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On July 1, 2023, Saechao Company purchased for \$2,000,000 equipment having
an estimated useful life of 6 years with an estimated salvage value of \$200,000. Depreciation is
taken for the portion of the year the asset is used.
Instructions
Calculate the depreciation expense for 2023 and 2024 using the:
1. Straight-line method
2. Sum-of-the-years'-digits method.
3. Double-declining balance method.

The cost of acquiring property, plant, and equipment is a
cost of doing business. Most assets wear out over time
and/or become obsolete, limiting their useful life.
 Depreciation is a means of allocating the cost of
property, plant, and equipment over the accounting
periods in which they provide benefits.
 Land is the only asset that is presumed to not lose its
usefulness over time. Therefore, land is not depreciated.
Why is Depreciation Recognized?
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Depreciation is the systematic and rational allocation of
the cost of property, plant, and equipment to the time
periods in which the PPE is used.
Systematic allocation means that the allocation is not
random. The costs are allocated to time periods using an
orderly process.
Rational allocation means that the way costs are allocated
makes sense given the manner in which the assets are
used.

What is Depreciation?

Accounting depreciation matches the cost of plant assets to the
periods in which they are used to generate revenue.
 Depreciation is not a process of valuing the asset. The amount of
depreciation recognized in a particular accounting period is not a
measure of the decline in market value during the period.
 The book value of a depreciable asset, which is the value reported
in the balance sheet, is the amount of the original cost that has not
yet been allocated as an expense of doing business. It is not
intended to represent market value.

Definitions to Remember
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Book value: Original cost less accumulated
depreciation to date.
 Depreciable cost: Total cost to be expensed over
the useful life of an asset. [Original cost minus
salvage value]
 Salvage value: The net proceeds the company
expects to receive upon disposal of an asset at
the end of its useful life. An assets book value
cannot be lower than its salvage value.

Cost Allocation Terminology
Assets included in property, plant, and equipment
are depreciated.
 Natural resources are depleted.
 Intangible assets are amortized.

Each of these involve a systematic and rational allocation
of an assets cost over its useful life.

Calculating Depreciation
The amount of depreciation recognized each
accounting period depends on the following:
 Capitalized cost
 Estimated useful life
 Estimated salvage value
 Allocation method selected by company

Straight-Line Method
Depreciation expense is the same each year; the
depreciable cost is allocated evenly over that
asset’s useful life.
 This method is rational when the asset will provide
essentially the same benefits each year. For
example, buildings are appropriately depreciated
on a straight-line basis.
 Computation:
(Cost – salvage value)/ useful life = depreciation
Example:
Equipment cost \$17,000
Salvage value 2,000
Useful life 5 years
Annual depreciation = (\$17,000 - \$2,000)/5
= \$3,000 per year
Straight-Line Method

depreciation rate per service hour is calculated.
 The hours that the asset was in service during each year
is measured and multiplied by the depreciation rate per
service hour.
 Depreciation will generally not be the same each year.
 This method is rational if the amount of benefit is the
same for each hour of service. For example, a delivery
vehicle could be depreciated based on service hours.
Service Hours Method
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Example:
Equipment cost \$17,000
Salvage value 2,000
Useful life 10,000 hours
Depreciation rate = (\$17,000 - \$2,000)/10,000
= \$1.50 per service hour

In year one, asset provided 2200 hours of service.
Depreciation = 2200 x \$1.50 = \$3,300

The useful life is stated in units of output and the
depreciation rate per unit of output is calculated.
 The units of output during each year are multiplied by
the depreciation rate per unit of output.
 Depreciation will not be the same each year.
 This method is rational if the amount of benefit is the
same for each unit produced. For example, oil drilling
equipment could be depreciated based on number of
barrels produced.
Units of Output Method
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Example:
Equipment cost \$17,000
Salvage value 2,000
Useful life 1,000 units
Depreciation rate = (\$17,000 - \$2,000)/1,000
= \$15 per unit produced
In year one, 190 units are produced.
Depreciation = 190 x \$15 = \$2,850
*Activity method based on output, as described in text
Units of Output Method*
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Accelerated Depreciation Methods

 Depreciate assets faster in the earlier years of an asset’s life.
 Theoretical justifications that support using accelerated methods to
better match expenses with related revenues:
 Asset is more productive in its early years.
 Maintenance costs are often higher in the later years of an assets life. If
one considers the cost of using an asset to be the cost of the asset itself
and the cost of maintenance, the overall costs of using an asset will be
more evenly distributed over its life if depreciation is higher when the
maintenance costs are lower.

Sum-of-the-Years’ Digits Method
First compute the sum of the years’ digits as follows:
5 year life = 5 + 4 + 3 + 2 + 1 = 15
4 year life = 4 + 3 + 2 + 1 = 10
Obviously, the above computation is not practical if an asset has a
relatively long life. The sum of the years’ digits can be computed with
the following formula, if n = useful life in years:
n(n+1) / 2
5 year life = (5 x 6)/2 = 15
4 year life = (4 x 5)/2 = 10
Sum-of-the-Years

