Principles of Engineering Economic Analysis, 5th edition Chapter 9 Depreciation

Principles of Engineering Economic Analysis, 5th edition

Chapter 9Chapter 9

Depreciation


Systematic Economic Analysis Technique 1. Identify the investment alternatives 2. Define the planning horizon 3. Specify the discount rate 4. Estimate the cash flows 5. Compare the alternatives 6. Perform supplementary analyses 7. Select the preferred investment


Questions about Depreciation• What is depreciation?

Depreciation is a bookkeeping method reflecting the reduction in the value of an asset based on age, use, or output.

• Is depreciation a cash flow?Depreciation is not a cash flow.

• Why do we consider depreciation?Depreciation is of interest to us because of its impact on income taxes (which are cash flows!)


Engineers need to learn about depreciation because their design decisions can affect the way

investments and annual operating costs are treated from an income tax perspective.


Depreciation Amount

“The amount of the annual depreciation depends upon several factors, including (1) cost basis or investment in the property, (2) date placed in service, (3) property class or estimated useful life, (4) salvage value for certain methods, and (5) method of depreciation used.”

Department of TreasuryInternal Revenue Service


Business expenditures are either expensed or depreciated. Expensing an expenditure is akin to depreciating it fully in the year in which it occurs. Expenditures for labor, materials, and energy are examples of items that are fully deducted from taxable income. Expenditures for production equipment, vehicles, and buildings, on the other hand, cannot be fully deducted from taxable income in the year in which they occur; instead, they must be spread out or distributed over some allowable recovery period.


Depreciable AssetsDepreciable property (1) must be used in business or be held for the production of income, (2) must have a life longer than a year and be determinable, (3) must be something that wears out, decays, is consumed, becomes obsolete, or loses value from natural causes.

Depreciable property may be tangible or intangible; tangible property may be real or personal. Land is “never” depreciable.


Depreciation Terminologycost basis: taxpayer’s investment (purchase price plus improvements, additions, and/or installation) – also called unadjusted basisdepreciation allowance: the depreciation charge or deduction for a given year

book value: cost basis less capital recovered, such as depreciation allowances – also called unrecovered investment, adjusted cost basis, and adjusted basis


Depreciation Terminology (cont’d)recovery period: time over which the cost basis can be recovered, keyed to 3, 5, 7, 10, 15, 20, 27.5, or 31.5 years, depending on type of property involved.

salvage value: estimated market value at the end of the asset’s useful life

useful life: estimate of duration of use of the asset by the taxpayer


Straight-Line (SLN) Depreciation

Let

P = cost basis

F = salvage value

n = recovery period

dt = depreciation allowance for year t

Bt = book value at the end of year t

dt = (P – F)/n =SLN(P,F,n)

Bt = P - tdt


Example 9.2A surface mount placement machine is being purchased for $500,000; it has an estimated useful life of 10 years and a salvage value of $50,000 at that time. Determine the depreciation allowance for the 5th year and the book value at the end of the 5th year using SLN.

P = $500,000; F = $50,000; n = 10; t = 5

d5 = ($500,000 - $50,000)/10 = $45,000

=SLN(500000,50000,10) = $45,000

B5 = $500,000 – 5($45,000) = $275,000


Example 9.2A surface mount placement machine is being purchased for $500,000; it has an estimated useful life of 10 years and a salvage value of $50,000 at that time. Determine the depreciation allowance for the 5th year and the book value at the end of the 5th year using SLN.

P = $500,000; F = $50,000; n = 10; t = 5

d5 = ($500,000 - $50,000)/10 = $45,000

=SLN(500000,50000,10) = $45,000

B5 = $500,000 – 5($45,000) = $275,000

Notice: no minus signsNotice: no minus signs


Declining Balance (DB) DepreciationIn addition to the previously defined notation, let

p = declining balance percentage, rate, or fraction, e.g. 1.5/n, 2/n*

=-RATE(n,,-P,F)

dt = pP(1 – p)t-1 = (1 – p)dt-1

Bt = P(1 – p)t

DB(cost,salvage,life,period,month)

DDB(cost,salvage,life,period,month)

VDB(cost,salvage,life,start_period,end_period,

factor,no_switch)*When p = 2/n, called double declining balance (DDB)


Example 9.3A surface mount placement machine is being purchased for $500,000; it has an estimated useful life of 10 years and a salvage value of $50,000 at that time. Determine the depreciation allowance for the 5th year and the book value at the end of the 5th year using declining balance depreciation.

