1/1/2012

Chapter 11 Mini CaseCash Flow Estimation

Situation

a. Define “incremental cash flow.”

(1.) Should you subtract interest expense or dividends when calculating project cash flow?

Analysis of New Expansion ProjectPart I: Input Data

Equipment cost Key Output: NPV = $0 Shipping chargeInstallation chargeEconomic LifeSalvage ValueTax RateCost of CapitalUnits SoldSales Price Per UnitIncremental Cost Per UnitNWC/SalesInflation rate

Shrieves Casting Company is considering adding a new line to its product mix, and the capital budgeting analysis is being conducted by Sidney Johnson, a recently graduated MBA. The production line would be set up in unused space in Shrieves' main plant. The machinery’s invoice price would be approximately $200,000, another $10,000 in shipping charges would be required, and it would cost an additional $30,000 to install the equipment. The machinery has an economic life of 4 years, and Shrieves has obtained a special tax ruling that places the equipment in the MACRS 3-year class. The machinery is expected to have a salvage value of $25,000 after 4 years of use.

The new line would generate incremental sales of 1,250 units per year for 4 years at an incremental cost of $100 per unit in the first year, excluding depreciation. Each unit can be sold for $200 in the first year. The sales price and cost are expected to increase by 3% per year due to inflation. Further, to handle the new line, the firm’s net working capital would have to increase by an amount equal to 12% of sales revenues. The firm’s tax rate is 40%, and its overall weighted average cost of capital is 10%.

(2.) Suppose the firm had spent $100,000 last year to rehabilitate the production line site. Should this be included in the analysis? Explain.

(3.) Now assume that the plant space could be leased out to another firm at $25,000 per year. Should this be included in the analysis? If so, how?

(4.) Finally, assume that the new product line is expected to decrease sales of the firm’s other lines by $50,000 per year. Should this be considered in the analysis? If so, how?

Annual Depreciation Expense

Depreciable Basis = Equipment + Freight + InstallationDepreciable Basis = $0

Year % x Basis = Depr.1 0.33 $0 $0 $0 2 0.45 0 0 03 0.15 0 0 04 0.07 0 0 0

d. Construct annual incremental operating cash flow statements.

Annual Operating Cash FlowsYear 1 Year 2 Year 3 Year 4

Units 0 0 0 0Unit price $0.00 $0.00 $0.00 $0.00 Unit cost $0.00 $0.00 $0.00 $0.00

Sales $0 $0 $0 $0 Costs 0 0 0 0 Depreciation 0 0 0 0 Operating income before taxes (EBIT) $0 $0 $0 $0 Taxes (40%) 0 0 0 0

$0 $0 $0 $0 Depreciation 0 0 0 0 Net operating CF $0 $0 $0 $0

Annual Cash Flows due to Investments in Net Working Capital

Year 0 Year 1 Year 2 Year 3 Year 4Sales $0 $0 $0 $0 NWC (% of sales) 0 0 0 0 CF due to investment in NOWC) 0 0 0 0 0

b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual depreciation expenses?

Remaining Book Value

c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include inflation when estimating cash flows?

EBIT (1 – T)

e. Estimate the required net working capital for each year, and the cash flow due to investments in net working capital.

f. Calculate the after-tax salvage cash flow.

After-tax Salvage Value

Salvage value $0 Book value 0 Gain or loss $0 Tax on salvage value 0 Net terminal cash flow $0

Projected Net Cash FlowsYear 0 Year 1 Year 2 Year 3 Year 4

Investment Outlay: Long Term Assets $0 Operating Cash Flows $0 $0 $0 $0 CF due to investment in NWC 0 0 0 0 0

Salvage Cash Flows 0 Net Cash Flows $0 $0 $0 $0 $0

NPV $0 IRR Err:523 PV of InflowsTV of Inflows

$0 $0 Years

Find MIRR 0 1 2 3 4Net Cash Flows $0 $0 $0 $0 $0

0 0

0 PV= $0 TV = $0

MIRR = Err:502

Find Payback Years0 1 2 3 4

Cash Flow $0 $0 $0 $0 $0 Cumulative Cash Flow for Payback $0 $0 $0 $0 $0

Payback = 0.0

Hypothetical: If sold after 3 years for

Based on facts in case:

g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR, MIRR, and payback? Do these indicators suggest the project should be undertaken?

