RUNNING HEAD RANK AND CITATION BIAS .docx

RUNNING HEAD: RANK AND CITATION BIAS
1
RANK AND CITATION BIAS 2
Perceived Social Status of Military Rank and Influence on
Citation bias in the Airman and NCO Tiers of Security Forces
Student Name
26 August, 2017
Professor
Perceived Social Status of Military Rank and Influence on
Citation bias in the Airman and NCO
1. PROPOSED TOPIC: How does the perceived social status
of military rank influence citation bias in the Airman and NCO
tiers of Security Forces members at Cheyenne Mountain Air
Force Station, Peterson Air Force Base, Schriever Air Force
Base and the Air Force Academy?
Social status among military members is arguably one of the

most important aspects of military heritage. Instilled from day
one at basic training, recruits are taught to be respectful, listen
to orders and act in a dignified manner. In technical training,
Security Forces members are taught about law enforcement,
base security and combat tactics. Maintaining objectivity during
traffic stops and security enforcement is paramount to
operations. What happens when social status and law
enforcement meet? How does a person’s rank affect persuasive
measures, instructions or citations used by Security Forces? In
the military there is a great sense of rank structure. Humans rely
heavily on social hierarchies to determine their behavior, as
well social status may affect motivation and wellbeing in
humans (Zink et al., 2008, p. 273). When two ideas of social
responsibility are challenged it can create cognitive dissonance.
Those that are higher ranking are expected to be respected and
treated differently than those that are lower ranking. In Security
Forces low ranking individuals often enforce rules and laws on
military instillations. Within the career field itself members are
expected to have higher standards and hold themselves above
reproach. What happens when a low ranking Security Forces
member comes in contact with a high ranking member and must
provide enforcement? Will the Security Forces member be
affected by the perception of authority as to the severity of the
citation? Will the Security Forces member operate objectively
and enforce equally? Would the Security Forces member issue
the same citation for the same infraction that was caused by two
members of different rank? In examining these questions the
fairness of citation issuing will be determined. Social status in
humans can effect physiological changes and hormone levels as
well as behaviors of fairness and differences in social
interactions, in the military social status is easily seen in the
rank structure (Siart, Pflüger, & Wallner, 2016, p. 1). This
study will look into the effects of perceived social status (rank)
on citation bias among Security Forces members in the local
Colorado Springs area.
2. RESEARCH HYPOTHESIS: Individuals in the Airman tier

will display more bias in their citations than those individuals
in the NCO tier.
NULL HYPOTHESIS: There will be no observable difference in
bias between the Airman and NCO tiers.
During this study there should be several observations made.
First there should be direct correlation between lower ranking
Security Forces members and the lesser severity of traffic
citation given to higher ranking individuals. This result should
be caused by the lack of experience and perceived authority of
the higher ranking individuals. Additionally as the rank of a
Security Forces member increases the bias should decrease.
This should be the result of increased experience as well as
decreased effects of perceived status on their decision making
process. Rank is an independent variable in this study, while
citation severity is the dependent variable. The controlled
variable or constant will be the infraction (e.g. speed infraction
of five miles per hour over the speed limit). The severity of the
citation should depend on the violators rank.
3. PARTICIPANTS: Selected from Colorado Springs area
military bases.
Due to the variety of military personnel in terms of race, gender
and age no specific demographic in this area would be selected.
Rather two groups of Security Forces would be chosen. The first
group in the Airman tier (Airman Basic through Senior Airman)
and the Non Commissioned Officer (NCO) tier (Staff Sargent
through Technical Sergeant). Due to the Senior Non
Commissioned Officer (SNCO) tier being at the upper portion
of the enlisted rank structure this tier will not be selected. Race,
gender and age will vary among the participants. General racial
statistics can offer some insight into what potential races will
participate based on overall Air Force statistics. Approximately
70% of the participants can be expected to be white, 14% Black
or African American, 3.8% Asian and the remainder American
Indian, Hawaiian, or mixed race (Air Force Personnel Center,
2017). Average age of participants according the Air Force wide
demographics will be averaging 28 years old with the majority

being blow 26 years old due to lower tiers having younger
individuals present. Finally, based on gender statistics
approximately 19.7% of the participants will be women with the
remaining 80.3% being men (Air Force Personnel Center, 2017).
These statistics reflect overall Air Force Enlisted numbers and
should be taken as approximate representations of Security
Forces specific demographic numbers at the target locations of
Peterson Air Force Base, Schriever Air Force Base, Cheyenne
Mountain Air Force Station and the Air Force Academy. The
process for selection will be volunteer based opportunity for
involvement disseminated from leadership elements to ensure
maximum amount of personnel have the opportunity for
involvement. The target participants will be at least twenty five
personnel in the Airman tier and twenty five in the NCO tier.
The reason behind selecting these specific tiers is that these are
the personnel making most contact with the public and
performing law enforcement duties. Those in the SNCO tier are
not the primary law enforcers on military installations.
4. SAMPLING METHOD: A Stratified Random Sampling
method will be used to identify the two groups of the Airman
and NCO tiers.
The purpose of this project is to gain perception on a specific
sample and later apply it to the overall Security Forces
population. The sample chosen will only be from the bases in
the Colorado Springs area. Because there are four bases this
will provide an adequate number of individuals to participate.
Determining how the sample population responds to the
stimulus throughout the project will provide insight into how
the overall population will react, also this will explain several
aspects of the overall population (Leedy & Ormrod, 2016, p.
159). Though the information may be useful in determining
trends within the overall population, the study will be limited to
one geographical region. Provided every member in the local
area is notified of the opportunity this will give the sample
population equal opportunity for participation. An easy method
to ensure this would be email notification followed up by

personal contact with potential participants. The target number
of total participants is fifty, with twenty five in the Airman tier
and twenty five in the NCO tier. These two groups will identify
the strata within the research study. Depending on the number
of respondents these numbers can be adjusted, however equal
numbers in each tier will be important in determining
differences between the two groups when it comes to bias. From
the respondents an equal number of each will be taken for the
research study. Additionally, an equal number of the separate
ranks can be taken to further study the possible change of bias
as ones rank increases. One benefits for this type of study
would be a decreased estimation error as may be present in a
simple random sampling (The Pennsylvania State University,
2017). Though these samples are not a representation of the
overall Air Force population in terms of rank proportion, the
purpose of the study is to collect information that is not
dependent on relation to overall population. Other methods of
sampling may not be as useful. It is important in this study to
have an equal number of each rank tier, the tiers are the
stratified populations within the study.
References
Air Force Personnel Center. (2017, June 30). Air Force
Demographics. Retrieved from http://www.afpc.af.mil/Air-
Force-Demographics/
Leedy, P. D., & Ormrod, J. E. (2016). Practical research:
Planning and design [Vitalsource Ebook] (11th ed.). Retrieved
from
https://bookshelf.vitalsource.com/#/books/9781323484418/cfi/6/
22!/4/2/2/[email protected]:0.00
The Pennsylvania State University. (2017). 6.1 How to Use
Stratified Sampling | STAT 506. Retrieved from
https://onlinecourses.science.psu.edu/stat506/node/27
Siart, B., Pflüger, L. S., & Wallner, B. (2016). Corrigendum:
Pulling Rank: Military Rank Affects Hormone Levels and
Fairness in an Allocation Experiment. Frontiers in Psychology,
7(1750). doi:10.3389/fpsyg.2017.00955

Zink, C. F., Tong, Y., Chen, Q., Bassett, D. S., Stein, J. L., &
Meyer-Lindenberg, A. (2008). Know Your Place: Neural
Processing of Social Hierarchy in Humans. Neuron, 58(2), 273-
283. doi:10.1016/j.neuron.2008.01.025
Sheet1InputsEquipment & shipping & installation
costs$710,000,000The salvage value of the fixed assets
(7.5%)$53,250,000Units sold, Year 12,500,000Annual change in
units sold, after Year 18.50%Sales price per unit, Year
1$260.00Annual change in sales price, after Year
12.50%Variable cost per unit (VC), Year 1$205.00Annual
change in VC, after Year 12.50%Nonvariable cost (Non-VC),
Year 1$0Annual change in Non-VC, after Year 10.00%Project
WACC12.25%Tax rate26.70%Working capital as % of next
year's sales10.00% Accelerated DepreciationDepreciable
basis:$710,000,000Rate/year10%18%14%12%9%7%7%7%7%7
%3%Dollars/year$71,000,000$127,800,000$102,240,000$81,79
2,000$65,462,000$52,327,000$46,505,000$46,505,000$46,576,
000$46,505,000$23,288,000Cash FlowsVariables Used in the
Cash Flow Forecast01234567891011Unit
sales2,500,0002,712,5002,943,0633,193,2233,464,6473,759,142
4,078,6694,425,3564,801,5115,209,6395,652,459Sales price per
unit$260$267$273$280$287$294$302$309$317$325$333Variab
le cost per
unit$205$210$215$221$226$232$238$244$250$256$262Cash
Flows At End of YearInvestment Outlays at Time =
001234567891011Equipment-$710,000,000Initial investment in
working capital-65,000,000Net Cash Flows Over the Project's
LifeSales revenues = Units ×
Price/unit$650,000,000$722,881,250$803,934,310$894,075,445
$994,323,654$1,105,812,194$1,229,801,386$1,367,692,866$1,5
21,045,429$1,691,592,648$1,881,262,473Variable costs =
Units ×
Cost/unit512,500,000569,964,063633,871,283704,944,101783,9
85,958871,890,383969,651,0931,078,373,2211,199,285,8191,33

3,755,7411,483,303,104Depreciation: Accelerated, from table
above71,000,000127,800,000102,240,00081,792,00065,462,000
52,327,00046,505,00046,505,00046,576,00046,505,00023,288,0
00Operating profit
(EBIT)$66,500,000$25,117,188$67,823,027$107,339,344$144,8
75,696$181,594,810$213,645,293$242,814,645$275,183,610$31
1,331,906$374,671,369Taxes on operating profit
17,755,5006,706,28918,108,74828,659,60538,681,81148,485,81
457,043,29364,831,51073,474,02483,125,619100,037,256Net
operating profit after
taxes$48,744,500$18,410,898$49,714,279$78,679,739$106,193,
885$133,108,996$156,602,000$177,983,135$201,709,586$228,2
06,287$274,634,114Add back
depreciation71,000,000127,800,000102,240,00081,792,00065,4
62,00052,327,00046,505,00046,505,00046,576,00046,505,0002
3,288,000Salvage value (taxed as ordinary
income)53,250,000Tax on salvage value-14,217,750Change in
WC: Outflow (–) or recovery (+)-7,288,125-8,105,306-
9,014,113-10,024,821-11,148,854-12,398,919-13,789,148-
15,335,256-17,054,722-18,966,983188,126,247Project net cash
flows: Time Line-
$775,000,000$112,456,375$138,105,592$142,940,165$150,446,
918$160,507,031$173,037,077$189,317,852$209,152,878$231,2
30,864$255,744,305$525,080,611
2. Sens.ERROR:#REF!Section 11.5 Sensitivity AnalysisTab 2
extends the basic model (shown in Tab 1) to include sensitivity
analysis. Tab 2 also illustrates special cases of sensitivity
analysis, incuding breakeven analysis, one-way data tables with
multiple outputs, and two-way data tables. We also include a
brief tutorial for Data Tables.For ease of reference, we repeat
Figure 11-1, Analysis of an Expansion Project: Inputs and Key
Results (Dollars in Thousands)Part 1. Inputs and Key
ResultsInputsBase-CaseKey Results Equipment cost$3,400NPV
$36Salvage value, equipment, Year
4$300IRR10.35%Opportunity cost$0MIRR10.23%Externalities
(cannibalization)$0PI1.01Units sold, Year

