Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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SECTION J 6A.3 Determination
of
MACRS Rates
derived by using the applicable rate for the DB method.
The
subscripts DB and
SL
have b
ee
n inserted along with the
year
t.
For
the first
year
t = 1,
1 1 1
d
DB
.
1
= -
or
d = - -
n SL,I 2 n
For
summation purposes only, we introduce the subscript i
(i
=
1,2,
...
,
t)
on
d.
Then
the depreciation rates for years t = 2
,3,
...
, n are
d
DB
,/ =
d(1
-iII
di)
(= I
[16A.14]
[16A.1S]
Also, for y
ea
r n + I, the
MACRS
rate is
one-half
the
SL
rate
of
the previous
year
n.
I
d = - -
SL,II+ I
2d
SL,II
[16A.l6]
The
DB and
SL
rates
are
compared
each
year
to
determine
which is larger and
when the
sw
itch to
SL
depreciation should occur.
EXAMPLE 16A.5
.'>.
Verify the MACRS rates in Table
16
- 2 for a 3-year recovery period. The rates
in
per-
cent are 33.33, 44.45, 14.81, and 7.41.
Solution
The fixed rate for DDB with n = 3 is d =
2/3
= 0.6667. Using the half-year conven-
tion
in
year 1 and Equations [16A.
14]
through [16A.16J, the results are as follows:
dOB
,1 = 0.5d = 0.5(0.6667) = 0.3333
d
2
.
Cumulative depreciation rate
is
0.3333.
d
OB
,2 = 0,6667(1 - 0.3333) = 0.4445
d = I - 0.3333 = 0.2267
SL
.2
3 - 2 + 1.5
(l
arger value)
d
3
.
Cumulative depreciation rate
is
0.3333 + 0.4445 = 0.7778.
d
oB
,3 = 0.6667(1 - 0.7778) = 0,
1481
1-0.7778
d
Sl
.
3
= 3 _ 3 +
1.5
= 0.1481
Both
va
lues are the sa
me
; switch
to
straight
li
ne
depreciation.
d
4
.
This rate is 50%
of
the
la
st SL rate.
d
4
= 0.5(d
su
) = 0.5(0,1481) = 0.0741
565
566
CHAPTER
16
Depreciation Methods
APPENDIX PROBLEMS
Sum-of-Year-Digits Depreciation
16A.I A European manufacturing company
has new equipment with a first cost
of
12
,000 euro, an estimated salvage
value
of
2000 euro, and a recovery pe-
riod
of
8 years.
Use
the
SYD
method
to tabulate annual depreciation and
book value.
16A.2 Earthmoving equipment with a first
cost
of
$150,000 is expected to have a
life
of
10
years. The salvage value
is
expected to be 10%
of
the first cost.
Calculate
(a) by hand and
(b)
by com-
puter
th
e depreciation charge and book
value for years 2 and 7 using the
SYD
method.
16A.3 If
B = $
12
,000, n = 6 years, and S
is
estimated at
15
%
of
B, use the
SYD
method to determine
(a)
the book
val ue after 3 years and
(b)
the rate
of
depreciation and the depreciation
amount
in
year 4.
Switching Methods
1
6AA
An asset has a first cost
of
$45,000, a
recove
ry
period
of
5 years, and a
$3
000
salvage value. Use the switch-
ing procedure from DDB to
SL
depre-
ciation, and calculate the present
worth
of
depreciation at i = 18% per
year.
16A.5
If
B = $45,
000
, S = $3000, and n =
5-year recovery period, use a spread-
sheet and
i = 18% per year to maxi-
mize the present worth
of
depreciation,
using the following methods: DDB-to-
SL
switching (this was determined
in
Problem 16AA) and MACRS. Given
that
MACRS is the required deprecia-
tion system
in
the United States, com-
ment on the results.
16A.6 Hempstead Industries has a new
milling machine with
B = $ 110,000,
n = 10 years, and S =
$10
,
000
. Deter-
mine the depreciation schedule and
present worth
of
depreciation at i =
12%
per
year, using the 175% DB
method for the first 5 years and switch-
ing to the classical
SL
method for the
last 5 years.
Use a spreadsheet to solve
this problem.
16A.7 Reliant Electric Company has erected a
large portable building with a first cost
of
$155,000 and an anticipated salvage
of
$50,000 after 25 years. (a) Should
the switch from DDB to
SL
deprecia-
tion be made?
