# Trading real options analysis course - business cases and software applic - Mun P.D.

ISBN 047-43001-3

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The next step is to run a stochastic optimization analysis. That is, given the uncertain environment of multiple interacting stochastic variables, you

Underlying Asset Lattice

1265.09 1421.64

1125.79

1597.56 1795.25 2017.41 2267.05 2547.58 2862.83 3217.09 3615.19 4062.55

1265.09 1421.64 1597.56 1795.25 2017.41 2267.05 2547.58 2862.83 3217.09

1001.82 1125.79 1265.09 1421.64 1597.56 1795.25 2017.41 2267.05 2547.58

891.50 1001.82 1125.79 1265.09 1421.64 1597.56 1795.25 2017.41

793.33 891.50 1001.82 1125.79 1265.09 1421.64 1597.56

705.97 793.33 891.50 1001.82 1125.79 1265.09

628.23 705.97 559.05 793.33 628.23 497.49 891.50 705.97 559.05 442.71 1001.82 793.33 628.23 497.49 393.96

Equity Lattice

740.69 869.83

575.64

1017.22 1185.08 1375.94 1592.69 1838.65 2117.55 2433.60 2791.53 3196.66

685.50 811.72 956.14 1120.89 1308.47 1521.77 1764.09 2039.17 2351.20

426.23 517.85 624.42 747.45 888.63 1049.97 1233.91 1443.38 1681.69

292.73 366.21 453.75 556.71 676.36 814.07 971.59 1151.51

177.51 231.86 299.56 382.36 481.60 597.98 731.67

85.86 119.46 164.72 224.63 302.12 399.20

25.24 38.45 0.00 58.57 0.00 0.00 89.22 0.00 0.00 0.00 135.92 0.00 0.00 0.00 0.00

Valuation Lattice

429.48 536.65

261.86

663.76 812.44 984

342.38 442.50 564

125.90 176.06 244

35.01 53

0

.19 1180.86 1405.70

.39 709.06 875.52

.26 335.61 455.68

.33 81.24 123.76

.00 0.00 0.00

0.00 0.00

0.00

FIGURE 7.11 Resulting underlying asset lattice, equity lattice, and valuation lattice.

Combining Forecasting, DCF Modeling, Real Options, and Optimization

209

know that the asset value of the project is highly volatile. Given this uncertainty, what is the optimal level of royalty rates that should be paid over time such that the best outcome can be guaranteed at a certain probability, subject to satisfying some constraints? By contractual agreement, the firm must pay a royalty rate between 5 percent and 10 percent for the first 2 years, between 10 percent and 15 percent for the following 2 years, and between 10 percent and 20 percent in year 5. This result is seen through the first step in the optimization process using OptQuest (Figure 7.12).

Next, by internal management-set constraints, the total amount of royalties paid for the next 5 years should fall between 20 percent and 50 percent (Figure 7.13). Next, the optimization is set to maximize the mean of the total project expanded net present value (ENPV), including the strategic options value, at the same time satisfying the requirement that at least 90 percent of the time, the project should yield at least $400 million in NPV (Figure 7.14). The stochastic optimization is run for 10 minutes to produce an initial answer (Figure 7.15).

FIGURE 7.12 Decision variable selection in OptQuest.

FIGURE 7.13 Setting up constraints in OptQuest.

v Forecost Selection: Select on objective and ony requirements {reqs. must hove a bound).

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Requirement * NPV Percentile (90) - 100 Step byStepAnalyciCJdc Step II - DCF J0

IMfl T Vniniiiiiy Wfinn Step hyfilpp Annt/sift vis fltftp II DCF F4I

FIGURE 7.14 Setting up the objective in OptQuest.

210

EXTENDED PROBLEMS

FIGURE 7.15 OptQuest’s stochastic optimization preferences.

Based on running 1,000 simulation trials for each optimization set, the results indicate that the optimal decision is to provide a 5 percent royalty rate for the first 2 years, see what happens, then increase the royalty rate to 10 percent for the third and fourth years, before going to 20 percent the final year (Figure 7.16). Based on these royalty rates, the project will yield at least $400 million in NPV while maximizing the overall strategic profitability of the project and at the same time still satisfying management and other legal contractual obligations.

Finally, based on the performance graph, it would seem that these royalty rates are the most efficient and optimal, and that slight variations from these rates will yield fairly insignificant increases in value (Figure 7.17).

r" Status and Solutions

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Simulation MmimizR Ohjprtivp ENPV Mean RnquirnrnRnt NPV 4UU <- Pcrccntilc (aU) Royalty 2003 Royalty 2004 Royalty 2005 Royalty 2006 Royalty 2007

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? 479 114 4751?«) 5 5933F-n? 5 221 RF-fl? fl 107451 0101703 0115F4F

11 31 500.154 502.071 444.145 442.340 6.4312E-D2 5 9495E-02 5.0 D00E-D2 5.0 D00E-D2 0.100000 0.100000 0.100000 0.100000 0.185688 0.190505

~T Best 4U bub.ai 2 14b.«/2 b UJUUt-U2 b.tllWUh-U2 UllUUUU U.llUUUU 0.21UUUI

FIGURE 7.16 OptQuest’ s status and solutions screen.

Combining Forecasting, DCF Modeling, Real Options, and Optimization

211

FIGURE 7.17 Resulting performance graph.

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