrac{4}{12} = ₹1{,}000\)
2018-19: \(3{,}000 \times \tfrac{8}{12} = ₹2{,}000\)
2016-17: \(3{,}000 \times \tfrac{4}{12} = ₹1{,}000\)
2018-19: \(3{,}000 \times \tfrac{8}{12} = ₹2{,}000\)
M3: bought 30 June 2017, so depreciation runs from 1 July → 9 months in 2017-18.
\(80{,}000 \times 10\% = ₹8{,}000\) full year
2017-18: \(8{,}000 \times \tfrac{9}{12} = ₹6{,}000\)
2017-18: \(8{,}000 \times \tfrac{9}{12} = ₹6{,}000\)
Add down each column.
2015-16: \(6{,}000\) = ₹6,000
2016-17: \(6{,}000 + 1{,}000\) = ₹7,000
2017-18: \(1{,}500 + 3{,}000 + 6{,}000\) = ₹10,500
2018-19: \(2{,}000 + 8{,}000\) = ₹10,000
2016-17: \(6{,}000 + 1{,}000\) = ₹7,000
2017-18: \(1{,}500 + 3{,}000 + 6{,}000\) = ₹10,500
2018-19: \(2{,}000 + 8{,}000\) = ₹10,000
Profit or loss on each sale
| M1 — sold 30 Jun 2017 | M2 — sold 1 Dec 2018 | |
|---|---|---|
| Cost | ₹60,000 | ₹30,000 |
| Depreciation to date of sale | 6,000 + 6,000 + 1,500 = ₹13,500 | 1,000 + 3,000 + 2,000 = ₹6,000 |
| Written down value | 60,000 − 13,500 = ₹46,500 | 30,000 − 6,000 = ₹24,000 |
| Sale proceeds | ₹36,000 | ₹26,000 |
| Result | LOSS ₹10,500 → P&L A/c Dr. / To Machinery A/c | PROFIT ₹2,000 → Machinery A/c Dr. / To P&L A/c |
Why this question is setIt contains every single trap in the topic, once each:
· Installation capitalised (M1: ₹54,000 → ₹60,000)
· A machine bought mid-year (M2, 4 months)
· A machine sold mid-year (M1, 3 months; M2, 8 months)
· A purchase and a sale on the same date (30 June 2017)
· One sale at a loss and one at a profit — so you cannot assume a sign
· Four years, with machines entering and leaving — the grid is the only way to keep it straight
If you can do this one, the other four on the sheet will not surprise you.
· Installation capitalised (M1: ₹54,000 → ₹60,000)
· A machine bought mid-year (M2, 4 months)
· A machine sold mid-year (M1, 3 months; M2, 8 months)
· A purchase and a sale on the same date (30 June 2017)
· One sale at a loss and one at a profit — so you cannot assume a sign
· Four years, with machines entering and leaving — the grid is the only way to keep it straight
If you can do this one, the other four on the sheet will not surprise you.
Presentation note: the question says "calculate depreciation for four years", so the four annual totals are the answer. But show the per-machine working and the two profit/loss computations underneath — markers award the workings, and the sale results are the part most likely to appear as a follow-up sub-question.
Extra SLM problems4 questions · attempt cold
X1Basic SLM
Q. A machine costs ₹8,00,000, with freight ₹30,000 and installation ₹70,000. Estimated life 10 years, scrap value ₹1,00,000. Compute the annual depreciation and the rate of depreciation on original cost.
Solution
Freight and installation both bring the asset into working condition → capitalised.
Cost \(= 8{,}00{,}000 + 30{,}000 + 70{,}000 = \)₹9,00,000
SLM formula.
\(\dfrac{9{,}00{,}000 - 1{,}00{,}000}{10} = \)₹80,000 per year
Rate is always expressed on the original cost, not on the depreciable amount.
\(\dfrac{80{,}000}{9{,}00{,}000} \times 100 = \)8.89% p.a.
The subtlety in the rateThe rate is not 10% even though the life is 10 years, because a scrap value was deducted. Only when scrap value is nil does "life of N years" translate to a rate of \(100/N\)%. Watch for this whenever a question gives both a life and a residual value.
X2Capitalise or not?
Q. A firm buys a second-hand lathe for ₹2,40,000. It spends: ₹15,000 transporting it, ₹25,000 overhauling it before use, ₹40,000 on a new motor that raises its output by 20%, and ₹8,000 on routine servicing three months after it starts running. What amount is depreciated?
Solution
| Item | ₹ | Treatment | Why |
|---|---|---|---|
| Purchase price | 2,40,000 | Capital | The asset itself. |
| Transport | 15,000 | Capital | Brings the asset to the site. |
| Overhaul before use | 25,000 | Capital | Reconditioning of a second-hand asset — §7.7(A) names this exactly. |
| New motor, +20% output | 40,000 | Capital | Capacity improved — the test in §7.7(A). |
| Routine servicing after it starts running | 8,000 | Revenue | Maintains; does not improve. → Repairs A/c, P&L. |
| Depreciable cost | 3,20,000 | 2,40,000 + 15,000 + 25,000 + 40,000 |
The single question to askWas the spending needed to get the asset working, or to make it better than it was? Either way it is capital. Was it needed only to keep it working as before? Revenue. The timing word — "before use" versus "after it starts running" — is the examiner telling you the answer.
