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, property, plant and equipment can be measured at fair value with changes in fair value recorded in equity as reserves. This option is not available in US GAAP.

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 over 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.

The best way to think about this is if a company paid $15,000 for an asset that is expected to produce products for 3 years generating $10,000 sales evenly each year, we should match the cost paid of $15,000 by expensing $5,000 each year to match the $10,000 annual sales, instead of recognizing a one-off expense of $15,000 at year one. This creates a better picture for financial reporting.

Depreciation is a mathematical concept and you just need to be familiar with the different methods of calculating it. However, 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.

Depreciable base	XXX
Divide by: Estimated useful life	XXX
Annual depreciation charge	XXX

Where the depreciable base is the cost of the asset that we are spreading over the asset’s useful life. This is calculated as follows:

Cost	XXX
Less: salvage value	(XXX)
Depreciable base	XXX

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.

Under the straight-line method, the depreciation schedule is presented below:

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

In addition, the depreciation expense column is the amount to be used in the annual journal entries. Notice that it is the same all throughout the life of the asset at $16,000.

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:

Net book value at the beginning of the year	XXX
Multiply: double declining rate	XXX
Depreciation charge for the year	XXX

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. For example for an asset with a useful life of 4 years, the double declining rate would be computed as follows:

$$\begin{array}{rl}\text{Double declining rate}& =2\times \frac{1}{\text{Useful life}}\\ & =2\times \frac{1}{4\text{ years}}\\ & =2\times 25\%\\ & =50\%\end{array}$$

This means that every year, the asset is being depreciated by 50% of its beginning balance.

It is very important to remember that the net book value is calculated without considering the salvage value of the asset. However, it should be considered in the final year of depreciation. An example is shown 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 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:

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

In addition, the depreciation expense column is the amount to be used in the annual journal entries. Notice that it is highest in the earlier life of the asset.

Common pitfall: The double declining balance (DDB) method ignores salvage value in its annual calculation - it applies the declining rate to the full net book value, not a salvage-reduced base. Salvage value only enters in the final year, when the depreciation expense is “plugged” to bring the net book value down to the salvage value exactly (in the example above, that plug is $1,664 - not $10,000 × 40%). This is different from the straight-line, SYD, and units-of-production methods, which all depreciate a fixed depreciable base (cost minus salvage value) set up front. As you’ll see below, SYD applies a declining fraction to that fixed base each year, while DDB applies a fixed rate to a declining book value - don’t mix up the two.

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.

For example if the asset’s useful life is four (4) years, then the denominator would be computed as follows:

$$\begin{array}{rl}\text{SYD}& =1+2+3+4\\ & =10\end{array}$$

In this case, the depreciation expense at the end of the first year is calculated as follows:

$$\begin{array}{rl}\text{Depreciation expense}& =\text{Depreciable cost}\times \text{SYD ratio}\\ & =\text{Depreciable cost}\times \frac{\text{Remaining life}}{\text{SYD}}\\ & =\text{Depreciable cost}\times \frac{4}{10}\end{array}$$

And at the end of the second year, the ratio would be 3/10, and so on until the final year where the net book value would be equal to the salvage value.

In arriving at the $\text{SYD}$, you can add the digits manually like above or also use the following 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:

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

To check:

$$\begin{array}{rl}\text{SYD}& =1+2+3+4+5\\ & =15\end{array}$$

Then we can apply them to a depreciation schedule:

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

Unlike the double declining balance method, we use a uniform depreciable cost in the SYD method and not the book value at the beginning of the period.

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. In addition, the depreciation expense column is the amount to be used in the annual journal entries. Notice that the amount of depreciation expense is higher in earlier periods.

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:

	Cost (A)	Salvage value (B)	Depreciable cost (C = A - B)	Actual production (D)	Depreciation expense (D x $4)	Accumulated depreciation (E)	Net book value (A - E)
Beg. bal.	$90,000	$10,000	$80,000	-	-	-	$90,000
Year 1	$90,000	$10,000	$80,000	1,500	$6,000	$6,000	$84,000
Year 2	$90,000	$10,000	$80,000	2,000	$8,000	$14,000	$76,000
Year 3	$90,000	$10,000	$80,000	3,500	$14,000	$28,000	$62,000

The depreciation expense column is the amount to be used in the annual journal entries.

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