The Most Taxing
Questions or We
Depreciate You
©2004 Dr. B. C. Paul
Conventions on Spreading
Cost
 We already met Depreciation with
Earnest and Crader Mining
 Method was called “Straight Line”
 Starts with a “Cost Basis” what the asset
originally cost
 Trucks cost $700,000 and lasted 7 years
 Calculation is
 $700,000/7 = $100,000
 Cost Basis/ Life = Annual Depreciation
Plot Thickens
 Some assets may have a salvage value
at discard
 Straight Line is actually
 (Cost Basis – Salvage)/ Life = Depreciation
 Example before treated the salvage value as
0
 This assumption is common for tax calculations
Problem of Real Behavior
 Auto illustration
 Typical new car in $24,000 range
 Drops in value about $4,000 when drives off
lot
 Drops in value rapidly at first (at age 5 or 6 it
may be only worth $4,000 or $5,000)
 Loss of market value slows down
 At 10 years may be worth $2,500
The Gap Problem
 Most people buy cars on credit
 Auto pay-off may be linear with simple interest
 Will be slow at first with compound interest loan
 Market value of car is dropping faster than your
debt
 What happens if you get hit by a semi pulling off car
lot and have a vehicle worth $20,000, but you owe
$24,000
 Insurance pays you what vehicle is worth and
leaves you holding bag with the loan
 Gaps of $10,000 are not uncommon (insurance often uses
low value estimates on wholesale used car market while
you bought the car retail)
Solutions
 Some insurance offers replacement cost
for first few years
 But only if accident is your fault and covered
under comprehensive
 If other guys fault his insurance still try low
wholesale market value
 Gap Insurance
 Difference between market and loan
Back to Depreciation
 Gap problem can occur for tax purposes if
government forces you to spread out cost in a
manner that does not reflect loss of value
 Need for method that depreciates fast at first
and then slows down
 Two methods commonly meet requirement
 Sum of Years Digits
 Declining Balance
Sum of Years Digits
 (Basis – Salvage) * Factor
 Factor = (N – t + 1)/(SOYD)
 N= number years depreciable life
 t = the current year for example depreciation in year
three would have t = 3
 SOYD = Sum of Years Digits
 If life is 5 years then
 SOYD = 5 + 4 + 3 + 2 + 1 = 15
 There is a formula to save you undignified counting
 N * (N+1)/2 = SOYD
Application
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If Earnest Depreciated his truck by SOYD
Basis = $700,000 (assume no salvage)
Factor 1 =(7 – 1 + 1)/ ((7/2)*(7+1)) = 0.25
Depreciation Year 1 = $700,000*0.25= $175,000
Year 2 6/28*$700,000 = $150,000
Year 3 5/28*$700,000 = $125,000
Year 4 4/28*$700,000 = $100,000
Year 5 3/28*$700,000 = $75,000
Year 6 2/28*$700,000 = $50,000
Year 7 1/28*$700,000 = $25,000
Declining Balance
Methods
 Need one more term – Book Value
 Book Value = (Cost Basis – Salvage – Depreciation
Taken to Date)
 Annual Depreciation = Book Value * Dbalance
factor
 Dbalance factor = (% rate)/(100*N) where N is
the life of the item
 Percentage rate is any ratio of initial depreciation to
straight line that is desired
 Ie the system has infinite adaptations
 In practice 150% and 200% are historical conventions
Lets Do Earnest’s Truck with
150% Declining Balance
 Book Value 1 = $700,000
 Dbalance factor 1 = 150/(100*7) =
0.214286
 Depreciation Year 1 = $150,000
 Note that Dbalance factor will not change
like with SOYD, but Book Value will
 Year 2
 0.214286*($700,000 – 150,000) = $117,857
Continuing
Year 3 0.212486*(700,000 – 267854)=$92,602
Year 4 0.212486*(700,000 – 360,459) = $72,759
Year 5 0.212486*(700,000 – 433,218) = $57,168
Year 6 0.212486*(700,000 – 490,386) = $44,917
Year 7 0.212486*(700,000 – 535,303) = $35,292
Year 8 0.212486*(700,000 – 570,595) = $27,730
Year 9 0.212486*(700,000 – 598,324) = $21,788
Wait a Cotton Picken Minute Here - The truck was
dead at 7 years – how long does this depreciation go
on
 Answer – Till you are dead too (forever)
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Houston- We have a
problem
 Declining balance methods start out fine,
but going on forever makes no sense
 Solution – Do a straight line calculation in
parallel with the declining balance
calculation and switch when straight line
is more
Implementation
 Year 1 SL = Book Value/ Remaining Life
 $700,000/ 7 = $100,000
 Declining Balance says $150,000
 $150,000 > $100,000 – select declining balance
 Year 2 SL = $550,000/ 6 = $91,667
 Declining Balance says $117,857
 $117,857 > $91,667 – select declining balance
 Year 3 SL = $432,143/ 5 = $86,439
 Declining Balance says $92,602
 $92,602 > $86,439 – select declining balance
Implementation Continued
 Year 4 SL $339,541/4 = $84,885
 Declining Balance says $72,759
 $84,885 > $72,759 - switch to SL for rest of
depreciation
 Thus
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Year 5 is $84,885
Year 6 is $84,885
Year 7 is $84,885
Depreciation is done
Things to Note
 Depreciation is funny money
 Money really moves like the cash flow
 Why do people use funny money?
