# ENGM 661 Engineering Economics Depreciation & Taxes.

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ENGM 661 Engineering Economics Depreciation & Taxes

Taxable Income + Gross Income - Depreciation Allowance - Interest on Borrowed Money - Other Tax Exemptions = Taxable Income

Corporate Tax Rate

Corporate Tax Ex: Suppose K-Corp earns \$5,000,000 in revenue above manufacturing and operations cost. Suppose further that depreciation costs total \$800,000 and interest paid on short and long term debt totals \$1,500,000. Compute the tax paid.

Corporate Tax Gross Income\$ 5,000,000 Depreciation- 800,000 Interest - 1,500,000 Taxable Income\$ 2,700,000

Corporate Tax Gross Income\$ 5,000,000 Depreciation- 800,000 Interest - 1,500,000 Taxable Income\$ 2,700,000 Tax= \$ 113,900 +.35(2,700,000 - 335,000) = \$ 941,650

After Tax Cash Flow + Gross Income - Interest = Before Tax Cash Flow

After Tax Cash Flow + Gross Income - Interest = Before Tax Cash Flow - Tax = After Tax Cash Flow

After Tax Cash Flow Ex: Suppose K-Corp earns \$5,000,000 in revenue above manufacturing and operations cost. Suppose further that depreciation costs total \$800,000 and interest paid on short and long term debt totals \$1,500,000. Compute the after tax cash flow.

After Tax Cash Flow Gross Income \$ 5,000,000 Depreciation- 800,000 Interest - 1,500,000 Before Tax Cash Flow \$ 2,700,000

After Tax Cash Flow Gross Income \$ 5,000,000 Interest - 1,500,000 Before Tax Cash Flow \$3,500,000 Less Tax 941,650 After Tax Cash Flow \$ 2,558,350

Methods of Depreciation u Straight Line (SL) u Sum-of-Years Digits (SYD) u Declining Balance (DB) u Prior to 1981 u Accelerated Cost Recovery System (ACRS) u 1981-86 u Modified Accelerated Cost Recovery (MACRS) u 1986 on

Straight Line (SLD) Let P = Initial Cost n = Useful Life s = Salvage Value year n D t = Depreciation Allowance in year t B t = Unrecovered Investment (Book Value) in year t Then D t = (P - S) / n B t = P - [ (P - S) / n ] t

Ex: Straight Line Depr. Let P = \$100,000 n = 5 years s = \$ 20,000 Then D t = (P - S) / n = \$ 16,000 B 5 = P - [ (P - S) / n ] 5 = \$ 20,000

Declining Balance In declining balance, we write off a constant %, p, of remaining book value D 1 = pP,P = initial cost B 1 = P - D 1 = P - pP = P(1-p) D 2 = pB 1 = pP(1-p)

Declining Balance In declining balance, we write off a constant %, p, of remaining book value B 2 = B 1 - D 2 = P(1-p) - pB 1

Declining Balance In declining balance, we write off a constant %, p, of remaining book value B 2 = B 1 - D 2 = P(1-p) - pB 1 = P(1-p) - pP(1-p)

Declining Balance In declining balance, we write off a constant %, p, of remaining book value B 2 = B 1 - D 2 = P(1-p) - pB 1 = P(1-p) - pP(1-p) = P(1-p)[1 - p]

Declining Balance In declining balance, we write off a constant %, p, of remaining book value B 2 = B 1 - D 2 = P(1-p) - pB 1 = P(1-p) - pP(1-p) = P(1-p)[1 - p] = P(1-p) 2

Declining Balance In declining balance, we write off a constant %, p, of remaining book value B 2 = B 1 - D 2 = P(1-p) - pB 1 = P(1-p) - pP(1-p) = P(1-p) 2 D t = p [ P (1 - p) t - 1 ] B t = P (1 - p) t

Ex: Declining Balance P = \$100,000 n = 5 years S = \$20,000 p = 2/5 (200% declining balance) Then D 1 = (2/5)(100,000) = \$40,000 D 5 = ?,B 5 = ?

Ex: Declining Balance P = \$100,000 n = 5 years S = \$20,000 p = 2/5 (200% declining balance) Then D 1 = (2/5)(100,000) = \$40,000 B 1 = 100,000 - 40,000 = \$ 60,000 D 5 = ?,B 5 = ?

Ex: Declining Balance P = \$100,000 n = 5 years S = \$20,000 p = 2/5 (200% declining balance) Then D 1 = (2/5)(100,000) = \$ 40,000 B 1 = 100,000 - 40,000 = \$ 60,000 D 2 = (2/5)(60,000) = \$ 24,000 D 5 = ?,B 5 = ?

