1. Lecture slides to accompany
Depreciation Methods
Lecture slides to accompany
Engineering Economy
7th edition
Leland Blank
Anthony Tarquin
© 2012 by McGraw-Hill All Rights Reserved

2. LEARNING OUTCOMES Understand basic terms of asset depreciation
Apply straight line method of depreciation
Apply DB and DDB methods of depreciation
Apply MACRS (Modified Accelerated Cost Recovery System) method of depreciation
© 2012 by McGraw-Hill All Rights Reserved

3. 1.0 DEPRECIATION
Decrease in value of physical properties with passage of time and use
Accounting concept establishing annual deduction against before-tax income i.e. to reduce income tax.
Taxes = (income – deductions)(tax rate)

4. DEPRECIABLE PROPERTY TANGIBLE (depreciation) - can be seen or touched
personal property - includes assets such as machinery, vehicles, equipment, furniture, etc...
real property - anything erected on, growing on, or attached to land
(Since land does not have a determinable life itself, it is not depreciable)
INTANGIBLE (amortization) - personal property, such as copyright, patent or franchise

5. 2.0 CONCEPTS & TERMINOLOGY
Adjusted cost basis -- allowable adjustment (increase or decrease) to original cost basis, used to calculate depreciation and depletion deductions
Basis, or cost basis -- also called unadjusted cost -- initial cost of acquiring an asset, plus sales tax, transportation, and normal costs of making asset serviceable

6. Book Method or Book Value (BV) is a noncash depreciation to represent the reduction in value of a tangible asset. It represents the decreasing value of the asset to the owner and to represent the diminishing value of the capital fund.
The Book Value (BV) of an asset is the asset's cost minus the asset's accumulated depreciation.

7. 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)

8. 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.

9. 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. 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. book depreciation can be calculated using any method
Definition: Book (noncash) method to represent decrease in value of
a tangible asset over time
Two purposes of analysis: book depreciation and tax depreciation
Book depreciation: used for internal accounting to track value of assets
Tax depreciation: used to determine taxes due based on tax laws
In USA only, tax depreciation must be calculated using MACRS;
book depreciation can be calculated using any method
© 2012 by McGraw-Hill All Rights Reserved

12. 3.0 Common Depreciation Terms
First cost P or unadjusted basis B: Total installed cost of asset
Book value BVt: Remaining undepreciated capital investment in year t
Recovery period n: Depreciable life of asset in years
Market value MV: Amount realizable if asset were sold on open market
Salvage value S: Estimated trade-in or MV at end of asset’s useful life
Depreciation rate dt: Fraction of first cost or basis removed each year t
Personal property: Possessions of company used to conduct business
Real property: Real estate and all improvements (land is not depreciable)
Half-year convention: Assumes assets are placed in service in midyear
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13. 4.0 SYMBOLS
The following terms are used in the classical (historical) depreciation method equations:
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* = cummulative 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

14. 5.0 DEPRECIATION METHOD

16. 5.1 Straight Line Depreciation
Book value decreases linearly with time
Dt =
(B – S)dt
Where: Dt = annual depreciation charge
t = year
B = first cost or unadjusted basis
S = salvage value
n = recovery period
B - S
Dt = n
BVt = B - tDt
Where: BVt = book value after t years
SL depreciation rate is constant for each year: d = dt = 1/n
© 2012 by McGraw-Hill All Rights Reserved

17. Example: SL Depreciation
An argon gas processor has a first cost of $20,000 with a
$5,000 salvage value after 5 years. Find (a) D3 and (b) BV3
for year three. (c) Plot book value vs. time.
Solution: (a ) D3 = (B – S)/n
= (20,000 – 5,000)/5
= $3,000
(c) Plot BV vs. time
BVt
20,000
(b) BV3 = B – tDt
= 20,000 – 3(3,000)
= $11,000
11,000
5,000 3 5
Year, t
© 2012 by McGraw-Hill All Rights Reserved

18. Example: SL Depreciation using Excel Function
An argon gas processor has a first cost of $20,000 with a
$5,000 salvage value after 5 years. Find (a) D3 and (b) BV3
for year three. (c) Plot book value vs. time.
Excel Function;
Dt = SLN(B,S,n)

