ESD.70J Engineering Economy Fall 2007 Session Four Michel-Alexandre Cardin – macardin@mit.edu Prof. Richard de Neufville – ardent@mit.edu ESD.70J Engineering Economy Module - Session 4

Questions for “Big vs. small” The past three sessions have covered ways to model uncertainty. It seems like the big plant is better… Does it feel right? Note: we had assumed a commitment to building one small plant each year regardless of what demand reality turns out to be down the road. So much for flexibility and common sense. Let’s correct that oversight! ESD.70J Engineering Economy Module - Session 4

Session four – Flexibility Objectives: Build flexibility into the model See how that impacts our decision-making Perform simple breakeven analysis using Goal Seek Excel self-study references ESD.70J Engineering Economy Module - Session 4

Key limitation of NPV analysis It assumes that future decisions are made today, for example for constructing small plants Year 1 Year 2 Year 3 Decide whether to build a plant But the decisions are actually made each year Year 1 Year 2 Year 3 Decide whether to build a plant Decide whether to build a plant Decide whether to build a plant ESD.70J Engineering Economy Module - Session 4

Key limitation of NPV analysis There is a LOT of value in delaying decisions until: More information becomes available Forecast uncertainty decreases with time and collection of additional data Ability to delay decisions into the future is flexibility Flexibility is the magic bullet against uncertainty! ESD.70J Engineering Economy Module - Session 4

Modeling contingency decisions Recall the spreadsheet we built for Session Two ESD70session2-2.xls Press “F9”: which plan is better? Now think about the following decision rule: After the first plant is built in year 1 for Plan B, we build an additional small plant only if we observe a bigger demand than capacity How do we model that? ESD.70J Engineering Economy Module - Session 4

Modeling contingency decisions Open ESD70session4-1.xls http://ardent.mit.edu/real_options/ROcse_Excel_latest/ESD70session4-1.xls ESD.70J Engineering Economy Module - Session 4

Modeling contingency decisions In “Plan B RAND with Flexibility” tab: in Cell G3 type: “=IF(E5>E4,E3+1,E3)” In Cell I3 type: “=IF(G5>G4,G3+1,G3)” Press “F9” Now which plan is better? How easily can the traditional analysis be misleading, despite properly simulating the uncertainties! ESD.70J Engineering Economy Module - Session 4

Logical Functions in Excel IF(logical_test,value_if_true,value_if_false): Returns one value if the test evaluates to TRUE and another value if it evaluates to FALSE MAX(number1,number2,...): Returns the largest value in a set of values When maximizing among the alternatives MIN(number1,number2, ...): Returns the smallest number in a set of values ESD.70J Engineering Economy Module - Session 4

Check with your neighbors… Check the solution sheet… Ask me questions… Give it a try! Check with your neighbors… Check the solution sheet… Ask me questions… ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Questions How different is this kind of analysis from sensitivity analysis? What is the effect on VARG curve and histogram for Plan B? This approach is different from sensitivity analysis because in SA, you simply run different numbers without adapting the model to changes in uncertain conditions. In this approach, building flexibility in the spreadsheet not only runs different numbers, but shows how pro-active management in face of uncertainty can add value to the system. In a word, the model is now flexible and adapts to changing numbers. Compared with ESD70session2-2.xls. The left tail of the VARG curve for Plan B is moved to the right, showing a reduction in potential losses through pro-active management. The right tail is moved to the right, showing there are now greater opportunities for gain. Plan A still shows higher NPV expectations due to the possibility to capture extra demand in years 1 and 2 due to overcapacity built for 900 units. This movement from left to right also increases the mean NPV for Plan B. The histogram for Plan B also shows a more complete spectrum of NPV values, not cut-off for high NPV values as it was earlier. ESD.70J Engineering Economy Module - Session 4