P = $500,000; F = $50,000; n = 10; t = 5

p =-RATE(10,,-500000,50000) = 20.5672%

d5 = 0.205672($500,000)(1.0 – 0.205672)5-1 = $40,939.70=DB(500000,50000,10,5) = $40,937.30

B5 = $500,000(1.0 – 0.205672)5 = $163,840.00


Depreciation allowances and book values for Examples 9.2 and 9.4

d5 = DDB(500000,50000,10,5) = $40,960.00

d5 = VDB(500000,50000,10,4,5,2) = $40,960.00

t SLN d t SLN B t DB d t DB B t DDB d t DDB B t VDB d t VDB B t

0 $500,000.00 $500,000.00 $500,000.00 $500,000.001 $45,000.00 $455,000.00 $103,000.00 $397,000.00 $100,000.00 $400,000.00 $100,000.00 $400,000.002 $45,000.00 $410,000.00 $81,782.00 $315,218.00 $80,000.00 $320,000.00 $80,000.00 $320,000.003 $45,000.00 $365,000.00 $64,934.91 $250,283.09 $64,000.00 $256,000.00 $64,000.00 $256,000.004 $45,000.00 $320,000.00 $51,558.32 $198,724.78 $51,200.00 $204,800.00 $51,200.00 $204,800.005 $45,000.00 $275,000.00 $40,937.30 $157,787.47 $40,960.00 $163,840.00 $40,960.00 $163,840.006 $45,000.00 $230,000.00 $32,504.22 $125,283.25 $32,768.00 $131,072.00 $32,768.00 $131,072.007 $45,000.00 $185,000.00 $25,808.35 $99,474.90 $26,214.40 $104,857.60 $26,214.40 $104,857.608 $45,000.00 $140,000.00 $20,491.83 $78,983.07 $20,971.52 $83,886.08 $20,971.52 $83,886.089 $45,000.00 $95,000.00 $16,270.51 $62,712.56 $16,777.22 $67,108.86 $16,943.04 $66,943.0410 $45,000.00 $50,000.00 $12,918.79 $49,793.77 $13,421.77 $53,687.09 $16,943.04 $50,000.00


Switching from DDB to SLN with VDB

Excel’s VDB worksheet function includes an optional feature: it can switch from using a specified declining balance rate to a straight-line rate when optimum to do so. But, what criterion is used to define optimum?

Assuming a TVOM > 0%, since depreciation charges can be deducted from taxable income, ATPW is maximized when the PW of depreciation charges is maximized. Hence, we prefer to depreciate an asset sooner, rather than later. Therefore, accelerated depreciation methods are preferred to SLN depreciation, but only up to a point, and VDB determines that point.


Double Declining Balance Switching toDouble Declining Balance Switching toStraight Line DepreciationStraight Line Depreciation

The optimum time to switch from DDB to SLN is when, for the first time, the depreciation allowance with SLN is greater than the depreciation allowance with DDB allowance, i.e., switch the first year for which

(Bt-1 – F)/(n – t + 1) > pBt-1 where p = 2/n for DDB


Example 9.4For the surface mount placement machine, when should a switch from DDB to SLN occur?

Switch at the smallest value of t for which

(Bt-1 – F)/(n – t + 1) > pBt-1


t VDB B t SLN d t DDB d tSLN dt > DDB dt?

VDB d t

0 $500,000.001 $400,000.00 $45,000.00 $100,000.00 No $100,000.002 $320,000.00 $38,888.89 $80,000.00 No $80,000.003 $256,000.00 $33,750.00 $64,000.00 No $64,000.004 $204,800.00 $29,428.57 $51,200.00 No $51,200.005 $163,840.00 $25,800.00 $40,960.00 No $40,960.006 $131,072.00 $22,768.00 $32,768.00 No $32,768.007 $104,857.60 $20,268.00 $26,214.40 No $26,214.408 $83,886.08 $18,285.87 $20,971.52 No $20,971.529 $66,943.04 $16,943.04 $16,777.22 Yes $16,943.0410 $50,000.00 $16,943.04



VDB d t


$29,428.57 = ($256,000 - $50,000)/(10 – 3)

(Bt-1 – F)/(n – t + 1) > pBt-1

Since $29,428.57 < $51,200, don’t switch!