 Accountants realized long ago that reporting profits and losses
based on when big purchases occurred put earning all over
the map – didn’t reflect how businesses asset position had
changed
 Depreciation allowed accounted earnings and losses to show
how the companies performance changed its asset position
 Why don’t we use them on cash flows
 We are valuing the earnings and investment of a project not
trying to put a value on the company every year
 We do things different because what we are trying to
do is different
The Funny Money Problem
 Everyone understands why we need to depreciate long
lived assets
 Getting people to agree on how to do it is another matter
 We have shown you 3 ways – and haven’t yet talked about
how we know how long the asset will last
 Everyone and his dog has a different way of calculating
profits
 SEC says how to do it for business reporting
 Enron, MCI, Tyco, and Arthur – Anderson do it any way that
looks good
 Feds say how to do it for their taxes
 States say how to do it for theirs
 Idea that companies have 5 sets of books is not
unusual
How do the Feds Do it?
 1971 U.S. Treasury Dept collected data
on equipment lives – plotted the midpoint
of the distribution and called it the Asset
Depreciation Range (ADR)
 This created standard lives for Property
 Reagan Revolution
 Economy in stagflation / World poised for
Nuclear annihilation with cold war
Reagan’s Solution
 Grow the economy out of stagnation and
bury the Soviets with military spending
 Key pin was stimulating investment and
activity
 He stimulated investment with tax credits
and an accelerated depreciation system
 He used artificially short depreciation lives
 Called Modified Accelerated Cost Recovery
System (MACRS)
Understanding MACRS
 Have to Divide Up Depreciable Property
 Tangible Property (can touch and feel it)
 We’ll deal with intangible later
 Tangible Property
 Real – land buildings, things upon or
attached to land
 Personal Property – things like equipment
and furniture are not really attached
Divide Personal Property
into Life Classes
 Three Year – Food and Bev handling equipment, tools for
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producing metal or plastic goods and autos, anything with an ADR
life of 4 or under
Five Year – Autos for business (not yours), trucks, aircraft,
research equipment, computers, oil drilling equipment, anything
with an ADR less than 10 years (and more than 4)
Seven Year – Office furniture, fixtures, rugs, equipment,
anything with ADR less than 16 years
Ten Year – Oil Refining Equipment, barges and ships, anything
with ADR less than 20 years
Fifteen Year – Telephone Distribution Lines, Sewerage Plants,
anything with an ADR less than 25 years
Twenty Year – Municipal sewers, personal property with an
ADR of more than 25 years
The Real Property Classes
 Commercial non-residential property
(including hotels and motels)
 Do 39 year straight-line
 Residential rental property (your landlord)
 Do 27.5 year straight-line
 Did You Say 27.5 Years?!!
Time Line Conventions
 With cash flows remember we accumulated
events and put them at one point in time
 Commonly we put all money events for a
compounding period at the end of the period
 Government also uses a convention about
where to put expenses for depreciation
purposes
 Use the “Mid Year Convention” – ie the years
purchases are treated as occurring exactly at the
middle of the year
 Thus on 3 year property you get half a year in year 1, full
years in 2 and 3, and a half in year 4
 There are also some rules that allow some property
(usually 7 year and under to be set by Mid-Quarter
Convention)
The Problem of Unwieldy
Math
 3, 5, 7, and 10 year property is
depreciated by 200% declining balance
converting to straight line
 15, and 20 year property is 150%
declining balance converting to straight
line
 Real Property is Straight Line
 Try that with Mid-Year and Mid-Quarter
Conventions
The IRS Solution
 IRS considered a $100 investment for
each type of property using mid-year, and
4 mid-quarter conventions where
applicable
 Calculated depreciation each year
 This just happens to be the %
depreciation allowable each year
 They then publish the numbers in a table
and spare you the need to understand how
they got them
Example
 Consider depreciation on a new carpet put in an office
building
 Carpeting cost $10,000
 Its 7 year Property
 The table says
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Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
14.29%*$10,000 = $1,429
24.49%*$10,000 = $2,449
17.49%*$10,000 = $1,749
12.49%*$10,000 = $1,249
8.93%*$10,000 = $893
8.93%*$10,000 = $893
8.93%*$10,000 = $893
4.46%*$10,000 = $446