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CHAPTER 7 DEPRECIATION AND INCOME TAXES. DEPRECIATION Decrease in value of physical properties with passage of time and useDecrease in value of physical.

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Presentation on theme: "CHAPTER 7 DEPRECIATION AND INCOME TAXES. DEPRECIATION Decrease in value of physical properties with passage of time and useDecrease in value of physical."— Presentation transcript:

1 CHAPTER 7 DEPRECIATION AND INCOME TAXES

2 DEPRECIATION Decrease in value of physical properties with passage of time and useDecrease in value of physical properties with passage of time and use Accounting concept establishing annual deduction against before-tax incomeAccounting 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 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 - to match yearly fraction of value used by asset in production of income over asset’s economic life

3 PROPERTY IS DEPRECIABLE IF IT MUST : be used in business or held to produce incomebe used in business or held to produce income have a determinable useful life which is longer than one yearhave a determinable useful life which is longer than one year wear out, decay, get used up, become obsolete, or lose value from natural causeswear out, decay, get used up, become obsolete, or lose value from natural causes not be inventory, stock in trade, or investment propertynot be inventory, stock in trade, or investment property

4 DEPRECIABLE PROPERTY TANGIBLE - can be seen or touchedTANGIBLE - can be seen or touched personal property - includes assets such as machinery, vehicles, equipment, furniture, etc... personal property - includes assets such as machinery, vehicles, equipment, furniture, etc... real property - anything erected on, growing on, or attached to land 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 - personal property, such as copyright, patent or franchiseINTANGIBLE - personal property, such as copyright, patent or franchise

5 WHEN DEPRECIATION STARTS AND STOPS Depreciation starts when property is placed in service for use in business or for production of incomeDepreciation 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 yetProperty 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 is removed or it is retired from serviceDepreciation stops when cost of placing it in service is removed or it is retired from service

6 DEPRECIATION METHODS Time ImplementedMethod Before 1981 (SL) Straight-Line (DB) Declining Balance (DB) Declining Balance (SYD) Sum-of-the-years-digits (SYD) Sum-of-the-years-digits > 1980 > 1987 (ACRS) Accelerated Cost Recovery System Implemented by (ERTA) Economic RecoveryTax Act of 1981 > 1980 > 1987 (ACRS) Accelerated Cost Recovery System Implemented by (ERTA) Economic RecoveryTax Act of 1981 >1986 (MACRS) Modified Accelerated Cost Recovery System Brought about by (TRA 86) TaxReform Act of 1986

7 DEPRECIATION CONCEPTS Adjusted cost basis -- allowable adjustment (increase or decrease) to original cost basis, used to calculate depreciation and depletion deductionsAdjusted 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 serviceableBasis, or cost basis -- also called unadjusted cost -- initial cost of acquiring 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 and depletion deductionsAdjusted 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 serviceableBasis, or cost basis -- also called unadjusted cost -- initial cost of acquiring an asset, plus sales tax, transportation, and normal costs of making asset serviceable

8 DEPRECIATION CONCEPTS Book Value (BV) -- Worth of depreciable property as shown on accounting recordsBook Value (BV) -- Worth of depreciable property as shown on accounting records -- Original cost basis of property, including adjustments, less allowable depletion or depreciation deductions -- Original cost basis of property, including adjustments, less allowable depletion or depreciation deductions -- Represents amount of capital remaining invested in property and must be recovered in future through accounting -- Represents amount of capital remaining invested in property and must be recovered in future through accounting (Book Value) k = adjusted cost basis -  k j=1 (depreciation deduction) j

9 DEPRECIATION CONCEPTS Market Value (MV) -- Amount paid by willing buyer to willing seller for property where no advantage and no compulsion to transactMarket Value (MV) -- Amount paid by willing buyer to willing seller for property where no advantage and no compulsion to transact -- apporximates present value of what will be received through ownership of property, including time-value of money (or profit) -- apporximates present value of what will be received through ownership of property, including time-value of money (or profit)

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

11 DEPRECIATION CONCEPTS Salvage Value (SV) -- Estimated value of property at the end of useful life.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 -- 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 -- 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 classical methods of depreciation, estimated salvage value is established and used -- with MACRS, the salvage value of depreciable property is defined to be zero -- with MACRS, the salvage value of depreciable property is defined to be zero Salvage Value (SV) -- Estimated value of property at the end of useful life.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 -- 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 -- 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 classical methods of depreciation, estimated salvage value is established and used -- with MACRS, the salvage value of depreciable property is defined to be zero -- with MACRS, the salvage value of depreciable property is defined to be zero

12 DEPRECIATION CONCEPTS 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.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.