VDB d t


$16,943.04 = ($83,886.08 - $50,000)/(10 – 8)

(Bt-1 – F)/(n – t + 1) > pBt-1

Since $16,943.04 > $16,777.22, switch!


Modified Accelerated Cost Recovery System SLN is the most commonly used depreciation

method for financial reporting MACRS is the most commonly used depreciation

method for computing income tax liability MACRS is the only depreciation method approved

for use in the U.S. for income tax purposes Two forms of MACRS

General Depreciation System (GDS) MACRS-GDS uses 200% and 150% DB switching to SLN depreciation

Alternative Depreciation System (ADS) MACRS-ADS uses SLN depreciation

(Unless stated otherwise, when we refer to MACRS, we are referring to MACRS-GDS)


Modified Accelerated Cost Recovery System GDS is based on DDB switching to SLN ADS is based on SLN Both have pre-established recovery periods for

most property Both include a half-year convention, whereby it is

assumed that a property is bought and sold at mid-year


MACRSGDS Property Classes 3-year property: class life of 4 years or less, e.g.,

over-the-road-tractors, special tools for manufacture of automobiles, etc.

5-year property: class life between 4 and 10 yrs, e.g., automobiles, computers & peripherals, office equipment, and general – purpose trucks

7-year property: class life between 10 and 16 yrs, property without class life, and not included in 27.5 – and 39-year classes, e.g., office furniture and wide range of production equipment


MACRSGDS Property Classes 3-year property: class life of 4 years or less, e.g.,

over-the-road-tractors, special tools for manufacture of automobiles, etc.

5-year property: class life between 4 and 10 yrs, e.g., automobiles, computers & peripherals, office equipment, and general – purpose trucks

7-year property: class life between 10 and 16 yrs, property without class life, and not included in 27.5 – and 39-year classes, e.g., office furniture and wide range of production equipment

SMP machines: 5-year property

Theme park and amusement park equipment: 7-year property


GDS Property Classes 10-year property: class life of 16 or more and less

than 20 years, e.g., vessels, tugs 15-year property: class life of 20 or more and less

than 25 years, e.g., sidewalks, roads 20-year property: class life of 25 or more yrs other

than real property with a class life of 27.5 years or more, plus municipal sewers, e.g. farm buildings

27.5-year residential rental property 39-year nonresidential real property: class life of

27.5 or more years and not residential rental property

MACRS


MACRSIn general, a half-year depreciation charge is allowed by the IRS, regardless of when an asset is placed in service or disposed of during the year. The exceptions are a) 27.5-Year and 39-Year property and b) when a mid-quarter convention applies. The latter applies to all property, other than nonresidential real property and residential rental property, if more than 40% of the cumulative depreciation charges for property placed in service and disposed of during a year occur during the last three months of a tax year. In the examples and end-of-chapter problems, we assume exception b) does not occur. To be consistent with end-of-year cash flow assumptions in previous chapters and assumptions made by authors of other engineering economics texts, we assume investments occur at the end of year zero and the first, half-year, depreciation charge occurs at the end of year one. We do so, realizing that in practice, the half-year depreciation charges and investments generally occur in the same tax year.


Computing MACRS Allowance For 3-, 5-, 7-, and 10-year classes. MACRS

allowances are determined by using double declining balance and switching to straight line depreciation at the optimum time with a half-year convention (200% DBSLH)

For 15- and 20-year classes, 150% DB with switching to SLN depreciation at the optimum time with a half-year convention is used (150% DBSLH)

For 27.5- and 39-year class, SL with a mid-month convention (SLM) is used


EOY3-Year Property

5-Year Property

7-Year Property

10-Year Property

15-Year Property

20-Year Property

1 33.33 20.00 14.29 10.00 5.00 3.750

2 44.45 32.00 24.49 18.00 9.50 7.219

3 14.81 19.20 17.49 14.40 8.55 6.677

4 7.41 11.52 12.49 11.52 7.70 6.177

5 11.52 8.93 9.22 6.93 5.713

6 5.76 8.92 7.37 6.23 5.285

7 8.93 6.55 5.90 4.888

8 4.46 6.55 5.90 4.522

9 6.56 5.91 4.462

10 6.55 5.90 4.461

11 3.28 5.91 4.462

12 5.90 4.461

13 5.91 4.462

14 5.90 4.461

15 5.91 4.462

16 2.95 4.461

17 4.462

18 4.461

19 4.462

20 4.461

21 2.231

MACRS-GDS percentages for 3-, 5-, 7-, and 10-year property are 200% DBSLH and 15- and 20-year property are 150% DBSLH