1550Payback3.41Annual change in units sold, after Year
14.00%Discounted payback3.98Sales price per unit, Year
1$11.60Annual change in sales price, after Year
12.00%Variable cost per unit (VC), Year 1$6.00Annual change
in VC, after Year 12.00%Nonvariable cost (Non-VC), Year
1$2,000Annual change in Non-VC, after Year 12.00%Project
WACC10.00%Tax rate40.00%Working capital as % of next
year's sales12.65%If you change any of the blue values above,
the model below will change instantly, causing changes in NPV
and other output variables. You can see the effect in the Key
Results box shown above. If you change an input value but later
want to return to the base case, use Scenario Manager to select
the Base-Case. In Excel 2003, select Tools, Scenarios. In Excel
2007, select Data, What-If-Analysis, Scenario Manager.For ease
of reference, we repeat Figure 11-2. Analysis of a New
(Expansion) Project: Cash Flows and Performance Measures
(Dollars in Thousands)Part 2. Cash Flows and Performance
MeasuresVariables Used in the Cash Flow Forecast01234Unit
sales550572595619Sales price per
unit$11.60$11.83$12.07$12.31Variable cost per
unit$6.00$6.12$6.24$6.37Nonvariable costs (excluding
depreciation)$2,000$2,040$2,081$2,122Cash Flows At End of
YearInvestment Outlays at Time = 001234Equipment-
$3,400Initial investment in working capital-807Opportunity
cost, after taxes0Net Cash Flows Over the Project's LifeSales
revenues = Units ×
Price/unit$6,380$6,768$7,179$7,616Variable costs = Units ×
Cost/unit3,3003,5013,7133,939Nonvariable costs (excluding
depreciation)2,0002,0402,0812,122Depreciation: Accelerated,
from table below1,1221,530510238Operating profit (EBIT)-
$42-$303$875$1,316Taxes on operating profit -17-
121350526Net operating profit after taxes-$25-
$182$525$790Add back
depreciation1,1221,530510238Opportunity cost, after
taxes0000Cannibalization or complementary effects, after
taxes0000Salvage value (taxed as ordinary income)300Tax on

salvage value (SV is taxed at 40%)-120Change in WC: Outflow
(–) or recovery (+)-49-52-55963Project net cash flows: Time
Line-$4,207$1,048$1,296$980$2,171Project EvaluationResults
NPV $36IRR10.35%MIRR10.23%Profitability
index1.01Payback3.41Discounted payback3.98Calculations for
PaybackYear:01234 Cumulative cash flows for payback-
$4,207-$3,159-$1,863-$883$1,288 Discounted cash flows for
disc. payback-$4,207$952$1,071$736$1,483 Cumulative
discounted cash flows-$4,207-$3,255-$2,183-$1,447$36
Accelerated DepreciationDepreciable
basis:$3,400Rate/year33%45%15%7%Dollars/year$1,122$1,530
$510$238SENSITIVITY ANALYSIS (Section 11.5)Risk in
capital budgeting really means the probability that the actual
outcome will be worse than the expected outcome. For example,
if there were a high probability that the expected NPV as
calculated above will actually turn out to be negative, then the
project would be classified as relatively risky. The reason for a
worse-than-expected outcome is, typically, because sales were
lower than expected, costs were higher than expected, or the
project turned out to have a higher than expected initial cost. In
other words, if the assumed inputs turn out to be worse than
expected, then the output will likewise be worse than expected.
We use data tables below to examine the project's sensitivity to
changes in the input variables.Following is a tutorial for
constructing a Data Table to be used in sensitivity analysis.
This section may be skipped if you already know how to
construct data tables.Instructions for Constructing Data
Tables:Step 1:DeviationSalesNPV Set up the Data Table by
typing in the labels and numbers shown here. The column for
sales price/unit is the input range and the column for NPV is the
output range. Data Tables take each input value and then
automatically calculate a new output based on the input. Be sure
to type in the actual sales price of $11.60 and not a formula.
Every year we have students who make this mistake! Don't be
one of them!from BasePrice/unit-30%0%$11.6030%Step
2:DeviationSalesNPV Enter the formula =$B$117*(1+A116)

into the light green cell and then copy it into the light blue cell.
This sets up the input range's values of sales prices for which
you want new NPV's to be calculated. It is ok to have a formula
in the input range, but be sure that none of these inputs is a
formula that refers back to the actual value of sales in the input
section of the worksheet.from BasePrice/unit-
30%$8.120%$11.6030%$15.08Step 3:DeviationSalesNPV
Enter into the tan cell a formula that refers to the cell in the
results section which shows the NPV for the given set of inputs.
In this example, that is =$I$15. Notice that the tan cell will
show the current value of NPV.from BasePrice/unit$35.84-
30%$8.120%$11.6030%$15.08DeviationSalesNPVNow use your
cursor to hightlight the range we show in gray (this is called the
Data Table range); notice that this highlighted range includes
the cells for the new inputs for price and the cell for the
reference to NPV.from BasePrice/unit$35.84-
30%$8.120%$11.6030%$15.08With the range still highlighted,
open the Table dialog box. In Excel 2003, you go the Main
Menu, select Data, then Table. In Excel 2007, select Data,
What-If-Analysis, then Data Table.This next step is a bit tricky,
so be careful. The cursor in the dialog box will be blinking in
the "Row input cell:" box. Here you have to tell Excel if the
inputs in your Data Table are arranged in a row or a column.
Excel assumes a row, but this is not correct in our example--
your inputs are in a column, Column B. So, you click on the
"Column input cell" box, causing the cursor to blink in that
box.Excel wants to know where the input variable, sales price,
first enters the model. If you look up in the Input Data section,
you will see that it enters in cell E21, so you type E21 in the
Column input cell (or click on cell E21 to enter it). Here's the
final, completed, dialog box:When you click OK, Excel will
calculate NPV at the three input values specified in your Data
Table, insert them in the table, leaving the Data Table as shown
below.DeviationPriceNPVfrom Base$35.84-30%$8.12-
$3,838.740%$11.60$35.8430%$15.08$3,910.42We used Data
Tables to create inputs for the sensitivity graph. (First, be sure

the Base-Case scenario is showing.) Note that the portion of the
rows that are in the Data Tables are shown in shaded
colors.Deviation
Mike Ehrhardt: Change the cells below to get different
deviations. All other inputs will be updated
automatically.EquipmentNPVDeviationUnit
SalesNPVDeviationSales Price/unitNPVfrom Base$36from
Base$36from Base$36-30%$2,380$716-30%385-$1,791-
30%$8.12-$3,8390%3,400360%550360%11.603630%4,420-
64530%7151,86330%15.083,910DeviationVC/UnitNPVDeviatio
nNon-VCNPVDeviationProject WACCNPVfrom Base$36from
Base$36from Base$36-30%$4.20$2,083-30%$1,400$1,209-
30%7.00%$3610%6.00360%2,000360%10.00%3630%7.80-
2,01130%2,600-1,13730%13.00%-254The following graph is
meaningful only if the scenario is set to the Base-Case.Figure
11-3. Sensitivity Graph for Solar Water Heater Project (Dollars
in Thousands)Data for Sensitivity Graph DeviationNPV with
Variables at Different Deviations from Basefrom
BaseEquipmentPriceUnitsVC/UnitNon-VCWACC-30%$716-
$3,839-$1,791$2,083$1,209$3610%$36$36$36$36$36$3630%-
$645$3,910$1,863-$2,011-$1,137-
$254Range$1,361$7,749$3,655$4,095$2,346$615Tornado
DiagramsTornado diagrams are another way to present results
from sensitivity analysis. The first step is to rank the range of
possible NPV's for each of the input variables that is being
changed. In our example, the range for sales price/unit is the
largest and the range for WACC is the smallest. The ranges for
each variable are then plotted, with the largest range on top and
the smallest range on the bottom. It is helpful to also plot a
vertical line showing the base-case NPV. We present a tornado
diagram in Figure 11-4. Notice that the diagram is like a
tornado in that it is widest at the top and smallest at the bottom,
hence its name. The tornado diagram makes it immediately
obvious which inputs have the biggest impact on NPV.
Additional data for Tornado DiagramScratch for Tornado

Diagram BelowRank of Range of NPV from Sensitivity Table
AboveEquipmentPriceUnitsVC/UnitNon-VCWACCBase NPV
=Y-axisRank264531$368For diagram
below264531366264531361Figure 11-4. Tornado Diagram for
Solar Water Heater Project: Range of Outcomes for Input
Deviations from Base-Case (Dollars in Thousands)NPV
Breakeven AnalysisIn breakeven analysis, we find the value of
the input variable that produes a zero NPV. It is easiest to do
this with Goal Seek. For example, the screen shot below shows
the Goal Seek inputs we used to set the cell for NPV to a value
of zero by changing the cell for the sales price. We repeated
this for the other inputs.Table 11-1. NPV Breakeven Analysis
(Dollars in Thousands)InputInput Value that Produces Zero
NPVSales price per unit, Year 1$11.57Variable cost per unit
(VC), Year 1$6.03Annual change in units sold, after Year
13.58%Units sold, Year 1547Nonvariable cost (Non-VC), Year
1$2,018Project WACC10.35%Data Tables: Multiple Outputs for
a Single InputData tables can easily be extended to show
multiple outputs for a single input. Simply add an additional
column with a cell reference to the desired additional output.
Highlight the specified values for the input and highlight all the
columns for the output as we show shaded in gray below (be
sure to also highlight the cell references above the outputs).
Then use the Data, Tables, and set "Column input" to the cell
refernce of the desired input. Example: NPV and IRR for
Changes in Sales Price% DeviationSALES
PRICEfromSalesNPVIRRBase CasePrice$3610.4%-30%$8.12-
$3,839-45.0%-15%$9.86-$1,901-
11.3%0%$11.60$3610.4%15%$13.34$1,97327.8%30%$15.08$3,
91042.8%Two-Way Data Tables: Two Inputs and One
OutputData tables can also be extended to show the output
given two inputs. Put one set of input variables in the left-most
column of the data table (shown in a red font below) and the
other set of inputs in the top row of the data table (shown in
white font); put the cell reference to the output you want (like
NPV) in the intersection of the row and column for inputs (we

show this in a pale green font). Highlight the range that
includes the specified values for the inputs, as shown in the
gray shaded region below (this will also highlight the cell
reference for the output). Then use the Data, Tables, and set
"Row input" to the cell reference for the inputs shown in the
table's row E19 for units sold) and set "Column input" to the
cell refernce for the input shown in the table's column E21 for
sales price). Example: NPV for Changes in Sales Price and
Units Sold% Deviation from Base Case-30%-15%0%15%30%%
Deviation fromNPV cell referenceUnits SoldBase
Case$36385468550633715-30%Sales Price$8.12-$4,504-$4,171-
$3,839-$3,506-$3,174-15%$9.86-$3,148-$2,525-$1,901-$1,278-
$6550%$11.60-$1,791-$878$36$949$1,86315%$13.34-
$435$769$1,973$3,177$4,38230%$15.08$921$2,416$3,910$5,4
05$6,900
Price
-0.3 0 0.3 -3838.7448808082895 35.836539226936111
3910.4179592621649 Units
-0.3 0 0.3 -1791.4880445614981 35.836539226936111
1863.1611230153703 VC/Unit
-0.3 0 0.3 2083.0933754737289 35.83
6539226936111 -2011.4202970198558 Non-VC
-0.3 0 0.3 1208.9157551274893 35.836539226936111
-1137.2426766736166 Equipment
-0.3 0 0.3 716.21367193644983 35.836539226936111
-644.54059348257761 WACC
-0.3 0 0.3 360.566849929417 35.836539226936111 -
253.98814890681342
% Deviation from Base

NPV
($)
Price
-3838.7448808082895 35.836539226936111
3910.4179592621649 6 6 6 Units
-1791.4880445614981 35.836539226936111
1863.1611230153703 4 4 4 VC/Unit
2083.0933754737289 35.836539226936111 -
2011.4202970198558 5 5 5 Non-VC
1208.9157551274893 35.836539226 936111 -
1137.2426766736166 3 3 3 Equipment
716.21367193644983 35.836539226936111 -
644.54059348257761 2 2 2 WACC
360.566849929417 35.836539226936111 -
253.98814890681342 1 1 1 Base NPV =
35.836539226936111 35.836539226936111
35.836539226936111 8 6 1
NPV
1
2
3
1
2
4

