engineering economy

1. CHAPTER 7
Depreciation And Income Taxes
Created By : Eng.Maysa
Gharaybeh

2. Depreciation
 Decrease in value of physical properties with passage of
time and use.
 More specifically:
Accounting concept establishing annual deduction against
before-tax income to reflect effect of time and use on asset’s
value in firm’s financial statements
 to match yearly fraction of value used by asset in production
of income over asset’s economic life

3. Property Is Depreciable if it Meets These
Requirements :
 be used in business or held to produce income.
 have a determinable useful life which is longer
than one year
 wear out, decay, get used up, become obsolete,
or lose value from natural causes
 not be inventory, stock in trade, or investment
property

4. Depreciable Property (Tangible , Intangible )
 Tangible : can be seen or touched
personal property(‫ : )االموال المنقولة‬includes assets such as
machinery, vehicles, equipment, furniture, etc...
real property(‫ : )االموال غير المنقولة‬anything erected on, growing
on, or attached to land
(Since land does not have a determinable life itself, it
is not depreciable)
 Intangible : personal property, such as copyright, patent( ‫براءات‬
‫ )االختراع‬or franchise(‫)إعفاء معين,امتياز‬

5. When Depreciation Starts And Stops
 Depreciation starts when property is placed in service for
use in business or for production of income.
 Property is considered in service when ready and available
for specific use, even if not actually used yet.
 Depreciation stops when cost of placing it in service has
been recovered or when it is soled, whichever occurs first.

6. Additional Definitions
 Basis, or cost basis : (unadjusted cost ) initial cost of purchase
an asset, plus sales tax, transportation, and normal costs of
making asset serviceable
 Adjusted cost basis : allowable adjustment (increase or
decrease) to original cost basis, used to calculate depreciation
deductions
Improvement of the asset increases the original cost basis
Casualty or theft loss decrease the original cost basis

7. Additional Definitions
 Book Value (BV) : Worth of depreciable property as shown on
company records
 Represents amount of capital remaining invested in property and
must be recovered in future through accounting process
(Book Value)k=
k
adjusted cost basis - Σ (depreciation deduction)j
j=1

8. Additional Definitions
 Market Value (MV) : Amount paid by willing buyer to willing
seller for property where no advantage and no compulsion to
transact
 approximates present value of what will be received through
ownership of property, including time-value of money (or profit)

9. Additional Definitions
 Recovery Period :Number of years over which basis of property
is recovered through accounting process.
Normally the useful life for classical methods
Property class for General Depreciation System (GDS)
under MACRS
Class Life for Alternative Depreciation System (ADS)
 Recovery Rate :Percentage for each year of MACRS recovery
period used to calculate an annual depreciation deduction.

10. Additional Definitions
 Salvage Value (SV) : Estimated value of property at the end of
useful life.
expected selling price of property when asset can no longer be
used productively
net salvage value used when expenses incurred in disposing of
property; cash outflows must be deducted from cash inflows for
final net salvage value
with classical methods of depreciation, estimated salvage value is
established and used
with MACRS, the salvage value of depreciable property is defined
to be zero

11. Additional Definitions
 Useful Life : Expected (estimated) period of time property will be
used in trade or business or to produce income; sometimes referred to
as depreciable life.

12. The Classical Depreciation Methods
N = depreciable life of the asset in years
B = cost basis, including allowable adjustments
d k = annual depreciation deduction in year k (1< k <N)
d k* = cumulative depreciation through year k
BV k = book value at the end of year k
BV N = book value at the end of the depreciable (useful) life
SV N = salvage value at the end of year N
R = the ratio of depreciation in any one year to the BV at the beginning of the
year

13. Straight-Line (SL) Method
 Simplest depreciation method
 Assumes constant amount is depreciated each year over depreciable
(useful) life
 N = depreciable life
 B = cost basis
 dk = depreciaton in k
 BVk = book value at end of k
 SVN = salvage value