To find MIRR, we could now find the discount rate that equates the PV and TV. But it is easier to use the MIRR function.

(3.) How is each type of risk used in the capital budgeting process?

Evaluating Risk: Sensitivity Analysis

Sensitivity of NPV and to Variations in Input Variablesj. (1.) What is sensitivity analysis?

We summarize the data tables and show the sensitivity analysis graph below:

% Deviation WACC % Deviation 1st YEAR UNIT SALES % Deviation SALVAGEfrom NPV from Units NPV from Variable NPV

Base Case WACC 0 Base Case Sold $0 Base Case Cost $0-30% $0 -30% $0 -30% $0-15% 0 -15% 0 -15% 0

0% 0 0% 0 0% 015% 0 15% 0 15% 030% 0 30% 0 30% 0

h. What does the term ”risk” mean in the context of capital budgeting; to what extent can risk be quantified; and when risk is quantified, is the quantification based primarily on statistical analysis of historical data or on subjective, judgmental estimates?

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, and/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 Excel to examine the project's sensitivity to changes in the input variables.

i. (1.) What are the three types of risk that are relevant in capital budgeting?

(2.) How is each of these risk types measured, and how do they relate to one another?

(2.) Perform a sensitivity analysis on the unit sales, salvage value, and cost of capital for the project. Assume that each of these variables can vary from its base-case, or expected, value by plus and minus 10%, 20%, and 30%. Include a sensitivity diagram, and discuss the results.

Here we use an Excel "Data Table" to find the NPVs for changes in unit sales, salvage value, and WACC holding other things constant--changing one variable at a time. This produces the sensitivity analys as shown below.

Evaluating Risk: Sensitivity Analysis

Deviation NPV Deviation from Base Casefrom Units

Base Case WACC Sold Salvage-30% $0 $0 $0 -15% 0 0 0 0% 0 0 0

15% 0 0 0 30% 0 0 0

Range $0 $0 $0

(1.) What is scenario analysis?

(2.) What is the worst-case NPV? The best-case NPV?

(3.) What is the primary weakness of sensitivity analysis? What is its primary usefulness?

k. Assume that Sidney Johnson is confident of her estimates of all the variables that affect the project’s cash flows except unit sales and sales price: If product acceptance is poor, unit sales would be only 900 units a year and the unit price would only be $160; a strong consumer response would produce sales of 1,600 units and a unit price of $240. Sidney believes that there is a 25% chance of poor acceptance, a 25% chance of excellent acceptance, and a 50% chance of average acceptance (the base case).

Scenario 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.

(3.) Use the worst-, most likely, and best-case NPVs and probabilities of occurrence to find the project’s expected NPV, standard deviation, and coefficient of variation.

-40% -30% -20% -10% 0% 10% 20% 30% 40%0

1

1

Sensitivity Analysis

Deviation from Base-Case Value

NPV ($)

Salvage Value

Units Sold

WACC

Evaluating Risk: Scenario Analysis

Scenario Analysis Squared Deviation

Scenario Probability Unit Sales Unit Price NPV times Probability

Best Case 25%Base Case 50%

Worst Case 25%Quick calculation:

Expected NPV = $0 $0 Standard Deviation = $0 $0

Coefficient of Variation = Std Dev / Expected NPV = #DIV/0!

Monte Carlo Simulation

Risk Adjusted Cost of Capital

Cost of capital for average projects: 0%Adjustment for risky projects:

Risk adjusted cost of capital:

NPV with risk-adjusted cost of capital: $0

(3.) Are there any subjective risk factors that should be considered before the final decision is made?