3
3
3. Scen.ERROR:#REF!Section 11.6 Scenario AnalysisTab 3
extends the basic model (shown in Tab 1) to include scenario
analysis. On this tab we modify the Tab 1 Basic Model in
several ways (but note that only the accelerated depreciation
case is analyzed here).We add worst-case and best-case
scenarios, including the probability that each scenario will
occur, as shown below in Figure 11-5. Management determined
that some of the inputs were not likely to stray far from the
base-case levels, and the NPV was not terribly sensitive to them
anyway, so in our analysis we change only 6 inputs: equipment
cost, units sold in Year 1, annual change in units sold after Year
1, sales price per unit, variable cost per unit, nonvariable cost,
and the tax rate. Management gathered advice from experts in
their marketing, operations, logistics, HR, accounting, and
finance departments for the probability of each scenario and the
values to use for the worst-case and best-case scenarios.We
show these base-case, worst-case, and best-case value in the
input columns for scenarios in Figure 11-5 below, identified by
the cells with larger, non-black fonts. If you change any input
for any scenario, the key results shown immediately below the
input column will be updated, but our analysis focuses only on
the 7 critical inputs determined by management.If you change
an input for the Base-Case scenario in Column E below, it will
make changes in the analysis section for the Base-Case shown
below Figure 11-5. If you make a change in the inputs for the
Worst-Case scenario (in Column G below), it will make changes
in the analysis section for the Worst-Case shown in yellow to
the right and below Figure 11-5. Similarly, if you make make a
change in the inputs for the Best-Case scenario (in Column I
below), it will make changes in the analysis section for the
Best-Case shown in green to the right and below Figure 11-
5.Analysis for Worst and Best Scenarios in yellow and green
boxes below and to the right.Figure 11-5. Inputs and Key
Results for Each Scenario (Dollars in Thousands)Don’t change

any values in the yellow box below.
If you want to change an input, do it in Column G to the
left.Don’t change any values in the green box below.
If you want to change an input, do it in Column I to the
left.Scenarios:Worst-Case ScenarioBest-Case
ScenarioInputs:BaseWorstBestInputsWorstInputsBestProbabilit
y of Scenario50%25%25%Equipment
cost$3,400$4,250$2,550Equipment cost$4,250Equipment
cost$2,550Salvage value, equipment, Year
4$300$300$300Salvage value, equipment, Year 4$300Salvage
value, equipment, Year 4$300Opportunity
cost$0$0$0Opportunity cost$0Opportunity cost$0Externalities
(cannibalization)$0$0$0Externalities
(cannibalization)$0Externalities (cannibalization)$0Units sold,
Year 1550412688Units sold, Year 1412Units sold, Year
1688Annual change in units sold, after Year 14.00%-
6.00%14.00%Annual change in units sold, after Year 1-
6.00%Annual change in units sold, after Year 114.00%Sales
price per unit, Year 1$11.60$8.70$14.50Sales price per unit,
Year 1$8.70Sales price per unit, Year 1$14.50Annual change in
sales price, after Year 12.00%2.00%2.00%Annual change in
sales price, after Year 12.00%Annual change in sales price,
after Year 12.00%Variable cost per unit (VC), Year
1$6.00$7.50$4.50Variable cost per unit (VC), Year
1$7.50Variable cost per unit (VC), Year 1$4.50Annual change
in VC, after Year 12.00%2.00%2.00%Annual change in VC,
after Year 12.00%Annual change in VC, after Year
12.00%Nonvariable cost (Non-VC), Year
1$2,000$2,500$1,500Nonvariable cost (Non-VC), Year
1$2,500Nonvariable cost (Non-VC), Year 1$1,500Annual
change in Non-VC, after Year 12.00%2.00%2.00%Annual
change in Non-VC, after Year 12.00%Annual change in Non-
VC, after Year 12.00%Project
WACC10.00%10.00%10.00%Project WACC10.00%Project
WACC10.00%Tax rate40.00%50.00%30.00%Tax
rate50.00%Tax rate30.00%Working capital as % of next year's

sales12.65%12.65%12.65%Working capital as % of next year's
sales12.65%Working capital as % of next year's
sales12.65%Key Results:BaseWorstBestKey Results:WorstKey
Results:BestNPV $36-$5,847$13,379NPV -$5,847NPV
$13,379IRR10.35%Not found112.01%IRRNot
foundIRR112.01%MIRR10.23%-100.00%60.30%MIRR-
100.00%MIRR60.30%PI1.01-0.244.51PI-
0.24PI4.51Payback3.41Not found1.00PaybackNot
foundPayback1.00Discounted payback3.98Not
found1.09Discounted paybackNot foundDiscounted
payback1.09Analysis for Base-Case Scenario shown in blue box
below.BaseWorst-Case ScenarioBest-Case ScenarioVariables
Used in the Cash Flow Forecast01234Variables Used in the
Cash Flow Forecast01234Variables Used in the Cash Flow
Forecast01234Unit sales550572595619Unit
sales412387364342Unit sales6887848941,019Sales price per
unit$11.60$11.83$12.07$12.31Sales price per
depreciation)$2,000$2,040$2,081$2,122Nonvariable costs
(excluding depreciation)$2,500$2,550$2,601$2,653Nonvariable
costs (excluding depreciation)$1,500$1,530$1,561$1,592Cash
Flows At End of YearCash Flows At End of YearCash Flows At
End of YearInvestment Outlays at Time = 001234Investment
Outlays at Time = 001234Investment Outlays at Time =
001234Equipment-$3,400Equipment-$4,250Equipment-
$2,550Initial investment in working capital-807Initial
investment in working capital-453Initial investment in working
capital-1,262Opportunity cost, after taxes0Opportunity cost,
after taxes0Opportunity cost, after taxes0Net Cash Flows Over
the Project's LifeNet Cash Flows Over the Project's LifeNet
Cash Flows Over the Project's LifeSales revenues = Units ×
Price/unit$6,380$6,768$7,179$7,616Sales revenues = Units ×

Price/unit$9,976$11,600$13,489$15,685Variable costs = Units
× Cost/unit3,3003,5013,7133,939Variable costs = Units ×
Cost/unit3,0902,9632,8412,724Variable costs = Units ×
depreciation)2,0002,0402,0812,122Nonvariable costs (excluding
from table below1,1221,530510238Depreciation: Accelerated,
from table below8421,148383179Operating profit (EBIT)-$42-
$303$875$1,316Operating profit (EBIT)-$3,408-$3,988-$2,784-
$2,515Operating profit (EBIT)$4,539$5,323$7,359$9,047Taxes
on operating profit -17-121350526Taxes on operating profit -
1,704-1,994-1,392-1,257Taxes on operating profit
1,3621,5972,2082,714Net operating profit after taxes-$25-
$182$525$790Net operating profit after taxes-$1,704-$1,994-
$1,392-$1,257Net operating profit after
taxes$3,177$3,726$5,152$6,333Add back
depreciation1,1221,530510238Add back
depreciation8421,148383179Opportunity cost, after
taxes0000Opportunity cost, after taxes0000Opportunity cost,
after taxes0000Cannibalization or complementary effects, after
taxes0000Salvage value (taxed as ordinary income)300Salvage
value (taxed as ordinary income)300Salvage value (taxed as
ordinary income)300Tax on salvage value (SV is taxed at 40%)-
120Tax on salvage value (SV is taxed at 40%)-150Tax on
(–) or recovery (+)-49-52-55963Change in WC: Outflow (–) or
recovery (+)191817400Change in WC: Outflow (–) or recovery
(+)-205-239-2781,984Project net cash flows: Time Line-
$4,207$1,048$1,296$980$2,171Project net cash flows: Time
Line-$4,703-$283-$64-$737-$410Project net cash flows: Time

Line-$3,812$3,813$4,634$5,256$8,705Project
EvaluationProject EvaluationProject EvaluationResults Results
Results NPV $36NPV -$5,847NPV
$13,379IRR10.35%IRRERROR:#NUM!IRR112.01%MIRR10.23
%MIRR-100.00%MIRR60.30%Profitability
index1.01Profitability index-0.24Profitability
index4.51Payback3.41PaybackERROR:#N/APayback1.00Discou
nted payback3.98Discounted paybackERROR:#N/ADiscounted
payback1.09Calculations for PaybackYear:01234Calculations
for PaybackYear:01234Calculations for PaybackYear:01234
Cumulative cash flows for payback-$4,207-$3,159-$1,863-
$883$1,288 Cumulative cash flows for payback-$4,703-
$4,986-$5,050-$5,787-$6,198 Cumulative cash flows for
payback-$3,812$1$4,635$9,892$18,597 Discounted cash flows
for disc. payback-$4,207$952$1,071$736$1,483 Discounted
cash flows for disc. payback-$4,703-$257-$53-$554-$280
Discounted cash flows for disc. payback-
$3,812$3,466$3,830$3,949$5,946 Cumulative discounted cash
flows-$4,207-$3,255-$2,183-$1,447$36 Cumulative discounted
cash flows-$4,703-$4,961-$5,013-$5,567-$5,847 Cumulative
discounted cash flows-$3,812-$346$3,484$7,434$13,379
Accelerated Depreciation Accelerated Depreciation
basis:$3,400Rate/year33%45%15%7%Depreciable
$510$238Dollars/year$1,403$1,913$638$298Dollars/year$842$
1,148$383$179Scenario analysis extends risk analysis in two
ways: (1) It allows us to change more than one variable at a
time, hence to see the combined effects of changes in several
variables on NPV, and (2) It allows us to bring in the
probabilities of changes in the key variables.Figure 11.6 (shown
below) presents the cash flows for each scenario (the cash flows
are obtained from the 3 scenarios' analsyes conducted above in
the blue, bright yellow, and green boxes). It also shows the
NPV for each scenario. Using the NPV and probability for each

scenario, we calculate the expected NPV, the standard
deviation, and the coefficient of variation. Later in the analysis
we consider the possibility of abandoning the project if the
worst case occurs, but our present analysis assumes that we
cannot abandon the project.Note: the scenario analysis below is
meaningful only if the values in the input section in Cells
E37:E51 are set to the original base-case.Figure 11-6. Scenario
Analysis: Expected NPV and Its Risk (Dollars in
Thousands)Predicted Cash Flows for Alternative
ScenariosCalculating σ step-by-stepQuick NPV and
sProb:01234WACCNPVDeviationSqrd devSqrd*prob Best25%-
$3,812$3,813$4,634$5,256$8,70510.00%$13,379114781317556
42$32,938,910Base50%-
$4,207$1,048$1,296$980$2,17110.00%$36-
18653478447$1,739,224 Worst 25%-$4,703-$283-$64-$737-
$41010.00%-$5,847-774860037190$15,009,298Expected NPV
=$1,901Variance =$49,687,432$1,901 =Expected NPVStandard
Deviation (SD) =$7,049σ =$7,049$7,049 = Standard
Deviation (SD)Coefficient of Variation (CV) = Std.
Dev./Expected NPV =3.71Scratch work for chartWorst-Case-
$5,84725%-$5,8470%Most-Likely$3650%$360%Best-
Case$13,37925%$13,3790%Expected NPV$1,9010%$1,901-
15%Scenario ManagerRather than have 3 sets of analyses, it is
possible to have only one set and use the Excel feature called
Scenario Manager. (To open the Scenario Manager dialog box in
Excel 2003, select Tools, Scenarios; in Excel 2007, select Data,
What-if-Analysis, then Scenarios.) If you open the Scenario
Manager dialog box, you see the box shown below:You can
select a scenario, click "Show", and the values for that scenario
will be substituted into the input cells in Column E (E35:E51).
So if we had not repeated the analysis in Columns K through
AC, Scenario Manager makes it easy to show any set of inputs
in a single model for analysis. Scenario Manager also makes it
easy to create a summary of all scenarios using the Summary
feature in the dialog box shown above. For example, if you
select Summary, you will see the box below:We selected the

cells with key results, E53:E58. When you click OK, the output
of the summary will be created in a new worksheet; this new
worksheet is "8. Scenario Summary". It provides the same key
results as the three separate analyses did, but you need only to
create one analysis with multiple sets of inputs saved as
scenarios. We encourgage you to explore the Scenaro Manager
feature in our Excel Tutorial.Figure 11-6. Scenario Analysis:
Can AbandonPredicted Cash Flows for Alternative
ScenariosCalculating σ step-by-
stepProb:01234WACCNPVDeviationSqrd
devSqrd*probBest25%-
$3,812$3,813$4,634$5,256$8,70510.00%$13,379$11,153124,39
9,61631,099,904Base 50%-
$4,207$1,048$1,296$980$2,17110.00%$36-
$2,1904,796,4862,398,243Worst -$4,703-$283-$64-$737-
$41025%-$4,703-$283$500$0$010.00%-$4,547-
$6,77345,877,34211,469,336If abandon, can liquidate for $500
at t = 2.Expected NPV =$2,226Variance =44,967,482Standard
Deviation (SD) =$6,706σ =$6,706Coefficient of Variation
(CV) = Std. Dev./Expected NPV =3.01Figure 11-7. Decision
Tree with Multiple Decision PointsFirm can abandon the project
at t = 2WACC =10.0%Time Periods, Cash Flows, Probabilities,
and Decision PointsWACC =10.0%0123456WACC
=10.0%Product: NPVCalculating σ step-by-step1st
InvestProb.2nd InvestProb.3rd
InvestInflowInflowInflowInflowNPVJoint Prob x Joint
ProbDeviationSqrd devSqrd*prob45%-
$3,812$3,813$4,634$5,256$8,705$10,50336%$3,781$25564782
$23,32180%-$50040%-$4,207$1,048$1,296$980$2,171-
$52532%-$168-3694136490414367693.00407027-
$10015%Stop$0$0$0$0-$55512%-$67-
$3,59312909858$1,549,18320%Stop$0$0$0$0$0-$10020%-$20-
3546125775472515509Expected NPV =$3,526Sum =
variance8455707Standard Deviation (SD) =$2,908Sq root of
Var = σ$2,908Coefficient of Variation (CV) = Std.
Dev./Expected NPV =0.82

