Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)
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environmentally friendly process should
be implemented. Estimates or actual val-
ues for the two processes are summarized
below.
She
performed an after-tax re-
placement analysis at
10% per year and
the corporation's effective tax rate
of32
%
to determine that economica
ll
y,
the new
process should be chosen. Was she cor-
rect? Why
or
why not? (Note: Canadian
tax law does not impose the half-year
convention requirement.)
Curre
nt
New
Proce
ss Process
First cost 7 years ago, $ - 450,000
First cost, $
-700,000
Rema
ini
ng
li
fe,
years 5
10
Current market
va
lue, $ 50,000
AOC,
$/year
-
160
,000 - 150,000
Future salvage, $ 0
50,000
Depreciation method
SL SL
17
.52 (a)
The
Los Angeles,
Ca
li
fornia, city en-
gineer is analyzing a for-profit public
works project at the port authority,
using
an
after-tax replacement analy-
sis
of
the installed system (defender)
and a challenger as detailed below.
All values are
in
$1000 units.
The
ef-
fective state tax rate
of
6%
is
applica-
ble, but no federal taxes are imposed.
The municipal after-tax return
of
6%
per year
is
required. Assume sal-
vages
in
the future occur at the esti-
mated amounts and use classical
SL
depreciation. Perform the analysis.
(b) Would the decision be different if a
before-tax replacement analysis were
performed at
i = 12%
per
year?
Defender
Challen
ge
r
First cos
t,
$
- 28,000 -
15
,000
AOC,
$/year
- 1,200 - 1,500
<:;a
lvage estimate, $
2,000 3,000
v1arket
value, $
15
,000
,ire,
years
10
8
'ears
in
service 5
PROBLEMS
615
17.53
In
Problem 17.52(a), assume that 5 addi-
tional years have passed and the challenger
has been
in
place all 5 years. A new city en-
gineer decides to privatize the for-profit
entities
of
the city government and sells
the implemented challenger system for
$10,000,000. Was the decision made
5 years earlier to select the challenger an
economically correct one?
Use the same
values as before: 6% effective tax rate,
6% per year after-tax rate
of
return, and
classical
SL depreciation.
17.54 Apple Crisp Foods signed a contract
some years ago for maintenance services
on its fleet
of
trucks and cars. The contract
is up for renewal now for a period
of
1 year
or
2 years only. The contract quote
is
$300,000 per year
if
taken for 1 year
and
$240,000 per year
if
taken for 2 years.
The
finance vice president wants to renew
the contract for 2 years without further
analysis, but the vice president for engi-
neering believes it is more economical to
perform the maintenance inhouse.
Since
much
of
the fleet is aging and must be re-
placed in the near future, a fixed 3-year
study period has been agreed upon.
The
estimates for the inhouse (challenger)
alternative are as follows:
First cost, $
AOC, $/year
Life, years
Estimated salvage, $
MACRS depreciation
- 800,000
- 120,000
4
Loses 25%
of
P annually:
End year I
600,000
End year 2 400,000
End year 3 200,000
End year 4 0
3-year recovery period
The
effective tax rate is 35%, and the
after-tax
MARR
is 10% per year. Per-
form an after-tax AW analysis, and deter-
mine which vice president has the better
economic strategy over the next 3 years.
616
CHAPTER
17
After-Tax
Economic
Anal ysi s
17.55 Nuclear safety devices installed several
years ago have been depreciated from a
first cost
of
$200,000
to
zero using
MACRS. The devices can be sold on the
used equipment market for an estimated
$15,000. Or they can be retained in service
for 5 more years with a
$9000 upgrade
now a
nd
an AOC
of
$6000 per year. The
upgrade investment will be depreciated
over 3 years with no salvage
va
l
ue.
The
challenger
is
a replacement with newer
technology at a first cost
of
$40,000, n =
5 years, and S =
O.
The new units will have
operating expenses
of
$7000 per year.