(b)
For
what values
of
the unjform depreciation rate in the
DB method would it
be
advantageous
to switch from DB to
SL
depreciation
at
some
point
in
the life
of
the
building?
MACRS Rates
16A.8 Verify the 5-year recovery period rates
for
MACRS
given
in
Table
16-2
. Start
with the DDB model in year I, and
switch to
SL
depreciation when it of-
fers a larger recovery rate.
16A.9 A video recording system was pur-
chased 3 years ago at a cost
of
$30,000.
A 5-year recovery period and
MACRS
depreciation have been used to write
off
the basis.
The
system is to be pre-
maturely replaced with a trade-in value
of
$5000. Determine the
MACRS
depreciation, using the switching rules
to
find
the difference between the book
value and the trade-in value after the
3 year
s.
l6A.l
0 Use the computations in Equations
[16A.lO] through [16A.12]
to
determine
the MACRS annual depreciation for the
following asset data:
B = $50,000 and a
recovery period
of7
years.
APPENDIX PROBLEMS 567
16A.ll
The 3-year MACRS recovery rates are
33.33
%,
44.45
%,
14.81
%,
and 7.41
%,
respectively. (a) What are the corre-
sponding rates for the alternative
MACRS straight line ADS model with
the half-year convention imposed?
(b) Compare the
PWD
values for these
two methods
if
B = $80,000 and i =
15
% per year.
LU
t-
I
u
After-Tax Economic
Analysis
This
chapter
provides
an
overview
of
tax
terminology,
income
tax
rates, and
tax
equations
pertinent
to
an
after-tax
economic
analysis. The
transfer
from
estimating
cash
flow
before
taxes (CFBT)
to
cash
flow
after
taxes (CFAT)
involves a
consideration
of
significant
tax
effects
that
may
alter
the
final
decision,
as
well
as
estimate
the
magnitude
of
the
tax
effect
on cash
flow
over
the
li
fe
of
the
alternative.
Mutual
ly exclusive
alternative
comparisons
using after-tax
PW,
AW,
and
ROR
methods
are
explained
with
majortax
implications
considered
. Replace-
ment
studies are discussed
with
tax effects
that
occur
at
the
time
that
a
defender
is
replaced. Also,
the
after-tax
economic
value
added
by
an
alter-
native
is
discussed in
the
context
of
annual
worth
analysis.
All
these
methods
use
the
procedures
learned
in earlier chapters,
except
now
with
tax
effects
considered.
An after-tax
evaluation using any
method
requires
more
computations
than
those
in
previous chapters. The
computer
greatly
reduces
the
analysis
time
due
to
the
power
of
spreadsheet
formatting
and functions. Templates
for
tabulation
of
cash
flow
after
taxes
by
hand
and
by
computer
are
devel-
oped.
Additional
information
on
U.S
. federal
taxes-tax
law, and annually
updated
tax
rates-is
available
through
Internal Revenue Service
publica-
tions
and,
more
readil
y,
on
the
I
RS
websi
te
www.irs.
gov
. Publications 542,
Corporations,
and 544, Sales
and
Other
Dispositions
of
Assets, are especially
applicable
to
this
chapter
. Some differences in
tax
considerations
outside
the
United
States are summarized
in
the
last section.
The case
study
provides
the
opportunity
to
perform
a
complete
after-tax
analysis
of
debt
versus
equity
financing,
with
asset
depreciation
included.
It
is
an
app
lication
of
the
generalized
cash flow analysis
model.
LEARNING OBJECTIVES
Purpose: Perform an economic evaluation
of
one
or
more alternatives considering
the
effect
of
income taxes and
other
pertinent
tax
regulations.
Terminology and rates
CFBT and CFAT
Taxes and depreciation
Depreciation recapture
and capital ga
in
s
After-tax analysis
Spreadsheets
After
-
tax
replacement
Value-
added
analysis
Taxes outside
the
United
States
This
chapter
wi
ll
help
yo
u:
1.
Correctly
use
the
basic
terminology
and
income
tax rates
for
corporate
(and individual) taxpayers.
2.
Ca
lculate
before-tax
and after-tax cash fl
ow
.
3.
Demonstrate
the
tax
advantage
of
accelerated
depreciation
and
a
shortened
recovery
period.
4.
Compute
the
tax
impact
of
dep
reci
at
ion
recapt
ure and
capital gains (losses).