13 DEPRECIATION CONCEPTS 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

14 STRAIGHT-LINE (SL) METHOD Simplest depreciation methodSimplest depreciation method Assumes constant amount is depreciated each year over depreciable (useful) lifeAssumes constant amount is depreciated each year over depreciable (useful) life d k = ( B - SV N ) / N d k* = kd k for 1 < k < N BV k = B - d k* This method requires an estimate of the final SV ( also the final book value at the end of year N )This method requires an estimate of the final SV ( also the final book value at the end of year N )

15 DECLINING BALANCE (DB) METHOD Sometimes called constant percentage method or Matheson formulaSometimes called constant percentage method or Matheson formula Assumed annual cost of depreciation is fixed percentage of BV at beginning of yearAssumed annual cost of depreciation is fixed percentage of BV at beginning of year R is constant R = 2 / N when 200% declining balance used R = 1.5 / N when 150% declining balance usedR is constant R = 2 / N when 200% declining balance used R = 1.5 / N when 150% declining balance used d 1 = 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 SV N will be zero or other desired valueBecause declining balance method never reaches BV = 0, it’s permissible to switch from this to straight-line method so asset’s SV N will be zero or other desired value

16 UNITS-OF-PRODUCTION METHOD Not based on the idea that decrease in value of property is a function of timeNot based on the idea that decrease in value of property is a function of time Decrease in value is mostly a function of useDecrease 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.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 = ( B - SV N ) / ( Estimated lifetime production in units ) Depreciation per unit of production = ( B - SV N ) / ( Estimated lifetime production in units )

17 ACCELERATED COST RECOVERY SYSTEM (ACRS) RecognizesRecognizes an asset as belonging to one of four (tangible) property classes IRSIRS prescribes the specific series of depreciation per property class RatesRates are based on 150% Declining Balance depreciation, switching to Straight-Line

18 MODIFIED ACCELERATED COST RECOVERY SYSTEM (MACRS) The principal method for computing depreciation deductions for property in engineering projects.The principal method for computing depreciation deductions for property in engineering projects. Applies to most tangible depreciable property placed in service after December 31, 1986Applies to most tangible depreciable property placed in service after December 31, 1986 SV N is defined to be 0 ; useful life estimates are not used directly in calculating depreciation amountsSV N is defined to be 0 ; useful life estimates are not used directly in calculating depreciation amounts Consists of two systems for computing depreciation deductions:Consists of two systems for computing depreciation deductions: 1. The General Depreciation System (GDS) 1. The General Depreciation System (GDS) 2. The Alternative Depreciation System (ADS) Provides longer recovery period and uses only straight-line method of depreciation 2. The Alternative Depreciation System (ADS) Provides longer recovery period and uses only straight-line method of depreciation Assets depreciated under ADS include property placed in any tax-exempt use and property used predominantly outside the U.S. Assets depreciated under ADS include property placed in any tax-exempt use and property used predominantly outside the U.S.

19 INFORMATION NEEDED TO CALCULATE MACRS DEPRECIATION 1. The cost basis 2. The date the property was placed in service 3. The property class and recovery period 4. The MACRS depreciation used (GDS or ADS) 5. The time convention that applies (half year)

20 GENERAL DEPRECIATION SYSTEM (GDS) BASIC INFORMATION 1. Tangible depreciable property assigned to one of six personal property classes (3, 5, 7, 10, 15 and 20-year) - Corresponds to GDS recovery period; personal depreciable property not corresponding to these periods is considered 7-yr property class. 2. Real property assigned to two real property classes -- nonresidential real property and residential rental property. 3. GDS recovery period is 39 years for nonresidential real property (31.5 years if in service before May 13, 1993) and 27.5 years for residential rental property.

21 ALTERNATIVE DEPRECIATION SYSTEM (ADS) BASIC INFORMATION 1. ADS recovery period for tangible personal property is normally the same as the class life of the property, with some exceptions ( i.e., asset class and ) 2. Any tangible personal property that does not fit into one of the asset classes is depreciated using a 12-year ADS recovery period 3. ADS recovery period for nonresidential real property is 40 years

