APPENDIX C Guide to the Sensitivity Toolkit C.1 INTRODUCTION The Sensitivity Toolkit is an Excel add - in for sensitivity analysis, which involves varying one or more inputs and determining the effect on the outputs. The Toolkit includes four sensitivity tools: Data Sensitivity Tornado Chart Solver Sensitivity Crystal Ball Sensitivity The Sensitivity Toolkit was created by Bob Burnham at the Tuck School of Business and is provided free on the school s website ( http://mba.tuck. dartmouth.edu/toolkit/ ). C.2 DATA SENSITIVITY The most basic sensitivity question we can ask is how the output of a model varies as one or more inputs vary. For example, we might ask in the Advertising Budget model how Price (in cell C7) or Q1 Advertising (in cell D18) affect Profit (in cell C21). The Data Sensitivity tool is designed to answer this type of question quickly. Select Add-ins Sensitivity Toolkit Data Sensitivity. The window shown in Figure C.1 will appear. Select One - way Table and enter the cell address of the desired output (Toolkit!C21) in the field labeled Results Cell(s). Select Next and the window in Figure C.2 will appear. Enter the cell address of the parameter you want to change (Toolkit!D18) under Cell to Vary, select Begin, End, Increment in the field labeled Input Type, and enter First Value (10,000), Last Value (20,000), and Increment/N (500). Select Finish and the results will appear as in Figure C.3. Because of diminishing returns, Profit increases to a peak and then declines with Q1 Advertising. Modeling for Insight: A Master Class for Business Analysts, by Stephen G. Powell & Robert J. Batt Copyright 2008 by John Wiley & Sons, Inc. 456
DATA SENSITIVITY 457 Figure C.1. First input window for Data Sensitivity. Figure C.2. Second input window for Data Sensitivity.
458 GUIDE TO THE SENSITIVITY TOOLKIT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 A B C $D$18 Profit $10,000 $69,662 $10,500 $69,778 $11,000 $69,882 $11,500 $69,976 $12,000 $70,060 $12,500 $70,134 $13,000 $70,198 $13,500 $70,254 $14,000 $70,302 $14,500 $70,342 $15,000 $70,374 $15,500 $70,398 $16,000 $70,416 $16,500 $70,427 $17,000 $70,431 $17,500 $70,429 $18,000 $70,421 $18,500 $70,407 $19,000 $70,388 $19,500 $70,363 $20,000 $70,333 Figure C.3. Results of Data Sensitivity. C.3 TORNADO CHART Most models have dozens or even hundreds of inputs, many of which do not have a substantial effect on the output. It is often helpful to identify inputs that have a strong influence and those that do not. The first group is worth additional research, whereas the second group is not. The Sensitivity Toolkit includes a tool called the Tornado Chart, which displays each parameter s impact and ranks the impact of all parameters from biggest to smallest. The Tornado Chart tool offers three ways to generate this type of graph: Constant percentage Variable percentage Percentiles In a constant percentage tornado chart, each parameter is varied up and down by the same percentage (typically 10 percent) of its base case value. The output cell is recorded for both cases, the difference between these results is calculated, and the results are displayed in order of size. The other two options work in a similar fashion; for more information, consult the Help option within the Sensitivity Toolkit add - in. We invoke the Tornado Chart tool by selecting Add - ins Sensitivity Toolkit Tornado Chart. The first window that appears (Figure C.4 ) requires
TORNADO CHART 459 Figure C.4. First input window for Tornado Chart. Figure C.5. Second input window for Tornado Chart. us to enter the Result Cell (Profit: Toolkit!C21), the Input Parameters (Toolkit!C7:G15), and the Analysis Type (Constant Percentage). Select Next and the second input window appears (Figure C.5 ). Choose the percentage change for each parameter (10 percent in this case). Select Finish and the results will be created in a separate sheet as shown in Figure C.6. The table is created first, by varying each parameter by +10 percent and recording the output, and then by 10 percent and recording the output. Then the range between the first and second values is calculated, and finally the parameters are sorted in decreasing order by range. The chart is then created showing the ranges around the base case output value. Since the parameters are sorted by range, the chart tends to look like a tornado. In the example
