This document discusses depreciation methods and provides examples of calculating depreciation using straight line, sum-of-years digits, and double declining balance methods. It defines depreciation as a decrease in the value of an asset over its useful life. Three main depreciation methods are described - straight line calculates equal depreciation amounts each year, sum-of-years digits uses a weighted schedule, and double declining balance uses a declining percentage. Examples are provided to demonstrate calculating depreciation schedules using each method for assets with initial costs, salvage values, and useful lives provided.

1. 10: Depreciation
Dr. Mohsin Siddique
Assistant Professor
msiddique@sharjah.ac.ae
Ext: 29431
Date:
Engineering Economics
University of Sharjah
Dept. of Civil and Env. Engg.

2. 2
Part I

3. Outcome of Today’s Lecture
3
After completing this lecture…
The students should be able to:.
Describe depreciation
Distinguish various types of depreciable property and
differentiate between depreciation expenses and other
business expenses. .
Use depreciation methods to calculate the annual
depreciation charge and book value over the asset's life.

4. Depreciation
4
Introduction
Depreciation Calculation Fundamentals
Depreciation Methods:
Straight Line
Sum ofYear’s Digits
Declining Balance

5. Depreciation
5
Depreciation is a decrease in value of an asset each year:
a decrease in market value
a decrease in the value to the owner
Important reasons for depreciation include
deterioration
obsolescence
Accountants define depreciation as follows:
the systematic allocation of the cost of an asset over its useful, or
depreciable life
The latter definition is used for determining income taxes,
which is most important because it affects the taxes that firms
pay:
TAXES proportional to TAXABLE INCOME (PROFIT –COSTS)
COSTS = Maintenance Cost + Depreciated Initial Cost

6. Depreciation
6
Depreciable life is the number of years over which a
machine is depreciated. It is also called Recovery Period.
This period may differ from the useful life.The depreciation method
determines the depreciable life.
At least six different depreciation methods are available.
Depreciation is a noncash cost. No money changes hands.
Usually you pay for the asset “up front”, but depreciate it over time
(e.g., a new truck).
Depreciation is a business expense the government allows to offset
the loss in value of business assets.
Depreciation deductions reduce the taxable income of businesses
and thus reduce the amount of tax paid.

7. Depreciation Calculation Fundamentals
7
Example:A PC costs $1,800. Its annual depreciation charges are
$800, $600, and $350 for three years.
$1,800 is called the cost, initial cost, or cost basis.
dt denotes the depreciation deduction in year t
d1= $800, d2= $600, d3= $350
BVt denotes the book value at the end of year t

8. Depreciation Calculation Fundamentals
8
Book value = Cost –Depreciation charges made to date
BVt= Cost Basis –(d1+ d2+ … + dt) = BVt-1- dt
i.e.,BV2= BV2-1- d2= BV1- d2
This equation is used to compute the book value of an asset at the
end of any time t.
Book value can be viewed as the remaining unallocated cost of an
asset.
If the item has a salvage value then the final book value will be the
salvage value.
Example:The book value of the PC declines during the
useful life from a value of B = $1,800 at time 0, to a value of
S = $50 at time 3.
Numerous depreciation methods are possible.

9. Depreciation Methods
9
Depreciation Methods:
Straight Line
Sum ofYear’s Digits
Declining Balance

10. (1). Straight Line (SL) Depreciation
10
Straight line depreciation is the simplest and best known:
Annual depreciation charge, dt= (B-S)/N
Example: An asset has a cost of B = $900, a useful life of N = 5
years, and an EOL salvage value of S = $70.
Using straight line, depreciation:
Annual depreciation charge: dt= (B-S)/N = (900-70)/5 = 830/5 = $166each
year

11. (1). Straight Line (SL) Depreciation
11

12. (2). Sum-of-Years Digits (SOYD) Depreciation
12

13. Sum-of-Years Digits (SOYD) Depreciation
13
Example: An asset has a cost of B = $900, a useful life of N = 5
years, and an EOL salvage value of S = $70.With SOYD
depreciation, we would compute the following
t

14. (2). Sum-of-Years Digits (SOYD) Depreciation
14

15. (3). Declining Balance Depreciation
15
For straight line depreciation with N years, the rate of decrease each year is
1/N.
Declining balance depreciation uses a rate of either 150% or 200% of the
straight-line rate.
Since 200% is twice the straight-line rate, it is called double declining balance
(DDB).
The DDB equation for any year is:
Since Book value = Initial cost –total charges to date

