Home

User Manual SLS 2010

Contents

1. 1 Customized Real Options Results 3 Assumptions Lattice Maker 4 PY Asset Value 5 Volatility 24 l Basic Inputs Basic Option 6 Risk free Rate PY Asset iv Implementation Cost 100 z i Volatility 7 Combination Options 9 Lattice Steps Risk free 2 _ Expansion Factor 10 Option Type Dividend i 1 Implementation Cost Maturity Years C Contraction Factor 13 Expansion Factor Lattice Steps 10 14 Expansion Cost C Abandonment Salvage 15 Contraction Factor American Option 16 Contraction Saving European Option 17 Abandonment Salvage pa 18 19 inderiging Asset Lattice 20 21 22 123 63 23 12363 13269 14241 15285 24 j_10733j 11519 12363 13269 25 26 27 28 29 6 80 60 968 6543 30 52 92 5680 31 32 Option atuation Lattice 33 34 2319 2805 3358 3977 46 64 S416 6236 7127 8094 9143 102 81 35 36 1544 1936 2399 2935 3543 4221 4964 5772 6651 7607 37 _Continue Continue Continue Continue Continue Continue Continue Continue _ Continue Execute 38 893 1177 1533 1968 2486 30 86 3757 4488 5285 39 Continue Continue Continue Continue Continue Continue Continue Continue Execute 40 MAX I24 J40 J42 yi 2007 2610 3269 41 _Continue Continue Continue Continue Continue Continue Continue Execute 42 109 169 263 4
2. Example OptionOpen Figure 65 Up and Out Upper American Barrier Option User Manual 90 Real Options Super Lattice Solver software manual American and European Double Barrier Options and Exotic Barriers The Double Barrier Option is solved using the binomial lattice This model measures the strategic value of an option this applies to both calls and puts that comes either in the money or out of the money when the Asset Value hits either the artificial Upper or Lower Barriers Therefore an Up and In and Down and In option for both calls and puts indicates that the option becomes live if the asset value either hits the upper or lower barrier Conversely for the Up and Out and Down and Out option the option is live only when neither the upper nor lower barrier is breached Examples of this option include contractual agreements whereby if the upper barrier is breached some event or clause is triggered The value of barrier options is lower than standard options as the barrier option will have value within a smaller price range than the standard option The holder of a barrier option loses some of the traditional option value and therefore should sell it at a lower price than a standard option Figure 66 illustrates an American Up and In Down and In Double Barrier Option This is a combination of the Upper and Lower Barrier Options shown previously The same exact logic applies to this Double Barrier Option Figure 66 illustrates
3. Example 1 2 10 20 35 an Fe a Max Cost Asset 0 Black Scholes 42 88 Closed Form American 42 88 Binomial European 42 87 20 75 Example Max Asset Cost 0 Binomial American 42 87 Custom Equations _ _ _ _ ______ _____________________ Result Intermediate Node Equation Options Before Expiration Custom Option 24 4213 Max Cost Asset OptionOpen Benchmark Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Figure 40 American and European Put Options using SLS User Manual 63 Real Options Super Lattice Solver software manual Exotic Chooser Options Many types of user defined and exotic options can be solved using the SLS and MSLS For instance Figure 41 shows a simple Exotic Chooser Option example file used Exotic Chooser Option In this simple analysis the option holder has two options a call and a put Instead of having to purchase or obtain two separate options one single option is obtained which allows the option holder to choose whether the option will be a call or a put thereby reducing the total cost of obtaining two separate options For instance with the same input parameters in Figure 41 the American Chooser Option is worth 6 7168 as compared to 4 87 for the call and 2 02 for the put 6 89 total cost for two separate options Figure 41 Single Asset Super Lattice Solver File Help Comment American amp European C
4. PV Underlying Asset 100 RiskfreeRatel 5 y Implementation Cost s 80 DividendRae i 0 Maturity Years 5 Nolatiity 5 Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Benchmark If Asset lt LowerBarier Asset gt UpperBamier Max Asset Cost 0 0 Example Max Asset Cost 0 Custom Equations _ _ _ lt __ iP esllt Intermediate Node Equation Options Before Expiration Custom Option 41 9996 If Asset lt LowerBamier Asset gt UpperBamier Max Asset Cost OptionOpen OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Example OptionOpen Figure 66 Up and In Down and In Double Barrier Option User Manual 92 Real Options Super Lattice Solver software manual SECTION III EMPLOYEE STOCK OPTIONS User Manual 93 Real Options Super Lattice Solver software manual American ESO with Vesting Period Figure 67 illustrates how an employee stock option ESO with a vesting period and blackout dates can be modeled Enter the blackout steps 0 39 Because the blackout dates input box has been used you will need to enter the Terminal Node Equation TE Intermediate Node Equation IE and Intermediate Node Equation During Vesting and Blackout Periods IEV Enter Max Stock Strike 0
5. Figure 13 Installing Microsoft NET Framework 2 0 User Manual 137 Real Options Super Lattice Solver software manual Microsoft NET Framework 2 0 Setup Figure 14 Completing the Installation of Microsoft NET Framework 2 0 User Manual 138 Real Options Super Lattice Solver software manual STEP THREE Installing Real Options SLS Step 3 1 Insert the installation CD or go to the download page to get the software installation file Figure 15 www realoptionsvaluation com downloads and scroll down to the software section Make sure you download the SLS 20 0 files Click on the Trial version if you have not yet purchased the software or click the Full version if you have already purchased the software and have the relevant license keys A Downloading Information Microsoft Internet Explorer File Edit View Favorites Tools Help Q sak Q x a EA JO search She Favorites Q A 9 Se LJ E citi Fel 33 Address http www realoptionsvaluation com downloadj yr om Is Search Web v New 9 Er Ea CI my Web lt Messenger 7 Q Bookmarks My Yahoo w Yahoo g Finance I L Downloading Information F Add Tab SOFTWARE DOWNLOAD REAL OPTIONS SLS 2 0 WITH SUPER SPEED FULL amp TRIAL VERSION DOWNLOAD Download the Real Options Super Lattice Solver TRIAL VERSION INFO This fully functional full version expires in 14 days upon which you will need to purchase the software and we will e mail you a permanen
6. ain Menu 10 Step Trinomiai Super Lattice 37 94 Trinomial Super Lattice Steps 10Steps v nalyze 27183 245 96 Underlying Stock Price Lattice 110 52 100 00 __ 90 48 6703 6703 60 65 54 88 Option Valuation Lattice 2136 1699 11 08 835 360 Figure 70 ESO Toolkit Results of a Call Option accounting for Suboptimal Behavior User Manual 97 Real Options Super Lattice Solver software manual American ESO with Vesting and Suboptimal Exercise Behavior Next we have the ESO with vesting and suboptimal exercise behavior This is simply the extension of the previous two examples Again the result of 9 22 Figure 71 is verified using the ESO Toolkit as seen in Figure 72 example file used ESO Vesting with Suboptimal Behavior Figure 71 Single Asset Super Lattice Solver File Help Comment Employee Stock Option with vesting period and suboptimal exercise behavior ate oo pera Value Starting Step BE az sn V Underlying Asset 20 Risk Free Rate 4 Implementation Cost Dividend Rate Maturity Years l D Volatility Lattice Steps y Al inputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option e39 Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Cost 0 Example Max Asset Cost 0 Custom Equations Intermediate Node Eq
7. approach or explaining the rationale why we analyzed it the way we did Hence let us look at the assumptions required and explain the rationale behind them Assumption 1 We assume that the underlying distribution of the asset fluctuations is normal We can assume normality because the distribution of the final nodes on a super lattice is normally distributed In fact the Brownian Motion equation shown earlier requires a random standard normal distribution In addition a lot of distributions will converge to the normal distribution anyway a Binomial distribution becomes normally distributed when number of trials increase a Poisson distribution also becomes normally distributed with a high average rate a Triangular distribution is a normal distribution with truncated upper and lower values an so forth and it is not possible to ascertain the shape and type of the final NPV distribution if the DCF model is simulated with many different types of distributions e g revenues are Lognormally distributed and are negatively correlated to one another over time while operating expenses are positively correlated to revenues but are assumed to be distributed following a Triangular distribution while the effects of market competition are simulated using a Poisson distribution with a small rate times the probability of technical success simulated as a Binomial distribution We cannot determine theoretically what a Lognormal minus a Triangular times Poiss
8. go en Mea en 1353 __ 1353 Bs __ 1353 8 21 498 498 3 02 Vesting Calculation ss sa ee 14741 32 8901 71 535982 535982 321155 321155 1908 55 _____ 190855 __ 190855 111825 111825 111825 638 91 _ 63891 63891 63891 345 23 __ 34817 __ 34817 34817 183 29 S 18129 17674 1718 17183 9659 __ 9229 8687 7893 6488 ES re E Le E E _ E EL Nm Option Valuation Lattice Figure 68 ESO Valuation Toolkit Results of a Vesting Call Option User Manual 95 Real Options Super Lattice Solver software manual American ESO with Suboptimal Exercise Behavior This example shows how suboptimal exercise behavior multiples can be included into the analysis and how the custom variables list can be used as seen in Figure 69 example file used ESO Suboptimal Behavior and steps was changed to 100 in this example The TE is the same as the previous example but the IE assumes that the option will be suboptimally executed if the stock price in some future state exceeds the suboptimal exercise threshold times the strike price Notice that the IEV is not used because we did not assume any vesting or blackout periods Also the Suboptimal exercise multiple variable is listed on the customs variable list with the relevant value of 1 85 and a starting step of 0 This means that 1 85 is applicable starting from step 0 in the lattice all
9. Blackout Steps and Vesting Period Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Cost 0 Example Max Asset Cost 0 Custom Equations Max Asset Cost OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Figure 52 Simple Trinomial Lattice Solution User Manual 76 Real Options Super Lattice Solver software manual Figure 53 Single Asset Super Lattice Solver File Help Comment Plain Vanila American and European Call Options Option Type Custom Variables Ca European B j Variable Name Value Starting Step Basic Inputs PV Underlying Asset 100 Risk Free Rate Implementation Cost 100 Dividend Rate Maturity Years 5 Volatility 3 Lattice Steps 10 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Benchmark Example Max Asset Cost 0 Custom Equations intermediate Node Equation Options Before Expiration Example Max Asset Cost OptionOpen intermediate Node Equation During Blackout and Vesting Period Example OptionOpen Figure 53 10 Step Binomial Lattice Comparison Result User Manual 77 Real Options Super Lattice Solver software manual American and European Mean Reversion Options Using Trinomial Lattices The Mean
10. Click on the 2 License Functions amp Options Valuator link and write down or copy the HARDWARE FINGERPRINT it should be an 8 digit alphanumeric code Purchase a license at www realoptionsvaluation com by clicking on the Purchase link 5 E mail admin realoptionsvaluation com these two identification numbers and we will send you your license file and license key Once you receive these please install the license using the steps below Installing Licenses 1 Save the SLS license file to your hard drive the license file we sent you after you purchased the software and then start Real Options SLS click on Start Programs Real Options Valuation Real Options SLS Real Options SLS 2 Click on the 1 License Real Options SLS and select ACTIVATE then browse to the SLS license file that we sent you 3 Click on the 2 License Functions amp Options Valuator and enter in the NAME and KEY combination we sent you User Manual 130 Real Options Super Lattice Solver software manual Appendix E Detailed Installation Instructions STEP ONE Checking System Requirements Step 1 1 Verify that you have Windows XP or later Step 1 2 Verify that you have Excel XP Excel 2003 or Excel 2007 Step 1 3 Verify that you have Administrative privileges to install software Most home computers have administrative privileges installed by default which means you can proceed to Step 1 4 However some corporate computers with strict I
11. Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period OptionOpen Example OptionOpen Figure 35 Bermudan Option to Expand Contract and Abandon User Manual 57 Real Options Super Lattice Solver software manual Figure 36 Single Asset Super Lattice Solver File Help Comment Customized Expansion Contraction and Abandonment Options Option Type American V European V Bermudan Custom Basic Inputs T_T PV Underlying Asset 100 Risk Free Rate 100 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option 0 50 Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Benchmark Asset Contraction Contract Savings Salvage Closed Form American Binomial European Example Max Asset Cost 0 Binomial American Custom Equations __ Result Intermediate Node Equation Options Before Expiration Custom Option 115 6590 Max Asset Asset Expansion EpandCost Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Max Asset Contraction Contract Savings Salvage OptionOpen Eases Opiates Figure 36 Custom Options with Mixed Expand Contract and Abandon Capabilities User Manual 58 Real Options Super Lattice Solver software manual Figure 37 Si
12. FLOOR LOG MAX MIN REMAINDER ROUND SIN SINH SQRT TAN TANH TRUNCATE and IF o Variables in SLS 2010 are case sensitive except for function names Models that mix and match cases will not work in SLS 2010 Therefore it is suggested that when using custom variables in SLS and MSLS you are consistent with the use of case for the custom variable names e ANDO and OR functions are missing and are replaced with special characters in SLS 2010 The amp and symbols represent the AND and OR operators For example Asset gt 0 Cost lt 0 means OR Asset gt 0 Cost lt 0 while Asset gt 0 amp Cost lt 0 is AND Asset gt 0 Cost lt 0 e Blackout Step Specifications To define the blackout steps use the following examples as a guide 3 Step 3 is a blackout step 3 Steps 3 and 5 are blackout steps 3 5 7 Steps 3 5 6 7 are blackout steps 1 3 5 6 Steps 1 3 5 6 are blackout steps 5 7 Steps 5 6 7 are blackout steps 5 10 Steps 5 7 9 are blackout steps the symbol means skip size 5 143 Steps 5 8 11 14 are blackout steps 5 63 Step 5 is a blackout step 5 6 3 Step 5 is a blackout step white spaces are ignored e Identifiers An identifier is a sequence of characters that begins with a z A Z _ or After the first character a z A Z 0 9 _ are valid characters in the sequence Note that space is not a valid character However it can be used if the v
13. If a complete lattice is required simply enter 10 steps in the SLS and the full 10 step lattice will be generated instead The Intermediate Computations and Results are for the Super Lattice based on the number of lattice steps entered and not based on the 10 step lattice generated To obtain the Intermediate Computations for 10 step lattices simply re run the analysis inputting 0 as the lattice steps This way the Audit Worksheet generated will be for a 10 step lattice and the results from SLS will now be comparable Figure 6 e The worksheet only provides values as it is assumed that the user was the one who entered the terminal and Intermediate Node Equations hence there is really no need to recreate these equations in Excel again The user can always reload the SLS file and view the equations or print out the form if required by clicking on File Print The software also allows you to save or open analysis files That is all the inputs in the software will be saved and can be retrieved for future use The results will not be saved because you may accidentally delete or change an input and the results will no longer be valid In addition re running the super lattice computations will only take a few seconds and it is always advisable for you to re run the model when opening an old analysis file You may also enter Blackout Steps These are the steps on the super lattice that will have different behaviors than the terminal or intermed
14. Node Equaliers pliers Boise Exphalion Custom Option 41 2242 f Asset gt Barier Max Asset Cost OptionOpen OptionOpen Example Max Asset Cost OptionOpen ediate Node Equation During Blackout and Figure 64 Up and In Upper American Barrier Option User Manual 89 Real Options Super Lattice Solver software manual Figure 65 Single Asset Super Lattice Solver File Help Comment Upper Barier Up and Out Call This option is live only when the asset value doesnt breach the upper banier Option Type TO Custom Variables TT Z American European Petra Custom Variable Name Value Starting Step Barrier 10 Basic Inputs T_T PV Underlying Asset Risk Free Rate Implementation Cost O0 Dividend Rate 3 Maturity Years 5 Volatility 2 Lattice Steps 100 _ Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Teminal Node Equation Options at Expiration Benchmark if Asset lt Barier Max Asset Cost 0 0 Black Scholes Closed Form American Binomial European Tria ee Saal Binomial American Custom Equations i ________ _ _ Result Intermediate Node Equation Options Before Expiration Custom Option 23 6931 If Asset lt Bamier Max Asset Cost OptionOpen OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period
15. Solving a Multiple Investment Simultaneous Compound Option using MSLS User Manual 74 Real Options Super Lattice Solver software manual American and European Options Using Trinomial Lattices Building and solving trinomial lattices is similar to building and solving binomial lattices complete with the up down jumps and risk neutral probabilities but it is more complicated due to more branches stemming from each node At the limit both the binomial and trinomial lattices yield the same result as seen in the following table However the lattice building complexity is much higher for trinomial or multinomial lattices The only reason to use a trinomial lattice is because the level of convergence to the correct option value is achieved more quickly than by using a binomial lattice In the sample table notice how the trinomial lattice yields the correct option value with fewer steps than it takes for a binomial lattice 1 000 as compared to 5 000 Because both yield identical results at the limit but trinomials are much more difficult to calculate and take a longer computation time the binomial lattice is usually used instead However a trinomial is required only when the underlying asset follows a mean reverting process An illustration of the convergence of trinomials and binomials can be seen in the following example Steps 5 10 100 1 000 5 000 Binomial Lattice 30 73 29 22 29 72 29 77 29 78 Trinomial Lattice 29 22 29 50 29 75 29 78 2
16. cccccssssssssssssssssscsssscssssssesssssssssessseees ID American ESO with Vesting Period iii 94 American ESO with Suboptimal Exercise Behavior iii 96 American ESO with Vesting and Suboptimal Exercise Behavior iii 98 American ESO with Vesting Suboptimal Exercise Behavior Blackout Periods and Forfeiture Rate 100 Appendix A Lattice Convergence iii 102 Appendix B Volatility Estimates iii 103 Volatility Estimates Logarithmic Cash Flow Returns Stock Price Returns Approach ii 103 Volatility Estimates Logarithmic Present Value Returns M ii 108 Appendix C Technical Formulae Exotic Options Formulas iii 120 Black and Scholes Option Model European Version iii 120 Black and Scholes with Drift Dividend European Version 121 Black and Scholes with Future Payments European Version iii 122 Chooser Options Basic Chooser iii 123 Complex ChOOSeri ne si o lat ad Li 124 Compound Options on Options 125 Forward Starl Oplons sx ilaele al Rea ER OD 126 Generalized Black Scholes Model iii 127 Optionson Eutires nasce lai LIL e lella Lana 128 Two Correlated Assets Option rulla ile iaia 129 Appendix D Quick Install and Licensing Guide i 130 Licensing Preparation rca ara 130 Installine Eicensesi scche illa babele bea sen
17. offshore rig The 10 year risk free rate is 5 and the volatility of the project is found to be at an annualized 45 using historical oil prices as a proxy If the expedition is highly successful oil prices are high and production rates are soaring then the company will continue its operations However if things are not looking too good oil prices are low or moderate and User Manual 43 Real Options Super Lattice Solver software manual production is only decent it is very difficult for the company to abandon operations why lose everything when net income is still positive although not as high as anticipated and not to mention the environmental and legal ramifications of simply abandoning an oil rig in the middle of the ocean Hence the oil company decides to hedge its downside risk through an American Contraction Option The oil company was able to find a smaller oil and gas company a former partner on other explorations to be interested in a joint venture The joint venture is structured such that the oil company pays this smaller counterparty a lump sum right now for a 10 year contract whereby at any time and at the oil company s request the smaller counterparty will have to take over all operations of the offshore oil rig i e taking over all operations and hence all relevant expenses and keep 30 of the net revenues generated The counterparty is in agreement because it does not have to partake in the billions of dollars required
