INDR 202
ENGINEERING ECONOMICS
CHAPTER 9
DEPRECIATION & INCOME TAXES
SPRING 2015
COURSE CONTENT
Engineering Economic Decisions Time Value of Money
Money Management Inflation Present-Worth Analysis Annual-Equivalence Analysis Rate-of-Return Analysis Benefit-Cost Analysis
Depreciation & Income Taxes Project Cash-Flow Analysis Project Uncertainty
DEPRECIATION & INCOME TAXES
Depreciation
DEPRECIATION
Decline in the value of a fixed asset
End of
Year Market Value DEPRECIATIONLoss of Value
2012 $15,000
2013 $10,000 $5,000
2014 $8,000 $2,000
2015 $6,000 $2,000
2016 $5,000 $1,000
DEPRECIATION
Unlike maintenance, material & labor costs, fixed assets are capitalized, i.e., their initial costs are allocated over their depreciable lives.
Depreciation is critical to determine the effects of income taxes on project cash flows.
Net Income = Taxable Income – Income Taxes
Taxable Income = Gross Income – Expenses
DEPRECIATION
Economic Depreciation
gradual decrease in an asset’s value with use &
time
Accounting Depreciation
systematic allocation of an asset’s value in portions
over its depreciable life
ACCOUNTING DEPRECIATION
Systematic allocation of an asset’s initial cost over its depreciable life such that cost pattern roughly matches service pattern
A fraction of the asset cost is chargeable as an expense in each accounting period during which the asset provides service to the firm.
Each charge is a percentage of the whole cost which “matches” the percentage of the value utilized in the given period.
ACCOUNTING DEPRECIATION
Depreciable Property
Cost Basis
Useful Life & Salvage Value
Depreciable Life
DEPRECIABLE PROPERTY
Depreciable: buildings, machinery, equipment, vehicles, intangible properties like copyrights
NOT Depreciable: inventories, land
To qualify for depreciation deductions against income, an asset MUST:
(1) be used in business or held for the production of income,
(2) have a definite service life, which must be longer than one year,
COST BASIS
Invoice Price (Price + Sales Tax) $22,700
Freight $525
Installation Cost $1,350
Site Preparation $2,125
COST BASIS $26,700
Actual Cost
Incidental Costs
Cost basis generally includes the actual cost of an asset and all incidental expenses.
USEFUL LIFE & SALVAGE VALUE
USEFUL LIFE
necessary to determine asset’s depreciable life
asset depreciation ranges (ADRs) published by Internal Revenue Service (IRS) guidelines
SALVAGE VALUE
asset’s estimated value at the end of its life
DEPRECIATION METHODS
BOOK DEPRECIATION
For reporting purposes, e.g., when reporting net income to investors & shareholders
Used in pricing decisions
TAX DEPRECIATION
For tax purposes
BOOK DEPRECIATION METHODS
STRAIGHT-LINE (SL) METHOD
DECLINING-BALANCE (DB) METHOD
STRAIGHT-LINE METHOD
Given cost basis 𝐼, salvage value 𝑆, depreciable life 𝑁: Depreciation rate: 1/𝑁
Annual depreciation: 𝐷' = 𝐷 = )*+ ,
Book value: 𝐵' = 𝐼 − 𝑛𝐷
EXAMPLE 1: STRAIGHT-LINE METHOD
𝐼 = $10,000, 𝑁 = 5 years, 𝑆 = $2,000
𝐷
'=
𝐼 − 𝑆
𝑁
= $1,600
𝑛 𝐷' 𝐵'
0 $10,000
1 $1,600 $8,400
2 $1,600 $6,800
3 $1,600 $5,200
4 $1,600 $3,600
