1-Base-CaseTool KitChapter 11112118Note Calculations are automa

1-Base-CaseTool KitChapter 1111/21/18Note: Calculations are
automatic, including for tables. This will make the calculations
take longer to complete. You can disable automatic calculations
for tables by following the steps shown here.Cash Flow
Estimation and Risk AnalysisWorksheet 1-Base-CaseThis
worksheet contains the base-case model. It calculates an
expansion project's cash flows and performance measures using
base-case, or most likely, values for the input variables. It also
includes the basic analysis but with straight-line depreciation
and bonus depreciation.Go to the menu "Files" at the top left of
the menu bar.Select "Options" from the items in the first
column.This will give you the screen shown below:The second
worksheet (2-Sens) extends the basic model to include
sensitivity analysis using Data Tables (we include a brief
tutorial on the use of Data Tables). Worksheet 2-Sens also
illustrates special cases of sensitivity analysis, including
breakeven analysis, one-way data tables with multiple outputs,
and two-way data tables.Worksheet 3a-Sens extends the basic
model to include scenario analysis. Worksheet 3b-ScenMgr
shows how to use Excel's Scenario Manager for scenario
analysis.Worksheet 4-Sim extends the basic model to include
simulation analysis. Worksheet 5-Replmt illustrates the
analysis for a proposed cost-reducing replacement investment.
Replacement decisions differ from expansion decisions because
most of the cash flows are found by subtracting the old project's
cash flows from those of the new project to calculate
incremental cash flows for use in the analysis.Worksheet 6-
DecTree extends the scenario analysis to examine two decision
trees in which the decision is made in stages. The first one
simply shows the situation where the firm can abandon the
project if things are not working out and cash flows are
negative. The second one involves a marketing study and a
prototype of the final product designed to learn more about
demand before deciding to go into full production.Worksheet

Appendix 11-A provides depreciation tables as described in
Appendix A of the textbook. It also shows examples using
straight-line depreciation and bonus depreciation.11-1
Identifying Relevant Cash FlowsA proposal’s relevant project
cash flows are the differences between the cash flows the firm
will have if it implements the project versus the cash flows it
will have if it rejects the project. These are called incremental
cash flows.Choose "Formulas" in the first column.11-2 Analysis
of an Expansion ProjectThis will give you the screen shown
below.The figure below shows the inputs and key results of
Project L (one of the projects whose cash flows are used in the
previous chapter); the actual analysis is conducted further
below in the worksheet. The values in the Inputs section are
linked to the model, as are the values shown in Key Results. If
you change any of the values in the Input Section, the model
recalculate almost 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 2016, select Data, What-If-Analysis,
Scenario Manager.11-2a Base Case Inputs and Key
ResultsFigure 11-1Analysis of an Expansion Project: Inputs and
Key Results (Dollars in Thousands)Part 1. Inputs and Key
ResultsScenario:InputsBase-CaseKey Results Equipment
cost$10,000NPV $1,070Salvage value, equipment, Year
4$1,000IRR13.8%Opportunity cost$0MIRR12.4%Externalities
(cannibalization)$0PI1.09Units sold, Year
110,000Payback2.94Units sold, Year 2, Pct. change from Year
120%Discounted payback3.65Units sold, Year 3, Pct. change
from Year 220%Units sold, Year 4, Pct. change from Year
3−30%Sales price per unit, Year 1$2.00Annual change in sales
price, after Year 14%Variable cost per unit (VC), Year
1$1.56Annual change in VC, after Year 13%Nonvariable cost
(Non-VC), Year 1$1,107Annual change in Non-VC, after Year
13%Project WACC10%Tax rate25%The first panel is
"Calculation options". Working capital as % of next year's

sales10%Choose "Automatic except for data tables". Remember
to repeat this process and select Automatic when you are using
data tables.The model uses the "Base-Case" input values shown
below to calculate the NPV and other performance measures.
The model assumes that the firm correctly incorporates
inflation in prices and costs. The base-case model uses MACRS
for depreciation. Use Scenario Manager to see the results if
straightline depreciation or bonus depreciation are used.11-2b
through 11-2d: Cash Flow Projections: Intermediate
Calculations, Estimating Net Operating Profit After Taxes
(NOPAT), and Completing the CalculationsFigure 11-2 Analysis
of a New (Expansion) Project: Cash Flows and Performance
Measures
(Dollars in Thousands)Part 2. Cash Flows and Performance
MeasuresScenario:Base-CaseIntermediate
Calculations01234Unit sales10,00012,00012,0007,000Sales
price per unit$2.000$2.080$2.163$2.250Variable cost per unit
(excl. depr.)$1.560$1.607$1.655$1.705Nonvariable costs (excl.
depr.)$1,107$1,140$1,174$1,210Sales revenues = Units ×
Price/unit$20,000$24,960$25,958$15,748NOWCt =
15%(Revenuest+1)$2,000$2,496$2,596$1,575$0Basis for
depreciation$10,000Annual depreciation rate
(MACRS)33.33%44.45%14.81%7.41%Annual depreciation
expense$3,333$4,445$1,481$741Remaining undepreciated value
(book value)$6,667$2,222$741$0Forecast Project Cash
Flows01234Sales revenues = Units ×
Price/unit$20,000$24,960$25,958$15,748Variable costs =
Units × Cost/unit$15,600$19,282$19,860$11,933Nonvariable
costs (excluding
depr.)$1,107$1,140$1,174$1,210Depreciation$3,333$4,445$1,4
81$741Earnings before int. and taxes
(EBIT)−$40$93$3,443$1,865Taxes on operating profit (25%
rate)−$10$23$861$466Net operating profit after
taxes−$30$70$2,582$1,39901234Net operating profit after
taxes−$30$70$2,582$1,399Add back
depreciation$3,333$4,445$1,481$741Equipment

purchases−$10,000Salvage value$1,000Cash flow due to tax on
salv. val.−$250Cash flow due to change in
NOWC−$2,000−$496−$100$1,021$1,575Opportunity cost, after
taxes$0$0$0$0$0After-tax externalities$0$0$0$0Project cash
flows: Time Line−$12,000$2,807$4,415$5,084$4,464Project
Evaluation MeasuresNPV
$1,070=NPV(E71,F116:I116)+E116IRR13.75%=IRR(E116:I116
)MIRR12.37%=MIRR(E116:I116,E71,E71)Profitability
index1.09=NPV(E71,F116:I116)/(-
E116)Payback2.94=PERCENTRANK(E125:I125,0,6)*I124Note:
see Ch 10 Tool Kit.xls for a detailed explanation of how to use
the PERCENTRANK function to calculate payback.Disc.
payback3.65=PERCENTRANK(E127:I127,0,6)*I124Calculation
s for PaybackYear:01234 Cumulative cash flows for
payback−$12,000−$9,193−$4,778$306$4,771 Disc. cash flows
for disc. payback−$12,000$2,552$3,649$3,820$3,049
Cumulative discounted cash
flows−$12,000−$9,448−$5,799−$1,980$1,070Taxation of
SalvageSuppose GPC terminates operations before the
equipment is fully depreciated. The after-tax salvage value
depends upon the price at which GPC can sell the equipment
and upon the book value of the equipment (i.e., the original
basis less all previous depreciation charges). See below for
calculations of yearly book values.Year:1234Beginning book
value$10,000.0$6,667.0$2,222.0$741.0Depreciation$3,333.0$4,
445.0$1,481.0$741.0Ending book
value$6,667.0$2,222.0$741.0$0.0If GPC terminates at Year 2
and can sell the equipment for $2,170, what is the after-tax
salvage cash flow? What if GPC can only sell the equipment for
$522 at Year 2?Case 1: GainCase 2: LossMarket value when
salvaged at Year 2$2,570.0$522.0Book value when salvaged at
Year 2$2,222.0$2,222.0Expected gain or loss$348.0-
$1,700.0Tax expense (credit)$87.0-$425.0Cash from
sale$2,570.0$522.0Tax expense (credit)$87.0-$425.0Net cash
flow from salvage$2,483.0$947.0 In Case 1, the sales price is
greater than the book value. Here the depreciation charges

exceeded the "true" depreciation, and the difference is called
"depreciation recapture." It is taxed as ordinary income. In
Case 2, the sales price is less than the book value. This
represents a shortfall in depreciation taken versus "true"
depreciation, and it is treated as an operating expense at the
time of the sale. Because it is a noncash expense, it reduces the
company's overall tax bill. In other words, it acts as a tax credit
if the company has other taxable income. The actual book value
at the time of disposition depends on the month of disposition.
We have simplified the analysis and assumed that there will be
a full year of depreciation. The Impact of Omitting InflationTo
determine the impact if inflation is incorrectly omitted, the
easiest way is to change the inputs for inflation to zero. And the
easiest way to do this is to use Excel's Scenario Manager. Open
Data, What-If-Analysis, and Scenario Manager. Pick the
scenario that has no inflation and click "Show." You can get the
original inputs back by repeating the process by select the base-
case scenario and click "Show."Current Scenario:Base-CaseNPV
based on current scenario:$1,070Value of NPV in Base-
Case:$1,070Value of NPV in Base-Case but Ignore
Inflation:$131The Impact of Different Depreciation MethodsThe
base-case uses MACRS to determine annual depreciation
expenses. To determine the impact if inflation is incorrectly
omitted, the easiest way is to change the inputs for inflation to
zero. And the easiest way to do this is to use Excel's Scenario
Manager. Open Data, What-If-Analysis, and Scenario Manager.
Pick the scenarios that have MACRS depreciation (or Bonus
depreciation or Straight-line depreciation) and click "Show."
You can get the original inputs back by repeating the process by
select the base-case scenario and click "Show."Value of NPV if
Use MACRS Depreciation:$1,070Value of NPV if Use Bonus
Depreciation:$1,262Value of NPV if Use Straight-Line
Depreciation:$967
2-Sens11/21/18Worksheet 2-Sensitivity AnalysisThis worksheet
extends the basic model (shown in Tab 1-Base-Case) to include
sensitivity analysis. This worksheet also illustrates special cases

