Depreciation of PPE

Property, plant and equipment is subsequently measured at cost net of depreciation and impairment. The presentation in the balance sheet is as follows:

Property, plant and equipment (PPE)	XXX
Less: Accumulated depreciation Less: Accumulated impairment	(XXX) (XXX)
Net book value of PPE	XXX

Under IFRS (IAS 16), a company may instead choose the revaluation model: PPE is carried at fair value at the revaluation date less subsequent depreciation, with increases recorded in OCI as a revaluation surplus and decreases charged to profit or loss (except to the extent they reverse a prior surplus). U.S. GAAP does not permit revaluation; PPE stays at historical cost. A fuller comparison of U.S. GAAP and IFRS treatment of long-lived assets appears in a later chapter.

Depreciation

Depreciation is the systematic allocation of the cost of an asset over its useful life. The useful life is the expected period in which the company is expected to generate benefits from the asset. This is an application of the matching principle in accounting wherein we match the cost of the asset over the revenues over the period, instead of recognizing the whole cost as an expense at the time of the purchase of the asset.

Despite the different methods, the journal entry to record depreciation is the same:

Account	Debit	Credit	Financial statement element
Depreciation expense	XXX		Expense
Accumulated depreciation		XXX	Asset (contra)
To record depreciation of property, plant and equipment

We credit depreciation to a contra-asset account instead of crediting the asset account directly. This allows us to monitor the cost and the net book value in the financial statements.

Straight-line method

The straight-line method is the simplest method of depreciation. In this method, we normally determine the annual depreciation charge, which remains constant throughout the useful life of the asset:

$$\text{Annual depreciation expense}=\frac{\text{Cost}-\text{Salvage value}}{\text{Useful life}}$$

The numerator, cost minus salvage value, is called the depreciable base - the portion of the asset’s cost being spread over its useful life. The salvage value (or the residual value) is the estimated value of the asset at the end of its estimated useful life. If the salvage value is zero, then the depreciable base is equal to the asset’s cost. Under the straight-line method, the asset cannot be depreciated beyond its salvage value.

Achievable Co. buys an asset on January 1, Year 1 for $90,000 with a salvage value of $10,000. The expected useful life is 5 years. Calculate the depreciation charges using the straight-line method.

The depreciable base is $90,000 - $10,000 = $80,000, so the annual depreciation expense is $80,000 ÷ 5 = $16,000 each year. Under the straight-line method, the depreciation schedule is presented below:

	Depreciation expense (depreciable base / 5 years)	Accumulated depreciation (D)	Net book value (cost - D)
Beg. bal.	-	-	$90,000
Year 1	$16,000	$16,000	$74,000
Year 2	$16,000	$32,000	$58,000
Year 3	$16,000	$48,000	$42,000
Year 4	$16,000	$64,000	$26,000
Year 5	$16,000	$80,000	$10,000

Notice that at the end of Year 5, the net book value of the asset is equal to the salvage value.

Double declining balance

The double declining balance method of depreciation results in depreciation charges that are not the same throughout the estimated useful life. In particular, it results in higher charges at the beginning of the life of the asset. For this reason, this is considered as an accelerated depreciation method.

In this method, you need to calculate the depreciation charge every year using the following formula:

$$\text{Depreciation expense}=\text{Beginning-of-year net book value}\times \text{Double declining rate}$$

The formula for the double declining rate is as follows:

$$\text{Double declining rate}=2\times \frac{1}{\text{Useful life}}$$

You will notice that it is simply twice the straight-line rate. An example is shown below, followed by a pitfall to watch for involving salvage value.

Achievable Co. buys an asset on January 1, Year 1 for $90,000 with a salvage value of $10,000. The expected useful life is 5 years. Calculate the depreciation charges using the double declining balance method.

Under the double declining balance method, we first need to determine the double declining rate as follows:

$$\begin{array}{rl}\text{Double declining rate}& =2\times \frac{1}{\text{Useful life}}\\ & =2\times \frac{1}{5\text{ years}}\\ & =2\times 20\%\\ & =40\%\end{array}$$

Then we apply it to the depreciation schedule:

	Depreciation expense (prior year C × 40%)	Accumulated depreciation (B)	Net book value (C = cost - B)
Beg. bal.	-	-	$90,000
Year 1	$36,000	$36,000	$54,000
Year 2	$21,600	$57,600	$32,400
Year 3	$12,960	$70,560	$19,440
Year 4	$7,776	$78,336	$11,664
Year 5	$1,664	$80,000	$10,000

The depreciation expense for each year is calculated based on the net book value at the beginning of the year (i.e., end of the previous period). Hence the depreciation expense for Year 2 is $54,000 × 40%.

The depreciation expense at the final year is not calculated using the double declining rate but is determined by the amount of depreciation expense that would make the net book value equal to the salvage value of $10,000. The depreciation expense is highest in the earlier years of the asset’s life.