18. or allowing it to expire worthless if it is at the money or out of the money Figure 4 Single Asset Super Lattice Solver File Help Comment Plain Vanila American and European Call Options lower number of steps Useful for testing convergence ena cib n Variable Name Value Starting Step PV Underlying Asset Risk Free Rate Implementation Cost Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Cost 0 Example Max Asset Cost 0 Intermediate Node Equation Options Before Expiration Max Asset Cost OptionOpen Example Max Asset Cost OptionOpen emediate Node Equal JU gJ DIAC Figure 4 Custom Equation Inputs In addition you can create an Audit Worksheet in Excel to view a sample 10 step binomial lattice by checking the box Generate Audit Worksheet For instance loading the example file Plain Vanilla Call User Manual 13 Real Options Super Lattice Solver software manual Option I and selecting the box creates a worksheet as seen in Figure 5 There are several items that should be noted about this audit worksheet e The audit worksheet generated will show the first 10 steps of the lattice regardless of how many you enter That is if you enter 1 000 steps the first 10 steps will be generated
19. returns You get greedy and keep it for one more period when you should have sold it and obtain the capital gains The next period the asset goes back down to 100 which means you lost half User Manual 106 Real Options Super Lattice Solver software manual the value or 50 absolute returns Your stockbroker calls you up and tells you that you made an average of 25 returns in the two periods the arithmetic average of 100 and 50 is 25 You started with 100 and ended up with 100 You clearly did not make a 25 return Thus an arithmetic average will over inflate the average when fluctuations occur fluctuations do occur in the stock market or for your real options project otherwise your volatility is very low and there s no option value and hence no point in doing an options analysis A geometric average is a better way to compute the return The computation is seen below and you can clearly see that as part of the geometric average calculation relative returns are computed That is if 100 goes to 200 the relative return is 2 0 and the absolute return is 100 or when 100 goes down to 90 the relative return is 0 9 anything less than 1 0 is a loss or 10 absolute returns Thus to avoid over inflating the computations we use relative returns in Step 2 i Period 1 End Value Period 2 End Value Period n End Value 200 100 Geometric Average Kai 1 0 Period 1 Start Value Period 2 Start Value Period n
20. s link for the MSLS Result to incorporate the right number of rows otherwise the analysis will not compute properly For example the default shows 3 option valuation lattices and by selecting the MSLS Results cell in the spreadsheet and clicking on nsert Function you will see that the function links to cells A24 H26 for these three rows for the OVLattices input in the function If you add another option valuation lattice change the link to A24 H27 and so forth You can also leave the list of custom variables as is The results will not be affected if these variables are not used in the custom equations Finally Figure 16 shows a Changing Volatility and Changing Risk free Rate Option In this model the volatility and risk free yields are allowed to change over time and a non recombining lattice is required to solve the option In most cases it is recommended that you create option models without the changing volatility term structure because getting a single volatility is difficult enough let alone a series of changing volatilities over time If different volatilities that are uncertain need to be modeled run a Monte Carlo simulation on volatilities instead This model should only be used when the volatilities are modeled robustly are rather certain and change over time The same advice applies to a changing risk free rate term structure User Manual 23 Real Options Super Lattice Solver software manual MULTIPLE SUPER LATTICE SOLVER MULTI
21. 0 3 4 returns 3 ifa gt 0 else 4 ABS 3 MAX a b c MIN d e a gt b IF a gt 0 b lt 0 3 4 IF c lt gt 0 3 4 IF IF a lt 3 4 5 lt gt 4 a a b MA X My Cost 1 My Cost 2 Asset 2 Asset 3 o o o 0000 0600 060 000 0 00 0 0 This concludes a quick overview and tour of the software You are now equipped to start using the SLS software in building and solving real options financial options and employee stock options problems These applications are introduced starting the next section However it is highly recommended that you first review Dr Johnathan Mun s Real Options Analysis Tools and Techniques Second Edition Wiley 2006 for details on the theory and application of real options User Manual 33 Real Options Super Lattice Solver software manual SECTION Il REAL OPTIONS ANALYSIS User Manual 34 Real Options Super Lattice Solver software manual American European Bermudan and Customized Abandonment Options The Abandonment Option looks at the value of a project s or asset s flexibility in being abandoned over the life of the option As an example suppose that a firm owns a project or asset and that based on traditional discounted cash flow DCF models it estimates the present value of the asset PV Underlying Asset to be 120M for the abandonment option this is the net present value of the project or asset Monte Carlo simulation indicates that the Volatility of this asset valu
22. 10 Dividend Rate VariableName Value StartingStep PV Underlying Asset 2 10 ha Implementation Cost 100 Volatility 7 25 Volatility 2 25 Risk Free Rate 5 Maturity Years 5 Lattice Steps 10 Blackout Steps and Vesting Period Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Asset2 Cost 0 Example Max Asset Cost 0 Pentanomial Rainbow Two Asset Lattice 61 7481 intermediate Node Equation Options Before Expiration Max Asset Asset2 Cost OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Figure 61 Pentanomial Lattice Solving a Dual Asset Rainbow Option User Manual 84 Real Options Super Lattice Solver software manual American and European Lower Barrier Options The Lower Barrier Option measures the strategic value of an option this applies to both calls and puts that comes either in the money or out of the money when the Asset Value hits an artificial Lower Barrier that is currently lower than the asset value Therefore a Down and In option for both calls and puts indicates that the option becomes live if the asset value hits the lower barrier Conversely a Down and Out option is live only when the lower barrier is not breached Examples of this option include contractual agreements whereby if the lower barrier is breached some event or clause is triggered The value of a barrier option is lowe
23. 21 30 20 30 Aug 04 27 30 27 68 2685 27 11 45125980 24 25 0 0127 21 25 21 23 Aug 04 27 27 27 67 27 09 2746 40526880 24 56 0 0123 22 29 22 16 Aug 04 27 03 27 50 26 89 27 20 52571740 2426 0 0066 22 29 23 9 Aug 04 27 26 27 75 2686 27 02 51244080 24 10 0 0041 22 42 24 2 Aug 04 28 27 28 55 27 06 27 14 56739100 24 20 0 0488 22 42 25 26 Jul 04 28 36 28 81 28 13 2849 65555220 25 41 0 0163 21 97 26 19 Jul 04 27 62 29 89 27 60 28 03 114579322 25 00 0 0198 22 11 27 12 Jul 04 27 67 28 36 27 25 2748 57970740 24 51 0 0138 22 02 28 G6 Jul 04 28 32 28 33 27 55 27 86 61197249 24 85 0 0250 22 04 29 28 Jun 04 28 60 28 84 28 17 2857 66214339 25 48 0 0000 22 07 30 21 Jun 04 28 22 28 66 27 81 2857 82202478 25 48 0 0079 22 30 31 14 Jun 04 26 55 28 50 26 53 28 35 97727643 25 28 0 0574 22 48 Figure B2 Computing Microsoft s 1 Year Annualized Volatility Clearly there are advantages and shortcomings to this simple approach This method is very easy to implement and Monte Carlo simulation is not required to obtain a single point volatility estimate This approach is mathematically valid and is widely used in estimating volatility of financial assets However for real options analysis there are several caveats that deserve closer attention When cash flows are negative over certain time periods the relative returns will have negative values and the natural logarithm of a negative value does not exist Hence the volatility measure
24. 22 Percentile of Worst Case Scenario 10 00 23 24 Implied Volatility Estimate 25 26 27 ead a NPY of Project 28 29 100M 30 P 31 10th percentile Figure B9 Excel Probability to Volatility Model 1 2 3 Probability to Volatility Best Case Scenario 4 5 Expected NPV of the Asset 6 Alternate Best Case Scenario NPV 144 85 T Percentile of Best Case Scenario 90 00 8 Implied Volatility Estimate 1 Goal Seek 12 Set cell F9 13 To value 35 14 By changing cel gF 6 15 i 3 Cs 17 Figure B10 Excel Volatility to Probability Model Figure B9 allows you to enter the expected NPV and the alternate values best case and worst case as well as its corresponding percentiles That is given some probability and its value we can impute the volatility Conversely Figure B10 shows how you can use Excel s Goal Seek function click on Tools Goal Seek in Excel to find the probability from a volatility For instance say the project s expected NPV is 100M a 35 volatility implies that 90 of the time the NPV will be less than 144 85M and that only 10 best case scenario of the time will the true NPV exceed this value Now that you understand the mechanics of estimating volatilities this way again we need to explain why we did what we did Merely understanding the mechanics is insufficient in justifying the User Manual 116 Real Options Super Lattice Solver software manual
25. Asset 100 Dividend Rate VariableName Value StartingStep PV Underlying Asset 2 8 Long Term Rates 100 Implementation Cost 100 ReversionRate Volatility 25 Market Price of Risk Volatility 2 Jump Rate Risk Free Rate 5 Jump Intensity Maturity Years 5 Correlation Lattice St OO All inputs are annualized rates Blackout Steps and Vesting Period Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Cost 0 Result Example Max Asset Cost 0 Trinomial Lattice 31 9863 Custom Equalione Trinomial Mean Reverting Lattice 18 6183 Intermediate Node Equation Options Before Expiration Max Asset Cost OptionOpen Example Max Asset Cost OptionOpen User Manual 79 Real Options Super Lattice Solver software manual Figure 55B Multinomial Lattice Solver File Help Comment American Put Option using a Trinomial Lattice Model V Trinomial v Trinomial Mean Reverting Quadranomial Jump Diffusion C Pentanomial Rainbow Two Asset om Variables Underlying Asset 100 Dividend Rate VariableName Value StartingStep Pv PV Underlying Asset 2 Long Term Rate Implementation Cost 100 Reversion Rate 25 Market Price of Risk Risk Free Rate Maturity Years Lattice Steps Blackout Steps and Vesting Period Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Ma
26. Because both yield identical results at the limit but trinomials are much more difficult to calculate and take a longer computation time in practice the binomial lattice is usually used instead Nonetheless using the SLS software the computation times are only seconds making this traditionally difficult to run model computable almost instantly However a trinomial is required only under one special circumstance when the underlying asset follows a mean reverting process With the same logic quadranomials and pentanomials yield identical results as the binomial lattice with the exception that these multinomial lattices can be used to solve the following different special limiting conditions e Trinomials Results are identical to binomials and are most appropriate when used to solve mean reverting underlying assets e Quadranomials Results are identical to binomials and are most appropriate when used to solve options whose underlying assets follow jump diffusion processes e Pentanomials Results are identical to binomials and are most appropriate when used to solve two underlying assets that are combined called rainbow options e g price and quantity are multiplied to obtain total revenues but price and quantity each follows a different underlying lattice with its own volatility but both underlying parameters could be correlated to one another See the sections on Mean Reverting Jump Diffusion and Rainbow Options for more details e
27. Framework 2 0 Download Microsoft NET Framework 2 0 required for Real Options SLS 2 0 if your system does not already have it Download Microsoft Installer 3 1 Reg yed to install Real Options SLS 2 0 if your system does not already have it Please view the FAQ if you have any questions about system requirements or problems installing the software SOFTWARE DOWNLOAD EMPLOYEE STOCK OPTIONS VALUATION 38 File Download Security Warning FULL VERSION Download the Employee Stock Options Toolkit a license key is TRIAL VERSION Download the Employee Stock Options Valuation Toolkit trial Do you want to run or save this file Be aware that you will be prompted for a license key to permanently activate the jase Name anet EKE Use the user name and key that was assigned to you when you purchased the Tipee Application SAM Ifyou are only interested in a trial version please download the TRIAL versions APEEP From www realoptionsvaluation com System requirements FAQ and additional resources Windows XP Excel XP or 2003 256 MB RAM 10 MB Hard Drive and administra Please view the FAQ if you have any questions about system requirements or pi SOFTWARE MANUALS potentially harm your computer If you do not trust the source do not The following are the software user manuals and help files available for downld Cer ava tes ae hE He TGR Risk Simulator 1 1 User Manual Risk Simulator 1 1 Help Real Options SLS 1 0 User Manual Real O
28. Install Real Options Super Lattice Solver 2 0 for yourself or for anyone who uses this computer Everyone O Just me Coa SD Figure 17 Installing Real Options SLS ie Real Options Super Lattice Solver 2 0 Confirm Installation The installer is ready to install Real Options Super Lattice Solver 2 0 on your computer Click Next to start the installation Cancel lt Back Figure 18 Installing Real Options SLS User Manual 140 Real Options Super Lattice Solver software manual ie Real Options Super Lattice Solver 2 0 Installing Real Options Super Lattice Solver 2 0 Real Options Super Lattice Solver 2 0 is being installed Please wait Figure 19 Installing Real Options SLS ie Real Options Super Lattice Solver 2 0 Installation Complete Real Options Super Lattice Solver 2 0 has been successfully installed Click Close to exit Please use Windows Update to check for any critical updates to the NET Framework Figure 20 Completing the Installation of Real Options SLS User Manual 141 Real Options Super Lattice Solver software manual Appendix F Activating Permanent Licensing There are two licenses required to run Real Options SLS The first is a license for the Real Options SLS software single asset lattice models multiple assets and multiple phased models multinomial lattices and the lattice maker The second is a license for the Exotic Fin
29. Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period OptionOpen Example OptionOpen Figure 23 Bermudan Abandonment Option with 100 Step Lattice Sometimes the salvage value of the abandonment option may change over time To illustrate in the previous example of an acquisition of a startup firm the intellectual property will most probably increase over time because of continued research and development activities thereby changing the salvage values over time An example is seen in Figure 24 where there are five salvage values over the 5 year abandonment option This can be modeled by using the Custom Variables Type in the Variable Name Value and Starting Step and hit ENTER to input the variables one at a time as seen in Figure 24 s Custom Variables list Notice that the same variable name Salvage is used but the values change over time and the starting steps represent when these different values become effective For instance the salvage value 90 applies at step 0 until the next salvage value of 95 takes over at step 21 This means that for a 5 year option with a 100 step lattice the first year including the current period steps 0 to 20 will have a salvage value of 90 which then increases to 95 in the second year steps 21 to 40 and so forth Notice that as the value of the firm s intellectual property increases over time the option valuation User Manual 41 Real
30. Option using MSLS User Manual 65 Real Options Super Lattice Solver software manual Sequential Compound Options Sequential Compound Options are applicable for research and development investments or any other investments that have multiple stages The MSLS is required for solving Sequential Compound Options The easiest way to understand this option is to start with a two phased example as seen in Figure 44 In the two phased example management has the ability to decide if Phase II PII should be implemented after obtaining the results from Phase I PI For example a pilot project or market research in PI indicates that the market is not yet ready for the product hence PII is not implemented All that is lost is the PI sunk cost not the entire investment cost of both PI and PII An example below illustrates how the option is analyzed PHASE Il PHASE I START END Volatility Measure based on these END uncertain cash flows e ex O_O OO OO START 5M 80M 30 M 35M 40M 48M INVE STMENT CASH FLOW PERIOD PERIOD Figure 44 Graphical Representation of a Two Phased Sequential Compound Option The illustration in Figure 44 is valuable in explaining and communicating to senior management the aspects of an American Sequential Compound Option and its inner workings In the illustration the Phase I investment of 5M in present value dollars in Year 1 is followed by Phase II investment of 80M in present value dollars
31. Put Delta Gamma Hedging Value at Risk Correlation Method Exotic Options and Derivatives i Put Call Parity and Option Sensitivity Real Options Analysis Volatility Implied for Default Risk Value at Risk Volatility Portfolio Risk and Retums Warrants Diluted Value Writer Ettendible Call Option Search Writer Extendible Put Option Model Description Computes the Value at Risk using the Variance Covariance and Correlation method accounting for a specific VaR percentile land holding period Single Input Parameters Horizon Days fi000 Percentile 090 input Input input input Input7 Input Input Input 10 0 inputi input12 Input 13 Multiple Series Input Parameters Values are SPACE separated Rows are SEMICOLON separated Figure 18 Exotic Financial Options Valuator User Manual 28 Real Options Super Lattice Solver software manual Payoff Charts Tornado Convergence Scenario and Sensitivity Analysis The main Single Asset SLS module also comes with payoff charts sensitivity tables scenario analysis and convergence analysis Figure 18A To run these analyses first create a new model or open and run an existing model e g from the first tab Options SLS click on File Examples and select Plain Vanilla Call Option I then hit Run to compute the option value and click on any one of the tabs To use these tools you need to first have a model specified in the main Options SLS tab Here are brief explanations
32. Reversion Option in MNLS calculates both the American and European options when the underlying asset value is mean reverting A mean reverting stochastic process reverts back to the long term mean value Long Term Rate Level at a particular speed of reversion Reversion Rate Examples of variables following a mean reversion process include inflation rates interest rates gross domestic product growth rates optimal production rates price of natural gas and so forth Certain variables such as these succumb to either natural tendencies or economic business conditions to revert to a long term level when the actual values stray too far above or below this level For instance monetary and fiscal policy will prevent the economy from significant fluctuations while policy goals tend to have a specific long term target rate or level Figure 54 illustrates a regular stochastic process dotted red line versus a mean reversion process solid line Clearly the mean reverting process with its dampening effects will have a lower level of uncertainty than the regular process with the same volatility measure Underlying Asset 4 Regular process AAN A Y N tM r f J Licia mean value 1 4 J VA VU Mean reverting process Time Figure 54 Mean Reversion in Action Figure 55 shows the call and put results from a regular option modeled using the Trinomial Lattice versus calls and puts assumi
33. Risk Free Rate 400 Implementation Cost 250 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option 0 80 Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Benchmark di Max Asset Asset Expansion Cost Black Scholes 204 01 Closed Form American 205 19 Binomial European 204 02 Example Max Asset Cost 0 Binomial American 205 67 Custom Equations e ee Re Intermediate Node Equation Options Before Expiration Custom Option 570 4411 Max Asset Expansion Cost OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period OptionOpen Example OptionOpen Figure 32 Bermudan Expansion Option User Manual 54 Real Options Super Lattice Solver software manual Figure 33 Single Asset Super Lattice Solver AS File Help Comment Custom Bermudan Option to Expand with changing rates of expansion over time and blackout periods Option Type lt A A Custom Variables ____ J American J European Bermudan V Custom Variable Name Value Starting Stet Basic Inputs PV Underlying Asset Risk Free Rate 400 Implementation Cost 250 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period Fo
34. S X r q Sd oT AT Put X eQ ln 5 X 1 9 Z0 DT la S X e_9 2069 oT CIT In S X r q 03 2 T ENT In S X r q 0 DT Se Q o vT o VT po NT p User Manual 129 Real Options Super Lattice Solver software manual Appendix D Quick Install and Licensing Guide This section is the quick install guide for more advanced users For a more detailed installation guide please refer to the next section The SLS 2010 software requires the following minimum requirements e Windows XP or Vista and beyond Excel XP or Excel 2003 or Excel 2007 NET Framework 2 0 Administrative rights during installation only 512MB of RAM or more 30MB of free hard drive space To install the software make sure that your system has all the prerequisites Windows XP Excel XP Excel 2003 and beyond NET Framework 2 0 administrative rights 256MB of RAM or more and 30MB of free hard drive space If you require NET Framework 2 0 please browse the software installation CD and install the file named dotnetfx20 exe or if you do not have the installation CD you can download the file from www realoptionsvaluation com attachments dotnetfx20 exe You need to first install INET Framework 2 0 before proceeding with the SLS 2010 software installation Note that INET 2 0 works in parallel with NET 1 1 and you do not and should not uninstall one version in preference to the other You should have both versions running concurrently o
