Depreciation under the written down value method
Compute three years of depreciation on the reducing balance and carry the written down value forward correctly.
Marks
4 marks
Exam time
6 min
Difficulty
Easy
The question
A machine is purchased on 1 April for ₹8,00,000. Depreciation is charged at 15% per annum under the written down value method. Compute the depreciation for each of the first three years and the written down value at the end of the third year.
- Given
- Cost of machine = ₹8,00,000Rate of depreciation = 15% p.a. (WDV)Period = 3 years, full year in each
Formulas used
- Depreciation for the year = Opening WDV × Rate
- Closing WDV = Opening WDV − Depreciation for the year
Step-by-step working
01Year 1
1Opening WDV ₹8,00,000 Less: Depreciation @ 15% ₹1,20,000 ───────── Closing WDV ₹6,80,000In year one, and only year one, the WDV base equals cost.
02Year 2
1Opening WDV ₹6,80,000 Less: Depreciation @ 15% ₹1,02,000 ───────── Closing WDV ₹5,78,000The rate is applied to ₹6,80,000, not to the original ₹8,00,000. This is the whole difference between WDV and straight line.
03Year 3
1.5Opening WDV ₹5,78,000 Less: Depreciation @ 15% ₹ 86,700 ───────── Closing WDV ₹4,91,30004Summarise
0.5Year 1 depreciation ₹1,20,000 Year 2 depreciation ₹1,02,000 Year 3 depreciation ₹ 86,700 ───────── Total depreciation (3 years) ₹3,08,700 WDV at end of year 3 ₹4,91,300Cost ₹8,00,000 less total depreciation ₹3,08,700 equals ₹4,91,300 — a one-line check worth writing.
Depreciation Y1 / Y2 / Y3 · Closing WDV
₹1,20,000 · ₹1,02,000 · ₹86,700 · WDV ₹4,91,300
Where marks are lost
- Applying the rate to original cost every year, which is straight line, not WDV.
- Deducting residual value before applying the rate — under WDV the rate is applied to the book value, and residual value is not separately deducted.
- Ignoring a part-year when the asset is bought mid-year; depreciation must then be time-apportioned.
- Rounding intermediate WDV figures, which compounds the error across years.
In the exam
This computation is worth practising until it is automatic, because it appears as a sub-part inside much larger questions — asset disposal, insurance claims and revaluation problems all begin with a correct WDV schedule.
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Talk to usWhen is WDV preferred over straight line?
WDV suits assets that give more service in their early years and need rising repairs later — vehicles and machinery are typical. The combined charge of depreciation plus repairs then stays more even across the asset's life.
What if the machine were bought on 1 October instead?
Year one depreciation would be for six months: ₹8,00,000 × 15% × 6/12 = ₹60,000, giving a closing WDV of ₹7,40,000. Every subsequent year would then be a full year on the reducing balance.
Reading a solution is not practice. Writing one is.
Generate fresh numericals on this exact chapter, attempt them under time, and have your written working evaluated step by step.
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