Common pitfall: DDB applies the declining rate to the full beginning-of-year net book value - salvage value is never subtracted before applying the rate. But no year’s charge may take the net book value below salvage value, so depreciation stops once net book value reaches salvage (Year 5 above, where the charge is plugged at $1,664 instead of $11,664 × 40%). This is the opposite of SYD, which applies a declining fraction to a fixed depreciable base (cost minus salvage) set up front.

Sum of the years digits (SYD)

This is also an accelerated depreciation technique. Under this approach, depreciation expenses are higher in the earlier years of an asset’s useful life and gradually decrease over time.

As the name suggests, the method is based on the sum of the digits of the asset’s useful life. The depreciable cost (that is, the asset’s cost less its salvage value) is multiplied by a fraction:

• The numerator is the remaining useful life of the asset in a given year.
• The denominator is the sum of all the digits of the asset’s estimated useful life.

This results in a front-loaded depreciation schedule that recognizes greater expense in the early years and smaller amounts in later years, until the final year, when the net book value equals the salvage value.

You can find the denominator - the sum of the years’ digits - by adding the digits manually, or with the formula:

$$\text{Sum of the years digits}=\frac{\text{n}(\text{n}+1)}{2}$$

Where $\text{n}$ is the life of the asset. A more detailed example is presented below.

Achievable Co. buys an asset on January 1, Year 1 for $90,000 with a salvage value of $10,000. The expected useful life is 5 years. Calculate the depreciation charges using the SYD method.

Under the SYD method, we first need to determine the denominator in the ratio, as follows:

$$\begin{array}{rl}\text{SYD}& =\frac{\text{n}(\text{n}+1)}{2}\\ & =\frac{5(5+1)}{2}\\ & =\frac{5(6)}{2}\\ & =\frac{30}{2}\\ & =15\end{array}$$

The depreciable cost is $90,000 - $10,000 = $80,000. Then we can apply them to a depreciation schedule:

	SYD ratio (D)	Depreciation expense (depreciable cost × D)	Accumulated depreciation (E)	Net book value (cost - E)
Beg. bal.	-	-	-	$90,000
Year 1	5 / 15	$26,667	$26,667	$63,333
Year 2	4 / 15	$21,333	$48,000	$42,000
Year 3	3 / 15	$16,000	$64,000	$26,000
Year 4	2 / 15	$10,667	$74,667	$15,333
Year 5	1 / 15	$5,333	$80,000	$10,000

This makes this more similar to the straight-line method except that we are calculating higher depreciation expense at the beginning of an asset’s life.

Units of production

The units of production is a method that allocates the depreciable cost based on usage and not based on time. This is appropriate for assets that are being employed directly on production of goods because companies can estimate:

1. The amount of expected units of goods that the asset can produce in its lifetime; and
2. The actual units produced every year.

These two inputs are then used in the annual calculation of the depreciation expense. Consider an example below:

Achievable Co. buys an asset on January 1, Year 1 for $90,000. The asset is expected to produce 20,000 units of products in its lifetime before it can get disposed of for its scrap value of $10,000. Calculate the depreciation charges using the units of production method if the actual units produced for the first 3 years of operations are as follows:

• Year 1: 1,500 units
• Year 2: 2,000 units
• Year 3: 3,500 units

The machine is expected to produce a total of 20,000 units all throughout its life.

Under the units of production method, we first need to determine the depreciation rate per unit of production. This is calculated as follows:

$$\begin{array}{rl}\text{Depreciation rate per unit}& =\frac{\text{Depreciable cost}}{\text{Estimated number of units to be produced}}\\ & =\frac{90,000-10,000}{20,000}\\ & =\frac{80,000}{20,000}\\ & =\$4\end{array}$$

We can then apply the rate to the depreciation schedule for the first three years of operations:

	Actual production (D)	Depreciation expense (D x $4)	Accumulated depreciation (E)	Net book value (cost - E)
Beg. bal.	-	-	-	$90,000
Year 1	1,500	$6,000	$6,000	$84,000
Year 2	2,000	$8,000	$14,000	$76,000
Year 3	3,500	$14,000	$28,000	$62,000

Which depreciation method is best?

The method of depreciation to be selected should reflect the expected manner of benefits that will be derived from the long term asset. This is in line with the matching principle.

If an asset is used in production that heavily wears out during its usage, then it could be appropriate to use the units of production method because the actual production, which will be sold and transformed into revenues, are directly related to the wear and tear of the asset;

If the use of an asset can be attributed evenly over time to the company’s revenue producing activities, then a straight-line depreciation might be appropriate. For example, the building in which the administrative activities are being held are commonly depreciated under the straight-line method

If an asset is losing its value quickly in earlier years, such as a vehicle, then an accelerated depreciation method may be appropriate like the SYD or the double-declining balance method.

Choosing a depreciation method is a matter of accounting policy but you will be tested to recommend the best depreciation method for a given set of facts.