1. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 1 Lecture slides to accompany Basics of Engineering Economy by Leland Blank and Anthony Tarquin Chapter 12 Depreciation Methods

2. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 2 Chapter 12 – Depreciation Methods PURPOSE Use a specific model to reduce the value of an asset (by depreciation) or natural resource (by depletion) TOPICS Depreciation terminology Straight line Declining balance MACRS Switching models Depletion methods Spreadsheet usage

3. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 3 Sec 12.1 - Terminology Depreciation is the reduction in value of an asset over time Depreciation represents the loss in value due to: –Use, and wear and tear on the asset –Deterioration over time –Obsolescence –Technological replacement Depreciation represents the diminishing amount of capital invested in the asset Deprecation represents an amount of money charged against future income produced by the asset

4. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 4 Sec 12.1 - Terminology In most countries, depreciation is a tax deductible expense. It reduces tax liability for a corporation Unlike other, real expenses, depreciation is not an actual cash flow amount Two types of depreciation used by corporations  Book depreciation -- Used internal to the corporation for financial and accounting purposes  Tax depreciation -- Per government regulations, used in calculating income taxes due In an economic analysis, tax depreciation is usually concentrated upon

5. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 5 Sec 12.1 - Terminology Time, years BV, $ S First cost, B – Total cost of asset including purchase, installation, fees, etc. Book Value, BV – Remaining, undepreciated investment after all depreciation to date is removed Recovery period, n – Depreciable life in years. Tax and book depreciation lives often vary Salvage, S – Estimated market value at end of recovery period

6. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 6 Sec 12.1 - Terminology Some additional terms to know Depreciation rate, d – fraction of first cost removed each year. (Rate is d t when it varies each year t) Half-year convention – assumes asset is placed into initial service or disposed of in midyear, regardless of when it actually occurs. (Used in US-approved tax depreciation method called MACRS) There are two types of depreciable property  Personal – Income- producing, tangible property of a corporation, e.g., vehicles, equipment, etc.  Real – Real estate and its improvements, such as, buildings, factories, other construction Note: Land itself is not depreciable

7. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 7 Sec 12.1 – Depreciation Methods Some methods used in the US and other countries  Straight Line (SL) Standard against which other methods are compared Book value decreases linearly over time  Declining Balance (DB) Accelerated write-off compared to SL method Defers part of tax liability to later in recovery period  Modified Accelerated Cost Recovery System (MACRS) Required tax depreciation method in US since 1986

8. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 8 Sec 12.2 – Summary of Notation B – First cost or basis for depreciation n – Recovery period in years S – Estimated salvage value at end of recovery period t – year, t = 1, 2, …, n D t – Depreciation charge for year t d t – Depreciation rate for year t (d, if same each year) BV t – Book value after t years of depreciation

9. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 9 Sec 12.2 – Straight Line D t = BV t = B - t×D t = BV t-1 - D t d t = d = 1/n Excel function to display D t : = SLN(B,S,n) (Used in Sec 12.7) Example:  First cost is $50,000 with life of 5 years and estimated salvage of $10,000  Plot SL book value B = $50,000 S = $10,000 n = 5 years B – S n

10. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 10 Sec 12.2 – Straight Line - Example Year, tDtDt BV t 0$8,000$50,000 1 8,000 42,000 2 8,000 34,000 3 8,000 26,000 4 8,000 18,000 5 8,000 10,000 SL depreciation:D t = (50,000-10,000)/5 = $8,000 SL book value: BV t = BV t-1 – D t

11. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 11 Sec 12.3 – Declining Balance (DB) DB write-off of asset value is accelerated compared to SL Larger annual depreciation amounts in the early years of recovery period Also called fixed percentage or uniform percentage method Annual depreciation D t equals book value at beginning of year BV t-1 (which is same as end of previous year) times fixed rate d D t = d × BV t-1

12. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 12 Sec 12.3 – Declining Balance Values of d are related to SL depreciation rate  2 times SL rate: d = 2/n  This is d MAX and is largest allowed by law  If n = 5, d MAX = 2/n = 0.4  40% of BV is removed each year  Known as double declining balance (DDB)  150% of SL rate: d = 1.5/n  If d is 100% of SL rate, d = 1/n, which is SL depreciation Notation reminder: d is the fixed percentage of BV removed each year d t is the depreciation rate for each year t

13. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 13 Sec 12.3 – Declining Balance Annual depreciation determined in either of 2 ways Using book value of previous year D t = d × BV t-1 Using first cost basis B D t = 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 – ΣD i

14. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 14 Sec 12.3 – Declining Balance Characteristic book value plots of SL, DB and DDB SL depreciation DB depreciation at 150% SL rate DDB depreciation

15. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 15 Sec 12.3 – Declining Balance Annual depreciation rate for each year t, relative to first cost B, is d t = 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. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 16 Sec 12.3 – Declining Balance Example P = $80,000S = $10,000n = 5 years Compare BV values for two methods: DDB and DB at 150% SL rate  DB rate is d=1.5/5 = 0.3  DDB rate is d MAX =2/5 = 0.4 cont →

17. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 17 Sec 12.3 – Declining Balance Example Neither method used the estimated S of $10,000 to calculate D t or BV t, except … For DDB, depreciation in year 5 is limited, since BV 5 would go below S = $10,000 Only a $368 write-off is allowed in year 5, which is much less than the calculated amount of D 5 = d(BV 4 ) = 0.4(10,368) = $4,147 Note: For the only US-government approved depreciation method, MACRS (covered next), the estimated S is not used since the entire first cost B is always depreciated to zero cont →

18. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 18 Sec 12.3 – Declining Balance Example

19. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 19 Sec 12.4 - MACRS  MACRS became the only allowed tax depreciation method in the US in 1986  Statutory depreciation rates d t are tabulated  Rates are derived using the DDB or DB method initially with a switch to SL at the optimal time  Recovery period n is prescribed and tabulated by asset types  MACRS incorporates the half-year convention into the rates and recovery period

20. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 20 Sec 12.4 - MACRS ‡Personal Property -- Recovery periods are set at 3, 5, 7, 10, 15 and 20 years ‡For n = 3, 5, 7, and 10 -- Depreciation rates start with DDB method, and switch to SL rates to ensure faster write-off of B ‡For n = 15 and 20 -- Depreciation rates start with 150% DB method, and switch to SL rates to ensure faster write-off of B  Half-year convention -- Built in to allow only 50% of first year depreciation; leftover amount is removed in year n+1 (This removes some of the advantage of accelerated depreciation)

21. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 21 Sec 12.4 – MACRS Rates – Personal Property

22. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 22 Sec 12.4 – MACRS Rates – Real Property oReal property includes buildings and permanent improvements (not land) oMACRS rates utilize SL method for n = 39 years with half-year convention built in oDepreciation rates in % are:

23. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 23 Sec 12.4 – MACRS - Example 1 Use MACRS to depreciate asset with B = $400,000 and n = 3 years Year, t MACRS rate, d t Depreciation, D t = rate × B Book value, BV t =BV t-1 - D t 0$400,000 10.3333$133,320 266,680 20.4445 177,800 88,880 30.1481 59,240 29,640 40.0741 29,640 0 Totals$400,000

24. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 24 Sec 12.4 – MACRS - Example 2 Compare MACRS tax depreciation with DDB book depreciation for B = $400,000 and n = 3 years cont →

25. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 25 Sec 12.4 – MACRS – Example 2 Observations about MACRS and DDB methods ►MACRS always depreciates to $0; no S considered ► MACRS depreciation in year 1 is ½ the DDB or DB amount due to implicit half-year convention ► MACRS takes one additional year for write-off due to implicit half-year convention ► DDB method depreciates to an implied S value at end of the recovery period ►Book value curves vary between the two methods DDB MACRS

26. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 26 Sec 12.4 – MACRS Recovery periods for MACRS Two methods – GDS and ADS  GDS (General Depreciation System)  Used for most assets  Tabulates MACRS-allowed years for different types of assets  Recovery ranges from 3 to 39 years; 7 years is default  ADS (Alternative Depreciation System)  Uses SL depreciation instead of MACRS rates  Recovery period is longer than for GDS  Removes early-life tax advantage of MACRS rates  Good for start-up businesses with lower annual revenues

27. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 27 Sec 12.5 – Switching Methods MACRS has imbedded switching from DDB or 150% DB to SL rates to improve the tax advantage, but half-year convention removes some of the advantage Objective of switching is to Maximize PW of total depreciation Maximizing PW D will minimize PW of taxes paid over entire recovery period

28. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 28 Sec 12.5 – Switching Methods General rules for switching between two methods Usually, DB method to the SL method works best 1.Switch to new method in year that new D t exceeds old D t 2.Can switch only one time during recovery period 3.Never depreciate below estimated S, if there is one (not a problem for MACRS, since all of B is removed) 4.Whenever no switch is made, the BV is used as the basis for next year’s depreciation calculation Note: MACRS uses these rules to determine the annual rates, with the half-year convention imposed in years 1 and n+1

29. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 29 Sec 12.5 – Switching Methods Procedure to switch from DDB to SL

30. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 30 Sec 12.5 – Switching Methods - Example B = $100,000n = 5 yearsi = 15%/year Apply DDB-to-SL switching and determine PW D t = 1: DDB d = 2/5 = 0.4 D DDB = $40,000 SL d = 1/5 = 0.2 D SL = $20,000 Select $40,000 New B = $60,000 t = 2: DDB d = 2/5 = 0.4 D DDB = $24,000 SL d = 1/4 = 0.25 D SL = $15,000 Select $24,000 New B = $36,000 cont →

31. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 31 Sec 12.5 – Switching Methods - Example PW of depreciation at i = 15% is $73,943

32. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 32 Sec 12.6 – Depletion Depreciation is applied to assets that can be replaced – computers, machines, etc. Depletion applies to natural resources not easily replaced, such as –Forests (timber) –Geothermal deposits –Mineral deposits and quarries (gold and other ores, gravel, copper, zinc, etc.) –Oil and gas wells  Two methods of depletion Percentage depletion Cost depletion

33. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 33 Sec 12.6 – Percentage Depletion  This method is a special consideration for natural resources  A constant stated percentage of the resource’s gross income (GI) may be depleted each year, provided it does not exceed 50% of the firm’s taxable income  Annually calculate the depletion using Percentage depletion = allowed % × GI  Percentage depletions rates are tabulated  Total depletion may exceed first cost of resource

34. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 34 Sec 12.6 – Percentage Depletion Annual percentage depletion allowances Example: Gold mine with GI = $8 M for years 1-5 GI = $5 M thereafter Years 1-5: Depletion is 0.15(8 M) = $1.2 M Years 6+: Depletion is 0.15(5 M) = $750,000 Note: This assumes that no annual depletion > 50% of TI

35. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 35 Sec 12.6 – Cost Depletion Annual depletion based on level of activity or usage of natural resource Initially calculate the depletion factor p t Annual depletion = p t × annual activity level Total depletion can not exceed first cost of resource If resource capacity changes (through reassessment), new p t is determined

36. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 36 Sec 12.6 – Cost Depletion - Example $700,000 purchased timber cutting rights for an estimated 350 M board-feet. Determine first 2 years depletion if 15 M and 22 M board-feet are harvested p t = 700,000/350 = $2,000/M board-feet Year 1: Depletion = 2,000(15) = $30,000 Year 2: Depletion = 2,000(22) = $44,000 After 2 years, reassessment due to pine bark beetle damage estimates remaining timber at only 250 M board- feet, find new p t New p t = (700,000-74,000)/250 = $2,504/M board-feet

37. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 37 Sec 12.7 – Spreadsheet Usage Excel functions used for depreciation calculations  Straight Line SLN(P,S,n) Same value each year  Double Declining Balance DDB(P,S,n,t,d) Different value each year t Fixed rate d is between 1 and 2 Rate entry is optional; assumed 2 for DDB, if omitted Rate of 1.5 used for 150% DB method

38. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 38 Sec 12.7 – Spreadsheet Usage Excel functions used for depreciation calculations  MACRS VDB(P,0,n,MAX(0,t-1.5),MIN(n,t-0.5),d) There is no Excel function to calculate MACRS directly Salvage value entered as zero MAX and MIN functions replace start and end periods in VDB Rate d is entered as 2 (DDB) for MACRS recovery periods of n = 3, 5, 7, and 10 Rate d is entered as 1.5 (150% DB) for MACRS recovery periods of n = 15 and 20  Switching VDB(P,S,n,start_pd,end_pd,d)  Switch from DB to SL to maximize PW of depreciation  Optional rate d is between 1 and 2; DDB assumed, if omitted  Start_pd and end_pd are always one year apart

39. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 39 Sec 12.7 – Spreadsheet Usage B = $500,000S = $5,000n = 5 years Straight Line function: =SLN(500000,5000,5)

40. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 40 Sec 12.7 – Spreadsheet Usage B = $500,000S = $5,000n = 5 years 150% DB function: =DDB(500000,5000,5,t,1.5)

41. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 41 Sec 12.7 – Spreadsheet Usage B = $500,000S = $5,000n = 5 years DDB function: =DDB(500000,5000,5,t,2)

42. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 42 Sec 12.7 – Spreadsheet Usage B = $500,000S = $5,000n = 5 years MACRS function: = VDB(500000,0,5,MAX(0,t-1.5),MIN(5,t-0.5),2)

43. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 43 Sec 12.7 – Spreadsheet Usage B = $500,000S = $5,000n = 5 years DDB-to-SL switch function: = VDB(500000,5000,5,t,t+1)

44. Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 © 2008, McGraw-Hill All rights reserved 12 - 44 Sec 12.7 – Spreadsheet Usage Table and graph of BV for depreciation methods