5.
Evaluate alternatives using after-tax
PW,
AW,
and
ROR
analysis.
6.
Develop
spreadsheets that structure after-tax evaluation
of
two
or
more
alternatives.
7. Evaluate a
defender
and
challenger
in
an
after-tax
repl
acement
study.
8.
Eval
uat
e alternatives using after-tax
economic
value-added
analysis.
9.
Understand
the
after
-
tax
impact
of
tax
laws in
countr
ies
outside
the
United
States.
570
CHAPTER
17
After-Tax Economic Analy
si
s
17.1 INCOME TAX TERMINOLOGY
AND
RELATIONS
FOR
CORPORATIONS (AND INDIVIDUALS)
Some basic corporate tax terms and relationships useful in engineering economy
studies are explained here.
Gross
income (GI) is the total income realized from all revenue-producing
sources
of
the corporation, plus any income from other sources such as sale
of
assets, royalties, and license fees. The incomes are listed
in
the revenue
section
of
an
income statement.
Income
tax
is
the amount
of
taxes based on some form
of
income or profit
that must be delivered to a federal (or lower-level) government agency. A
large percentage
of
U.S. tax revenue is based upon taxation
of
income. The
Internal Revenue Service, which is a part
of
the U.S. Department
of
the
Treasury, collects the taxes. Corporate income tax payments are usually
submitted quarterly, and the last payment
of
the year
is
submitted with the
annual tax return. Taxes are actual cash flows.
Operating
expenses E include all corporate costs incurred
in
the transaction
of
business. These expenses are tax deductible for corporations. For engi-
neering economy alternatives, the AOC (annual operating cost) and M&O
(maintenance and operations) costs are applicable here.
The amount
of
GI and E must be estimated for
an
economy study and
expressed as
Gross income - expenses = GI - E
Taxable income (TI) is the amount upon which taxes are based. For corpora-
tions, depreciation D and operating expenses are tax-deductible, so
TI
= gross income - expenses -
depreciation
=
GI
- E - D [17.1]
Tax
rate
T
is
a percentage,
or
decimal equivalent,
ofTI
owed
in
taxes. The tax
rate, tabulated by level
ofTI,
is
graduated; that is, higher rates apply as the
TI increases. The general formula for tax computation uses the applicable
T value.
Taxes = (
taxable
income) X (applicable
tax
rate
)
=
(TI
)(T)
[17.2]
Net profit
after
taxes (NPAT)
is
the amount remaining each year when income
taxes are subtracted from taxable income.
NPAT =
taxable
income
- taxes =
TI
-
(TI)(D
=
(TI)(l
-
T)
[17.3]
This
is
the amount
of
money returned to the corporation as a result
of
the
capital invested during the year. It is a component
of
after-tax value-added
analysis. NPAT
is
also referred to as net income (NI) and net operating
profit after taxes (NOPAT).
SECTION 1
7.
1
In
come
Ta
x Terminology a
nd
Rela
ti
o
ns
TABLE
17-1 U.
S.
Corporate Federal Income Tax Rate Schedule (2003)
(mil = million $)
TI TI
Tax
Maximum
Tax
Maximum
Limits
Range
Rate
T
for
TI
Range
Tax
Incurred
(1)
(2)
(3)
(4) =
(2)T
(5) =
Sum
of
(4)
$1- $50,000 $ 50,000 0.15 $ 7,500
$
7,500
$50,00 1
-7
5,000 25,000 0.
25
6,250 13,750
$75,001- 100,000
25,000 0.34 8,500
22,250
$100,001- 335,000
235,000 0.39 91,650
113
,900
$335,001-
10
mil
9.665
mi
l 0.34 3.
2861
mi
l 3.4 m
il
Over $ I 0-
15
mi
l 5 mil
0.35
l.
75
mil
5.15
mi
l
Over $
15
- 18.33
mil
3.33
mil
0.38 1.267
mil
6.417 mil
Over $18.33
mil
Un
l
im
ited
0.35
Un
li
mited Ulllimited
A variety
of
different bases may be used by federal, state, and local agencies
for tax revenue.
Some
bases (and taxes) other than
income
are the total sales
(sales tax); appraised value
of
property (property tax); value-added tax (VAT);
net capital investment (asset tax); winnings from gambling (part
of
income
tax);
and retail value
of
items imported (import tax). Similar and different bases are
utilized by different countries, provinces, and local tax districts.