1
Probability Distribution of Scenarios:
Outcomes and Probabilities
Worst-Case
-5847.4708240748023 -5847.4708240748023 0.25 0
Most-Likely
35.836539226936111 35.836539226936111 0.5 0
Best-Case
13379.382149246569 13379.382149246569 0.25 0
Expected NPV
1900.8961009064096 1900.8961009064096 0 -0.15
NPV
1
2
1
2
3
3
3
2
4. Sim.ERROR:#REF!Section 11.7 Scenario AnalysisNote: this
section is relatively technical and some instructors may choose
to skip it with no loss in continuity.Monte Carlo simulation is
similar to scenario analysis in that different values of key inputs
are used. Unlike scenario analysis, Monte Carlo simulation
draws a trial set of input values from specified probability
distributions and then computes the NPV for this trial. This
process is repeated for hundreds, or even thousands, of trials,

with key results (like NPV) saved from each trial. After
running the number of desired trials, the NPVs from the trials
can be averaged to estimate the project's expected NPV; the
trial results can also be used to provide a histogram showing the
project's possible outcomes.Panel A, shown in the blue-bordered
box below and slightly to the right, shows the inputs from the
previous scenario analysis. It also shows the expected value and
standard deviation for those inputs based on the probability of
each scenario. To compare apples and apples, we will assume
that the inputs for the simulation analysis are drawn from a
normal distribution with the same expected value and standard
deviation as the inputs from the scenario analysis (these are
shown Figure 11-7 in blue in Columns C and D below.
However, any of the the blue values in Columns C and D may
be changed by the user if desired. Cell D53 also has the input
for the assumed correlation between units sold in Year 1 and
changes in units sold in later years.Fgirue 11-7, shown in the
box below, also shows the trial inputs and key results. The
inputs are shown in red and are drawn from a normal
distribution with the mean and standard deviation specified in
Columns C and D. We do this in a 2-step process. Column E
shows a standard normal random variable created with Excel's
random number generator. Column F transforms the standard
normal random variable into a normal random variable with the
desired mean and standard deviation. To see updated values,hit
the F9 key.Figure 11-7: Inputs and Key Results for the Current
Simulation Trial (Dollars in Thousands)Panel A: Values from
Scenario Analysis and Their Expected Values and Standard
DeviationsTo change an input, change one of the blue values in
Columns C or D. To see an updated set of trial values, hit the
F9 key. Inputs and key results will update for the current
trial.Inputs for Simulation Probability DistributionsRandom
Variables Used in Current Simulation TrialInputs from Scenario
Analysis for Comparison to SimulationExpected Value of
InputStandard Deviation of InputStandard Normal Random
Variable

Mike Ehrhardt: The RAND() function generates a random
number between 0 and 1. When this value is the argument in the
NORMSINV function, the NORMSINV interprets the value as
the cumulative probability of a standard normal distribution.
Then the NORMSINV function finds a standard normal variable
Z such that its the probability of drawing a value of Z or less is
equal to the argument. This means the formula
=NORMSINV(RAND()) returns a random standard normal
variable. Value used in Current TrialBaseWorstBestExpected
Value of InputStandard Deviation of InputProbability of
Scenario50%25%25%Inputs:Equipment cost$3,400$601-
0.69$2,987$3,400$4,250$2,550$3,400$601Salvage value,
equipment, Year 4$300$300$300$300Opportunity
cost$0$0$0$0Externalities (cannibalization)$0$0$0$0Units
sold, Year 1550980.5059955041268855098Annual change in
units sold, after Year 14.00%7.07%-0.13
Mike Ehrhardt: We must use a slightly different formula to get a
standard normal for the annual change in units that is correlated
with the unit sales in the first year. We do that by forming a
variable that is a combination of the standard normal variable
for units in the 1st year and an uncorrelated standard normal,
with the "weights" in the combination depending on the desired
correlation.3.08%4.00%-6.00%14.00%4.00%7.07%Sales price
per unit, Year 1$11.60$2.05-
0.05$11.51$11.60$8.70$14.50$11.60$2.05Annual change in
sales price, after Year 12.00%2.00%2.00%2.00%Variable cost
per unit (VC), Year
1$6.00$1.061.33$7.41$6.00$7.50$4.50$6.00$1.06Annual
change in VC, after Year 12.00%2.00%2.00%2.00%Nonvariable
cost (Non-VC), Year
1$2,000$3540.38$2,136$2,000$2,500$1,500$2,000$354Annual
change in Non-VC, after Year 12.00%2.00%2.00%2.00%Project
WACC10.00%10.00%10.00%10.00%Tax rate40.00%7.07%-
0.2038.60%40.00%50.00%30.00%40.00%7.07%Working capital

as % of next year's sales12.65%12.65%12.65%12.65%Assumed
correlation between units sold in Year 1 and annual change in
units sold in later years:r =65.00%Key Results Based on
Current TrialKey ResultsBaseWorstBestNPV -$1,342$36-
$5,847$13,379IRR-4.95%10.35%Not found112.01%MIRR-
1.14%10.23%-100.00%60.30%PI0.651.01-0.244.51PaybackNot
found3.41Not found1.00Discounted paybackNot found3.98Not
found1.09Panel B: Project Analysis for Current Trial in
SimulationVariables Used in the Cash Flow Forecast01234Unit
sales599617636656Sales price per
depreciation)$2,136$2,179$2,223$2,267Cash Flows At End of
YearInvestment Outlays at Time = 001234Equipment-
$2,987Initial investment in working capital-872Opportunity
cost, after taxes0Net Cash Flows Over the Project's LifeSales
revenues = Units ×
Price/unit$6,891$7,245$7,617$8,009Variable costs = Units ×
$941$44$378Taxes on operating profit -257-36317146Net
operating profit after taxes-$409-$578$27$232Add back
taxes0000Salvage value (taxed as ordinary income)300Tax on
(–) or recovery (+)-45-47-501,013Project net cash flows: Time
Line-$3,858$532$719$426$1,639Project EvaluationResults
NPV -$1,342IRR-4.95%MIRR-1.14%Profitability
index0.65PaybackERROR:#N/ADiscounted
paybackERROR:#N/ACalculations for PaybackYear:01234
$2,182-$543 Discounted cash flows for disc. payback-
$3,858$483$594$320$1,119 Cumulative discounted cash
flows-$3,858-$3,375-$2,780-$2,461-$1,342 Accelerated

DepreciationDepreciable
basis:$2,987Rate/year33%45%15%7%Dollars/year$986$1,344$
448$209How the Simulation WorksWe use a Data Table to
perform the simulation (the Data Table is below shaded in
lavender). When the Data Table is updated, it will insert new
random variables for each of the inputs we allow to change in
Figure 11-7 above, run the analysis in Panel B above, and then
save the NPV for each trial. (We also save the input variables
for each trial so that we can verify that they are behaving as we
expect.) We set the first column of the Data Table (the variable
to be changed in each row) to numbers from 1-100. We don't
really use these numbers anywhere in the analyis, but if we tell
the Data Table to treat these as the Column inputs, Excel will
recalculate all items in the Data Table, including the random
inputs and the resulting NPV. In other words, we "trick" Excel
into doing a simulation. We tell Excel to insert each of the
Column inputs in the Data Table into the cell immediately
below this box. This cell isn't linked to anything else, but each
time Excel updates a row of the Data Table, all the random
values will be updated.Column input cell to "trick" Excel into
updating random variables in Data Table:1
Mike Ehrhardt: Do not delete or change this cell or row.Don't
change the the red cell.Excel normally updates all values in a
Data Table each time any cell that is related to the Data Table
changes. In our case, we have random variables in the Data
Table, so each time any cell in the worksheet makes a
calculation, the Data Table is updated. If the Data Table has
many rows, updating it can take up to 20 or 30 seconds. This is
ok when we want to update the Table, but it is annoying to wait
30 seconds any time we make any changes in the worksheet.
The "check box" explained below helps with this annoyance.To
put random variables in the Data Table for the simulation, the
box shown below must be checked; otherwise, the Data Table
contains only zero's and doesn't update when the sheet makes a
calculation (other than the first time you check this box or if

you insert or delete rows or columns). If the box is unchecked
and you check it, the check mark won't show up until the Table
is updated, so don't get impatient and click it twice. After you
have checked the box, the Data Table will update any time you
change a cell in the worksheet. So to make the Data Table
update, make sure the box is checked and then hit the F9
key.Put a check in the box below to put trials into the data
table; otherwise, the data table will have only
zeros.FALSERemember to uncheck the box above when you are
through with the simulation, or the Data Table will recalculate
any time you make a change in the worksheet, which will slow
down all other calculations in the worksheet. You don't need to
change anything in this section. It will be updated
automatically if you do a simulation. The summary of the
simulation results and the histogram are based on the simulation
trials n the Data Table below and are updated automatically
when you do a simulation. Note: If results ae all zeros, go back
to row 144 and "check" the box by clicking it with your
cursor.Figure 11-8 Summary of Simulation Results (Thousands
of Dollars)Number of Trials =0Simulated Input
VariablesEquipment costUnits sold, Year 1Annual change in
units sold, after Year 1Sales price per unit, Year 1Variable cost
per unit (VC), Year 1Nonvariable
cost
(Non-VC), Year 1Tax rateKey Results:NPV
Average$000.0%$0.00$0.00$00.0%$0Standard
deviation000.0%0.000.0000.0%$0Maximum000.0%0.000.0000.0
%$0Minimum000.0%0.000.0000.0%$0Correlation with unit
salesERROR:#DIV/0!Median$0Probability of NPV >
0ERROR:#DIV/0!Coefficient of
variationERROR:#DIV/0!Scratch work for chart: see
comments.Count
Mike Ehrhardt: This column counts the umber of simulation
trials with NPVs greater than the bottom of range and less than
top the top of the range.Range bottom

