1. ESD.70J Engineering Economy Module - Session 41 ESD.70J Engineering Economy Fall 2006 Session Four Alex Fadeev - afadeev@mit.edu Link for this PPT: http://ardent.mit.edu/real_options/ROcse_Excel_latest/ExcelSession4.pdf

2. ESD.70J Engineering Economy Module - Session 42 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. Lets correct that oversight!

3. ESD.70J Engineering Economy Module - Session 43 Outline Building flexibility into the model VAR chart Breakeven analysis - Goal Seek Excel self-study references

4. ESD.70J Engineering Economy Module - Session 44 Key limitation of NPV analysis It assumes that future decisions are made today, for example for constructing small plants Decide whether to build a plant Year 1Year 2Year 3 But the decisions are actually made each year Decide whether to build a plant Year 1Year 2Year 3

5. ESD.70J Engineering Economy Module - Session 45 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 Key limitation of NPV analysis

6. ESD.70J Engineering Economy Module - Session 46 Modeling contingency decisions Recall the spreadsheet we built for Session Two Press “F9” and check which plan is better? Think about the following decision rule: –After the first plant is built in year 1, we build an additional small plant only if we observe a bigger demand than capacity How do we model that?

7. ESD.70J Engineering Economy Module - Session 47 In “Plan B” sheet: –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 now? How easily can the traditional analysis be misleading, despite properly simulating the uncertainties! Modeling contingency decisions

8. ESD.70J Engineering Economy Module - Session 48 Check the solution sheet. Please ask questions now…

9. ESD.70J Engineering Economy Module - Session 49 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....

10. ESD.70J Engineering Economy Module - Session 410 Value at Risk (VAR) Chart Value at Risk (VAR): –A loss that will not be exceeded at some specified confidence level. The VAR chart is aimed at making a representation of –“We are X percent certain that we will not lose more than Y dollars for this project.” VAR is a common language on Wall Street, It stresses downside risk, though we should also look at CDF for upside potential of a project

11. ESD.70J Engineering Economy Module - Session 411 Building VAR Chart 1.Add a new sheet to our latest file, and name it “VAR” 2.Type “NPVA” in Cell A1, “Rank” in Cell B1, “NPVB” in Cell E1, “Rank” in Cell F1 3.Type “=Simulation!B8” in cell A2, drag down to A2001; Type” =Simulation!D8” in cell E2, drag down to E2001 4.Type “=RANK(A2,$A$2:$A$2001,1)” in cell B2, and drag down to B2001; Type “=RANK(E2,$E$2:$E$2001,1)” in cell F2, and drag down to F2001

12. ESD.70J Engineering Economy Module - Session 412 5.Type “98%” in cell J1 and link J2 to J1 6.In cell C2 type “=IF(B2=(1-$J$1)*2000,A2,0)”, and drag down to C2001; 7.In cell G2 type “=IF(F2=(1-$J$2)*2000,E2,0)”, and drag down to G2001 8.In cell D2 type “=IF(C2=0,0,1)”, and drag down to D2001 9.In cell H2 type “=IF(G2=0,0,1)”, and drag down to H2001 10.Type “VAR for NPVA is” in cell K1; type “VAR for NPVB is” in cell K2 11.In cell L1 type “=SUM(C2:C2001)/SUM(D2:D2001)” 12.In cell L2 type “=SUM(G2:G2001)/SUM(H2:H2001)” 13.Copy the CDF chart from the “Simulation” sheet to “VAR” sheet

13. ESD.70J Engineering Economy Module - Session 413 14.Type “=L1” in K5, type “=L1” in L5, type “1” in K6, and type “0” in L6 15.Type “=L2” in K8, type “=L2” in L8, type “1” in K9, and type “0” in L9 16.Type "=TEXT(J1,"?%")&" VAR for NPVA"" in M5, type "=TEXT(J2,"?%")&" VAR for NPVB"" in M8 17.Right click the CDF chart, click “Chart Options”, change “Chart title:” from “CDF” to “VAR” 18.Right click the VAR chart, click “Source Data”, click “Series”. Click “NPVA Mean” in the left hand window, change “Name:” to “=VAR!$M$5”, change “X Values:” to “=VAR!$K$5:$L$5”, change “Y Values:” to “=VAR!$K$6:$L$6”, Click “NPVB Mean” in the left hand window, change “Name:” to “=VAR!$M$8”, change “X Values:” to “=VAR!$K$8:$L$8”, change “Y Values:” to “=VAR!$K$9:$L$9”, 19.Click

