# 3 METHODS OF DEPRECIATION (STRAIGHT-LINE, REDUCING BALANCE AND SUM OF THE YEARS DIGITS)

Depreciation is the decrease in the value of assets of an organisation over time.

Except for land, all fixed assets are subject to depreciation.

There are three major methods of calculating depreciation, namely; straight line, reducing balance, and sum-of-the-year's digit method of depreciation.

## Straight line depreciation

This is perhaps the most widely used method of depreciation.

In the straight-line method of depreciation, each year of usage is assigned an equal amount of the asset's cost until the asset reaches its scrap value

That is, the depreciation amount is the same throughout the useful years of the machine.

Indeed, the straight line method of depreciation gets its name from the fact that plotting successive depreciation on a graph results in a straight line with a slope equal to the annual rate of depreciation.

The annual computation of straight line depreciation expenses is calculated as follows:

$\text{depreciation}=\frac{\text{cost}-\text{residual value}}{\text{useful life of asset}}$

#### Example

Consider an asset with a cost of N440,000, a residual value of N40,000 and an estimated useful life of 8 years.

The annual depreciation will be calculated as follows:

$\frac{440,000-40,000}{8}=N50,000$

## Reducing balance method

This is a method of calculating depreciation where the annual depreciation is a fixed percentage of the net book value of the assets at the end of the previous accounting period.

Compared to the straight-line method, the reducing balance method of depreciation results in more depreciation charges in the early years of the depreciation and less depreciation charge in the latter years of the depreciation.

Reducing balance depreciation is so named because it results in a decreasing amount of depreciation as the asset is used

The formula for calculating the reducing balance depreciation charge is as follows:

Depreciation=Net book Value×Depreciation rate.

Net book value is the amount cost of an asset that has not been depreciated. It is calculated by subtracting the asset's cost from its accumulated depreciation.

Depreciation rate refers to the percentage decrease in the value of an asset.

#### Example

Equipment, which is expected to last for 5 years, was purchased by a business for N200,000. Calculate the depreciation charges for the first, second, and third years, assuming that the equipment depreciates at a rate of 20% per year.

Solution:

Depreciation=Net book Value×Depreciation rate, as you may recall.

The depreciation charges for the first year will be:

$\frac{20}{100}×N200,000=N40,000$

The depreciation charges for the second year are:

NBV=200,000-40,000=N160,000

$\frac{20}{100}×N160,000=N32,000$

The depreciation charges for the third year are:

NBV=160,000-32,000=N128,000

$\frac{20}{100}×N128,000=N25,600$

Hence, the depreciation charge for the first, second and third years respectively are N40,000, N32,000 and N25,600

## Sum-of-the-year digit method

Just as its name seems to suggest, the method of depreciation adds to the remaining life of an asset together and uses it to calculate the depreciation rate.

In the sum of the year method of calculating depreciation, the sum of an asset's estimated useful life is summed together, and each digit is then divided by the sum to give the depreciation rate.

For example, if an asset is expected to last for 4 years, the sum of the year's digit will be 4+3+2+1=10.

Year one's depreciation rate will be 4/10, year two's depreciation rate will be 3/10, and so on.

Using the sum of digit method, the depreciation method can be calculated as follows:

$\text{Depreciation}=\frac{\text{useful life of the asset remaining}}{\text{sum of useful life digit}}×\text{depreciable amount}$

Note: the depreciable amount is the cost of the asset minus the scrap value of the assets

#### Example

Joshua Plc. bought furniture worth N300,000, which is expected to be sold for N30,000 at the end of its 5 years useful life.

Determine the depreciation charges for the first, second and third year using the sum o digits method of depreciation.

Solution:

Recalled that $\text{Depreciation}=\frac{\text{useful life of the asset remaining}}{\text{sum of useful life digit}}×\text{depreciable value}$

We need to obtain the depreciable amount

Depreciable amount=N300,000-N30,000=N270,000

The depreciation for the first year is

$\frac{5}{15}×270,000=N90,000$

The depreciation for the second year is

$\frac{4}{15}×270,000=N72,000$

The depreciation for the third year is

$\frac{3}{15}×270,000=N54,000$

Therefore, the depreciation charges for the first, second and third are N90,000, N72,000 and N54,000 respectively.

Final words

Although the three major methods of depreciation are the straight line, reducing the balance, and the sum of the year's digit, there are alternative methods of depreciation such as depreciation fund, revaluation, sinking fund, machine hours and production unit method of depreciation.