Year 1 2 3 4 5 6 7 8 9 10 11 121 3.485% 3.182% 2.879% 2.576% 2.273% 1.970% 1.667% 1.364% 1.061% 0.758% 0.455% 0.152%

2-9 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636%10-26* 3.637% 3.637% 3.637% 3.637% 3.637% 3.637% 3.637% 3.637% 3.637% 3.637% 3.637% 3.637%11-27** 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636%

28 1.970% 2.273% 2.258% 2.879% 3.182% 3.485% 3.636% 3.636% 3.636% 3.636% 3.636% 3.636%29 0.152% 0.455% 0.758% 1.061% 1.364% 1.667%

Year 1 2 3 4 5 6 7 8 9 10 11 121 2.461% 2.247% 2.033% 1.819% 1.605% 1.391% 1.177% 0.963% 0.749% 0.535% 0.321% 0.107%

2-39 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 2.564%40 0.107% 0.321% 0.535% 0.749% 0.963% 1.177% 1.391% 1.605% 1.819% 2.033% 2.247% 2.461%

* even-numbered year** odd-numbered year

Month in Tax Year Property Placed in Service

Month in Tax Year Property Placed in Service

MACRS-GDS percentages for 27.5-year residential rental property using mid-month convention

MACRS-GDS percentages for 39-year nonresidential real property using mid-month convention


Computing MACRS Allowance Tables 9.4 and 9.5 can be used to calculate

the MACRS depreciation allowance Given the allowance, pt,

dt = ptP

Bt = P(1 - p1 - p2 - … - pt-1 - pt)

The Excel® VDB worksheet function can be used to calculate the MACRS depreciation rates

Example 9.6 illustrates the use of the Excel® VDB worksheet function


5-Year Property: Recall, VDB(cost,salvage,life,start_period,end_period,factor,no_switch) Let cost = 1, salvage = 0, life = 5, and factor = 2. For start_period = 0 and end_period = 0.5, =VDB(1,0,5,0,0.5,2) = 20%, which isthe beginning half-year rate. For start_period = 0.5, end_period = 1.5, =VDB(1,0,5,0.5,1.5,2) = 32%. For start_period = 1.5, end_period = 2.5, =VDB(1,0,5,1.5,2.5,2) = 19.2%. For start_period = 2.5, end_period = 3.5, =VDB(1,0,5,2.5,3.5,2) = 11.52%. For start_period = 3.5, end_period = 4.5, =VDB(1,0,5,3.5,4.5,2) = 11.52%. For start_period = 4.5, end_period = 5, =VDB(1,0,5,4.5,5,2) = 5.76%, which is thefinal half-year rate.

From the text


Example 9.7The IRS classifies surface mount placement machines as 5-year equipment. What are the depreciation charges and book values for a $500,000 SMP machine?

d1 = 0.20($500,000) = $100,000d2 = 0.32($500,000) = $160,000d3 = 0.192($500,000) = $96,000d4 = 0.1152($500,000) = $57,600d5 = 0.1152($500,000) = $57,600d6 = 0.0576($500,000) = $28,800

B1 = $500,000 - $100,000 = $400,000B2 = $400,000 - $160,000 = $240,000B3 = $240,000 - $96,000 = $144,000B4 = $144,000 - $57,600 = $86,400B5 = $86,400 - $57,600 = $28,800B6 = $28,800 - $28,800 = $0


Example 9.8Compare SLN, DDB, and MACRS for the SMP machine, assuming a negligible salvage value. Consider SLH, 200%DBH, MACRS, SLN, DDB, and DDB/SLN. Compute the present worth of the depreciation allowances, based on a 10% MARR. Which depreciation method maximizes the PW?


Depreciation Allowances for Example 9.8.