Ex: Declining Balance (cont)  D t = p [ P (1 - p) t - 1 ]  D 5 =.4(100,000)(.6) 4 = \$ 5,184 B t = P (1 - p) t B 5 = 100,000(.6) 5 = \$ 7,776

Ex: Declining Balance (cont)  D t = p [ P (1 - p) t - 1 ]  D 5 =.4(100,000)(.6) 4 = \$ 5,184 B t = P (1 - p) t B 5 = 100,000(.6) 5 = \$ 7,776 Note that Declining Balance will never depreciate book value to \$0. It will, however, depreciate past the salvage value

Time Value of Tax Savings (Tax Rate = 40%)

DDB/SL Conversion (Salvage = \$0)

Class Problem Ex: Suppose K-Corp is interested in purchasing a new conveyor system. The cost of the conveyor is \$180,000 and may be depreciated over a 5 year period. K-Corp uses 150% declining balance method with a conversion to straight line. Compute the depreciation schedule over the 5 year period.

Class Problem

Class Problem (p = 1.5/5 =.3)

Class Problem

DDB/SL Conversion ( Half-Year Convention)

Class Problem A \$180,000 piece of machinery is installed and is to be depreciated over 5 years. You may assume that the salvage value at the end of 5 years is \$ 0. The method of depreciation is to be double declining balance with conversion to straight line using the half-year convention (you may only deduct 1/2 year of depreciation in year 1). Establish a table showing the depreciation and the end of year book value for each year.

Class Problem

Solution

MACRS Tables

Modified Accelerated Cost Property Classes 3 yr. - useful life < 4 yrs. autos, tools 5 yr. - 4 yrs. < useful life < 10 yrs. office epuipment, computers, machinery 7 yr. - 10 < UL < 16 office furniture, fixtures, exploration 10 yr. - 16 < UL < 20 vessels, tugs, elevators (grain) 15 yr. - 20 < UL < 25 data communication, sewers, bridges, fencing

MACRS (Cont.) 20 yr. - UL > 25 farm buildings, electric generation 27.5 - residential rental property 31.5 - non-residential real property Depreciation class (3, 5, 7, 10 yr.) uses 200% declining balance switching to straight-line @ optimal year class (15, 20) 150% DB switch to SLD class (27.5, 31.5) use straight-line

After Tax Cash Flow Formulas BTCF = Before Tax Cash Flow = Revenues - Expenses

After Tax Cash Flow Formulas BTCF = Before Tax Cash Flow = Revenues - Expenses TI = Taxable Income = Cash Flow - Interest - Depreciation

After Tax Cash Flow Formulas BTCF = Before Tax Cash Flow = Revenues - Expenses TI = Taxable Income = Cash Flow - Interest - Depreciation Tax = TI * Tax Rate

After Tax Cash Flow Formulas BTCF = Before Tax Cash Flow = Revenues - Expenses TI = Taxable Income = Cash Flow - Interest - Depreciation Tax = TI * Tax Rate ATCF = After Tax Cash Flow = BTCF - Tax

Ex: After Tax Cash Flow

Borrowed Money

Class Problem A company plans to invest in a water purification system (5 year property) requiring \$800,000 capital. The system will last 7 years with a salvage of \$100,000. The before-tax cash flow for each of years 1 to 6 is \$200,000. Regular MACRS depreciation is used; the applicable tax rate is 34%. Construct a table showing each of the following for each of the 7 years.

Solution

Residential Rental

MACRS - ADS Election u Straight Line with either a half-year or half- month convention. u Required for property u outside U.S. u having tax-exempt status u financed by tax-exempt bonds u covered by executive order

Example Ex: A press forming machine is purchased for the manufacture of steel beams for \$300,000. The press is considered a 7 year property class (MACRS-GDS = 7). Compute the annual depreciation using the MACRS Alternative Depreciation Election.

Example Soln: MACRS - ADS has a longer life than does MACRS - GDS. In this case 14 years. D n = \$300,000/14 = \$21,428n = 2,..., 14 = \$21,428 / 2 = \$10,714n = 1, 15

Units of Production Method u Allows for equal depreciation for each unit of output where U t = units produced during the year U = total units likely to be produced during life (P-F) = depreciable amount allowed

Operating Day Method u Allows for equal depreciation for each unit of output where Q t = total hours used during the year Q = total hours available during the year (P-F) = depreciable amount allowed Q Q FPD t t )( 

Income Forecast Method u Allows for equal depreciation for each unit of output where R t = rent income earned during the year R = total likely rent to be earned during life (P-F) = depreciable amount allowed R R FPD t t )( 

Depletion Method u Allows for equal depreciation for each unit of output where V t = volume extracted during the year V = total volume available in reserve (P-F) = depreciable amount allowed V V FPD t t )( 

Example Ex: NorCo Oil has a 10 year, \$27,000,000 lease on a natural gas reservoir in western South Dakota. The reservoir is expected to produce 10 million cubic ft. of gas each year during the period of the lease. Compute the expected depletion allowance for each year.