15. Declining Balance (DB) Method
 Sometimes called constant percentage method or Matheson formula
 Assumed annual cost of depreciation is fixed percentage of BV at
beginning of year
 R is constant R = 2 / N when 200% declining balance OR R = 1.5 / N
when 150% declining balance used
d1=B(R)
d k = B ( 1 - R ) k-1( R )
d k* = B [ 1 - (1 - R ) k ]
BV k = B ( 1 - R ) k
BV N = B ( 1 - R ) N
 Because declining balance method never reaches BV = 0, it’s
permissible to switch from this to straight-line method so asset’s SVN
will be zero or other desired value

17. Units-of-Production Method
 Not based on the idea that decrease in value of property is a
function of time
 Decrease in value is mostly a function of use
 Method results in cost basis (minus final SV) being allocated
equally over the estimated number of units produced during useful
life of asset.
Depreciation per unit of production =

19. DB with Switchover to SL
 DB method will NEVER reach BV =0
 You can switch from DB to SL
 The switch over occurs in the year in which a larger
depreciation amount is obtained from SL method

21. Table 7-1 page 328
d k = ( B - SVN ) / N
But the basis B from
Col(1)Changed every year and N is
the remaining years As followes :
Year (3)
1 4,000/10 years =400
2 3,200/9 year = 355.65
3 2,560/8years = 320
And so on
We select the largest depreciation
amount .

22. Taxable Income
(Before Taxable Income)
taxable income =
gross income - all expenses - depreciation

23. The disposal of a depreciable asset
can result in a gain or loss based on
the sale price (market value) and the
current book value
A gain is often referred to as depreciation recapture,
and it is generally taxed as the same as ordinary
income. A loss is a capital loss. An asset sold for
more than it’s cost basis results in a capital gain.

24. After Tax Economic Analysis

25. Rk = revenues (and savings from the project: cash inflow from project
during period ‘k’
Ek = cash outflows during year k for deductible expenses and interest
dk = depreciation
t = effective income tax rate on ordinary income (federal, state and other);
assumed to remain constant during the study period
Tk= income taxes paid during year ‘k’
BTCFk = Before Tax Cash Flow for year k
ATCFk = After Tax Cash Flow for year k

26. The taxable income = ( Rk – Ek- dk )
The income tax: Tk = - t ( Rk – Ek – dk )
BTCFk = Rk – Ek
ATCFk = BTCFk + Tk
= (Rk – Ek ) - t ( Rk – Ek – dk )
= (1 – t)(Rk – Ek ) + t dk

27. Example:
 An asset is expected to produce a net cash inflows of 70,000
per year for the six year period , where the cost basis is
260,000 and the market value is 20,000. MARR is 10% use
SL method …..
 A) develop BTCF
 B)develop ATCF
 C) Calculate the PW for both CFs

28. BTCF
0 -260,000
PW= -260,000 + 70,000 (P/A,10%,6)+
1 70,000 20,000(P/F,10%,6) =
2 70,000 -260,000 +70,000(4.3553) +20,000 (0.5645)=56,161
3 70,000 PW >0 it is acceptable alternative
4 70,000
5 70,000
SL = (260,000 -20,000)/6 =
6 70,000 40,000 per year
6 20,000

29. ATCF
EOY A B C=A – B D= - 0.4C E= A+D
BTCF Depreciation Taxable Income Tax ATCF
Deduction Income
0 -260,000 -260,000
1 70,000 40,000 30,000 -12,000 58,000
2 70,000 40,000 30,000 -12,000 58,000
3 70,000 40,000 30,000 -12,000 58,000
4 70,000 40,000 30,000 -12,000 58,000
5 70,000 40,000 30,000 -12,000 58,000
6 70,000 40,000 30,000 -12,000 58,000
6(market 20,000 20,000 20,000
value)
PW= -260,000 + 58,000 (P/A,10%,6)+
20,000(P/F,10%,6) =
-260,000 +58,000(4.3553) +20,000 (0.5645)=
3,897.4
PW >0 it is acceptable alternative