X3Count the months
Q. Books close 31 March. Compute the fraction of a year's depreciation for a machine (a) bought 1 August (b) bought 15 November (treat part-months as full) (c) sold 31 December (d) bought 1 Feb and sold 30 Nov of the following financial year.
Solution
| (a) bought 1 Aug | Aug→Mar | 8/12 |
| (b) bought 15 Nov | Nov→Mar, counting Nov as a full month | 5/12 |
| (c) sold 31 Dec | Apr→Dec | 9/12 |
| (d) bought 1 Feb, sold 30 Nov next FY | Year 1: Feb, Mar Year 2: Apr→Nov | 2/12 then 8/12 |
The counting methodCount on your fingers from the month of the event to the month of the year end, inclusive. Bought 1 Aug, year ends March: Aug, Sep, Oct, Nov, Dec, Jan, Feb, Mar = 8. For a sale, count from April to the month of sale, inclusive.
Mid-month convention: unless the question says otherwise, treat the month of purchase as owned in full and the month of sale as owned in full. Say which convention you used if the date is mid-month — it costs one line and protects the mark.
Mid-month convention: unless the question says otherwise, treat the month of purchase as owned in full and the month of sale as owned in full. Say which convention you used if the date is mid-month — it costs one line and protects the mark.
Q. On 1 Jan 2000 Shakti & Co. purchases machinery worth ₹50,000. On 1 July 2002 it buys additional machinery worth ₹10,000 and spends ₹1,000 on its erection. Accounts close 31 December. Depreciation 10% p.a. Show the machinery account for 5 years under SLM.
Solution
| Year | Opening | Addition | Depreciation | Closing |
|---|---|---|---|---|
| 2000 | 50,000 | — | 5,000 (50,000 × 10%) | 45,000 |
| 2001 | 45,000 | — | 5,000 | 40,000 |
| 2002 | 40,000 | 11,000 on 1 Jul | 5,550 = 5,000 + (11,000 × 10% × 6/12) | 45,450 |
| 2003 | 45,450 | — | 6,100 = 5,000 + 1,100 | 39,350 |
| 2004 | 39,350 | — | 6,100 | 33,250 |
| 2005 | 33,250 | Balance b/d | ||
Two things to take from this
1. The erection cost of ₹1,000 is capitalised — the addition is ₹11,000, not ₹10,000. The textbook footnotes it: "Erection amount Rs. 1,000 is also capitalised."
2. Under SLM, the depreciation on the first machine stays at ₹5,000 forever, even as its book value falls. That is the defining property, and it is what makes SLM easy: once you know a machine's annual charge, you never recompute it.
Note the closing balance in 2002 is HIGHER than in 2001 (₹45,450 vs ₹40,000), because the ₹11,000 addition outweighs the ₹5,550 charge. A rising machinery balance is not an error when there has been a purchase.
2. Under SLM, the depreciation on the first machine stays at ₹5,000 forever, even as its book value falls. That is the defining property, and it is what makes SLM easy: once you know a machine's annual charge, you never recompute it.
Note the closing balance in 2002 is HIGHER than in 2001 (₹45,450 vs ₹40,000), because the ₹11,000 addition outweighs the ₹5,550 charge. A rising machinery balance is not an error when there has been a purchase.
Topic 3 of 4 · Faculty sheet Q2 & Q3 · Textbook Illustration 1 · 10 questions
Written Down Value Method — Computation
Same routine, one difference: the base shrinks every year. That single change is what makes additions and sales "tedious", in the textbook's own word — and it is exactly why the faculty set two WDV problems with both.
How to know a question belongs to this topic
Give-away words
Diminishing Balance MethodWritten Down Value
WDVreducing balanceon the book value
The formula
\(\text{Dep}_t = \text{Opening book value}_t \times \text{Rate}\% \times n/12\), and then \(\text{Closing BV} = \text{Opening BV} - \text{Dep}\), which becomes next year's opening.
Scrap value
Not used. WDV applies a rate to a balance; it never deducts a residual first. The asset approaches zero but never reaches it.
The two places marks are lost
1. Applying the rate to the original cost in year 2 and later. The base must be the opening balance of that year.
2. On a fractional sale, forgetting that the fraction applies to the current book value of the whole, not to the original cost. (Under SLM you take the fraction of the original cost; under WDV you take the fraction of the running balance. Both give the same proportion, but only if you are consistent.)
2. On a fractional sale, forgetting that the fraction applies to the current book value of the whole, not to the original cost. (Under SLM you take the fraction of the original cost; under WDV you take the fraction of the running balance. Both give the same proportion, but only if you are consistent.)
Round or don't?
WDV produces paise. Keep two decimals through the working and round only at the end, stating what you did. Rounding early compounds through every later year.
Faculty Depreciation sheet — Q2WDV · two machines · sale defined by its loss · sheet p. 1
Q. A company purchased machinery for ₹50,000 on 1st October 2015. Another machinery costing ₹10,000 was purchased on 1st December 2016. On 31st March 2018 the machinery purchased in 2015 was sold at a loss of ₹5,000. The company charges depreciation @ 15% p.a. on the Diminishing Balance Method. Accounts are closed on 31st March every year. Calculate depreciation for 3 years.
