Depreciation

By:
Prof. Endrick D Contractor
Assistant Professor,
Chemical Engineering Department
GCET
 Content
• Introduction,
• types and causes of depreciation,
• Methods of Depreciation calculation - Straight Line method, Double
Declining Balance Method, Sum of Years Digits Method /Sinking Fund
Method.
• Comparison of various methods,
• Numerical problems
 What is depreciation?
• An analysis of costs and profits for any business operation requires
recognition of the fact that physical assets decrease in value with age.
• This decrease in value may be due to physical decay, technological
advances, economic changes or other factors which ultimately will cause
retirement of the property.
• The reduction in value due to any of these causes is a measure of the
depreciation.
• A land is the only exception which cannot be depreciated as the value of
land appreciates with time.

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✓When a corporation constructs a new plant, the firm expects that it will last for a
number of years.

✓It is expected that when the plant begins producing it will be worth the outlay of
funds needed to construct it.

✓However, as the plant runs it tends to wear out and/or become obsolete.

✓Depreciation is the means by which this loss in value can be deducted as a business
expense.

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Purpose of depreciation as a cost
• First, it reduces federal income taxes, because the amount of depreciation
occurring in any one year is considered as an expense.
• i.e., Consideration of depreciation as a cost permits realistic evaluation of profits
earned by a company and therefore, provides a basis for determination of income
taxes.

• Second, it is a means whereby the stockholder can assess the physical value of a
company.
• i.e., Simultaneously, the consideration of depreciation as a cost provides a means
whereby funds are set aside regularly to provide recovery of the invested capital.

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 Two types of Depreciation : Physical & Functional depreciation
• Physical Depreciation
• The decrease in value due to changes in physical aspect of the property:
❑Wear and tear
❑Corrosion
❑Accident
❑Deterioration due to age

• The serviceability of the property is reduced because of physical

changes.
• Functional depreciation: The depreciation due to all other causes is called functional
depreciation:
❑Obsolescence
❑Change in demand
❑Shifting of population
❑Change in requirement of public authority
❑Insufficient capacity for the service required
❑Abandonment of the enterprise
Depreciable Investments
• In general, all property with a limited useful life of more than 1 year that is used in a
trade or business, or held for the production of income, is depreciable. Physical
facilities, including such costs as design and engineering, shipping, and field erection,
are depreciable.
• Land is not depreciable, but improvements to the land, such as grading and adding
utility services, are depreciable. Working capital and start-up costs are not depreciable.
• Inventories held for sale are not depreciable. In project terminology, the fixed-capital
investment, not including land, is depreciable.
• Maintenance is necessary for keeping a property in good condition; repairs connote the
mending or replacing of broken or worn parts of a property. The costs of maintenance
and repairs are direct operating expenses and thus are not depreciable.
• The total amount of depreciation that may be charged is equal to the amount of the
original investment in a property—no more and no less.
common terms used in depreciation analysis
• Initial cost is the total cost of acquiring the asset.

• Salvage value represents estimated market value of the asset at the end of its useful life. It is the expected
cash inflow that the owner of the asset will receive by disposing it at the end of useful life.

• Book value is the value of asset recorded on the accounting books of the firm at a given time period. It is
generally calculated at the end of each year. Book value at the end of a given year equals the initial cost less
the total depreciation amount till that year.

• Market value: The price which could be obtained for an asset if it were placed on sale in the open market
is designated as the market value.

• Useful life represents the expected number of years the asset is useful in terms of generating revenue. The
asset may still be in working condition after the useful life but it may not be economical. Useful life is also
known as depreciable life. The asset is depreciated over its useful life.
How to calculate depreciation in small business?