35. and lists the input variables with the highest impact to the lowest impact You can control the option type lattice steps and sensitivity to test The results will be returned in the form of a tornado chart J and sensitivity analysis table K Tornado analysis captures the static impacts of each input variable on the outcome of the option value by automatically perturbing each input some preset amount captures the fluctuation on the option value s result and lists the resulting perturbations ranked from the most significant to the least The results are shown as a sensitivity table with the starting base case value the perturbed input upside and downside the resulting option value s upside and downside and the absolute swing or impact The precedent variables are ranked from the highest impact to the lowest impact The tornado chart illustrates this data in graphic form Green bars in the chart indicate a positive effect while red bars indicate a negative effect on the option value For example Implementation Cost s red bar is on the right side indicating a negative effect of investment cost in other words for a simple call option implementation cost option strike price and option value are negatively correlated The opposite is true for PV Underlying Asset stock price where the green bar is on the right side of the chart indicating a positive correlation between the input and output Scenario Analysis The Scenario tab
36. by 1 D E where D E is the debt to equity ratio of the public firm That is we have 3 _ O EQUITY RO 1 2 E This approach can be used if there are market comparables such as sector indexes or industry indexes It is incorrect to state that a project s risk as measured by the volatility estimate is identical to the entire industry sector or the market There are a lot of interactions in the market such as diversification overreaction and marketability issues that a single project inside a firm is not exposed to Great care must be taken in choosing the right comparables as the major drawback of this approach is that it is sometimes hard to find the right comparable firms and the results may be subject to gross manipulation by subjectively including or excluding certain firms The benefit is its ease of use industry averages are used and requires little to no computation User Manual 119 Real Options Super Lattice Solver software manual Appendix C Technical Formulae Exotic Options Formulas Black and Scholes Option Model European Version This is the famous Nobel Prize winning Black Scholes model without any dividend payments It is the European version where an option can only be executed at expiration and not before Although it is simple enough to use care should be taken in estimating its input variable assumptions especially that of volatility which is usually difficult to estimate However the Black Scholes mode
37. exceeds the suboptimal threshold above the strike price the option will be summarily and suboptimally executed If vested but not exceeding the threshold the option will be executed only if the post vesting forfeiture occurs but the option is kept open otherwise This means that the intermediate step is a probability weighted average of these occurrences Finally when an employee forfeits the option during the vesting period all options are forfeited with a pre vesting forfeiture rate In this example we assume identical pre and post vesting forfeitures so that we can verify the results using the ESO Toolkit Figure 74 In certain other cases a different rate may be assumed Figure 73 Single Asset Super Lattice Solver File Help Comment Employee Stock Option with vesting period suboptimal exercise behavior and forfeiture rates Variable Name Value Starting Step si Suboptimal 1 8 0 i i ForfeiturePost 0 1 0 PV Underlying Asset Risk Free Rate ForfeiturePre 0 1 0 0 Implementation Cost 100 Dividend Rate DT 0 1 Maturity Years 10 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option 0 39 Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Cost 0 Black Scholes Closed Form American Binomial European Pepi Elenina n I Binomial American Intermediate Node Equation Options Before Expiration C
38. for small datasets where a higher standard deviation implies a wider distributional width and thus carries a higher risk The variation of each point around the mean is squared to capture its absolute distances otherwise for a symmetrical distribution the variations to the left of the mean might equal the variations to the right of the mean creating a zero sum and the entire result is taken to the square root to bring the value back to its original unit Finally the denominator n adjusts for a degree of freedom in small sample sizes To illustrate suppose there are three people in a room and we ask all three of them to randomly choose a number of their choice as long as the average is 100 The first person might choose any value and so could the second person However when it comes to the third person he or she can only choose a single unique value such that the average is exactly 100 Thus in a room of 3 people n only 2 people n are truly free to choose So for smaller sample sizes taking the n 1 correction makes the computations more conservative This is why we use sample standard deviations in Step 4 User Manual 107 Real Options Super Lattice Solver software manual volatility Step 5 Compute the annualized volatility The volatility used in options analysis is annualized for several reasons The first reason is that all other inputs are annualized inputs e g annualized risk free rate annualized dividen
39. for the TE Max Stock Strike 0 OptionOpen for the IE and OptionOpen for IEV example file used ESO Vesting This means the option is executed or left to expire worthless at termination execute early or keep the option open during the intermediate nodes and keep the option open only and no executions are allowed during the intermediate steps when blackouts or vesting occurs The result is 49 73 Figure 67 which can be corroborated with the use of the ESO Valuation Toolkit Figure 68 ESO Valuation Toolkit is another software tool developed by Real Options Valuation Inc specifically designed to solve ESO problems following the 2004 FAS 123 In fact this software was used by the Financial Accounting Standards Board to model the valuation example in their final FAS 123 Statement in December 2004 Before starting with ESO valuations it is suggested that the user read Dr Johnathan Mun s book Valuing Employee Stock Options Wiley 2004 as a primer Figure 67 Single Asset Super Lattice Solver File Help Comment Employee Stock Option with a vesting period Variable Name Value Starting Step PV Underlying Asset Risk Free Rate Implementation Cost Dividend Rate Maturity Years 10 Volatility 3 Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option 0 39 Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Cost 0 Black
40. have licensed the applicable Microsoft operating system product described below each an C Do Not Agree Agree Print Software Update Installation Wizard Updating Your System Ay Please wait while setup inspects your curent configuration archives i your current files and updates your files Finishing installation Details Performing cleanup n e Figure 11 Installing Microsoft Installer User Manual 136 Real Options Super Lattice Solver software manual Software Update Installation Wizard Completing the Windows Installer 3 1 KB893803 Installation Wizard You have successfully completed the KB893803v2 Setup Wizard To apply the changes the wizard has to restart Windows To restart Windows automatically click Finish If you want to restart later select the Do not restart now check box and then click Finish TT Do not restart now Figure 12 Completing the Installation of Microsoft Installer STEP 2 6 Continue with the INET Framework 2 0 installation Figure 13 You will be prompted once the installation has been successful Figure 14 Click FINISH and proceed to STEP 3 iis Microsoft NET Framework 2 0 Setup Installing components The items you selected are being installed Installation Progress Validating install Property DD_IESO1FOUND_X86 3643236F_FC70_11D3_A536_0090278A41BB8 Signature SearchForIE501_ENU_X86 3643236F_FC70_11D3_A536_0090278A1BB8 Cancel
41. of real options of actual cases It is highly recommended that the user familiarizes him or herself with the fundamental concepts of real options as outlined in Real Options Analysis Tools and Techniques 2nd Edition Wiley 2006 The Real Options SLS software s design and analytics were created by Dr Johnathan Mun and the software s programming was developed by lead developer J C Chin User Manual 3 Real Options Super Lattice Solver software manual TABLE OF CONTENTS SECTION I GETTING STARTED sscesccussscestespacessenascssessssectssoupicseoutpscesteponssesenescctensssuavseseacoeed 6 Introduction to the Super Lattice Software SLS iii 7 Single Asset Super Lattice Solver nica lana piana 10 Multiple Asset Super Lattice Solver MSLS iiii 17 Multinomial Lattice Solver i casciana hehe esc nad ats ened eg tas ahaa lana ara 19 SESE OMI eM AKO oi sli ALE a a De AR ERGs a SoMa eR ees 21 SLS Excel Solution SLS MSLS and Changing Volatility Models in Excel 22 SES EUNCHONS RR REI RIE n la 26 Exotic Financial Options Valuator iii 28 Payoff Charts Tornado Convergence Scenario and Sensitivity Analysis iii 29 Key SLS Notes Gn Tips lato edile illa i alan ala 31 SECTION II REAL OPTIONS ANALYSIS oerrtrrrrrrrrerererererererenere ren ee eee se senese ceca seceeenecenee 34 American European Bermudan and Customized Abandonment Options ii 35 America
42. result reverts to 550 the static expand now scenario indicating that the option is worthless Figure 31 This result means if the cost of waiting as a proportion of the asset value as measured by the dividend rate is too high then execute now and stop wasting time deferring the expansion decision Of course this decision can be reversed if the volatility is significant enough to compensate for the cost of waiting That is it might be worth something to wait and see if the uncertainty is too high even if the cost to wait is high Other applications of this option simply abound To illustrate here are some additional quick examples of the contraction option as before providing some additional sample exercises e Suppose a pharmaceutical firm is thinking of developing a new type of insulin that can be inhaled and the drug will directly be absorbed into the blood stream A novel and honorable idea Imagine what this means to diabetics who no longer need painful and frequent injections The problem is this new type of insulin requires a brand new development effort but if the uncertainties of the market competition drug development and FDA approval are high perhaps a base insulin drug that can be ingested is first developed The ingestible version is a required precursor to the inhaled version The pharmaceutical firm can decide to either take the risk and fast track development into the inhaled version or buy an option to defer to first
43. returns The standard deviation of these natural logarithm returns is the periodic volatility of the cash flow series The resulting periodic volatility from the sample dataset in Figure B1 is 25 58 This value will then have to be annualized User Manual 103 Real Options Super Lattice Solver software manual No matter what the approach used the periodic volatility estimate used in a real options or financial options analysis has to be an annualized volatility Depending on the periodicity of the raw cash flow or stock price data used the volatility calculated should be converted into annualized values using ovP where P is the number of periods in a year and o is the periodic volatility For instance if the calculated volatility using monthly cash flow data is 10 the annualized volatility is 10 V12 35 Similarly P is 365 or about 250 if accounting for trading days and not calendar days for daily data 4 for quarterly data 2 for semiannual data and 1 for annual data Notice that the number of returns in Figure B1 is one less than the total number of periods That is for time periods 0 to 5 we have six cash flows but only five cash flow relative returns This approach is valid and correct when estimating the volatilities of liquid and highly traded assets historical stock prices historical prices of oil and electricity and is less valid for computing volatilities in a real options world where the underlying asset generates cash flow
44. riskless asset 5 year U S Treasury Note with zero coupons for the next 5 years is found to be 7 Further suppose that the firm has the option to expand and double its operations by acquiring its competitor for a sum of 250 million Implementation Cost at any time over the next 5 years Maturity What is the total value of this firm assuming that you account for this expansion option The results in Figure 29 indicate that the strategic project value is 638 73 M using a 10 step lattice which means that the expansion option value is 88 73M This result is obtained because the net present value of executing immediately is 400M x 2 250M or 550M Thus 638 73 M less 550M is 88 73M the value of the ability to defer and to wait and see before executing the expansion option The example file used is Expansion American and European Option Increase the dividend rate to say 2 and notice that both the American and European Expansion Options are now worth less and that the American Expansion Option is worth more than the European Expansion Option by virtue of the American Option s ability for early execution Figure 30 The dividend rate implies that the cost of waiting to expand to defer and not execute the opportunity cost of waiting on executing the option and the cost of holding the option is high then the ability to defer reduces In addition increase the Dividend Rate to 4 9 and see that the binomial lattice s Custom Option
45. the American Barrier Option solved using the SLS To change these into a European Barrier Option set the Intermediate Node Equation Nodes to OptionOpen In addition for certain types of contractual options vesting and blackout periods can be imposed For solving such Bermudan Barrier Options keep the same Intermediate Node Equation as the American Barrier Options but set the Intermediate Node Equation During Blackout and Vesting Periods to OptionOpen and insert the corresponding blackout and vesting period lattice steps Finally if the Barrier is a changing target over time put in several custom variables named Barrier with the different values and starting lattice steps Exotic Barrier Options exist when other options are combined with barriers For instance an option to expand can only be executed if the PV Asset exceeds some threshold or a contraction option to outsource manufacturing can only be executed when it falls below some breakeven point Again such options can be easily modeled using the SLS User Manual 91 Real Options Super Lattice Solver software manual Figure 66 Single Asset Super Lattice Solver File Help Comment Double Barier Up amp In Down amp In Call This option is live only when the asset value breaches either bamer Option Type lt lt Custom Variables T_____ American European Bermudan Custom innamora LowerBarrier 90 UpperBarrier 110 0 Basic Inputs
46. the projected future cash flows to be 30 The risk free rate on a riskless asset 5 year U S Treasury Note with zero coupons is found to be yielding 5 Further suppose the firm has the option to contract 10 of its current operations at any time over the next 5 years thereby creating an additional 50 million in savings after this contraction These terms are arranged through a legal contractual agreement with one of its vendors who had agreed to take up the excess capacity and space of the firm At the same time the firm can scale back and lay off part of its existing workforce to obtain this level of savings in present values The results indicate that the strategic value of the project is 1 001 71M using a 10 step lattice as seen in Figure 25 which means that the NPV currently is 1 000M and the additional 1 71M comes from this contraction option This result is obtained because contracting now yields 90 of 1 000M 50M or 950M which is less than staying in business and not contracting and obtaining 1 000M Therefore the optimal decision is to not contract immediately but keep the ability to do so open for the future Hence in comparing this optimal decision of 1 000M to 1 001 71M of being able to contract the option to contract is worth 1 71M This should be the maximum amount the firm is willing to spend to obtain this option contractual fees and payments to the vendor counterparty In contrast if Savings were 200M inste
47. to implement the rig in the first place and it actually obtains some cash up front for this contract to assume the downside risk The oil company is also in agreement because it reduces its own risks if oil prices are low and production is not up to par and it ends up saving over 75M in present value of total overhead expenses which can then be reallocated and invested somewhere else Jn this example the contraction option using a 100 step lattice is valued to be 14 24M using SLS This means that the maximum amount that the counterparty should be paid should not exceed this amount Of course the option analysis can be further complicated by analyzing the actual savings on a present value basis For instance if the option is exercised within the first 5 years the savings is 75M but if exercised during the last 5 years then the savings is only 50M The revised option value is now 10 57M e A manufacturing firm is interested in outsourcing its manufacturing of children s toys to a small province in China By doing so it will produce overhead savings of over 20M in present value over the economic life of the toys However outsourcing this internationally will mean lower quality control delayed shipping problems added importing costs and assuming the added risks of unfamiliarity with the local business practices In addition the firm will only consider outsourcing only if the quality of the workmanship in this Chinese firm is up to the st
48. 0 Single Asset Super Lattice Solver File Help Comment American Option to Expand To change to European deselect Custom and select European Option Type TTT Custom Variables lt lt American European Bean Custom Variable Name Value Starting Step Expansion 200 Basic Inputs _______________________ suonati Asset 400 Risk FreeRate 7 Implementation Cost 1250 DividendRate J Maturity Years 5 Volatity 5 Lattice Steps 40 Allinputsare annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Call Put Max Asset Asset Expansion Cost Black Scholes 204 01 Closed Form American 205 19 Binomial European 204 02 Example Max Asset Cost 0 Binomial American 205 67 Custom Equations Result ntemediate Node Equation Options Before Expiration American Option 578 9030 Max Asset Expansion Cost OptionOpen European Option 565 8139 Benchmark Example Max Asset Cost OptionOpen intermediate Node Equation During Blackout and Vesting Period Create Audit Sheet Run Example OptionOpen Figure 30 American and European Options to Expand with a Dividend Rate User Manual 52 Real Options Super Lattice Solver software manual Figure 31 Single Asset Super Lattice Solver File Help Comment American Option to E
49. 00 120 00 120 00 120 00 __ 12000 120 00 100 56 100 56 100 56 100 56 84 26 84 26 84 26 84 26 ci i o M o A o 59 17 5917 __ 5917 __ 5917 4958 4958 455 __ 455 455 3462 __ 3482 2917 2917 Option Valuation Lattice 589 03 493 59 49359 413 61 41361 34659 34659 346 59 2904 290 43 243 43 243 37 24337 24337 204 30 204 06 20394 203 94 172 07 171 61 17145 17088 17089 14601 145 36 4461 4377 143 20 125 48 124 77 123 88 12277 12122 120 00 108 49 107 41 105 93 103 20 97 95 97 13 96 03 94 57 91 44 goss 9013 90 00 90 00 90 00 90 00 90 00 90 00 90 00 90 00 9000 Figure 20 Audit Sheet for the Abandonment Option User Manual 38 Real Options Super Lattice Solver software manual Figure 21 shows the same abandonment option but with a 100 step lattice To follow along open the Single Asset SLS example file Abandonment American Option Notice that the 10 step lattice yields 125 48 while the 100 step lattice yields 125 45 indicating that the lattice results have achieved convergence The Terminal Node Equation is Max Asset Salvage which means the decision at maturity is to decide if the option should be executed selling the asset and receiving the salvage value or not to execute holding on to the asset The Intermediate Node Equation
50. 077 632 980 1519 43 Continue Continue Continue Continue Continue __ Continue Execute 44 oof oc oof oc oc ooo 45 _ Continue Continue Continue Continue Continue Ena 46 oof ooo oc oo 47 _Continue Continue Continue Continue End 48 000 49 50 51 52 53 54 55 Figure 12 Lattice Maker Module and Worksheet Results with Visible Equations User Manual 21 Real Options Super Lattice Solver software manual SLS Excel Solution SLS MSLS and Changing Volatility Models in Excel The SLS software also allows you to create your own models in Excel using customized functions This is an important functionality because certain models may require linking from other spreadsheets or databases run certain Excel macros and functions or certain inputs need to be simulated or inputs may change over the course of modeling your options This Excel compatibility allows you the flexibility to innovate within the Excel spreadsheet environment Specifically the sample worksheet solves the SLS MSLS and Changing Volatility model To illustrate Figure 13 shows a Customized Abandonment Option solved using SLS from the Single Asset Module click on File Examples Abandonment Customized Option The same problem can be solved using the SLS Excel Solution by clicking on Start Programs Real Options Valuation Real Options SLS Excel Solution The sample solution is seen in Figure 14 Notice that the results are the same using the S
51. 100 Step Lattice 12 313 Binomial 1 000 Step Lattice 12 336 Figure Al Convergence of the Binomial Lattice Results to Closed Form Solutions 4 This proprietary algorithm was developed by Dr Johnathan Mun based on his analytical work with FASB in 2003 2004 his books Valuing Employee Stock Options Under the 2004 FAS 123 Requirements Wiley 2004 Real Options Analysis Tools and Techniques Wiley 2002 Real Options Analysis Course Wiley 2003 Applied Risk Analysis Moving Beyond Uncertainty Wiley 2003 creation of his software Real Options Analysis Toolkit versions 1 0 and 2 0 academic research and previous valuation consulting experience at KPMG Consulting A nonrecombining binomial lattice bifurcates splits into two every step it takes so starting from one value it branches out to two values on the first step 2 two becomes four in the second step 2 and four becomes eight in the third step 2 and so forth until the 1 000th step 2 or over 105 values to calculate and the world s fastest supercomputer won t be able to calculate the result within our lifetimes User Manual 102 Real Options Super Lattice Solver software manual Appendix B Volatility Estimates There are several ways to estimate the volatility used in the option models The most common and valid approaches are e Logarithmic Cash Flow Returns Approach or Logarithmic Stock Price Returns Approach Used mainl