Solution
The unusual feature: you are not told the sale price. You are told the loss, and you must find the WDV first to derive the price. Note also that the sale is on 31 March — the last day of the year — so a full year's depreciation is charged before it goes.
Machine A — ₹50,000, bought 1 October 2015
Why this stepWhat to write
FY 2015-16: bought 1 Oct, year ends 31 Mar → 6 months.
\(50{,}000 \times 15\% \times \tfrac{6}{12} = \)₹3,750
WDV 31.3.2016 \(= 50{,}000 - 3{,}750 = ₹46{,}250\)
WDV 31.3.2016 \(= 50{,}000 - 3{,}750 = ₹46{,}250\)
FY 2016-17: full year, on the new opening balance of ₹46,250 — not on ₹50,000.
\(46{,}250 \times 15\% = \)₹6,937.50
WDV 31.3.2017 \(= 46{,}250 - 6{,}937.50 = ₹39{,}312.50\)
WDV 31.3.2017 \(= 46{,}250 - 6{,}937.50 = ₹39{,}312.50\)
FY 2017-18: full year again, base ₹39,312.50. Sold on 31 March — the last day — so the whole year is charged before disposal.
\(39{,}312.50 \times 15\% = \)₹5,896.88
WDV at sale \(= 39{,}312.50 - 5{,}896.88 = \)₹33,415.62
WDV at sale \(= 39{,}312.50 - 5{,}896.88 = \)₹33,415.62
The loss is given. Work backwards: Loss = WDV − Proceeds, so Proceeds = WDV − Loss.
Sale proceeds \(= 33{,}415.62 - 5{,}000 = \)₹28,415.62
Machine B — ₹10,000, bought 1 December 2016
FY 2016-17: Dec, Jan, Feb, Mar = 4 months.
\(10{,}000 \times 15\% \times \tfrac{4}{12} = \)₹500
WDV 31.3.2017 \(= ₹9{,}500\)
WDV 31.3.2017 \(= ₹9{,}500\)
FY 2017-18: full year on ₹9,500.
\(9{,}500 \times 15\% = \)₹1,425
WDV 31.3.2018 \(= ₹8{,}075\)
WDV 31.3.2018 \(= ₹8{,}075\)
| Year | Machine A | Machine B | Total depreciation |
|---|---|---|---|
| FY 2015-16 | 3,750.00 | — | ₹3,750.00 |
| FY 2016-17 | 6,937.50 | 500.00 | ₹7,437.50 |
| FY 2017-18 | 5,896.88 | 1,425.00 | ₹7,321.88 |
The thing this question is really checkingLook at Machine A across the three years: ₹3,750 → ₹6,937.50 → ₹5,896.88.
The rise from year 1 to year 2 is not an error — year 1 was only six months. The fall from year 2 to year 3 is the WDV property doing its work: same rate, smaller base.
Under SLM the same machine would have charged ₹3,750, ₹7,500, ₹7,500 — flat after the stub. Seeing the two side by side is the clearest way to feel the difference between the methods.
The rise from year 1 to year 2 is not an error — year 1 was only six months. The fall from year 2 to year 3 is the WDV property doing its work: same rate, smaller base.
Under SLM the same machine would have charged ₹3,750, ₹7,500, ₹7,500 — flat after the stub. Seeing the two side by side is the clearest way to feel the difference between the methods.
On the decimals: ₹6,937.50 and ₹5,896.88 are exact to the paisa (₹5,896.875 rounded). Carry them; do not round to ₹6,938 in year 2, because year 3's base would then be wrong. State "figures rounded to the nearest paisa" in one line and you are safe.
Faculty Depreciation sheet — Q3WDV · fractional disposal + same-day purchase · sheet p. 1
Q. M/s. P & Q purchased machinery for ₹40,000 on 1st October 2015. Depreciation is provided @ 10% p.a. on the Diminishing Balance. On 31st January 2018, one-fourth of the machinery was found unsuitable and disposed off for ₹5,600. On the same date new machinery at a cost of ₹15,000 was purchased. Calculate depreciation for the years ended 31st March 2016, 2017 and 2018.
Solution
The strategy: depreciate the whole ₹40,000 machine normally for 2015-16 and 2016-17. Then, at the start of 2017-18, split its book value into one-fourth and three-fourths and treat them as two separate assets for the rest of the year.
Years 1 and 2 — one machine
Why this stepWhat to write
FY 2015-16: bought 1 Oct → 6 months.
\(40{,}000 \times 10\% \times \tfrac{6}{12} = \)₹2,000
WDV 31.3.2016 \(= ₹38{,}000\)
WDV 31.3.2016 \(= ₹38{,}000\)
FY 2016-17: full year on ₹38,000.
\(38{,}000 \times 10\% = \)₹3,800
WDV 31.3.2017 \(= ₹34{,}200\)
WDV 31.3.2017 \(= ₹34{,}200\)
Year 3 — split the asset
At 1 April 2017 the whole machine stands at ₹34,200. Split it in the stated proportion.