Mike Ehrhardt: This column of data contains the ranges into
which the NPV's are grouped. The numbers shown are the
bottoms of each range. The ranges are automatically selected so
that the ranges will fit the data for the particular simulation.
Mike Ehrhardt: The RAND() function generates a random
number between 0 and 1. When this value is the argument in the
NORMSINV function, the NORMSINV interprets the value as
the cumulative probability of a standard normal distribution.
Then the NORMSINV function finds a standard normal variable
Z such that its the probability of drawing a value of Z or less is
equal to the argument. This means the formula
=NORMSINV(RAND()) returns a random standard normal
variable. 100Percent
Mike Ehrhardt: This column shows the percent of trials with
NPVs in the range.
Mike Ehrhardt: We must use a slightly different formula to get a
standard normal for the annual change in units that is correlated
with the unit sales in the first year. We do that by forming a
variable that is a combination of the standard normal variable
for units in the 1st year and an uncorrelated standard normal,
with the "weights" in the combination depending on the desired
correlation.$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR
:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#
DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DI
V/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/
0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!
$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$0
0ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00E
RROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ER
ROR:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!$00ERR
OR:#DIV/0!$00ERROR:#DIV/0!Sum- 0ERROR:#DIV/0!Output
of Simulation in Data TableTrial NumberEquipment costUnits

sold, Year 1Annual change in units sold, after Year 1Sales price
per unit, Year 1Variable cost per unit (VC), Year 1Nonvariable
cost (Non-VC), Year 1Tax rateNPV
00000000100000000200000000300000000400000000500000000
60000000070000000080000000090000000010000000001100000
00012000000001300000000140000000015000000001600000000
17000000001800000000190000000020000000002100000000220
00000002300000000240000000025000000002600000000270000
00002800000000290000000030000000003100000000320000000
03300000000340000000035000000003600000000370000000038
00000000390000000040000000004100000000420000000043000
00000440000000045000000004600000000470000000048000000
00490000000050000000005100000000520000000053000000005
40000000055000000005600000000570000000058000000005900
00000060000000006100000000620000000063000000006400000
00065000000006600000000670000000068000000006900000000
70000000007100000000720000000073000000007400000000750
00000007600000000770000000078000000007900000000800000
00008100000000820000000083000000008400000000850000000
08600000000870000000088000000008900000000900000000091
00000000920000000093000000009400000000950000000096000
0000097000000009800000000990000000010000000000
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
NPV ($)
Probability
Must be checked to put random variable in data table for
simulation
5. ReplacementERROR:#REF!Section 11.9 Replacement
AnalysisAs this model is set up, the cost of the new machine,
the salvage value of the old machine, the tax rate, the WACC,

and the operating costs before depreciation for the new machine
can be varied and the output will automatically recalculate.
Only these input variables, in BLUE TYPE, should be changed
unless you want to modify the model, which could be a fairly
big job.Note that the projects analyzed here are not related at all
to the projects on other Tabs.Figure 11-9. Replacement
AnalysisApplies to:Part I. Inputs:Both MachinesOld
MachineNew MachineCost of new machine$2,000After-tax
salvage value old machine$400Sales revenues
(fixed)$2,500Annual operating costs except
depreciation$1,200$280Tax
rate40%WACC10%Depreciation1234Totals:Depr. rates (new
machine)33%45%15%7%100%Depreciation on new
machine$660$900$300$140$2,000Depreciation on old
machine$400$400$400$400$1,600∆: Change in
depreciation$260$500-$100-$260$400Part II. Net Cash Flows
Before Replacement: Old Machine01234Sales
revenues$2,500$2,500$2,500$2,500Operating costs except
depreciation1,2001,2001,2001,200Depreciation400400400400
Total operating costs$1,600$1,600$1,600$1,600Operating
income$900$900$900$900Taxes 40%360360360360After-tax
operating income$540$540$540$540Add back
depreciation400400400400Net cash flows before
replacement$0$940$940$940$940Part III. Net Cash Flows
After Replacement: New Machine01234New machine cost:-
$2,000After-tax salvage value, old machine$400Sales
revenues$2,500$2,500$2,500$2,500Operating costs except
depreciation280280280280Depreciation660900300140 Total
operating costs$940$1,180$580$420Operating
income$1,560$1,320$1,920$2,080Taxes
40%624528768832After-tax operating
income$936$792$1,152$1,248Add back
depreciation660900300140Net cash flows after replacement-
$1,600$1,596$1,692$1,452$1,388Part IV. Incremental CF: Row
51 - Row 38-$1,600$656$752$512$448Part V. EvaluationNPV
=$308.51IRR =19.33%MIRR =14.96%Part VI. Alternative

Calculation for Net Cash FlowsNew machine cost-
$2,000Salvage value, old machine400Net cost of new machine-
$1,600Other operating cost savings = Old —
New$920$920$920$920 A-T savings = Other cost savings × (1
— Tax rate) 552552552552∆ Depreciation = (New —
Old)260500-100-260Depr'n tax savings = ∆ Depreciation × Tax
rate 104200-40-104NCF = A-T cost savings + Depr'n tax
savings-$1,600$656$752$512$448The Net Cash Flow time line
is the sum of the larger, boldfaced, boxed, red numbers. The
cash flows on Row 64 are IDENTICAL to those on Row 53.
6. Dec. TreesERROR:#REF!Section 11.10 Decision TreesTab 5
extends the scenario analysis (shown in Tab 3) to incorporate
the possibility of abandoning the project if demand is low. We
also provide an introduction to real options. For convenience,
we repeat the scenario analysis before addressing
abandonment.See Tab 3 for details concerning the scenario
analysis.Analysis for Worst and Best Scenarios in yellow and
green boxes below and to the right.Figure 11-5 (Repeated from
Tab 3) Inputs and Key Results for Each Scenario (Dollars in
Thousands)Don’t change any values in the yellow box below.
If you want to change an input, do it in Column G to the
left.Don’t change any values in the green box below.
If you want to change an input, do it in Column I to the
left.Scenarios:Worst-Case ScenarioBest-Case
ScenarioInputs:BaseWorstBestInputsWorstInputsBestProbabilit
y of Scenario50%25%25%Equipment
cost$3,400$4,250$2,550Equipment cost$4,250Equipment
cost$2,550Salvage value, equipment, Year
4$300$300$300Salvage value, equipment, Year 4$300Salvage
value, equipment, Year 4$300Opportunity
cost$0$0$0Opportunity cost$0Opportunity cost$0Externalities
(cannibalization)$0$0$0Externalities
(cannibalization)$0Externalities (cannibalization)$0Units sold,
Year 1550412688Units sold, Year 1412Units sold, Year
1688Annual change in units sold, after Year 14.00%-
6.00%14.00%Annual change in units sold, after Year 1-

6.00%Annual change in units sold, after Year 114.00%Sales
price per unit, Year 1$11.60$8.70$14.50Sales price per unit,
Year 1$8.70Sales price per unit, Year 1$14.50Annual change in
sales price, after Year 12.00%2.00%2.00%Annual change in
sales price, after Year 12.00%Annual change in sales price,
after Year 12.00%Variable cost per unit (VC), Year
1$6.00$7.50$4.50Variable cost per unit (VC), Year
1$7.50Variable cost per unit (VC), Year 1$4.50Annual change
in VC, after Year 12.00%2.00%2.00%Annual change in VC,
after Year 12.00%Annual change in VC, after Year
12.00%Nonvariable cost (Non-VC), Year
1$2,000$2,500$1,500Nonvariable cost (Non-VC), Year
1$2,500Nonvariable cost (Non-VC), Year 1$1,500Annual
change in Non-VC, after Year 12.00%2.00%2.00%Annual
change in Non-VC, after Year 12.00%Annual change in Non-
VC, after Year 12.00%Project
WACC10.00%10.00%10.00%Project WACC10.00%Project
WACC10.00%Tax rate40.00%50.00%30.00%Tax
rate50.00%Tax rate30.00%Working capital as % of next year's
sales12.65%12.65%12.65%Working capital as % of next year's
sales12.65%Working capital as % of next year's
sales12.65%Key Results:BaseWorstBestKey Results:WorstKey
Results:BestNPV $36-$5,847$13,379NPV -$5,847NPV
$13,379IRR10.35%Not found112.01%IRRNot
foundIRR112.01%MIRR10.23%-100.00%60.30%MIRR-
100.00%MIRR60.30%PI1.01-0.244.51PI-
0.24PI4.51Payback3.41Not found1.00PaybackNot
foundPayback1.00Discounted payback3.98Not
found1.09Discounted paybackNot foundDiscounted
payback1.09Analysis for Base-Case Scenario shown in blue box
below.BaseWorst-Case ScenarioBest-Case ScenarioVariables
Used in the Cash Flow Forecast01234Variables Used in the
Cash Flow Forecast01234Variables Used in the Cash Flow
Forecast01234Unit sales550572595619Unit
sales412387364342Unit sales6887848941,019Sales price per

depreciation)$2,000$2,040$2,081$2,122Nonvariable costs
(excluding depreciation)$2,500$2,550$2,601$2,653Nonvariable
costs (excluding depreciation)$1,500$1,530$1,561$1,592Cash
Flows At End of YearCash Flows At End of YearCash Flows At
End of YearInvestment Outlays at Time = 001234Investment
Outlays at Time = 001234Investment Outlays at Time =
001234Equipment-$3,400Equipment-$4,250Equipment-
$2,550Initial investment in working capital-807Initial
investment in working capital-453Initial investment in working
capital-1,262Opportunity cost, after taxes0Opportunity cost,
after taxes0Opportunity cost, after taxes0Net Cash Flows Over
the Project's LifeNet Cash Flows Over the Project's LifeNet
Cash Flows Over the Project's LifeSales revenues = Units ×
Price/unit$9,976$11,600$13,489$15,685Variable costs = Units
× Cost/unit3,3003,5013,7133,939Variable costs = Units ×
Cost/unit3,0902,9632,8412,724Variable costs = Units ×
$303$875$1,316Operating profit (EBIT)-$3,408-$3,988-$2,784-
$2,515Operating profit (EBIT)$4,539$5,323$7,359$9,047Taxes
on operating profit -17-121350526Taxes on operating profit -
1,704-1,994-1,392-1,257Taxes on operating profit
1,3621,5972,2082,714Net operating profit after taxes-$25-
$182$525$790Net operating profit after taxes-$1,704-$1,994-

$1,392-$1,257Net operating profit after
taxes$3,177$3,726$5,152$6,333Add back
taxes0000Opportunity cost, after taxes0000Opportunity cost,
after taxes0000Cannibalization or complementary effects, after
taxes0000Salvage value (taxed as ordinary income)300Salvage
value (taxed as ordinary income)300Salvage value (taxed as
ordinary income)300Tax on salvage value (SV is taxed at 40%)-
120Tax on salvage value (SV is taxed at 40%)-150Tax on
(–) or recovery (+)-49-52-55963Change in WC: Outflow (–) or
recovery (+)191817400Change in WC: Outflow (–) or recovery
(+)-205-239-2781,984Project net cash flows: Time Line-
$4,207$1,048$1,296$980$2,171Project net cash flows: Time
Line-$4,703-$283-$64-$737-$410Project net cash flows: Time
Line-$3,812$3,813$4,634$5,256$8,705Project
EvaluationProject EvaluationProject EvaluationResults Results
Results NPV $36NPV -$5,847NPV
$13,379IRR10.35%IRRERROR:#NUM!IRR112.01%MIRR10.23
%MIRR-100.00%MIRR60.30%Profitability
index1.01Profitability index-0.24Profitability
index4.51Payback3.41PaybackERROR:#N/APayback1.00Discou
nted payback3.98Discounted paybackERROR:#N/ADiscounted
payback1.09Calculations for PaybackYear:01234Calculations
for PaybackYear:01234Calculations for PaybackYear:01234
$883$1,288 Cumulative cash flows for payback-$4,703-
$4,986-$5,050-$5,787-$6,198 Cumulative cash flows for
payback-$3,812$1$4,635$9,892$18,597 Discounted cash flows
for disc. payback-$4,207$952$1,071$736$1,483 Discounted
cash flows for disc. payback-$4,703-$257-$53-$554-$280
Discounted cash flows for disc. payback-