(a) Use a 5-year study period,
an
effec-
tive tax rate
of
40%, an after-tax
MARR
of
12 % per year, and an as-
sumption
of
classical straight line de-
preciation (no half-year convention)
to perform an after-tax replacement
study.
(b)
If
the challenger
is
known to be sal-
able after 5 years for an amount be-
tween
$2000 and $4000, will the
challenger A W value become more
or less costly? Why?
17
.
56
Develop a spreadsheet like the one in
Table
17
- 8 for Example 17.l3. Redo the
after-tax replacement analysis, using the
estimates that the market value
of
the de-
fender is only
$275,000 and that the chal-
lenger will
be
sold on the international
market for
$100,000. Salvage value is
not considered
in
computing challenger
depreciation.
17.57 Three years ago, Silver House
Steel pur-
chased a new quenching system for
$550,000. The salvage value
af
te
r 10 years
at that time was estimated to be
$50,000.
Currently the expected remaining life is
7 years with an
AOC
of
$27,000 per year.
The new president h
as
recommended
early replacement
of
the system with one
that costs
$400,000 and has a 12-year life,
a
$35,000 salvage value, and an estimated
AOC
of
$50,000 per year. The MARR for
the corporation
is
12% per year. The pres-
ident wishes to know the replacement
value that will make the recommenda-
tion to replace now economically advan-
tageous.
Use a spreadsheet and the
SOLVER tool to find the minimum trade-
in value
(a) before taxes and (b) after
taxe
s,
using an effective tax rate
of
30
%.
For solution purposes,
us
e classical SL
depreciation for both systems. Comment
on the difference
in
replacement value
made by the consideration
of
taxes.
Economic
Value Added
17.58 (a) What does the term economic value
added
(EVA) mean relative to the
bottom line
of
a corporation?
(b) Why might
an
investor in a public
corporation prefer to use the EVA
estimates over the CFAT estimates
for a project?
17.59 An asset has a first cost
of
$12,000, SL
depreciation
of
$4000 for each year
of
its
3-year recovery period and no salvage
value, and an estimated CFBT
of
$5000
per year. The effective tax rate
is
50
%,
and the after-tax
MARR
of
the Harriet
Corporation
is
10% per year. Use hand or
spreadsheet solution as indicated by your
instructor to demonstrate
(a) that the pre-
sent worth values
of
the EVA and CFAT
series are identical and
(b)
that when the
equivalent
of
the first cost is "charged"
against annual CFAT, the resulting PW
value
is
equal to the PW
of
EVA, as
di
s-
cussed in Example 17
.14(b).
17.60 For Example 17.3 and an interest rate
of
10% per year, do the following:
(a) Determine the EVA estimates for
each year.
(b) Show that the annual worth of
EVA
estimates is numerically the same a
the A W
of
the CFAT estimates, if the
actual
sa
lvage value in year 6 is zero,
not
$150,000. (This makes the CFAT
value
in
year 6 equal to $82,588.)
17.61 Sun
Micr
osystems has developed part-
nerships with several large manufactur-
ing corporations to use Java software
in
th
eir
consumer and industrial products. A
new corporation will be formed to man-
age these applica
ti
ons.
One
major project
involves using
Java
in
commercial and
industrial app
li
ances that store and cook
food.
The
gross income and expenses are
expected to follow the relations sh
ow
n
for the estimated life
of
6 years.
For
t = 1
to 6 year
s,
Annual gross income = 2,800,
000
- 100,000t
Annual expenses = 950,000 + 50,000t
CASE STUDY
CASE
STUDY
617
The effective tax rate is 35%, the interest
rate is 12% per year, and the depreciation
method chosen for the
$3,000,000 in cap-
ital investment is the 5-year
MACRS
al-
ternative that allows straight line write-
off with the half-year convention
in
years
1 and 6. Using a spreadsheet, estimate
(a) the annual economic contribution
of
the project to the new corporation and
(b) the equi valent annual worth
of
these
contributions.