One-fourth \(= 34{,}200 \div 4 = \)₹8,550
Three-fourths \(= 34{,}200 \times \tfrac{3}{4} = \)₹25,650
Three-fourths \(= 34{,}200 \times \tfrac{3}{4} = \)₹25,650
The one-fourth was disposed on 31 January 2018 → owned April to January = 10 months. Charge depreciation up to the date of disposal.
\(8{,}550 \times 10\% \times \tfrac{10}{12} = \)₹712.50
WDV at disposal \(= 8{,}550 - 712.50 = ₹7{,}837.50\)
WDV at disposal \(= 8{,}550 - 712.50 = ₹7{,}837.50\)
The three-fourths was retained all year.
\(25{,}650 \times 10\% = \)₹2,565
WDV 31.3.2018 \(= ₹23{,}085\)
WDV 31.3.2018 \(= ₹23{,}085\)
The new machine was bought 31 January 2018 → February and March = 2 months.
\(15{,}000 \times 10\% \times \tfrac{2}{12} = \)₹250
WDV 31.3.2018 \(= ₹14{,}750\)
WDV 31.3.2018 \(= ₹14{,}750\)
Add the three components of FY 2017-18.
\(712.50 + 2{,}565 + 250 = \)₹3,527.50
| Year ended | Depreciation |
|---|---|
| 31 March 2016 | ₹2,000.00 |
| 31 March 2017 | ₹3,800.00 |
| 31 March 2018 | ₹3,527.50 (712.50 + 2,565 + 250) |
Loss on disposal — compute it even though the question did not ask
WDV of the quarter at the date of disposal.
₹7,837.50
Proceeds were ₹5,600.
\(7{,}837.50 - 5{,}600 = \)LOSS ₹2,237.50 → debited to P&L
Three points that decide this question
1. Take the fraction of the BOOK VALUE, not the cost. One-fourth of ₹34,200, not one-fourth of ₹40,000. Under WDV the whole machine has already been written down together, so the quarter carries its share of that write-down.
2. "Disposed off on 31st January" means 10 months of ownership, not 9 and not a full year. April, May, June, July, August, September, October, November, December, January.
3. The new machine bought on the SAME DATE gets 2 months, not 10. Two events on one date, two completely different month counts — that is the whole reason the date is shared.
Closing machinery balance at 31.3.2018 = ₹23,085 (retained three-fourths) + ₹14,750 (new machine) = ₹37,835.
2. "Disposed off on 31st January" means 10 months of ownership, not 9 and not a full year. April, May, June, July, August, September, October, November, December, January.
3. The new machine bought on the SAME DATE gets 2 months, not 10. Two events on one date, two completely different month counts — that is the whole reason the date is shared.
Closing machinery balance at 31.3.2018 = ₹23,085 (retained three-fourths) + ₹14,750 (new machine) = ₹37,835.
Extra WDV problems6 questions · attempt cold
X1SLM vs WDV, same asset
Q. A machine costs ₹1,00,000 with an estimated life of 5 years and no scrap value. Compute the depreciation for each of the first three years under (a) SLM at 20% and (b) WDV at 20%. Comment on the difference.
Solution
| Year | SLM @ 20% | WDV @ 20% | ||
|---|---|---|---|---|
| Depreciation | Closing BV | Depreciation | Closing BV | |
| 1 | 20,000 (on 1,00,000) | 80,000 | 20,000 (on 1,00,000) | 80,000 |
| 2 | 20,000 (on 1,00,000) | 60,000 | 16,000 (on 80,000) | 64,000 |
| 3 | 20,000 (on 1,00,000) | 40,000 | 12,800 (on 64,000) | 51,200 |
| Total, 3 yrs | 60,000 | 48,800 | ||
CommentYear 1 is identical under both methods — the base is the original cost either way. They diverge from year 2 onwards.
SLM charges a flat ₹20,000 forever and reaches exactly nil at the end of 5 years.
WDV charges more early and less later. After 5 years the book value would still be ₹32,768, never reaching zero — a percentage of a shrinking base always leaves something behind.
The managerial point to add: WDV front-loads the expense, so early-year profits look lower and later-year profits higher. Since repairs move the opposite way (low when new, high when old), the combined charge of depreciation plus repairs is far steadier under WDV. That is the textbook's core argument for it, and it is why Indian tax law accepts WDV and not SLM.
SLM charges a flat ₹20,000 forever and reaches exactly nil at the end of 5 years.
WDV charges more early and less later. After 5 years the book value would still be ₹32,768, never reaching zero — a percentage of a shrinking base always leaves something behind.
The managerial point to add: WDV front-loads the expense, so early-year profits look lower and later-year profits higher. Since repairs move the opposite way (low when new, high when old), the combined charge of depreciation plus repairs is far steadier under WDV. That is the textbook's core argument for it, and it is why Indian tax law accepts WDV and not SLM.
Q. Same facts as Topic 2 X4 (Shakti & Co: ₹50,000 on 1 Jan 2000; ₹10,000 + ₹1,000 erection on 1 Jul 2002; 10% p.a.; books close 31 Dec). Show the machinery account for 5 years under the Diminishing Balance Method.