14. ESD.70J Engineering Economy Module - Session 414 Explanation RANK(number,ref,order): Returns the rank of a number in a list of numbers. Columns C & G pick out N-th simulation value corresponding to the desired confidence interval. Column D and H resolve ties and would support calculation of C-VAR –Right now we only look at what happens at xx-%, but that event may not be representative –Frequently want to know “how bad do things get below xx-%”.

15. ESD.70J Engineering Economy Module - Session 415 Try different confidence intervals by changing values in J1 and J2… Compare 98% VAR value for –Plan A –Plan B without flexibility –Plan B with flexibility Add C-VAR calculation

16. ESD.70J Engineering Economy Module - Session 416 Check the solution sheet. Please ask questions now…

17. ESD.70J Engineering Economy Module - Session 417 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 break-even variable cost point for Plan A where the two plans are equivalent?

18. ESD.70J Engineering Economy Module - Session 418 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 by “Goal Seek” In a simulation, we can not use DataTables (sim on sim). However, we still can do trial-and-error search

19. ESD.70J Engineering Economy Module - Session 419 Spinner 1.In “Entries” enter “=Simulation!D1-Simulation!D4” next to “Simulated Avg NPV A – NPV B ” in cells G3 and H3 2.Choose   3.Click button and draw a Spinner from E18 to E19 4.Spinner works with integers, so modify Plan-A variable cost in cell C18 to equal = C17/100. Set C18 to 128 5.Right click the spinner and click “Format Control” 6.Change “Current value:” to “128”, put “C17” in “Cell link:”

20. ESD.70J Engineering Economy Module - Session 420 Spinner 7.Hit F9 and see how “NPV A – NPV B ” values change. 8.Somewhere around 1.24 the NPVA – NPVB approaches 0 9.Note: what we are really trying to do is run a “simulation on simulation” to find the Plan-A’s variable cost where average NPVs for the two plans are equal. –Excel does not support recursive simulations ;-( –(try it anyway if you are curious – how would you do it?) –Spinner gives an approximate answer, but requires manual input.

21. ESD.70J Engineering Economy Module - Session 421 Check the solution sheet. Please ask questions now…

22. ESD.70J Engineering Economy Module - Session 422 GoalSeek  Solver In class 1 we used GoalSeek to get the exact break-even point. Solver supports constrained optimization –Want to maximize NPV for Plan B (small plant) 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, 900} –Set salvage cost calculation to “=MIN(Entries!C29, MAX(C11,E11,G11))” on “Plan B” sheet.

23. ESD.70J Engineering Economy Module - Session 423 Solver  use Solver to find optimum plant size Go to  Set target sell to “H5” “equal to” MAX Set “By changing cells” to “C15” Constrain the cost to be positive:  Fill out: {Cell Reference, Relationship, Constraint} with {“$C$15”, “=>”, “=0”} Hit … … Optimal small plant size is …

24. ESD.70J Engineering Economy Module - Session 424 Check the solution sheet. Please ask questions now…

25. ESD.70J Engineering Economy Module - Session 425 Summary Incorporated flexibility into the models VAR Chart Break-even analysis Excel as 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 cool and very profitable !

26. ESD.70J Engineering Economy Module - Session 426 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

27. ESD.70J Engineering Economy Module - Session 427 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

28. ESD.70J Engineering Economy Module - Session 428 Using Excel Help Ways to search –Contents –Answer wizard –Index –Online at http://support.microsoft.com –Google your questions Explore links to related topics