17.62 Review the situations
in
Examples 17.6
and 17.11. Assume the
NBA
contract is
now for 6 years, that the gross income
and expenses continue for all 6 years, and
that neither analyzer has any realized
sa
lvage value. Use
an
EVA analysis to
choose between the two analyzers. The
MARR
is 10% per year, and Te = 35%.
AFTER-TAX EVALUATION
OF
DEBT
AND EQUITY FINANCING
The Proposal
Young Brothers, In
c.
, a
hi
ghway
eng
in
ee
ring company located in
Seattle, Washington, wants to
develop new business opportu-
nities
in
Portland, Oregon.
Brother Charles historically has
lo
oked after the financial end
of
the compa
ny.
He
is
concerned
about
th
e method
of
financing the new office, wo
rk
yard, and equipme
nt
at
th
e planned Portland site. Debt
financing (loan) from
theiT
Seattle bank and equity
fi-
nancing from company retained
ea
rnings are possible
wa
ys
to finance
th
e new office, but the best mix
of
debt
a
nd
equity funds is unknown at this time. To help,
Charles has read a section
of
a handbook on general-
ized cash flow analysis,
especially the part on after-tax
analysis
of
the two financing method
s-de
bt versus
equity. What he learned and has summarized for him-
self follows.
Debt and Equity Financing
(Copied from the Handbook)
In a company lIses loans and bonds to raise capital, it
is ca
ll
ed debt financing (
DF
).
Loans require payment
of
periodic interest, and bonds require that periodic
dividends be paid to the investor.
The
loan principal or
bond face value is repaid after a stated number
of
years. These various loan and bond cash flows affect
taxes and CFAT differently, as shown
in
the table.
618
CHAPTER
17
After-Tax Economic Analysis
Type
of
Debt
Cash
Flow Involved
Loan Receive principal
Loan
Pay interest
Loan Repay principal
Bond Receive face value
Bond
Pay dividend
Bond Repay face value
Only loan interest and bond dividends are tax-
deductible.
Use
th
e
sy
mbol DF,
to
identify the sum
of
these
tw
o.
To
develop a relation that explains the tax
impact of debt financing, start with the fundamental
net cash
flow
relation, that
is
, receipts minus disburse-
ments. Identify receipts from debt financing
as
DFR = loan principal receipt + bond sale receipt
Define debt
fin
ancing disbursements
as
OF
f)
= loan interest payment
+ bond dividend payment
+ loan principal repayment
+ bond face value repayment
It is common that a loan or bond sale, not both, is in-
volved
in
a single asset purchas
e.
The two terms in the
first line
of
the
DF
f)
equation represent DF, mentioned
earlier.
If
a company uses its own resources for capital
investment, it is called equity financing (EF). This
includes
(1) the use
of
a corporation's own funds,
such as retained earnings; (2) the sale
of
corporation
stock; and (3) the sale
of
corporate assets to raise
capital. There are no direct tax advantages for equity
financing. Expended retained earnings and stock div-
idends paid will reduce cash flow, but neither will
reduce
TI.
To
explain the impact
of
equity financing, again
start with the fundamental net cash flow
relation-
receipts minus disbursements. Equity financing dis-
bursements, de
fin
ed as
EFf),
are the portion of the first
cost
of
an
asset covered
by
a corporation's own
resources.
EFt)
= corporate owned funds
Tax
Treatment Effect
on
CFAT
No
effect Increases it
Deductible Reduces it
Not deductible Reduces it
No effect
Increases it
Deductible Reduces it
Not deductible Reduces it
Any equity financing receipts are
EF
R = sale
of
corporate assets + stock sale receipts
In EFt), stock dividends are a part of disbursements,
but they are small in comparison to other disburse-
ments and their timing depends on the financial
success
of
the corporation overall,
so
they can be
neglected.
Combine the
DF
and
EF
terms to estimate annual
CFAT.
The initial investment
is
equal to the amount
of
corporate owned funds committed to the alternative's
first cost; that is,
P = EFt).
