Engineering Economic Analysis
Chapter 12  Income Taxes
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Taxes
The Congress shall have power to lay and collect taxes on
incomes, from whatever source derived, without apportionment
among the several States, and without regard to any census or
enumeration.
-Amendment XVI, U.S. Constitution
It takes only a majority to institute the Fair Tax but a 2/3 vote to
repeal an amendment.
Thus it is possible to have the Fair Tax enacted with continued
taxation under the current IRS.
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Personal Income
Personal Exemptions $3400
Itemized deductions
Excessive medical and dental exceeding 1.5% of AGI
State and local tax
Home mortgage interest
Charitable donations
Casualty and theft losses (> $100 + 10% AGI)
Miscellaneous deductions (> 2% of AGI)
Car and other business expenses
Tax benefits for work-related education
Standard Deduction
Single taxpayer $5350
Married filing jointly ($10,700)
Taxable income = AGI – PE – Itemized-deduct or Standard Deduction
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Taxes
Income
Property
Sales
Excise
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Classification of Business Expenditures
Capital Expenditures
Depreciable assets
Non-depreciable assets
Expensed
All other business expenditures
Taxable income = GI – Expensed - Depreciation
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Corporate Taxes
Item
Gross income ~ total income from all revenue producing sources
Expenses ~ all corporate costs incurred in the business
Cost of goods sold
Depreciation
Operating expenses
Taxable operating income ~ amount on which taxes are assessed
Income taxes ~ amount of taxes based on some form of income
Net income
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Corporate Tax Rate
Taxable Income
Tax Rate
Corporate Income tax
Not over $50K
15%
15% over $0
7500
$50K-75K
25%
$7.5K+25% over $50K
6250
$75K-100K
34%
$13.75K+34% over $75K
8500
$100K-335K
39%
$22.25K+39% over $100K
91650
$335K-10M
34%
$113.9K+34% over $335K
3.2861M
$10M-15M
35%
$3.4M+35% over $10M
1.75M
$15M-18.3M
38%
5.150M+38% over $15M
1.254M
$18.3M and up
35%
6.416666 + 0.35% over 18.3M
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Taxable Income
Year 1
$200
-60
Year 2
$200
0
Year 3
$200
0
Gross Income
Special Tooling
(3-year life)
Expenditures
-140
-140
-140
Cash results
$0
$60
$60
Use st line depreciation with 0 salvage to get 60/3 = $20
Taxable Income
$40
$40
$40
Computed as (200 – 20 – 140) = $40 to show that taxable
income is a better indicator of performance
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Computing Corporate Tax
A corporation buys a $75K machine that for the first year brings
in $200K of revenue with $84K operating expenses and $4K of
depreciation. Compute taxes paid at 30% rate and net income.
How much was generated from operations?
Taxable income = GI – Expensed – Depreciation
= 200K – 84K – 4K
= 112K
Taxes = 112K * 0.30 = $33.6K taxes paid =>
Net Income = Taxable Income * 0.70 = 112K * 0.7 = $78.4K
$78.4K + 4K = $82.4K generated from operations.
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Corporate Tax
Given a boat was bought for $80K with a 10-year life and
$10K salvage value. First year operating expenses and
revenues show
Operating revenue $250,000
Operating expenses $90,000
Depreciation
$7,000
If the company’s tax rate is 34%, compute the net income
for the first year.
(250K – 90K – 7K) * 0.66 = $100,980
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Corporate Tax
Taxable Income
Tax Rate
Corporate Income tax
Not over $50K
15%
15% over $0
$50K-75K
25%
$7.5K+25% (X - $50K)
$75K-100K
34%
$13.75K+34%(X – $75K)
Compute the effective tax rate and marginal tax rate for a firm with
taxable income of $90,000.
Taxes paid = 0.15(50K) + 0.25(25K) + 0.34(15K) = $18,850
= 13.75K + 0.34(90K – 75K) = $18,850
Effective tax = 18,850 / 90,000 = 20.94%; marginal tax rate = 34%
Effective rate is also called the average tax rate.
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MACRS Depreciation
A 5-year MACRS tool costing $60K has calculated salvage values
of $20K in year 3, $10K in year 5 and $5K in year 6. Compute the
gain or loss if disposed of in years 3, 5 and 6.
DC3 = $60K(0.2 + 0.32 + 0.192/2) = $36,960 => BV3 = $23,040
Loss = 20K – 23,040 = -$3,040
DC5 = $60K(0.2 + 0.32 + 0.192 + 0.1152 + 0.1152/2) = $53,088
BV5 = $60K – 53,088 = $6,912 => Gain = 10K - $6,912 = $3,088.
DC6 = $60K with BV6 = 0 => Gain is $5K.