52. 17 78930 0 0000 D MSFT 1 0 456040 0 062391 7 309364 0 0000 AR 1 0 967490 0 027575 35 08601 0 0000 Variance Equation C 0 151406 0 028717 5 272435 0 0000 ARCH 1 0 148308 0 053559 2 769061 0 0056 GARCH 1 0 735869 0 097780 7 525790 0 0000 GARCH 2 0 867066 0 083186 10 42325 0 0000 R squared 0 898576 Mean dependent var 24 48620 Adjusted R squared 0 884424 S D dependent var 1 290867 S E of regression 0 436649 Akaike info criterion 1 106641 Sum squared resid 6 281300 Schwarz criterion 1 374324 Log likelihood 20 66602 F statistic 63 49404 Durbin Watson stat 1 308287 Prob F statistic 0 000000 Inverted AR Roots 97 Figure B5 Sample GARCH Results Management Assumption Approach A simpler approach is the use of Management Assumptions This approach allows management to get a rough volatility estimate without performing more protracted analysis This approach is also great for educating management what volatility is and how it works Mathematically and statistically the width or risk of a variable can be measured through several different statistics including the range standard deviation 0 variance coefficient of variation and percentiles Figure B6 illustrates two different stocks historical prices The stock depicted as a dark bold line is clearly less volatile than the stock with the dotted line The time series data from these two stocks can be redrawn as a probability distribution as seen in Figure B7 Although the expected v
53. 2003 2004 2005 2006 Revenue 100 00 200 00 300 00 400 00 500 00 Cost of Revenue 40 00 80 00 120 00 160 00 200 00 Gross Profit 60 00 120 00 180 00 240 00 300 00 Operating Expenses Depreciation Expense Interest Expense 22 00 66 00 88 00 110 00 5 00 5 00 5 00 5 00 5 00 3 00 3 00 3 00 3 00 3 00 sellele Income Before Taxes 30 00 68 00 106 00 144 00 182 00 Taxes 3 00 6 80 10 60 14 40 18 20 Income After Taxes 27 00 61 20 95 40 129 60 163 80 42 Non Cash Expenses 46 Cash Flow 39 00 73 20 107 40 141 60 175 80 47 48 Implementation Cost 49 50 Volatility Estimates Logarithmic PV Approach 51 PV 0 39 00 63 65 81 21 93 10 100 51 52 PV 1 N A 73 20 93 39 107 07 115 59 53 Static PV 0 39 00 63 65 81 21 93 10 100 51 54 Variable X 0 0307 55 Volatility Simulate Figure B4 Log Present Value Approach Now that you understand the mechanics of computing volatilities this way we need to explain why we did what we did Merely understanding the mechanics is insufficient in justifying the approach or explaining the rationale why we analyzed it the way we did Hence let us look at the steps undertaken and explain the rationale behind them Step 1 Compute the present values at times 0 and 1 and sum them The theoretical price of a stock is the sum of the present values of all future dividends for non dividend paying stocks we use market replic
54. 9 78 Figure 52 shows another example using the Multinomial Option The computed American Call is 31 99 using a 5 step trinomial and is identical to a 10 step binomial lattice seen in Figure 53 Therefore due to the simpler computation and the speed of computation the SLS and MSLS use binomial lattices instead of trinomials or other multinomial lattices The only time a trinomial lattice is truly useful is when the underlying asset of the option follows a mean reversion tendency In that case use the MNLS module instead When using this MNLS module just like in the single asset lattices you can modify and add in your own customized equations and variables and the concepts are identical to that of the SLS examples throughout this user manual User Manual 75 Real Options Super Lattice Solver software manual Figure 52 Multinomial Lattice Solver File Help Comment American Call Option using a Trinomial Lattice Model Lattice Type Trinomial E Trinomial Mean Reverting E Quadranomial Jump Diffusion E Pentanomial Rainbow Two Asset Basic Inputs _ _ _ _ _ Custom Variables PV Underlying Asset 100 Dividend Rate z 88 0 PV Underlying Asset 2 avs Long Term Rate Implementation Cost 100 Reversion Rate Volatility 2 Market Price of Risk Volatility 2 Jump Rate Risk Free Rate Jump Intensity Maturity Years Correlation Lattice St All inputs are annualized rates
55. ADR Installed On 2 2 2006 Ga Office 2003 Service Pack 2 SP2 MAINSPZop Installed On 2 2 2006 Ga Microsoft Office Professional Plus 2007 Beta Size 616 00MB Ga Microsoft Office Project Professional 2003 Size 166 00MB l el Figure 1 Microsoft NET Framework 2 0 listing on the Add Remove Programs in Control Panel User Manual 131 Real Options Super Lattice Solver software manual STEP TWO Installing NET Framework 2 0 Step 2 1 If you do not have NET Framework 2 0 installed insert the installation CD and install the dotnetfx20 exe file If you do not have the CD simple download the file by going to www realoptionsvaluation com downloads scroll down to the SLS 20 0 Software download sections and click on Microsoft Net Framework 2 0 Figure 2 Click on SAVE to start the download and installation Q sak Q e a A JO Search sly Favorites B S 9 nd m E citi ga 33 Address http www realoptionsvaluation com downloads Y7 E Search Web New lt 7 Er l C My Web J Messenger f Bookmarks My yahoo _ Downloading Information Add Ta SOFTWARE DOWNLOAD REAL OPTIONS SLS 2 0 WITH SUPER SPEED Please check back regularly for this upgrade Expected release date is August 15 2006 Beta version is currently available Please contact us for details System requirements FAQ and additional resources Windows XP Excel XP or 2003 256 MB RAM 30 MB Hard Drive administrative rights and NET
56. American 359 52 Custom Equations e e ee Resu Intermediate Node Equation Options Before Expiration Custom Option 1005 1970 Max Asset Contraction Savings OptionOpen Benchmark Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Figure 28 A Customized Option to Contract with Changing Savings User Manual 48 Real Options Super Lattice Solver software manual American European Bermudan and Customized Expansion Options The Expansion Option values the flexibility to expand from a current existing state to a larger or expanded state Therefore an existing state or condition must first be present in order to use the expansion option That is there must be a base case to expand upon If there is no base case state then the simple Execution Option calculated using the simple Call Option is more appropriate where the issue at hand is whether or not to execute a project immediately or to defer execution As an example suppose a growth firm has a static valuation of future profitability using a discounted cash flow model in other words the present value of the expected future cash flows discounted at an appropriate market risk adjusted discount rate that is found to be 400 million PV Asset Using Monte Carlo simulation you calculate the implied Volatility of the logarithmic returns on the assets based on the projected future cash flows to be 35 The Risk Free Rate on a
57. Blackout and Vesting Period Figure 62 Down and In Lower American Barrier Option User Manual 86 Real Options Super Lattice Solver software manual Figure 63 Single Asset Super Lattice Solver File Help Option Type American European C Bermudan Basic Inputs PV Underlying Asset 100 Risk Free Rate 80 Dividend Rate 5 Volatility 4 100 All inputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration If Asset gt Bamier Max Asset Cost 0 0 Example Max Asset Cost 0 Custom Equations Intermediate Node Equation Options Before Expiration I Asset gt Bamier Max Asset Cost OptionOpen OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Custom Vaiabes _ _ Variable Name Value Starting Step Barrier 90 Benchmark Figure 63 Down and Out Lower American Barrier Option User Manual 87 Real Options Super Lattice Solver software manual American and European Upper Barrier Options The Upper Barrier Option measures the strategic value of an option this applies to both calls and puts that comes either in the money or out of the money when the Asset Value hits an artificial Upper Barrier that is currently higher than the asset value Therefore
58. LS versus the SLS Excel Solution file You can use the template provided by simply clicking on File Save As in Excel and use the new file for your own modeling needs Figure 13 Single Asset Super Lattice Solver File Help Comment Bermudan Abandonment Option with changing salvage values over time v7 n Variable Name Value Starting Step Salvage 90 0 Salvage 95 21 PV Underlying Asset Risk Free Rate due Implementation Cost 90 Dividend Rate Salvage 105 61 Salvage 110 81 Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option 0 10 Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Salvage Black Scholes Closed Form American Binomial European Example Max Asset Cost 0 Binomial American Intermediate Node Equation Options Before Expiration Gian Option 130 3154 Max Salvage OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period OptionOpen Example OptionOpen Figure 13 Customized Abandonment Option using SLS User Manual 22 Real Options Super Lattice Solver software manual A B C D E E 1 2 SUPER LATTICE SOLVER SINGLE ASSET 3 4 Option Type Custom Variables List 5 Pl Underlying Asset 120 00 Variable Name Value Starting Steps 6 Annualized Volatility 25 00 7 Maturity Years 8 implementatio
59. NPV of the project This breakeven point provides valuable insights for the decision maker into the interactions between the levels of uncertainty inherent in the project and the cost of waiting to execute The same analysis can be extended to Multiple Investment Simultaneous Compound Options as seen in Figure 51 example file used Multiple Phased Simultaneous Compound Option Figure 50 Multiple Asset Super Lattice Solver File Help Comment Simultaneous Compound Option for Two Phases Pv Asset Volatility Notes Value Starting Step 1000 25 Blackout and Vesting Period Steps Name Cost Risk Free Div Steps Terminal Equation Intermediate Equation Blacko PhaseA 500 5 0 100 Max Underlying Cost 0 Max Underlying Cost OptionOpen PHASEB 483 2670 PhaseB 200 5 0 100 Max PhaseA Cost 0 Max PhaseA Cost OptionOpen Figure 50 Solving a Simultaneous Compound Option using MSLS User Manual 73 Real Options Super Lattice Solver software manual BO rave 51 Mii aeset Super some File Help Maturity 5 Comment Simultaneous Compound Option for Multiple Phases Underyina Assets AA AOo amp a lt _ A AA Custom Variables Name PV Asset Volatility Notes Name Value Starting Step Underlying 0000 Option Valuations Cost Risk Free Div Steps Terminal Equation Intermediate Equation PhaseG 100 5 0 100 MafPhaseFCost0 MaxfPhaseF Cost Optionope Figure 51
60. Options Super Lattice Solver software manual results also increase which makes logical sense You can also model in blackout vesting periods for the first 6 months steps 0 10 in the blackout area The blackout period is very typical of contractual obligations of abandonment options where during specified periods the option cannot be executed a cooling off period Note that you may use TAB on the keyboard to move from the variable name column to the value column and on to the starting step column However remember to hit ENTER on the keyboard to insert the variable and to create a new row so that you may enter a new variable Figure 24 Single Asset Super Lattice Solver File Help Comment Bermudan Abandonment Option with changing salvage values over time O ption Type Custom Variables _ _ _ eee ts Tele masi Variable Name Value Starting Step Salvage Basic Inputs PV Underlying Asset 120 Risk Free Rate Implementation Cost 90 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 All inputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option 0 10 Example 1 2 10 20 35 Tesi ik peo a of Cindi Benchmark Max Asset Salvage Black Scholes Closed Form American Binomial European Example Max Asset Cost 0 Binomial American Custom Equations ee Result Intermediate Node Equation Options Before Expiration Custom Option 130 3154 M
61. PLE ASSET amp MULTIPLE PHASES Maturity Years MSLS Result 134 0802 Blackout Steps Correlation nei Underlying Asset Lattices Custom Variables Starting Steps Lattice Name PV Asset Volatility Value 100 00 90 00 80 00 Name Salvage Salvage Salvage Savage T0000 Savage 9 Contract I Expansion SO Savings 0 rr Option Valuation Lattices Terminal Equation Intermediate Equation Intermediate Equation for Blackout Max Underlying Expansion Cost Underlying Salvage _ Max Underlying Expansion Cost Salvage Max Phase3 Phase3 Contract Savings Salvage 0 Max Phase3 Contract Savings Salvage Max Phase2 Salvage 0 Max Salvage Lattice Name C ost 50 00 Note This is the Excel version of the Multiple Super Lattice Solver useful when running simulations or when linking to and from other spreadsheets Use this sample spreadsheet for your models You can simply click on File Save As to save as a different file and start using the model Because this is an Excel solution the correlation function is not supported and is linked to an empty cell Figure 15 Complex Sequential Compound Option using SLS Excel Solver Changing Volatility and Risk Free Rates Assumptions Results PV Asset Generalized Black Scholes Implementation Cost 10 Step Super Lattice 49 15 Maturity in Years 10 00 Super Lattice Steps 10Steps v Vesting in Years Dividend Rate A
62. Period Steps Cost Risk Free Dividend Steps Terminal Equation Figure 8 Multiple Super Lattice Solver User Manual 17 Real Options Super Lattice Solver software manual To illustrate the power of the MSLS a simple illustration is in order Click on Start Programs Real Options Valuation Real Options SLS Real Options SLS In the Main Screen click on New Multiple Asset Option Model and then select File Examples Simple Two Phased Sequential Compound Option Figure 9 shows the MSLS example loaded In this simple example a single underlying asset is created with two valuation phases Figure 9 Multiple Asset Super Lattice Solver File Help Maturity Comment Simple Two Phased Sequential Compound Option Name Underlying PV Asset Volatility 9 Notes 100 30 Value Starting Step Blackout and Vesting Period Steps Name Phase2 80 5 Phasel 5 5 Cost Risk Free Dividend Steps Terminal Equation Intermediate Equation 0 100 Max Underlying Cost 0 Max Underlying Cost OptionOpen 0 50 Max Phase2 Cost 0 Max Phase2 Cost OptionOpen PHASE1 27 6734 E Create Audit Sheet Figure 9 MSLS Solution to a Simple Two Phased Sequential Compound Option The strategy tree for this option is seen in Figure 10 The project is executed in two phases the first phase within the first year costs 5 million while the second phase within two yea
63. REAL OPTIONS SUPER LATTICE SOLVER USER MANUAL L Dr Johnathan Mun Ph D MBA MS BS CFC CRM FRM MIFC Real Options SLS 2010 This manual and the software described in it are furnished under license and may only be used or copied in accordance with the terms of the end user license agreement Information in this document is provided for informational purposes only is subject to change without notice and does not represent a commitment as to merchantability or fitness for a particular purpose by Real Options Valuation Inc No part of this manual may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying and recording for any purpose without the express written permission of Real Options Valuation Inc Materials based on copyrighted publications by Dr Johnathan Mun Written designed and published in the United States of America To purchase additional copies of this document contact Real Options Valuation Inc at the address below Admin RealOptions Valuation com 2006 2010 by Dr Johnathan Mun All rights reserved Real Options Valuation Inc and Real Options SLS are registered trademarks of the company Microsoft is a registered trademark of Microsoft Corporation in the U S and other countries Other product names mentioned herein may be trademarks and or registered trademarks of the respective holders PREFACE Welcome to the Real Options S
64. SLS in Figure 40 The sample results of this calculation indicate the strategic value of the project s NPV and provide an option to sell the project within the specified Maturity in years There is a chance that the project value can significantly exceed the single point estimate of PV Asset Value measured by the present value of all uncertain future cash flows discounted at the risk adjusted rate of return or be significantly below it Hence the option to defer and wait until some of the uncertainty becomes resolved through the passage of time is worth more than executing immediately The value of being able to wait before executing the option and selling the project at the Implementation Cost in present values is the value of the option The NPV of executing immediately is simply the Implementation Cost less the Asset Value 0 The option value of being able to wait and defer selling the asset only if the condition goes bad and becomes optimal for selling is the difference between the calculated result total strategic value and the NPV or 24 42 for the American Option and 20 68 for the European Option The American put option is worth more than the European put option even when no dividends exist contrary to the call options seen previously For simple call options when no dividends exist it is never optimal to exercise early However it may sometimes be optimal to exercise early for put options regardless of whether dividend yields exist In
65. Scholes Closed Form American Binomial European E ee eee Binomial American intemediate Node Equation Options Before Expiretion Custom Option 49 7310 Max Asset Cost 0 OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period OptionOpen Example OptionOpen Figure 67 SLS Results of a Vesting Call Option User Manual 94 Real Options Super Lattice Solver software manual merican on with Vesting Requirements Assumptions Intermediate Calculations Stock Price 3 Stepping Time di Strike Price Up Step Size up Maturity in Years Down Step Size down Risk Free Rate Risk Neutral Probability prob Dividends Volatility 26 a Vesting in Years 400 10 Step Lattice Results Generalized Black Scholes Ce American Ciosed Form Approx 100 Step Binomial Super Lattice Main Menu Binomial Super Lattice Steps Trw_ 10 Step Trinomiai Super Lattice 44 95 alyze 5 A Trinomial Super Lattice Steps 10Steps v 14841 32 9001 71 545982 ______ 5459 82 200855 200855 200855 Underlying Stock Price Lattice mn an rn 738897 ooe M M ___ str mms as ans ans a 16487 16487 16487 16487 16487 coo oo oo oo 000 1000 6065 6065 6066 6065 6065 3679 3679 3679 3679 3679
66. Start Value 100 200 Step 3 Compute natural logarithm of the relative returns The natural log is used for two reasons The first is to be comparable to the exponential Brownian Motion stochastic process That is recall that a Brownian Motion is written as os z ol Morta S To compute the volatility 0 used in an equivalent computation regardless of whether it is used in simulation lattices or closed form models because these three approaches require the Brownian Motion as a fundamental assumption a natural log is used The exponential of a natural log cancels each other out in the above equation Second in computing the geometric average relative returns were used then multiplied and taken to the root of the number of periods By taking a natural log of a root n we reduce the root n in the geometric average equation This is why natural logs are used in Step 3 Step 4 Compute the sample standard deviation to obtain the periodic volatility A sample standard deviation is used instead of a population standard deviation because your dataset might be small For larger datasets the sample standard deviation converges to the population standard deviation so it is always safer to use the sample standard deviation Of course the sample standard deviation seen below is simply the average sum of all and then divided by some variation of n of the deviations of each point of a dataset from its mean x x adjusted for a degree of freedom
67. Super Lattice Solver MSLS The MSLS is an extension of the SLS in that the MSLS can be used to solve options with multiple underlying assets and multiple phases The MSLS allows the user to enter multiple underlying assets as well as multiple valuation lattices These valuation lattices can call to user defined custom variables Some examples of the types of options that the MSLS can be used to solve include Sequential Compound Options two three and multiple phased sequential options Simultaneous Compound Options multiple assets with multiple simultaneous options Chooser and Switching Options choosing among several options and underlying assets Floating Options choosing between calls and puts Multiple Asset Options 3D binomial option models The MSLS software has several areas including a Maturity and Comment area The Maturity value is a global value for the entire option regardless of how many underlying or valuation lattices exist The Comment field is for your personal notes describing the model you are building There is also a Blackout and Vesting Period Steps section and a Custom Variables list similar to the SLS The MSLS also allows you to create Audit Worksheets Notice too that the user interface is resizable e g you can click and drag the right side of the form to make it wider Multiple Asset Super Lattice Solver File Help Maturity PV Asset Volatility Notes Value Starting Step Blackout and Vesting
68. T policies may require you to first contact a systems administrator or IT professional before any software can be installed Step 1 4 Verify that you have Microsoft NET 2 0 installed To verify this click on Start Control Panel Add or Remove Programs Scroll down the list of installed programs and look for Microsoft Net Framework 2 0 and see if it exists Figure 1 If you do not see it listed or if you only see version 1 1 listed proceed to STEP TWO to install NET Framework 2 0 Otherwise if you already have it installed proceed to STEP THREE and start installing Real Options SLS Note that versions 1 1 and 2 0 are not interchangeable and both versions should and can be installed together on the same machine E Add or Remove Programs _ Currently installed programs and updates Show updates Change or Remove A Microsoft NET Framework 1 1 Programs gt iB Microsoft NET Framework 1 1 Hotfix KB886903 Di i Microsoft NET Framework 2 0 _ Clic re for support information Add New Programs To change this program or remove it from your computer click Change Remove Microsoft ActiveSync 3 8 Add Remove Windows Q Microsoft IntelliPoint 5 3 Size Components Ga Microsoft Office FrontPage 2003 Size 372 00MB Ga Microsoft Office Professional Edition 2003 Size 692 00MB Set Program Ga Update for Outlook 2003 Junk E mail Filter KB905648 OUTLFLTR Installed On 2 2 2006 pa Ca Update for Office 2003 KB907417 OTKLO