Solution
| Year | Opening | Addition | Depreciation | Closing |
|---|---|---|---|---|
| 2000 | 50,000 | — | 5,000 10% of 50,000 | 45,000 |
| 2001 | 45,000 | — | 4,500 10% of 45,000 | 40,500 |
| 2002 | 40,500 | 11,000 1 Jul | 4,600 = 4,050 + (11,000 × 10% × 6/12 = 550) | 46,900 |
| 2003 | 46,900 | — | 4,690 | 42,210 |
| 2004 | 42,210 | — | 4,221 | 37,989 |
| 2005 | 37,989 | Balance b/d | ||
Compare with the SLM versionSame machine, same rate, same dates. After five years: SLM leaves ₹33,250; WDV leaves ₹37,989. WDV has written off ₹4,739 less, because its base kept shrinking.
Note 2002 in both versions. Once the addition arrives, the two components must be tracked separately for the part-year, then merged. The textbook footnotes it: "Depreciation 10% on Rs. 40,500 for one year & 10% on Rs. 11,000 for 6 months." In WDV the existing machine's base is ₹40,500 (its book value), while in SLM it stays ₹50,000 (its cost). That one line is the entire difference between the methods.
Note 2002 in both versions. Once the addition arrives, the two components must be tracked separately for the part-year, then merged. The textbook footnotes it: "Depreciation 10% on Rs. 40,500 for one year & 10% on Rs. 11,000 for 6 months." In WDV the existing machine's base is ₹40,500 (its book value), while in SLM it stays ₹50,000 (its cost). That one line is the entire difference between the methods.
X3Find the rate
Q. A machine bought for ₹80,000 has a book value of ₹51,200 after two years under WDV. Find the rate of depreciation.
Solution
Under WDV, after \(n\) years the book value is \(\text{Cost} \times (1-r)^n\).
\(80{,}000 (1-r)^2 = 51{,}200\)
Divide through and take the square root.
\((1-r)^2 = \dfrac{51{,}200}{80{,}000} = 0.64\)
\(1-r = 0.8\)
\(1-r = 0.8\)
Solve.
\(r = 0.20 = \)20% p.a.
Check it forwardYear 1: 80,000 × 20% = 16,000 → 64,000. Year 2: 64,000 × 20% = 12,800 → 51,200 ✓.
The general formula is worth having: \(r = 1 - \sqrt[n]{\dfrac{\text{Book value}}{\text{Cost}}}\). It occasionally appears as a short two-mark question, and it is trivial with a calculator.
The general formula is worth having: \(r = 1 - \sqrt[n]{\dfrac{\text{Book value}}{\text{Cost}}}\). It occasionally appears as a short two-mark question, and it is trivial with a calculator.
X4The base error
Q. A machine costing ₹2,00,000 is depreciated at 15% WDV. A student writes: Year 1 ₹30,000, Year 2 ₹30,000, Year 3 ₹30,000. What has gone wrong, and what are the correct figures?
Solution
The errorThe student applied the rate to the original cost every year — that is SLM, not WDV. Under the diminishing balance method the base is the opening book value of each year, which falls.
Year 1 is the only year the two methods agree, which is why the error hides.
\(2{,}00{,}000 \times 15\% = \)₹30,000 ✓
Closing BV = ₹1,70,000
Closing BV = ₹1,70,000
Year 2: base is ₹1,70,000, not ₹2,00,000.
\(1{,}70{,}000 \times 15\% = \)₹25,500
Closing BV = ₹1,44,500
Closing BV = ₹1,44,500
Year 3: base is ₹1,44,500.
\(1{,}44{,}500 \times 15\% = \)₹21,675
Closing BV = ₹1,22,825
Closing BV = ₹1,22,825
How to catch this in your own workIf your WDV figures are equal in any two consecutive full years, you have made this mistake. Under WDV a repeated figure is impossible unless an addition happens to offset the decline exactly. Glance down your column before you move on.
X5Fractional sale under WDV
Q. Machinery bought 1 April 2020 for ₹60,000, depreciated at 20% WDV, year ending 31 March. On 30 September 2022 half the machinery is sold for ₹12,000. Compute the depreciation for 2022-23 and the profit or loss on sale.
Solution
Why this stepWhat to write
Depreciate the whole machine for the first two full years.
2020-21: \(60{,}000 \times 20\% = 12{,}000\) → BV ₹48,000
2021-22: \(48{,}000 \times 20\% = 9{,}600\) → BV ₹38,400
2021-22: \(48{,}000 \times 20\% = 9{,}600\) → BV ₹38,400
At 1 April 2022 split the book value in half.
Each half \(= 38{,}400 \div 2 = \)₹19,200
The half sold: owned April to September = 6 months.
\(19{,}200 \times 20\% \times \tfrac{6}{12} = \)₹1,920
WDV at sale \(= 19{,}200 - 1{,}920 = ₹17{,}280\)
WDV at sale \(= 19{,}200 - 1{,}920 = ₹17{,}280\)
The half retained: owned all year.
\(19{,}200 \times 20\% = \)₹3,840
WDV 31.3.2023 \(= ₹15{,}360\)
WDV 31.3.2023 \(= ₹15{,}360\)
Total for the year.
\(1{,}920 + 3{,}840 = \)₹5,760
Proceeds against the WDV of the half sold.