(macrs 5)
 (20.0 32.0 19.2 11.52 11.52 5.76)
(Dmacrs 60e3 5)  (12000 19200 11520 6912 6912 3456)
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Federal and State Tax
A corporation has $2M in revenue and $1.2M in expenses. If the
marginal federal tax rate is 34% and the state rate is 6% compute
the combined taxes paid.
Taxable Income = $2M – $1.2M = $800K
Method I: 0.34 + 0.06 – (0.34 * 0.06) = 37.96% combined F&S
$800K * 0.3796 = $303,680.
Method II: State Tax = $800K * 0.06 =
$ 48,000
Federal tax = (800K – 48K) = 752K (* 0.34) = $255,680
$303,680
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Personal Income Tax
2007
Individual income tax rate schedule for single and married filing jointly
Taxable Income
Tax Rate
$
Filing Single
0.10
$0–7,825
0.15
0.25
0.28
0.33
0.35
$7,826–31,850
$31,851–77,100
$77,101–160,850
$160,851–349,700
Over $349,700
Filing Married and Jointly
$0–15,650
$15,651–63,700
$63,701–128,500
$128,501–195,850
$195,851–349,700
Over $349,700
a) Compute tax for a single with a taxable income of $55K.
Tax = 0.10(7,825) + 0.15(24,024) + 0.25(23,149) = $10,173.35
b) Compute tax for a couple filing jointly with a taxable income of $150K.
Tax = 0.1(15,650) + 0.15(48049) + 0.25(64799) + 0.28(150K – 128,501)
= $30,991.82 => effective tax rate of 30991.82/150K = 20.66%
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Personal Income Tax
Joe and Holly earn $82K and have 4 personal exemptions
and the standard deduction of $9500. Interest & dividends
amount to $6050
Gross income = salaries + interest & dividends, capital-g
= $82K + 3550 + 2500 = $88,050
Taxable income = gross – exemptions – deductions
= 88,050 -4(3100) – 9500 = $66,150.
Taxes = 15,651(0.10) + 63,700 – 15,650)0.15 +
(66,150 – 63,700)(0.25)
= $9385; of which 9385/88050 = 10.7% effective.
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Income Taxes
Find the breakeven number of days for purchasing a truck for $13K
with 3K salvage value at end of a 7- year life with $1100 annual
expense and $35 daily expense, or lease for $83 a day based on 10%
ATCF and 50% tax rate. Use straight line depreciation
N
0
1-7
7
BTCF
SLine TI
50% Tax
-$13K
48X–1100 1428.57 48X–2528.57 –24X+1264.29
3000
ATCF
-$13K
24X+164.29
3000
13K(F|P,10%,7) = (24X+164.29)(F|A,10%,7) + 3000
25,333.32 = 226.69X+ 1558.64 +3000
X = 91.61 days
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Income Taxes
12-47. House and lot sell for $155K. Land is $45K and home is $110K. Rent
inputs $12K yearly with st-line depreciation 27.5 year life. Mary wants a 10%
ATCF. Find selling price at year n = 10 for Mary in 28% tax rate.
n
0
1-10
10
BTCF
-155K
12K
X
SLN
110K/27.5 = 4K
TI
28%Tax
ATCF
-155K
8K
-2.24K
9.76K
(X – 115K) -0.28X + 32.2K 0.72X + 32.2K
BV10 = 155K – 10(4K) = 115K
155K = 9.76K(P/A, 10%, 10) + (0.72X + 32.2K)(P/F, 10%, 10)  X = $297,612.25.
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Incremental ATCF Analysis 12-52
MARR = 10%
B
C
D
E
F
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-25
1-5
-10
1-5
-5
1-5
-15
1-5
-30
1-5
BTCF
DC
TI
20% Tax
7.5
5
2.5
- 0.50
3
2
1
- 0.20
1.7
1
0.7
- 0.14
5
3
2
- 0.40
8.7
6
1.7
- 0.34
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ATCF
-25
7
-10
2.8
-5
1.56
-15
4.6
-30
8.16
IRR
12.38%
12.38%
16.92%
16.17%
11.21%
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Incremental ATCF Analysis
MARR = 10%
D is > MARR; begin incremental analysis in order of cost.
C-D (IRR ‘(-5 1.24 1.24 1.24 1.24 1.24))  7.63%
E-D (IRR ‘(–10 3.04 3.04 3.04 3.04 3.04))  15.8% E
B-E (IRR ‘(-10 2.4 2.4 2.4 2.4 2.4))  6.4% => E
F-E (IRR ‘(-15 3.56 3.56 3.56 3.56 3.56))  6% => E
E is best.