16. (3). Declining Balance Depreciation
16
Example: An asset has a cost of B = $900, a useful life of N = 5
years, and an EOL salvage value of S = $70.With DDB depreciation,
we would compute the following:
Year Multiplier Depreciation Sum of
Depreciation
BookValue
t 2/N dt=(2/N)BVt-1 ∑dt BVt=B-∑dt
0 900
1 2/5 (2/5)900= 360 360 900-360=540
2 2/5 (2/5)540 =216 576 900-576=324
3 2/5 (2/5)324 = 130 706 900-706=194
4 2/5 (2/5)194= 78 784 900-784=116
5 2/5 (2/5)116= 46 830 900-830=70

17. (3). Declining Balance Depreciation
17

18. (3). Declining Balance Depreciation
18
Example: An asset has a cost of B = $900, a useful life of N = 5
years, and an EOL salvage value of S = $70.With 150% Declining
depreciation method, we would compute the following:
Year Multiplier Depreciation Sum of
Depreciation
BookValue
t 1.5/N dt=(1.5/N)BVt-1 ∑dt BVt=B-∑dt
0 900
1
2
3
4
5

19. Double Declining Balance Depreciation
19
Summary
DDB is an accelerated depreciation compared to straight
line method
Book value (not first cost) is reduced by same fraction
(or %) each year (not same constant amount, as in
straight line)
Converges to an implied salvage value usually different
than estimated salvage value

20. 20
Part II
Problem: 11-4, 11-5, 11-7

21. 11-4
21
Some special handling devices can be obtained for
$12,000.At the end of 4 years, they can be sold for $600.
Compute the depreciation schedule for the devices using
the following methods:
(a) Straight-line depreciation.
(b) Sum-of-years' -digits depreciation.
(c) Double declining balance depreciation.

22. 11-4
22
Year Initial Book Value Depreciation Charge EOY Book Value
B dt=(B-S)/N B-dt
0 12000
1 12000 2125 9875
2 9875 2125 7750
3 7750 2125 5625
4 5625 2125 3500
P=B=$12,000 S=$3,500 N=4
(a) Straight Line Depreciation

23. 11-4
23
Year Life Multiplier B-S Depreciation Charge EOY book Value
t (N-t+1)/SOYD (N-t+1)/SOYD*(B-S)
0 12000
1 4 0.4 8500 3400 8600
2 3 0.3 8500 2550 6050
3 2 0.2 8500 1700 4350
4 1 0.1 8500 850 3500
10 SOYD
P=B=$12,000 S=$3,500 N=4
(b) Sum-of-Years Digits Depreciation

24. 11-4
24
Year Multiplier
Depreciation
Charge
Sum of
Depreciation
EOY Book
Value
t 2/N dt=(2/N)BVt-1
∑dt BVt=B-∑dt
0 12000
1 0.50 6000 6000 6000
2 0.50 3000 9000 3000
3 0.50 1500 10500 1500
4 0.50 750 11250 750
P=B=$12,000 S=$3,500 N=4
(c) Double Declining Balance Depreciation
DDB in any year = 2/N(BookValue)

25. 11-5
25
The company treasurer is uncertain which of three
depreciation methods the firm should use for office
furniture that costs $50,000, and has a zero salvage value
at the end of a 1O-year depreciable life. Compute the
depreciation schedule for the office furniture using the
methods listed:
(a) Straight line.
(b) Double declining balance.
(c) Sum-of-years' -digits.
The computations for the first three methods (SL, DB,
SOYD) are similar to Problem 11-4

26. 11-7
26
The Acme Chemical Company purchased $45,000 of
research equipment, which it believes will have zero
salvage value at the end of its 5-year life. Compute the
depreciation schedule for the equipment by each of the
following methods:
(a) Straight line.
(b) Sum-of-years'-digits.
(c) Double declining balance.

27. 11-7
27
(a) Straight Line
SL depreciation in any year= ($45,000 - $0)/5= $9,000
(b) SOYD
sum = (n/2) (n+1) = (5/2) (5) = 15
Depreciation inYear 1 = (5/15) ($45,000 - $0) = $15,000
Gradient = (1/15) ($45,000 - $0) = -$3,000
(c) DDB
Year DDB
1 (2/5) ($45,000 - $0)= $18,000
2 (2/5) ($45,000 - $18,000)= $10,800
3 (2/5) ($45,000 - $28,800)= $6,480
4 (2/5) ($45,000 - $35,280)= $3,888
5 (2/5) ($45,000 - $39,168)= $2,333

28. 28
ThankYou
Feel Free to Contact
msiddique@sharjah.ac.ae