22 CALCULATING DEPRECIATION DEDUCTIONS UNDER MACRS Depreciation Personal Approach Method Property Class GDS 3-, 5-, 7-200% DB method 10-yearwith switch to SL when deduction greater GDS 3-, 5-, 7-200% DB method 10-yearwith switch to SL when deduction greater GDS 15- & % DB method yearwith switch to SL when deduction greater GDS 15- & % DB method yearwith switch to SL when deduction greater GDS residentialSL over fixed GDS recovery & real rental periods GDS residentialSL over fixed GDS recovery & real rental periods ADS personal &SL method over fixed ADS realrecovery periods ADS personal &SL method over fixed ADS realrecovery periods Depreciation Personal Approach Method Property Class GDS 3-, 5-, 7-200% DB method 10-yearwith switch to SL when deduction greater GDS 3-, 5-, 7-200% DB method 10-yearwith switch to SL when deduction greater GDS 15- & % DB method yearwith switch to SL when deduction greater GDS 15- & % DB method yearwith switch to SL when deduction greater GDS residentialSL over fixed GDS recovery & real rental periods GDS residentialSL over fixed GDS recovery & real rental periods ADS personal &SL method over fixed ADS realrecovery periods ADS personal &SL method over fixed ADS realrecovery periods

23 HALF-YEAR TIME CONVENTIONS FOR MACRS DEPRECIATION CALCULATIONS All assets placed in service during the year are treated as if use began in the middle of the year -- 1/2- year depreciation is allowedAll assets placed in service during the year are treated as if use began in the middle of the year -- 1/2- year depreciation is allowed If asset is disposed of before the full recovery period is used, only half of the normal depreciation deduction can be taken for that yearIf asset is disposed of before the full recovery period is used, only half of the normal depreciation deduction can be taken for that year All assets placed in service during the year are treated as if use began in the middle of the year -- 1/2- year depreciation is allowedAll assets placed in service during the year are treated as if use began in the middle of the year -- 1/2- year depreciation is allowed If asset is disposed of before the full recovery period is used, only half of the normal depreciation deduction can be taken for that yearIf asset is disposed of before the full recovery period is used, only half of the normal depreciation deduction can be taken for that year

24 MACRS (GDS) PROPERTY CLASSES AND CLASS LIFE GDS Property Class andClass Life Depreciation Method GDS Property Class andClass Life Depreciation Method 3-year, 200% DB with4 years or less switchover to SL 3-year, 200% DB with4 years or less switchover to SL 5-year, 200% DB withMore than 4 years switchover to SL to less than 10 years 5-year, 200% DB withMore than 4 years switchover to SL to less than 10 years 7-year, 200% DB with10 years to less than switchover to SL16 7-year, 200% DB with10 years to less than switchover to SL16 10-year, 200% DB with16 years to less than switchover to SL20 10-year, 200% DB with16 years to less than switchover to SL20 15-year, 150% DB with20 years to less than switchover to SL25 15-year, 150% DB with20 years to less than switchover to SL25 20-year, 150% DB with25 years or more switchover to SL 20-year, 150% DB with25 years or more switchover to SL 27.5 year, SLN / A 27.5 year, SLN / A 39-year, SLN / A 39-year, SLN / A GDS Property Class andClass Life Depreciation Method GDS Property Class andClass Life Depreciation Method 3-year, 200% DB with4 years or less switchover to SL 3-year, 200% DB with4 years or less switchover to SL 5-year, 200% DB withMore than 4 years switchover to SL to less than 10 years 5-year, 200% DB withMore than 4 years switchover to SL to less than 10 years 7-year, 200% DB with10 years to less than switchover to SL16 7-year, 200% DB with10 years to less than switchover to SL16 10-year, 200% DB with16 years to less than switchover to SL20 10-year, 200% DB with16 years to less than switchover to SL20 15-year, 150% DB with20 years to less than switchover to SL25 15-year, 150% DB with20 years to less than switchover to SL25 20-year, 150% DB with25 years or more switchover to SL 20-year, 150% DB with25 years or more switchover to SL 27.5 year, SLN / A 27.5 year, SLN / A 39-year, SLN / A 39-year, SLN / A

25 MACRS DEPRECIATION GDS OR ADS ?

26 MACRS DEPRECIATION GDS OR ADS ? Ascertain property class; Same as recovery period for personal Ascertain recovery period GDSADS

27 MACRS DEPRECIATION GDS OR ADS ? Ascertain property class; Same as recovery period for personal Ascertain recovery period GDSADS Obtain recovery rates Compute depreciation amount; Asset’s cost basis SL = Recovery period

28 MACRS DEPRECIATION GDS OR ADS ? Ascertain property class; Same as recovery period for personal Ascertain recovery period GDSADS Obtain recovery rates Compute depreciation amount; Asset’s cost basis SL = Recovery period Compute depreciation deduction in year k (d k ) by multiplying cost basis by recovery period. Compute depreciation deduction in year k (d k )

