Lecture # 7 depreciation i
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  • 1. Lecture # 7 Cost Estimation Depreciation – part 1 16-1 Dr. A. Alim
  • 2. What is Depreciation ?  Federal tax law permits the reduction of Gross Income (GI) by a category of elements termed “deductions”.  Deductions are the costs incurred.  Costs are divided into two categories * expensed costs (E) * capitalized (depreciated) costs (D)  Expensed costs are those consumed over short periods of time. They do not lose value gradually over time. Examples are wages, utilities, materials, insurance,..etc  These expenses are written off (deducted) in the year they occur. 16-2 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 3. What is Depreciation ?  Capitalized costs are due to capital assets. They are not written off when they occur. Capital assets lose value gradually and are depreciated over an extended period of time.  In general, a business asset can be depreciated if it meets three criteria: 1) The property must be used to produce income. 2) Must have a defined service life longer then one year. 3) The asset wears out, decays, becomes obsolete, or loses value over the useful life.  Depreciation thus is how the government allows businesses to recover the lost value of their capitalized assets over a period of time. 16-3 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 4. Depreciation is a tax Deduction  While expenses are real cash flows, depreciation amounts represent “non-cash flow” streams within an accounting period.  Federal and state tax laws recognize various forms of depreciation amounts to be “tax deductible” – but are not real cash flows per se. 16-4 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 5. Important Terms  First Cost or Unadjusted Basis - B  Initial purchase price + all costs incurred in placing the asset in service  Book Value - BV  Remaining undepreciated capital investment on the accounting books  Recovery Period – n  Depreciable life of the asset in question – often set by law  Market Value - MV  Amount realized by sale on the open market at any time  Salvage Value - S  Estimated trade-in value or market value at the end of the asset’s useful life  Depreciation Rate - dt  The fraction of the first cost removed by depreciation in year t  Depreciation Charge - Dt  Amount of annual depreciation in year t  Personal Property  All property except real estate used in the pursuit of profit or gain  Real Property  Real estate and improvements, buildings and certain structuresLand is Real Property, but by law is NOT depreciable for tax purposes 16-5 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 6. Types of Depreciation  Book Depreciation Used by a firm for internal financial and managerial management.  Tax Depreciation Used by a firm for state and federal income tax reporting. Follows strict rules and regulations. 16-6 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 7. Book Depreciation  Value of the asset on the firm’s accounting records at any given point in time.  Used for internal managerial decision making.  Management is free to use any method they so choose to compute book depreciation amounts.  Examples of methods used:  Straight Line,  Declining Balance;  Sum of the years digits;  Other. 16-7 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 8. Tax Depreciation  Tax Depreciation:  Must follow current state and federal law pertaining to acceptable methods for computing depreciation for income tax purposes.  US Federal Law (2001)  MACRS Methods  By US Federal Tax Law, all assets placed in service and eligible for depreciation MUST use the current MACRS methods of calculation of depreciation amounts.  Tax Law permits states to have their own respective depreciation methods for state income tax purposes (complicating factor) MACRS – Modified Accelerated Cost Recovery System 16-8 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 9. Straight Line (SL) Depreciation  The standard on which all other depreciation models are compared t t Notation: t = year (t = 1,2,...,n) D = annual depreciation charge B = first cost or unadjusted basis S = Estimated salvage value n = recovery period d = depreciation rate tD =(B-S)d B-S = n 1 t t t BV B tD d d n     Excel Function: Dt = SLN(B,S,n) 16-9 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 10. Example: B = $ 160,000, n = 10 years. Tabulate the SL depreciation for each of the 10 years if S = $ 10,000 The Excel function is SLN(160000,10000,10) Year D Acc D BV 1 $15,000.00 $15,000.00 $145,000.00 2 $15,000.00 $30,000.00 $130,000.00 3 $15,000.00 $45,000.00 $115,000.00 4 $15,000.00 $60,000.00 $100,000.00 5 $15,000.00 $75,000.00 $85,000.00 6 $15,000.00 $90,000.00 $70,000.00 7 $15,000.00 $105,000.00 $55,000.00 8 $15,000.00 $120,000.00 $40,000.00 9 $15,000.00 $135,000.00 $25,000.00 10 $15,000.00 $150,000.00 $10,000.00 16-10 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 11. Declining Balance (DB) and Double Declining Balance (DDB) Depreciation  DB is an accelerated depreciation method;  Provides greater depreciation amounts in the early time periods over straight line.  