(c) 2001 Contemporary Engineering Economics Chapter 10 Depreciation Asset Depreciation Factors Inherent to Asset Depreciation Book Depreciation Tax Depreciation Depletion Repairs or Improvements to Depreciable Assets (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Depreciation Definition: Loss of value for a fixed asset Example: You purchased a car worth $15,000 at the beginning of year 2000. End of Year Market Value Loss of 1 2 3 4 5 $15,000 10,000 8,000 6,000 5,000 4,000 $5,000 2,000 1,000 Depreciation (c) 2001 Contemporary Engineering Economics

Why Do We Need to Consider Depreciation? Business Expense: Depreciation is viewed as part of business expenses that reduce taxable income. Gross Income -Expenses: (Cost of goods sold) (Depreciation) (operating expenses) Taxable Income - Income taxes Net income (profit) (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Depreciation Concept Economic Depreciation Purchase Price – Market Value (Economic loss due to both physical deterioration and technological obsolescence) Accounting Depreciation A systematic allocation of cost basis over a period of time. (c) 2001 Contemporary Engineering Economics

Asset Depreciation Physical depreciation Economic depreciation the gradual decrease in utility in an asset with use and time Functional depreciation Depreciation Book depreciation Accounting depreciation The systematic allocation of an asset’s value in portions over its depreciable life—often used in engineering economic analysis Tax depreciation (c) 2001 Contemporary Engineering Economics

Factors to Consider in Asset Depreciation Depreciable life (how long?) Salvage value (disposal value) Cost basis (depreciation basis) Method of depreciation (how?) (c) 2001 Contemporary Engineering Economics

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. Can you depreciate land? (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Cost Basis Cost of new hole-punching machine (Invoice price) $62,500 + Freight 725 + Installation labor 2,150 + Site preparation 3,500 Cost basis to use in depreciation calculation $68,875 (c) 2001 Contemporary Engineering Economics

Cost Basis with Trade-In Allowance Old hole-punching machine (book value) $4,000 Less: Trade-in allowance 5,000 Unrecognized gains $1,000 Cost of new hole-punching machine $62,500 Less: Unrecognized gains (1,000) Freight 725 Installation labor 2,150 Site preparation 3,500 Cost of machine (cost basis) $67,875 (c) 2001 Contemporary Engineering Economics

Asset Depreciation Range (years) Assets Used Lower Limit Midpoint Life Upper Limit Office furniture, fixtures, and equipment 8 10 12 Information systems (computers) 5 6 7 Airplanes Automobiles, taxis 2.5 3 3.5 Buses 9 11 Light trucks 4 Heavy trucks (concrete ready-mixer) Railroad cars and locomotives 15 18 Tractor units Vessels, barges, tugs, and water transportation system 14.5 21.5 Industrial steam and electrical generation and or distribution systems 17.5 22 26.5 Manufacturer of electrical and nonelectrical machinery Manufacturer of electronic components, products, and systems Manufacturer of motor vehicles 9.5 Telephone distribution plant 28 35 42 (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Types of Depreciation 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 (c) 2001 Contemporary Engineering Economics

Book Depreciation Methods Purpose: Used to report net income to stockholders/investors Types of Depreciation Methods: Straight-Line Method Declining Balance Method Sum of the Years’ Digits Method Unit Production Method (c) 2001 Contemporary Engineering Economics

Straight – Line (SL) Method Principle A fixed asset as providing its service in a uniform fashion over its life Formula Annual Depreciation Dn = (I – S) / N, and constant for all n. Book Value Bn = I – n (D) where I = cost basis S = Salvage value N = depreciable life (c) 2001 Contemporary Engineering Economics

Example 10.3 – Straight-Line Method Annual Depreciation Book Value $10,000 D1 Total depreciation at end of life I = $10,000 N = 5 Years S = $2,000 D = (I - S)/N $8,000 D2 $6,000 D3 D4 B1 $4,000 n Dn Bn 1 1,600 8,400 2 1,600 6,800 3 1,600 5,200 4 1,600 3,600 5 1,600 2,000 B2 D5 B3 $2,000 B4 B5 n 0 1 2 3 4 5 (c) 2001 Contemporary Engineering Economics