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Taxable Income
A small company has taxable income of $50K and is thinking of another project
which will increase taxable income by $45K.
a) Compute the increase in taxes if the project is assumed.
b) Repeat analysis if taxable income is $400K.
a) (0.15 * 50K) = $7500 without project (under $50 K => 15% tax)
With 95K TI 13,750 + (0.34 * 20K) = $20,550
Taking on the $45K project increases taxes by ($20.55K - $7.5K) = $13.05K,
implying 13,050/45,000 = 29% of project is taxes.
b) 113.9K + (0.34 * 65K) = $136,000 taxes for TI = $400K
136/400 = 34% which is about the same for the additional $45K project.
0.34 * $45K = $15,300 for total tax of $151,300.
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ATCF
Deductions other
than interest and
depreciation
Gross income
(Income less
After-tax
Cash flow
Tax
exemptions)
Income taxes
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borrowed money
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After Tax Cash Flow
= - Pn
(capital investments)
+ Sn (revenues from sales of assets)
- t(Sn - Bn) (taxes on gains from sales of assets)
- W
(net working capital)
+ (1 – t)Rn (after tax ordinary revenues)
- (1 – t)En (AT operating expenses, labor energy, materials
+ tDn
(depreciation tax savings)
- (1 –t)IPn (AT interest payments)
- PPn
(Principal payments)
+ B
(loans received)
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Problem 12-21
n
0
1
2
3
4
5
6
6
BTCF
-100K
30K
30K
35K
40K
10K
10K
6.25K
DDB
TI
46% Tax
50K
25K
12.5K
6.25K
0
0
0
-20K
5K
22.5K
33.75K
10K
10K
9.2K
-2.3K
-10.35K
-15.525K
-4.6K
-4.6K
ATCF
-100K
39.2K
27.7K
24.65K
24.475K
5.4K
11.65K
Tools sold for salvage value of $6,250
(IRR ‘(-100000 39200 27700 24650 24470 5400 11650))  11.61%
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Problem 12-22
Loan Payment = $25,237.66
n
0
1
2
3
4
5
6
6
BTCF
- 20K
30K
30K
35K
40K
10K
10K
6.25K
DDB
P
I
TI
46% Tax
ATCF
- 20,000.00
50K
17237.66 8000
-28,000 12,880
17,642.34
25K
18961.43 6276.23 -1276.23 587.06
5,349.40
12.5K 20857.57 4380.09 18,119.91 -8,335.16
1,427.18
6.25K 22943.33 2294.33 31,455.67 -14,469.60
292.74
0
10,000
- 4,600
5,400.00
0
10,000
- 4,600
11,650.00
0
0
(IRR ‘(-20000 17642.34 5349.40 1427.18 292.74 5400 11650))  34.31%.
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Problem 12-39
First cost = $25K, life 4 years, salvage value = $5K,
UAB = $8K MARR = 10% in 40% tax bracket, MACRS 3
n BTCF Dep
TI
Tax (40%)
ATCF
0 -25K
-25K
1 8K
8333 -333
133.20
8133.2
2 8K
11112 -3112 1244.8
9244.8
3 8K
3702 4292 -1719.20
6280.8
4 8K
1852 6148 -2459.20
5540.80 + 5K
(list-pgf '(-25e3 8133.2 9244.8 6280.8 10540.8) 10)
 $1952.51 => Granny should invest. RoR = 13.48%
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Problem 12-54
Year
A
B
n~A
0
1
2
3
4
5
0~B
1
2
3
4
5
IRRB-A:
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1
2
3
4
5
ATAX = 10%
-3K
1K
1K
1K
1K
1K
SOYD
-5K
1K
1.2K
1.4K
2.6K
2.8K ST-LINE
BTCF Dep
TI
Tax 34%
ATCF
-3K
-3K
1K
1K
0
0
1K
1K
800
200
-68
932
1K
600
400
-136
864
1K
400
600
-204
796
1K
200
800
-272
728 14.39% ATCF-A
-5K
-5K
1K
1K
0
0
1K
1.2K
1K
200
-68
1132
1.4K
1K
400
-136
1264
2.6K
1K
1600
-544
2056
2.8K
1K
1800
-612
2188 13.68% ATCF-B
(IRR '(-2e3 0 200 400 1260 1460))  12.99% => B > A
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Problem 12-57
Buy for $1M or lease for $200K/yr. Annual income is
$800K, annual costs are 200K with resale value at $400K.
10-year life with st-line, tax at 40%, ATCF i = 10%
n
BTCF Dep TI
Tax 40%
ATCF
0
-1M
-1M
1-10 600K 60K 540K -216K
384K
10
400K
-1M(A/P,10%, 10) + 384K + 400K(A/F, 10%, 10) = $246,352.76 BUY
LEASE: (800K -200K -200K)0.40 = $160K tax or $240K cash flow
EUAB – EUAC = $800K - $200K - $200K -160K = $240K
Better to Buy and net $6352.76
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ATCF
Use st-line depreciation with an ATCF of 8% and tax rate of 40% to choose
the best system for 6-year lives.