The method is more complex that the SL method.  Requires assuming a DB rate – normally taken to equal R x SL rate.  R is between 1 and 2. Often R = 2, this is called Double declining balance (DDB)  Given the DB rate,  Dt for year t is found by multiplying the beginning of time period book value by the rate.  The maximum DB rate set by law is:  dMAX = 2(1/n) or twice the straight line rate 16-11 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 12. DDB illustration, B=1000, n=5 therefore: d=2/5=0.4 n Dt BV 0 0 1000 1 0.4 (1000) (1000) (1 – 0.4) 2 0.4 (1000) (1 – 0.4) (1000) (1 – 0.4) 2 3 0.4 (1000) (1 – 0.4) 2 (1000) (1 – 0.4) 3 4 0.4 (1000) (1 – 0.4) 3 (1000) (1 – 0.4) 4 5 0.4 (1000) (1 – 0.4) 4 (1000) (1 – 0.4) 5 16-12 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 13. DB Family of Depreciation n Dt BV 0 0 B 1 dB B(1-d) 2 dB(1-d) B(1-d) 2 3 dB(1-d) 2 B(1-d) 3 …. t dB(1-d) t-1 B(1-d) t 16-13 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 14. Declining Balance Expressions Annual depreciation determined in either of 2 ways  Using book value of previous year Dt = d × (BV)t-1  Using first cost basis B Dt = dB(1-d )t-1 Annual book value determined in either of 2 ways  Using first cost basis B (BV)t = B(1-d)t  Using sum of accumulated depreciation for years i=1 to t (BV)t = B – ΣDi …………………………………………………………………………………………………… …… 16-14 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 15. Declining Balance Expressions  Annual depreciation rate for each year t, relative to first cost B, is dt Dt = dt B = dB (1-d)t-1 dt = d(1-d)t-1  Salvage value is not used in DB method formulas  Implied salvage is book value in year n Implied S = (BV)n = B(1-d)n  If a salvage value is estimated, and estimated S > implied S, stop depreciating whenever expected S value is reached 16-15 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 16. Implied S is the BV at n. We have three cases: 1) Implied S > Estimated S. This leads to an asset not fully depreciated. 2) Implied S = Estimated S. Asset is “just” fully depreciated. 3) Implied S < Estimated S. Asset is fully depreciated, but in less than n years. In this case, Excel stops depreciating the asset at time “t” years, forcing BV to remain constant at S, with no further depreciation for the remainder of n. The concept of Implied S Estimated Salvage value 16-16 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 17. Declining Balance Expressions Excel function for DDB depreciation: Dt = DDB(B,S,n,t,R) S is estimated salvage value R is between 1 and 2. If omitted, a value of 2 is assumed, i.e. DDB 16-17 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 18. 16-18 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 Example 16.2, Page 420 Blank, 7th ed.
  • 19. Slide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 16-19 S = 2500 B = 25000 t D Acc D BV 1 $4,167 $4,167 $20,833 2 $3,472 $7,639 $17,361 3 $2,894 $10,532 $14,468 4 $2,411 $12,944 $12,056 5 $2,009 $14,953 $10,047 6 $1,674 $16,628 $8,372 7 $1,395 $18,023 $6,977 8 $1,163 $19,186 $5,814 9 $969 $20,155 $4,845 10 $808 $20,962 $4,038 11 $673 $21,635 $3,365 12 $561 $22,196 $2,804
  • 20. Modified Accelerated Cost Recovery System (MACRS)  MACRS was derived from the 1981 ACRS system and went into effect in 1986.  Defines statutory recovery (depreciation) percentages.  Percentages were derived from the DDB method with a switch to SL at the optimal time and,  Incorporates the half- year convention.  By current law – MACRS assumes all assets depreciated by this method will have a “0” salvage value at the end of the recovery life.  Dt = dtB  dt is provided in tabulated form.  BVt = BV t-1 – Dt  BVt = first cost – sum of accumulated depreciation 1 t t j j BV B D     16-20 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 21. The Half-year convention  During a tax year, assets are purchased and installed throughout the first year.  Under past laws, the first year of depreciation had to be prorated by the number of months remaining in the tax year.  Under current federal tax law the first and last years are handled using the half- year convention.  Half-year convention assumes that assets are placed in service and disposed of in midyear, regardless of when these events actually occur during the year.  Half-year convention therefore adds one year to the recovery period. 16-21 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 22. Nominal Recovery Periods  3- year property is really recovered over 4 years;  5-year property is really recovered over 6 years;  And so forth for each of the other classes.  