69. Then the values are summed and the following logarithmic ratio is calculated gt PVCF X In where PVCF is the present value of future cash flows at different time periods i This approach is more appropriate for use in real options where actual assets and projects cash flows are computed and their corresponding volatility is estimated This is applicable for project and asset cash flows and can accommodate less data points However this approach requires the use of Monte Carlo simulation to obtain a volatility estimate This approach reduces the measurement risks of autocorrelated cash flows and negative cash flows User Manual 108 Real Options Super Lattice Solver software manual Time Period Cash Flows Present Value at Time 0 Present Value at Time 1 Li 100 00 0 100 1 0 1 S125 113 64 125 125 00 1 125 1 0 1 1 0 1 395 _ 78 51 95 _ _ 86 36 2 95 1 0 1 1 0 1 105 78 89 105 86 78 3 105 1 0 1 1 0 1 8155 _ 105 87 SARE 4 155 1 0 1 1 0 1 146 L 590 65 146 _ _ 999 79 5 146 1 0 1 1 0 1 SUM 567 56 514 31 Figure B3 Log PV Approach In the example above X is simply n 514 31 567 56 0 0985 Using this intermediate X value perform a Monte Carlo simulation on the discounted cash flow model thereby simulating the individual cash flows and obtain the resulting forecast distribution of X As seen previously the sampl
70. Thus how much is this safety net or insurance policy worth One can create competitive advantage in negotiation if the counterparty does not have the answer and you do Further assume that the 5 year Treasury Note Risk Free Rate zero coupon is 5 from the U S Department of Treasury The American Abandonment Option results in Figure 19 show a value of 125 48M indicating that the option value is 5 48M as the present value of the asset is 120M Hence the maximum value one should be willing to pay for the contract on average is 5 48M This resulting expected value weights the continuous probabilities that the asset value exceeds 90M versus when it does not where the abandonment option is valuable Also it weights when the timing of executing the abandonment is optimal such that the expected value is 5 48M In addition some experimentation can be conducted Changing the salvage value to 30M this means a 90M discount from the starting asset value yields a result of 120M or 0M for the option This result means that the option or contract is worthless because the safety net is set so low that it will never be utilized Conversely setting the salvage level to thrice the prevailing asset value or 360M would yield a result of 360M and the results indicate 360M which means that there is no option value there is no value in waiting and having this option or simply execute the option immediately and sell the asset if someone is willing to
71. Using the same parameters in Figure 62 and changing the volatility and risk free rates the following examples illustrate what happens e Ata volatility of 75 the option value is 4 34 e Ata volatility of 25 the option value is 3 14 e Ata volatility of 5 the option value is 0 01 The lower the volatility the lower the probability that the asset value will fluctuate enough to breach the lower barrier such that the option will be executed By balancing volatility with the threshold lower barrier you can create optimal trigger values for barriers In contrast the Lower Barrier Option for Down and Out Call option is shown in Figure 63 Here if the asset value breaches this lower barrier the option is worthless but is only valuable when it does not breach this lower barrier As call options have higher values when the asset value is high and lower value when the asset is low this Lower Barrier Down and Out Call Option is hence worth almost the same as the regular American option The higher the barrier the lower the value of the lower barrier option will be example file Barrier Option Down and Out Lower Barrier Call For instance e Ata lower barrier of 90 the option value is 42 19 e Ata lower barrier of 100 the option value is 41 58 Figures 62 and 63 illustrate American Barrier Options To change these into European Barrier Options set the Intermediate Node Equation Nodes to OptionOpen In addition for certain types of cont
72. V Underlying Asset or starting stock price is 100 and the Implementation Cost or strike price is 100 with a 5 year maturity The annualized risk free rate of return is 5 and the historical comparable or future expected annualized volatility is 10 Click on RUN or Alt R and a 100 step binomial lattice is computed with the results indicating a value of 23 3975 for both the European and American call options Benchmark values using Black Scholes and partial differential Closed Form American approximation models as well as standard plain vanilla Binomial American and Binomial European Call and Put Options with 1 000 step binomial lattices are also computed Notice that only the American and European Options are selected and the computed results are for these simple plain vanilla American and European Call Options Plain Vanilla Call Option I Single Asset Super Lattice Solver File Help Comment Plain Vanila American and European Call Options lower number of steps Useful for testing convergence Z Ameri 7 E F B j Variable Name Value Starting Step PV Underlying Asset Risk Free Rate Implementation Cost Dividend Rate Maturity Years Volatility Lattice Steps A inputs are annualized rates Terminal Node Equation Options at Expiration Figure 2 SLS Results of a Simple European and American Call Option User Manual 11 Real Options Super Lattice Solver software manu
73. ad then the strategic project value becomes 1 100M which means that starting at 1 000M and contracting 10 to 900M and keeping the 200 in savings yields 1 100M in total value Hence the additional option value is 0M which means that it is optimal to execute the contraction option immediately as there is no option value and no value to wait to contract So the value of executing now is 1 100M as compared to the strategic project value of 1 100M there is no additional option value and the contraction should be executed immediately That is instead of asking the vendor to wait the firm is better off executing the contraction option now and capturing the savings Other applications include shelving an R amp D project by spending a little to keep it going but reserving the right to come back to it should conditions improve the value of synergy in a merger and acquisition where some management personnel are let go to create the additional savings reducing the scope and size of a production facility reducing production rates a joint venture or alliance and so forth To illustrate here are some additional quick examples of the contraction option as before providing some additional sample exercises for the rest of us e A large oil and gas company is embarking on a deep sea drilling platform that will cost the company billions to implement A DCF analysis is run and the NPV is found to be 500M over the next 10 years of economic life of the
74. af pole In S X b 0 2 T Se NT ste a oyT Real Options Super Lattice Solver software manual Options on Futures The underlying security is a forward or futures contract with initial price F Here the value of F is the forward or futures contract s initial price replacing S with F as well as calculating its present value Definitions of Variables implementation cost futures single point cash flows risk free rate time to expiration years volatility cumulative standard normal distribution continuous dividend payout Lagann Computation Cali Fer of E PAC errant VERA oVT oVT Bas of rt pos of meee ovT ovT User Manual 128 Real Options Super Lattice Solver software manual Two Correlated Assets Option The payoff on an option depends on whether the other correlated option is in the money This is the continuous counterpart to a correlated quadranomial model Definitions of Variables S present value of future cash flows X implementation cost r risk free rate T time to expiration years O volatility Q cumulative bivariate normal distribution function p correlation between the two assets qi continuous dividend payout for the first asset q2 continuous dividend payout for the second asset Computation In S X r q 03 2 T Lasi In S X r q 07 2 T Call Sse Q CAT ea o NT po T p Sao In S X r q 03 2 T In
75. ain amount and then the contract becomes void if it exceeds some price ceiling User Manual 88 Real Options Super Lattice Solver software manual Figures 64 and 65 illustrate American Barrier Options To change these into European Barrier Options set the Intermediate Node Equation Nodes to OptionOpen In addition for certain types of contractual options vesting and blackout periods can be imposed For solving such Bermudan Barrier Options keep the same Intermediate Node Equation as the American Barrier Options but set the Intermediate Node Equation During Blackout and Vesting Periods to OptionOpen and insert the corresponding blackout and vesting period lattice steps Finally if the Barrier is a changing target over time put in several custom variables named Barrier with the different values and starting lattice steps Figure 64 Single Asset Super Lattice Solver File Help Comment Upper Barier Option Up and In Call This option is live only when the asset value breaches the upper bamer Variable Name Value Starting Step Barrier 110 0 PV Underlying Asset 100 Risk Free Rate Implementation Cost 80 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 A inputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration If Asset gt Bamier Max Asset Cost 0 0 Example Max Asset Cost 0 bileenedisie
76. al The benchmark results use both closed form models Black Scholes and Closed Form Approximation models and 1 000 step binomial lattices on plain vanilla options You can change the steps to 000 in the basic inputs section to verify that the answers computed are equivalent to the benchmarks as seen in Figure 3 Notice that of course the values computed for the American and European options are identical to each other and identical to the benchmark values of 23 4187 as it is never optimal to exercise a standard plain vanilla call option early if there are no dividends Be aware that the higher the lattice step the longer it takes of course to compute the results It is advisable to start with lower lattice steps to make sure the analysis is robust and then progressively increase lattice steps to check for results convergence See Appendix A on convergence criteria on lattices for more details about binomial lattice convergence as to how many lattice steps are required for a robust option valuation Figure 3 Single Asset Super Lattice Solver File Help Comment Plain Vanila American and European Call Options lower number of steps Useful for testing convergence 7 Ameri F E B tn Variable Name Value Starting Step PV Undertying Asset Risk Free Rate Implementation Cost Dividend Rate Maturity Years Volatility 22 Lattice Steps All inputs are annualized rates Terminal Node Equation Options a
77. alue of both stocks are similar their volatilities and hence their risks are different The x axis depicts the stock prices while the y axis depicts the frequency of a particular stock price occurring and the area under the curve between two values is the probability of occurrence The second stock dotted line in Figure B6 has a wider spread a higher standard deviation 02 than the first stock bold line in Figure B6 The width of Figure B7 s x axis is the same width from Figure B6 s y axis One common measure of width is the standard deviation Hence standard deviation is a way to measure volatility The term volatility is used and not standard deviation because the volatility computed is not from the raw cash flows or stock prices themselves but from the natural logarithm of the User Manual 113 Real Options Super Lattice Solver software manual relative returns on these cash flows or stock prices Hence the term volatility differentiates it from a regular standard deviation Stock prices Time Figure B6 Volatility Frequency lt gt Probability area under the curve H p2 Stock price Figure B7 Standard Deviation However for the purposes of explaining volatility to management we relax this terminological difference and on a very high level state that they are one and the same for discussion purposes Thus we can make some management assumptions in estimating volatilities For instance starting from
78. alysis by the manufacturer the NPV of this micro drive is expected to be 45M with a cash flow volatility of 40 and it would take another 3 years before the micro drive technology is successful and goes to market Assume that the 3 year risk free rate is 5 In addition it would cost the manufacturer 45M in present value to develop this drive internally If using an NPV analysis the manufacturer should build it themselves However if you include an abandonment option analysis whereby if this specific micro drive does not work the startup still has an abundance of intellectual property patents and proprietary technologies as well as physical assets buildings and manufacturing facilities that can be sold in the market at up to 40M The abandonment option together with the NPV yields 51 83 making buying the User Manual 36 Real Options Super Lattice Solver software manual startup worth more than developing the technology internally and making the purchase price of 50M worth it Figure 19 shows the results of a simple abandonment option with a 10 step lattice as discussed previously while Figure 20 shows the audit sheet that is generated from this analysis Figure 19 Single Asset Super Lattice Solver File Help Comment This American Abandonment Option can be executed at any time up to and including expiration Variable Name Value Starting Step ae aaa American n _ Bermudan Basic Inputs PV Underlying Asset 120 Ris
79. ame and key that was assigned to you when you purchased Ifyou are only interested in a trial version please download the TRIAL versid Name WindowsInstaller31 exe Type Application 2 46 MB From www realoptionsvaluation com Run Save System requirements FAQ and additional resources Windows XP Excel XP or 2003 256 MB RAM 10 MB Hard Drive and admini Please view the FAQ if you have any questions about system requirements SOFTWARE MANUALS While files from the Internet can be useful this file type can potentially harm your computer If you do not trust the source do not run or save this software What s the risk 9 The following are the software user manuals and help files available for do Risk Simulator 1 1 User Manual Risk Simulator 1 1 Help Real Options SLS 1 0 User Manual Real Options SLS 2 0 User Manual Employee Stock Options Toolkit 1 1 User Manual Figure 7 Downloading Microsoft Installer from www realoptionsvaluation com downloads 134 Real Options Super Lattice Solver software manual File Download 9 You are downloading the file J WindowsInstaller31 exe From www realoptionsyaluation com Would you like to open the file or save it to your computer Always ask before opening this type of file Figure 8 Saving Microsoft Installer Setup File You can either SAVE the file or OPEN and run the file while online Figure 8 When prompted click on NEXT to start the installation o
80. ample 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Salvage Example Max Asset Cost 0 Intermediate Node Equation Options Before Expiration Max Salvage OptionOpen Example Max Asset Cost OptionOpen Figure 21 American Abandonment Option with 100 Step Lattice User Manual 39 Real Options Super Lattice Solver software manual Figure 22 Single Asset Super Lattice Solver File Help Comment This option to abandon can only be executed at expiration and not before Variable Name Value Starting Step 90 0 PV Underlying Asset Risk Free Rate Implementation Cost 90 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Salvage Example Max Asset Cost 0 intermediate Node Equation Options Before Expiration OptionOpen Figure 22 European Abandonment Option with 100 Step Lattice Sometimes a Bermudan option is appropriate where there might be a vesting period or blackout period when the option cannot be executed For instance if the contract stipulates that for the 5 year abandonment buy back contract the airline customer cannot execute the abandonment option within the first 2 5 years This is shown in Figure 23 using a Bermuda
81. an expected NPV the mean value you can obtain an alternate NPV value with its probability and get an approximate volatility For instance say that a project s NPV is expected to be 100M Management further assumes that the best case scenario exceeds 150M if everything goes really well and that there is only a 10 probability that this best case scenario will hit Figure B8 illustrates this situation If we assume for simplicity that the underlying asset value will fluctuate within a normal distribution we can compute the implied volatility using the following equation User Manual 114 Real Options Super Lattice Solver software manual a Percentile Value Mean Volatility Inverse of the Percentile x Mean For instance we compute the volatility of this project as 150M 100M _ 50M Inverse 0 90 x 100M 1 2815x 100M Volatility 39 02 Where the Inverse of the Percentile can be obtained by using Excel s NORMSINV 0 9 function Similarly if the worst case scenario occurring 10 of the time will yield an NPV of 50M we compute the volatility as Volatility ee __ 20M 39 02 Inverse 0 10 x 100M 1 2815 x 100M Frequency Best Case Scenario 150M 10 probability NPV of Project Expected NPV 100M 90th percentile Figure B8 Going from Probability to Volatility This implies that the volatility is a symmetrical measure That is at an expected NPV of 100M a 50 increase is equi
82. an Up and In option for both calls and puts indicates that the option becomes live if the asset value hits the upper barrier Conversely for the Up and Out option the option is live only when the upper barrier is not breached This is very similar to the Lower Barrier Option but now the barrier is above the starting asset value and for a binding barrier option the implementation cost is typically lower than the upper barrier That is the upper barrier is usually gt implementation cost and the upper barrier is also gt starting asset value Examples of this option include contractual agreements whereby if the upper barrier is breached some event or clause is triggered The values of barrier options are typically lower than standard options as the barrier option will have value within a smaller price range than the standard option The holder of a barrier option loses some of the traditional option value and therefore a barrier option should sell at a lower price than a standard option An example would be a contractual agreement whereby the writer of the contract can get into or out of certain obligations if the asset or project value breaches a barrier The Up and In Upper American Barrier Option has slightly lower value than a regular American call option as seen in Figure 64 This is because some of the option value when the asset is less than the barrier but greater than the implementation cost is lost Clearly the higher the upper barrier the
83. ancial Valuator and the SLS Functions accessible inside Excel To license your software follow the simple steps below Preparation 1 Start Real Options SLS click on Start Programs Real Options Valuation Real Options SLS Real Options SLS 2 Click on the I License Real Options SLS link and you will be provided with your HARDWARE ID this starts with the prefix SLS and should be between 12 and 20 digits Write this information down or copy it by selecting the identification number right click your mouse and select Copy and then Paste it in an e mail to us 3 Click on the 2 License Functions amp Options Valuator link and write down or copy the HARDWARE FINGERPRINT it should be an 8 digit alphanumeric code 4 Purchase a license at www realoptionsvaluation com by clicking on the Purchase link 5 E mail admin realoptionsvaluation com these two identification numbers and we will send you your license file and license key Once you receive these please install the license using the steps below Installing Licenses 1 Save the SLS license file to your hard drive the license file we sent you after you purchased the software and then start Real Options SLS click on Start Programs Real Options Valuation Real Options SLS Real Options SLS Click on the 1 License Real Options SLS and select ACTIVATE then browse to the SLS license file that we sent you Click on the 2 License Functions amp Opti
84. ariable is enclosed in a pair of curly braces Identifiers are case sensitive except for function names The following are some examples of valid identifiers myVariable MYVARIABLE _myVariable myVariable myVariable This is a single variable e Numbers A number can be an integer defined as one or more characters between 0 and 9 The following are some examples of integers 0 1 00000 12345 Another type of number is a real number The following are some examples of real numbers 0 3 0 0 0 1 3 9 5 934 3E3 3 5E 5 0 2E 4 3 2E 2 3 5e 5 e Operator Precedence The operator precedence when evaluating the equations is shown below However if there are two terms with two identical precedence operators the expression is evaluated from left to right 3 o Parenthesized expression has highest precedence le Not and unary minus e g 3 le A o O lt gt o al gt lt lt a a User Manual 32 Real Options Super Lattice Solver software manual o amp e Mathematical Expression The following shows some examples of valid equations usable in the custom equations boxes Review the rest of the user manual recommended texts and example files for more illustrations of actual options equations and functions used in SLS 2010 Max Asset Cost 0 Max Asset Cost OptionOpen 135 12 24 12 24 36 48 3 ABS 3 3 MAX 1 2 3 4 MIN 1 2 3 4 SQRT 3 ROUND 3 LOG 12 IF a gt