29 DEPLETIONDEPLETION Used to indicate the decrease in the value of the resource base when natural resources are being consumed in producing products or services.Used to indicate the decrease in the value of the resource base when natural resources are being consumed in producing products or services. Term most commonly used in connection with mining properties, oil and gas wells, timberlands, etc...Term most commonly used in connection with mining properties, oil and gas wells, timberlands, etc... Amounts charged as depletion cannot be used to replace sold resourcesAmounts charged as depletion cannot be used to replace sold resources Used to indicate the decrease in the value of the resource base when natural resources are being consumed in producing products or services.Used to indicate the decrease in the value of the resource base when natural resources are being consumed in producing products or services. Term most commonly used in connection with mining properties, oil and gas wells, timberlands, etc...Term most commonly used in connection with mining properties, oil and gas wells, timberlands, etc... Amounts charged as depletion cannot be used to replace sold resourcesAmounts charged as depletion cannot be used to replace sold resources

30 PAYMENTS TO RESOURCE OWNERS Annual payments to resource owners consist of two parts: Annual payments to resource owners consist of two parts: 1. Earned profit 2. Portion of owner’s capital returned, marked as depletion

31 TWO WAYS TO COMPUTE DEPLETION ALLOWANCE 1. Cost method Applies to all types of property and is more widely used method Applies to all types of property and is more widely used method Depletion unit is determined by dividing adjusted cost basis by the number of units to be mined or harvested Depletion unit is determined by dividing adjusted cost basis by the number of units to be mined or harvested Depletion allowance for tax year is the product of the number of units sold times the depletion unit Depletion allowance for tax year is the product of the number of units sold times the depletion unit

32 TWO WAYS TO COMPUTE DEPLETION ALLOWANCE 2. The Percentage Method Based on percentage of year’s gross income, provided amount charged does not exceed 50% of net income (before deduction of depletion allowance) Based on percentage of year’s gross income, provided amount charged does not exceed 50% of net income (before deduction of depletion allowance) Can be used for most types of metal mines, geothermal deposits and coal mines Can be used for most types of metal mines, geothermal deposits and coal mines Can not be used for timber and, in most cases, is not applicable to oil and gas Can not be used for timber and, in most cases, is not applicable to oil and gas When percentage method applies, depletion allowance must be calculated by cost and percentage method -- the larger of the two applies When percentage method applies, depletion allowance must be calculated by cost and percentage method -- the larger of the two applies

33 TYPES OF TAXES 1. Income taxes - assessed as a function of gross revenues minus allowable deductions - levied at federal, most state, and some municipal governments - levied at federal, most state, and some municipal governments 2. Property taxes - assessed as a function of owned property value; - independent of income or profit of firm - independent of income or profit of firm - levied at municipal, county, and / or state level - levied at municipal, county, and / or state level 3. Sales taxes - assessed on purchases of goods and services - independent of gross income or profits - independent of gross income or profits - relevent to engineering studies as added cost - relevent to engineering studies as added cost 4. Excise taxes - assessed on sale of certain nonessential goods and services - independent of business income and profit - independent of business income and profit - cost ultimately to consumer, despite original target - cost ultimately to consumer, despite original target

34 BEFORE-TAX MARR ( Before Tax MARR ) [ ( 1- effective income tax rate ) ] After Tax MARR ~ ~ -

35 BEFORE-TAX MARR ( Before Tax MARR ) [ ( 1- effective income tax rate ) ] After Tax MARR After-tax MARR Before-tax MARR ( 1 - effective tax rate ) ( 1 - effective tax rate ) ~ ~ ~ ~ -

36 BEFORE-TAX MARR ( Before Tax MARR ) [ ( 1- effective income tax rate ) ] After Tax MARR After-tax MARR Before-tax MARR ( 1 - effective tax rate ) ( 1 - effective tax rate ) If the asset is nondepreciable and there are no gains or losses on disposal, tax credits, or other types of deductions involved this approximation in the equation above is exactIf the asset is nondepreciable and there are no gains or losses on disposal, tax credits, or other types of deductions involved this approximation in the equation above is exact ~ ~ ~ ~ -