of sensitivity analysis, including 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)Figure
11-1 (Repeated Here for Convenience)Analysis of an Expansion
Project: Inputs and Key Results (Dollars in Thousands)Part 1.
Inputs and Key ResultsInputsBase-CaseKey Results Equipment
cost$10,000NPV $1,070Salvage value, equipment, Year
4$1,000IRR13.75%Opportunity
cost$0MIRR12.37%Externalities
(cannibalization)$0PI1.09Units sold, Year
110,000Payback2.94Units sold, Year 2, Pct. change from Year
120%Discounted payback3.65Units sold, Year 3, Pct. change
from Year 220%Units sold, Year 4, Pct. change from Year
3−30%Sales price per unit, Year 1$2.00Annual change in sales
price, after Year 14.00%Variable cost per unit (VC), Year
1$1.56Annual change in VC, after Year 13%Nonvariable cost
(Non-VC), Year 1$1,107Annual change in Non-VC, after Year
13%Project WACC10%Tax rate25%Working capital as % of
next year's sales10%The model uses the "Base-Case" input
values shown below to calculate the NPV and other performance
measures. The model assumes that the firm uses accelerated
depreciation; a modified version of the model, shown to the
model's right, shows the results if the firm elects to use
straight-line depreciation. This analysis demonstrates that
accelerated depreciation improves project profitability.Figure
11-2 (Repeated Here for Convenience)Analysis of a New
(Expansion) Project: Cash Flows and Performance Measures
(Dollars in Thousands)Part 2. Cash Flows and Performance
MeasuresScenario:Base-CaseIntermediate
Calculations01234Unit sales10,00012,00012,0007,000Sales
price per unit$2.00$2.08$2.16$2.25Variable cost per unit (excl.
depr.)$1.56$1.61$1.66$1.70Nonvariable costs (excl.
Price/unit$20,000$24,960$25,958$15,748NOWCt =

expense$3,333$4,445$1,481$741Remaining undepreciated
value$6,667$2,222$741$0Cash Flow ForecastCash Flows at End
of Year01234Sales revenues = Units ×
costs (excluding
depreciation)$1,107$1,140$1,174$1,210Depreciation$3,333$4,4
45$1,481$741Earnings before interest and taxes
(EBIT)−$40$93$3,443$1,865Taxes on operating profit (40%
rate)−$10$23$861$466Net operating profit after
taxes−$30$70$2,582$1,399Add back
salvage value (25% rate)−$250Cash flow due to change in
WC−$2,000−$496−$100$1,021$1,575Opportunity cost, after
taxes$0$0$0$0$0After-tax cannibalization or complementary
effect$0$0$0$0Project cash flows: Time
Line−$12,000$2,807$4,415$5,084$4,464Project Evaluation
MeasuresNPV $1,070IRR13.75%MIRR12.37%Profitability
index1.09Payback2.94Discounted payback3.65Calculations for
PaybackYear:01234 Cumulative cash flows for payback-
$12,000-$9,193-$4,778$306$4,771 Discounted cash flows for
disc. payback-$12,000$2,552$3,649$3,820$3,049 Cumulative
discounted cash flows-$12,000-$9,448-$5,799-$1,980$1,07011-
5 Sensitivity AnalysisRisk 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:Sales Set up the Data Table
by typing in the labels shown here. You don't need to shade the
areas, but we did because it will help us explain where other
values and formulas go. The purple area defines how much each
input (the sales price per unit in this example) will deviate from
the base case value. The light blue cells will show the inputs
that correspond to the deviations. The orange cells will show
the results, which will be the NPV for each different input
value. We explain the other cells in the next step.
DeviationPrice/unitNPVfrom Base-30%0%30%Step 2:Sales
Type the actual number in the green cell for the base case value
of the input, which is an intial sales price of $2.00. Be sure to
type in the actual sales price of $2.00 and not a formula. Every
year we have students who make this mistake! Don't be one of
them!
If you type in a fomula in the green cell that is a link back to
the Part 1 Inputs at the top of this sheet, your data table will
have a circular reference and will not give you the correct
results. We repeat: Type in the actual sales price of $2.00 and
not a formula.DeviationPrice/unitNPVfrom Base$2.00-
30%0%30%Step 3:Sales Enter the formula =$B$121*(1+A122)
into the light blue range's (the input range's) first cell, B122.
Notice that the formula will multiply the base-case value of the
input (which is shown as a number in B121, not a formula in
B121) and use the deviation in the purple range to create a new
input value in the light blue range. It is ok to have a formula in
the input range, but be sure that none of these formulas is
linked back to the Part 1 Inputs at the top of this
sheet.DeviationPrice/unitNPVfrom Base$2.00-
30%$1.400%30%Step 4:Sales Copy the formula in the input

(light blue) range's top cell down for the other cells in the input
(light blue) range. This will give inputs the match the
deviations in the purple range. Note: We changed the formula to
be =$B$128*(1+A130) so that the table in Step 4 would be
correct; if we had applied all these steps to a single data table
instead of a different table for each Step, then we would not
have had to change the formula. DeviationPrice/unitNPVfrom
Base$2.00-30%$1.400%$2.0030%$2.60Step 5:Sales Enter
into the bright yellow cell a formula that refers to the desired
output cell in the section at the top of the sheet for Part 1 Key
Results. We want NPV, so we the formula is: =$I$15. Notice
that the bright yellow cell will show the current value of NPV.
Be sure that none of the formulas in the blue input cells
refers back to the cell for sales at the Part 1 Inputs section at
the top of the sheet. If it does, the resulting data table will have
a circular reference.DeviationPrice/unitNPVfrom
Base$2.00$1,070-30%$1.400%$2.0030%$2.60Step 6:Sales
Now use your cursor to highlight the range we show in gray
(this is called the Data Table range); notice that this highlighted
range includes the previous green cell (which contains the
actual number for sales price), the previous yellow cell cell
(which had a link to the desired output value), the previous light
blue cells (which have the inputs for the data table), and the
previous orange cells (which will be for the data table's
outputs).DeviationPrice/unitNPVfrom Base$2.00$1,070-
30%$1.400%$2.0030%$2.60With the range still highlighted,
open the Table dialog box. In Excel for Windows, select Data,
What-If-Analysis, then Data Table. You will get the dialog box
shown below.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 at the Part 1 Input Data section at the top of the
worksheet, you will see that it enters in cell E23, so you type
E23 in the Column input cell (or click on cell E23 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.Step 7:SalesDeviationPrice/unitNPVfrom
Base$2.00$1,070-30%$1.40-
$14,2640%$2.00$1,07030%$2.60$16,403We 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. We
made one change to make it easier. By carefully using the
permanent cell reference in the formula in B198, we can simply
copy this formula into the other data tables and only use 1
column for deviation.Deviation
Mike Ehrhardt: Change the cells below to get different
deviations. All other inputs will be updated
automatically.EquipmentNPVUnit SalesNPVSales
Price/unitNPVVC/UnitNPVfrom
Base$10,000$1,07010,000$1,070$2.00$1,070$1.56$1,070-
30%$7,000$3,4467,000-$2,2961.40-
$14,264$1.09$13,0370%$10,000$1,07010,000$1,0702.00$1,070
$1.56$1,07030%$13,000-$1,30613,000$4,4362.60$16,403$2.03-
$10,898Range =$4,752Range =$6,732Range =$30,667Range
=$23,935The 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
BaseEquip.PriceUnitsVC/Unit−30%$3,446−$14,264−$2,296$13,
0370%$1,070$1,070$1,070$1,07030%−$1,306$16,403$4,436−$
10,898Range$4,752$30,667$6,732$23,935Tornado
DiagramsTornado diagrams are another way to present results
from sensitivity analysis. A tornado shows the range of

outcomes caused by changes in each input variable in graphic
form, with the input variable causing the widest range shown at
the top of the chart and the input variable causing the smallest
range at the bottom, which makes the chart look like a
tornado.The good news is that a tornado diagram makes it
immediately obvious which inputs have the biggest impacts on
NPV. The bad news is that there is no way to create a tornado
diagram in Excel directly from the results of a sensitivity
analysis. An intermediate step is required, as we describe
below.The first step is to rank the range of possible NPV's for
each of the input variables that is being changed. We used the
RANK function, as shown in the rose-colored area below. In our
example, the range for sales price/unit is the largest and the
range for the equipment cost is the smallest. In the yellow
figure below, we created an XY scatter chart with four series
(Equipment, Price, Units, and VC/Unit). Each series has 3
observations. The X-values for each series are the NPVs shown
in the olive green range (these correspond to the -30%, 0%, and
30% deviations of the inputs). The Y-values for each series are
its corresponding rank in the range of NPVs (with the same rank
repeated for all 3 X-values, shown in the aqua region below).
To summarize, each variable is plotted so that its "width" on the
X-axis is determined by the impact it has on NPV, and its
"height" on the chart (the Y-axis) determined by the input's rank
in terms of the NPV's sensitivity.It is helpful to also plot a
vertical line showing the base-case NPV. To do this, we have all
3 X-values equal to the base-case NPV and let the
corresponding Y-values go from the lowest rank to the highest
rank (shown in the bright yellow area below.) In the final
presentation of the tornado diagram below, we set the vertical
axis to cross the horizontal axis at the maximum vertical value
(i.e., we put the X-axis at the top of the chart instead of at the
bottom). For the vertical axis (the Y-axis), we checked "None"
for tick marks and for labels, so the chart doesn't show this axis.
Finally, we formatted the "right" data points for each series to
show the series name. These changes are purely cosmetic in