85. art Options Definitions of Variables S present value of future cash flows X implementation cost r risk free rate t time when the forward start option begins years T time to expiration of the forward start option years o volatility D cumulative standard normal distribution q continuous dividend payout Computation In1 r g 0 2 T t oT t a cruz N a r q 0 2 T t Se na el Uda JM 2 1 0 T t oT t In1 a r q 0 2 T t oT t In 1 r q 0 2 T t oT t where a is the multiplier constant Note If the option starts at X percent out of the money that is a will be J X If it starts at the money a will be 1 0 and 1 X if in the money Call Se le PMO Put Se a eV o T t 2 Sed e 2 User Manual 126 Real Options Super Lattice Solver software manual Generalized Black Scholes Model Definitions of Variables implementation cost risk free rate time to expiration years volatility carrying cost o oegQgIIT kxa Computation In S X b 0 2 T present value of future cash flows cumulative standard normal distribution continuous dividend payout Call Se NT oVT Ke 2 stat of ue o IDT ovT Notes b 0 Futures options model b r q Black Scholes with dividend payment b r Simple Black Scholes formula b r r Foreign currency options model User Manual 127
86. as a percentage of the Asset Value increases it is better not to defer and wait that long Therefore the higher the dividend rate the lower the strategic option value For instance at an 8 dividend rate and 15 volatility the resulting value reverts to the NPV of 15M which means that the option value is zero and that it is better to execute immediately as the cost of waiting far outstrips the value of being able to wait given the level of volatility uncertainty and risk Finally if risks and uncertainty increase significantly even with a high cost of waiting e g 7 dividend rate at 30 volatility it is still valuable to wait This model provides the decision maker with a view into the optimal balancing between waiting for more information Expected Value of Perfect Information and the cost of waiting You can analyze this balance by creating strategic options to defer investments through development stages where at every stage the project is reevaluated as to whether it is beneficial to proceed to the next phase Based on the input assumptions used in this model the Sequential Compound Option results show the strategic value of the project and the NPV is simply the PV Asset less both phases Implementation Costs In other words the strategic option value is the difference between the calculated strategic value minus the NPV It is recommended for your consideration that the volatility and dividend inputs are varied to determine their int
87. ate the project otherwise Based on the input assumptions the results in the MSLS indicate the calculated strategic value of the project while the NPV of the project is simply the PV Asset less all Implementation Costs in present values if implementing all phases immediately Therefore with the strategic option value of being able to defer and wait before implementing future phases because due to the volatility there is a possibility that the asset value will be significantly higher Hence the ability to wait before making the investment decisions in the future is the option value or the strategic value of the project less the NPV Figure 47 shows the results using the MSLS Notice that due to the backward induction process used the analytical convention is to start with the last phase and going all the way back to the first phase the Multiple Asset module s example file used Sequential Compound Option for Multiple Phases In NPV terms the project is worth 500 However the total strategic value of the stage gate investment option is worth 41 78 This means that although on an NPV basis the investment looks bad but in reality by hedging the risks and uncertainties through sequential investments the option holder can pull out at any time and not have to keep investing unless things look promising If after the first phase things look bad pull out and stop investing and the maximum loss will be 100 Figure 47 and not the entire 1 500 inves
88. ating portfolios and comparables and the funds to pay these dividends are obtained from the company s net income and free cash flows The theoretical value of a project or asset is the sum of the present value of all future free cash flows or net income Hence the price of a stock is equivalent to the price or value of an asset the NPV Thus the sum of the present values at time 0 is equivalent to the stock price of the asset at time 0 the value today The sum of the present value of the cash flows at time 1 is equivalent to the stock price at time 1 or a good proxy for the stock price in the future We use this as a proxy because in most DCF models cash flow forecasts are only a few periods Hence by running Monte Carlo simulation we are changing all future possibilities and capturing the uncertainties in the DCF inputs This future stock price is hence a good proxy of what may happen to the future stream of cash flows remember that sum of the present value of future cash flows at time 1 included in its computations all future cash flows from the DCF thereby capturing future fluctuations and uncertainties This is why we perform Step 1 when we compute volatilities using the Log Present Value Returns Approach Step 2 Calculate the intermediate variable X This X variable is identical to the logarithmic relative returns in the Log Cash Flow Returns Approach It is simply the natural logarithm of the User Manual 111 Real Options Super Lattic
89. ax Salvage OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period OptionOpen Example OptionOpen Figure 24 Customized Abandonment Option User Manual 42 Real Options Super Lattice Solver software manual American European Bermudan and Customized Contraction Options A Contraction Option evaluates the flexibility value of being able to reduce production output or to contract the scale and scope of a project when conditions are not as amenable thereby reducing the value of the asset or project by a Contraction Factor but at the same time creating some cost Savings As an example suppose you work for a large aeronautical manufacturing firm that is unsure of the technological efficacy and market demand for its new fleet of long range supersonic jets The firm decides to hedge itself through the use of strategic options specifically an option to contract 10 of its manufacturing facilities at any time within the next 5 years i e the Contraction Factor is 0 9 Suppose that the firm has a current operating structure whose static valuation of future profitability using a discounted cash flow model in other words the present value of the expected future cash flows discounted at an appropriate market risk adjusted discount rate is found to be 1 000M PV Asset Using Monte Carlo simulation you calculate the implied volatility of the logarithmic returns of the asset value of
90. but if you enter into Australia you can still enter into Japan or U K but not Japan and U K User Manual 72 Real Options Super Lattice Solver software manual Simultaneous Compound Options The Simultaneous Compound Option evaluates a project s strategic value when the value of the project depends on the success of two or more investment initiatives executed simultaneously in time The Sequential Compound Option evaluates these investments in stages one after another over time while the simultaneous option evaluates these options in concurrence Clearly the sequential compound is worth more than the simultaneous compound option by virtue of staging the investments Note that the simultaneous compound option acts like a regular execution call option Hence the American Call Option is a good benchmark for such an option Figure 50 shows how a Simultaneous Compound Option can be solved using the MSLS example file used Simple Two Phased Simultaneous Compound Option Similar to the sequential compound option analysis the existence of an option value implies that the ability to defer and wait for additional information prior to executing is valuable due to the significant uncertainties and risks as measured by Volatility However when the cost of waiting as measured by the Dividend Rate is high the option to wait and defer becomes less valuable until the breakeven point where the option value equals zero and the strategic project value equals the
91. cannot be executed If you also wish to enter the Intermediate Node Equation the Custom Option should be first chosen otherwise you cannot use the Intermediate Node Equation box The Custom Option result will use all the equations you have entered in the Terminal Intermediate and Intermediate with Blackout sections The Custom Variables list is where you can add modify or delete custom variables the variables that are required beyond the basic inputs For instance when running an abandonment option you will require the salvage value You can add this in the Custom Variables list provide it a name a variable s name must be a single word without spaces the appropriate value and the starting step when this value becomes effective For example if you have multiple salvage values i e if salvage values change over User Manual 14 Real Options Super Lattice Solver software manual time you can enter the same variable name e g salvage several times but each time its value changes and you can specify when the appropriate salvage value becomes effective For instance in a 10 year 100 step super lattice problem where there are two salvage values 100 occurring within the first 5 years and increases to 150 at the beginning of Year 6 you can enter two salvage variables with the same name 100 with a starting step of 0 and 150 with a starting step of 51 Be careful here as Year 6 starts at step 51 and not 61 That is for a 10 year
92. ces to closed form differential equations and analytical methods for valuing exotic options as well as other options related models such as bond options volatility computations delta gamma hedging and so forth Figure 18 illustrates the valuator You can click on the Load Sample Values button to load some samples to get started Then select the Model Category left panel as desired and select the Model right panel you wish to run Click COMPUTE to obtain the result Note that this valuator complements the ROV Risk Modeler and ROV Valuator software tools with more than 800 functions and models also developed by Real Options Valuation Inc ROV which are capable of running at extremely fast speeds and handling large datasets and linking into existing ODBC compliant databases e g Oracle SAP Access Excel CSV and so forth Finally if you wish to access these 800 functions including the ones in this Exotic Financial Options Valuator tool use the ROV Modeling Toolkit software instead where in addition to having access to these functions and more you can run Monte Carlo simulation on your models using ROV s Risk Simulator software ae ROV Options Valuator C Program Files Real Options Valuation Real Options SLS ModuleDefaultVa File Languages Model Category Model Selection q Two Asset Cash or Nothing Up Down Basic Options Models Two Asset Correlation Call Bond Related Options Pricing and Yields Two Asset Correlation
93. d version immediately The loss in returns generated each year does not sufficiently cover the risks incurred e An oil and gas company is currently deciding on a deep sea exploration and drilling project The platform provides an expected NPV of 1 000M This project is wrought with risks price of oil and production rate are both uncertain and the annualized volatility is computed to be 55 The firm is thinking of purchasing an expansion option by spending an additional 10M to build a slightly larger platform that it does not currently need but if the price of oil is high or when production rate is low the firm can execute this expansion option and execute additional drilling to obtain more oil to sell at the higher price which will cost another 50M thereby increasing the NPV by 20 The economic life of this platform is 10 years and the risk free rate for the corresponding term is 5 Is obtaining this slightly larger platform worth it Using the SLS the option value is worth 27 12M when applying a 100 step lattice Therefore the option cost of 10M is worth it However this expansion option will not be worth it if annual dividends exceed 0 75 or 7 5M a year this is the annual net revenues lost by waiting and not drilling as a percentage of the base case NPV Figure 32 shows a Bermudan Expansion Option with certain vesting and blackout steps while Figure 33 shows a Customized Expansion Option to account for the expansion factor chang
94. dard normal distribution Z score is such that x x H this means that o 2H Oo Z and because we normalize the volatility as a percentage o we divide this by the mean to obtain Tx ot TH Zu In layman s terms we have Percentile Value Mean Volatility Inverse of the Percentile x Mean Again the inverse of the percentile is obtained using Excel s function NORMSINV User Manual 117 Real Options Super Lattice Solver software manual Distribution of Microsoft Stock Prices N wo w oa S a So N N So 1 Frequency a oso 342 I l O m O L E D D 0 N Oo o ct D oO N N O y LO D Q ie x co f x 2 T Lo 2 N 9 Q N O oO m O oO oO o Co ce mn Ke O A A n ni N N N m fap M t ike A A A A A A A A A A A A A Bin Figure B11 Probability Distribution of Microsoft s Stock Price Since 1986 Distribution of Microsoft Stock Log Returns a oO Frequency 3 oO 250 200 w 50 g O 5 ei TI bun SLL eee eee Ee eee RRS LFF XK 4 O0 A Q O rr SO Cre RF LO SSP Veg SAS re gt DATI gt O gt GAI BSE e erst 1100 DORIA TO AEDT NE ORO CO Oss RITIRO Me DA CO RUDI ree ly ae CD N 6 lt cdi KF di sd GCG OB K Sir GO 60 N DB GA OK Ow SME eI MR Eran eee a Sg nee nae Cag gO Log Returns Figure B12 Probability Dis
95. dditional Assumptions Year Risk free Year Volatility Please be aware that by applying multiple changing volatilities over time a non recombining lattice is required which increases the computation time significantly In addition only smaller lattice steps may be computed The function used is SLSBinomialChangingVolatility 10 00 30 00 Figure 16 Changing Volatility and Risk Free Rate Option User Manual 25 Real Options Super Lattice Solver software manual SLS Functions The software also provides a series of SLS functions that are directly accessible in Excel To illustrate its use start the SLS Functions by clicking on Start Programs Real Options Valuation Real Options SLS SLS Functions and Excel will start When in Excel you can click on the function wizard icon or simply select an empty cell and click on nsert Function While in Excel s equation wizard select the ALL category and scroll down to the functions starting with the SLS prefixes Here you will see a list of SLS functions that are ready for use in Excel Figure 17 shows the Excel equation wizard Suppose you select the first function SLSBinomialAmericanCall and hit OK Figure 17 shows how the function can be linked to an existing Excel model The values in cells BI to B7 can be linked from other models or spreadsheets can be created using VBA macros or can be dynamic and changing as in when running a simulation If you are a new user of R
96. dging and so forth This valuator complements the ROV Risk Modeler and ROV Valuator software tools with more than 800 functions and models also developed by Real Options Valuation Inc ROV which are capable of running at extremely fast speeds handling large datasets and linking into existing ODBC compliant databases e g Oracle SAP Access Excel CSV and so forth e The SLS Excel Solution implements the SLS and MSLS computations within the Excel environment allowing users to access the SLS and MSLS functions directly in Excel This feature facilitates model building formula and value linking and embedding as well as running simulations and provides the user sample templates to create such models e The SLS Functions are additional real options and financial options models accessible directly through Excel This module facilitates model building linking and embedding and running simulations e The Option Charts are used to visually analyze the payoff structure of the options under analysis the sensitivity and scenario tables of options to various inputs convergence of the lattice results and other valuable analyses The SLS software is created by Dr Johnathan Mun professor consultant and the author of numerous books including Real Options Analysis Tools and Techniques 2nd Edition Wiley 2005 Modeling Risk Wiley 2006 and Valuing Employee Stock Options Under 2004 FAS 123 Wiley 2004 This software also accompanies the ma
97. djusted rate of return which can also be seen as discounting at 5 risk free rate to account for time value of money and discounted again at the market risk premium of 10 for risk or simply discounted one time at 15 As discussed in Chapter 2 if you do not separate the market and private risks you end up discounting the private risks heavily and making the DCF a lot more profitable than it actually is i e if the costs that should be discounted at 5 are discounted at 15 the NPV will be inflated By separately discounting these cash flows the present value of cash flows and implementation costs can be computed cells H9 and H10 The difference will of course be the NPV The separation here is also key because from the Black Scholes equation below the call option is computed as the present value of net benefits discounted at some risk adjusted rate of return or the starting stock price S times the standard normal probability distribution less the implementation cost or strike price X discounted at the risk free rate and adjusted by another standard normal probability distribution D If volatility 0 is zero the uncertainty is zero and is equal to 100 the value inside the parenthesis is infinity meaning that the standard normal distribution value is 100 alternatively you can state that with zero uncertainties you have a 100 certainty By separating the cash flows you can now use these as inputs into the options model wheth
98. does not fully capture the possible cash flow downside and may produce erroneous results In addition autocorrelated cash flows estimated using time series forecasting techniques or cash flows following a static growth rate will yield volatility estimates that are erroneous Great care should be taken in such instances This flaw is neutralized in larger datasets that only carry positive values such as historical stock prices or price of oil or electricity This approach is valid and correct as computed in Figure B2 for liquid and traded assets with a lot of historical data The reason why this approach is not valid for computing the volatility of cash flows in a DCF for the purposes of real options analysis is because of the lack of data For instance the following annualized cash flows 100 200 300 400 500 would yield a volatility of 20 80 as compared to the following annualized cash flows 100 200 400 800 1600 which would yield a volatility of 0 versus the following cash flows 100 200 100 200 100 200 which yields 75 93 All these cash flow streams seem fairly deterministic and yet provided very different volatilities In addition the third set of negatively autocorrelated cash flows should actually be less volatile due to its predictive cyclical nature User Manual 105 Real Options Super Lattice Solver software manual and reversion back to a base level but its volatility is computed to be the highest The second cash flow str
99. ds and maturity in years Second if a cash flow or stock price stream of 10 to 20 to 30 that occurs in three different months versus three different days has very different volatilities Clearly if it takes days to double or triple your asset value that asset is a lot more volatile All these have to be common sized in time and be annualized Finally the Brownian Motion stochastic equation has the values o dt That is suppose we have a 1 year option modeled using a 12 step lattice then of is 1 12 If we use monthly data compute the monthly volatility and use this as the input this monthly volatility will again be partitioned into 12 pieces per 0 Ot Therefore we need to first annualize the volatility to an annual volatility multiplied by the square root of 12 input this annual volatility into the model and let the model partition the volatility multiplied by the square root of 1 12 into its periodic volatility This is why we annualize volatilities in Step 5 Volatility Estimates Logarithmic Present Value Returns The Logarithmic Present Value Returns Approach to estimating volatility collapses all future cash flow estimates into two present value sums one for the first time period and another for the present time Figure B3 The steps are shown below The calculations assume a constant discount rate The cash flows are discounted all the way to Time 0 and again to Time 1 with the cash flows in Time 0 ignored sunk cost
100. e standard deviation of the forecast distribution of X is the volatility estimate used in the real options analysis It is important to note that only the numerator is simulated while the denominator remains unchanged The downside to estimating volatility this way is that the approach requires Monte Carlo simulation but the calculated volatility measure is a single digit estimate as compared to the Logarithmic Cash Flow or Stock Price Approach which yields a distribution of volatilities that in turn yield a distribution of calculated real options values The main objection to using this method is its dependence on the variability of the discount rate used For instance we can expand the X equation as follows n CF CF CF CF gt PVCF z vi X sa 1 D 1 D 1 D 1 D x CF CF CF CF gt PVCF D 1 D D D where D represents the constant discount rate used Here we see that the cash flow series CF for the numerator is offset by one period and the discount factors are also offset by one period Therefore by performing a Monte Carlo simulation on the cash flows alone versus performing a Monte Carlo simulation on both cash flow variables as well as the discount rate will yield very different X values The main critique of this approach is that in a real options analysis the variability in the present value of cash flows is the key driver of option value and not the variability of discount rates used i
101. e Solver software manual relative returns of the future stock price using the sum of present values at time 1 as a proxy from the current stock price the sum of present values at time 0 We then set the sum of present values at time 0 as static because it is the base case and by definition of a base case the values do not change The base case can be seen as the NPV of the project s net benefits and is assumed to be the best estimate of the project s net benefit value It is the future that is uncertain and fluctuates hence we simulate the DCF model and allow the numerator of the X variable to change during the simulation while keeping the denominator static as the base case Step 3 Simulate the model and obtain the standard deviation as volatility This approach requires that the model be simulated This makes sense because if the model is not simulated means that there is no uncertainties in the project or asset and hence the volatility is equal to zero You would only simulate when there are uncertainties hence you obtain a volatility estimate The rationale for using the sample standard deviation as the volatility is similar to the Log Cash Flow Returns approach If the sums of the present values of the cash flows are fluctuating between positive and negative values during the simulation you can again move up the DCF model and use items like EBITDA and net revenues as proxy variables for computing volatility Another alternative volat