\(12{,}000 - 17{,}280 = \)LOSS ₹5,280
Same shape as faculty Q3Split at the start of the year of sale, using the book value, then run each half on its own month count. Faculty Q3 uses a quarter and a ten-month stub; this uses a half and a six-month stub. The method does not change.
X6Which method would you advise?
Q. A manufacturer asks which depreciation method to adopt for a fleet of delivery vans. Advise, with reasons.
Solution
AnswerRecommend the Diminishing Balance (WDV) Method, with three reasons:
1. It matches the economics of a van. A vehicle loses most of its value in its first years and repairs escalate as it ages. WDV charges heavy depreciation when the van is new and light depreciation when it is old — so the combined charge of depreciation plus repairs stays roughly level across the life. SLM would give rising total costs and misleadingly declining profits.
2. It is recognised by the Indian income-tax authorities, so the books and the tax computation agree and no separate reconciliation is needed. SLM is not recognised.
3. It reflects resale value. A van's second-hand price falls in the same curved shape as a WDV balance, so the balance sheet carries a figure closer to reality.
The honest caveat to add: neither SLM nor WDV sets aside any money for replacement — both leave the depreciation invested in the business. If the manufacturer's real concern is having cash available when the fleet must be replaced, advise a Sinking Fund arrangement alongside the WDV charge.
1. It matches the economics of a van. A vehicle loses most of its value in its first years and repairs escalate as it ages. WDV charges heavy depreciation when the van is new and light depreciation when it is old — so the combined charge of depreciation plus repairs stays roughly level across the life. SLM would give rising total costs and misleadingly declining profits.
2. It is recognised by the Indian income-tax authorities, so the books and the tax computation agree and no separate reconciliation is needed. SLM is not recognised.
3. It reflects resale value. A van's second-hand price falls in the same curved shape as a WDV balance, so the balance sheet carries a figure closer to reality.
The honest caveat to add: neither SLM nor WDV sets aside any money for replacement — both leave the depreciation invested in the business. If the manufacturer's real concern is having cash available when the fleet must be replaced, advise a Sinking Fund arrangement alongside the WDV charge.
Topic 4 of 4 · Textbook §7.8–7.9 · Illustrations 2–3 · pp. 160–168 · 8 questions
Presentation — Machinery Account and Disposal
The computation is only half the marks. The other half is presenting it as a Machinery Account in T-form, with working notes, so the examiner can see every figure's origin.
What the account must contain
Debit side
To Balance b/d (opening WDV) · To Bank / Cash A/c (any purchase, at total capitalised cost) · To P&L A/c (profit on sale, if any)
Credit side
By Depreciation A/c · By Bank A/c (sale proceeds) · By P&L A/c (loss on sale, if any) · By Balance c/d
Below the account
Working notes — one block per machine, showing cost, each year's depreciation, accumulated depreciation, WDV at sale, proceeds, and the resulting profit or loss. Five lines.
Which method of accounting?
If the question says "show the Machinery Account", use Method A — depreciation credited straight to the asset, so the account shows the WDV. If it mentions a Provision for Depreciation, use Method B and keep the asset at cost in its own account.
Presentation bankTextbook Illustrations 2–3 and exam-shaped extras · answered
Q. Neha & Company, calendar year. Machinery bought 1 April 2006 ₹30,000; 1 October 2006 ₹20,000; 1 July 2007 ₹10,000. On 1 January 2008, one third of the machinery installed on 1 April 2006 became obsolete and was sold for ₹3,000. Show the Machinery Account, depreciation by fixed instalment at 10% p.a.
Solution
"Fixed instalment" = SLM. Calendar year, so the year ends 31 December — count months to December, not March.
Machinery Account
| Dr. | Cr. | ||
|---|---|---|---|
| 2006 Apr 1 To Bank A/c | 30,000 | 2006 Dec 31 By Depreciation A/c (30,000 × 10% × 9/12 = 2,250) (20,000 × 10% × 3/12 = 500) | 2,750 |
| 2006 Oct 1 To Bank A/c | 20,000 | 2006 Dec 31 By Balance c/d | 47,250 |
| 50,000 | 50,000 | ||
| 2007 Jan 1 To Balance b/d | 47,250 | 2007 Dec 31 By Depreciation A/c (50,000 × 10% = 5,000) (10,000 × 10% × 6/12 = 500) | 5,500 |
| 2007 Jul 1 To Bank A/c | 10,000 | 2007 Dec 31 By Balance c/d | 51,750 |
| 57,250 | 57,250 | ||
| 2008 Jan 1 To Balance b/d | 51,750 | 2008 Jan 1 By Bank A/c (sale) | 3,000 |
| 2008 Jan 1 By P&L A/c (loss on sale) | 5,250 | ||
| 2008 Dec 31 By Depreciation A/c (4,000 + 1,000) | 5,000 | ||
| 2008 Dec 31 By Balance c/d | 38,500 | ||
| 51,750 | 51,750 | ||
| 2009 Jan 1 To Balance b/d | 38,500 | ||
Working note — the loss on sale, exactly as the textbook prints it
One third of the machine installed 1 April 2006.