SLH 200%DBH MACRS SLN DDB DDB/SLNEOY d d d d d d

01 $50,000.00 $100,000.00 $100,000.00 $100,000.00 $200,000.00 $200,000.002 $100,000.00 $160,000.00 $160,000.00 $100,000.00 $120,000.00 $120,000.003 $100,000.00 $96,000.00 $96,000.00 $100,000.00 $72,000.00 $72,000.004 $100,000.00 $57,600.00 $57,600.00 $100,000.00 $43,200.00 $54,000.005 $100,000.00 $34,560.00 $57,600.00 $100,000.00 $25,920.00 $54,000.006 $50,000.00 $12,960.00 $28,800.00 $0.00 $0.00 $0.00

PW = $361,847.83 $363,382.91 $386,630.21 $379,078.68 $380,686.86 $405,498.88EOY B B B B B B

0 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.001 $450,000.00 $400,000.00 $400,000.00 $400,000.00 $300,000.00 $300,000.002 $350,000.00 $240,000.00 $240,000.00 $300,000.00 $180,000.00 $180,000.003 $250,000.00 $144,000.00 $144,000.00 $200,000.00 $108,000.00 $108,000.004 $150,000.00 $86,400.00 $86,400.00 $100,000.00 $64,800.00 $54,000.005 $50,000.00 $51,840.00 $28,800.00 $0.00 $38,880.00 $0.006 $0.00 $38,880.00 $0.00 $0.00 $38,880.00 $0.00


$0

$100,000

$200,000

$300,000

$400,000

$500,000

0 1 2 3 4 5 6

End of Year

Bo

ok

Val

ue

SLH 200%DBH MACRSSLN DDB DDB/SLN


Sum of Years’ Digits (SYD) DepreciationLet

P = cost basis

F = salvage value

n = recovery period

dt = depreciation allowance for year t

Bt = book value at the end of year t

dt = 2(n – t + 1)(P – F)/[n(n + 1)]

=SYD(cost,salvage,life,per)

Bt = F + (P – F)(n – t)(n – t + 1)/[n(n + 1)]


Example 9.A.1Calculate the SYD depreciation allowances and book values for the $500,000 surface mount placement machine, including a useful life of 10 years and a salvage value of $50,000.

d t B t

0 $500,000.001 $81,818.18 $418,181.822 $73,636.36 $344,545.453 $65,454.55 $279,090.914 $57,272.73 $221,818.185 $49,090.91 $172,727.276 $40,909.09 $131,818.187 $32,727.27 $99,090.918 $24,545.45 $74,545.459 $16,363.64 $58,181.82

10 $8,181.82 $50,000.00

SYDt


Pit Stop #9—Avoid the Pot Holes

1. True or False: Straight-line depreciation is the most popular depreciation method used in financial reporting.

2. True or False: The Modified Accelerated Cost Recovery System is the most popular depreciation method used in computing corporate income tax liabilities.

3. True or False: Based on maximizing the present worth of depreciation allowances, MACRS is preferred to SLN for recovery periods greater than 5 years.

4. True or False: Accelerated depreciation plans were adopted after World War II to stimulate capital investment.

5. True or False: Engineers seldom have an opportunity to influence the recovery period for expenditures.

6. True or False: MACRS is equivalent to DDB, switching to SLN, with a mid-year convention.

7. True or False: The most popular variation of MACRS is MACRS-ADS.8. True or False: Sum-of-Years’-Digits depreciation is a popular depreciation

method and is most often used to compute income tax liabilities.9. True or False: When given a choice of depreciation methods to use, choose

the one that maximizes the present worth of book value.10. True or False: Sinking fund depreciation is the only depreciation method

described in the book that is based on the time value of money.


Pit Stop #9—Avoid the Pot Holes

1. True or False: Straight-line depreciation is the most popular depreciation method used in financial reporting. True

2. True or False: The Modified Accelerated Cost Recovery System is the most popular depreciation method used in computing corporate income tax liabilities. True

3. True or False: Based on maximizing the present worth of depreciation allowances, MACRS is preferred to SLN for recovery periods greater than 5 years. True

4. True or False: Accelerated depreciation plans were adopted after World War II to stimulate capital investment. True

5. True or False: Engineers seldom have an opportunity to influence the recovery period for expenditures. False

6. True or False: MACRS is equivalent to DDB, switching to SLN, with a mid-year convention. True

7. True or False: The most popular variation of MACRS is MACRS-ADS. False8. True or False: Sum-of-Years’-Digits depreciation is a popular depreciation

method and is most often used to compute income tax liabilities. False9. True or False: When given a choice of depreciation methods to use, choose

the one that maximizes the present worth of book value. False10. True or False: Sinking fund depreciation is the only depreciation method

described in the book that is based on the time value of money. True

Documents

Principles of Engineering Economic Analysis, 5th edition Chapter 9 Depreciation