1. Depreciation Lecture No.20 Chapter 8 Fundamentals of Engineering Economics Copyright © 2008

2. Definition: Loss of value for a fixed asset between two periods Example: Market values of a vehicle over 5 years Depreciation End of Year Market Value Loss of Value 2004 2005 2006 2007 2008 2009 $20,000 14,000 10,000 7,000 5,000 4,000 $6,000 4,000 3,000 2,000 1,000 What is Depreciation?

3. Depreciation Concept  Economic Depreciation Purchase Price – Market Value (Economic losses due to both physical deterioration and technological obsolescence)  Accounting Depreciation A systematic allocation of the cost basis over a period of time.

4. Factors to Consider in Asset Depreciation  Depreciable life (how long?)  Salvage value (disposal value)  Cost basis (depreciation basis)  Method of depreciation (how?)

5. What Can Be Depreciated? Assets used in business or held for production of income Assets having a definite useful life and a life longer than one year Assets that must wear out, become obsolete or lose value A qualifying asset for depreciation must satisfy all of the three conditions above. Note: You never depreciate “land.”

6. Cost of a new hole-punching machine (Invoice price) $62,500 + Freight725 + Installation labor2,150 + Site preparation3,500 Cost basis to use in depreciation calculation $68,875 Cost Basis Cost basis – the total cost that is claimed as an expense over an asset's life, which includes the actual cost of the asset and all incidental expenses such as freight, insurance, and site preparation.

7. Old hole-punching machine (book value)$4,000 Less: Trade-in allowance5,000 Unrecognized gains$1,000 Cost of a new hole-punching machine$62,500 Less: Unrecognized gains(1,000) Freight725 Installation labor2,150 Site preparation3,500 Cost of machine (cost basis)$67,875 Cost Basis with Trade-In Allowance

8. Asset Depreciation Ranges (ADRs)

9. Book Depreciation  In reporting net income to investors/stockholders  In pricing decision Tax Depreciation  In calculating income taxes for the IRS  In engineering economics, we use depreciation in the context of tax depreciation Types of Depreciation

10. Types of Accounting Depreciation and Their Primary Purposes

11. Book Depreciation Methods Purpose: Used to report net income to stockholders/investors Types of Book Depreciation Methods:  Straight-Line Method  Declining Balance Method  Unit Production Method

12. Straight – Line (SL) Method  Principle A fixed asset as providing its service in a uniform fashion over its life  Formula Annual Depreciation D n = (I – S) / N, and constant for all n. Book Value B n = I – n (D) where I = cost basis S = Salvage value N = depreciable life

13. Example 8.2 – Straight-Line Method D1 D2 D3 D4 D5 B1 B2 B3 B4 B5 $10,000 $8,000 $6,000 $4,000 $2,000 0 1 2 3 4 5 Total depreciation at end of life nD n B n 11,6008,400 21,6006,800 31,6005,200 41,6003,600 51,6002,000 I = $10,000 N = 5 Years S = $2,000 D = (I - S)/N Annual Depreciation Book Value n

14. Declining Balance Method Principle: A fixed asset as providing its service in a decreasing fashion Formula Annual Depreciation Book Value where 0 <  < 2(1/N) Note: if  is chosen to be the upper bound,  = 2(1/N), we call it a 200% DB or double declining balance method.

15. Example 8.3 – Declining Balance Method D1 D2 D3 D4 D5 B1 B2 B3 B4 B5 $10,000 $8,000 $6,000 $4,000 $2,000 0 1 2 3 4 5 Total depreciation at end of life $778 Annual Depreciation Book Value n012345n012345 D n $4,000 2,400 1,440 864 518 B n $10,000 6,000 3,600 2,160 1,296 778 n

16. SL Dep. Rate = 1/5  (DDB rate) = (200%) (SL rate) = 0.40  Asset: Invoice Price $9,000 Freight 500 Installation 500  Depreciation Base$10,000  Salvage Value 0  Depreciation200% DB  Depreciable life5 years Example 8.4 DB Switching to SL

17. nDepreciation Book Value 1234512345 10,000(0.4) = 4,000 6,000(0.4) = 2,400 3,600(0.4) = 1,440 2,160(0.4) = 864 1,296(0.4) = 518 $6,000 3,600 2,160 1,296 778 n Book Depreciation Value 1234512345 4,000 $6,000 6,000/4 = 1,500 < 2,4003,600 3,600/3 = 1,200 < 1,4402,160 2,160/2 = 1,080 > 8641,080 1,080/1 = 1,080 > 518 0 (a) Without switching(b) With switching to SL Note: Without switching, we have not depreciated the entire cost of the asset and thus have not taken full advantage of depreciation’s tax deferring benefits. Case 1: S = 0