EXAMPLE 1: STRAIGHT-LINE METHOD
Annual Depreciation Book Value
𝐵< 𝐷<
1 2 3 4 5
DECLINING-BALANCE METHOD
Given cost basis 𝐼, salvage value 𝑆, depreciable life 𝑁, fraction 0 < 𝛼 ≤ 2/𝑁 :
Annual depreciation: 𝐷' = 𝛼𝐵'*< = 𝛼𝐼 1 − 𝛼 '*<
Book value: 𝐵' = 𝐼 1 − 𝛼 '
Double-declining-balance (200%-DB, DDB): 𝛼 = 2/𝑁
EXAMPLE 1: DECLINING-BALANCE METHOD
𝐼 = $10,000, 𝑁 = 5 years,
𝑆 = $1,681, 𝛼 =
1.5
𝑁
= 0.3
𝑛 𝐷' 𝐵'
0 $10,000
1 $3,000 $7,000
2 $2,100 $4,900
3 $1,470 $3,430
4 $1,029 $2,401
EXAMPLE 1: DECLINING-BALANCE METHOD
Annual Depreciation Book Value
𝐵< 𝐷<
1 2 3 4 5
EXAMPLE 1: DECLINING-BALANCE METHOD
𝐼 = $10,000, 𝑁 = 5 years,
𝑆 = $2,000, 𝛼 = 0.4
𝑛 𝐷' 𝐵'
0 $10,000
1 $4,000 $6,000
2 $2,400 $3,600
3 $1,440 $2,160
4 (864) $160 $2,000
5 $0 $2,000
EXAMPLE 1: DECLINING-BALANCE METHOD
Annual Depreciation Book Value
𝐵< 𝐷<
1 2 3 4 5
𝐷=
𝐷>
𝐵=
𝐵> 𝐵
? 𝐵@
Total
EXAMPLE 1: DECLINING-BALANCE METHOD
𝐼 = $10,000, 𝑁 = 5 years,
𝑆 = $0, 𝛼 = 0.4
Without Switching
𝑛 𝐷' 𝐵'
0 $10,000
1 $4,000 $6,000
2 $2,400 $3,600
3 $1,440 $2,160
4 $864 $1,296
DECLINING-BALANCE METHOD
𝐵, > 𝑆 does not take full advantage of depreciation’s tax-
deferring benefits.
Switching Rule: If DB depreciation in a year is less than or equal to SL depreciation for remaining years, switch to SL & use it for the rest of the asset’s depreciable life.
EXAMPLE 1: DECLINING-BALANCE METHOD
𝐼 = $10,000, 𝑁 = 5 years,
𝑆 = $0, 𝛼 = 0.4
With Switching to SL Depreciation
𝑛 𝐷' 𝐵'
0 $10,000
1 10000/5 < $4,000 $6,000 2 $6,000/4 < $2,400 $3,600 3 $3,600/3 < $1,440 $2,160 4 $2,160/2 > $864 $1,080
UNITS-OF-PRODUCTION METHOD
Given cost basis 𝐼, salvage value 𝑆: Annual depreciation:
𝐷' = Service units consumed in year 𝑛
Total service units 𝐼 − 𝑆
EXAMPLE 2: UNITS-OF-PRODUCTION METHOD
Cost: $55K
Service: 250K miles
Salvage value: $5K
Depreciation for truck usage of 30K miles:
30,000
NET INCOME
Net Income = Taxable Income – Income Taxes Taxable Income = Gross Income – Expenses
Expenses = Costs of Goods Sold + Depreciation + Interest Expenses + Operating Expenses
NET INCOME
TRUE COST OF DOING BUSINESS
Depreciation allowance in a year should match the portion of the asset’s total cost used up in that year.
The net income will not represent the cost of operations if the total cost is allocated in the year of purchase.
NET INCOME
GROSS INCOME (REVENUES) EXPENSES
COST OF GOODS SOLD DEPRECIATION
INTEREST EXPENSES OPERATING EXPENSES
TAXABLE INCOME
Item Amount Gross income (revenues) $50,000 Expenses
Cost of goods sold Depreciation
Operating expenses
$20,000 $4,000 $6,000
Taxable income $20,000
Taxes (40%) $8,000
Net income $12,000
YEAR 1 YEAR 2 Net cash inflow
before taxes 30,000 30,000
Depreciation 6,000 3,600
Taxable income 24,000 26,400
Income tax (40%) 9,600 10,560
Net income 14,400 15,840
Net cash inflow after taxes 20,400 (=14,400+6,000) 19,440 (=15,840+3,600) 2,400 1,440
Net income is an accounting measure of firm’s profitability based on the matching concept. Costs become expenses as they are matched against revenues. The actual timing of cash inflows & outflows are ignored.