CFAT
=
-equity
financed investment
+ gross income - operating expenses
+ salvage value - taxes
+ debt financing receipts
- disbursements
+ equity financing
receipts
= - EF
f)
+ GI - E + S -
Tl(T
e)
+
(DF
R
DFf)
+
EFR
Since DFf) includes
DF"
which is the tax-deductible
portion
of
debt financing, taxes are
Taxes
=
(TI)(T.)
= (gross income - operating expenses
- depreciation - loan interest
and bond dividends)
(Te)
= (GI - E - D -
DF,)(T
e
)
These relations are easy to use when the investment
involves only
100% equity financing or 100% debt
fi-
nancing, since only the relevant terms have nonzero
values. Together they form the model for generalized
cash flow analysis.
The Financial Picture
After consulting with their accountant, the brothers
have agreed
on
the following estimates for the Port-
land branch,
if
it is pursued.
Initial investment
= $1,500,000
Annual gross income = $700,000
Annual operating expenses = $100,000
Effective tax rate = 35%
All $1.5 million
of
the initial capital investment can
be depreciated u
si
ng
MACRS with a 5-year recovery
period.
Young Brothers is not a public corporation, so
stock sales are not an option for equity financing; re-
tained earnings
mu
st be used. And a loan
is
the only
Debt
Percentage
Loan
Amount
0%
50
$ 750,000
70 1,050,000
90
1,350,000
Case Study Exercises
1.
For each funding option, perform a spreadsheet
ana
ly
sis that shows the total CFAT and its present
worth over a 6-year period, the time
it
will take to
realize the full advantage
of
MACRS deprecia-
tion.
An
after-tax return
of
10%
is
expected.
Which funding option is best for Young Broth-
ers?
(Hint: For the spreadsbeet, sample column
beadings are:
Year
, GI -
E,
Loan interest, Loan
principal, Equity investment, Depreciation rate,
Depreciation, Book value, TI, Taxes, and
CFAT.)
2.
Observe tbe cbanges
in
tbe total 6-year CFAT
as
the D-E percentages change.
If
the time value
of
money is neglected,
wh
at is the constant amount
CASE STUDY
619
viable form
of
debt financing. The loan would be
through the Seattle bank at 6% per year simple inter-
est based on the initial loan principal. Repayment
would be
in
five
equal annual payments
of
interest and
principal.
The percentage
of
debt financing is the real ques-
tion for Young Brothers.
If
the Portland branch does
not
"make it," there is a loan commitment to repay that
the Seattle operation will have
to
bear. Howeve
r,
if
the
financing is mostly from equity, the company will be
"cash poor" for a while, thus limiting its ability to fund
smaller projects
as
they arise. Therefore, a range
of
debt-equity
CD-E)
financing options to raise
th
e
$1
,500,000 should be studied. These options have
been identified:
Equity
Percentage
Investment
Amount
100% $1,500,000
50
750,000
30
450,000
10
150,000
by which this sum changes for every 10% in-
crease
in
equity funding?
3.
Charles's brother noticed that the CFAT total and
PW values go in opposite directions as the equity
percentage increases. He wants to know why tbis
pbenomenon occurs. How should Charles ex-
plain this to his brother?
4.
The brotbers have decided on the 50-50 sp.lit of
debt and equity financing. Charles wants to know
what additional bottom-line contributions
to
the
economic worth
of
the company may be added
by the new Portland office. What are the best
estimates at this time?
1
UJ
u
Formalized Sensitivity
Analysis and Expected
Value Decisions
This
chapter
includes several related
topics
about
alternative
evaluation. All
these
techniques
build
upon
the
methods
and
models
used
in
previous
chapters, especially
those
of
the
first
eight
chapters
and
the
basics
of
breakeven analysis in
Chapter
13. This
chapter
should
be
considered
prepa-
ration
for
the
topics
of
simulation
and decision
making
under
risk,
presented
in
the
next
chapter
.
The
first
two
sections
expand
our
capability
to
perform
a sensitivity analy-
sis
of
one
or
more
parameters
and
of
an
entire
alternative
. Then
the
deter-
mination
and use
of
the
expected
value
of
a cash
flow
series are
treated.