19. 5.2 Declining Balance (DB) and
Double Declining Balance (DDB) Depreciation
Also known as fixed percentage or uniform percentage method.
Accelerate the asset value write-off because annual depreciation charge Dt is determined
by multiplying book value (BV) at the beginning of the year by a fixed percentage of
depreciation rate d, which double the depreciation rate of SL method.
d = 2 / n

20. Dt = dB(1 – d)t-1 BVt = B(1 – d)t
Determined by multiplying BV at beginning of year by fixed percentage d
Max rate for d is twice straight line rate, i.e., d ≤ 2/n
Cannot depreciate below salvage value
Depreciation for year t is obtained by relation:
Dt = dB(1 – d)t-1
Where: Dt = depreciation for year t
d = uniform depreciation rate (2/n for DDB)
B = first cost or unadjusted basis
BVt -1 = book value at end of previous year
Book value for year t is given by:
BVt = B(1 – d)t
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21. Example: Double Declining Balance
A depreciable construction truck has a first cost of $20,000 with a
$4,000 salvage value after 5 years. Find the (a) depreciation, and
(b) book value after 3 years using DDB depreciation.
Solution: (a) d = 2/n = 2/5 = 0.4
D3 = dB(1 – d)t-1
= 0.4(20,000)(1 – 0.40)3-1
= $2880
(b) BV3 = B(1 – d)t
= 20,000(1 – 0.4)3
= $4320

22. Solution: (a) d = 2/n = 2/5 = 0.4 D3 = dB(1 – d)t-1
A depreciable construction truck has a first cost of $20,000 with a
$4,000 salvage value after 5 years. Find the (a) depreciation, and
(b) book value after 3 years using DDB depreciation.
Solution: (a) d = 2/n = 2/5 = 0.4
D3 = dB(1 – d)t-1
= 0.4(20,000)(1 – 0.40)3-1
= $2880
Dt = DB(B,S,n,t)
Dt = DDB(B,S,n,t,d)
d= between 1 to 2
(b) BV3 = B(1 – d)t
= 20,000(1 – 0.4)3
= $4320

23. 5.3 Spreadsheet Functions for Depreciation
Straight line function: SLN(B,S,n)
Declining balance function: DB(B,S,n,t)
Double declining balance function: DDB(B,S,n,t,d)
Note: It is better to use the DDB function for DB and DDB depreciation. DDB function checks for BV < S and is more accurate than the DB function.
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24. 5.4 MACRS Depreciation Dt = dtB BVt = B - ∑Dj
Required method to use for tax depreciation in USA only
Originally developed to offer accelerated depreciation for economic growth
Where: Dt = depreciation charge for year t
B = first cost or unadjusted basis
dt = depreciation rate for year t (decimal)
Dt = dtB
Get value for dt from IRS table for MACRS rates
j = t
BVt = B - ∑Dj
Where: Dj = depreciation in year j
∑ Dj = all depreciation through year t
j = 1
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25. Always depreciates to zero; no salvage value considered
Incorporates switching from DDB to SL depreciation
Standardized recovery periods (n) are tabulated
MACRS recovery time is always n+1 years;
half-year convention assumes purchase in midyear
No special spreadsheet function; can arrange VDB
function to display MACRS depreciation each year
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26. MACRS Table

27. Example: MACRS Depreciation
A finishing machine has a first cost of $20,000 with a $5,000
salvage value after 5 years. Using MACRS, find (a) D and (b) BV
for year 3.
Solution:
(a) From table, d3 = 19.20
D3 = 20,000(0.1920)
= $3,840 Y1 Y2 Y3
(b) BV3 = 20, ,000( )
= $5,760
Note: Salvage value S = $5,000 is not used by MACRS and BV6 = 0
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28. Summary of Important Points
Two types for depreciation: tax and book
Classical methods are straight line and declining balance
In USA only, MACRS method is required for tax depreciation
Determine MACRS recovery period using either GDS or ADS
Switching between methods is allowed; MACRS switches
automatically from DDB to SL to maximize write-off
Depletion (instead of depreciation) used for natural resources
Two methods of depletion: cost (amount resource removed × CDt factor) and percentage (gross income × tabulated %)
© 2012 by McGraw-Hill All Rights Reserved