NET INCOME VS. NET CASH FLOW
EXPENSES
COST OF GOODS SOLD DEPRECIATION
INTEREST EXPENSES OPERATING EXPENSES
0 1 2 3 4 5 6 7 8
$28,000 Capital expenditure(actual cash flow)
$4,000
$6,850 $4,900
$3,500 $2,500 $2,500 $2,500 $1,250
Allowed depreciation expenses (not actual cash flows)
0 1 2 3 4 5 6 7 8
Item Amount Gross income (revenues) $50,000 Expenses
Cost of goods sold Depreciation
Operating expenses
$20,000 $4,000 $6,000
Taxable income $20,000
Taxes (40%) $8,000
Net income $12,000
EXAMPLE 3: NET INCOME VS. NET CASH FLOW
Cash Flow $50,000
-$20,000
-$6,000
-$8,000
$20,000 $0 $50,000 $40,000 $30,000 $20,000 $10,000 Net income Depreciation Income taxes Operating expenses
Cost of goods sold
Net cash flow $16,000 Gross income $50,000 $6,000 $8,000 $4,000 $12,000
Assuming revenues are received & expenses are paid in cash:
∆: taxable income in excess of lower bound of each tax bracket TAXABLE INCOME TAX RATE TAX COMPUTATION
0 - $50,000 15% $0+0.15∆
$50,001 - $75,000 25% $7,500+0.25∆
$75,001 - $100,000 34% $13,750+0.34∆
$100,001 - $335,000 39% $22,250+0.39∆
$335,001 - $10,000,000 34% $113,900+0.34∆
$10,000,001 - $15,000,000 35% $3,400,000+0.35∆
$15,000,001 - $18,333,333 38% $5,150,000+0.38∆
$18,333,334 & Up 35% $6,416,666+0.35∆
INCOME TAXES (U.S. - INDIVIDUAL)
TAXABLE INCOME TAX RATE TAX COMPUTATION
0 - $8,925 10% $0+0.10∆
$8,926 - $36,250 15% $892.50+0.15∆
$36,251 - $87,850 25% $4,991.25+0.25∆
$87,851 - $183,250 28% $17,891.25+0.28∆
$183,251 - $398,350 33% $44,603.25+0.33∆
$398,351 - $400,000 35% $115,586.25+0.35∆
$400,001 & Up 39.6% $116,163.75+0.396∆
Taxable Income Tax RateMarginal Amount of Taxes Cumulative Taxes
First $50,000 15% $7,500 $7,500 Next $25,000 25% $6,250 $13,750 Next $25,000 34% $8,500 $22,250 Next $235,000 39% $91,650 $113,900 Next $9,665,000 34% $3,286,100 $3,400,000 Next $5,000,000 35% $1,750,000 $5,150,000 Remaining $1M 38% $380,000 $5,530,000
Taxable Income: $16M
Capital Expenditure $290,000
Allowed Depreciation $58,000
Gross Income $1,250,000
Merchandise Sold in the Year $600,000
Employee Salaries & Benefits $150,000
Other Supplies & Expenses $90,000
Lease Expense $20,000
Expense
Expense
Expense
Expense
Expense
Income
Gross income $1,250,000
Expenses
- Cost of goods sold - Lease expense
- Depreciation
$840,000 $20,000 $58,000
Taxable income $332,000
Taxable
Income Tax RateMarginal of TaxesAmount Cumulative Taxes First $50K 15% $7,500 $7,500 Next $25K 25% 6,250 13,750 Next $25K 34% 8,500 22,250
EXAMPLE 8: CORPORATE TAXES
Average tax rate: $<<=,^>[
$>>=,[[[ = 33.95%
Marginal tax rate: 39%
(tax rate applied to the last dollar earned)
Before Undertaking Project After Undertaking Project Project Effect
Gross revenue $200,000 $240,000 $40,000
Expenses $130,000 $150,000 $20,000
Taxable income $70,000 $90,000 $20,000
Income taxes $12,500 $18,850 $6,350
Average tax rate 17.86% 20.94% 31.75%
rate to be used in evaluating the project in isolation from the rest of operations
Before After Incremental Taxable income $70,000 $90,000 $20,000
