Depreciation by Straight Line and Declining Balance

Spreads the cost of equipment or a vehicle over the years it is used. The straight-line method writes off the same amount every year, while the declining-balance method takes a fixed share of the remaining book value each year, at a rate of 2 ÷ the useful life (the 200% method).

Buying a 3000000 vehicle does not create a 3000000 expense in that year. The vehicle will be used for years, so its cost is spread across those years. That process is depreciation, and the number of years it is spread over is the useful life, set by the type of asset.

There are two main ways to spread it. The straight-line method writes off the same amount every year.

D = \dfrac{C}{L}

The declining-balance method takes the same percentage each year of whatever value is left on the books.

D_k = C(1 - d)^{k-1} \times d, \quad d = \dfrac{2}{L}

$C$ is the purchase cost
$L$ is the useful life in years
$D$ is the yearly charge under the straight-line method
$D_k$ is the charge in year $k$ under the declining-balance method
$d$ is the declining-balance rate

The rate $2 \div L$ is simply twice the straight-line rate of $1 \div L$ , which is why it is called the 200% declining-balance method.

Example

Take a cost of 3000000, a useful life of 6 years, and look at the position after year 3.

Under the straight-line method the rate is $1 \div 6$ , about 16.67%, and the charge is 500000 every year. After three years 1500000 has been written off and the book value is 1500000.

Under the declining-balance method the rate is $2 \div 6$ , about 33.33%. Year 1 takes 33.33% of 3000000, which is 1000000. Year 2 takes 33.33% of the remaining 2000000, about 666667. Year 3 takes 33.33% of the remaining 1333333, about 444444. The three years total about 2111111, leaving a book value of about 888889.

Over the same three years the declining-balance method has written off more than 600000 extra. Recognising cost sooner lowers the tax bill in the early years. The later years are correspondingly smaller, so across the full life both methods total the same.

Where tax filing differs

Japanese tax filing adds a further step to the declining-balance method. Taking a percentage of what is left never quite reaches zero, so once the yearly charge falls below a guaranteed minimum, the remaining value is divided evenly and written off by the end of the useful life. This calculator does not model that switch, so the later years will differ from a tax return.

Tax rules also leave one yen on the books after an asset is fully depreciated, as a reminder that the asset is still held. This calculator writes down to zero.

Points to watch

An asset bought part-way through a financial year is depreciated only for the months it was in use that year. This calculator assumes a full year.

Useful lives are not chosen freely. They are set by regulation for each class of asset, and a real filing must use the prescribed figure.