CAPITAL RECOVERY AND

1
CHAPTER XIII

• CAPITAL RECOVERY AND
• DEPLETION MODELS

2
CAPITAL RECOVERY MODELS

• TERMINOLOGY
• Depreciation - the reduction in value of assets.
  Depreciation methods are based on legally
  approved rules which do not necessarily
  accurately reflect an assets value.
• Book Value - the value of an asset remaining on
  the books after depreciation charges have been
  deducted.

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CAPITAL RECOVERY MODELS

• Market Value - the value an asset would bring if
  sold on the open market.
• Basis - the initial cost of an asset including
  all costs associated with readying the asset for
  use, i.e., procurement, installation, delivery,
  etc.
• Recovery Period - the time span over which an
  asset may be deprecated by law, not necessarily
  the useful life of the asset.

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CAPITAL RECOVERY MODELS

• Depreciation Rate - fraction of the basis removed
  through depreciation each year. May be constant
  or varying over time.
• Salvage Value - the expected market value of an
  asset at the end of its depreciable life. The
  salvage value should be adjusted for any removal
  and disposition costs.

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CAPITAL RECOVERY MODELS

• ACRS AND MACRS - ACRS, Accelerated Cost Recovery
  System, 1981, and MACRS, Modified Accelerated
  Cost Recovery System, 1986, are depreciation
  models which were introduced by the IRS to
  standardize depreciation methods. MACRS is the
  only depreciation model currently in use. Prior
  to 1981 many models were acceptable.

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CAPITAL RECOVERY MODELS

• STRAIGHT LINE DEPRECIATION MODEL
• Dt (B - SV) / n
• t year (1, 2, ... , n)
• Dt annual depreciation charge
• B first cost or basis
• SV salvage value
• n depreciable life

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CAPITAL RECOVERY MODELS
STRAIGHT LINE DEPRECIATION MODEL
BOOK VALUE
D1
D2
B
SV
1
2
3
4
5
6
7
8
9
YEAR
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CAPITAL RECOVERY MODELS

• DECLINING BALANCE, DB, AND DOUBLE DECLINING
  BALANCE, DDB, DEPRECIATION MODELS
• The theme of DB models is that a constant
  percentage of the Book Value is the depreciation
  charge for each year.
• Dt d BVt-1
• d constant depreciation
  rate
• BV book value

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CAPITAL RECOVERY MODELS

• DDB MODEL
• Prior to 1981 when the ACRS was adopted, a
  depreciation rate of two times the straight line
  rate was the maximum allowed by the IRS.
• A DB model with d 2/n is the DDB model

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CAPITAL RECOVERY MODELS

• D1 d BV0
• BV1 BV0 - D1 BV0 (1-d)
• BV2 BV1 - D2 BV1 - d BV1 BV1 (1-d)
  BV0 (1-d)2
• 0
• 
  0
• 
  0
• BVt
  BV0 (1-d)t
• BVt does not equal zero which implies
  SV BVt

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CAPITAL RECOVERY MODELS
DOUBLE DECLINING BALANCE
D1 for St. Line Model
BOOK VALUE
B
D1 for DDB Model
SV
1
2
3
4
5
YEAR
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CHAPTER XIII

• SWITCHING DEPRECIATION MODELS
• IRS has allowed one to switch depreciation models
  once during the life of the asset. The optimum
  (maximum present value of depreciation charges)
  method then is to use the DDB model initially,
  switching to St. Line when the annual
  depreciation for St. Line is greater than for DDB.

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CAPITAL RECOVERY MODELS

• The procedure for switching from DDB to St. Line
  is
• 1. For each year, t, compute the depreciation
  charges for both models
• DDB DD d BVt-1
• St Line DS BVt-1 / (n-t1)
• 2. Select the Max DD , DS for each year as the
  depreciation charge, Dt. Once Ds is selected
  that value is used throughout the remainder of
  the depreciation schedule.

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CHAPTER XIII

• EXAMPLE 13.1
• A milling machine is purchased with an
  acquisition and installation cost of 50,000.
  The machine is estimated to have a useful life of
  5 years. Compute the PW of the depreciation
  charges for a) St. Line, b) DDB and c) DDB to St.
  Line switching. Assume i 10.

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CAPITAL RECOVERY MODELS

• EXAMPLE 13.1 continued
• St Line
• yr. BVt-1 Dt
  (PF, .10, yr) PW
• 1 50,000 10,000 .9091
  9,091
• 2 40,000 10,000
  .8264 8,264
• 3 30,000 10,000 .7513
  7,513
• 4 20,000 10,000 .6810
  6,810
• 5 10,000 10,000 .6209
  6,209
• 
  TOTAL 37,887

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CAPITAL RECOVERY MODELS

• EXAMPLE 13.1 continued
• DDB
• yr BVt-1 Dt (PF,
  .10, yr) PW(Dt)
• 1 50,000 20,000 .9091
  18,182
• 2 30,000 12,000 .8264
  9,917
• 3 18,000 7,200 .7513
  5,409
• 4 10,800 4,320 .6810
  2,942
• 5 6,480 2,592 .6209
  1,609
• 
  TOTAL 38,059