Cost of 1/3 machinery \(= \tfrac{1}{3} \times 30{,}000 = \)₹10,000
2006: owned April to December = 9 months.
\(10{,}000 \times 10\% \times \tfrac{9}{12} = ₹750\)
2007: a full year.
\(10{,}000 \times 10\% = ₹1{,}000\)
Sold on 1 January 2008 — the first day. No 2008 depreciation on this portion.
Accumulated \(= 750 + 1{,}000 = ₹1{,}750\)
WDV \(= 10{,}000 - 1{,}750 = \)₹8,250
WDV \(= 10{,}000 - 1{,}750 = \)₹8,250
Against proceeds of ₹3,000.
\(3{,}000 - 8{,}250 = \)LOSS ₹5,250
Four things to copy from this layout
1. The depreciation line carries its own bracket working right there in the account, showing each machine's component. The examiner never has to hunt.
2. Three separate credits on the date of sale — proceeds, loss, and the later year-end depreciation — each on its own line with its own date.
3. 2008 depreciation is ₹5,000, not ₹5,500. The remaining two-thirds of the first machine (₹20,000 cost) gives ₹2,000; the October 2006 machine gives ₹2,000; the July 2007 machine gives ₹1,000. The sold third contributes nothing. Written as (4,000 + 1,000) in the textbook: ₹4,000 from the two 2006 machines' surviving cost of ₹40,000, plus ₹1,000 from the 2007 machine.
4. Every year's two sides are totalled and ruled off before the next year's balance is brought down.
2. Three separate credits on the date of sale — proceeds, loss, and the later year-end depreciation — each on its own line with its own date.
3. 2008 depreciation is ₹5,000, not ₹5,500. The remaining two-thirds of the first machine (₹20,000 cost) gives ₹2,000; the October 2006 machine gives ₹2,000; the July 2007 machine gives ₹1,000. The sold third contributes nothing. Written as (4,000 + 1,000) in the textbook: ₹4,000 from the two 2006 machines' surviving cost of ₹40,000, plus ₹1,000 from the 2007 machine.
4. Every year's two sides are totalled and ruled off before the next year's balance is brought down.
Q. A machine costs ₹1,00,000, depreciated at 10% SLM for three years. Show the Balance Sheet extract at the end of year 3 under (a) Method A — depreciation credited to the asset, and (b) Method B — a Provision for Depreciation A/c.
Solution
Method A — credited to the assetMethod B — Provision account
Entry each year:
Depreciation A/c Dr. 10,000
To Machinery A/c 10,000
Depreciation A/c Dr. 10,000
To Machinery A/c 10,000
Entry each year:
Depreciation A/c Dr. 10,000
To Provision for Depreciation A/c 10,000
Depreciation A/c Dr. 10,000
To Provision for Depreciation A/c 10,000
Machinery A/c itself falls: 1,00,000 → 90,000 → 80,000 → 70,000.
Machinery A/c stays at ₹1,00,000 always. The Provision builds up: 10,000 → 20,000 → 30,000.
Balance Sheet extract:
Method A
Machinery 70,000
Method B
Machinery (at cost) 1,00,000
Less: Provision for Depreciation (30,000)
70,000
Machinery 70,000
Method B
Machinery (at cost) 1,00,000
Less: Provision for Depreciation (30,000)
70,000
Same net figure, different informationBoth show ₹70,000 as the carrying value. But Method B also tells the reader the original cost and how much has been written off — which says how old the asset is and how much life may remain. That extra information is why company balance sheets use Method B.
Where you have already seen this: your L3 trial balance carries "Land & Building ₹13,00,000" on the debit side and "Land & Building — Depreciation ₹1,95,000" on the credit side — Method B. Immediately below, "Plant & Machinery — Net ₹6,60,000" is a single debit — Method A L3 slide 20.
The closing entry is identical under both: Profit and Loss A/c Dr. / To Depreciation A/c. The Depreciation account is a nominal account and empties into the P&L either way.
Where you have already seen this: your L3 trial balance carries "Land & Building ₹13,00,000" on the debit side and "Land & Building — Depreciation ₹1,95,000" on the credit side — Method B. Immediately below, "Plant & Machinery — Net ₹6,60,000" is a single debit — Method A L3 slide 20.
The closing entry is identical under both: Profit and Loss A/c Dr. / To Depreciation A/c. The Depreciation account is a nominal account and empties into the P&L either way.
Q. A machine costing ₹50,000 with accumulated depreciation of ₹32,000 (held in a Provision A/c) is sold for ₹20,000. Show the Machinery Disposal Account and all the entries.
Solution
| Step | Entry | ₹ |
|---|---|---|
| 1. Transfer cost and accumulated depreciation out | Machinery Disposal A/c Dr. To Machinery A/c (cost) and Provision for Depreciation A/c Dr. To Machinery Disposal A/c | 50,000 50,000 32,000 32,000 |
| 2. Record the proceeds | Bank A/c Dr. To Machinery Disposal A/c | 20,000 20,000 |
| 3. Close the account | Machinery Disposal A/c Dr. To Profit and Loss A/c (profit) | 2,000 2,000 |
Machinery Disposal Account
| Dr. | Cr. | ||
|---|---|---|---|
| To Machinery A/c (cost) | 50,000 | By Provision for Depreciation A/c | 32,000 |
| To P&L A/c (profit on sale) | 2,000 | By Bank A/c (sale proceeds) | 20,000 |
| 52,000 | 52,000 | ||
How to read the accountWDV = 50,000 − 32,000 = ₹18,000. Proceeds of ₹20,000 exceed it by ₹2,000, so there is a profit.