• There three methods commonly used to calculate depreciation. They are:

• Straight line method
• decline balance method
• sum of the year digit method
• shrinking fund method
Straight-Line Method

• This is the simplest method of all. It involves simple allocation of an even rate of
depreciation every year over the useful life of the asset.
• In the straight-line method for determining depreciation, it is assumed that the value of
the property decreases linearly with time.
• Equal amounts
• are charged for depreciation each year throughout the entire service life
of the property.
• The annual depreciation cost may be expressed in equation form as follows:
d= V - Vs
n
Where d = annual depreciation,
V = original value of the property at start of service life
Vs = salvage value of property at end of service life
n = service life, years
Straight-Line Method
• Example – Suppose a manufacturing company purchases a machinery for Rs.
100,000 and the useful life of the machinery are 10 years and the residual value of
the machinery is Rs. 20,000
• Annual Depreciation expense = (100,000-20,000) / 10 = Rs. 8,000
• Thus the company can take Rs. 8000 as the depreciation expense every year over the
next ten years as shown in depreciation table below.
Year Original cost – Residual value Depreciation expense
1 Rs. 80000 Rs. 8000
2 Rs. 80000 Rs. 8000
3 Rs. 80000 Rs. 8000
4 Rs. 80000 Rs. 8000
5 Rs. 80000 Rs. 8000
6 Rs. 80000 Rs. 8000
7 Rs. 80000 Rs. 8000
8 Rs. 80000 Rs. 8000
9 Rs. 80000 Rs. 8000
10 Rs. 80000 Rs. 8000
•
Impact of depreciation method on annual depreciation expense

• The asset value of the

equipment at any time during
the service life may be
determine is,
•
Va = V – a*d
Where ,
Va = asset or book value
a= no of years in actual use
Dd= annual depreciation
Straight-Line Method
Yearly depreciation = cost of asset – trade in value
years of life

Cost = $36,000
Years of life = 5 years
Trade in value = $6,000

Calculate the yearly depreciation using the above

equation……..
Answer

$36,000 - $6,000 = $30,000 =

5 years 5 years

$6,000

How about monthly?????

 Straight Line Method:
Truck with a trade in value of $6000
Yr Depreciation for the Year Accumulated Depr Book Value

1 18000 / 5 years = 3600 3600 24000 – 3600 =

20400
2 18000 / 5 years = 3600 3600 + 3600 = 7200 24000 – 7200 =
16800
3 18000 / 5 years = 3600 7200 + 3600 = 10800 24000 – 10800 =
13200
4 18000 / 5 years = 3600 10800 + 3600 = 14400 24000 – 14400 =
9600
5 18000 / 5 years = 3600 14400 + 3600 = 18000 24000 – 18000 =
6000
total $18000
 Declining-Balance (or Fixed Percentage) Method

• In this method, annual depreciation cost is a fixed percentage of the property

value at the beginning of the particular year.
• The fixed-percentage (or DB) factor remains constant throughout the entire
service life of the property,
• Annual cost for depreciation is different each year.
• The depreciation cost for the first year
= V * f,
where f = Fixed-percentage factor.

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• At the end of the first year Asset value =
Va1, = V(1 - f)
• At the end of the second year
Va2 = V(1 - f)2
• At the end of 3 years
Va3 = V(1 - f)3
• At the end of n years (i.e., at the end of service life)
Van = V(1 - f)n = Vs
Therefore, Vs = (1 - f)n
V
f = 1- (Vs / V)1/n
This equation represents the method for determining the fixed percentage factor, and the
equation is sometimes designated as the Matheson formula.

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• This method permits the investment to be paid off more rapidly during the early
years of life.
• The increased depreciation costs in the early years are very attractive.
• This reduces the income-tax load and recovery of depreciation is rapid in early
years.
• This method is seldom used in actual practice, because it places too much
emphasis on the salvage value.
• If salvage value is zero this method can not be used.
• To overcome this problem, the value of the fixed-percentage factor[ f = 2/n] is
often chosen arbitrarily using a sound economic basis.