Income taxes $12,500 $18,850 $6,350
Average tax rate 17.86% 20.94%
Incremental tax rate 31.75%
25% $5,000
$20,000 + 34%
$15,000
$20,000 = 31.75%
$20,000 incremental taxable income from
the project
Marginal tax rate 15% 25% 34%
Regular income from operation
$0 $20,000 $40,000 $60,000 $80,000 $100,000
$5,000
at 25% $15,000at 34%
Assets placed in service prior to 1981
Book Depreciation Methods – SL, DB, SOYD
Assets placed in service from 1981 to 1986
Accelerated Cost Recovery System (ACRS)
Assets placed in service after 1986
Modified Accelerated Cost Recovery System (MACRS)
Recovery
Period ADR Midpoint Class Applicable Property
3 years ADR ≤ 4 Special tools for manufacture of plastic products, fabricated metal products, motor vehicles
5 years 4 < ADR ≤ 10 equipment used for R&D, computerized telephone-Automobiles, light trucks, high-tech equipment, switching systems
7 years 10 < ADR ≤ 16 Manufacturing equipment, office furniture, fixtures
10 years 16 < ADR ≤ 20 Vessels, barges, tugs, railroad cars
15 years 20 < ADR ≤ 25 Waste-water plants, telephone- distribution plants, similar utility property
20 years 25 ≤ ADR Municipal sewers, electrical power plants 27.5 years Residential rental property
MACRS DEPRECIATION
Personal Property
Half-year convention Zero salvage value
Switching from DB method to SL method
Real Property
Mid-month convention Zero salvage value
An old automobile with a net book value of $5,000 is traded for a new one with $30,000 list price. The dealer gives $6,000 trade-in allowance, implying a purchase price of $24,000.
EXAMPLE 11: MACRS PERSONAL PROPERTY
Personal Property
Half-year convention Zero salvage value
Year Calculation Method MACRS
1 (0.5)(0.40)(100%) DDB 20%
2 (0.40)(100% - 20%)(1/4.5)(80%) DDB 32%
3 (0.4)(100% - 52%)(1/3.5)(48%) DDB 19.20%
4 (0.4)(100% - 71.20%)(1/2.5)(29.80%) SL 11.52%
5 (1/1.5)(17.28%) SL 11.52%
Cost Basis = Cash Paid + Book Value = $29,000
Recovery Period: 5 years
1 2 3 4 5 6
20% 32% 19.20% 11.52% 11.52% 5.76%
$5,800 $9,280 $5,568 $3,341 $3,341 $1,670
Full Full Full Full
Half-Year Convention
Conventional DDB switching to SL
1 2 3 4 5
$11,600 $6,960 $4,176 $3,132 $3,132
MACRS with half-year convention
1 2 3 4 5 6
$5,800 $9,280 $5,568 $3,341 $3,341 $1,670
MACRS REAL PROPERTY
Residential Property 27.5 years
Commercial Property 39 years
1st year depreciation rate for residential property placed in March:
𝐷< = 9.5 12
100%
EXAMPLE 12: MACRS REAL PROPERTY
Residential property bought on May 1 for $100,000 ($80,000 building cost & $20,000 land cost) & sold for $130,000 after 9.5 years, on October 1
Real Property
Mid-month convention Zero salvage value
Cost Basis = Building Cost = $80,000
Recovery Period: 27.5 years
Year 𝐷' Recovery
1 7.5
12
$80,000
27.5 = $1,818 2.273%
2 - 9 $80,000
27.5 = $2,909 3.636%
10 9.5
12
$80,000
27.5 = $2,303 2.879%
Gains & losses from selling a depreciable asset for
a price different than its book value affect income
taxes.