$3,812$3,466$3,830$3,949$5,946 Cumulative discounted cash
flows-$4,207-$3,255-$2,183-$1,447$36 Cumulative discounted
cash flows-$4,703-$4,961-$5,013-$5,567-$5,847 Cumulative
discounted cash flows-$3,812-$346$3,484$7,434$13,379
Accelerated Depreciation Accelerated Depreciation
$510$238Dollars/year$1,403$1,913$638$298Dollars/year$842$
1,148$383$179Note: the scenario analysis below is meaningful
only if the values in the input section in Cells E16:E30 are set
to the original base-case.Recall from Tab 3 that we can find the
value of the project under the assumption that the project must
be operated its full life. For convenience, we repeat that
analysis below.Figure 11-6 (Repeated from Tab 3). Scenario
Analysis: Cannot AbandonPredicted Cash Flows for Alternative
ScenariosCalculating σ step-by-stepQuick NPV and
sProb:01234WACCNPVDeviationSqrd devSqrd*prob Best25%-
$3,812$3,813$4,634$5,256$8,70510.00%$13,379114781317556
42$32,938,910Base50%-
$4,207$1,048$1,296$980$2,17110.00%$36-
18653478447$1,739,224 Worst 25%-$4,703-$283-$64-$737-
$41010.00%-$5,847-774860037190$15,009,298Expected NPV
=$1,901Variance =$49,687,432$1,901 =Expected NPVStandard
Deviation (SD) =$7,049σ =$7,049$7,049 = Standard
Deviation (SD)Coefficient of Variation (CV) = Std
Dev/Expected NPV =3.71Now assume that the project may be
terminated (abandoned) at Year 2 if the demand is low. The net
after-tax cash flow from salvage, legal fees, liquidation of
working capital, and all other termination cost/revenues is $500
and is shown at Year 2 for the low demand scenario. As shown
in Figure 11-9, the ability to abandon a project can add
significant value to its NPV.Figure 11-10. Simple Decision
Tree: Can Abandon Project in Worst-Case ScenarioPredicted
Cash Flows for Alternative ScenariosCalculating σ step-by-

stepProb:01234WACCNPVDeviationSqrd
devSqrd*probBest25%-
$3,812$3,813$4,634$5,256$8,70510.00%$13,379$11,153124,39
9,61631,099,904Base 50%-
$4,207$1,048$1,296$980$2,17110.00%$36-
$2,1904,796,4862,398,243Worst -$4,703-$283-$64-$737-
$41025%-$4,703-$283$500$0$010.00%-$4,547-
$6,77345,877,34211,469,336If abandon, can liquidate for $500
at t = 2.Expected NPV =$2,226Variance =44,967,482Standard
Deviation (SD) =$6,706σ =$6,706Coefficient of Variation
(CV) = Std Dev/Expected NPV =3.01Figure 11-11. Decision
Tree with Multiple Decision PointsFirm can abandon the project
at t = 2WACC =10.0%Time Periods, Cash Flows, Probabilities,
and Decision PointsWACC =10.0%0123456WACC
=10.0%Product: NPVCalculating σ step-by-step1st
InvestProb.2nd InvestProb.3rd
InvestInflowInflowInflowInflowNPVJoint Prob x Joint
ProbDeviationSqrd devSqrd*prob45%-
$3,812$3,813$4,634$5,256$8,705$10,50336%$3,781$6,9764866
8922$17,520,81280%-$50040%-
$4,207$1,048$1,296$980$2,171-$52532%-$168-
4051164139415252460.98569415-$10015%Stop$0$0$0$0-
$55512%-$67-$4,08116654799$1,998,576-
3526.483691141620%Stop$0$0$0$0$0-$10020%-$20-
3626131513842630277Expected NPV =$3,526Sum =
variance27402125Standard Deviation (SD) =$5,235Sq root of
Var = σ$5,235Coefficient of Variation (CV) = Std
Dev/Expected NPV =1.48
1
1
2
1
2
3
3
3

2
7. App. ADEPRECIATION
TABLESERROR:#REF!Depreciation percentages personal
property (i.e., assets otherActual IRS Depreciation Percentages
for Personalthan real estate) estate), rounded for
convenience.PropertyClass of InvestmentClass of
InvestmentOwnership Year3-Year5-Year7-Year10-
YearOwnership Year3-Year5-Year7-Year10-
Year133%20%14%10%133.33%20.00%14.29%10.00%245%32%
25%18%244.45%32.00%24.49%18.00%315%19%17%14%314.8
1%19.20%17.49%14.40%47%12%13%12%47.41%11.52%12.49
%11.52%511%9%9%511.52%8.93%9.22%66%9%7%65.76%8.9
2%7.37%79%7%78.93%6.55%84%7%84.46%6.55%97%96.56%
106%106.55%10.00%18.00%14.40%11.52%9.22%7.37%6.55%6
.55%6.56%6.55%3.28%113%113.28%100%100%100%100%100
.00%100.00%100.00%100.00%MACRS for Residential Real
PropertyMonth Property Placed in
ServiceYear12345678910111213.485%3.182%2.879%2.576%2.
273%1.970%1.667%1.364%1.061%0.758%0.455%0.152%2-
273.636%3.636%3.636%3.636%3.636%3.636%3.636%3.636%3.
636%3.636%3.636%3.636%281.970%2.273%2.576%2.879%3.1
82%3.458%3.636%3.636%3.636%3.636%3.636%3.636%290.00
0%0.000%0.000%0.000%0.000%0.000%0.152%0.455%0.758%1
.061%1.364%1.667%99.99%99.99%99.99%99.99%99.99%99.96
%99.99%99.99%99.99%99.99%99.99%99.99%MACRS for
Nonresidential Real PropertyMonth Property Placed in
ServiceYear12345678910111212.461%2.247%2.033%1.819%1.
605%1.391%1.177%0.963%0.749%0.535%0.321%0.107%2-
392.564%2.564%2.564%2.564%2.564%2.564%2.564%2.564%2.
564%2.564%2.564%2.564%400.107%0.321%0.535%0.749%0.9
63%1.177%1.391%1.605%1.819%2.033%2.247%2.461%100.00
%100.00%100.00%100.00%100.00%100.00%100.00%100.00%1
00.00%100.00%100.00%100.00%Rounded Percentages Used in
AnalysisProperty Life (in years):39Depreciation in Year 1
(assuming half-year convention):1.30%Rounded Depreciation in
Years 2-39:2.60%Depreciation in Year 40:1.30%

8. Scenario SummaryScenario SummaryCurrent Values:Base-
Case Scenario in Column EShow Worst-Case in Column EShow
Best-Case in Column ECreated by Mike Ehrhardt on 5/17/2009
Modified by Mike Ehrhardt on 5/17/2009Created by Mike
Ehrhardt on 5/17/2009
Modified by Mike Ehrhardt on 5/17/2009Created by Mike
Ehrhardt on 5/17/2009
Modified by Mike Ehrhardt on 5/17/2009Changing
Cells:$E$35BaseBaseWorstBest$E$3650%50%25%25%$E$37$3
,400$3,400$4,250$2,550$E$38$300$300$300$300$E$39$0$0$0
$0$E$40$0$0$0$0$E$41550550412688$E$424.00%4.00%-
6.00%14.00%$E$43$11.60$11.60$8.70$14.50$E$442.00%2.00
%2.00%2.00%$E$45$6.00$6.00$7.50$4.50$E$462.00%2.00%2.
00%2.00%$E$47$2,000$2,000$2,500$1,500$E$482.00%2.00%2
.00%2.00%$E$4910.00%10.00%10.00%10.00%$E$5040.00%40.
00%50.00%30.00%$E$5112.65%12.65%12.65%12.65%Result
Cells:$E$53$36$36-$5,847$13,379$E$5410.35%10.35%Not
found112.01%$E$5510.23%10.23%-
100.00%60.30%$E$561.011.01-0.244.51$E$573.413.41Not
found1.00$E$583.983.98Not found1.09Notes: Current Values
column represents values of changing cells attime Scenario
Summary Report was created. Changing cells for eachscenario
are highlighted in gray.
Introducing Uncertainty
------~----~----~- ---~ ----~------------
If we lived in a world of perfect certainty, the catfish fillet
project would be accepted without
question. After all, it appears that it will increase shareholder
wealth by $91,272.55.

Unfortunately, the world is not certain. Even in this simplified
example, it should be clear
that many sources of uncertainty may arise. For example, the
marketing department doesn't
really know that the finn will sell 200,000 pounds of catfish
fillets in the first year. Likewise,
it doesn't know that it will be able to get the assumed $2.50 per
pound or that demand will
grow at an annual rate of 8% per year. Consumer demand may
be far less than expected.
This could lead to a double whammy: Not only would unit
demand be less than expected,
but the wholesale price would likely be less than $2.50 per
pound. Poor first year acceptance
could also mean lower subsequent growth rates. These and many
other uncertainties
naturally result in uncertainty surrounding our expected annual
cash flows that, in tum,
results in uncertainty surrounding the estimated NPV
In such an uncertain world, it is helpful to develop models that
allow us to determine how
much uncertainty surrounds our estimate of the NPY. For
example, we might like to make an
educated guess as to the probability that the NPY will actually
tum out to be less than zero.
The following sections will lead us to an answer to this
question.
Sensitivity Analysis
As noted above, many uncertain variables exist in our catfish
fillet example. In fact, we
could say that virtually all of the variables are uncertain, as are
many others that we have not
explicitly considered. However, some of these variables have

more of an impact on the NPY
than others. Since it would take a lot of time and effort to
generate precise forecasts of every
variable, it is helpful to concentrate on only the most important
variables. Sensitivity
analysis is the tool that helps us to identify the variables that
deserve the most attention.
The idea is to make small changes in variables, one at a time,
and observe the effect on the
NPY (or any other decision criteria). For example, we might
change the selling price from
$2.50 per pound to $2.25 (a change of -I 0%) and then calculate
that the NPY would decline
to $34,291.68. Record this fact and reset the selling price to its
original value. Now, reduce
the terminal value of, the land to $315,000 (a change of -10%)
and note that the NPY
declines to $77,146.59. Reducing the selling price by 10% leads
to a much bigger decline in
the NPY than does a similar reduction in the terminal value of
the land. Therefore, we
should devote more resources to accurately determining the
selling price, and not spend
much time estimating the value of the land.
There are two problems with the procedure outlined above.
First, by making only a single
small change to each variable, we may miss nonlinear
relationships. Second, to carry out this
procedure for each uncertain variable would be cumbersome.
We would have to change a
,

365
CHAPTER 12: Risk and Capital Budgeting
variable, write down the resulting NPV, reset the variable to its
original value, change
another variable, write down the resulting NPV, and so on. To
solve the first problem, we can
simply make several changes in each variable, both up and
down. For example, we could
change the selling price per pound by -30% to +30% in, say,
10% increments. This,
however, exacerbates the second problem by making the
analysis even more onerous.
Fortunately, Excel provides a solution.
Using Data Tables
A data table is an Excel tool that automatically performs the
process described previously.
To see how they work, let's set up a simple example. Suppose
that we wish to see what
happens to the expected NPV as the sell ing price varies from
$1.50 to $3.50 per pound. To
start, enter $1 . 50 in G5 and $ 2.00 in H5.4 Now use AutoFill
to create the rest of the price
series. The next step is to enter a formula into F6. In this case,
we are interested in the NPV
so we need to enter: =NPV (B14, C2 8: G2 8) +B2 8.
FIGURE 12-3
THE DATA TABLE DIALOG Box

DataTable
~ow ",put cell: [$~i?~~~__ [ .~
!;oIumn ",put cell: r ... . _l~]
t:2.Cj[ ~ I
When we execute the data table command, Excel will
automatically substitute the values
from G5:K5 into our model (in cell B9) one at a time and record
the resulting NPVs in the
table. Select F5:K6 (this is the entire area of the table,
including the NPV formula) and then
choose Data !able... from the What-If Analysis button on the
Data tab. In the resulting
dialog box, type B 9 into the !!cow input cell edit box as shown
in Figure 12-3. After clicking
the OK button, this section of your worksheet should look like
the one in Exhibit 12-3.
EXHIBIT 12-3
THE DATA TABLE FOR DIFFERENT PRICES
$1.50 $2.00 $2.50 $3.00 $3.50
(136.650 91) (22,689.18) 91,272.55 205,234.27 319,196.00
-----_._--_._---
4. The data table can be created anywhere on this worksheet,
but it cannot be in another worksheet.
You can get around this limitation by carefully constructing
your formulas.