nature.The advantage of this method is that the chart below will
update automatically if you change the model (and also update
the data tables). For a slightly less complicated approach that
requires manual intervention, see the example to the
right.Additional data for Tornado DiagramRepeated from above
for convenience:NPV with Variables at Different Deviations
from BaseEquip.PriceUnitsVC/UnitX-values for diagram
below$3,446−$14,264−$2,296$13,037$1,070$1,070$1,070$1,07
0−$1,306$16,403$4,436−$10,898Rank of Range of NPV from
Sensitivity Table AboveScratch for Tornado Diagram Below
Mike Ehrhardt: This puts in the dotted vertical line in the
tornado diagram showing how the outcomes compare to the base
case.EquipmentPriceUnitsVC/UnitRange$4,752$30,667$6,732$
23,935Base NPV =Y-axisRank1423$1,0705Y-values for
diagram below14231,070414231,07011423Figure 11-4 Tornado
Diagram for Solar Water Heater Project: Range of Outcomes for
Input Deviations from Base-Case (Dollars in Thousands)Note:
this is an XY scatterplot, with four data series (one for each
input varaible being analyzed. Each data series has 3
observations corresponding to the 3 deviations in the data
tables. The X-values for a data series are its NPV's for each
deviation. A data series' Y-values are the same for each of its 3
observations are equal the rank of the data series NPV range
relative to the NPV ranges of the other data series. For example,
the rank of the data series for the Price variable is 4 for each of
its observations because Price has the highest ranked range in
NPVs compared to the other input variables.NPV Breakeven
AnalysisIn breakeven analysis, we find the value of the input
variable that produces 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. The result was $1.96.
We repeated this for the other inputs and report these results in
the table below.Table 11-1 NPV Break-Even Analysis (Dollars
in Thousands)Input Value that Produces Zero

NPVInputEquipment$11,351Units sold, Year 19047Sales price
per unit, Year 1$1.96Variable cost per unit (VC), Year
1$1.60Nonvariable cost (Non-VC), Year 1$1,539Project
WACC14.47%Data Tables: Multiple Outputs for a Single
InputNPV Breakeven Analysis (Dollars in Thousands)Data
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 cells above the outputs). Then use the Data,
Tables, and set "Column input" to the cell reference of the
desired input. Example: NPV and IRR for Changes in Sales
Price% DeviationSALES PRICEfromSales PriceNPVIRRBase
Case$2.00$1,07013.8%-30%$1.40-$14,264Not found-
15%$1.70-$6,597-
16.8%0%$2.00$1,07013.8%15%$2.30$8,73637.9%30%$2.60$16
,40358.9%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
purple 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 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 reference for the
input shown in the table's column E21 for sales price). Example:
NPV for Changes in Sales Price and Units SoldBase case units
sold =10,000Base case sales price =$2.00% Deviation from
Base Case-30%-15%0%15%30%% Deviation fromNPV cell
referenceUnits SoldBase
Case$1,0707,0008,50010,00011,50013,000-30%Sales

Price$1.40-$13,030-$13,647-$14,264-$14,881-$15,498-
15%$1.70-$7,663-$7,130-$6,597-$6,064-$5,5310%$2.00-
$2,296-
$613$1,070$2,753$4,43615%$2.30$3,070$5,903$8,736$11,569$
14,40230%$2.60$8,437$12,420$16,403$20,386$24,369
Price
-0.3 0 0.3 -14263.552350420054 1069.7676359196739
16403.087622259405 Units
Units
-0.3 0 0.3 -2296.1882912710898 1069.7676359196739
4435.7235631104413 VC/Unit
VC/Unit
-0.3 0 0.3 13037.131695068645 1069.7676359196739
-10897.59642322929 Equip.
Equip.
-0.3 0 0.3 3445.5903427019985 1069.7676359196739
-1306.0550708626506
% Deviation from Base
NPV ($)
Price
Price
-14263.552350420054 1069.7676359196739
16403.087622259405 4 4 4 Units
Units
-2296.1882912710898 1069.7676359196739 4435.7
235631104413 2 2 2 VC/Unit

VC/Unit
13037.131695068645 1069.7676359196739 -
10897.59642322929 3 3 3 Equip.
Equip.
3445.5903427019985 1069.7676359196739 -
1306.0550708626506 1 1 1 Base NPV =
Base = $1,070
1069.7676359196739 1069.7676359196739
1069.7676359196739 5 4 1
NPV
3a-Scen11/21/18Worksheet 3a-Scenario Analysis11-6 Scenario
AnalysisThis worksheet extends the basic model (shown in Tab
1-Base-Case) to include scenario analysis. On this tab we
modify the Tab 1-Base-Case 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 because the inputs for each set of inputs
are linked to a model for that particular set of inputs; these 3
models are shown to the right of Figure 11-5. If you want to
return to the our original inputs for any model, you can go to
Scenario Manager (Data, What-If Analysis, Scenario Manager)
and pick the original scenario for the 3 cases.We chose to create
a separate scenario with its own set of changing cells for each
of the three cases because this allows a user to modify each
scenario separately and still easily see the results from the other
two scenarios. However, in worksheet "3b. Scen." we show how
to put all three scenarios into a single group (i.e., all three
scenarios have the same changing cells) and use Scenario
Manager's Summary feature.Figure 11-5 Analysis for Scenario
Shown Below:Analysis for Scenario Shown Below:Analysis for
Scenario Shown Below:Inputs and Key Results for Each
Scenario (Dollars in Thousands)Worst-CaseBase-CaseBest-
CaseScenarios:Scenario NameWorst-CaseBase-CaseBest-
CaseAnalysis for each scenario is shown to the right.Probability
of Scenario25%50%25%Intermediate
Calculations01234Intermediate Calculations01234Intermediate
Calculations01234Inputs:Unit sales8,50010,20010,2005,950Unit
sales10,00012,00012,0007,000Unit
sales11,50013,80013,8008,050Equipment
cost$11,000$10,000$9,000Sales price per
unit$1.80$1.85$1.91$1.97Sales price per
unit$2.00$2.08$2.16$2.25Sales price per
unit$2.20$2.31$2.43$2.55Salvage value of equip. in Year
4$1,000$1,000$1,000Variable cost per unit (excl.
depr.)$1.72$1.79$1.86$1.93Variable cost per unit (excl.
depr.)$1.56$1.61$1.66$1.70Variable cost per unit (excl.
depr.)$1.40$1.43$1.46$1.49Opportunity cost$0$0$0Nonvariable
costs (excl. depr.)$941$969$998$1,028Nonvariable costs (excl .
depr.)$1,107$1,140$1,174$1,210Nonvariable costs (excl.
depr.)$1,273$1,311$1,351$1,391Externalities
(cannibalization)$0$0$0Sales revenues = Units ×

Price/unit$15,300$18,911$19,478$11,703Sales revenues = Units
× Price/unit$20,000$24,960$25,958$15,748Sales revenues =
Units × Price/unit$25,300$31,878$33,472$20,502Units sold,
Year 1$8,500$10,000$11,500NOWCt =
15%(Revenuest+1)$1,530$1,891$1,948$1,170$0NOWCt =
15%(Revenuest+1)$2,000$2,496$2,596$1,575$0NOWCt =
15%(Revenuest+1)$2,530$3,188$3,347$2,050$0Units sold,
Year 2, Pct. change from Year 120%20%20%Basis for
depreciation$11,000Basis for depreciation$10,000Basis for
depreciation$9,000Units sold, Year 3, Pct. change from Year
220%20%20%Annual depreciation rate
(MACRS)33.33%44.45%14.81%7.41%Annual depreciation rate
(MACRS)33.33%44.45%14.81%7.41%Annual depreciation rate
(MACRS)33.33%44.45%14.81%7.41%Units sold, Year 4, Pct.
change from Year 3-30%-30%-30%Annual depreciation
expense$3,666$4,890$1,629$815Annual depreciation
expense$3,333$4,445$1,481$741Annual depreciation
expense$3,000$4,001$1,333$667Sales price per unit, Year
1$1.80$2.00$2.20Remaining undepreciated
value$7,334$2,444$815$0Remaining undepreciated
value$6,667$2,222$741$0Remaining undepreciated
value$6,000$2,000$667$0% Δ in sales price, after Year
13%4%5%Cash Flow ForecastCash Flows at End of YearCash
Flow ForecastCash Flows at End of YearCash Flow
ForecastCash Flows at End of YearVar. cost per unit (VC), Year
1$1.72$1.56$1.40012340123401234% Δ in VC, after Year
14%3%2%Sales revenues = Units ×
Price/unit$15,300$18,911$19,478$11,703Sales revenues = Units
× Price/unit$20,000$24,960$25,958$15,748Sales revenues =
Units × Price/unit$25,300$31,878$33,472$20,502Nonvar. cost
(Non-VC), Year 1$941$1,107$1,273Variable costs = Units ×
Cost/unit$14,620$18,246$18,976$11,512Variable costs = Units
× Cost/unit$15,600$19,282$19,860$11,933Variable costs =
Units × Cost/unit$16,100$19,706$20,101$11,960% Δ in Non-
VC, after Year 13%3%3%Nonvariable costs (excluding
depreciation)$941$969$998$1,028Nonvariable costs (excluding