102. e is significant estimated at 25 Under these conditions there is a lot of uncertainty as to the success or failure of this project the volatility calculated models the different sources of uncertainty and computes the risks in the discounted cash flow DCF model including price uncertainty probability of success competition cannibalization and so forth and the value of the project might be significantly higher or significantly lower than the expected value of 120M Suppose an abandonment option is created whereby a counterparty is found and a contract is signed that lasts 5 years Maturity such that for some monetary consideration now the firm has the ability to sell the asset or project to the counterparty at any time within these 5 years indicative of an American option for a specified Salvage of 90M The counterparty agrees to this 30M discount and signs the contract What has just occurred is that the firm bought itself a 90M insurance policy That is if the asset or project value increases above its current value the firm may decide to continue funding the project or sell it off in the market at the prevailing fair market value Alternatively if the value of the asset or project falls below the 90M threshold the firm has the right to execute the option and sell off the asset to the counterparty at 90M In other words a safety net of sorts has been erected to prevent the value of the asset from falling below this salvage level
103. eal Options SLS or have upgraded from an older version do spend some time reviewing the Key SLS Notes and Tips starting on the next few pages to familiarize yourself with the modeling intricacies of the software User Manual 26 Real Options Super Lattice Solver software manual PY Asset Cost Maturity Risk Free Volatility Dividend Steps Result User Manual Search for a function Or select a category Real Options Y aluation v Select a Function SLSBinomialAmericanPut SLSBinomialChangingYolatility SLSBinomialDown SLSBinomialEuropeanCall SLSBinomialEuropeanPut SLSBinomialProbability SLSBinomialAmericanCall PYAsset Cost Maturity Riskfree Returns the American call option with dividends using the binomial approach Help on this function 100 00 100 00 SLSBinomial amp mericanCall 1 PYAsset 5 25 Cost 0 Maturity 100 Riskfree Yolatility 12 31 12 31130972 Returns the American call option with dividends using the binomial approach P Asset 12 31130972 Formula result Figure 17 Excel s Equation Wizard 27 Real Options Super Lattice Solver software manual Exotic Financial Options Valuator The Exotic Financial Options Valuator is a comprehensive calculator of more than 250 functions and models from basic options to exotic options e g from Black Scholes to multinomial latti
104. eam seems more risky than the first set due to larger fluctuations but has a volatility of 0 Therefore be careful when applying this method to small datasets When applied to stock prices and historical data that are nonnegative this approach is easy and valid However if used on real options assets the DCF cash flows may very well take on negative values returning an error in your computation i e log of a negative value does not exist However there are certain approaches you can take to avoid this error The first is to move up your DCF model from free cash flows to net income to operating income EBITDA and even all the way up to revenues and prices where all the values are positive If doing it this way then care must be taken such that all other options and projects are modeled this way for comparability s sake Also this approach is justified in situations where the volatility risk and uncertainty stem from a certain variable above the line is used For instance the only critical success factor for an oil and gas company is the price of oil price and the production rate quantity where both are multiplied to obtain revenues In addition if all other items in the DCF are proportional ratios e g operating expenses are 25 of revenues or EBITDA values are 10 of revenues and so forth then we are only interested in the volatility of revenues In fact if the proportions remain constant the volatilities computed are identica
105. en when in the SLS MSLS or MNLS models you can access the example files at File Examples e Current License information can be obtained in SLS MSLS or MNLS at Help About e A Variable List is available in SLS MSLS and MNLS by going to Help Variable List Specifically the following are allowed variables and operators in the custom equations boxes o Asset The value of the underlying asset at the current step in currency o Cost The implementation cost in currency o Dividend The value of dividend in percent o Maturity The years to maturity in years o OptionOpen The value of keeping the option open formerly in version 1 0 o RiskFree The annualized risk free rate in percent o Step The integer representing the current step in the lattice o Volatility The annualized volatility in percent Oo Subtract o Not o Not equal o amp And o Multiply o Divide o A Power o Or E Add o lt gt gt Comparisons o Equal e OptionOpen at Terminal Nodes in SLS or MSLS If OptionOpen is specified as the Terminal Node equation the value will always evaluate to Not a Number error NaN This is clearly a user error as OptionOpen cannot apply at the terminal nodes e Unspecified interval of custom variables If a specified interval with a custom variable has no value the value is assumed zero For example suppose a model e
106. enough in the early stages to be expanded into some spin off technology In addition during the post vesting period but prior to maturity the option to contract or abandon does not exist perhaps the technology is now being reviewed for spin off opportunities and so forth Finally Figure 37 uses the same example in Figure 36 but now the input parameters salvage value are allowed to change over time perhaps accounting for the increase in project asset or firm value if abandoned at different times example file used Expand Contract Abandon Customized Option ID Figure 35 Single Asset Super Lattice Solver File Help Comment Bermudan Option to Expand Contract and Abandon where there is a cooling off period blackout step periods i Variable Name Value Starting Step he Expansion 13 BAe ExpandCost 25 PV jonas Asset 100 Ri Costradion 0 9 Implementation Cost 100 Divi ContractSavi 25 z 100 Maturity Years 5 Lattice Steps 100 Alinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option 0 80 Example 1 2 10 20 35 Terminal Node Equation Options at Expiration risse Max Asset Asset Expansion ExpandCost Black Scholes Asset Contraction Contract Savings Salvage Closed Form American Binomial European Binomial American rms Node Equation Options Before Expiration Custom Option 116 8171 Max Asset Expansion ExpandCost Asset Contraction Contract Savings Salvage OptionOpen
107. ent MICROSOFT SOFTWARE SUPPLEMENTAL LICENSE TERMS MICROSOFT NET FRAMEWORK 2 0 Microsoft Corporation or based on where you live one of its affiliates licenses this supplement to you If you are licensed to use Microsoft Windows operating system software the software you may use this supplement You may not use it if you do not have a license for the software You may use a copy of this supplement with each validly licensed copy of the software v By clicking I accept the terms of the License Agreement and proceeding to use the product I indicate that I have read understood and agreed to the terms of the End User License Agreement y I accept the terms of the License Agreement si Figure 5 NET Framework 2 0 License Agreement 133 Real Options Super Lattice Solver software manual is Microsoft NET Framework 2 0 Setup Error Prerequisite programs are missing Setup has detected that the following prerequisite programs are not installed Microsoft Windows Installer 3 0 You must first install these programs before Microsoft NET Framework 2 0 can be installed Rerun setup after installing these programs Figure 6 Missing Microsoft Installer click EXIT here Step 2 5 You only need to complete this step if you got the error message in Figure 6 If you do make sure you click on EXIT Then go to www realoptionsvaluation com downloads to download the Microsoft Installer 3 1 package see Figu
108. eps use the ESO Function Figure 74 ESO Toolkit Results after accounting for Vesting Forfeiture Suboptimal Behavior and Blackout User Manual Periods 101 Real Options Super Lattice Solver software manual Appendix A Lattice Convergence The higher the number of lattice steps the higher the precision of the results Figure A1 illustrates the convergence of results obtained using a BSM closed form model on a European call option without dividends and comparing its results to the basic binomial lattice Convergence is generally achieved at between 500 1 000 steps Due to the high number of steps required to generate the results software based mathematical algorithms are used For instance a nonrecombining binomial lattice with 1 000 steps has a total of 2 x 10 nodal calculations to perform making manual computation impossible without the use of specialized algorithms Figure A1 also illustrates the binomial lattice results with different steps and notes the convergence of the binomial for a simple European call option using the Black Scholes model Convergence in Binomial Lattice Steps 17 20 5 17 10 4 17 00 16 90 4 Black Scholes 16 80 Option Value 16 70 4 16 60 16 50 1 10 100 1000 10000 Lattice Steps Black Scholes Result 12 336 Binomial 5 Step Lattice 12 795 Binomial 10 Step Lattice 12 093 Binomial 20 Step Lattice 12 213 Binomial 50 Step Lattice 12 287 Binomial
109. er it s using the Black Scholes or binomial lattices 2 Cali sof MELD tete w a MELD E o a oT oVT Continuing with the example in Figure B4 the calculations of interest are on rows 51 to 55 Row 51 shows the present values of the cash flows to Year 0 assume that the base year is 2002 while row 52 shows the present values of the cash flows to Year 1 ignoring the sunk cost of cash flow at Year 0 These two rows are computed in Excel and are linked formulas You should then copy and paste the values only into row 53 use Excel s Edit Paste Special Values Only to do this Then compute the intermediate variable X in cell D54 using the following Excel formula LN SUM E52 H52 SUM D53 H53 Then simulate this DCF model using Risk Simulator by assigning the relevant input assumptions in the model and set this intermediate variable X as the output forecast The standard deviation from this X is the periodic volatility Annualizing the volatility is required by multiplying this periodic volatility with the square root of the number of periodicities in a year User Manual 110 Real Options Super Lattice Solver software manual gt O RER F G spe Log Present Value Approach Input Parameters Discount Rate Cash Flow 15 00 Discount Rate Impl Cost 5 00 Results Present Value Cash Flow 328 24 Present Value Impl Cost 189 58 Tax Rate 10 00 Net Present Value 138 67 2002
110. eractions specifically where the breakeven points are for different combinations of volatilities and dividends Thus using this information you can make better go or no go decisions for instance breakeven volatility points can be traced back into the discounted cash flow model to estimate the probability of crossing over and that this ability to wait becomes valuable Figure 45 Multiple Asset Super Lattice Solver File Help Comment Simple Two Phased Sequential Compound Option Name PV Asset Volatility Notes Value Starting Step Underlying 100 30 Blackout and Vesting Period Steps Name Cost Risk Free Div Steps Terminal Equation Intermediate Equation Bla Phase2 80 5 0 100 Max Underlying Cost 0 Max Underlying Cost OptionOpen PHASE1 27 6734 Phasel 5 5 0 50 Max Phase2 Cost 0 Max Phase2 Cost OptionOpen Create Audit Sheet Figure 45 Solving a Two Phased Sequential Compound Option using MSLS User Manual 67 Real Options Super Lattice Solver software manual Multiple Phased Sequential Compound Options The Sequential Compound Option can similarly be extended to multiple phases with the use of MSLS A graphical representation of a multi phased or stage gate investment is seen in Figure 46 The example illustrates a multi phase project where at every phase management has the option and flexibility to either continue to the next phase if everything goes well or to termin
111. erlying Asset x ype Gas gt aa Lattice Steps 100 Plain Vanilla Call Option I Single Asset Super Lattice Solver This analysis runs a quick static sensitivity of each input variable of the model one at a time and lists the input variables with the highest impactto the lowest For sensitivity of lattice steps please use the Convergence analysis Option Type Lattice Steps Show Decimals Sensitivity Plain Vanilla Call Option I Single Asset Super Lattice Solver The higher the number of lattice steps the higher the level of precision of the option result the result remains the same for additional decimal precision Atsome point the lattice result converges This convergence testwill run between 5 and 5000 steps to test for the convergence level Once there is convergence further lattice steps are notrequired Figure 18A Payoff Charts Sensitivity Analysis Scenario Tables and Convergence Analysis Key SLS Notes and Tips Here are some noteworthy changes from the previous version and interesting tips on using Real Options SLS e The User Manual is accessible within SLS MSLS or MNLS For instance simply start the Real Options SLS software and create a new model or open an existing SLS MSLS or MNLS model Then click on Help User Manual e Example Files are accessible directly in the SLS Main Scre
112. es the following inputs Phase 3 Terminal Max Underlying Expansion Cost Underlying Salvage Intermediate Max Underlying Expansion Cost Salvage OptionOpen Steps 50 Phase 2 Terminal Max Phase3 Phase3 Contract Savings Salvage 0 Intermediate Max Phase3 Contract Savings Salvage OptionOpen Steps 30 Phase 1 Terminal Max Phase2 Salvage 0 Intermediate Max Salvage OptionOpen Steps 10 User Manual 71 Real Options Super Lattice Solver software manual Path Dependent Path Independent Mutually Exclusive Non Mutually Exclusive and Complex Combinatorial Nested Options Sequential Compound Options are path dependent options where one phase depends on the success of another in contrast to path independent options like those solved using SLS Figure 49 shows that in a complex strategy tree at certain phases different combinations of options exist These options can be mutually exclusive or non mutually exclusive In all these types of options there might be multiple underlying assets e g Japan has a different risk return or profitability volatility profile than the U K or Australia You can build multiple underlying asset lattices this way using the MSLS and combine them in many various ways depending on the options The following are some examples of path dependent versus path independent and mutually exclusive versus non mutually exclusive options e Path Independent and Mutually Exclusive Options Use the SLS to solve these t
113. escence lat eee 130 Appendix E Detailed Installation Instructions 131 Appendix F Activating Permanent Licensing 142 User Manual 5 Real Options Super Lattice Solver software manual SECTION GETTING STARTED Single Asset Super Lattice Solver SLS Multiple Asset Super Lattice Solver MSLS Multinomial Lattice Solver MNLS Lattice Audit Sheet Lattice Maker SLS Excel Solution SLS Functions User Manual 6 Real Options Super Lattice Solver software manual Introduction to the Super Lattice Software SLS The Real Options Super Lattice Software SLS comprises several modules including the Single Super Lattice Solver SLS Multiple Super Lattice Solver MSLS Multinomial Lattice Solver MNLS Lattice Maker Advanced Exotic Options Valuator SLS Excel Solution and SLS Functions These modules are highly powerful and customizable binomial and multinomial lattice solvers and can be used to solve many types of options including the three main families of options real options which deals with physical and intangible assets financial options which deals with financial assets and the investments of such assets and employee stock options which deals with financial assets provided to employees within a corporation This text illustrates some sample real options financial options and employee stock options applications that users will most frequently encounter e The Single Asset Model is used primarily for solving options
114. f Y XY E o ag fo where the first equation s dependent variable y is a function of exogenous variables x with an error term The second equation estimates the variance squared volatility 07 at time t which depends on a historical mean news about volatility from the previous period measured as a lag of the squared residual from the mean equation 7 and volatility from the previous period 0 The exact modeling specification of a GARCH model is beyond the scope of this book and will not be discussed Suffice it to say that detailed knowledge of econometric modeling model specification tests structural breaks and error estimation is required to run a GARCH model making it less accessible to the general analyst The other problem with GARCH models is that the model usually does not provide a good statistical fit That is it is impossible to predict say the stock market and of course equally if not harder to predict a stock s volatility over time Figure B5 shows a GARCH 1 2 on Microsoft s historical stock prices User Manual 112 Real Options Super Lattice Solver software manual Dependent Variable MSFT Method ML ARCH Date 02 25 05 Time 00 20 Sample adjusted 3 52 Included observations 50 after adjusting endpoints Convergence achieved after 67 iterations Bollerslev Wooldrige robust standard errors amp covariance Coefficient Std Error z Statistic Prob C 23 14431 1 301024
115. f Windows Installer Figure 9 Software Update Installation Wizard Use this wizard to install the following software update Windows Installer 3 1 KB893803 Before you install this update we recommend that you Back up your system Close all open programs You might need to restart your computer after you complete this update To continue click Next Cancel Figure 9 Installing Microsoft Installer Click on J AGREE at the license agreement prompt Figure 10 and NEXT to start the installation Figure 11 You will then be prompted if and when the installation has been successful Figure 12 We suggest rebooting at this point Continue and backtrack to Step 2 1 once your system has rebooted or simply double click to run the dotnetfx20 exe NET Framework 2 0 installation file that you have previously downloaded and continue to Step 2 6 User Manual 135 Real Options Super Lattice Solver software manual Software Update Installation Wizard License Agreement Ay Please read the following license agreement To continue with setup you must accept the agreement SUPPLEMENTAL END USER LICENSE AGREEMENT FOR MICROSOFT SOFTWARE Supplemental EULA IMPORTANT READ CAREFULLY The Microsoft operating system components accompanying this Supplemental EULA including any online or electronic documentation OS Components are subject to the terms and conditions of the agreement under which you
116. f the same options but with a dividend yield Of course European Options can only be executed at termination and not before while in American Options early exercise is allowed versus a Bermudan Option where early exercise is allowed except during blackout or vesting periods Notice that the results for the three options without dividends are identical for simple call options but they differ when dividends exist When dividends are included the simple call option values for American gt Bermudan gt European in most basic cases as seen in Figure 39 insert a 5 dividend rate and blackout steps of 0 50 Of course this generality can be applied only to plain vanilla call options and do not necessarily apply to other exotic options e g Bermudan options with vesting and suboptimal exercise behavior multiples tend to sometimes carry a higher value when blackouts and vesting occur than regular American options with the same suboptimal exercise parameters Figure 38 Single Asset Super Lattice Solver File Help Comment American European and Bermudan Basic Call Options without Dividends Variable Name Value Starting Step v American v European Bermudan PV Underlying Asset Risk Free Rate Implementation Cost Dividend Rate Maturity Years 1 Volatility Lattice Steps 100 A inputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Optio
117. fact a dividend yield will decrease the value of a call option but increase the value of a put option This is because when dividends are paid out the value of the asset decreases Thus the call option will be worth less and the put option will be worth more The higher the dividend yield the earlier the call option should be exercised and the later the put option should be exercised The put option can be solved by setting the Terminal Node Equation as Max Cost Asset 0 as seen in Figure 40 example file used Plain Vanilla Put Option Puts have a similar result as calls in that when dividends are included the basic put option values for American gt Bermudan gt European in most basic cases You can confirm this by simply setting the Dividend Rate at 3 and Blackout Steps at 0 80 and re running the SLS module User Manual 62 Real Options Super Lattice Solver software manual Figure 40 Single Asset Super Lattice Solver File Help Comment American Put Option Make it European by setting INE OptionOpen or deselect Custom and select European Option Type eh Custom Variables o _ _ _ American Y European C Bermudan Custom Variable Value Starting Basic Inputs PV Underlying Asset 100 Risk Free Rate Implementation Cost 100 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option
