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

Mun P.D. Trading real options analysis course - business cases and software applic - Wiley publishing , 2003. - 318 p.
ISBN 047-43001-3
Download (direct link): tradingohnathan2003.pdf
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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)
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%
Volatility Measure:
Logarithmic Returns Volatility 11.67% 0.0968 -0.1660 -0.0544 -0.1310
FIGURE 3.6 Applying Monte Carlo simulation on a DCF model.
(product lifecycle) all can be stochastically accounted for in the model. In contrast, more advanced stochastic uncertainties can be modeled through the use of interacting and correlated stochastic processes. To illustrate, suppose the project under consideration is a utility power plant. The revenues generated are simply the multiplication of prices and quantity demanded. However, prices may be modeled after a mean-reversion with Poisson jumpdiffusion stochastic process, while quantity demanded may be modeled as an impulse-response function process, but negatively correlated to the price of electricity. This negative correlation only holds for a particular price trench when the price elasticity of demand is highly elastic, but drops off at a lower price level (Figure 3.6).
These interacting stochastic processes and variables should not be modeled separately in a real options approach but modeled together, flowing into and through a DCF model. The DCF model will filter out all the interacting relationships, causalities, correlations, and co-movements among
46
FRAMING REAL OPTIONS
variables. Otherwise, modeling these stochastic variables in real options lattices will yield mathematically intractable models—each stochastic variable will now have its own binomial lattice, and modeling n stochastic variables will yield a 2n-nomial. For instance, modeling 2 stochastic variables will yield a quadranomial with 4 branches on a lattice at each node, and 5 variables a 32-branch multinomial lattice! The mathematical complexity involved in calculating a 32-branch multinomial lattice is staggering and should not be attempted. In contrast, the analyst can model in as many stochastic variables as he or she chooses in the DCF using Monte Carlo simulation, watch how they interact with each other through the DCF, and capture the resulting cashflow stream as input into the real options modeling paradigm.
STEP 5: FRAMING THE REAL OPTIONS
Now that the DCF models have been created for the projects that survived an initial management screening process, what next? Which projects should undergo a real options analysis? Should all projects be scrutinized this closely? The answer comes in several parts:
? Projects that are close to at-the-money or slightly in-the-money or slightly out-of-the-money will benefit most from a real options analysis.
? Projects that are lumped together and hard to separate or prioritize from a DCF standpoint can benefit greatly from real options analysis.
? Projects that face great uncertainty in the future but yet possess an element of flexibility to hedge against downsides and capture the upside premiums can benefit greatly from real options analysis.
? Projects that by themselves produce little value but when viewed in their entirety, accounting for strategic downstream opportunities they create, can benefit greatly from real options analysis.
One powerful visualization method to observe the “clumping” of project valuation is the use of a three-dimensional (3D) option space as shown in Figure 3.7. The horizontal axis is a measure of a project’s profitability index (Q-Ratio), that is, the ratio of the sum of present value of future net cash flows to the sum of the present value of investment or implementation costs. The former is discounted at a market-risk adjusted discount rate of return and the latter using the risk-free rate, to account for differences between market risk and private risks. A Q-Ratio greater than one means that the NPV is positive and the project is financially feasible and profitable, whereas a Q-Ratio less than one means the NPV is negative. Break-even projects have a Q-Ratio of one.
Step 5: Framing the Real Options
47
Profitability Index (Q Ratio = S X)
0 NPV < 0 Unprofitable 1.0 NPV > 0 Profitable
lower
"7-
o
Call option value increases in these directions
?o
c
IB
higher
FIGURE 3.7 Option value in 3D space. The option value increases with increases in the volatility and value to cost.
The vertical axis measures the volatility index, essentially the standard deviation of the NPV or IRR value after performing Monte Carlo simulation, multiplied by the square root of the project’s maturity in years. The project’s maturity in years can be calculated either as the amount of time left to implement the project, or the project’s economic life. Either way, as long as the calculation is applied consistently across all projects, the volatility index indicates a project’s uncertainty, adjusted for time. A higher volatility index implies a higher option value but a potentially risky project. Figure 3.8 illustrates a completed 3D option space matrix.
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