We could find the NPV by entering the value of unit sales and price for each scenario and then recording the NPV (this is what we did for the table below). Alternatively, we could use Tools, Scenarios to define the inputs for each scenario, which we did and show in the Scenario Summary Tab below. In fact, you could even use Tools, Scenarios, and then click the Summary button on the dialog box, and it will automatically create a table similar to the one below. This is a powerful feature of Excel, and we encourage you to explore it.

l. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal advantages and disadvantages.

Monte Carlo simulation is similar to scenario analysis in that different values of key input variables are used. Unlike scenario analysis, Monte Carlo simulation draws the input values from specified probability distributions and then computes the NPV. It repeats this process hundreds, or even thousands, of times. It then averages the NPVs from each repetition.

m. (1.) Assume that Shrieves' average project has a coefficient of variation in the range of 0.2 to 0.4. Would the new line be classified as high risk, average risk, or low risk? What type of risk is being measured here?

(2.) Shrieves typically adds or subtracts 3 percentage points to the overall cost of capital to adjust for risk. Should the new line be accepted?

The CV of this project is 1.15, which is larger than the CV range of the firm's average project. Consequently, this project is riskier than the firm's average project, so management should add 3% to the WACC to risk adjust.

m. What is a real option? What are some types of real options?

$200,000$10,000$30,000

4$25,000

40%10%1,250$200 $100 12%

3%

$200,000$10,000$30,000

4$25,000

40%10%1,600$240 $100 12%

3%

G49

This differs slightly from the Powerpoint solution due to rounding in intermediate steps in the Powerpoint solution.

C106

This differs slightly from the Powerpoint solution due to rounding in intermediate steps in the Powerpoint solution.

G141

Do not delete or change this cell or row.

$200,000$10,000$30,000

4$25,000

40%10%

900$160 $100 12%

3%

$200,000$10,000$30,000

4$25,000

40%10%1,250$200 $100 12%

0%

Scenario Summary

Current Values: Base Case Best CaseChanging Cells:

$D$36 $200,000 $200,000 $200,000$D$37 $10,000 $10,000 $10,000$D$38 $30,000 $30,000 $30,000$D$39 4 4 4$D$40 $25,000 $25,000 $25,000 $D$41 40% 40% 40%$D$42 10% 10% 10%$D$43 1,250 1,250 1,600$D$44 $200 $200 $240 $D$45 $100 $100 $100 $D$46 12% 12% 12%$D$47 3% 3% 3%

Result Cells:$C$113 $88,030 $88,030 $278,965 $C$114 23.9% 23.9% 48.3%

Notes: Current Values column represents values of changing cells attime Scenario Summary Report was created. Changing cells for eachscenario are highlighted in gray.

Worst Case Base-but forget inflation

$200,000 $200,000$10,000 $10,000$30,000 $30,000

4 4$25,000 $25,000

40% 40%10% 10%900 1,250

$160 $200 $100 $100 12% 12%

3% 0%

($48,514) $78,387 1.0% 22.7%

Section 11.7 Scenario Analysis

Analysis of New Expansion ProjectPart I: Input Data

Equipment cost $200,000 Key Output: NPV =Shipping charge $10,000Installation charge $30,000Economic Life 4Salvage Value $25,000 Tax Rate 40%

Cost of Capital 10% Std. Dev.Units Sold Random variable = 1,440 1,250 200Sales Price Per Unit Random variable = $226 $200 $30 Incremental Cost Per Unit $100 NWC/Sales 12%Inflation rate 3%

Annual Depreciation Expense

Depreciable Basis = Equipment + Freight + InstallationDepreciable Basis = $240,000

Year % x Basis = Depr.1 0.33 $240,000 $79,200 2 0.45 240,000 108,000

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.

The green area below is the same project as in the mini case, but we have replaced the inputs fro units sold and sales price with random variables drawn from normal distributions with the expected values and means shown next to the inputs. Notice that each time the sheet makes a calculation, the values for unit sales, sales price, and NPV change (Hint: you can make the sheet calculate by hitting the F9 key).