A
B
C
First cost
$40K
$50K
$35K
UAB
5K
3.5K
10K
Salvage
8K
5K
3K
Year
A 1-6
B 1-6
C 1-6
BTCF
5K
3.5K
10K
St-Line
5.333K
7.5K
5.333K
TI
Tax 40%
-0.333
133.33
-4K
1600
4666.67 -1866.67
ATCF
5133; 8K Salvage
5100; 5K
8133; 3K
(UIRR 40e3 5133 6 8e3)  -0.75% (UIRR 5e3 -3e3 6 5e3)  -200% A-C
(UIRR 50e3 5100 6 10e)  -8.23% (UIRR 5e3 -3033 6 2e3)  -88% B-C
(UIRR 35e3 8133 6 3e3)  11.95% C is best
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ATCF
An asset bought for $100K with S = $20K after 5 years is depreciated
MACRS 5-year rates. Expense average $18K annually with an
effective tax rate of 30%. After 5 years of service the asset is sold for
$22K. The ATCF for the sale of the asset is closest to
a) $27,760
b) $17,130
c) $26,870
d) $20,585
(dmacrs 100e3 5)  (20000 32000 19200 11520 11520 5760)
22K + 5,760 = $27,760
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Taxes on Capital Gains
A 3-year property class type equipment bought for $30,000
is sold for $20,000 at the end of three years.
The company is at a 34% tax bracket. The tax is
a) $5,125.89
b) $7,201.45 c) $6,044.18 d) $7,182.35
(dmacrs 30E3 3)  (9999 13335 4443 2223)
Must pay capital gains on (20K – 2223) = $17777 or
0.34 * 17777 = $6044.18
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Corporate Taxes
Pace Corporation had a taxable income of $300,000 in
2007. Which of the following expression may be used to
compute the federal income tax liability for the company?
a) 15% of taxable income
b) 25% of taxable income
c) $113,900 + 34% over $100,000
d) $22,250 + 39% over $100,000
See Tax table Page 395 of text,
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Taxes
First cost of equipment = $6,000; Salvage value after 5 years = $1,500
MACRS depreciation is used as a 5-year property; Income-tax rate for the
company = 34%; Capital gains are taxed at 15% rate.
Cash flow is -6000 1600 1600 1600 1600 1600 1600 + 9000 salvage
Find ATCF RoR (dmacrs 6E3 5)  (1200 1920 1152 691.2 691.2 345.6)
n BTCF Dep
TI
Tax Rate
ATCF
0 -6000
-$6000
1
1600 1200
400
-136
1464
2
1600 1920
-320 108.8
1708.8
3
1600 1152
448 -152.32
1447.68
4
1600
691.2
908.8 -309
1291.00
5
1600
691.2
908.8 -309
1291.0
6
1600
345.6
1254.4 -426.5
1173.5
6
9000 Capital gain = Market value – Cost basis = 9K - 6K = 3K at 15%
Depreciation recapture is cost basis – book value = $6000 – 0 tax @ 34%
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Income or Profit and Loss Statement
Revenue
Operating Expenses
Gross Profit
Administrative Costs
Other Income
$300,000
250,000
50,000
10,000
5,000
Net Income Before Tax
Tax
Net Income of Net Profit After tax
Dividends
Retained Earnings
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45,000
20,000
25,000
10,000
15,000
33
Balance Sheet
Assets
Cash
$50,000
Securities
5,000
Accounts Receivable 5,000
Inventory
90,000
Equipment
200,000
Buildings
100,000
Total Assets
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Liabilities and Owners Equity
Accounts Payable
$30,000
Note Payable
20,000
Taxes Payable
10,000
Common Stock
300,000
Retained Earnings
90,000
Total Liability and
Owners Equity
$450,000
rd
$450,000
34
Balance Sheet Engineered Industries K
Assets
Current assets
Cash
Accounts Receivable
Securities
Inventories
(-) Bad debt provision
1940
950
4100
1860
-80
Fixed assets
Land
Plant & Equipment 6500
(-) Accumulated depr
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1150
80
Accrued expense
Total current liabilities
950
2180
Long-term liabilities
1200
Equity
Preferred stock
Common stock
Capital Surplus
Retained earnings
Total equity
110
650
930
8745
10,435
335
-2350
Other assets
Prepays/deferred charges 140
Intangibles
420
Total other assets
560
Total assets
Liabilities
Current liabilities
Accounts Payable
Notes Payable
13,815
Total liabilities and equity
rd
13,815
35