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• The value of the asset cannot be zero at the end of the service life and may
possibly be greater than the salvage or scrap value.
• To handle this difficulty, sometimes for early portion of service life declining-
balance method is used and for remaining service life, straight-line method is used
this is known as the combination method
• The main advantage of this method that they permit greater depreciation
allowances in the early life of the property than in the later life.
• They are particularly applicable for units in which the greater proportion of the
production occurs in the early part of the useful life or when operating costs
increase markedly with age

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Double declining-balance method
• The double declining balance method is simply a declining balance method in
which double (200%) of the straight line depreciation rate is used.
• The first step in declining balance method is to calculate a straight line
depreciation rate, that is calculated using the following formula:
• Straight-line depreciation rate = 1/Useful life of the asset
• After calculating straight line rate, the accelerated depreciation rate is calculated to
be used in the declining balance method. It is calculated using the following
formula:
• Accelerated depreciation rate = straight-line depreciation rate × Specific
percentage
• Finally, the depreciation expense is calculated using the following formula:
• Depreciation expense = Remaining book value × Accelerated depreciation rate 22
• What Assets Are DDB Best Used for?
• DDB is ideal for assets that very rapidly lose their values or quickly become
obsolete. This may be true with certain computer equipment, mobile devices, and
other high-tech items, which are generally useful earlier on but become less so as
newer models are brought to market.

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• The Farma company provides the following information:
• Cost of the equipment: $500,000
• Salvage value: $50,000
• Useful life: 5 years
• Required: Prepare a depreciation schedule using double declining balance
method.

• Step 1 – Straight-line depreciation rate: 1/5 = 0.2 or 20%

• Step 2 – Declining balance rate (accelerated depreciation rate): 20% × 2 = 40%
• Step 3 – calculation of depreciation expense and preparation of schedule:

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• The book value of the equipment at the beginning of year 5 is $64,800 whose
40% is $2,5920. If this depreciation is used, the book value of the equipment at
the end of year 5 will be $38,880 ($64,800 – $25,920) that is less than the
salvage value. As stated earlier, the asset is depreciated only to its salvage value
under declining balance method.
• Therefore, the depreciation in year 5 has been provided as follows:
= Book value at the beginning of the year – Salvage value
= $64,800 – $50,000
= $14,800 25
Double Declining Balance Method
 Accelerated Depreciation Method- It depreciates MOST
in the beginning.
 Trade in value/Salvage Value is not considered
 Calculated using asset’s book value (original –A/D)

 Follow these steps to determine the DDB rate

1. compute the annual straight line depreciation rate

Year/useful life – 1÷5 = 20%
2. multiply the rate by 2. this is the DDB rate
20% x 2 = 40%
Double Declining Balance Method
$16,000 , life of 5 years, salvage $1500
yr Depreciation for Year Accumulated Depreciation BV = Cost – Accum
Depreciation
1 16000 x 40% = 6400 6400 16000-6400=9600
2 9600 x 40% = 3840 6400 + 3840= 10240 16000-10240=5760
3 5760 x 40% = 2304 10240 + 2304 = 12544 16000-12544=3456
4 3456 x 40% = 1382.4 12544 + 1382.4 = 13926.4 16000-13926.4=2073.6
5 2073.6 x 40% = 829.44 13926.4 + 573.6 = 14500 16000-14500= 1500
Cannot exceed salvage,
So 2073.6-1500= 573.6 is Salvage value
the amt of depreciation
used

1/5 = .2 x 2 = .4 x 100 = 40%

Sum-of-the-Years-Digits Method
• This method is an arbitrary process for determining depreciation.
• Results are similar to those obtained by the declining-balance method.
• Larger costs for depreciation are allotted during the early-life years than during the
later years.
• This method has the advantage of permitting the asset value to decrease to zero or
a given salvage value at the end of the service life.
• The annual depreciation is based on the number of service-life years remaining
and the sum of the arithmetic series of numbers from 1 to n service life.