Here is a tip for simulating a project analysis. If you have already done the analysis and it is in a different worksheet, see how many rows it takes. Delete the green area below and add enough rows so that there will be room for your previous analysis. For example, this model was in the "Model" tab in the file Ch 11 Mini Case.xls, rows 33-132. We went into that file, selected Rows 32-135, copied them, and then pasted them into Rows 32-135 of this Worksheet. Because we pasted them into the same row numbers from which we copied them, all the formula references remained correct. We then edited this worksheet.

Expected Value

b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual depreciation expenses?

3 0.15 240,000 36,000 4 0.07 240,000 16,800

d. Construct annual incremental operating cash flow statements.

Annual Operating Cash FlowsYear 1 Year 2 Year 3

Units 1,440 1,440 1,440Unit price $226.30 $233.09 $240.09 Unit cost $100.00 $103.00 $106.09

Sales $325,806 $335,580 $345,655 Costs 143,969 148,288 152,736 Depreciation 79,200 108,000 36,000 Operating income before taxes (EBIT) $102,637 $79,292 $156,919 Taxes (40%) 41,055 31,717 62,768

$61,582 $47,575 $94,151 Depreciation 79,200 108,000 36,000 Net operating CF $140,782 $155,575 $130,151

Annual Cash Flows due to Investments in Net Working Capital

Year 0 Year 1 Year 2 Year 3Sales $325,806 $335,580 $345,655 NWC (% of sales) 39,097 40,270 41,479 42,722 CF due to investment in NOWC) (39,097) (1,173) (1,209) (1,243)

f. Calculate the after-tax salvage cash flow.After-tax Salvage Value

$25,000 $10,000 Salvage value $25,000 $25,000 $10,000 Book value 0 16,800 16,800 Gain or loss $25,000 $8,200 ($6,800)Tax on salvage value 10,000 3,280 (2,720)Net terminal cash flow $15,000 $21,720 $12,720

Projected Net Cash FlowsYear 0 Year 1 Year 2

Investment Outlay: Long Term Assets ($240,000)Operating Cash Flows $140,782 $155,575 CF due to investment in NWC (39,097) (1,173) (1,209)

Salvage Cash Flows

c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include inflation when estimating cash flows? See answer to part d.

EBIT (1 – T)

e. Estimate the required net working capital for each year, and the cash flow due to investments in net working capital.

Hypothetical: If sold after 3 years for

Based on facts in case:

g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR, MIRR, and payback? Do these indicators suggest the project should be undertaken?

Net Cash Flows ($279,097) $139,609 $154,366

NPV $197,692 IRR 38.6% PV of InflowsTV of Inflows

$476,789 $698,067 Years

Find MIRR 0 1 2Net Cash Flows ($279,097) $139,609 $154,366

PV= ($279,097)

To find MIRR, we could now find the discount rate that equates the PV and TV. But it is easier to use the MIRR function.MIRR = 25.8%

Find Payback Years0 1 2

Cash Flow ($279,097) $139,609 $154,366 Cumulative Cash Flow for Payback ($279,097) ($139,488) $14,878

Payback = 1.9

How the Simulation Works

Column input cell to "trick" Excel into updating random variables in Data Table: 1

Figure 11-27 Summary of Simulation Results (Thousands of Dollars)

We use a Data Table to perform the simulation (the Data Table is below, shaded bright yellow). When the Data Table is updated, it will insert new random variables for each of the inputs we allow to change in Panel A above, run the analysis is Panel C 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.

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. With only 100 rows, it updates very quickly. But if it bothers you, you can set the worksheet to do automatic calculation except for data tables.

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. You can do an updated simulation by hitting the F9 key.