18. End of Year DepreciationBook Value 10.4($10,000) = $4,000$10,000 - $4,000 = $6,000 20.4(6,000) = 2,4006,000 – 2,400 = 3,600 30.4(3,600) = 1,4403,600 –1,440 = 2,160 40.4(2,160) = 864 > 1602,60 – 160 = 2,000 502,000 – 0 = 2,000 Note: Tax law does not permit us to depreciate assets below their salvage value. Case 2: S = $2,000

19. Units-of-Production Method  Principle Service units will be consumed in a non time-phased fashion  Formula Annual Depreciation D n = Service units consumed for year total service units (I - S)

20. Example 8.5 Units-of-Production Depreciation  Given: I = $55,000, S = $5,000, Total service units = 250,000 miles, usage for this year = 30,000 miles  Solution:

21. Tax Depreciation  Purpose: Used to compute income taxes for the IRS  Assets placed in service prior to 1981 Use book depreciation methods (SL, DB, SOYD)  Assets placed in service from 1981 to 1986 Use ACRS (Accelerated Cost Recovery System) Table  Assets placed in service after 1986 Use MACRS (Modified ACRS) Table

22. Modified Accelerated Cost Recovery Systems (MACRS)  Personal Property Depreciation method based on DB method switching to SL Half-year convention Zero salvage value  Real Property SL Method Mid-month convention Zero salvage value

23. Recover y Period ADR Midpoint ClassApplicable Property Personal Property 3-year Special tools for manufacture of plastic products, fabricated metal products, and motor vehicles. 5-year Automobiles, light trucks, high-tech equipment, equipment used for R&D, computerized telephone switching systems 7-year Manufacturing equipment, office furniture, fixtures 10-year Vessels, barges, tugs, railroad cars 15-year Waste-water plants, telephone- distribution plants, or similar utility property. 20-year Municipal sewers, electrical power plant. Real Property 27.5- year Residential rental property 39-year Nonresidential real property including elevators and escalators ADR: Asset Depreciation Range MACRS Property Classifications

24. MACRS Depreciation Schedules for Personal Property with Half-Year Convention

25. Example 8.6 MACRS Depreciation: Personal Property

26. Year (n) 1 2 3 4 5 6 Calculation in % (0.5)(0.40)(100%)20% (0.4)(100%-20%) 32% SL = (1/4.5)(80%)17.78% (0.4)(100%-52%) 19.20% SL = (1/3.5)(48%)13.71% (0.4)(100%-71.20%)Switch to SL11.52% SL = (1/2.5)(29.80%)11.52% SL = (1/1.5)(17.28%)11.52% SL = (0.5)(11.52%)5.76% MACRS (%) DDB SL MACRS Percentage Calculation: 5-Year Property

27. MACRS for Real Property 27.5-year (Residential) 39-year (Commercial) SL Method Zero salvage value Mid-month convention Example: Placed a residential property in service in March. Find the depreciation allowance in year 1. D 1 = (9.5/12)(100%/27.5) = 2.879%  Types of Real Property  Underlying assumptions 9.5 months JanDec

28. Depreciation Allowances for a 10-year Ownership of the Property Year (n)CalculationAllowed Depreciation (%) 1(9.5/12)(100%/27.5)2.8788% 2100%/27.53.6364% 3100%/27.53.6364% 4100%/27.53.6364% 5100%/27.53.6364% 6100%/27.53.6364% 7100%/27.53.6364% 8100%/27.53.6364% 9100%/27.53.6364% 10(11.5/12)(100%/27.5)3.4848% Assume that the property will be sold in December of the10th year.

29.  The entire cost of replacing a machine cannot be properly charged to any one year’s production; rather, the cost should be spread (or capitalized) over the years in which the machine is in service.  The cost charged to operations during a particular year is called depreciation.  From an engineering economics point of view, our primary concern is with accounting depreciation; The systematic allocation of an asset’s value over its depreciable life. Summary

30. Component of Depreciation Book DepreciationTax depreciation (MACRS) Cost basisBased on the actual cost of the asset, plus all incidental costs such as freight, site preparation, installation, etc. Same as for book depreciation Salvage valueEstimated at the outset of depreciation analysis. Make sure that the book value cannot be lower than the salvage value at any time. Salvage value is zero for all depreciable assets

31. Component of Depreciation Book DepreciationTax depreciation (MACRS) Depreciable life Firms may select their own estimated useful lives or follow the government guidelines for asset depreciation ranges (ADRs) Eight recovery periods– 3,5,7,10,15,20,27.5,or 39 years– have been established; all depreciable assets fall into one of these eight categories. Method of depreciation Firms may select from the following: Straight-line Accelerated methods (declining balance, double declining balance) Units-of-proportion Exact depreciation percentages are mandated by tax legislation but are based largely on DDB and straight-line methods.