460 GUIDE TO THE SENSITIVITY TOOLKIT A B C D E F G H I J 1 DATA TABLE PARAMETER INFO 2 Parameter -10 Pct +10 Pct Range Base Case Result Base Case % Sensitivity -% +% 3 Price 15389.75 123934.45 108544.70 69662.10 40.00 10.00 36.00 44.00 4 Cost 109568.24 29755.96 79812.28 69662.10 25.00 10.00 22.50 27.50 5 $C$12 55295.89 84028.31 28732.42 69662.10 35.00 10.00 31.50 38.50 6 OHD rate 79239.58 60084.63 19154.95 69662.10 0.15 10.00 0.14 0.17 7 $G$9 65352.24 73971.97 8619.73 69662.10 1.20 10.00 1.08 1.32 8 $E$9 65711.40 73612.81 7901.42 69662.10 1.10 10.00 0.99 1.21 9 $D$9 66429.71 72894.50 6464.79 69662.10 0.90 10.00 0.81 0.99 10 $F$9 66788.86 72535.35 5746.48 69662.10 0.80 10.00 0.72 0.88 11 $C$13 67994.79 71310.29 3315.50 69662.10 3000.00 10.00 2700.00 3300.00 12 $F$14 70562.10 68762.10 1800.00 69662.10 9000.00 10.00 8100.00 9900.00 13 $G$14 70562.10 68762.10 1800.00 69662.10 9000.00 10.00 8100.00 9900.00 14 $D$14 70462.10 68862.10 1600.00 69662.10 8000.00 10.00 7200.00 8800.00 15 $E$14 70462.10 68862.10 1600.00 69662.10 8000.00 10.00 7200.00 8800.00 16 Ad Budget 69662.10 69662.10 0.00 69662.10 40000.00 10.00 36000.00 44000.00 17 18 19 20 Output Measure 21 15389.75 35389.75 55389.75 75389.75 95389.75 115389.75 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 Price Cost $C$12 OHD rate $G$9 $E$9 $D$9 $F$9 $C$13 $F$14 $G$14 $D$14 $E$14 Ad Budget -10 Pct +10 Pct Parameter Figure C.6. Results for Tornado Chart. here, the top four parameters have a substantial impact, whereas the remaining parameters have little influence. C.4 SOLVER SENSITIVITY Solver identifies the values of decision variables in a model that optimize a single cell called the objective function. If we wish to determine the sensitivity of the optimal solution to changes in other parameters, we must run Solver several times. The Solver Sensitivity tool in the Sensitivity Toolkit automates this process. In Appendix A, we illustrated how Solver could be used to identify the optimal pattern of advertising expenditures when total spending was constrained by a budget. Then, we asked how changes in the budget would affect the optimal results. This is an application for Solver Sensitivity. We select Add - ins Sensitivity Toolkit Solver Sensitivity and the window shown in Figure C.7 appears. Solver Sensitivity automatically identifies the
CRYSTAL BALL SENSITIVITY 461 Figure C.7. First input window for Solver Sensitivity. objective function if Solver has been run previously on the model. If the results of additional cells are needed, they can be input under Other Cell(s). Select Next and the window shown in Figure C.8 will appear. Input the cell address of the budget (Solver!C15) under Cell to Vary. Then select Begin, End, Increment, and input the First Value (40,000), Last Value (100,000), and Increment/N (5,000). Select Finish and the results will appear as in Figure A.6. C.5 CRYSTAL BALL SENSITIVITY Crystal Ball estimates the probability distribution of one or more Forecast cells given probability distributions for one or more Assumption cells. When we want to determine how some aspect of a Forecast cell distribution, such as the mean or maximum value, varies with an input parameter, we must run Crystal Ball many times. The Crystal Ball Sensitivity tool in the Sensitivity Toolkit automates this process. In Appendix B, we showed how to estimate the distribution of Profit using Crystal Ball. We then asked how the mean and standard deviation of Profit change as the Overhead Rate changes (cell C10). This is an application for Crystal Ball Sensitivity. We select Add - ins Sensitivity Toolkit Crystal Ball Sensitivity and the window shown in Figure C.9 appears. Crystal Ball Sensitivity automatically
462 GUIDE TO THE SENSITIVITY TOOLKIT Figure C.8. Second input window for Solver Sensitivity. Figure C.9. First input window for Crystal Ball Sensitivity.
CRYSTAL BALL SENSITIVITY 463 Figure C.10. Second input window for Crystal Ball Sensitivity. identifies the Forecast cells in the model. It also offers to capture any of the following six statistics for each Forecast cell: Number of trials Mean Standard deviation Minimum Maximum Mean standard error Finally, an option is presented for a one - way or a two - way table. Select Next and the window shown in Figure C.10 appears. In this window, enter the Cell to Vary (the budget in C10), and then select Begin, End, Increment/N, First Value (0.15), Last Value (0.25), and Increment/N (0.01). The results appear as in Figure B5.