Finally,
the
technique
of
decision trees
is
covered
. This
approach
helps
an
analyst
make
a series
of
economic
decisions
for
alternatives
that
have
differ-
ent,
but
closely
connected,
stages.
The case
study
involves a
thorough
sensitivity analysis
of
a
multiple
-
alternative,
multiple-attribute
(factor)
project
set
in
the
public
sector.
LEARNING OBJECTIVES
Purpose: Perform a formal sensitivity analysis
of
one
or
more parameters; and
perform
expected value and decision
tree
evaluations
of
alternatives.
Sensitivity
to
variation
Three estimates
Expected value
Expected value
of
cash
flows
Decision
tree
This
chapter
will
help
you:
1.
Calculate a measure
of
worth
to
explain sensitivity
to
variation in
one
or
more
parameters
.
2.
Choose
the
better
alternative
using
three
estimates
for
selected
parameters.
3.
Calculate
the
expected
value
of
a variable.
4. Evaluate
an
alternative using
the
expected
value
of
cash flows.
5.
Construct
a decision
tree
and use
it
to
evaluate alternatives
stage
by
stage.
622
Cost es
rim
ates
Sec.
19.1
CHAPTER
18
Formalized
Sensitivity Analysis and
Expected
Value Decisions
18
.1 DETERMINING SENSITIVITY
TO
PARAMETER VARIATION
The
term parameter is used in this chapter to represent any variable
or
factor for
which an estimate
or
stated value is necessary. Example parameters are first cost,
salvage value,
AOC, estimated life, production rate, materials costs, etc. Esti-
mates such as the loan interest rate, and the inflation rate are also parameters
of
the analysis.
Economic analysis uses estimates
of
a parameter's future value to assist deci-
sion makers. Since future estimates are always incolTect to some degree, inaccu-
racy is present
in
the economic projections.
The
effect
of
variation may be deter-
mined by u
si
ng sensitivity analysis. In reality,
we
have applied this approach
(informally) throughout previous chapters. Usually, one factor at a time is varied,
and independence with other factors is assumed. This assumption is not com-
pletely correct
in
real world situations, but it is practical since
it
is
difficult to ac-
curately account for these dependencies.
Sensitivity analysis determines how a measure
of
worth-PW
,
AW,
ROR,
or
B/C-and
the selected alternative will be altered
if
a particular parameter varies
over a stated range
of
values.
For
example, variation
in
a parameter such as
MARR
would not alter the decision to select an alternative when all compared
alternatives return considerably more than the
MARR;
thus, the decision
is
rela-
tively
in
sensitive to the MARR. However, variation
in
the
11
value may indicate
that selection from the
same
alternatives is very sensitive to the estimated life.
Usually the variations
in
life, annual costs, and revenues result from variations
in
selling price, operation at different levels
of
capacity, inflation, etc. For exam-
ple, if an operating level
of
90
%
of
airline seating capacity for a
dome
stic route
is
compared with
50
% for a proposed international route, the operating cost and
revenue per passenger mile will increase, but anticipated aircraft life will proba-
bly decrease only slightly. Usually several important parameters are
st
udied to
learn how
th
e uncertainty
of
estimates affects the economic analysis.
Sensitivity analysis usually concentrates on the variation expected
in
est
i-
mates
of
P,
AOC,
S,
11,
unit costs, unit revenues, and similar parameters. These
parameters are often the result
of
design questions and their answers, as dis-
cussed
in
Chapter
15
. Parameters that are interest rate-based are not treated
in
the
same manner.
Parameters
such as MARR,
and
other
interest rates (loan rates, inflation
rate)
are
more stable from project to project.
If
performed, sensitivity
analysis on them is for specific values
or
over a
narrow
range
of
values.
Therefore, the sensitivity analysis
is
more constrained for interest rate
parameters.
This point is important to remember if simulation is used for decision making
under
ri
sk (C
hapter]
9).
