Asset Depreciation

Depreciation is the gradual decrease in

utility of fixed assets with use and time.

Physical Depreciation
It is the reduction in an asset's capacity to
perform its service due to physical
impairment.

Functional Depreciation
It occurs as a result of changes in the
organization or in technology that decrease
or eliminate the need for an asset.
 Economic Depreciation
Economic Depreciation
=
purchase price - market value

Both physical and functional depreciation are

categories of economic depreciation.
 Accounting Depreciation
It is the systematic allocation of the initial cost
of an asset (machine or equipment) in parts
over a time known as its depreciable life.
(Financial statements - Balance Sheet and Income Statement)

In engineering economic analysis, we use the

concept of accounting depreciation exclusively.
This is because accounting depreciation provides
a basis for determining the income taxes
associated with any project undertaken.
 Depreciable Property
For the purposes of tax, any depreciable property has the
following Characteristics .
1. It must be used in business or must be held for the
production of income.
2. It must have a definite service life, and that life must be
longer than 1 year.
3.It must be something that wears out, decays, gets used
up, becomes obsolete, or loses value from natural causes.
Depreciable property includes buildings, machinery, equipment, and
vehicles.
Inventories are not depreciable property, because they are held
primarily for sale to customers in the ordinary course of business.
If an asset has no definite service life, the asset cannot be
depreciated (For example, Land)
 Physical Depreciation
Economic
Depreciation

A gradual decrease in Functional

utility of asset Depreciation

Depreciation
Book Depreciation

Accounting
Depreciation

The systematic Tax Depreciation

allocation of an asset's
value in parts over its
depreciable life
 Net Income
When a project's revenue exceeds its expenses, we
say that the project generated a profit or income. If
the project's revenue is less than its expenses, then
we say that the project resulted in a loss.

Revenue
- Expenses (cost of goods sold)
Gross Profit
- Operating expenses
- Depreciation
Taxable Income (Income before tax)
Retained Income
- Income Tax
Net Income

Cash flow = net income + depreciation

 Depreciation Methods

The most widely used methods are:

1. Straight-line Method
2. Declining Balance Method, and
3. Sum-of-years'- digit method
1. Straight-Line Method
In this method, it is assumed that the fixed asset is
depreciated in a uniform way.
I S
D n

Where N
Dn = the depreciation charge during n year
I or P = the cost of the asset, including installation
expenses S = salvage value at the end of the useful life
of asset N = the useful life

The book value = cost base - total depreciation

charges

Bn = I - (D1 + D2 +……….+ Dn)

 EXAMPLE: Straight-Line Depreciation

D= (I-S)/N= (10000-2000)/5=1600

Total Depreciation upto three years D3= n(I-S)/N=3* (10000-2000)/5=4800

Bn=I-Dn=10000-4800=5200= B3
Ex. I=10000 S=2000 N= 5Yrs.
Find Dn and Bn for n=2,4,5
N Dn=n(I-S)/N Bn=I-Dn

5
2. Declining Balance Method
In this method, a fixed fraction of the initial book
balance is deducted each year. The fraction or
declining balance rate is obtained by
(Accelerated Method)
d = 1/N

The most common multiplier is '1'. If this is '2', then

it is called double-declining balance method.

D1 = dI
D2 = d(I - D1) = dI(1-d)
D3 = d(I - D1- D2) =dI(1-d)2
For 'n' year, Dn = dI(1-d)n-1
We can also compute the total DB depreciation
at the end of 'n' years

TDB = D1 + D2 + D3 + D4 + …….. + Dn

= dI +dI(1 -d) +dI(1-d)2+ ……. +dI(1-d)n-1

TDB = I[1-(1-d)n]

Book Value Bn=I[(1-d)n]

EXAMPLE: Double Declining-Balance Depreciation

declining balance rate d = 2/N , For 'n' year, Dn = dI(1-d)n-1

Book Value Bn=I[(1-d)n]

