Lecture slides to accompany Basics of Engineering Economy

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

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

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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 3 © 2008, Mc. Graw-Hill All rights reserved

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 Ø Book depreciation -- Used internal to the corporation for financial and accounting purposes Ø Tax depreciation -- Per government regulations, used in calculating income taxes due In an economic analysis, tax depreciation is usually concentrated upon Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 4 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 1 - Terminology First cost, B – Total cost of asset including purchase, installation, fees, etc. Salvage, S – Estimated market value at end of recovery period BV, $ Book Value, BV – Remaining, undepreciated investment after all depreciation to date is removed S Time, years Recovery period, n – Depreciable life in years. Tax and book depreciation lives often vary Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 5 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 1 - Terminology Some additional terms to know There are two types of depreciable property • Depreciation rate, d – fraction of first cost removed each year. (Rate Ø Personal – Incomeproducing, tangible property of a corporation, e. g. , vehicles, equipment, etc. Ø Real – Real estate and its improvements, such as, buildings, factories, other construction is dt 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) Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 6 Note: Land itself is not depreciable © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 1 – Depreciation Methods Some methods used in the US and other countries q Straight Line (SL) ü Standard against which other methods are compared ü Book value decreases linearly over time q Declining Balance (DB) ü Accelerated write-off compared to SL method ü Defers part of tax liability to later in recovery period q Modified Accelerated Cost Recovery System (MACRS) ü Required tax depreciation method in US since 1986 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 7 © 2008, Mc. Graw-Hill All rights reserved

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 Dt – Depreciation charge for year t dt – Depreciation rate for year t (d, if same each year) BVt – Book value after t years of depreciation Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 8 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 2 – Straight Line Example: ¬ First cost is $50, 000 with life of 5 years and estimated salvage of $10, 000 ¬ Plot SL book value Dt = B – S n BVt = B - t×Dt = BVt-1 - Dt dt = d = 1/n Excel function to display Dt: = SLN(B, S, n) (Used in Sec 12. 7) Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 9 B = $50, 000 S = $10, 000 n = 5 years © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 2 – Straight Line - Example SL depreciation: Dt = (50, 000 -10, 000)/5 = $8, 000 SL book value: BVt = BVt-1 – Dt Year, t Dt BVt 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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 10 © 2008, Mc. Graw-Hill All rights reserved

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 Dt equals book value at beginning of year BVt-1 (which is same as end of previous year) times fixed rate d Dt = d × BVt-1 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 11 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 3 – Declining Balance Values of d are related to SL depreciation rate v 2 times SL rate: d = 2/n Ø This is d. MAX and is largest allowed by law Ø If n = 5, d. MAX = 2/n = 0. 4 Ø 40% of BV is removed each year Ø Known as double declining balance (DDB) v 150% of SL rate: d = 1. 5/n v 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 dt is the depreciation rate for each year t Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 12 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 3 – Declining Balance Annual depreciation determined in either of 2 ways • Using book value of previous year Dt = d × BVt-1 • Using first cost basis B Dt = d. B(1 -d )t-1 Annual book value determined in either of 2 ways v Using first cost basis B BVt = B(1 -d )t v Using sum of accumulated depreciation for years i=1 to t BVt = B – ΣDi Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 13 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 3 – Declining Balance Characteristic book value plots of SL, DB and DDB SL depreciation DB depreciation at 150% SL rate DDB depreciation Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 14 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 3 – Declining Balance ü Annual depreciation rate for each year t, relative to first cost B, is dt = d(1 -d)t-1 ü Salvage value is not used in DB method formulas q Implied salvage is book value in year n Implied S = BVn = B(1 -d)n q If a salvage value is estimated, and estimated S > implied S, stop depreciating whenever expected S value is reached Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 15 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 3 – Declining Balance Example P = $80, 000 S = $10, 000 n = 5 years Compare BV values for two methods: cont → 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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 16 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 3 – Declining Balance Example • Neither method used the estimated S of $10, 000 to calculate Dt or BVt, 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 cont → 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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 17 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 3 – Declining Balance Example Slide to accompany Blank and Tarquin Basics

Sec 12. 4 - MACRS q MACRS became the only allowed tax depreciation method in the US in 1986 q Statutory depreciation rates dt are tabulated q Rates are derived using the DDB or DB method initially with a switch to SL at the optimal time q Recovery period n is prescribed and tabulated by asset types q MACRS incorporates the half-year convention into the rates and recovery period Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 19 © 2008, Mc. Graw-Hill All rights reserved

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 writeoff of B v 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) Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 20 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 4 – MACRS Rates – Personal Property Slide to accompany Blank and