Example Ex:

Percentage Depletion u Depletion is taken as a constant percentage of gross income Allowable Percentages Oil/Gas15% Natural Gas22% Sulphur/Uranium22% Gold, silver, …15% Coal10%

Example Ex: NorCo Oil has a 10 year, \$27,000,000 lease on a natural gas reservoir in western South Dakota. The reservoir is expected to produce 10 million cubic ft. of gas each year during the period of the lease at \$1.50 per cubic ft. Gross Income = 1.5(10,000,000) = 15,000,000 Depletion= 15,000,000 (0.22) = \$3,300,000

Capital Gains/Losses u Compute net long/short term gains or losses Short-term gains\$20,000 Short-term losses- 28,500 Net short term loss(\$ 8,500) Long term gains 85,000 Long term losses- 19,500 Net long term gain\$ 65,500

Gain Consolidation u Compute net long/short term gains or losses Net long term gain\$ 65,500 Net short term loss(\$ 8,500) Net Capital gain\$ 57,000

Gain Consolidation u Compute net long/short term gains or losses Net long term gain\$ 65,500 Net short term loss(\$ 8,500) Net Capital gain\$ 57,000 Taxed as ordinary (35%) \$ 19,950 Taxed at capital gain (28%) \$ 15,960

Example K-Corp earned \$ 750,000 as ordinary income and has \$100,000 in net capital gain. Compute the tax on the net capital gain.

Example K-Corp earned \$ 750,000 as ordinary income and has \$100,000 in net capital gain. Compute the tax on the net capital gain. Taxed at ordinary (34%)34,000 Taxed at capital (28%)28,000 Tax at capital gain rate\$28,000

Example K-Corp earned \$ 60,000 as ordinary income and has \$100,000 in net capital gain. Compute the tax on the net capital gain.

Example K-Corp earned \$ 60,000 as ordinary income and has \$100,000 in net capital gain. Compute the tax on the net capital gain. Taxed at ordinary (25%) 25,000 Taxed at capital (28%) 28,000 Tax at ordinary rate\$25,000

Example LOSS K-Corp earned \$ 300,000 as ordinary income and has \$100,000 in net capital LOSS. Compute the tax on the net capital gain.

Example LOSS K-Corp earned \$ 300,000 as ordinary income and has \$100,000 in net capital LOSS. Compute the tax on the net capital gain. 35 A Net Capital Loss may be carried back up to 3 years or carried forward up to 5 years to offset other net capital gains.

Example Suppose K-Corp had the following NI, Gains, and taxes in the 3 previous years. 1995 1996 1997 Net Income500,000700,000650,000 Capital Gain(80,000)120,000 50,000 Tax170,000238,000221,000 Gain Tax 0 33,600 14,000 Total Tax170,000271,600235,000

Example We would carry this year’s net loss back to 1996 to offset net capital gain giving 1995 1996 1997 Net Income500,000700,000650,000 Capital Gain(80,000) 20,000 50,000 Tax170,000238,000221,000 Gain Tax 0 5,600 14,000 Total Tax170,000243,600235,000

Depreciation Recapture Ex: K-Corp purchases a Loader for \$250,000 which has a 7 year property class life. After 3 years, \$140,675 has been depreciated and the book value is now \$109,325. K-Corp now sells the loader for \$150,000.

Depreciation Recapture Ex: K-Corp purchases a Loader for \$250,000 which has a 7 year property class life. After 3 years, \$140,675 has been depreciated and the book value is now \$109,325. K-Corp now sells the loader for \$150,000. Recapture = 150,000 - 109,325 = \$40,675

Depreciation Recapture Ex: K-Corp purchases a Loader for \$250,000 which has a 7 year property class life. After 3 years, \$140,675 has been depreciated and the book value is now \$109,325. K-Corp now sells the loader for \$150,000. Recapture = 150,000 - 109,325 = \$40,675 \$40,675 taxed as ordinary income

Depreciation Recapture Ex: Suppose K-Corp were able to sell this same loader for \$ 275,000. Capital Gain = 275,000 - 250,000 = \$25,000 Depr. Recapture = 250,000 - 109,325 = \$140,675

Depreciation Recapture Ex: Suppose K-Corp were able to sell this same loader for \$ 275,000. Capital Gain = 275,000 - 250,000 = \$25,000 Depr. Recapture = 250,000 - 109,325 = \$140,675 \$ 25,000 taxed at 28% \$140,675 taxed at 35%

Depreciation Recapture Non residential or commercial real property IfThen F t > PF t - P is section 1231 capital gain B t < F t < PF t - B t recaptured as ordinary income F t < B t B t - F t is section 1231 loss

Depreciation Recapture Non residential or commercial real property IfThen F t > PF t - P is section 1231 capital gain B t < F t < PF t - B t recaptured as ordinary income F t < B t B t - F t is section 1231 loss Residential or Commercial real property IfThen B t < F t F t - B t is section 1231 gain F t < B t B t - F t is section 1231 loss

Investment Tax Credit u Stimulate investment by providing reduced taxation in year in which asset is placed in service. u On-again, off-again u Repealed in 1985 with tax rate 46% 35%

Investment Tax Credit K-Corp purchases a CNC machine for \$100,000. ITC = 100,000(0.10) = 10,000 Initial Cost Basis (for depreciation) is reduced 5% P adj = 100,000(.95) = 95,000

Investment Tax Credit K-Corp purchases a CNC machine for \$100,000. ITC = 100,000(0.10) = 10,000 Initial Cost Basis (for depreciation) is reduced 5% P adj = 100,000(.95) = 95,000

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