depreciation)$1,107$1,140$1,174$1,210Nonvariable costs
(excluding depreciation)$1,273$1,311$1,351$1,391Project
WACC10%10%10%Depreciation$3,666$4,890$1,629$815Depre
ciation$3,333$4,445$1,481$741Depreciation$3,000$4,001$1,33
3$667Tax rate25%25%25%Earnings before interest and taxes
(EBIT)−$3,927−$5,194−$2,125−$1,652Earnings before interest
and taxes (EBIT)−$40$93$3,443$1,865Earnings before interest
and taxes (EBIT)$4,927$6,860$10,688$6,484NOWC as % of
next year's sales10%10%10%Taxes on operating profit (25%
rate)-$982−$1,298−$531−$413Taxes on operating profit (25%
rate)−$10$23$861$466Taxes on operating profit (25%
rate)$1,232$1,715$2,672$1,621Key Results:Net operating profit
after taxes−$2,945−$3,895−$1,594−$1,239Net operating profit
after taxes−$30$70$2,582$1,399Net operating profit after
taxes$3,695$5,145$8,016$4,863NPV −$9,795$1,070$15,073Add
back depreciation$3,666$4,890$1,629$815Add back
depreciation$3,333$4,445$1,481$741Add back
depreciation$3,000$4,001$1,333$667IRR−32.6%13.8%57.5%Eq
uipment purchases−$11,000Equipment
purchases−$10,000Equipment
purchases−$9,000MIRR−24.8%12.4%35.6%Salvage
value$1,000Salvage value$1,000Salvage
value$1,000Profitability index0.221.092.31Cash flow due to tax
on salvage value (25% rate)−$250Cash flow due to tax on
salvage value (25% rate)−$250Cash flow due to tax on salvage
value (25% rate)−$250PaybackNot found2.941.61Cash flow due
to change in WC−$1,530−$361−$57$778$1,170Cash flow due to
change in WC−$2,000−$496−$100$1,021$1,575Cash flow due
to change in WC−$2,530−$658−$159$1,297$2,050Discounted
paybackNot found3.651.81Opportunity cost, after
taxes$0$0$0$0$0Opportunity cost, after
taxes$0$0$0$0$0Opportunity cost, after taxes$0$0$0$0$0After -
tax cannibalization or complementary effect$0$0$0$0After-tax
cannibalization or complementary effect$0$0$0$0After-tax
cannibalization or complementary effect$0$0$0$0Project cash
flows: Time Line−$12,530$360$938$813$1,496Project cash

flows: Time Line−$12,000$2,807$4,415$5,084$4,464Project
cash flows: Time
MeasuresProject Evaluation MeasuresProject Evaluation
MeasuresNPV -$9,795NPV $1,070NPV $15,073IRR-
32.64%IRR13.75%IRR57.53%MIRR-
24.82%MIRR12.37%MIRR35.57%Profitability
index0.22Profitability index1.09Profitability
index2.31PaybackERROR:#N/APayback2.94Payback1.61Discou
nted paybackERROR:#N/ADiscounted payback3.65Discounted
payback1.81Calculations for PaybackYear:01234Calculations
for PaybackYear:01234Calculations for PaybackYear:01234
Cumulative cash flows for payback-$12,530-$12,170-$11,233-
$10,420-$8,923 Cumulative cash flows for payback-$12,000-
$9,193-$4,778$306$4,771 Cumulative cash flows for payback-
$11,530-$5,493$3,493$14,139$22,469 Discounted cash flows
for disc. payback-$12,530$327$775$611$1,022 Discounted
cash flows for disc. payback-$12,000$2,552$3,649$3,820$3,049
Discounted cash flows for disc. payback-
$11,530$5,489$7,426$7,998$5,689 Cumulative discounted
cash flows-$12,530-$12,203-$11,428-$10,817-$9,795
Cumulative discounted cash flows-$12,000-$9,448-$5,799-
$1,980$1,070 Cumulative discounted cash flows-$11,530-
$6,041$1,385$9,383$15,073Scenario 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' analyses 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.Figure 11-6 Scenario Analysis:
Expected NPV and Its Risk (Dollars in Thousands)Predicted
Cash Flows for Alternative
ScenariosProb:01234WACCNPVBest
→25%−$11,530$6,037$8,986$10,646$8,33010.00%$15,073Base
→50%−$12,000$2,807$4,415$5,084$4,46410.00%$1,070Worst
→25%−$12,530$360$938$813$1,49610.00%−$9,795Expected
NPV =$1,854Standard Deviation (SD) =$8,827Coefficient of
Variation (CV) = Std. Dev./Expected NPV =4.76Scratch work
for chartWorst-Case−$9,79525%−$9,7950%Base-
Case$1,07050%$1,0700%Best-
Case$15,07325%$15,0730%Expected NPV$1,8540%$1,854-
15%Scenario Analysis: Expected Csh Flows and NPV of
Expected Cash FlowPredicted Cash Flows for Alternative
ScenariosProb:01234WACCNPVBest
→25%−$11,530$6,037$8,986$10,646$8,33010.00%Base→50%−
$12,000$2,807$4,415$5,084$4,46410.00%Worst
→25%−$12,530$360$938$813$1,49610.00%Expected
CF−$12,015$3,003$4,688$5,407$4,689NPV of Exp.
CF.$1,854Squared Deviations of Cash Flows from Expected
CF01234Best
→$235,225$325,888,243$441,043,786$513,516,201$413,914,59
9Base→$144,000,000$7,879,249$19,492,689$25,849,417$19,93
1,411Worst
→$157,000,900$129,416$878,906$660,883$2,239,002Sum of
Sq.
Dev.$301,236,125$333,896,909$461,415,381$540,026,500$436,
085,012
1
Probability Distribution of Scenarios:
Outcomes and Probabilities
Worst-Case
[Y VALUE]
[SERIES NAME]
[X VALUE]

-9795.3734464517456 -9795.3734464517456 0.25 0
Base-Case [Y VALUE]
1069.7676359196739 1069.7676359196739 0.5 0
Best-Case [Y VALUE]
15072.851034253141 15072.851034253141 0.25 0
Expected NPV
1854.2532149101858 1854.2532149101858 0 -0.15
NPV
1
1
3b-ScenMgr11/21/18Worksheet 3b-Scenario ManagerThe
previous worksheet used three different independent scenarios --
each of the scenarios had different changing cells. In this
worksheet, we explain how to have multiple scenarios with the
same changing cells. We also explain how to use Scenario
Manager's Summary feature.The section for Inputs and Key
results differs from that in the previous worksheet in several
ways. First, there is only 1 column for inputs and results. Each
of the three scenarios used in Scenario Manager in this sheet
specify values for the inputs below. In other words, all three
scenarios have the same changing cells. This is in contrast to
the previous worksheet in which each scenario had its own
separate changing cells. The values shown in the inputs section
are the values for the active scenario.Second, we have given
each cell for the inputs and key results a name. We do this so
that the Summary feature in the Scenario Manager will show
names instead of cell references. To name a cell, put your
cursor in the Name Box and give the cell a name. For example,
suppose we want to assign the name "Yellow" to the bright
yellow cell below. Following are instructions.ColorBefore
renaming cell: Our cursor is in cell A19, and the Name Box

shows A19.After renaming cell: When our cursor had selected
the yellow cell, we put our cursor in the Name Box and typed in
the name "Yellow". Notice that the Name Box in the screen shot
below now shows the cell's new name.To change the values in
the input section below, go to Data, What-If Analysis, Scenario
Manager, select a scenario, and click "Show." The model to the
right is linked to the inputs. The model calculates results, and
passes those results to the Key Results section below.Figure:
Not in Printed BookAnalysis for Scenario Shown Below:Inputs
and Key Results for Active Scenario (Dollars in
Thousands)Base-CaseScenario NameBase-CaseWorst-CaseBase-
CaseBest-CaseIntermediate Calculations01234Probability of
Scenario50%25%50%25%Unit
sales10,00012,00012,0007,000Inputs:Sales price per
unit$2.00$2.08$2.16$2.25Equipment
cost$10,000$11,000$10,000$9,000Variable cost per unit (excl.
depr.)$1.56$1.61$1.66$1.70Salvage value, equipment, Year
4$1,000$1,000$1,000$1,000Nonvariable costs (excl.
depr.)$1,107$1,140$1,174$1,210Opportunity
cost$0$0$0$0Sales revenues = Units ×
Price/unit$20,000$24,960$25,958$15,748Externalities
(cannibalization)$0$0$0$0NOWCt =
15%(Revenuest+1)$2,000$2,496$2,596$1,575$0Units sold,
Year 110,0008,50010,00011,500Basis for
depreciation$10,000Units sold, Year 2, Pct. change from Year
120%20%20%20%Annual depreciation rate
(MACRS)33.33%44.45%14.81%7.41%Units sold, Year 3, Pct.
change from Year 220%20%20%20%Annual depreciation
expense$3,333$4,445$1,481$741Units sold, Year 4, Pct. change
from Year 3-30%-30%-30%-30%Remaining undepreciated
value$6,667$2,222$741$0Sales price per unit, Year
1$2.0000$1.8000$2.0000$2.2000Cash Flow ForecastCash Flows
at End of YearAnnual change in sales price, after Year
14%3%4%5%01234Variable cost per unit (VC), Year
1$1.5600$1.7200$1.5600$1.4000Sales revenues = Units ×
Price/unit$20,000$24,960$25,958$15,748Annual change in VC,