Dn = dI(1-d)n-1
EXAMPLE: Double Declining-Balance Depreciation
for Final Book Value (Bn)  Salvage Value (S)
Case I Bn>S
Switching to DB to Straight Line (When S=0)
Case II Bn<S
3. Sum-of-years'-Digit Method (SOYD)

In this method,

SOYD = 1 +2 +……. +N =N(N +1)/N

Where,
N = the useful life
Dn =(N - n +1)(I- S)/SOYD
Bn=I-Dn
Sum of Year’s Digit Method
I=10,000 N=5 Yrs S=2000 Find Bn & Dn
Year Depreciation Book Value Bn=I-Dn
Dn =(N - n +1)(I- S)/SOYD

1 D1= (I-S)x(N-n+1)/SOYD B1=10000-2667

=(10000-2000)x5/15=2667 =7333
2 D2=8000x4/15=2133 B2=7333-2133=5200
3 D3=8000x3/15=1600 B3=5200-1600=3600
4 D4=8000x2/15=1067 B4=3600-1067=2533
5 D5=8000x1/15=533 B5=2533-533=2000

Bn=I-Dn
Tutorial
What are the depreciable properties? A second hand
bulldozer acquired at the beginning of the fiscal year at a
cost of Rs. 3,000,000 has an estimated salvage value of
Rs.250,000 and an estimated useful life of 5 years.
Determine the following
(a) The amount of annual depreciation charge and book
value for each year by the straight-line method.
(b) The amount of depreciation for the third year, computed
by the double-declining balance method.
(c) The amount of depreciation for the second year,
computed by the sum-of-years digits method.
Tutorial
Upjohn Company purchased new packaging equipment with an estimated
useful life of five years. The cost of the equipment was $35,000, and the
salvage value was estimated to be $5,000 at the end of year 5. Compute the
annual depreciation expenses over the five-year life of the equipment under
each of the following methods of book depreciation:
(a) Straight-line method.
(b) Double-declining-balance method. (Limit the depreciation expense in the
fifth year to an amount that will cause the book value of the equipment at
year-end to equal the $5,000 estimated salvage value.)
(c) Sum-of-years’-digits method.
 Tutorial
XYZ company purchased new CNC machine at the beginning of
the fiscal year at a cost of Rs. 68,000 has an estimated salvage
value of Rs. 9,500 and an estimated useful life of 12 years.
Determine the following
(a) The amount of annual depreciation charge and book value
for each year by the straight-line method.
(b) The amount of depreciation for the third year, computed by
the double-declining balance method.
(c) The amount of depreciation for the second year, computed
by the sum-of-years digits method.
Tutorial
Equipment for immersion cooling of electronic components
has an installed value (I) of NRs. 1,82000 with an estimated
trade in value (S) of NRs. 400,000 after 15 years
Determine the depreciation (Dn) and the book value (Bn) for
years 2,5,10 using following book depreciation methods.
a) Single declining balance (SDB) book depreciation
b) Double declining Balance (DDB) book depreciation
c) Sum of years Digit Method (SOYD)
Tutorial
What are depreciable properties? The double declining balance
method is to be used for an asset with a cost of NRs. 68,000 an
estimated salvage value of NRs. 12000 and an estimated useful
life of six years
i) What is the depreciation for the first three years , assuming
that the asset was placed in service at the beginning of the
year?
ii) If switching to the straight line method is allowed when is
the optimal time to switch?
Tutorial:
Define declining balance method depreciation and sum of digits
method depreciation. Which method is favorable from investor
point of view?
4. Units of production Method
Depreciation charges are made proportional to the ratio of actual
output to the total expected output, usually this ratio is figured in
machine hours.
Dn= ((I-S)*Service Units Consumed during year n)/Total Service units
Q. A truck for hauling coal has an estimated net cost of $55,000 and is
expected to give service for 250,000 miles, resulting in a $5,000 salvage value.
Compute the allowed depreciation amount for a truck usage of 30,000 miles.