Plotting the sensitivity
of
PW
,
AW
,
or
ROR
versus the parameter(s) studied
is very helpful. Two alternatives can be compared with respect to a given param-
eter and the breakeven point. This is the value at which the two alternatives are
SECTION
18.1
Determining Sensitivity
to
Parameter Variation
economically equivalent. However, the breakeven chart commonly represents
only one parameter per chart. Thus, several charts are constructed, and indepen-
dence
of
each parameter
is
assumed. In previous uses
of
breakeven analysis, we
computed the measure
of
worth at only two values
of
a parameter and connected
the points with a straight line. However,
if
the results are sensitive to the para-
meter value, several intermediate points should be used to better evaluate the
sensitivity, especially
if
the relationships are not linear.
When several parameters are studied, sensitivity analysis can become quite
complex.
It
may be performed one parameter at a time using a spreadsheet or
computations by hand. The computer facilitates comparison
of
multiple parame-
ters and multiple measures
of
worth, and the software can rapidly plot the results.
There
is
a general procedure to follow when conducting a thorough sensitiv-
ity analysis.
1.
Determine which parameter(s)
of
interest might vary from the most likely
estimated value.
2.
Select the probable range and an increment
of
variation for each parameter.
3.
Select the measure
of
worth.
4. Compute the results for each parameter, using the measure
of
worth as a
basis.
5.
To
better interpret the sensitivity, graphically display the parameter versus
the measure
of
worth.
This sensitivity analysis procedure should indicate the parameters that warrant
closer study or require additional information. When there are two or more alter-
natives, it is better
to
use the
PW
or A W measure
of
worth in step 3.
If
ROR is
used, it requires the extra efforts
of
incremental analysis between alternatives.
Example
IS.1 illustrates sensitivity analysis for one project.
EXAMPLE
18.1
Wi
ld Rice, Inc., expects to purchase a new asset for automated rice handli
ng.
Most likely
estimates are a
first cost
of
$80,000, zero salvage value, and a cash flow before taxes
(CFBT) per year
t that follows the relation $27,000 - 2000t. The
MARR
for the company
varies from
10% to 25% per year for different types
of
investments. The economic life
of
simiIar machinery varies from 8 to
12
years. Evaluate the sensitivity
of
PW
by
varying
(a) MARR, while assuming a constant n value
of
10
years, and (b)
n,
while MARR is con-
stant at 15% per year.
Perform the analysis by hand and
by
computer.
Solution
by
Hand
(a) Follow the procedure above to understand the sensitivity
ofPW
to
MARR variation.
I.
MARR
is
the parameter
of
interest.
2.
Select 5% increments
to
evaluate sensitivity to MARR; the range
is
10% to 25%.
3.
The measure
of
worth is
PW.
4.
Set
up
the PW relation for 10 years. When MARR = 10%,
623
pw
~
Low High
Parameters
624
CHAPTER 18
Formalized Sens
iti
vity Analysis a
nd
Expected Va
lu
e Decisions
PW =
-8
0,000 + 25,000(P/A,10%,1O) - 2000(P/ G,
1O
%,10)
= $27,830
The
PW
for all four values
at
5% intervals
is
as follows:
MAR
R
PW
10%
$
27,830
15
11,512
20
-9
62
25
-
10
,711
5.
A plot
of
MARR versus
PW
is shown in Figure 18-1.
The
steep negative slope
indicates that the decision to accept the proposal based on PW is quite sensitive
to
variations
in
the MARR.
If
the
MARR
is
established at the upper end
of
the
range, the investment
is
not attractive.
(b)
1.
Asset life n
is
the parameter.
2. Select 2-year increments
to
evaluate
PW
sensitivity over the range 8 to
12
years.
3.
The
measure
of
worth is
PW.
30,000
20,000
<1'7
10
.000
-5
15
~
c:
~
~
0
0.-
-
10
,0
00
- 20,000
Figure 18-1
10
r
I
J
6
Plot
of
PW
versus MARR and n for sensitivity analysis, Example
18.l.
MARR
%
Lif
e n