after Year 13%4%3%2%Variable costs = Units ×
Cost/unit$15,600$19,282$19,860$11,933Nonvariable cost (Non-
VC), Year 1$1,107.00$941.00$1,107.00$1,273.00Nonvariable
costs (excluding depreciation)$1,107$1,140$1,174$1,210Annual
change in Non-VC, after Year
13%3%3%3%Depreciation$3,333$4,445$1,481$741Project
WACC10%10%10%10%Earnings before interest and taxes
(EBIT)−$40$93$3,443$1,865Tax
rate25.0%25.0%25.0%25.0%Taxes on operating profit (25%
rate)−$10$23$861$466Working capital as % of next year's
sales10%10%10%10%Net operating profit after
taxes−$30$70$2,582$1,399Add back
depreciation$3,333$4,445$1,481$741Key Results:NPV
$1,070−$9,795$1,070$15,073Equipment
purchases−$10,000IRR13.75%−32.64%13.75%57.53%Salvage
value$1,000MIRR12.37%−24.82%12.37%35.57%Cash flow due
to tax on salvage value (25% rate)−$250Profitabilit y
index1.090.221.092.31Cash flow due to change in
WC−$2,000−$496−$100$1,021$1,575Payback2.94Not
found2.941.61Opportunity cost, after
taxes$0$0$0$0$0Discounted payback3.65Not
found3.651.81After-tax cannibalization or complementary
MeasuresTo create a summary sheet showing all scenarios, go to
Data, What-If Analysis, Scenario Manager, and click on
Summary, and select the cells with the key results. The
Summary will be shown in a new worksheet. For convenience,
we have copied that worksheet and show it below. If you make
changes to any scenarios, you must run the Summary again--it
does NOT automatcially update.NPV
$1,070IRR13.75%MIRR12.37%Profitability
$12,000-$9,193-$4,778$306$4,771 Discounted cash flows for
disc. payback-$12,000$2,552$3,649$3,820$3,049 Cumulative

discounted cash flows-$12,000-$9,448-$5,799-$1,980$1,070We
copied the Scenario Summary from the worksheet where it was
created and moved it here. It will not update
automatically.Scenario SummaryCurrent Values:Worst-
CaseBase-CaseBest-CaseChanging Cells:ScenarioBase-
CaseWorst-CaseBase-CaseBest-
CaseProbability50%25%50%25%$E$72Equipment$10,000$11,0
00$10,000$9,000Salvage$1,000$1,000$1,000$1,000OppCost$0$
0$0$0Externalities$0$0$0$0Units_Sold10,0008,50010,00011,50
0Yr1_unit_g20%20%20%20%Yr2_unit_g20%20%20%20%Yr4_
unit_g-30%-30%-30%-
30%Sales_Price$2.0000$1.8000$2.0000$2.2000Growth_in_Sale
s_Price_per_Unit4%3%4%5%Variable_cost_per_unit$1.5600$1.
7200$1.5600$1.4000Growth_in_VC_per_Unit3%4%3%2%Nonv
ariable_Costs$1,107.00$941.00$1,107.00$1,273.00Growth_in_
Nonvariable_costs3%3%3%3%WACC10%10%10%10%Tax_Rat
e25.0%25.0%25.0%25.0%NOWC_as_percent_of_next_year_sa1
0%10%10%10%Result
Cells:NPV$1,070−$9,795$1,070$15,073IRR13.75%−32.64%13.
75%57.53%MIRR12.37%−24.82%12.37%35.57%Profitability_I
ndex1.090.221.092.31Payback2.94Not
found2.941.61Discounted_Payback3.65Not found3.651.81No tes:
Current Values column represents values of changing cells
attime Scenario Summary Report was created. Changing cells
for eachscenario are highlighted in gray.
4a-Sim10011/21/18Worksheet 4-Simulation with 100
TrialsSimulation control, check boxes, and formsNote: this
section is relatively technical and some instructors may choose
to skip it with no loss in continuity.You might wonder "what's
the deal about this check box and why does it work this way?"
There are 2 parts to this question: Why it is useful for the
simulation and how do you use a check box for it? Let's answer
the "why it is useful for a simulation" question first, then talk
about check boxes. This check box is linked to cell B17. If you
click on the box, B17 returns a "TRUE" value, and if the box is
unchecked then it returns a "FALSE" value. The reason you

can't see anything in B17 is because we made the font color the
same as the background color so it wouldn't be distracting.
Below, here's what is in cell B17:To put random variables in the
Data Table for the simulation, the box shown below must be
checked; otherwise, the Data Table contains only zeroes 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.FALSESee, B17 reads
either True or False, depending on whether the box is checked
or not. The formulas in the simulation data table in cells B200
to I200 use this value to determine whether or not the data table
should be evaluated. For example, the formula in B200 is
=IF($B$17,F54,0). If B17 is TRUE, then the cell returns the
value in F54, which is the simulated equipment cost. If B17 is
FALSE, then it returns 0. The other formulas in that row are
similar. The end result is that if B17 is FALSE, then the data
table has no formulas to evaluate (everything is zero) and if it is
TRUE, then it has formulas to evaluate and it records the
simulation results. You didn't really need a check box; you
could just as well have left B17 visible and either put a 1 or a 0
in it, and had the IF statements in row 200 check, instead, for
whether B17 is equal to 1. But the check box is neat.Put a check
in the box below to run simulation; otherwise, the simulation
data table will have only zeros.Uncheck the box when you
finish!!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. Now for
how to use Forms in Excel. To insert a check box in Excel 2010
you must first enable the Developer tab on your Ribbon. These
are instructions for Excel 2010 For later versions of Excel you

can find instructions for this by searching on "check box" in
Excel help. Click the File tab, then click Options, then click
Customize Ribbon. Under Customize the Ribbon and under
Main Tabs, select the Developer check box.
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.On the Developer tab, in the Controls group, click on
Insert and then, in the Form Controls section, click on Insert
(the picture that like a tool box). Look at the Forms Control
section and click on the icon that looks like a check mark. Move
your cursor to where you'd like the check box to go, and click
there. A name, like Check Box 25, will show up next to the box.
Right click on the check box and click on Format Control. Then
under the Control tab, make sure the "unchecked" button is
pressed, then put in a cell reference in the Cell link box. We had
$B$17 in that box. Suppose you put in $B$19 for your box. You
are mostly done! Now when you click on the check box, cell
B19 will display TRUE and when it is not checked, B19will
display FALSE. You can use these two logical values in your
Excel programming. All that is left is to put in a useful
description for the check box. You don't want your users to be
confused about what the box is for. Just click on the check box
area and edit the name to be something like "Click this box if
you want something special to happen to the spreadsheet" (like
enable the data table to do its calculations!).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 in the figure below in the blue section in
Columns C and D. However, any of the input values in
Columns C and D may be changed by the user if desired. In
addition to the inputs for all the variables used previously, the
inputs section also has an input value for the assumed
correlation between units sold in Year 1 and changes in units
sold in later years.The figure below shows the trial inputs and
key results. The inputs used further below in the model are
shown in dark 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 (But showing results of current simulation
iteration.) Panel A: Values from Scenario Analysis and Their
Expected Values and Standard DeviationsInputs and Key
Results for the Current Simulation Trial (Dollars in
Thousands)To 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 from Scenario Analysis for Comparison to
SimulationValues for Column E used for Figure 7 in printed
book. See this cell's Comment.
Mike Ehrhardt: To "replicate" Figure 7 in the printed book, you
would need to copy these values into Column E, replacing the
random variables. If you do so, be sure to "undo" your change
so that the formulas for the random variables in Column E will
be restored.Inputs for Simulation Probability
DistributionsRandom Variables Used in Current Simulation

TrialWorst-CaseBase-CaseBest-CaseExpected Value of
InputStandard Deviation of InputExpected 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
NORM.S.INV function, the NORM.S.INV interprets the value
as the cumulative probability of a standard normal distribution.
Then the NORM.S.INV 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
=NORM.S.INV(RAND()) returns a random standard normal
variable. Value Used in Current TrialProbability of
Scenario25%50%25%Equipment
cost$10,000$7070.698$10,493$11,000$10,000$9,000$10,000$7
07Salvage value of equip. in Year 4——
$1,000$1,000$1,000$1,000Opportunity cost——
$0$0$0$0Externalities (cannibalization)——$0$0$0$0Units
sold, Year
110,0001,0610.82010,8708,50010,00011,50010,0001,061Units
sold, Year 2——13,04420%20%20%Units sold, Year 3——
13,04420%20%20%Units sold, Year 4——7,609-30%-30%-
30%Sales price per unit, Year
1$2.00$0.14−1.505$1.79$1.80$2.00$2.20$2.00$0.14% Δ in
sales price, after Year 14.00%0.71%1.564
Michael Ehrhardt: We must use a slightly different formula to
get a standard normal for the percentage change in sale price
after Year 1. If demand is high for Year 1 units, then the
percentage change in prices after Year 1 can be higher due to
the stronger than expected demand. The reverse is true if unit
sales in Year 1 are owr than expected. In other words, the
percentage cahnge in prices after Year 1 is positively correlate d
with the unit sales in Year 1. We incorporate this into the
model by forming a variable that is a weighted 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.5.11%3.00%4.00%5.00%4.00%0.71%Var. cost per
unit (VC), Year
1$1.56$0.11−0.883$1.46$1.72$1.56$1.40$1.56$0.11% Δ in VC,
after Year
13.00%0.71%54.77%3.39%4.00%3.00%2.00%3.00%0.71%Nonv
ar. cost (Non-VC), Year
1$1,107$1170.554$1,171.97$941$1,107$1,273$1,107$117% Δ
in Non-VC, after Year 1——3%3.00%3.00%3.00%Project
WACC10.00%10.00%10.00%10.00%Tax rate——
25.00%25.00%25.00%25.00%NOWC as % of next year's sales—
—15.00%10.00%10.00%10.00%Assumed correlation between
units sold in Year 1 and annual change in units sold in later
years:r =0.60Key ResultsKey Results Based on Current
TrialWorst-CaseBase-CaseBest-
CaseNPV−$1,475−$9,795$1,070$15,073NPVIRR5.46%−32.64%
13.75%57.53%IRRMIRR6.84%−24.82%12.37%35.57%MIRRPI0
.890.221.092.31PIPayback3.57Not
found2.941.61PaybackDiscounted paybackNot foundNot
found$3.65$1.81Discounted payback Panel B: Project Analysis
for Current Trial in Simulation Using Inputs from Figure 11-7
Column FIntermediate Calculations01234Unit
sales10,87013,04413,0447,609Sales price per
unit$1.79$1.88$1.97$2.08Variable cost per unit (excl.
Price/unit$19,427$24,503$25,754$15,790NOWCt =