Governmen
ts
that have no income tax must utilize bases other than
income
to devel
op
revenue.
No
government entity survives for long without
some
form
of
tax revenue.
Th
e annual federal tax rate T is based upon the principle
of
graduated fax
rates,
which means that corporations pay
higher
rates for larger taxable incomes.
Table
17- ] presents T values for U.S. corporations.
The
rates and
TI
limits
change based on legislation and IRS interpretation
of
tax law and economic
conditions. Additionally each year the IRS reviews and/or alters the
TI
li
mits to
account for inflation and other factors.
Th
is action is called indexing.
The
portion
of
each new dollar
of
TI is taxed at what is called the marginal tax rate. As an
illustration, scan the tax rates
in
Table
17
- 1. A business with an annu
al
TI
of
$50,000 has a marginal rate
of
15
%.
Howev
er, a business with
TI
=
$100
,
000
pays
15
% for
th
e first $
50
,
000
, 25% on the next
$2
5,000, and
34%
on the
remai nder.
Taxes = 0.15(50,000) + 0.25(75,000 - 50,000) + 0.34(100,000 - 75,000)
=
$22
,250
The
graduated tax rate system gives businesses with small taxable incomes a
slight advantage.
The
marginal rates are
in
the middle to upper thirty percent-
ages for TI values
above
(roughly) $ 100,
000
, while smaller TIs have rates in the
15
% to
25%
range.
Example
17
.1 further illustrates the use
of
graduated tax
rates.
Because the marginal tax rates change with
TI
, it
is
not possible to quote
directly the percent
of
Tr paid
in
income taxes. Alternatively, a single-value
571
572
CHAPTER
17
After-Tax Economic Analysis
number
, the average tax rate,
is
calculated as
total taxes paid taxes
Average tax rate
=
----"---
taxable income
TI
[17.4]
For
a small business with
TI
= $100,000, the federal
income
tax burden aver-
ages
$22,
250
/10
0,
000
= 22.25%.
If
TI
= $15 million, the av
erage
tax rate
(Table
17
- 1) is $5.15 million/
IS
million = 34.33%.
As mentioned
ear
li
er
, there are federal, state, and local taxes imposed.
For
the
sake
of
simplicity, the tax rate u
se
d in an eco
nomy
st
udy is often a single-figure
effective tax rate T
e
,
which accounts for all taxes. Effective tax rates are
in
the
ran
ge
of
35% to 50%.
One
reason to use the effective tax rate is that state taxes
are deductible for federal tax computation.
The
effective tax rate and taxes are
calc
ul
ated as
Te = state
rate
+
(1
- state rate)(federal rate)
Taxes
=
(TI)(T
e
)
EXAMPLE 17.1
[17.5]
[17.6]
If
the security division
of
OnStar has an annual gross income
of
$2,750,000 with
expenses and depreciation totaling
$1
,9
50,000, (a) compu
te
the company's exact
federal income taxes.
(b) Estimate total federal a
nd
state taxes if a state tax ra
te
is 8%
a
nd
a 34% federal average tax rate applies.
Solution
(a) Compute the
TI
by Equation [17.1) and the income taxes using Table
17
- 1 rates.
TI
= 2,750,000 - 1
,9
50,000 = $800,000
Taxes = 50,000(0.
15
) + 25,000(0.25) + 25,000(0.34)
+ 235,000(0.39) + (800,000 - 335,000)(0.34)
= 7500 + 6250 + 8500 +
91
,650 + 158,
lOO
= $272,000
A faster approach uses the amount
in
column 5
of
Table
17
- 1
th
at
is
closest to
the total
TI
and adds
th
e tax for
th
e next
TI
range.
Taxes
=
113
,9
00 + (800,000 - 335,000)(0.34) = $272,000
(b) Equation [17.5) determines the effective t
ax
rate.
Te = 0.08 +
(1
- 0.08)(0.34) = 0.3928
Estimate total taxes by Equation [17.6).
Taxes
= (TI)(TJ = (800,000)(0
.3
928) = $3
14
,240
These two amounts are not comparable, because the tax
in
patt (a) does not
include state taxes.
SECTION
17
.1
Income Tax Term
in
ology a
nd
Relations
T
ABLE
17-2
U.S. Individual Federal Income Tax Rate Schedule for
Single and Married Filing Jointly
(2003)
Tax Rate T
(1
)
0.