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• The following formula is used to calculate depreciation expense under sum of
years’ digits method
•

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 Example:
• The Monster company purchased a machine on January 1, 2015. The
relevant information is given below:
• Cost of the machine: $250,000, Expected useful life of machine: 5 years
• Salvage value: $25,000
• Prepare a schedule showing the depreciation expense of each year of the
useful life of the machine using sum of years’ digits method.
• Depreciable cost (depreciable base):
• $250,000 – $25,000 = $225,000
• Depreciation expense at the end of the first year:
• $225,000 × (5/15) = $75,000
• Book value at the end of the first year:
• $250,000 – $75,000 = $175,000

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Sinking-Fund Method
• The use of compound interest is involved in the sinking-fund method.
• It is assumed that the basic purpose of depreciation allowances is to accumulate a
sufficient fund to provide for the recovery of the original capital invested in the
property.
• An ordinary annuity plan is set up wherein a constant amount of money should
theoretically be set aside each year.
• At the end of the service life, the sum of all the deposits plus accrued interest must
equal the total amount of depreciation

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• Now the generalized expression for depreciation in any given year ‘m’ can be
written as follows

• Similarly the generalized expression for book value at the end of any year ‘m’ is
given by

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example
• Using the information provided, calculate the annual depreciation and book value
of the construction equipment using sum-of-years-digits method and sinking fund
method.
• The interest rate is 8% per year.

Solution:
• P = Rs.3500000
• SV = Rs.500000
• n = 10 years

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• For sum-of-years-digits method, the depreciation amount for a given year is
calculated using equation

• Depreciation for 1st year = Rs.545454.55

• The book value at the end of 1st year is equal to initial cost less the
depreciation in the 1st year.
• Book value at the end of 1st year: Rs.2954545.45
• Depreciation for 2nd year : Rs.490909.09
• Book value at the end of 2nd year: Rs.2463636.36 34
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• For sinking fund method, the depreciation amount for a given year is
calculated using equation

The interest rate per year = i = 8% =0.08

• Depreciation amount for 1st year: Rs.207088.47

• Book value at the end of 1st year: Rs.3292911.53
• Depreciation amount for 2nd year: Rs.223655.55
• Book value at the end of 2nd year: Rs.3069255.98
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• The book value at the end of a given year can also be calculated by using equation
(3.48). Using this equation, the book value at the end of 2 nd year is given by;

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What Is Group Depreciation?

• Group depreciation is a combines similar fixed assets into a pool with a common
cost base for calculating depreciation on financial statements.
• The assets grouped together should be similar in the way they function, or
each asset should be small enough that it is not considered material on its own.
• Because modern accounting software easily records depreciation for individual
assets, the use of group depreciation has become less common.

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Understanding Group Depreciation

• Group depreciation is also known as "composite depreciation."

• By pooling assets that are similar in nature, such as all of a company's delivery
trucks that travel about the same distance every year, a company can simplify its
depreciation calculation and save time and expense for accounting and auditing
tasks.
• However, before deciding to pool assets into one group, it is important to consider
how each asset will be depreciated individually, (referred to as unit depreciation)
and whether it makes sense to group this asset with any others.
• In general, group depreciation is meant to be used for multiple smaller items of
lower cost.
• However, larger, more expensive items, including buildings, may not be pooled
for group depreciation purposes.

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• Example Calculations
• In this case, Grande's accountants designate the four asset categories as a single
asset class "Office Equipment." Group depreciation begins with a summary of
depreciation information for assets in each of the four office equipment categories.

Office Equipment Original Salvage Depreciable Depreciable Straight Line

Assets Cost Value Cost Life Deprec.
per Year
Computers $65,000 $5,000 $60,000 3years $20,000
Copy/Fax Mach $12,000 $2,000 $10,000 5 years $2,000
Printers $6,000 $1,000 $5,000 5 years $1,000
Phone Switch Eq $93,000 $3,000 $90,000 9 years $10,000
Total $176,000 $11,000 $165,000 — $33,000 41
• Notice that composite depreciation will base calculations for all asset categories
in the Office Equipment group on the straight-line (SL) method. From these
figures, the firm calculates a composite rate and a composite life.
• Composite rate = Total depreciation per year / Total original cost
= $33,000 / $176,000
= 0.188
• Composite life = Total depreciable cost / Total depreciation per year
= $165,000 / n$33,000
= 5.0
• Composite depreciation expense each year equals the composite depreciation
rate applied to the total historical cost. Here, assuming no assets join or leave
the asset set, composite depreciation for each of five reporting years is:
• Composite Depreciation Expense = (0.188 ) ($176,000) = $33,088
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