costs (excluding
(EBIT)−$1,114−$1,059$2,599$1,455Taxes on operating profit
(25% rate)−$278−$265$650$364Net operating profit after
taxes−$835−$794$1,949$1,091Add back
MeasuresNPV -$1,475IRR5.46%MIRR6.84%Profitability
index0.89Payback3.57Discounted
paybackERROR:#N/ACalculations for PaybackYear:01234
Cumulative cash flows for payback-$13,407-$11,506-$7,824-
$2,826$2,160 Discounted cash flows for disc. payback-
$13,407$1,901$3,043$3,755$3,406 Cumulative discounted
cash flows-$13,407-$11,506-$8,463-$4,708-$1,302How 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 analysis, 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 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 at the top of the sheet helps with
this annoyance.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 in the Data Table below and are
updated automatically when you do a simulation. Note: If
results are all zeros, go back to row 17 and "check" the box by
clicking it with your cursor.Figure 11-8 (But is current
simulation and is based only on 100 iterations.)Summary of
Simulation Results (Thousands of Dollars)Number of
Trials:0Input VariablesSummary Statistics for
Simulated Input VariablesEquipment costUnits sold, Year
1Sales price per unit, Year 1% Δ in sales price, after Year 1Var.
cost per unit (VC), Year 1% Δ in VC, after Year 1Nonvar. cost
(Non-VC), Year
1Average$00$0.000.00%$0.000.00%$0.00Standard
deviation$00$0.000.00%$0.000.00%$0.00Maximum$00$0.000.0
0%$0.000.00%$0.00Minimum$00$0.000.00%$0.000.00%$0.00C
orrelation with unit salesERROR:#DIV/0!Scratch work for
chart: see comments.Summary Statistics for Simulated
ResultsCount

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.NPVRange 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.100Percent
Mike Ehrhardt: This column shows the percent of trials with
NPVs in the range.
percentage cahnge in prices after Year 1 is positively correlated
combination depending on the desired correlation.
be restored.

variable.
top the top of the range.
that the ranges will fit the data for the particular simulation.
Mike Ehrhardt: Do not delete or change this cell or
row.Average$0$00ERROR:#DIV/0!Standard
deviation$0$00ERROR:#DIV/0!Maximum$0$00ERROR:#DIV/0
!Minimum$0$00ERROR:#DIV/0!Median$0$00ERROR:#DIV/0!
Probability of NPV > 00.0%$00ERROR:#DIV/0!Coefficient of
variationERROR:#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!$00ERROR:#DIV/0!$00ERRO
R:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!Sum-
0ERROR:#DIV/0!Output of Simulation in Data TableTrial
NumberEquipment costUnits sold, Year 1Sales price per unit,
Year 1% Δ in sales price, after Year 1Var. cost per unit (VC),
Year 1% Δ in VC, after Year 1Nonvar. cost (Non-VC), Year
1NPV000000001000000002000000003000000004000000005000
00000600000000700000000800000000900000000100000000011
00000000120000000013000000001400000000150000000016000
00000170000000018000000001900000000200000000021000000

00220000000023000000002400000000250000000026000000002
70000000028000000002900000000300000000031000000003200
00000033000000003400000000350000000036000000003700000
00038000000003900000000400000000041000000004200000000
43000000004400000000450000000046000000004700000000480
00000004900000000500000000051000000005200000000530000
00005400000000550000000056000000005700000000580000000
05900000000600000000061000000006200000000630000000064
00000000650000000066000000006700000000680000000069000
00000700000000071000000007200000000730000000074000000
00750000000076000000007700000000780000000079000000008
00000000081000000008200000000830000000084000000008500
00000086000000008700000000880000000089000000009000000
00091000000009200000000930000000094000000009500000000
960000000097000000009800000000990000000010000000000
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
4b-Sim1000011/21/18Worksheet 4-Simulation with 100
TrialsSimulation control, check boxes, and formsNote: this
section is relatively technical and some instructors may choose
to skip it with no loss in continuity.You might wonder "what's
the deal about this check box and why does it work this way?"
There are 2 parts to this question: Why it is useful for the
simulation and how do you use a check box for it? Let's answer
the "why it is useful for a simulation" question first, then talk
about check boxes. This check box is linked to cell B17. If you
click on the box, B17 returns a "TRUE" value, and if the box is

unchecked then it returns a "FALSE" value. The reason you
can't see anything in B17 is because we made the font color the
same as the background color so it wouldn't be distracting.
Below, here's what is in cell B17:To put random variables in the
Data Table for the simulation, the box shown below must be
checked; otherwise, the Data Table contains only zeroes 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.FALSESee, B17 reads
either True or False, depending on whether the box is checked
or not. The formulas in the simulation data table in cells B200
to I200 use this value to determine whether or not the data table
should be evaluated. For example, the formula in B200 is
=IF($B$17,F54,0). If B17 is TRUE, then the cell returns the
value in F54, which is the simulated equipment cost. If B17 is
FALSE, then it returns 0. The other formulas in that row are
similar. The end result is that if B17 is FALSE, then the data
table has no formulas to evaluate (everything is zero) and if it is
TRUE, then it has formulas to evaluate and it records the
simulation results. You didn't really need a check box; you
could just as well have left B17 visible and either put a 1 or a 0
in it, and had the IF statements in row 200 check, instead, for
whether B17 is equal to 1. But the check box is neat.Put a check
in the box below to run simulation; otherwise, the simulation
data table will have only zeros.Uncheck the box when you
finish!!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. Now for
how to use Forms in Excel. To insert a check box in Excel 2010
you must first enable the Developer tab on your Ribbon. These

are instructions for Excel 2010 For later versions of Excel you
can find instructions for this by searching on "check box" in
Excel help. Click the File tab, then click Options, then click
Customize Ribbon. Under Customize the Ribbon and under
Main Tabs, select the Developer check box.
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.On the Developer tab, in the Controls group, click on
Insert and then, in the Form Controls section, click on Insert
(the picture that like a tool box). Look at the Forms Control
section and click on the icon that looks like a check mark. Move
your cursor to where you'd like the check box to go, and click
there. A name, like Check Box 25, will show up next to the box.
Right click on the check box and click on Format Control. Then
under the Control tab, make sure the "unchecked" button is
pressed, then put in a cell reference in the Cell link box. We had
$B$17 in that box. Suppose you put in $B$19 for your box. You
are mostly done! Now when you click on the check box, cell
B19 will display TRUE and when it is not checked, B19will
display FALSE. You can use these two logical values in your
Excel programming. All that is left is to put in a useful
description for the check box. You don't want your users to be
confused about what the box is for. Just click on the check box
area and edit the name to be something like "Click this box if
you want something special to happen to the spreadsheet" (like
enable the data table to do its calculations!).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 in the figure below in the blue section in
Columns C and D. However, any of the input values in
Columns C and D may be changed by the user if desired. In
addition to the inputs for all the variables used previously, the
inputs section also has an input value for the assumed
correlation between units sold in Year 1 and changes in units
sold in later years.The figure below shows the trial inputs and
key results. The inputs used further below in the model are
shown in dark 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 (But showing results of current simulation
iteration.) Panel A: Values from Scenario Analysis and Their
Expected Values and Standard DeviationsInputs and Key
Results for the Current Simulation Trial (Dollars in
Thousands)To 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 from Scenario Analysis for Comparison to
SimulationValues for Column E used for Figure 7 in printed
book. See this cell's Comment.
be restored.Values used in textbook.Inputs for Simulation

Probability DistributionsRandom Variables Used in Current
Simulation TrialInputs for Simulation Probability
DistributionsRandom Variables Used in Current Simulation
TrialWorst-CaseBase-CaseBest-CaseExpected Value of
InputStandard Deviation of InputExpected Value of
InputStandard Deviation of InputStandard Normal Random
Variable
variable. Value Used in Current TrialProbability of
ScenarioExpected Value of InputStandard Deviation of
InputStandard Normal Random VariableValue Used in Current
Trial25%50%25%Equipment
cost$10,000$707−0.591$9,582$11,000$10,000$9,000$10,000$7
07Equipment cost$10,000$707−1.034$9,269Salvage value of
equip. in Year 4——$1,000$1,000$1,000$1,000Salvage value of
equip. in Year 4——$1,000Opportunity cost——
$0$0$0$0Opportunity cost——$0Externalities
(cannibalization)——$0$0$0$0Externalities (cannibalization)—
—$0Units sold, Year
110,0001,061−1.5948,3098,50010,00011,50010,0001,061Units
sold, Year 110,0001,0611.37811,461Units sold, Year 2——
9,97120%20%20%Units sold, Year 2——13,754Units sold, Year
3——9,97120%20%20%Units sold, Year 3——13,754Units
sold, Year 4——5,816-30%-30%-30%Units sold, Year 4——
8,023Sales price per unit, Year
1$2.00$0.140.965$2.14$1.80$2.00$2.20$2.00$0.14Sales price
per unit, Year 1$2.00$0.140.065$2.01% Δ in sales price, after
Year 14.00%0.71%−1.549

combination depending on the desired
correlation.2.90%3.00%4.00%5.00%4.00%0.71%% Δ in sales
price, after Year 14.00%0.71%0.9034.64%Var. cost per unit
(VC), Year
1$1.56$0.11−1.753$1.36$1.72$1.56$1.40$1.56$0.11Var. cost
per unit (VC), Year 1$1.56$0.110.220$1.58% Δ in VC, after
Year 13.00%0.71%-
8.90%2.94%4.00%3.00%2.00%3.00%0.71%% Δ in VC, after
Year 13.00%0.71%69.95%3.49%Nonvar. cost (Non-VC), Year
1$1,107$1170.481$1,163.47$941$1,107$1,273$1,107$117Nonv
ar. cost (Non-VC), Year 1$1,107$1170.879$1,210.16% Δ in
Non-VC, after Year 1——3%3.00%3.00%3.00%% Δ in Non-VC,
after Year 1——3%Project WACC——
10.00%10.00%10.00%10.00%Project WACC——10.00%Tax
rate——25.00%25.00%25.00%25.00%Tax rate——
25.00%NOWC as % of next year's sales——
15.00%10.00%10.00%10.00%NOWC as % of next year's sales—
—15.00%Assumed correlation between units sold in Year 1 and
annual change in units sold in later years:Assumed correlation
between units sold in Year 1 and annual change in units sold in
later years:r =0.60Key Resultsr =0.60Key Results Based on
Current TrialWorst-CaseBase-CaseBest-CaseKey Results Based
on Current
TrialNPV$5,565−$9,795$1,070$15,073NPVNPV$2,358IRR28.3