Number of Trials = 100Simulated Input Variables and Key Results

Units Sold

Key Results:

NPVMean $1,440 226 $75,299

Standard deviation 0 0 $80,677Maximum 1,440 226 $290,674Minimum 1,440 226 -$143,868

Median $62,790Probability of NPV > 0 86.0%

Coefficient of variation 1.07

Output of Simulation in Data Table

Units Sold NPV

Sales Price Per

Unit

Trial NumberSales Price Per Unit

-290,674

-269,911

-249,149

-228,386

-207,624

-186,862

-166,099

-145,337

-124,574

-103,812

-83,050

-62,287

-41,525

-20,762

0

20,762

41,525

62,287

83,050

103,812

124,574

145,337

166,099

186,862

207,624

228,386

249,149

269,911

290,674

NPV ($)

Probability

1,440 $226 $197,692 1 1439.6877 226.30337 36898.672972 1439.6877 226.30337 108529.35693 1439.6877 226.30337 -143868.3884 1439.6877 226.30337 21118.94725 1439.6877 226.30337 63909.325736 1439.6877 226.30337 52979.827957 1439.6877 226.30337 -19885.95748 1439.6877 226.30337 -14229.25659 1439.6877 226.30337 102776.8539

10 1439.6877 226.30337 96800.2120111 1439.6877 226.30337 195884.010612 1439.6877 226.30337 -99964.358613 1439.6877 226.30337 30541.1362614 1439.6877 226.30337 -28987.329415 1439.6877 226.30337 200124.442316 1439.6877 226.30337 1386.18079417 1439.6877 226.30337 279026.63618 1439.6877 226.30337 30533.0603119 1439.6877 226.30337 54924.5008520 1439.6877 226.30337 99352.137921 1439.6877 226.30337 -11404.100922 1439.6877 226.30337 13703.4852123 1439.6877 226.30337 131198.610124 1439.6877 226.30337 66002.6974925 1439.6877 226.30337 77235.3687626 1439.6877 226.30337 43151.9435827 1439.6877 226.30337 33042.016628 1439.6877 226.30337 -64906.257629 1439.6877 226.30337 40156.42630 1439.6877 226.30337 115286.455331 1439.6877 226.30337 133806.277732 1439.6877 226.30337 2376.41035433 1439.6877 226.30337 139751.853234 1439.6877 226.30337 22735.4436935 1439.6877 226.30337 35267.8052736 1439.6877 226.30337 63177.4083137 1439.6877 226.30337 77632.1327838 1439.6877 226.30337 180756.376339 1439.6877 226.30337 115847.572640 1439.6877 226.30337 109112.798741 1439.6877 226.30337 119353.570742 1439.6877 226.30337 120900.856643 1439.6877 226.30337 59183.4337844 1439.6877 226.30337 122022.256545 1439.6877 226.30337 56310.5230546 1439.6877 226.30337 136338.764447 1439.6877 226.30337 -1591.0620248 1439.6877 226.30337 20061.0801949 1439.6877 226.30337 -8994.5750350 1439.6877 226.30337 -47354.030751 1439.6877 226.30337 211515.38352 1439.6877 226.30337 255143.019353 1439.6877 226.30337 48820.36118

54 1439.6877 226.30337 93468.9737755 1439.6877 226.30337 76647.5005856 1439.6877 226.30337 67501.2124257 1439.6877 226.30337 -74703.63958 1439.6877 226.30337 177628.654359 1439.6877 226.30337 1453.50201560 1439.6877 226.30337 258052.621361 1439.6877 226.30337 134957.704762 1439.6877 226.30337 19162.1693963 1439.6877 226.30337 126708.769164 1439.6877 226.30337 22730.2650865 1439.6877 226.30337 38413.2629666 1439.6877 226.30337 613.117683267 1439.6877 226.30337 231019.816168 1439.6877 226.30337 101212.166369 1439.6877 226.30337 29173.5031170 1439.6877 226.30337 60296.8140271 1439.6877 226.30337 40400.8621772 1439.6877 226.30337 62403.0122973 1439.6877 226.30337 -9205.0480874 1439.6877 226.30337 168393.363675 1439.6877 226.30337 29807.268976 1439.6877 226.30337 159567.065777 1439.6877 226.30337 42768.5776278 1439.6877 226.30337 -8080.1283479 1439.6877 226.30337 142867.635380 1439.6877 226.30337 167257.986581 1439.6877 226.30337 126131.523982 1439.6877 226.30337 18897.8523383 1439.6877 226.30337 124424.805184 1439.6877 226.30337 44789.9950185 1439.6877 226.30337 155758.264786 1439.6877 226.30337 35057.4300387 1439.6877 226.30337 86051.2601688 1439.6877 226.30337 40772.7750289 1439.6877 226.30337 31401.9142890 1439.6877 226.30337 290673.703691 1439.6877 226.30337 120389.240492 1439.6877 226.30337 64531.5159593 1439.6877 226.30337 199926.690394 1439.6877 226.30337 69763.856795 1439.6877 226.30337 31467.5240196 1439.6877 226.30337 223450.240697 1439.6877 226.30337 65857.2213698 1439.6877 226.30337 -11864.554999 1439.6877 226.30337 112509.5981