Question for “Big vs. small” Since Plan B with flexibility is better than Plan A, the manager is tempted to go with small plant. Just then the Chief Operations Officer reports the variable cost for the big plant can be further cut (the variable cost for a small plant remains the same) What is the breakeven variable cost point for Plan A where the two plans are equivalent? ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Breakeven analysis A breakeven level for a parameter – a target value where some particularly interesting event occurs In a deterministic case, a breakeven point can be determined using “Goal Seek” We cannot use Goal Seek with Data Tables (sim on sim). However, we still can do trial-and-error search ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Spinner In “Entries” tab, enter “=Simulation!D4-Simulation!D1” next to “mean NPVB – mean NPVA” in cell H3 Choose menu “View”  “Toolbar”  “Forms” Click button and draw a Spinner from E18 to E19 Spinner works with integers, so modify Plan A variable cost in cell C18 to equal = C17/100. Set C17 to 128 Right click the spinner and click “Format Control” Change “Current value:” to “128”, put “C17” in “Cell link:” ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Spinner Hit F9 and see how “mean NPVB – mean NPVA” values change Somewhere around 1.24 this value approaches 0 Note: what we are really trying to do is run a “simulation on simulation” to find Plan A’s variable cost where mean NPVs for both plans are equal Excel does not support recursive simulations Spinner gives an approximate answer, but requires manual input ESD.70J Engineering Economy Module - Session 4

Check with your neighbors… Check the solution sheet… Ask me questions… Give it a try! Check with your neighbors… Check the solution sheet… Ask me questions… ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Goal Seek  Solver In Session 1 we used Goal Seek to get the exact breakeven point Solver supports constrained optimization Now maximize NPV for Plan B by varying size of constructed plant Assume 1:1 correlation between small plant’s cost and manufacturing capacity ($300M  300K units) Set C23 = C15 on the “Entries” sheet Change demand expectations to {200, 600, 800} Erase Data Tables to speed up analysis In “Plan B - Solver”, set Salvage value cell I12 to “=MIN(Entries!C29, MAX(C11,E11,G11))” We want to know what is the maximum NPV we can get with Plan by changing the size of the plant, assuming the size corresponds to the number of units it can produce. Changing size implies the plant will cost less, and therefore we make the additional assumption that size is correlated 1:1 with the cost of the plant. We change demand expectations just to have a different situation. This choice of values also gives a value from the solver that is different than from the non-optimized case. If {200, 600, 900} is selected, the optimum is still capacity for 300k units, which is not different than the original case. For the last line: the MAX() condition picks the new investment value that results from varying size plant (which by the 1:1 correlation reduces the investment). The MIN() condition picks the smallest of the two salvage values between $300M and the one chosen by the algorithm at a particular iteration, ensuring that it never goes beyond $300M if the size of the plant goes beyond 300k units produced. This is simply to keep our rationale that salvage value is one rounded value to simplify the problem. However, if the investment is lower than $300M, it makes sense to accordingly reduce the salvage value, which is what this program line does. ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Solver  use Solver to find optimum plant size Go to “Tools”  “Solver” In “Entries” tab, set target cell to “H5” “equal to” “MAX” Set “By changing cells” to “C15” “Subject to the Constraints:” $C$15 => 0 Hit “Solve”… Optimal small plant size is? 266.666644 ESD.70J Engineering Economy Module - Session 4

Check with your neighbors… Check the solution sheet… Ask me questions… Give it a try! Check with your neighbors… Check the solution sheet… Ask me questions… ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Summary Incorporated flexibility into the models Breakeven analysis Excel is a powerful modeling tool. It will accompany you throughout your career We hope this short course increased your awareness of Excel’s functionality Uncertainty/risk management is way cool and very profitable ! ESD.70J Engineering Economy Module - Session 4

Excel self-study references MS Support center http://support.microsoft.com/?scid=ph;en-us;2512 “Advanced Excel for Scientific Data Analysis” by Robert De Levie “Advanced modeling in finance using Excel and VBA” by Mary Jackson, Mike Staunton www.amazon.com ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Big picture of Excel Basics Names References Formula Functions Charts Statistical analysis Optimization (Solver) Macros Visual Basic – now sky is the limit ! Database integration Date and time f’ns Engineering f’ns Financial f’ns Information f’ns Logical f’ns Lookup and reference f’ns Math and trigonometry f’ns Text f’ns Add more things – Macros, VB, etc ESD.70J Engineering Economy Module - Session 4

ESD.70J Engineering Economy Module - Session 4 Using Excel Help Ways to search Contents Answer wizard Index Online at http://support.microsoft.com Google your questions Explore links to related topics ESD.70J Engineering Economy Module - Session 4