Think about what "depreciation" actually is before touching any formula. A machine bought for ₹1,00,000 will not be worth ₹1,00,000 forever. It wears out, becomes obsolete, loses resale value. Accounting has to spread that loss of value across the years the asset is used, so that each year's profit reflects the cost of using the asset that year. The question is: how do you spread it?
Two answers dominate. One says "spread it evenly." The other says "lose a fixed fraction of whatever is left each year." That is the whole story. Everything else is arithmetic.
The straight-line method
The intuition is dead simple: the asset loses the same rupee amount every year. If a machine costs ₹1,00,000, has a scrap (salvage) value of ₹10,000, and lives 5 years, the total depreciation to be charged is ₹90,000, and you charge ₹18,000 each year.
The book value falls in a straight line when you plot it against time — hence the name.
Annual depreciation=Useful lifeCost−Scrap value
Let C be cost, S the scrap value, n the life in years. Then
D=nC−S
and the book value after k years is
BVk=C−kD=C−k⋅nC−S
Notice the book value decreases by a constant absolute amount each year. It hits exactly S at the end of year n.
The written-down-value method
Here the logic is different. Many assets — vehicles, computers, machinery — lose a percentage of their current value each year, not a fixed rupee amount. A ₹1,00,000 machine losing 20% is worth ₹80,000 after one year; the next year it loses 20% of ₹80,000, i.e. ₹16,000, not ₹20,000. The depreciation charge shrinks every year because the base shrinks.
This is the reducing-balance or written-down-value (WDV) method. The rate r is applied to the opening book value of each year.
BVk=C(1−r)k
The depreciation charged in year k is the fall in book value that year:
Dk=BVk−1−BVk=C(1−r)k−1r
The book value decays geometrically. It never quite reaches zero in finite time — it only approaches it — which is why the WDV method is often paired with a scrap value that the rate is calibrated to reach.
Where the rate comes from
In the straight-line method you are given the life and scrap value and you compute the charge. In the WDV method you are usually given the rate, but sometimes you are given cost, scrap value and life, and must find the rate that makes the book value land on the scrap value after n years. Set C(1−r)n=S and solve:
1−r=(CS)1/n⟹r=1−(CS)1/n
A very common error is to compute the WDV rate as nCC−S — that is the straight-line rate, not the reducing-balance rate. The two are different numbers, and using the wrong one is the single most frequent mistake in this topic.
Comparing the two
Take C=₹1,00,000, S=₹10,000, n=5 years.
Straight line: D=590,000=₹18,000 every year.
WDV rate: r=1−(0.1)1/5=1−0.6310=0.3690, i.e. about 36.9% per year.
| Year | SL depreciation | SL book value | WDV depreciation | WDV book value |
|---|
| 0 | — | 1,00,000 | — | 1,00,000 |
| 1 | 18,000 | 82,000 | 36,900 | 63,100 |
| 2 | 18,000 | 64,000 | 23,280 | 39,820 |
| 3 | 18,000 | 46,000 | 14,690 | 25,130 |
| 4 | 18,000 | 28,000 | 9,270 | 15,860 |
| 5 | 18,000 | 10,000 | 5,860 | 10,000 |
Both end at ₹10,000, but the paths are completely different. WDV front-loads the depreciation: heavier charges early, lighter later. Straight line is flat. …