366
The values in G6:K6 are the NPYs. For example, if the price per
pound was $1.50 the NPY
would be -$136,650.91. Similarly, if the price was $3.50 the
NPY would be $319,196. If
necessary, you can change any or all of the prices in row 5 and
the table will automatically
update.
Note that the original NPY formula in F6 is not a part of the
table per se, and it might
confuse some people. It is only there so that Excel knows what
formula to use when
calculating the table. We can easily hide this value by simply
selecting F6 and changing the
font color to white. This will make the table easier to read.
Excel allows for other types of data tables than we have
demonstrated here. The data table in
Exhibit 12-3 is called a row-oriented one-variable table because
our prices are in a row. If
the prices were in a column instead, we could create a column-
oriented one-variable table.
To create a column-oriented table, the only difference is that
you would enter the changing
cell (89) into the ~olumn input cell edit box (see Figure 12-3).
The result would be exactly
the same, except for the orientation table. We can also create
two-variable data tables that
allow for two changing variables. The procedure is similar, but

you should check the online
help for the details.
Since we have more than one uncertain variable in our catfish
fillet problem, we will need
several data tables. It will also be helpful, for comparison
purposes, to deviate a bit from the
methodology described above. Specifically, we can set up
several data tables based on
percentage changes in our uncertain variables. This will make it
easier to compare the result
from a change in unit sales to the result from a change in the
growth rate.
EXHIBIT 12-4
THE INPUT AREA SET UP FOR SENSITIVITY ANALYSIS
Frozen Catfish Fillet Project Inputs
Cost of Land
Cost of Buildings & Equipment
MACRS Class
Life of Project (Years)
Terminal Value of Land
Terminal Value of Buildings & Equipment
First Year Catfish Sales (lbs)
Price per Pound

Unit Sales Growth Rate
Variable Costs as % of Sales
Fixed Costs
Tax Rate
WACC
250,000
400,000
20
5
350,000
200,000
200,000
2.50
8%
60%
80,000
35%
10%

Sensitivity %
0%
0%
0%
0%
0%
0%
367
Let's start by changing the input area of the worksheet so that it
can accommodate this type
of sensitivity analysis more easily. In 05 enter: Sensitivity %,
and then in 06:011
enter: 0 % in each cell. Change 86 so that it has a formula rather
than a number:
= 3 5 0 0 0 0 * (1 +0 6) . Now if we put 10% into 06, for
example, the terminal value of the
land will change from $350,000 to $385,000. Make similar
changes in cells 87:8 II so that
those values change as we change the corresponding
percentages. Your input area should
now look like the one in Exhibit 12-4. Note that we will be
doing the sensitivity analysis on
only six of the variables.
At this point, we can proceed in a similar manner as we did
above'. Let's first create a
percentage-based data table for the terminal value of the land.
Go to A38 and enter:
Terminal Val ue of Land. In 838:H38 enter a series of numbers
from -30% to +30% in

10% increments (-30%,-20%, -10%, etc.). In A38, enter the Nrv
function:
=NPV(B14,C28:G28)+B28. We have now set up the table and
all that remains is to
select it and execute the Data Table ... command. In this case
the row input cell is 06, which
is the percentage that corresponds to the terminal value of the
land. The data table will plug
-30% into 06, which will change the terminal land value in 86
resulting in a different NPY.
Next, it will plug in -20% and so on.
Using the same procedure, create data tables for each of the
uncertain variables, each time
changing the row input cell (07, 08, etc.). You should end up
with six data tables as shown
in Exhibit 12-5. Note that, as mentioned above, we have hidden
the original NPY formula so
that the table is easier to read.
EXHIBIT 12-5
DATA TABLES FOR THE UNCERTAIN VARIABLES
A I B J c I D I E I II I G J H
37
lerminal Value of Land ·30%
48.895
Sensitivity Tables
-~OO;() ·10%

63.021 77.147
0%
91.273
10~i;l
105.399
20%
119.524
30%
133,650
38
'3;
'40
'it
nrValue of Buildings & l.quipmcnt -3()~·u
67.057
-20% ·!O%
75.129 83.201
0(1'(,
91,273
10%)

99.345
20110
107AI7
30%
115A88
f-;jt
'44 First Year Catfish Sales (Ibs) -30/% -20% ·10% O~·1u
IO(}';) 20% 30%
'45 (N.670) (22.689) 34.292 91.273 148.253 205.234 262.215
'46
f-'-=-
~ Price per Pound ·30% ·20% ·10')', 0%
101}'0 20lJo 30%
48 (79.670) (22/,89) 34,292 91.273 148.253 205.234 262,215
~
~
'itc..;:..;;..
Unit Sales Growth Rate -30~·~)
66.954
·20%) .] O~··(l
74.941 83.046
01%
9l.173
10(%

99,620
20%
108,091
30%
116.686
~
53r-;r Variable COSlS as 0;(1 ofSales ·30% 347,686
-20~"o ·10%
262,215 176,744
O~··;I
91,273
lorvo
5,801
20°;;)
(79,670)
30%
( 165,141)
---._---- ----- ----~

368
Sensitivity Diagrams
Some people can look at thc data tables and see at a glance that
the most important variables
are the unit sales, price per pound, and the variable cost as a
percentage of sales. Others,
however, find it helpfu I to create charts of the data. The most
appropriate type of chart for
this analysis is a Scatter chart. We can either create a separate
chart for each variable or put
all of the variables in one chart.
To create one chart that shows all of the variables, we must first
start with a chart of one of
the variables. Select B38:H38, and then Ctrl+c1ick each of the
NPY series. Create a Scatter
chart and place it somewhere convenient in the worksheet. For
this example problem, it
turns out that some of the lines overlap, so it is impossible to
tell them apart on the chart.
This is not generally the case. However, even when we don't
have this problem, it can be
much easier to see which variables are most important if they
are all in separate charts. This
is particularly true when we have a lot of variables.
FIGURE 12-4
SENSITIVITY DIAGRAMS FOR EACH VARIABLE

Sensltn il~ Diaj!nlln:
Land Valli"
..;> ~_lll.(l(I(1
Z
'<.Ii).
0
~
,(HI(j11
17[11;110 =t==117oll()fl '"
.10"0 -111"0 1(1""
')erc{'lIhtgi.> CIHlRj:!,C
Sen<dli,-il) Dlanram:
Prtcepcr Pound
,.'11.(11)11
;>
e, ~ , til1l'
1 WOOII
0
lit 1100
"
] 170 (I{lO)

117(1 (100)
,'II",. ·111",. 10"" 1(""
'"
Percentage Change
Z
*
Sensili'it) Diagram:
Buildin!.sand Equipment
,111101I
11111(1
~
1111111>1)
0 "
,(I(j(1I1
~ , IIOIIr
;>
=t=I ~II (1111 I '"
ru-,
I'erecntage ("IHinge

"iemiti"it) llillgram:
Growth Rate
' ~ II 1)1Ii I
> c, ~ 'II mu,
Z
rmnoo "
<IIIHII!
(7(1ei!".
~
0 ~11'1111011'
'11"" (0"" H"" 'II""
Pereenrage Cnaugc
Scnsith it~ Diagram:
t nu "illle'i (Ih ..)
..;> ~ '!I 11(111
I _~ II 11111 ' "
;11.11111)
<i! r-'looOJ
II'''"
Percentage Change
Z
*
Sensith it) Diagram:

var Cos to; 3 'Yo of Sale'"
~ _~". (II)I!
Z
" I '''Itl)(t c
'11'1011
(~Ii (10(11
~ ~I i ~II 'lilO1
Perccutage Change
Creating a separate chart for each variable is more time
consuming, and you need to make
sure that the scaling of the axes is the same in each chart. The
advantage to this approach is
that it is much easier to identify the individual data series. As
can be seen in Figure 12-4, the
lines with the steepest slopes are the same as those previously
identified as the most
important variables. In order to make this comparison, it is vital
that the axis scaling is
identical in each chart. To make creating all of these charts
easier, you can copy and paste
the first one and then simply change the data ranges. To change
the data series in a chart,
369
--------
~ .~,.._- -,,-_..

right-click in the chart and choose Select Data ... In the dialog
box, select a series and then
click the ~dit button to change the data ranges.
An alternative to the visual approach is to LIse the SLOPE
function to determine the slope of
each line. This function calculates a regression equation and
returns the slope. It is defined as:
SLOPE(KNOWN_Y'S, KNOWN_X'S)
where KNOWN_Y'S and KNOU'N_X'S are the Y and X data
ranges, respectively. For our
purpose, the Y variables are the NPVs, and the X variables are
the percentage changes. For
example, we can use =SLOPE (B3 9: H3 9, B3 8: H3 8) to find
that the slope of the line for
the terminal land value is 141,259.60. This can then be
numerically compared to the slopes
of the other lines. The larger the slope, the more important the
variable. Note that if any of
the slopes might be negative, then it is helpful to LIse the ABS
function to return the absolute
value of the slope. Adding this function to the formula will
change it to: =ABS (SLOPE (
B39 : H39, B38 : H3 8) ) . This allows us to compare
magnitudes without regard to signs.
Clearly, the most important variables are the unit sales, price
per pound, and the variable cost
as a percentage of sales. These are the variables that we will use
in our scenario analysis in
the next section.

Scenario Analysis
The sensitivity analysis has identified the three most important
variables, but we've only
seen their impact on the NPV in isolation. A scenario analysis
will allow us to see the
combined effects of changing all of these variables
simultaneously. Suppose that after seeing
the sensitivity analysis report, a meeting was held to determine
three possible scenarios. The
best and worst cases are shown in Table 12-3 along with the
base case, which represents the
original expectations. It also shows the probability that each
scenario will actually occur.
TABLE 12-3
THREE SCENARIOS
.. Variable
Worst Case
20%
Base Case
6()%
Best Caw
20% ......••..
Unit Sales 125,000 200,000 275,000
Price per Pound $2.25 $2.50 $2.65
Variable Cost % 65% 60% 55%
Note that the worst case scenario is one in which all of the

variables are at their worst
possible values. Similarly, the best case assumes that all of the
variables take on their best
possible values simultaneously. While such outcomes are
unlikely, they are useful for
determining the extreme boundaries around the expected NPY.
370
Team Final Project
Cost of Capital, Capital Structure,
and Capital Budgeting Analysis
1. Purpose of the project:
In this project, you are supposed to be a financial manager to
apply the knowledge obtained from the Financial Management
(FINC6352) course to estimate the cost of debt, cost of
preferred stock, cost of common equity, capital structure, and
the weighted average cost of capital (WACC) for a publicly-
traded corporation of your choice. You will use the estimated
WACC as the discount rate to perform capital budgeting
analysis for a hypothetical project (the information is given
below) that is under consideration by the selected company, and
decide whether the project should be accepted.
2. Outline for the project:
(1) Executive Summary (10 points)
- Summarize the major findings, results, and the analysis of the
report.
(2) Financial Ratio Analysis (40 points)
You are expected to apply the knowledge obtained in Financial
Management and Financial Statement Analysis (ACCT6351) to
the key financial ratios of the selected company.

- Perform trend analysis of the key financial ratios (i.e.,
liquidity ratios, asset management ratios, debt management
ratios, profitability ratios, market value ratios) of the company
during the most recent 5-year period.
- Perform industry (or benchmark companies) comparison
analysis of the key financial ratios of the company in the most
recent year.
- Based on the financial ratio analysis results, discuss/evaluate
the financial performance of the company.
(3) Estimate Capital Structure (25 points)
- Estimate the firm’s weights of debt, preferred stock, and
common stock using the firm’s balance sheet (book value) in the
most recent year.
- Estimate the firm’s weights of debt, preferred stock, and
common stock using the market value of each capital component
in the most recent year.
(4) Compute Weighted Average Cost of Capital (WACC)(35
points)
- Estimate the firm’s before-tax and after-tax component cost of
debt; (Note: If the information about the current corporate tax
rate is not available, you need to estimate the tax rate based on
the historical tax payments).
- Estimate the firm’s component cost of preferred stock;
- Use three approaches (CAPM, DCF, bond-yield-plus-risk-
premium) to estimate the component cost of common equity for
the firm.
- Calculate the firm’s weighted average cost of capital (WACC)
using the market-based capital weights.
(5) Cash Flow Estimation (40 points)
- We assume that the company you selected is considering a
new project. The project has 11 years’ life. This project requires
initial investment of $680 million to purchase equipment, and
$30 million for shipping & installation fee. The fixed assets fall

in the 10-year MACRS class. The salvage value of the fixed
assets is 7.5% of the purchase price (including the shipping &
installation fee). The number of units of the new product
expected to be sold in the first year is 2,500,000 and the
expected annual growth rate is 8.5%. The sales price is $260 per
unit and the variable cost is $205 per unit in the first year, but
they should be adjusted accordingly based on the estimated
annualized inflation rate of 2.5%. The required net operating
working capital (NOWC) is 10% of sales. Use the corporate tax
rate obtained in Step (4) for the project. The project is assumed
to have the same risk as the corporation, so you should use the
WACC you obtained from prior steps as the discount rate. Note:
you may revise the partial model in the file Ch11 P18 Build a
Model.xls on the website of the textbook (also posted in this
final project learning module in Blackboard) for capital
budgeting analysis, but you are NOT required to strictly follow
the partial model. Actually, you are encouraged to build a better
model by yourself.
- Compute the depreciation basis and annual depreciation of the
new project. (You can refer to Table 11A-2 MACRS allowances
on P.500 in the textbook)
- Estimate annual cash flows for 11 years.
- Draw a time line of the cash flows.
(6) Capital Budgeting Analysis (40 points)
- Using the WACC obtained from in Step (4) as the discount
rate for this project, apply capital budgeting analysis techniques
(NPV, IRR, MIRR, PI, Payback, Discounted Payback) to
analyze the new project.
- Perform a sensitivity analysis for the effects of key variables
(e.g., sales growth rate, cost of capital, unit costs, sales price)
on the estimated NPV or IRR in order to demonstrate the
sensitivity of the model. The Scenario analysis of several
variables simultaneously is encouraged (but not required). A
PDF document named Sensitivity Analysis in Excel is provided
in this learning module. The article introduces the Data Table