GAIN TAXES ON ASSET DISPOSALS
Disposal of MACRS Asset during Recovery
Personal Property
half-year convention applied in the year of disposal
Real Property
GAIN TAXES ON ASSET DISPOSALS
Book Value Calculation
•
5-‐year MACRS property with a cost basis of $100,000.
•
Dispose in year 3:
– 100000-‐100000(0.2+0.32+0.192/2)=38400
•
Dispose in year 5:
– 100000-‐100000(0.2+0.32+0.192+0.1152+0.1152/2)=11520
•
Dispose in year 6:
GAIN TAXES ON ASSET DISPOSALS
CASE 1: Salvage Value < Cost Basis
Gains = Salvage Value – Book Value
CASE 2: Salvage Value > Cost Basis
Gains = Salvage Value – Book Value
Gains = (Salvage Value – Cost Basis) + (Cost Basis – Book Value)
Depreciation Recapture
Capital Gains Ordinary Gains
Cost Basis Book Value Salvage Value
Total Gains
Capital Gains
Ordinary Gains or Depreciation
Recapture
Cost Basis = $230,000, sold at the end of 3 years Capital & ordinary gains taxed at rate 34%
EXAMPLE 13: 7-YEAR MACRS PROPERTY
1 2 3 4 5 6 7 8
14.29 24.49 17.49 12.49 8.93 8.92 8.93 4.46
Full Full Full Full Full Full
Total Allowed Depreciation:
$230,000(14.29% + 24.49% +17.49%/2) = $109,308
Book Value:
EXAMPLE 13: 7-YEAR MACRS PROPERTY
Book Value: $120,692
If sold at the end of 3 years for $150,000:
Gains = Salvage Value – Book Value
$150,000 - $120,692 = $29,308
Gain Taxes: (34%)($29,308) = $9,965
EXAMPLE 13: 7-YEAR MACRS PROPERTY
Book Value: $120,692
If sold at the end of 3 years for $100,000:
Losses = Book Value - Salvage Value
$120,692 - $100,000 = $20,692
Tax Savings: (34%)($20,692) = $7,035
The total cost of a fixed asset with service life more than a year cannot be charged to a single year;; it should be spread (capitalized) over its service life. Depreciation is the cost charged to operations of an asset during a particular year.
Engineering economics is concerned with accounting depreciation, i.e., systematic allocation of an asset’s value over its depreciable life.
Four components of depreciation are: cost basis, salvage value, depreciable life, depreciation method.
SUMMARY
Book Depreciation Tax Depreciation (MACRS)
Cost Basis actual & incidental costs of the asset same as for book depreciation
Salvage Value
estimated at the outset of depreciation analysis (adjusted if different from
final book value)
zero salvage value for all depreciable assets
Depreciable
Life estimated useful life or government guidelines 8 established categories
Depreciation
Method production methodsSL, DB, or units-of-
mandated by tax
Book depreciation is used in financial reports & pricing decisions. Tax depreciation is used in calculating income taxes as governed by tax legislation.
Many firms use straight-line method for book depreciation for its relative ease of calculation.
MACRS employs accelerated methods of depreciation & shorter-than-actual depreciable lives, so allows taxpayers to take earlier & faster advantage of tax-deferring benefits of depreciation.
Depreciation has a significant effect on a firm’s income & cash position.
Frequently changing nature of depreciation & tax laws suggests using percentages, depreciable lives, salvage values mandated at the time of purchase.
Taxable income is the difference between gross income & allowable deductions.
Some characteristics of the U.S. corporate tax system are:
§ progressive tax rates (the more you earn, the more you pay) § tax brackets (rates increase in stair-step fashion)
§ allowable exemptions & deductions
Marginal tax rate is the rate applied to the last dollar of income earned.
Average (effective) tax rate is the ratio of income tax paid to net income.
Incremental tax rate is the average rate applied to the incremental income generated by a new project.
Capital gains are currently taxed as ordinary income, the maximum rate is capped at 35%.
Capital losses are deducted from capital gains;; net remaining losses may be carried backward & forward for consideration in years other than the current tax year.