Example:
Equipment cost \$17,000
Salvage value \$2,000
Useful life 5 years
The sum of the years’ digits for this example is 15.
Depreciable cost = \$15,000 (\$17,000 - \$2,000)
Year one depreciation = 5/15 x \$15,000 = \$5,000
Year two depreciation = 4/15 x \$15,000 = \$4,000
Year three depreciation = 3/15 x \$15,000 = \$3,000
Year two depreciation = 2/15 x \$15,000 = \$2,000
Year one depreciation = 1/15 x \$15,000 = \$1,000
Total depreciation \$15,000
Sum-of-the-Years’ Digits Method
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Salvage value is NOT used in the computation of depreciation.
 Annual depreciation is based on the book value of the asset at the
beginning of the year.
 Must be careful that book value does not fall below salvage value.
Once book value reaches salvage value, stop depreciating asset.
 Any acceleration rate between 100% and 200% of the straight-line
rate can be used, with 150% and 200% being among the most
common. When the acceleration rate selected is 200%, the
depreciation method is often referred to as the “double declining
method”.
Declining Balance Method
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Double Declining Balance Method

(20% x 2)
Year one depreciation = \$17,000 x 40% = \$6,800
Year two depreciation = (\$17,000 - \$6,800) \$10,200 x 40% = \$4,080
Year three depreciation (\$10,200 - \$4,080) \$6,120 x 40% = \$2,448
Year four depreciation (\$6,120 - \$2,448) \$3,672 x 40% = \$1,469
Year five depreciation \$ 203*
Total depreciation \$15,000

150% of Declining Balance Method

Example:
Equipment cost \$17,000
Salvage value \$2,000
Useful life 5 years
Straight-line rate 20% (1/5)
Rate on Declining Balance 30% (20% x 150%

Year one depreciation = \$17,000 x 30% = \$5,100
Year two depreciation = (\$17,000 - \$5,100) \$11,900 x 30% = \$3,570
Year three depreciation (\$11,900 - \$3,570) \$8,330 x 30% = \$2,499
Year four depreciation (\$8,330 - \$2,499) \$5,831 x 30% = \$1,749
Year five depreciation \$2,082*
Total depreciation \$15,000
* amount that causes book value at end of five years to equal salvage value.
150% of Declining Balance Method

Declining Balance Method

The strict application of the declining balance method can result in the
asset being depreciated over fewer years than the estimated useful
life if the residual value is relatively high.
It can also result in a larger write-off in the last year of an assets useful
life, as in the previous example.
To avoid such results, firms will usually change to the straight-line
method at some point and allocate the remaining book value evenly
over the remaining useful life.
Straight-Line Sum-of-the-
Years’ Digits
Double Declining
Balance
Year One \$3,000 \$5,000 \$6,800
Year Two \$3,000 \$4,000 \$4,080
Year Three \$3,000 \$3,000 \$2,448
Year Four \$3,000 \$2,000 \$1,469
Year Five \$3,000 \$1,000 \$203
Total \$15,000 \$15,000 \$15,000
Comparison of Depreciation Methods

Partial Year Depreciation

Assets purchased during the year are depreciated based
on the fraction of the year in which they were used.
 Firms which have a relatively large number of assets
sometimes use a simplifying convention such as
depreciating all assets a full year in the year of
acquisition and taking no depreciation in the year of
disposal OR taking a half year’s depreciation in the year
of acquisition and a half year’s in the year of disposal.

Partial Year Depreciation
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Example:
Equipment cost \$17,000
Salvage value \$2,000
Useful life 5 years
Asset acquired July 1
Straight-line depreciation
Year one*: (\$3,000 first year depreciation x 6/12) \$1,500
Year two: \$3,000
Year three: \$3,000
Year four: \$3,000
Year five: \$3,000
Year six: \$1,500
*The year refers to the accounting period in which depreciation is
recognized and assumes a December 31 year-end.
Partial Year Depreciation
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Example:
Equipment cost \$17,000
Salvage value \$2,000
Useful life 5 years
Asset acquired July 1
Sum-of-the-Years’ Digits depreciation
Year one*: (\$5,000 x 6/12) \$2,500
Year two: [(\$5,000 x 6/12) + (\$4,000 x 6/12)] \$4,500
Year three: [(\$4,000 x 6/12) + (\$3,000 x 6/12)] \$3,500
Year four [(\$3,000 x 6/12) + (\$2,000 x 6/12)] \$2,500
Year five [(\$2,000 x 6/12) + (\$1,000 x 6/12)] \$1,500
Year six (\$1,000 x 6/12) \$ 500
*The year refers to the accounting period in which depreciation is
recognized and assumes a December 31 year-end.
Partial Year Depreciation
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Example:
Equipment cost \$17,000
Salvage value \$2,000
Useful life 5 years
Rate on Declining Balance 40%
Asset acquired July 1
Double declining balance depreciation
Year one* = \$17,000 x 40% x 6/12 \$3,400
Year two = (\$17,000 - \$3,400) \$13,600 x 40% = \$5,440
and so on
Note: Year two also = (\$6,800 x 6/12) + (\$4,080 x 6/12) = \$5,440
*The year refers to the accounting period in which depreciation is
recognized and assumes a December 31 year-end.

now look instructor feedback

Notice that the equipment was purchased on July 1, so the company only used it for half of 2023. Also, when you compute depreciation under sum-of-the-years-digits, you need to include the salvage value in your calculation.

Your straight-line and double-declining balance computations are correct for a full year. But you still haven't taken into account that the equipment was only owned by the company for half of 2023.

Your computation of 2023 depreciation is correct applying the sum-of-the-years-digits method. However, the computation for 2024 is not

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