Sec 12. 4 – MACRS Rates – Real Property o Real property includes buildings and permanent improvements (not land) o MACRS rates utilize SL method for n = 39 years with half-year convention built in o Depreciation rates in % are: Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 22 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 4 – MACRS - Example 1 Use MACRS to depreciate asset with B = $400, 000 and n = 3 years Year, MACRS rate, Depreciation, Book value, t dt Dt = rate × B BVt=BVt-1 - Dt 0 $400, 000 1 0. 3333 $133, 320 266, 680 2 0. 4445 177, 800 88, 880 3 0. 1481 59, 240 29, 640 4 0. 0741 29, 640 0 Totals $400, 000 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 23 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 4 – MACRS - Example 2 cont → Compare MACRS tax depreciation with DDB book depreciation for B = $400, 000 and n = 3 years Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 24 © 2008, Mc. Graw-Hill All rights reserved

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 ►Book value curves vary between the two methods ► 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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 25 DDB MACRS © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 4 – MACRS Recovery periods for MACRS Two methods – GDS and ADS q GDS (General Depreciation System) Ø Used for most assets Ø Tabulates MACRS-allowed years for different types of assets Ø Recovery ranges from 3 to 39 years; 7 years is default q ADS (Alternative Depreciation System) Ø Uses SL depreciation instead of MACRS rates Ø Recovery period is longer than for GDS Ø Removes early-life tax advantage of MACRS rates Ø Good for start-up businesses with lower annual revenues Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 26 © 2008, Mc. Graw-Hill All rights reserved

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 PWD will minimize PW of taxes paid over entire recovery period Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 27 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 5 – Switching Methods General rules for switching between two methods Usually, DB method to the SL method works best 1. 2. 3. Switch to new method in year that new Dt exceeds old Dt Can switch only one time during recovery period 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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 28 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 5 – Switching Methods Procedure to switch from DDB to SL Slide

Sec 12. 5 – Switching Methods - Example B = $100, 000 n = 5 years i = 15%/year Apply DDB-to-SL switching and determine PWD cont → t = 1: DDB d = 2/5 = 0. 4 DDDB = $40, 000 SL d = 1/5 = 0. 2 DSL = $20, 000 Select $40, 000 New B = $60, 000 t = 2: DDB d = 2/5 = 0. 4 DDDB = $24, 000 SL d = 1/4 = 0. 25 DSL = $15, 000 Select $24, 000 New B = $36, 000 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 30 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 5 – Switching Methods - Example PW of depreciation at i =

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 q Two methods of depletion ü Percentage depletion ü Cost depletion Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 32 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 6 – Percentage Depletion Ø This method is a special consideration for natural resources Ø 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 Ø Annually calculate the depletion using Percentage depletion = allowed % × GI Ø Percentage depletions rates are tabulated Ø Total depletion may exceed first cost of resource Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 33 © 2008, Mc. Graw-Hill All rights reserved

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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 34 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 6 – Cost Depletion • • • Annual depletion based on level of activity or usage of natural resource Initially calculate the depletion factor pt Annual depletion = pt × annual activity level Total depletion can not exceed first cost of resource If resource capacity changes (through reassessment), new pt is determined Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 35 © 2008, Mc. Graw-Hill All rights reserved

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 pt = 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 boardfeet, find new pt New pt = (700, 000 -74, 000)/250 = $2, 504/M board-feet Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 36 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 7 – Spreadsheet Usage Excel functions used for depreciation calculations Straight Line Same value each year SLN(P, S, n) 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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 37 © 2008, Mc. Graw-Hill All rights reserved

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 Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 38 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 7 – Spreadsheet Usage B = $500, 000 S = $5, 000 Straight Line function: Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 39 n = 5 years =SLN(500000, 5) © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 7 – Spreadsheet Usage B = $500, 000 S = $5, 000 150% DB function: Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 n = 5 years =DDB(500000, 5, t, 1. 5) 40 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 7 – Spreadsheet Usage B = $500, 000 S = $5, 000 DDB function: Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 n = 5 years =DDB(500000, 5, t, 2) 41 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 7 – Spreadsheet Usage B = $500, 000 S = $5, 000 n = 5 years MACRS function: = VDB(500000, 0, 5, MAX(0, t-1. 5), MIN(5, t-0. 5), 2) Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 42 © 2008, Mc. Graw-Hill All rights reserved

Sec 12. 7 – Spreadsheet Usage B = $500, 000 S = $5, 000 n = 5 years DDB-to-SL switch function: = VDB(500000, 5, t, t+1) Slide to accompany Blank and Tarquin Basics of Engineering Economy, 2008 43 © 2008, Mc. Graw-Hill All rights reserved