2%−32.64%13.75%57.53%IRRIRR17.25%MIRR20.80%−24.82
%12.37%35.57%MIRRMIRR14.78%PI1.450.221.092.31PIPI1.1
9Payback2.30Not
found2.941.61PaybackPayback2.86Discounted payback$2.60Not
found$3.65$1.81Discounted paybackDiscounted payback$3.36
Panel B: Project Analysis for Current Trial in Simulation Using
Inputs from Figure 11-7 Column FIntermediate
Calculations01234Unit sales8,3099,9719,9715,816Sales price
per unit$2.14$2.20$2.26$2.33Variable cost per unit (excl.
Price/unit$17,752$21,921$22,558$13,541NOWCt =
costs (excluding
(EBIT)$2,081$2,488$5,518$2,921Taxes on operating profit
(25% rate)$520$622$1,380$730Net operating profit after
taxes$1,561$1,866$4,139$2,191Add back
MeasuresNPV $5,565IRR28.32%MIRR20.80%Profitability

$12,245-$8,116-$2,086$4,824$10,506 Discounted cash flows
for disc. payback-$12,245$4,129$4,983$5,192$3,881
Cumulative discounted cash flows-$12,245-$8,116-
$3,133$2,059$5,940How 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 analysis, 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 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 at the top of the sheet helps with
this annoyance.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 in the Data Table below and are
updated automatically when you do a simulation. Note: If
results are all zeros, go back to row 17 and "check" the box by
clicking it with your cursor.Figure 11-8 (But is current
simulation and is based only on 100 iterations.)Summary of
Simulation Results (Thousands of Dollars)Number of
Trials:0Input VariablesSummary Statistics for
Simulated Input VariablesEquip-ment costUnits sold, Year
1Sales price per unit,
Year 1% Δ in sales price, after
Year 1Var. cost per unit (VC),
Year 1% Δ in VC, after Year 1Nonvar. cost (Non-VC),
Year 1Average$00$0.000.0%$0.000.0%$0Standard
deviation$00$0.000.0%$0.000.0%$0Maximum$00$0.000.0%$0.
000.0%$0Minimum$00$0.000.0%$0.000.0%$0Correlation with
unit salesERROR:#DIV/0!Scratch work for chart: see
comments.Summary Statistics for Simulated ResultsCount
top the top of the range.NPVRange bottom
that the ranges will fit the data for the particular
simulation.10000Percent
Mike Ehrhardt: This column shows the percent of trials with
NPVs in the range.

combination depending on the desired correlation.
be restored.
variable.
top the top of the range.
that the ranges will fit the data for the particular simulation.
Mike Ehrhardt: Do not delete or change this cell or
row.Average$0$00ERROR:#DIV/0!Standard
deviation$0$00ERROR:#DIV/0!Maximum$0$00ERROR:#DIV/0

!Minimum$0$00ERROR:#DIV/0!Median$0$00ERROR:#DIV/0!
Probability of NPV > 00.0%$00ERROR:#DIV/0!Coefficient of
variationERROR:#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!$00ERROR:#DIV/0!$00ERRO
R:#DIV/0!$00ERROR:#DIV/0!$00ERROR:#DIV/0!Sum-
0ERROR:#DIV/0!Average of simulated variables- 0- 0- 00.00%-
00.00%- 0- 0Std Dev of simulated variables00- 00.00%-
00.00%00Output of Simulation in Data TableTrial
NumberEquipment costUnits sold, Year 1Sales price per unit,
Year 1% Δ in sales price, after Year 1Var. cost per unit (VC),
Year 1% Δ in VC, after Year 1Nonvar. cost (Non-VC), Year
1NPV000000001000000002000000003000000004000000005000
00000600000000700000000800000000900000000100000000011
00000000120000000013000000001400000000150000000016000
00000170000000018000000001900000000200000000021000000
00220000000023000000002400000000250000000026000000002
70000000028000000002900000000300000000031000000003200
00000033000000003400000000350000000036000000003700000
00038000000003900000000400000000041000000004200000000
43000000004400000000450000000046000000004700000000480
00000004900000000500000000051000000005200000000530000
00005400000000550000000056000000005700000000580000000
05900000000600000000061000000006200000000630000000064
00000000650000000066000000006700000000680000000069000
00000700000000071000000007200000000730000000074000000
00750000000076000000007700000000780000000079000000008
00000000081000000008200000000830000000084000000008500
00000086000000008700000000880000000089000000009000000
00091000000009200000000930000000094000000009500000000
96000000009700000000980000000099000000001000000000010
10000000010200000000103000000001040000000010500000000

10600000000107000000001080000000010900000000110000000
00111000000001120000000011300000000114000000001150000
00001160000000011700000000118000000001190000000012000
00000012100000000122000000001230000000012400000000125
00000000126000000001270000000012800000000129000000001
30000000001310000000013200000000133000000001340000000
01350000000013600000000137000000001380000000013900000
00014000000000141000000001420000000014300000000144000
00000145000000001460000000014700000000148000000001490
00000001500000000015100000000152000000001530000000015
40000000015500000000156000000001570000000015800000000
15900000000160000000001610000000016200000000163000000
00164000000001650000000016600000000167000000001680000
00001690000000017000000000171000000001720000000017300
00000017400000000175000000001760000000017700000000178
00000000179000000001800000000018100000000182000000001
83000000001840000000018500000000186000000001870000000
01880000000018900000000190000000001910000000019200000
00019300000000194000000001950000000019600000000197000
00000198000000001990000000020000000000201000000002020
00000002030000000020400000000205000000002060000000020
70000000020800000000209000000002100000000021100000000
21200000000213000000002140000000021500000000216000000
00217000000002180000000021900000000220000000002210000
00002220000000022300000000224000000002250000000022600
00000022700000000228000000002290000000023000000000231
00000000232000000002330000000023400000000235000000002
36000000002370000000023800000000239000000002400000000
02410000000024200000000243000000002440000000024500000
00024600000000247000000002480000000024900000000250000
00000251000000002520000000025300000000254000000002550
00000002560000000025700000000258000000002590000000026
00000000026100000000262000000002630000000026400000000
26500000000266000000002670000000026800000000269000000
00270000000002710000000027200000000273000000002740000
00002750000000027600000000277000000002780000000027900

00000028000000000281000000002820000000028300000000284
00000000285000000002860000000028700000000288000000002
89000000002900000000029100000000292000000002930000000
02940000000029500000000296000000002970000000029800000
00029900000000300000000003010000000030200000000303000
00000304000000003050000000030600000000307000000003080
00000003090000000031000000000311000000003120000000031
30000000031400000000315000000003160000000031700000000
31800000000319000000003200000000032100000000322000000
00323000000003240000000032500000000326000000003270000
00003280000000032900000000330000000003310000000033200
00000033300000000334000000003350000000033600000000337
00000000338000000003390000000034000000000341000000003
42000000003430000000034400000000345000000003460000000
03470000000034800000000349000000003500000000035100000
00035200000000353000000003540000000035500000000356000
00000357000000003580000000035900000000360000000003610
00000003620000000036300000000364000000003650000000036
60000000036700000000368000000003690000000037000000000
37100000000372000000003730000000037400000000375000000
00376000000003770000000037800000000379000000003800000
00003810000000038200000000383000000003840000000038500
00000038600000000387000000003880000000038900000000390
00000000391000000003920000000039300000000394000000003
95000000003960000000039700000000398000000003990000000
04000000000040100000000402000000004030000000040400000
00040500000000406000000004070000000040800000000409000
00000410000000004110000000041200000000413000000004140
00000004150000000041600000000417000000004180000000041
90000000042000000000421000000004220000000042300000000
42400000000425000000004260000000042700000000428000000
00429000000004300000000043100000000432000000004330000
00004340000000043500000000436000000004370000000043800
00000043900000000440000000004410000000044200000000443
00000000444000000004450000000044600000000447000000004
48000000004490000000045000000000451000000004520000000