10
0.15
0.
25
0.28
0.33
0.35
Taxable In
come
, $
Filing Single
(2
)
0
-7,00
0
7,001- 28,400
28,401-68,800
68
,801-143,500
143,
501
-3
11
,950
Over 3
11
,950
Filing Married
and
Jointl
y
(3)
0-14
,000
14,001-56,800
56,801-114,650
114,
651
-1
74,700
174,
701
-3
11
,950
Over 311,950
It
is
interesting to understand how corporate tax and individual tax computa-
tions differ. Gross income for an individual taxpayer is comparable, with
business revenue replaced by salaries and wages. However, for an individual's
taxable income, most
of
the expenses for living and working are not tax-
deductible to the same degr
ee
as business expenses are for corporations.
For
individual taxpayers,
Gross
in
come = GI = salaries + wages + interest and dividends
+ other income
Taxable income
= GI - personal exemption
- standard
or
itemized deductions
Taxes
= (taxable income)(applicable tax rate) = (TI)(T)
For
TI
, corporate operating expenses are replaced by individual exemptions and
specific deduction
s.
Exemptions are yourself, spouse, children, and other depe
n-
dent
s.
Each exemption reduces TI by approximately $3000 per year, depending
upon current exemption allowances.
Like the corporate tax structure, tax rates for individuals are graduated by
TI
level. As shown
in
Table
17-2
, they range from
15
% to 35%
ofTI.
EXAMPLE
17.2
"
Josh and Allison submit a married-filing-jointly return to the IRS. During the year their
two
jobs
provided them with a combined income
of
$82,000. They had their second
child during
th
e year, and they plan to use the standard deduction
of
$9500 applicable for
the yea
r.
Dividends and interest amounted to $3550, and an investment
in
a stock mutual
fund had capital gains
of
$2500. Personal exemptions are $3100 currently. (a) Compute
their exact federal tax liability.
(b) Compute their average tax rate. (c)
What
percent
of
gross income is consumed
by
federal taxes?
573
574
CHAPTER 17 After-Tax Economic Analysis
Solution
(a) Josh and Allis
on
have four personal exemptions and the standa
rd
deduction
of
$9500.
Gross income = salaries + interest and dividends + capital gains
= 82,000 + 3550 + 2500 = $88,050
Taxable income = gross income - exemptions - deductions
= 88,050 - 4(3100) - 9500
= $66,150
Table
17
- 2 indicates the 25% marginal rate. Using colulllns 1 and
3,
federal
taxes are
Taxes
=
14
,000(0.10) + (56,800 -
14
,000)(0.
15
)
+ (66,150 - 56,800)(0.25)
= $10,158
(b) From Equation [17.4],
10,
158
Average tax rate = - - - = 15.4%
66,
150
This indicates that about 1 in 6 dollars
of
taxable income
is
paid to the
U.S.
government.
(c)
Of
the total $88,050, the percent paid
in
federal taxes
is
10,158/ 88,050 =
11
.5%.
Comment
There has been longstanding debate in the
U.S
. Congress about the
ad
visability of
changing from a graduated tax structure
to
a flat tax structure for individual taxpayers.
(This structure
is
applied
in
some countries presently.) There are many ways
to
legislate
taxe
s,
and the amount
to
be chosen for the flat rate can be a real controvers
y.
For example, the flat tax structure may allow
no
standard or itemized deductions and
have only the pers
on
al exemption allowance.
In
this example, were there a
flat
tax rate
as low as
15
%
on
gross income reduced only by the four personal exemptions, the
COIll-
putations would be
Gross income = $88,050
Flat rate taxable income = 88,050 - 4(3100) = $75,650
Flat rate taxes
=
75
,650(0.
15
) = $
11
,348
In this case, a
15
% flat tax rate would require that 11.7% more taxes be paid
by
this
family- $1l,348- compared to $10,158 using the graduated tax rates.
17.2 BEFORE-TAX
AND
AFTER-TAX
CASH
FLOW
Early in the text, the term net c
ashflow
(NCF) was identified as the best estimate
of
actual cash flow each year.
The
NCF
is calculated as cash inflows minus cash
outflows. Since then, the annual
NCF
amounts have been used many times to
perform alternative evaluations via the
PW
,
AW,
ROR, and B/C methods. Now
that the impact on cash flow
of
depreciation and related taxes will be considered,