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

ISBN 047-43001-3

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The second step is to create a discounted cash flow (DCF) model using the forecast revenues as shown in Figure 7.8. The following illustrates a simple DCF model. As the revenues are based on the forecast values with distributional assumptions, the resulting NPV will have Monte Carlo simulation performed as well. In addition, other stochastic variable inputs affecting the DCF model can also be accounted for. As an example, several adjustments to revenues such as competitive effects, cannibalization by other product substitutes, and market saturation effects are stochastic and unknown in the future. However, management can decide what the potential ranges of effects may be over time. These stochastic variables are linked to the DCF model and the resulting stream of net cash flows will be stochastic. Using the logarithmic cash-flow-returns approach, the asset’s volatility is estimated at 11.67 percent. The calculated volatility is also a distribution of values as the inputs into the DCF model are distributions of values.

TABLE 7.1 Crystal Ball Predictor Forecast Results

Date Lower: 5% Forecast Upper: 95%

Q1 2003 194.53 202.27 210.02

Q2 2003 202.15 210.25 218.35

Q3 2003 208.78 217.26 225.74

Q4 2003 221.39 230.30 239.21

Q1 2004 222.42 231.80 241.17

Q2 2004 229.96 239.86 249.76

Q3 2004 236.34 246.81 257.29

Q4 2004 249.47 260.60 271.73

Q1 2005 249.45 261.33 273.20

Q2 2005 256.75 269.47 282.19

Q3 2005 262.67 276.37 290.07

Q4 2005 276.06 290.90 305.74

Q1 2006 274.66 290.85 307.04

Q2 2006 281.27 299.08 316.89

Q3 2006 286.13 305.93 325.72

Q4 2006 298.93 321.20 343.47

Q1 2007 294.93 320.38 345.82

Q2 2007 299.00 328.69 358.38

Q3 2007 299.86 335.48 371.11

Q4 2007 306.97 351.50 396.03

Combining Forecasting, DCF Modeling, Real Options, and Optimization

207

Step II: DCF

- Input Parameters -------------

Discount Rate (Cash Flow) Discount Rate (Impl. Cost) Tax Rate

15.00%

5.00%

10.00%

Results -----------------------

Present Value (Cash Flow) Present Value (Impl. Cost) Net Present Value

$1,265.09

($865.90)

$399.20

Year 2003 2004 2005 2006 2007

Revenue $860.08 $979.07 $1,098.06 $1,217.06 $1,336.05

Adjustment to Revenue $51.60 $97.91 $197.65 $316.43 $467.62

Cost of Revenue $86.01 $97.91 $109.81 $121.71 $133.60

Royalties Paid $43.00 $48.95 $164.71 $182.56 $200.41

Gross Profit $679.46 $734.30 $625.90 $596.36 $534.42

Operating Expenses $135.89 $146.86 $125.18 $119.27 $106.88

Depreciation Expense $10.00 $10.00 $10.00 $10.00 $10.00

Interest Expense $100.00 $100.00 $100.00 $100.00 $100.00

Income Before Taxes $433.57 $477.44 $390.72 $367.09 $317.54

Taxes $43.36 $47.74 $39.07 $36.71 $31.75

Income After Taxes $390.21 $429.70 $351.65 $330.38 $285.78

Non-Cash Expenses $4.30 $4.90 $16.47 $18.26 $20.04

Cash Flow $394.51 $434.59 $368.1 2 $348.63 $305.82

Implementation Cost ($200.00) ($200.00) ($200.00) ($200.00) ($200.00)

FIGURE 7.8 Second step in the analysis: creating a DCF model.

Notice that another variable of interest is the royalty rate paid to the patent holders. These rates are subject to negotiation and as such are decision variables. These decision variables are to be used in a later step of stochastic optimization (Figure 7.9).

The next step is to input the results from the DCF and simulation analyses into the real options paradigm (Figure 7.10). The resulting present value of future cash flows now becomes the starting asset value in the real options analysis. The present value of implementation costs now becomes the implementation cost of the underlying option. The volatility of the simulated cash-flow stream now becomes the input volatility to the analysis. The other

Adjustment to Revenue: 2003 2004 2005 2006 2007

Competitive Effects 1.00% 2.00% 3.00% 4.00% 5.00%

Cannibalization Effects 5.00% 8.00% 10.00% 12.00% 15.00%

Market Saturation 0.00% 0.00% 5.00% 10.00% 15.00%

Adjustment to Revenue: 2003 2004 2005 2006 2007

Royalty Rate 5.00% 5.00% 15.00% 15.00% 15.00%

Minimum Rate 5.00% 5.00% 10.00% 10.00% 10.00%

Maximum Rate 10.00% 10.00% 15.00% 15.00% 20.00%

Maximum Total Rate 50.00% Minimum Total Rate 20.00%

Volatility Measure:

Logarithmic Returns 0.0968 -0.1660 -0.0544 -0.1310

Volatility 11.67%

FIGURE 7.9 Simulation assumptions, forecasts, and decision variables.

208

EXTENDED PROBLEMS

Step III: Real Options Analysis

Input Assumptions

Present Value of Future Cash Flows (asset) $1,265.09

Implementation Cost (cost) $865.90

Volatility (volatility) 11.67%

Maturity (maturity) 10

Risk-Free Rate (rf) 5.00%

Binomial Lattice Steps (steps) 10

Second Phase Implementation Cost (cost 2) $432.95

Time to Second Phase (time2) 5

Intermediate Calculations

Time Step (dt) 1.00

Up Jump (up) 1.1237

Down Jump (down) 0.8899

Risk-Neutral Probability (prob) 0.6901

- Results--------------------------------------------------------

Binomial Lattice Result I 429.48 ~|

FIGURE 7.10 Step three in the analysis: applying real options analysis.

input parameters are based on the initial set of assumptions. Then, a binomial approach is applied to value the sequential compound option. The resulting underlying asset lattice, equity lattice, and valuation lattice are shown in Figure 7.11.

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