37 BEFORE-TAX MARR ( Before Tax MARR ) [ ( 1- effective income tax rate ) ] After Tax MARR After-tax MARR Before-tax MARR ( 1 - effective tax rate ) ( 1 - effective tax rate ) If the asset is nondepreciable and there are no gains or losses on disposal, tax credits, or other types of deductions involved this approximation in the equation above is exactIf the asset is nondepreciable and there are no gains or losses on disposal, tax credits, or other types of deductions involved this approximation in the equation above is exact Otherwise, some degree of error is introduced, since the factors cited affect amount and timing of income tax paymentsOtherwise, some degree of error is introduced, since the factors cited affect amount and timing of income tax payments ~ ~ ~ ~ -

38 CALCULATING TAXABLE INCOME - NET INCOME BEFORE TAXES ( NIBT ) - Calculate Gross IncomeCalculate Gross Income Gross Profits ( revenues from sales - cost of goods sold ) + income from dividends, interest, rent, royalties, and gains (losses) from sale or exchange of capital assets + income from dividends, interest, rent, royalties, and gains (losses) from sale or exchange of capital assets Deduct all ordinary and necessary operating expenses to conduct businessDeduct all ordinary and necessary operating expenses to conduct business Include interest but exclude capital investments Deduct depreciationDeduct depreciation taxable income = gross income - all expenses - depreciation

39 NET INCOME AFTER TAXES (NIAT) The income after taxes have been deducted from the taxable income or Net Income Before TaxesThe income after taxes have been deducted from the taxable income or Net Income Before Taxes Net Income After Taxes = NIBT - income taxes

40 EFFECTIVE (MARGINAL) CORPORATE INCOME TAX RATE As personal income tax rates are based on income brackets, so, too, is corporate income taxAs personal income tax rates are based on income brackets, so, too, is corporate income tax Depending on the bracket a firm’s income falls within, the marginal federal rate can vary from 15% to a maximum of 39% (for incomes between $100,000 and $335,000)Depending on the bracket a firm’s income falls within, the marginal federal rate can vary from 15% to a maximum of 39% (for incomes between $100,000 and $335,000) Incomes above $18,333,333 are taxed at a flat rate of 35%Incomes above $18,333,333 are taxed at a flat rate of 35% –TRA 86 responsible for lowering maximum rate from 46% to 35% – Also created alternative minimum tax (AMT)

41 GAIN (LOSS) ON DISPOSAL OF A DEPRECIABLE TANGIBLE ASSET [ GAIN (LOSS) ON DISPOSAL ] N = MV N - BV N If gain, referred to as depreciation recaptureIf gain, referred to as depreciation recapture Tax for gain (loss) is usually the same as ordinary income gain (loss) -- effective income tax rate, tTax for gain (loss) is usually the same as ordinary income gain (loss) -- effective income tax rate, t For capital asset sold or exchanged, gain (loss) referred to as capital gain (loss)For capital asset sold or exchanged, gain (loss) referred to as capital gain (loss) capital assets are stocks, bonds, gold, silver, other metals, and real propertycapital assets are stocks, bonds, gold, silver, other metals, and real property

42 BEFORE-TAX ECONOMIC ANALYSIS NIBT = ( R k – E k - d k ) T k = - t ( R k – E k – d k ) R k = revenues (and savings from the project: cash inflow from project during period ‘k’ E k = cash outflows during year k for deductible expenses and interest d k = sum of all noncash, or book costs during year ‘k’, such as depreciation and depletion t = effective income tax rate on ordinary income (federal, state and other); assumed to remain constant during the study period T k = income taxes paid during year ‘k’

43 ECONOMIC VALUE ADDED (EVA) An economic measure for estimating wealth creation potential of capital investments: EVA = (Net Operating Profit After Taxes ) k – Cost of Capital Used to Produce Profit) k EVA = NOPAT k – . BV k-1 Where k = index for year in question (1 < k < N )  = after-tax  MARR based on firm’s cost of capital BV k-1 = Beginning of year book value  = after-tax  MARR based on firm’s cost of capital BV k-1 = Beginning of year book value N = the study (analysis) period in years

44 ECONOMIC VALUE ADDED (EVA) NOPAT K = ( 1 –t ) ( R k – E k –d k )NOPAT K = ( 1 –t ) ( R k – E k –d k ) EVA k = ( 1 –t ) ( R k – E k –d k ) – . BV k-1EVA k = ( 1 –t ) ( R k – E k –d k ) – . BV k-1 When k > 0, ATCF k = ( 1 –t ) ( R k – E k –d k ) + d k When k = 0, ATCF 0 = BV 0 ATCF k = EVA k + . BV k + d kATCF k = EVA k + . BV k + d k d k is the sum of all noncash, or book costs during the year k, such as depreciation or depletion


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