The disposal account does the arithmetic for you. Put the cost in on the debit side and everything that reduces it on the credit side; whatever is needed to make the two sides equal is the profit or loss. A debit balancing figure (as here) is a profit; a credit balancing figure is a loss.
When to bother with a disposal account: only if the question asks for one, or if a Provision for Depreciation account is in use. If the question just says "show the Machinery Account", credit the proceeds and the loss directly there, as Illustration 2 does — it is faster and equally correct.
The disposal account does the arithmetic for you. Put the cost in on the debit side and everything that reduces it on the credit side; whatever is needed to make the two sides equal is the profit or loss. A debit balancing figure (as here) is a profit; a credit balancing figure is a loss.
When to bother with a disposal account: only if the question asks for one, or if a Provision for Depreciation account is in use. If the question just says "show the Machinery Account", credit the proceeds and the loss directly there, as Illustration 2 does — it is faster and equally correct.
X1Full presentation, from scratch
Q. Show the Machinery Account for the three years ended 31 March 2018 for M/s P & Q (faculty Q3 facts: ₹40,000 on 1 Oct 2015, 10% WDV, one-fourth sold 31 Jan 2018 for ₹5,600, new machine ₹15,000 the same day).
Solution
Machinery Account
| Dr. | Cr. | ||
|---|---|---|---|
| 2015 Oct 1 To Bank A/c | 40,000 | 2016 Mar 31 By Depreciation A/c (6 mo) | 2,000 |
| 2016 Mar 31 By Balance c/d | 38,000 | ||
| 40,000 | 40,000 | ||
| 2016 Apr 1 To Balance b/d | 38,000 | 2017 Mar 31 By Depreciation A/c | 3,800 |
| 2017 Mar 31 By Balance c/d | 34,200 | ||
| 38,000 | 38,000 | ||
| 2017 Apr 1 To Balance b/d | 34,200 | 2018 Jan 31 By Depreciation A/c (on ¼, 10 mo) | 712.50 |
| 2018 Jan 31 To Bank A/c (new machine) | 15,000 | 2018 Jan 31 By Bank A/c (sale of ¼) | 5,600 |
| 2018 Jan 31 By P&L A/c (loss on sale) | 2,237.50 | ||
| 2018 Mar 31 By Depreciation A/c (¾: 2,565 + new: 250) | 2,815 | ||
| 2018 Mar 31 By Balance c/d | 37,835 | ||
| 49,200 | 49,200 | ||
| 2018 Apr 1 To Balance b/d | 37,835 | ||
Check the closing balance two waysFrom the account: 34,200 + 15,000 − 712.50 − 5,600 − 2,237.50 − 2,815 = ₹37,835 ✓
From the components: retained three-fourths ₹23,085 + new machine ₹14,750 = ₹37,835 ✓
Note the total depreciation for 2017-18 is split across two credit lines — ₹712.50 on 31 January (the portion sold, charged up to its disposal date) and ₹2,815 on 31 March (everything still held). They sum to ₹3,527.50, the figure computed in D-Q3. Splitting them by date is what makes the account readable.
From the components: retained three-fourths ₹23,085 + new machine ₹14,750 = ₹37,835 ✓
Note the total depreciation for 2017-18 is split across two credit lines — ₹712.50 on 31 January (the portion sold, charged up to its disposal date) and ₹2,815 on 31 March (everything still held). They sum to ₹3,527.50, the figure computed in D-Q3. Splitting them by date is what makes the account readable.
X2Where does each figure go?
Q. For one year a firm records: depreciation ₹18,000; loss on sale of machinery ₹4,000; sale proceeds ₹26,000; machinery at cost ₹3,00,000; accumulated depreciation ₹95,000. Say where each appears in the final accounts.
Solution
| Item | Goes to | Side | Why |
|---|---|---|---|
| Depreciation ₹18,000 | Profit & Loss A/c | Debit | An expense of the year. |
| Loss on sale ₹4,000 | Profit & Loss A/c | Debit | A loss. Separate from depreciation — do not merge them. |
| Sale proceeds ₹26,000 | Nowhere, on its own | — | Not income. It is already reflected: it reduced the Machinery A/c and produced the ₹4,000 loss figure. Showing it as income would double-count. |
| Machinery at cost ₹3,00,000 | Balance Sheet | Assets | Shown in the inner column. |
| Accumulated depreciation ₹95,000 | Balance Sheet | Deducted from Machinery | Inner column deduction; ₹2,05,000 in the outer column. |
The one people get wrongSale proceeds are not revenue. Selling a fixed asset is not a sale in the trading sense — it is the conversion of one asset (machine) into another (cash). Only the difference between the proceeds and the book value reaches the P&L, as a profit or a loss. Crediting ₹26,000 to Sales would inflate turnover and overstate profit by ₹26,000.