Declining Balance Method Principle: A fixed asset as providing its service in a decreasing fashion Formula Annual Depreciation Book Value where 0 < a < 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. (c) 2001 Contemporary Engineering Economics

Example 10.4 – Declining Balance Method Annual Depreciation Book Value $10,000 Total depreciation at end of life D1 $8,000 $6,000 D2 B1 n 1 2 3 4 5 Dn $4,000 2,400 1,440 864 518 Bn $10,000 6,000 3,600 2,160 1,296 778 $4,000 D3 B2 D4 $2,000 B3 D5 B5 B4 n 0 1 2 3 4 5 (c) 2001 Contemporary Engineering Economics

Example 10.5 DB Switching to SL Asset: Invoice Price $9,000 Freight 500 Installation 500 Depreciation Base $10,000 Salvage Value 0 Depreciation 200% DB Depreciable life 5 years SL Dep. Rate = 1/5 a (DDB rate) = (200%) (SL rate) = 0.40 (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Case 1: S = 0 (a) Without switching (b) With switching to SL n Depreciation Book Value 1 2 3 4 5 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 1 2 3 4 5 4,000 $6,000 6,000/4 = 1,500 < 2,400 3,600 3,600/3 = 1,200 < 1,440 2,160 2,160/2 = 1,080 > 864 1,080 1,080/1 = 1,080 > 518 0 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. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Case 2: S = $2,000 End of Year Depreciation Book Value 1 0.4($10,000) = $4,000 $10,000 - $4,000 = $6,000 2 0.4(6,000) = 2,400 6,000 – 2,400 = 3,600 3 0.4(3,600) = 1,440 3,600 –1,440 = 2,160 4 0.4(2,160) = 864 > 160 2,160 – 160 = 2,000 5 2,000 – 0 = 2,000 Note: Tax law does not permit us to depreciate assets below their salvage values. (c) 2001 Contemporary Engineering Economics

Sum-of-Years’ Digits (SOYD) Method Principle Depreciation concept similar to DB but with decreasing depreciation rate. Charges a larger fraction of the cost as an expense of the early years than of the later years. Formula Annual Depreciation Book Value where SOYD=N(N+1)/2 (c) 2001 Contemporary Engineering Economics

Example 10.7 – Sum-of-years’ digits method Annual Depreciation Book Value $10,000 Total depreciation at end of life D1 I = $10,000 N = 5 years S = $2,000 SOYD = 15 $8,000 $6,000 D2 B1 D3 $4,000 n 1 2 3 4 5 Dn (5/15)(8,000)=$2,667 (4/15)(8,000)=$2,133 (3/15)(8,000)=$1,600 (2/15)(8,000)=$1,067 (1/15)(8,000)=$533 Bn $7,333 5,200 3,600 2,533 2,000 B2 D4 D5 $2,000 B3 B5 B4 n 0 1 2 3 4 5 (c) 2001 Contemporary Engineering Economics

Units-of-Production Method Principle Service units will be consumed in a non time-phased fashion Formula Annual Depreciation Dn = Service units consumed for year total service units (I - S) (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Tax Depreciation Purpose: Used to compute income taxes for the IRS Assets placed in service prior to 1981 Use book depreciation methods (SL, BD, SOYD) Assets placed in service from 1981 to 1986 Use ACRS Table Assets placed in service after 1986 Use MACRS Table (c) 2001 Contemporary Engineering Economics

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 (c) 2001 Contemporary Engineering Economics

MACRS Property Classifications Recovery Period ADR Midpoint Class Applicable Property 3-year Special tools for manufacture of plastic products, fabricated metal products, and motor vehicles. (ADR =Asset Depreciation Range) 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. 27.5-year Residential rental property 39-year Nonresidential real property including elevators and escalators (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics MACRS Table (c) 2001 Contemporary Engineering Economics

MACRS Rate Calculation Example 10.9 Asset cost = $10,000 Property class = 5-year DB method = Half-year convention, zero salvage value, 200% DB switching to SL 20% $2000 32% $3200 Full 19.20% $1920 11.52% $1152 5.76% $576 1 2 3 4 5 6 Half-year Convention (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics 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 SL 11.52% 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 DDB DDB SL SL (c) 2001 Contemporary Engineering Economics