04530000000045400000000455000000004560000000045700000
00045800000000459000000004600000000046100000000462000
00000463000000004640000000046500000000466000000004670
00000004680000000046900000000470000000004710000000047
20000000047300000000474000000004750000000047600000000
47700000000478000000004790000000048000000000481000000
00482000000004830000000048400000000485000000004860000
00004870000000048800000000489000000004900000000049100
00000049200000000493000000004940000000049500000000496
00000000497000000004980000000049900000000500000000005
01000000005020000000050300000000504000000005050000000
05060000000050700000000508000000005090000000051000000
00051100000000512000000005130000000051400000000515000
00000516000000005170000000051800000000519000000005200
00000005210000000052200000000523000000005240000000052
50000000052600000000527000000005280000000052900000000
53000000000531000000005320000000053300000000534000000
00535000000005360000000053700000000538000000005390000
00005400000000054100000000542000000005430000000054400
00000054500000000546000000005470000000054800000000549
00000000550000000005510000000055200000000553000000005
54000000005550000000055600000000557000000005580000000
05590000000056000000000561000000005620000000056300000
00056400000000565000000005660000000056700000000568000
00000569000000005700000000057100000000572000000005730
00000005740000000057500000000576000000005770000000057
80000000057900000000580000000005810000000058200000000
58300000000584000000005850000000058600000000587000000
00588000000005890000000059000000000591000000005920000
00005930000000059400000000595000000005960000000059700
00000059800000000599000000006000000000060100000000602
00000000603000000006040000000060500000000606000000006
07000000006080000000060900000000610000000006110000000
06120000000061300000000614000000006150000000061600000
00061700000000618000000006190000000062000000000621000
00000622000000006230000000062400000000625000000006260

00000006270000000062800000000629000000006300000000063
10000000063200000000633000000006340000000063500000000
63600000000637000000006380000000063900000000640000000
00641000000006420000000064300000000644000000006450000
00006460000000064700000000648000000006490000000065000
00000065100000000652000000006530000000065400000000655
00000000656000000006570000000065800000000659000000006
60000000006610000000066200000000663000000006640000000
06650000000066600000000667000000006680000000066900000
00067000000000671000000006720000000067300000000674000
00000675000000006760000000067700000000678000000006790
00000006800000000068100000000682000000006830000000068
40000000068500000000686000000006870000000068800000000
68900000000690000000006910000000069200000000693000000
00694000000006950000000069600000000697000000006980000
00006990000000070000000000701000000007020000000070300
00000070400000000705000000007060000000070700000000708
00000000709000000007100000000071100000000712000000007
13000000007140000000071500000000716000000007170000000
07180000000071900000000720000000007210000000072200000
00072300000000724000000007250000000072600000000727000
00000728000000007290000000073000000000731000000007320
00000007330000000073400000000735000000007360000000073
70000000073800000000739000000007400000000074100000000
74200000000743000000007440000000074500000000746000000
00747000000007480000000074900000000750000000007510000
00007520000000075300000000754000000007550000000075600
00000075700000000758000000007590000000076000000000761
00000000762000000007630000000076400000000765000000007
66000000007670000000076800000000769000000007700000000
07710000000077200000000773000000007740000000077500000
00077600000000777000000007780000000077900000000780000
00000781000000007820000000078300000000784000000007850
00000007860000000078700000000788000000007890000000079
00000000079100000000792000000007930000000079400000000
79500000000796000000007970000000079800000000799000000

00800000000008010000000080200000000803000000008040000
00008050000000080600000000807000000008080000000080900
00000081000000000811000000008120000000081300000000814
00000000815000000008160000000081700000000818000000008
19000000008200000000082100000000822000000008230000000
08240000000082500000000826000000008270000000082800000
00082900000000830000000008310000000083200000000833000
00000834000000008350000000083600000000837000000008380
00000008390000000084000000000841000000008420000000084
30000000084400000000845000000008460000000084700000000
84800000000849000000008500000000085100000000852000000
00853000000008540000000085500000000856000000008570000
00008580000000085900000000860000000008610000000086200
00000086300000000864000000008650000000086600000000867
00000000868000000008690000000087000000000871000000008
72000000008730000000087400000000875000000008760000000
08770000000087800000000879000000008800000000088100000
00088200000000883000000008840000000088500000000886000
00000887000000008880000000088900000000890000000008910
00000008920000000089300000000894000000008950000000089
60000000089700000000898000000008990000000090000000000
90100000000902000000009030000000090400000000905000000
00906000000009070000000090800000000909000000009100000
00009110000000091200000000913000000009140000000091500
00000091600000000917000000009180000000091900000000920
00000000921000000009220000000092300000000924000000009
25000000009260000000092700000000928000000009290000000
09300000000093100000000932000000009330000000093400000
00093500000000936000000009370000000093800000000939000
00000940000000009410000000094200000000943000000009440
00000009450000000094600000000947000000009480000000094
90000000095000000000951000000009520000000095300000000
95400000000955000000009560000000095700000000958000000
00959000000009600000000096100000000962000000009630000
00009640000000096500000000966000000009670000000096800
00000096900000000970000000009710000000097200000000973

00000000974000000009750000000097600000000977000000009
78000000009790000000098000000000981000000009820000000
09830000000098400000000985000000009860000000098700000
00098800000000989000000009900000000099100000000992000
00000993000000009940000000099500000000996000000009970
00000009980000000099900000000100000000000100100000000
10020000000010030000000010040000000010050000000010060
00000001007000000001008000000001009000000001010000000
00101100000000101200000000101300000000101400000000101
50000000010160000000010170000000010180000000010190000
00001020000000001021000000001022000000001023000000001
02400000000102500000000102600000000102700000000102800
00000010290000000010300000000010310000000010320000000
01033000000001034000000001035000000001036000000001037
00000000103800000000103900000000104000000000104100000
00010420000000010430000000010440000000010450000000010
46000000001047000000001048000000001049000000001050000
00000105100000000105200000000105300000000105400000000
10550000000010560000000010570000000010580000000010590
00000001060000000001061000000001062000000001063000000
00106400000000106500000000106600000000106700000000106
80000000010690000000010700000000010710000000010720000
00001073000000001074000000001075000000001076000000001
07700000000107800000000107900000000108000000000108100
00000010820000000010830000000010840000000010850000000
01086000000001087000000001088000000001089000000001090
00000000109100000000109200000000109300000000109400000
00010950000000010960000000010970000000010980000000010
99000000001100000000001101000000001102000000001103000
00000110400000000110500000000110600000000110700000000
11080000000011090000000011100000000011110000000011120
00000001113000000001114000000001115000000001116000000
00111700000000111800000000111900000000112000000000112
10000000011220000000011230000000011240000000011250000
00001126000000001127000000001128000000001129000000001
13000000000113100000000113200000000113300000000113400

00000011350000000011360000000011370000000011380000000
01139000000001140000000001141000000001142000000001143
00000000114400000000114500000000114600000000114700000
00011480000000011490000000011500000000011510000000011
52000000001153000000001154000000001155000000001156000
00000115700000000115800000000115900000000116000000000
11610000000011620000000011630000000011640000000011650
00000001166000000001167000000001168000000001169000000
00117000000000117100000000117200000000117300000000117
40000000011750000000011760000000011770000000011780000
00001179000000001180000000001181000000001182000000001
18300000000118400000000118500000000118600000000118700
00000011880000000011890000000011900000000011910000000
01192000000001193000000001194000000001195000000001196
00000000119700000000119800000000119900000000120000000
00012010000000012020000000012030000000012040000000012
05000000001206000000001207000000001208000000001209000
00000121000000000121100000000121200000000121300000000
12140000000012150000000012160000000012170000000012180
00000001219000000001220000000001221000000001222000000
00122300000000122400000000122500000000122600000000122
70000000012280000000012290000000012300000000012310000
00001232000000001233000000001234000000001235000000001
23600000000123700000000123800000000123900000000124000
00000012410000000012420000000012430000000012440000000
01245000000001246000000001247000000001248000000001249
00000000125000000000125100000000125200000000125300000
00012540000000012550000000012560000000012570000000012
58000000001259000000001260000000001261000000001262000
00000126300000000126400000000126500000000126600000000
12670000000012680000000012690000000012700000000012710
00000001272000000001273000000001274000000001275000000
00127600000000127700000000127800000000127900000000128
00000000012810000000012820000000012830000000012840000
00001285000000001286000000001287000000001288000000001
28900000000129000000000129100000000129200000000129300

00000012940000000012950000000012960000000012970000000
01298000000001299000000001300000000001301000000001302
00000000130300000000130400000000130500000000130600000
00013070000000013080000000013090000000013100000000013
11000000001312000000001313000000001314000000001315000
00000131600000000131700000000131800000000131900000000
13200000000013210000000013220000000013230000000013240
00000001325000000001326000000001327000000001328000000
00132900000000133000000000133100000000133200000000133
30000000013340000000013350000000013360000000013370000
00001338000000001339000000001340000000001341000000001
34200000000134300000000134400000000134500000000134600
00000013470000000013480000000013490000000013500000000
01351000000001352000000001353000000001354000000001355
00000000135600000000135700000000135800000000135900000
00013600000000013610000000013620000000013630000000013
64000000001365000000001366000000001367000000001368000
00000136900000000137000000000137100000000137200000000
13730000000013740000000013750000000013760000000013770
00000001378000000001379000000001380000000001381000000
00138200000000138300000000138400000000138500000000138
60000000013870000000013880000000013890000000013900000
00001391000000001392000000001393000000001394000000001
39500000000139600000000139700000000139800000000139900
00000014000000000014010000000014020000000014030000000
01404000000001405000000001406000000001407000000001408
00000000140900000000141000000000141100000000141200000
00014130000000014140000000014150000000014160000000014
17000000001418000000001419000000001420000000001421000
00000142200000000142300000000142400000000142500000000
14260000000014270000000014280000000014290000000014300
00000001431000000001432000000001433000000001434000000
00143500000000143600000000143700000000143800000000143
90000000014400000000014410000000014420000000014430000
00001444000000001445000000001446000000001447000000001
44800000000144900000000145000000000145100000000145200

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