method that you can use for performing sensitivity analysis in
Excel.
- Discuss whether the project should be taken and summarize
your report.
3. Other information regarding the project:
(1) Choose a publicly-traded high-tech company. Your team
needs to inform the instructor of the company that you intend to
analyze. Different team should use different companies for their
projects. If two teams happen to select the same company, the
group that informed the instructor first will have the priority,
and the other group need to pick another company.
(2) Your project should be well-organized and typed in a Word
document and attach the important tables with your report. The
style and organization of the project is also very important. It
accounts for 10 points. Do not directly copy any contents from
any other resources. List the cited references in your project.
Document and Entity InformationDocument and Entity
Information - USD ($) $ in Billions12 Months EndedFeb. 02,
2019Mar. 02, 2019Aug. 04, 2018Document And Entity
Information [Abstract]Document Type10-KAmendment
FlagfalseDocument Period End DateFeb. 2,
2019Document Fiscal Year Focus2019Document
Fiscal Period FocusFYTrading SymbolTJXEntity Registrant
NameTJX COMPANIES INC /DE/Entity Central Index
Key0000109198Current Fiscal Year End Date--02-02Entity
Well-known Seasoned IssuerYesEntity Current Reporting
StatusYesEntity Voluntary FilersNoEntity Filer CategoryLarge
Accelerated FilerEntity Small BusinessfalseEntity Emerging
Growth CompanyfalseEntity Shell CompanyfalseEntity Common
Stock, Shares Outstanding1,214,588,500Entity Public Float$
60.5
Consolidated Statements of IncoConsolidated Statements of

Income - USD ($) shares in Thousands, $ in Thousands12
Months EndedFeb. 02, 2019Feb. 03, 2018Jan. 28, 2017Income
Statement [Abstract]Net sales$ 38,972,934$ 35,864,664$
33,183,744Cost of sales, including buying and occupancy
costs27,831,17725,502,16723,565,754Selling, general and
administrative
expenses6,923,5646,375,0715,768,467Impairment of goodwill
and other long-lived assets, related to Sierra099,2500Loss on
early extinguishment of debt0051,773Pension settlement
charge36,122031,173Interest expense,
net8,86031,58843,534Income before provision for income
taxes4,173,2113,856,5883,723,043Provision for income
taxes1,113,4131,248,6401,424,809Net income$ 3,059,798$
2,607,948$ 2,298,234Basic earnings per share:Net income,
Basic (in dollars per share)$ 2.47$ 2.05$ 1.75Weighted average
common shares - basic (in
share)1,241,1531,273,6541,311,294Diluted earnings per
share:Net income, Diluted (in dollars per share)$ 2.43$ 2.02$
1.73Weighted average common shares - diluted (in dollars per
share)1,259,2521,292,2091,328,864
Consolidated Statements of CompConsolidated Statements of
Comprehensive Income - USD ($) $ in Thousands12 Months
EndedFeb. 02, 2019Feb. 03, 2018Jan. 28, 2017Statement of
Comprehensive Income [Abstract]Net income$ 3,059,798$
2,607,948$ 2,298,234Additions to other comprehensive
income:Foreign currency translation adjustments, net of related
tax benefit of $8,233 in fiscal 2019, and provisions of $36,929
and $25,656 in fiscal 2018 and fiscal 2017,
respectively(192,664)211,752(52,611)Gain on net investment
hedges, net of related tax provision of $7,113 in fiscal
201919,53800Recognition of net gains/losses on benefit
obligations, net of related tax benefit of $19,813 in fiscal 2019,
provision of $8,989 in fiscal 2018 and benefit of $7,394 in
fiscal 2017(54,420)24,691(11,239)Reclassifications from other
comprehensive income to net income:Pension settlement charge,
net of related tax provision of $9,641 in fiscal 2019 and $12,369

in fiscal 201726,481018,804Amortization of loss on cash flow
hedge, net of related tax provisions of $304, $438 and $450 in
fiscal 2019, 2018 and 2017,
respectively847696684Amortization of prior service cost and
deferred gains/losses, net of related tax provisions of $4,280,
$9,592, and $11,584 in fiscal 2019, 2018 and 2017,
respectively11,75615,22817,608Other comprehensive (loss)
income, net of tax(188,462)252,367(26,754)Total
comprehensive income$ 2,871,336$ 2,860,315$ 2,271,480
Consolidated Statements of Co_2Consolidated Statements of
Comprehensive Income (Parenthetical) - USD ($) $ in
Thousands12 Months EndedFeb. 02, 2019Feb. 03, 2018Jan. 28,
2017Statement of Comprehensive Income [Abstract]Foreign
currency translation adjustments, related tax provisions
(benefit)$ 8,233$ 36,929$ 25,656Gain on investment hedges,
tax provision7,113Recognition of net gains/losses on benefit
obligations, related tax provision
(benefit)(19,813)8,989(7,394)Pension settlement charge, Tax
provision (benefit)9,641012,369Amortization of loss on cash
flow hedge, Tax provision (benefit)304438450Amortization of
prior service cost and deferred gains/losses, related tax
provisions$ 4,280$ 9,592$ 11,584
Consolidated Balance SheetsConsolidated Balance Sheets - USD
($) $ in ThousandsFeb. 02, 2019Feb. 03, 2018Current
assets:Cash and cash equivalents$ 3,030,229$ 2,758,477Short-
term investments0506,165Accounts receivable,
net346,298327,166Merchandise
inventories4,579,0334,187,243Prepaid expenses and other
current assets513,662706,676Total current
assets8,469,2228,485,727Net property at
cost5,255,2085,006,053Non-current deferred income taxes,
net6,4676,558Goodwill97,552100,069Other
assets497,580459,608TOTAL
ASSETS14,326,02914,058,015Current liabilities:Accounts
payable2,644,1432,488,373Accrued expenses and other current
liabilities2,733,0762,522,961Federal, state and foreign income

taxes payable154,155114,203Total current
liabilities5,531,3745,125,537Other long-term
liabilities1,354,2421,320,505Non-current deferred income
taxes, net158,191233,057Long-term
debt2,233,6162,230,607Commitments and
contingenciesSHAREHOLDERS’ EQUITYPreferred stock,
authorized 5,000,000 shares, par value $1, no shares
issued00Common stock, authorized 1,800,000,000 shares, par
value $1, issued and outstanding 1,217,182,508 and
1,256,018,044, respectively1,217,1831,256,018Additional paid-
in capital00Accumulated other comprehensive (loss)
income(630,321)(441,859)Retained
earnings4,461,7444,334,150Total shareholders’
equity5,048,6065,148,309TOTAL LIABILITIES AND
SHAREHOLDERS’ EQUITY$ 14,326,029$ 14,058,015
Consolidated Balance Sheets (PaConsolidated Balance Sheets
(Parenthetical) - $ / sharesFeb. 02, 2019Feb. 03, 2018Statement
of Financial Position [Abstract]Preferred stock, shares
authorized (in shares)5,000,000Preferred stock, par value ($ per
share)$ 1$ 1Preferred stock, shares issued (in shares)00Common
stock, shares authorized (in shares)1,800,000,000Common
stock, par value ($ per share)$ 1$ 1Common stock, shares
issued (in shares)1,217,182,5081,256,018,044Common stock,
shares outstanding (in shares)1,217,182,5081,256,018,044
Consolidated Statements of CashConsolidated Statements of
Cash Flows - USD ($) $ in Thousands12 Months EndedFeb. 02,
2019Feb. 03, 2018Jan. 28, 2017Cash flows from operating
activities:Net income$ 3,059,798$ 2,607,948$
2,298,234Adjustments to reconcile net income to net cash
provided by operating activities:Depreciation and
amortization819,655725,957658,796Loss on property disposals
and impairment charges17,6538,8715,207Deferred income tax
(benefit)(88,594)(137,440)(5,503)Share-based
compensation103,557101,362102,251Impairment of goodwill
and other long-lived assets, related to Sierra099,2500Loss on
early extinguishment of debt0051,773Pension settlement

charge36,122031,173Excess tax benefits from share-based
compensation00(70,999)Changes in assets and
liabilities:(Increase) in accounts
receivable(23,532)(62,358)(23,235)(Increase) decrease in
merchandise inventories(465,429)(450,377)11,862Decrease
(increase) in prepaid expenses and other current
assets236,342(317,850)(9,600)Increase in accounts
payable198,212205,11148,253Increase in accrued expenses and
other liabilities169,418334,522389,399Increase (decrease) in
income taxes
payable40,965(94,492)146,766Other(15,708)5,120(7,518)Net
cash provided by operating
activities4,088,4593,025,6243,626,859Cash flows from
investing activities:Property
additions(1,125,139)(1,057,617)(1,024,747)Purchases of
investments(161,625)(861,256)(716,953)Sales and maturities of
investments636,560906,137529,146Other26,6520(2,324)Net
cash (used in) investing
activities(623,552)(1,012,736)(1,214,878)Cash flows from
financing activities:Proceeds from issuance of long-term
debt00992,540Cash payments for extinguishment of
debt00(425,584)Cash payments for debt issuance
expenses00(9,921)Cash payments on build to suit
leases(7,115)(3,138)0Cash payments for rate lock
agreement00(3,150)Cash payments for repurchase of common
stock(2,406,997)(1,644,581)(1,699,998)Proceeds from issuance
of common stock255,241133,687164,190Cash payments of
employee tax withholdings for performance based stock
awards(16,014)(19,274)(24,965)Excess tax benefits from share-
based compensation0070,999Cash dividends
paid(922,596)(764,040)(650,988)Net cash (used in) financing
activities(3,097,481)(2,297,346)(1,586,877)Effect of exchange
rate changes on cash(95,674)113,0869,272Net increase
(decrease) in cash and cash
equivalents271,752(171,372)834,376Cash and cash equivalents
at beginning of year2,758,4772,929,8492,095,473Cash and cash

equivalents at end of year$ 3,030,229$ 2,758,477$ 2,929,849
Consolidated Statements of SharConsolidated Statements of
Shareholders' Equity - USD ($) $ in ThousandsTotalCommon
StockAdditional Paid-In CapitalAccumulated Other
Comprehensive Income (Loss)Retained EarningsBeginning
Balance at Jan. 30, 2016$ 4,307,075$ 1,326,992$ (667,472)$
3,647,555Beginning Balance (Shares) at Jan. 30,
20161,326,992,000Increase (Decrease) in Stockholders' Equity
[Roll Forward]Net income2,298,2342,298,234Other
comprehensive (loss), net of tax(26,754)(26,754)Cash dividends
declared on common stock(680,183)(680,183)Recognition of
share-based compensation102,251$ 102,251Issuance of common
stock under stock incentive plan and related tax effect209,974$
10,202204,873(5,101)Issuance of common stock under stock
incentive plan and related tax effect (shares)10,202,000Common
stock repurchased$ (1,699,998)$
(44,556)(307,124)(1,348,318)Common stock repurchased
(shares)(44,600,000)(44,556,000)Ending balance at Jan. 28,
2017$ 4,510,599$ 1,292,638(694,226)3,912,187Ending balance
(shares) at Jan. 28, 20171,292,638,000Increase (Decrease) in
Stockholders' Equity [Roll Forward]Net
income2,607,9482,607,948Other comprehensive (loss), net of
tax252,367252,367Cash dividends declared on common
stock(793,878)(793,878)Recognition of share-based
compensation101,362101,362Issuance of common stock under
stock incentive plan and related tax effect114,492$
7,790110,597(3,895)Issuance of common stock under stock
incentive plan and related tax effect (shares)7,790,000Common
stock repurchased$ (1,644,581)$
(44,410)(211,959)(1,388,212)Common stock repurchased
(shares)(44,400,000)(44,410,000)Ending balance at Feb. 03,
2018$ 5,148,309$ 1,256,018(441,859)4,334,150Ending balance
(shares) at Feb. 03, 20181,256,018,0441,256,018,000Increase
(Decrease) in Stockholders' Equity [Roll Forward]Net income$
3,059,7983,059,798Cumulative effect of new accounting
principle in period of adoption58,71258,712Other

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