Conventional DB Switching to SL 4,000 2,400 1,440 1,080 1,080 MACRS with half-year convention 2,000 3,200 1,920 1,152 1,152 576 (c) 2001 Contemporary Engineering Economics

MACRS for Real Property 27.5-year (Residential) 39-year (Commercial) SL Method Zero salvage value Mid-month convention Example: placed an asset (residential property) in March D1 = (9.5/12)(100%/27.5) = 2.879% (c) 2001 Contemporary Engineering Economics

Percentage Depletion vs. Cost Depletion (Example 10.12) Percentage Depletion Gross income from sale of 45,000 ounces $16,425,000 Depletion percentage Computed percentage depletion $2,463,750 Cost depletion = ($30,000,000/300,000)(45,000) = $4,500,000 Gross income from sale of 45,000 ounces $16,425,000 Less mining expenses 12,250,000 Taxable income from mine 4,175,000 Deduction limitation Maximum depletion deduction $2,088,000 Allowable deduction = $2,088,000 Select cost depletion with $4,500,000 (c) 2001 Contemporary Engineering Economics

Calculating the Allowable Depletion Deduction (c) 2001 Contemporary Engineering Economics

Percentage Depletion Allowances for Mineral Properties Deposits Percentage Oil and gas wells (only for certain domestic and gas production) 15 Sulfur and uranium, and, if from deposits in the United States, asbestos, lead, zinc, nickel, mica, and certain other ores and minerals 22 Gold, silver, copper, iron ore, and oil shale, if from deposits in the United States Coal, lignite, and sodium chloride 10 Clay and shale to be used in making sewer pipe or bricks 7.5 Clay (used for roofing tile), gravel, sand, and stone 5 Most other minerals; includes carbon dioxide produced from a well and metallic ores. 14 (c) 2001 Contemporary Engineering Economics

Repairs and Improvements Principle: Any repairs or improvements extends the life of the asset, the depreciation amount also needs to be adjusted. Book Depreciation: Change the current book value and spread the value over the extended life. Tax Depreciation: Treat the repairs or improvements as separate MACRS properties. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Summary 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. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Accounting depreciation can be broken into two categories: 1. Book depreciation—the method of depreciation used for financial reports and pricing products; 2. Tax depreciation—the method of depreciation used for calculating taxable income and income taxes; it is governed by tax legislation. The four components of information required to calculate depreciation are: 1. The cost basis of the asset, 2. The salvage value of the asset, 3. The depreciable life of the asset, and 4. The method of its depreciation. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Because it employs accelerated methods of depreciation and shorter-than-actual depreciable lives, the MACRS (Modified Accelerated Cost Recovery System) gives taxpayers a break: It allows them to take earlier and faster advantage of the tax-deferring benefits of depreciation. Many firms select straight-line depreciation for book depreciation because of its relative ease of calculation. (c) 2001 Contemporary Engineering Economics

(c) 2001 Contemporary Engineering Economics Depletion is a cost allocation method used particularly for natural resources. Cost depletion is based on the units-of-production method of depreciation. Percentage depletion is based on a prescribed percentage of the gross income of a property during a tax year. Given the frequently changing nature of depreciation and tax law, we must use whatever percentages, depreciable lives, and salvage values mandated at the time an asset is acquired. (c) 2001 Contemporary Engineering Economics

Component of Depreciation Book Depreciation Tax depreciation (MACRS) Cost basis Based on the actual cost of the asset, plus all incidental costs such as freight, site preparation, installation, etc. Same as for book depreciation Salvage value Estimated at the outset of depreciation analysis. If the final book value does not equal the estimated salvage value, we may need to make adjustments in our depreciation calculations. Salvage value is zero for all depreciable assets (c) 2001 Contemporary Engineering Economics

Component of Depreciation Book Depreciation Tax depreciation (MACRS) Depreciable life Firms may select their own estimated useful lives or follow 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, and sum-of- years’ digits) Units-of-proportion Exact depreciation percentages are mandated by tax legislation but are based largely on DDB and straight-line methods. The SOYD method is rarely used in the U.S. except for some cost analysis in engineering valuation. (c) 2001 Contemporary Engineering Economics