100 1439.6877 226.30337 55856.12035

1/1/2012

Section 11.7 Scenario Analysis

$197,692

$160,800 52,800

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

The green area below is the same project as in the mini case, but we have replaced the inputs fro units sold and sales price with random variables drawn from normal distributions with the expected values and means shown next to the inputs. Notice that each time the sheet makes a calculation, the values for unit sales, sales price, and NPV change (Hint:

Here is a tip for simulating a project analysis. If you have already done the analysis and it is in a different worksheet, see how many rows it takes. Delete the green area below and add enough rows so that there will be room for your previous

, rows 33-132. We went into that file, selected Rows 32-135, copied them, and then pasted them into Rows 32-135 of this Worksheet. Because we pasted them into the same row numbers from which we copied them, all the formula references remained correct. We then

b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual

Remaining Book Value

16,8000

d. Construct annual incremental operating cash flow statements.

Year 41,440

$247.29 $109.27

$356,020 157,315

16,800 $181,905

72,762 $109,143

16,800 $125,943

Year 4$356,020

42,722

Year 3 Year 4

$130,151 $125,943 (1,243) 42,722

15,000

c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include

e. Estimate the required net working capital for each year, and the cash flow due to investments in net working

g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR,

$128,908 $183,665

Years

3 4$128,908 $183,665

141,799 186,783

185,820 TV = $698,067

To find MIRR, we could now find the discount rate that equates the PV and TV. But it is easier to use the MIRR function.

Years3 4

$128,908 $183,665 $143,787 $327,452

Don't change the the red cell.

Figure 11-27 Summary of Simulation Results (Thousands of Dollars)

We use a Data Table to perform the simulation (the Data Table is below, shaded bright yellow). When the Data Table is updated, it will insert new random variables for each of the inputs we allow to change in Panel A above, run the analysis is Panel C 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

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. With only 100 rows, it updates very quickly. But if it bothers you, you can set the worksheet to do automatic calculation except for data tables.

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. You can do an updated simulation by hitting the F9 key.

Simulated Input Variables and Key Results

Scratch work for chart: see comments.Count

Range bottom 0 Percent-$290,674 0 0%-$269,911 0 0%

-$249,149 0 0%-$228,386 0 0%-$207,624 0 0%-$186,862 0 0%-$166,099 0 0%-$145,337 1 1%-$124,574 0 0%-$103,812 1 1%

-$83,050 2 2%-$62,287 1 1%-$41,525 1 1%-$20,762 8 8%

$0 8 8%$20,762 17 17%$41,525 10 10%$62,287 11 11%$83,050 6 6%

$103,812 10 10%$124,574 8 8%$145,337 2 2%$166,099 4 4%$186,862 3 3%$207,624 2 2%$228,386 1 1%$249,149 2 2%$269,911 2 2%$290,674 0 0%

Sum 100 100%

-290,674

-269,911

-249,149

-228,386

-207,624

-186,862

-166,099

-145,337

-124,574

-103,812

-83,050

-62,287

-41,525

-20,762

0

20,762

41,525

62,287

83,050

103,812

124,574

145,337

166,099

186,862

207,624

228,386

249,149

269,911

290,674

NPV ($)

Probability