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

ISBN 047-43001-3

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2. Recalculate the option value only for an expansion option. The option value is $14.49 ($114.49 ENPV less $100.00 PV Asset Value).

Option to Choose

133

3. Recalculate the option value only for a contraction option. The option value is $15.00 ($115.00 ENPV less $100.00 PV Asset Value).

4. Recalculate the option value only for an abandonment option. The option value is $6.32 ($106.32 ENPV less $100.00 PV Asset Value).

American Abandonment Option

Step 0 Step 1 Step 2

Ur da bin Assel Piiuvi Ladiu:

100 00 11C.10 134 99

06.07 100 00

74 08

I lelp

Input Parameterii

Expiration in Years 5.00

Volatility 15.00%

PV Asset Value $100.00

Riak-Free Rate 5.00%

Dividend l tate u.uu%

Salvage Value $100.00

Tnlnmnixlr* fV4 ii/ili:itiN

Number of Time Steps G

Time Step Size (dt) 1.0000

Up Jump Size (u) Down Jump Size (d) 1.1618 0.8607

Riak-Neutral Probability (p) 63 28%

Results

Binorr al Approach hNI V $106.32

Super Lattice luuustepc ^|B $106.44

Step 3 Step 4 Step 5

15G.G3 102.21 211.70

11C.1B 134.99 156.03

86 07 100.00 116.18

63 76 74.08 86.07

54.88 63.76

47.24

Reahoobans value antTvffdif?i?e- i 0 1 o

- ‘'•?.V Aband

Preei"rn Tunc vauc llnflerlying

Coat k.'?tr? ot9fo??r

Show Lattice | | show S Sterx:

- opt or valuation Lance -

106.32 11860

13b 58 166.83 182^1 211./0

106.89 117.88 134.99 166.83

100 00 100.00 104.86 116.18

100.00 100.00 100.00

100.00 100.00

100.00

Lattice-------------------------------------------------------

continue continue continue continue continue hnd

Abandon continue continue continue hnd

Abandon Abandon continue hnd

Abandon Abandon Abandon

Abandon Abandon Abandon

134

REAL OPTIONS BUSINESS CASES

5. Compare the results of the sum of these three individual options in Questions 2 through 4 with the results obtained in Question 1 using the option to choose (contract, expand, and abandon).

a. Why are the results different?

The option to choose is $19.03, compared to $35.81 ($14.49 + $15.00 + $6.32) for the sum of all three individual options. The results are different because of the mutually exclusive and independent characteristics of these real options. That is, at each node, management can only execute one of three options, not two or three options at the same time. By valuing the options separately, for instance, on certain nodes at the terminal period, each of the three options are executed at the same time, which cannot happen in reality.

b. Which value is correct?

The option to choose result is correct because it avoids any complications of redundant option values and multiple option executions.

6. Prove that if there are many interacting options, and if there is a single dominant strategy, the value of the project’s option value approaches this dominant strategy’s value; that is, perform the following steps, then compare and explain the results.

a. Reduce the expansion cost to $1.

Reducing the expansion cost to $1 means that it becomes more optimal to expand, thereby making expansion the dominant strategy. The resulting option analysis value is $130.48, which approximates the expansion option value alone, of $129 (the 1.3 expansion factor multiplied by the $100 asset value less $1 implementation cost). The remaining $1.48 comes from the other options as well as the errors stemming from using only 5 steps in the binomial lattice.

b. Increase the contraction savings to $100.

With such a high salvage value, it is optimal to abandon the project more often. Thus, the abandonment option is the dominant strategy. The resulting real options analysis provides a value of $190 (0.9 contraction factor multiplied by $100 plus the $100 savings value). The rest of the option values are insignificant.

c. Increase the salvage value to $150.

Similarly, with the high salvage value of $150, it is optimal to abandon the project more often. The resulting value is $150, indicating that abandonment is the optimal strategy.

Option to Choose

135

d. What inferences can you make based on these results?

If there are a few dominant real options strategies in an analysis, the value of the strategic options approaches these dominant strategy values. Valuing too many options is sometimes irrelevant because dominated strategies tend to have little value and will not change the results of the analysis.

Input Parameters IliputPdldllletelS

Expiration in Years 5.00 Expiration in Years 5.00

Volatility 15.00% Volatility 15.00%

PV Asset Value $100 00 PV Asset Value $100.00

Risk-free Rate 5.00% Risk-free Rate 5 00%

Dividend Rate 0 00% Dividend Rate 0 00%

Expansion Factor 1.30 Expansion Factor 1.30

Expansion Cost $1.00 Expansion Cost $20.00

Contraction Factor 0 90 Contraction Factor 0.90

Contraction Savings $25 00 Contraction Savings $100.00

Salvage Value $100.00 Salvage Value $100 00

Results Binomial Approach ENPV $130.4752 American Closed Form (Expand) $129.2212 Black-Scholes (Expand Only) $129.2212 Resits Binomial Approach ENPV $190.0000 American Closed Form (Expand) $114.4240 Black-Scholes (Expand Only) $114.4240

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