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

ISBN 047-43001-3

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5 00 5.00 5.00 5.00 500 6.00 5 00 5.00 5.00

5 00% 5.00% 5 00% 5 00% 5.00% 5 00% 6.00% 6.00% 5 00%

5 00% 5.00% 5 00% 5 00% 5.00% 5 00% 6.00% 5.00% 5 00%

50 00% 50.00% 5000% 50 00% 50 00% 50.00% 50 00% 50.00% 60.00%

Call Up-ln. Down-ln $49.57 $57.53 $46.84 $49.59 $49.54 $54.01 $51.01 $47.16 $55.97

Put Up-ln. Down-ln $27.39 $25.35 $32.39 $27.47 $27.33 $28.07 $25.02 $26.05 $33.85

Call Up-Out. Down-Out $0.02 $0.02 $0.01 $0.00 $0.06 $0.01 $0.02 $0.02 $0.00

Put Up-Out. Down-Out $0.09 $0.08 $0.13 $0.01 $0.15 $0.03 $0.09 $0.09 S0.01

2. Replicate the analysis using a Standard Lower-Barrier Option model.

InputG

Standard Lower-Barrier Option

Asset Value $100.00 $110.00 S100 00 S100 00 $100.00 S100 00 $100 OC S100 00 $100.00

Implementation Cost $90.00 S90 00 $100.00 S90 00 $90.00 S90 00 $90.00 S90 00 $90.00

Artificial Barrier $85.00 S85 00 S85 00 $95.00 $85 00 S85 00 $85.00 $85 00 $85 00

Cash Rphate so no $0 00 so no so nn $10.00 sn nn sn nn so nn so nn

Time to Maturity 1.00 too 1.00 1.00 1 00 2.00 1 00 1 00 1.00

Risk-Free Rate 5 00% 5.00% 5.00% 5.00% 5 00% 5.00% 6.00% 5.00% 5 00%

Dividend Rate 0 00% 0.00% 0.00% 0.00% 0 00% 0.00% 0 00% 2.00% 0.00%

Volatility 20 00% 20 00% 20.00% 20.00% 20 00% 20.00% 20 00% 20 00% 30.00%

Down-and-ln Call Option $1.36 $0.44 $0.50 $8.85 $7.38 $3.77 $1.36 $1.31 $4.11

Down-and-Out Call Option $15.34 $24.92 $9.95 $7.85 $18.93 $18.27 $15.99 $13.81 $15.59

Down-and-ln Put Option $2.28 $0.95 $492 $2.31 $8.31 $3.46 $2.08 $2.69 $5.30

Down-and-Out Put Option $0.03 $0.02 $0.66 $0.00 $3.61 $0.01 $0.03 $0.03 $0.01

Stochastic Timing Options

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3. Replicate the analysis using a Standard Upper-Barrier Option model.

Standard Upper-Barrier Option 1

Inputs

Asset Value Implementation Cost Artificial Bamer Cash Rebate Time to Maturity Risk-Free Rate Dividend Rate Volatility $100.00 $110.00 S100.00 S100.00 $100.00 $100.00 $100 00 $100 00 $100 00

$90 00 S90.00 $100.00 $90.00 $90.00 S90 00 $90 00 $90 00 $90 00

$120.00 $120.00 S120.00 $130.00 $120.00 $120.00 5120 00 $120 00 $120 00

S20.00 S20.00 S20.00 S20.00 $30.00 $20 00 $20 00 $20 00 $20 00

2.00 2 00 2 00 2 00 2 00 3.00 200 200 200

5.00% 5 00% 5 00% 5 00% 5 00% 5 00% 6.00% 5 00% 5 00%

0.00% 0 00% 0 00% 0 00% 0 00% 0 00% 0 00% 1.00% 0.00%

30.00% 30.00% 30.00% 30.00% 30 00% 30 00% 30 00% 30 00% 40.00%

Up-and-ln Call Option $31.57 $36.73 $26.93 $32.95 $34.52 $35.83 $32.22 $30.33 $35.55

Up-and-Out Call Option $13.68 $16.87 $13.27 $12.02 $20.23 $1446 $13.85 $13.41 $14.36

Up-and-ln Put Option $7.81 $5.75 $9.27 $9.13 $10.76 $7.71 $7.32 $8.16 $9.62

Up-and-Out Put Option $18.87 $19.29 $21.41 $17.28 $25.43 $20.05 $18.57 $19.00 $21.73

STOCHASTIC TIMING OPTIONS

Stochastic timing options are very powerful tools in real options analysis. Please refer to my previous book, Real Options Analysis, for a detailed discussion of the specifics. Briefly, a timing option provides the holder the option to defer making an investment decision until a later time without much restriction; that is, competitive or market effects (market share erosion, first to market, strategic positioning, etc.) have negligible effect on the value of the project. Assuming that this situation holds true, then shifting a project for execution in the future depends on only two factors: (1) the rate of growth of the asset over time; and (2) the discount rate or rate of erosion of the time value of money. For instance, putting off a project to the future provides a higher return due to the growth rate in asset over time, but at the same time, returns are eroded because value obtained in the future is less valuable than value obtained today by virtue of time value. A highly simplified example includes when to cut down a tree for its lumber. If the tree’s growth rate is substantial, the longer we wait, the more wood can be obtained. However, the higher the discount rate, the cost of money, or opportunity cost, the sooner the tree should be cut down. Therefore, what is the optimal time to wait before cutting down the tree?

Table 6.2 illustrates an example of stochastic timing options, where if the asset value at Time 0 is equivalent to the implementation cost $100, the discount rate is assumed to be 25 percent, and the corresponding risk-free rate is 5.5 percent, the calculated optimal time to execution is 4.52 years. Notice that the period 4.52 years provides the maximum NPV. Hence, this

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REAL OPTIONS BUSINESS CASES

TABLE 6.2 Optimal Timing Option with Maximum Calculated NPV

Time NPV ($)

1.00 4.40

2.00 7.05

3.00 8.47

4.00 9.05

4.52 9.12 This is the maximum NPV

5.00 9.07

6.00 8.72

7.00 8.16

8.00 7.48

Notes: Assumptions are Asset Value at time 0 is $100; Fixed Implementation Cost is $100; Discount Rate 25%; Growth Rate of Underlying Asset 5.5%; Calculated Optimal Time to Execution 4.52.

maximum NPV of $9.12 is the option value of waiting, as compared to $100 - $100 = $0 NPV if the project is executed immediately. The analysis is manually verified by shifting the asset value out to the corresponding times of execution. The maximum value is obtained at 4.52 years. The same results can be obtained using the software’s Stochastic Timing Option model.

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