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CAPITAL RECOVERY MODELS

• DDB - St Line Switching
• DDP 1st Year
• yr BVt-1 Dt St Line Dt
  Dt PW
• 1 50,000 20,000 10,000
  20,000 18,182
  
• 2 30,000 12,000 7,500
  12,000 9,917
  
• 3 18,000 7,200 6,000
  7,200 5,409
  
• 4 10,800 4,320 5,400
  5,400 3,677
• 5 6,480 2,592 6,480
  5,400 3,353
• TOTAL 40,538

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CAPITAL RECOVERY MODELS

• MACRS Method
• Two types of property recognized
• Personal Property - income producing
  possessions of a business, e.g., vehicles, mfg.
  eqpt., materials handling eqpt., computers,
  communication eqpt., etc.
• Real Property - Real estate and improvements
  thereto, e.g., factory and office buildings,
  warehouses, apartments, etc. Land is not
  considered real property and is not depreciable.

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CAPITAL RECOVERY MODELS

• MACRS Method continued
• Accelerated methods switching to St. Line are
  employed for personal property. DDB to St. Line
  for recovery periods of 3, 5, 7 and 10 years.
  150 DB to St. Line for 15 and 20 year periods.
• Half year convention is required which allows
  only half of the first years depreciation. This
  results in the remaining half of the first years
  depreciation being credited to year n1.

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CAPITAL RECOVERY MODELS

• MACRS Method continued
• Depreciation charges, Dt, are computed from
• Dt dt BV0
• where dt is derived from DB to St. Line with half
  year convention
• dt are shown in Table 13.2 page 396

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CAPITAL RECOVERY MODELS

• ST. LINE ALTERNATIVE TO MACRS
• The only alternative to MACRS is using the St.
  Line method with the half-year convention.
• This is obviously less desirable than MACRS but
  may be used for simplicity
• For this alternative
• dt 1/(2n) for year 1 and n1
• 1/n for years 2
  through n

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CAPITAL RECOVERY MODELS

• EXAMPLE 13.2
• Calculate the Present Worth of the
  depreciation charges for the asset in Example
  13.1 using the MACRS method.
• BV0 50,000 Recovery Period 5

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CAPTIAL RECOVERY MODELS

• yr BVt-1 dt Dt
  (PF, .10, t) PW
• 1 50,000 .20 10,000 .9091
  9,091
• 2 40,000 .32 16,000 .8264
  13,222
• 3 24,000 .192 9,600 .7513
  7,212
• 4 14,400 .115 5,750 .6810
  3,916
• 5 8,650 .115 5,750 .6209
  3,570
• 6 2,900 .058 2,900 .5645
  1,637
• 
  TOTAL 38,648

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CAPITAL RECOVERY MODELS

• COMPARISON OF DEPRECIATION SCHEDULES
• PRESENT WORTH
• ST. LINE - 37,887
• DDB - 38,059
• DDB - ST LINE SWITCHING - 40,538
• MACRS - 38,648

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DEPLETION METHODS

• Depreciation is a method of recovering the
  capital required to acquire a replaceable asset.
  Depletion is a method of recovering the value of
  an asset which can not be replaced. Examples are
  forests, mines, oil wells, etc. Two methods may
  be used

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DEPLETION METHODS

• METHOD I - Factor Depletion
• dt initial investment / resource capacity
• Annual Charge, Dt dt (usage or activity
  volume)
• Total Charges may not exceed initial investment

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DEPLETION METHODS

• METHOD II - Percentage Depletion
• Annual Charge flat of gross income provided
  it does not exceed 50 of taxable income.
• 
  ACTIVITY
• Oil and Gas
  Well 15
• Coal, Sodium
  Cloride 10
• Gravel,
  Sand, Peat 5
• Sulfur,
  Cobalt, Lead, Zinc 22
• Gold, Silver,
  Copper, Iron 15

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DEPLETION METHODS

• EXAMPLE 13.3
• A gold mine purchased for 750,000 is anticipated
  to produce 2750 troy oz. for 5 years and 2125
  thereafter. Assume the mine produces for 10
  years, i is 10, the price of gold is 400/oz.,
  and the total capacity of the mine is estimated
  to be 25,000 troy oz. what is the present value
  of the deplection charges for Methods I and II?

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DEPLETION METHODS

• Method I
• dt 750,000 / 25000 oz 30 / oz.
• Yr. 1 thru 5 D 2750 (30) 82,500
• Yr. 5 thru 10 D 2125 (30) 63,750
• PW 82.5 (PA, .1, 5) 63.75 (PA, .1,
  5)(PF, .1, 5)
• 312,000
  150,049 462,049

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DEPLETION METHODS

• Method II
• Year 1 thru 5 charge is 2750(400)0.15
  165,000
• Year 5 thru 10 charge is 2125(400)0.15
  127,500
• PW 165 (PA, .1, 5) 127.5 (PA, .1, 5) (PF,
  .1, 5)
• 625,482 486,436 1,111,918
• Not Bad for 750,000 Investment