118. g Asset 1000 Risk Free Rate Implementation Cost 1000 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Benchmark ma Max Asset Asset Contraction Savings Black Scholes 359 58 Closed Form American 359 58 Binomial European 359 52 Example Max Assat Cost 0 Binomial American 359 52 Custom Equations Result intermediate Node Equation Options Before Expiration American Option 1001 6361 European Option 1001 4524 Example Max Asset Cost OptionOpen intermediate Node Equation During Blackout and Vesting Period Exampie OptionOpen Figure 26 American and European Options to Contract with a 100 Step Lattice User Manual 46 Real Options Super Lattice Solver software manual Figure 27 Single Asset Super Lattice Solver File Help Comment Bermudan Contraction Option where contraction cannot occur at certain times Option Type A Crt Variables v American Z European V Bermudan Custom Variable Name Value Starting Step Contraction 09 0 Savings 50 0 sane Asset Risk Free Rate Implementation Cost 1000 DividendRate 0 Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Ste
119. hooser choose between Call and Put value exceeds Call Put due to ability to choose Bermudan WI Varia DASIC DU PV Underlying Asset Risk Free Rate Implementation Cost Dividend Rate Maturity Years l Volatility Lattice Steps All inputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Cost Cost Asset 0 Example Max Asset Cost 0 intermediate Node Equation Options Before Expiration Max Asset Cost Cost Asset OptionOpen Figure 41 American and European Exotic Chooser Option using SLS User Manual 64 Real Options Super Lattice Solver software manual A more complex Chooser Option can be constructed using the MSLS as seen in Figure 42 example Multiple Asset Option Module file used Exotic Complex Floating European Chooser and Figure 43 example file used Exotic Complex Floating American Chooser In these examples the execution costs of the call versus put are set at different levels An interesting example of a Complex Chooser Option is a firm developing a new technology that is highly uncertain and risky The firm tries to hedge its downside as well as capitalize its upside by creating a Chooser Option That is the firm can decide to build the technology itself once the research and development phase is complete versus selling the intellectual property of the technology both at d
120. iate steps For instance you can enter 000 as the lattice steps 0 400 as the blackout steps and some Blackout Equation e g OptionOpen This means that for the first 400 steps the option holder can only keep the option open Other examples include entering 3 5 10 if these are the lattice steps where blackout periods occur You will have to calculate the relevant steps within the lattice where the blackout exists For instance if the blackout exists in years 1 and 3 ona 10 year 10 step lattice then steps 1 3 will be the blackout dates This blackout step feature comes in handy when analyzing options with holding periods vesting periods or periods where the option cannot be executed Employee stock options have blackout and vesting periods and certain contractual real options have periods during which the option cannot be executed e g cooling off periods or proof of concept periods If equations are entered into the Terminal Node Equation box and American European or Bermudan Options are chosen the Terminal Node Equation you entered will be the one used in the super lattice for the terminal nodes However for the intermediate nodes the American option will assume the same Terminal Node Equation plus the ability to keep the option open the European option will assume that the option can only be kept open and not executed while the Bermudan option will assume that during the blackout lattice steps the option will be kept open and
121. ies themselves can be simulated ian ses ee ee eee eer a I J K Pesi 1 Downloaded Weekly Historical Stock Prices of Microsoft Volatility Computations 2 Date Open High Low Close Volume Adj Close E acre O 3 27 Dec 04 27 01 27 10 2668 2672 52388840 26 64 0 0108 17 87 4 20 Dec 04 27 01 27 17 26 78 27 01 77413174 26 93 0 0019 17 84 5 13 Dec 04 27 10 27 40 26 80 2696 108628300 26 88 0 0045 17 85 6 6 Dec 04 27 10 27 44 26 91 27 08 83312720 27 00 0 0055 18 00 One Year Annualized Volatility 7 29 Nov 04 26 64 27 44 2661 2723 83103200 27 15 0 0235 18 13 8 22 Nov 04 26 75 26 82 26 10 26 60 61834599 26 52 0 0098 18 03 Average 21 89 9 15 Nov 04 27 34 27 50 26 84 2686 75375960 26 78 0 0011 18 10 Median 22 30 10 8 Nov 04 29 18 30 20 2913 29 97 109385736 26 81 0 0223 18 20 11 41 Nov 04 28 16 29 36 2796 2931 85044019 26 22 0 0468 18 28 12 25 Oct 04 27 67 28 54 27 55 27 97 70791679 25 02 0 0084 17 71 13 18 Oct 04 28 07 28 89 27 58 27 74 74671318 24 81 0 0092 17 80 14 11 Oct 04 28 20 28 27 27 80 27 99 48396360 25 04 0 0000 19 68 15 4 Oct 04 28 44 28 59 27 97 27 99 52998320 25 04 0 0091 19 69 16 27 Sep 04 27 17 28 32 27 04 2825 61783760 25 27 0 0346 19 68 17 20 Sep 04 27 44 27 74 27 07 27 29 59162520 24 41 0 0082 19 62 18 13 Sep 04 27 53 27 57 26 74 27 51 51599880 2461 0 0008 20 52 19 7 Sep 04 27 29 27 51 27 14 2749 51935175 2459 0 0139
122. ifferent costs To further complicate matters you can use the MSLS to easily and quickly solve the situation where building versus selling off the option each has a different volatility and time to choose Figure 42 Multiple Asset Super Lattice Solver File Help PV Asset Volatility 5 Notes 60 25 Comment Exotic Complex Floating European Chooser Option can be either a call or put option Value Starting Step Blackout and Vesting Period Steps Cost Risk Free Div Steps Terminal Equation 55 5 0 100 Max Underlying Cost 0 OptionOpen COMBINATION 16 6035 65 5 0 100 Max Cost Underlying 0 OptionOpen 0 5 0 100 Max CallOption PutOption 0 OptionOpen Intermediate Equation Figure 42 Complex European Exotic Chooser Option using MSLS Figure 43 Multiple Asset Super Lattice Solver File Help Maturity Comment Exotic Complex Floating American Chooser Option either a call or put option PV Asset Volatility Notes 60 25 Value Starting Step Blackout and Vesting Period Steps Name Cost Risk Free Div Steps Terminal Equation CallOption 55 5 0 100 Max Underlying Cost 0 PutOption 65 5 O 100 Max Cost Underlying 0 Combination 0 5 0O 100 Max CallOption PutOption 0 Intermediate Equation Max Underlying Cost OptionOpen COMBINATION 16 8675 Max Cost Underlying OptionOpen Max CallOption PutOption OptionOpen Figure 43 Complex American Exotic Chooser
123. ility estimate is to combine both approaches if enough data exists That is from a DCF with many cash flow estimates compute the PV Cash Flows for periods 0 1 2 3 and so forth Then compute the natural logarithm of the relative returns of these PV Cash Flows The standard deviation is then annualized to obtain the volatility This is of course the preferred method and does not require the use of Monte Carlo simulation but the drawback is that a longer cash flow forecast series is required GARCH Approach Another approach is the GARCH Generalized Autoregressive Conditional Heteroskedasticity model which can be utilized to estimate the volatility of any time series data GARCH models are used mainly in analyzing financial time series data in order to ascertain its conditional variances and volatilities These volatilities are then used to value the options as usual but the amount of historical data necessary for a good volatility estimate remains significant Usually several dozens and even up to hundreds of data points are required to obtain good GARCH estimates In addition GARCH models are very difficult to run and interpret and require great facility with econometric modeling techniques GARCH is a term that incorporates a family of models can take on a variety of forms known as GARCH p q where p and q are positive integers which define the resulting GARCH model and its forecasts For instance a GARCH 1 1 model takes the form o
124. in Year 2 Hopefully positive net free cash flows CF will follow in Years 3 to 6 yielding a sum of PV Asset of 100M CF discounted at say a 9 7 discount or hurdle rate and the Volatility of these CFs is 30 At a 5 risk free rate the strategic value is calculated at 27 67 as seen in Figure 45 using a 100 step lattice which means that the strategic option value of being able to defer investments and to wait and see until more information becomes available and uncertainties become resolved is worth 12 67M because the NPV is worth 15M 100M 5M 85M In other words the Expected Value of Perfect Information is worth 12 67M which indicates that assuming market research can be used to obtain credible information to decide if this project is a good one the maximum the firm should be willing to spend in Phase I is on average no more than 17 67M i e 12 67M 5M if PI is part of the market research initiative or simply 12 67M otherwise If the cost to User Manual 66 Real Options Super Lattice Solver software manual obtain the credible information exceeds this value then it is optimal to take the risk and execute the entire project immediately at 85M The Multiple Asset module example file used is Simple Two Phased Sequential Compound Option In contrast if the volatility decreases uncertainty and risk are lower the strategic option value decreases In addition when the cost of waiting as described by the Dividend Rate
125. ing over time Of course other flavors of customizing the expansion option exist including changing the implementation cost to expand and so forth User Manual 50 Real Options Super Lattice Solver software manual Figure 29 Single Asset Super Lattice Solver File Help Comment American Option to Expand To change to European deselect Custom and select European Option Type Custom Variables_ 7 American V European ceo Cistom Variable Name Value Starting Step Expansion 2 0 Basic Inputs PV Underlying Asset 400 Risk Free Rate Implementation Cost 250 Dividend Rate Maturity Years 5 Volatility Lattice Steps 100 Allinputs are annualized rates Blackout Steps and Vesting Period For Custom amp Bermudan Option Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Benchmark Black Scholes 238 86 Closed Form American 238 86 Example Asset Binomial European 238 87 pinnae Binomial American 238 87 Custom Equations Result Intermediate Node Equation Options Before Expiration Custom Option 638 7315 Max Asset Expansion Cost OptionOpen Example Max Asset Cost OptionOpen Intermediate Node Equation During Blackout and Vesting Period Example OptionOpen Figure 29 American and European Options to Expand with a 100 Step Lattice User Manual 51 Real Options Super Lattice Solver software manual Figure 3
126. ions of products Figure 60 Be aware that certain combinations of inputs may yield an unsolvable lattice with negative implied probabilities If that result occurs a message will appear Try a different combination of inputs as well as higher lattice steps to compensate P3 Q3 P1 Ps Q4 rice i p ps quantity as P2 Q2 P6 Q6 Figure 60 Pentanomial Lattice Combining Two Binomial Lattice User Manual 83 Real Options Super Lattice Solver software manual Figure 61 shows an example Dual Asset Rainbow Option example file used MNLS Dual Asset Rainbow Option Pentanomial Lattice Notice that a high positive correlation will increase both the call option and put option values This is because if both underlying elements move in the same direction there is a higher overall portfolio volatility price and quantity can fluctuate at high high and low low levels generating a higher overall underlying asset value In contrast negative correlations will reduce both the call option and put option values for the opposite reason due to the portfolio diversification effects of negatively correlated variables Of course correlation here is bounded between 1 and 1 inclusive Figure 61 Multinomial Lattice Solver File Help Comment American Rainbow Call Option using Pentanomial Lattice Trinomial Mean Reverting T Quadranomial Jump Diffusion Pentanomial Rainbow Two Asset ariable PV Underying Asset
127. is copied down the entire column The formula in cell J3 is STDEV 13 154 SORT 52 which computes the annualized by multiplying the square root of the number of weeks in a year volatility by taking the standard deviation of the entire 52 weeks of the year 2004 data The formula in cell J3 is then copied down the entire column to compute a moving window of annualized volatilities The volatility used in this example is the average of a 52 week moving window which covers two years of data That is cell L8 s formula is AVERAGE J3 J54 where cell J54 has the following formula STDEV I54 1105 SORT 52 and of course row 105 is January 2003 This means that the 52 week moving window captures the average Go to http finance yahoo com and enter a stock symbol e g MSFT Click on Quotes Historical Prices and select Weekly and select the period of interest You can then download the data to a spreadsheet for analysis User Manual 104 Real Options Super Lattice Solver software manual volatility over a 2 year period and smoothes the volatility such that infrequent but extreme spikes will not dominate the volatility computation Of course a median volatility should also be computed If the median is far off from the average the distribution of volatilities is skewed and the median should be used otherwise the average should be used Finally these 52 volatilities can be fed into Monte Carlo simulation Risk Simulator software and the volatilit
128. k Free Rate 4 5 Implementation Cost 90 DividendRate 0 Maturity Years 5 Velatily 5 Lattice Steps 10 Allinputs are annualized rates ee Example 1 2 10 20 35 Terminal Node Equation Options at Expiration Max Asset Salvage Example Max Asset Cost 0 Custom Equations Intermediate Node Equation Options Before Expiration Max Salvage OptionOpen Example Max Asset Cost OptionOpen intermediate Node Equation During Blackout an Figure 19 Simple American Abandonment Option See the section on Expansion Option for more examples on how this startup s technology can be used as a platform to further develop newer technologies that can be worth a lot more than just the abandonment option User Manual 37 Real Options Super Lattice Solver software manual Option Valuation Audit Sheet Assumptions Intermediate Computations PV Asset Value 120 00 Stepping Time dt Implementation Cost 90 00 Up Step Size up Maturity Years 5 00 Down Step Size down Risk free Rate 5 00 Risk neutral Probability Dividends 0 00 Volatility 25 00 Results Lattice Steps 10 Auditing Lattice Result 10 steps Option Type Custom Super Lattice Result 10 steps User Defined Inputs Terminal Max Asset Salvage Intermediate Max Salvage Name BEE ess ae a re Value oca ee fe I e I I O EEE StatingStep oT Underlying Asset Lattice 589 03 120
129. l e g revenues of 100 200 300 400 500 versus a 10 proportional EBITDA of 10 20 30 40 50 yields identical 20 80 volatilities Finally taking the oil and gas example a step further computing the volatility of revenues assuming no other market risks exist below this revenue line in the DCF is justified because this firm may have global operations with different tax conditions and financial leverages different ways of funding projects The volatility should only apply to market risks and not private risks how good a negotiator the CFO is on getting foreign loans or how shrewd your CPAs are in creating offshore tax shelters Now that you understand the mechanics of computing volatilities this way we need to explain why we did what we did Merely understanding the mechanics is insufficient in justifying the approach or explaining the rationale why we analyzed it the way we did Hence let us look at the steps undertaken and explain the rationale behind them Step 1 Collect the relevant data and determine the periodicity and time frame You can use forecast financial data cash flows from a DCF model comparable data comparable market data such as sector indexes and industry averages or historical data stock prices or price of oil and electricity Consider the periodicity and time frame of the data In using forecast and comparable data your choices are limited to what is available or what models have been built and are t
130. l is useful in generating ballpark estimates of the true real options value especially for more generic type calls and puts For more complex real options analysis different types of exotic options are required Definitions of Variables S present value of future cash flows X implementation cost r risk free rate T time to expiration years O volatility D cumulative standard normal distribution Computation In S X r 0 2 T r n S X r o7 2 T Call SO Xe i ovT i ovT l Pu xeta meeer sof usin ee oVT oVT User Manual 120 Real Options Super Lattice Solver software manual Black and Scholes with Drift Dividend European Version This is a modification of the Black Scholes model and assumes a fixed dividend payment rate of q in percent This can be construed as the opportunity cost of holding the option rather than holding the underlying asset Definitions of Variables present value of future cash flows implementation cost risk free rate time to expiration years volatility cumulative standard normal distribution continuous dividend payout or opportunity cost Legana Computation oVT oVT T In S X r q 0 2 T ST In S X r q 0 2 T T S a E ee ge e E A ut OMT e oJT 2 2 Cai Se af BEI tt gte ar reef ED tege ar User Manual 121 Real Options Super Lattice Solver software manual Black and Scholes with Future Pay
131. lex Sequential Compound Option In reality an R amp D project will yield intellectual property and patent rights that s the firm can easily license off Abandon PHASE Ill _ e In addition at any phase the project s g development can be slowed down Contract or accelerated Expand depending on the outcome of each phase PHASE Il CONTRACT ABANDON PHASEI END ABANDON o END START An NPV analysis cannot account for these options to make midcourse corrections over time when uncertainty becomes resolved END Figure 48 Graphical Representation of a Complex Multi Phased Sequential Compound Option User Manual 70 Real Options Super Lattice Solver software manual Figure 49 Multiple Asset Super Lattice Solver File Help Comment Multiple Phased Complex Sequential Compound Option PV Asset Volatility Notes Name Value Starting Step 100 25 Salvage 100 31 Salvage 30 11 Salvage 80 0 Contract 0 9 0 Expansion 15 0 0 Savings 20 Cost Risk Free Div Steps Terminal Equation Intermediate Eq 50 5 0 50 Max Underlying Expansion Cost Underlying Salvage Max Underlying PHASE1 134 0802 0 30 Max Phase3 Phase3 Contract Savings Salvage 0 Max Phase3 Co 0 10 Max Phase2 Salvage 0 Max Salvage Opt E Create Audit Sheet Figure 49 Solving a Complex Multi Phased Sequential Compound Option using MSLS To illustrate Figure 49 s MSLS path dependent sequential option us
132. lower the up and in barrier option value will be as more of the option value is lost due to the inability to execute when the asset value is below the barrier example file used Barrier Option Up and In Upper Barrier Call For instance e When the upper barrier is 110 the option value is 41 22 e When the upper barrier is 120 the option value is 39 89 In contrast an Up and Out Upper American Barrier Option is worth a lot less because this barrier truncates the option s upside potential Figure 65 shows the computation of such an option Clearly the higher the upper barrier the higher the option value will be example file used Barrier Option Up and Out Upper Barrier Call For instance e When the upper barrier is 110 the option value is 23 69 e When the upper barrier is 120 the option value is 29 59 Finally note the issues of nonbinding barrier options Examples of nonbinding options are e Up and Out Upper Barrier Calls when the Upper Barrier lt Implementation Cost then the option will be worthless e Up and In Upper Barrier Calls when Upper Barrier lt Implementation Cost then the option value reverts to a simple call option Examples of Upper Barrier Options are contractual options Typical examples are e A manufacturer contractually agrees not to sell its products at prices higher than a pre specified upper barrier price level e A client agrees to pay the market price of a good or product until a cert
133. lues for the total value of the strategy Figure 34 Single Asset Super Lattice Solver File Help Comment American Option to Expand Contract and Abandon To make it European simple change INE to OptionOpen V European F Bemudan Variable Name Value Starting Step BIVANI SEN RE SME mn ASTE I Expansion 13 i ExpandCost 25 PV Underlying Asset Risk Free Rate Contraction 0 9 implementation Cost Dividend Rate aci ee 100 Maturity Years Volatility Lattice Steps Al inputs are annualized rates Reds ee ee Del wp DELLO Terminal Node Equation Options at Expiration Max Asset Asset Expansion ExpandCost Black Scholes 26 00 3 88 Asset Contraction ContractSavings Salvage Closed Form American 2600 641 Binomial European 26 00 3 88 Binomial American 26 00 6 44 Call Put ee 117 4220 European Option 116 3954 Figure 34 American European and Custom Options to Expand Contract and Abandon User Manual 56 Real Options Super Lattice Solver software manual Figure 35 illustrates a Bermudan Option with the same parameters but with certain blackout periods example file used Expand Contract Abandon Bermudan Option while Figure 36 example file used Expand Contract Abandon Customized Option J illustrates a more complex Custom Option where during some earlier period of vesting the option to expand does not exist yet perhaps the technology being developed is not yet mature
134. ments European Version Here cash flow streams may be uneven over time and we should allow for different discount rates risk free rate should be used for all future times perhaps allowing for the flexibility of the forward risk free yield curve Definitions of Variables S present value of future cash flows X implementation cost r risk free rate T time to expiration years O volatility D cumulative standard normal distribution q continuous dividend payout or opportunity cost CF cash flow at time i Computation S S CFe CF e CF e S 9 CFe i l ovT oVT Put xeo ee Abeer a steal ee eter a 2 e Call s a E LO i ica ar era X r q 0 ar oVT oVT User Manual 122 Real Options Super Lattice Solver software manual Chooser Options Basic Chooser This is the payoff for a simple chooser option when lt T or it doesn t work In addition it is assumed that the holder has the right to choose either a call or a put with the same strike price at time t and with the same expiration date T For different values of strike prices at different times we need a complex variable chooser option Definitions of Variables S present value of future cash flows X implementation cost r risk free rate ti time to choose between a call or put years T time to expiration years O volatility D cumulative standard normal distribution q continuou
135. mple Volatility computation file go to Start Programs Real Options Valuation Real Options SLS and select the relevant module