Why is this the case?  The actual recovery of a given class life assumes a half-year convention.  That is, it is assumed by law that an asset is placed in-service at the middle of the first year.  It does not matter when it is actually placed in-service;  So, only a ½ year of recovery is permitted in the first year.  Another ½ year of recovery is added at year n+1  MACRS depreciation rate for year n+1 is therefore one half the rate for year n. 16-22 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 23. MACRS Details  Under MACRS:  The entire basis (B) is fully depreciated (recovered) over a specified number of years (recovery periods).  A “0” salvage value is a functional part of the MACRS system – by law.  In reality, there may be a positive, “0”, or negative salvage value at some point in time.  Adjustments will have to be made at that time. (Disposal analysis)  There are 8 major classes and their corresponding recovery periods:  3- years  5-years  7-years  10-years  15-years, and  20-years  27.5-years  39-years  Half-year convention applies 16-23 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 24. MACRS Recovery Periods  3- Year Property:  Special manufacturing and handling devices, tractors  5- Year Property:  Computers and peripherals,  Duplicating equipment.  Automobiles, trucks, buses,  Cargo containers,  Some manufacturing equipment.  7 –Year Property:  Office furniture,  Some manufacturing equipment,  Railroad cars, engines and tracks,  Agricultural machinery,  Petroleum equipment and natural gas equipment,  All property not in another class!  The 7-year class is the ‘default’ class! 16-24 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 25. MACRS Recovery Periods  10-Year Class:  Water transportation equipment,  Petroleum refining,  Agricultural processing equipment,  Durable goods manufacturin g equipment,  Ship building.  15-Year Class:  Land improvements,  Landscaping,  Pipelines,  Nuclear power production equipment,  Telephone distribution and switching equipment.  20-Year Class:  Municipal sewers  Farm buildings,  Telephone switching equipment,  Power production equipment,  Water utilities equipment. 16-25 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 26. MACRS Recovery Periods  27.5-Year Property: (Real Property) Residential rental property (homes and mobile homes).  39-Year Property (Real Property) Nonresidential real property attached to the land, but NOT the land itself. 16-26 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 27. MACRS Recovery Rates Year-t 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year 1 0.3333 0.2000 0.1429 0.1000 0.0500 0.0375 2 0.4445 0.3200 0.2449 0.1800 0.0950 0.0722 3 0.1481 0.1920 0.1749 0.1440 0.0855 0.0668 4 0.0741 0.1152 0.1249 0.1152 0.0770 0.0618 5 0.1152 0.0893 0.0922 0.0693 0.0571 6 0.0576 0.0892 0.0737 0.0623 0.0529 7 0.0893 0.0655 0.0590 0.0489 8 0.0446 0.0655 0.0590 0.0452 9 0.0656 0.0591 0.0446 10 0.0655 0.0590 0.0446 11 0.0328 0.0591 0.0446 12 0.0590 0.0446 13 0.0591 0.0446 14 0.0590 0.0446 15 0.0591 0.0446 16 0.0295 0.0446 17 0.0446 18 0.0446 19 0.0446 20 0.0446 21 0.0223 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000  Current MACRS recovery percentages for the property classes  Assumes a 0 salvage value over the class life  Has the ½ year convention built into the tables  There is NO Excel function for MACRS  Simplifies depreciation computations but is less flexible than classic methods 16-27 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 28. MACRS vs. DDB : Example Example from Blank, 7th ed. Example 16.4, p. 424 DDB, MACRS 16-28 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 29. 16-29 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005 Example 16.4, page 424, Blank 7th ed.
  • 30. B = $400,000 S = $20,000 0 400,000 400,000 n = 3 1 266,680 133,320 2 88,880 44,444 MACRS ( Tax depreciation): 3 29,640 20,000 4 0 20,000 Year dt Dt = 400,000 X dt Cummulative D BVt 0 $400,000 1 0.3333 $133,320 $133,320 $266,680 2 0.4445 $177,800 $311,120 $88,880 3 0.1481 $59,240 $370,360 $29,640 4 0.0741 $29,640 $400,000 0 Total 1.0000 $400,000 DDB ( Book depreciation) d = 2/3 = 0.667 Year d Dt Cummulative D BVt 0 $400,000 1 0.6667 $266,667 $266,667 $133,320 2 0.6667 $88,889 $355,556 $44,444 3 0.6667 $24,444 $380,000 $20,000 Total $380,000 Note = D3 is not 0.6667 X 44,444 =29,644, since this leads to BV less than 20,000 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 BookValue YEARS YEARS MACRS DDB 16-30 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 31. 16-31 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005
  • 32. 16-32 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering Economy, 6th Edition, 2005