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

ISBN 047-43001-3

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Stepping Time Up Step-Size (up)

Down Step-Size (down) Risk-neutral Probability (prob)

Then complete the underlying asset lattice. The only required computation here is the up and down step sizes calculated previously.

Option to Contract

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Underlying Asset Lattice Asset x up5 $1000 x 1.6487s = $12182.5

Asset x up4 $1000 x 1.64874 = $7389.1

Assetxup3 $1000 x 1.64873 = $4481.7

Asset x up2 $1000 x 1.64872 = $2718.2

Assetxup $1000 x 1.6487 = $1648.7

Asset $1000.0 Asset x down x up $1000x 1.6487 x 0.6065 = 1000.0

Asset x down $1000 x 0.6065=$606.5

Asset x up x down3 $1000 x 1.6487 x 0.6065 = $368.0

Asset x up x down4 $1000 x 1.6487 x 0.6065 = $223.1

Asset x down5 $1000 x 0.6065 = $82.1

The next step is to calculate the option valuation lattice using the values calculated in the underlying asset lattice. We see that the sample terminal node (denoted G) reveals a value of $12,183 (rounded), which can be obtained through the value maximization of contraction versus continuation. At the end of 5 years, the firm has the option to contract its existing operations or not, thereby letting the option expire. Obviously, management will choose the strategy that maximizes profitability. The value of contracting 50 percent of its operations is equivalent to half of its existing operations plus the $400 million in savings. Hence, the value of contracting the firm’s operations is

0.5($l I) + $ ~~| = $ ~| million

The value of continuing with existing business operations can be found in the underlying asset lattice, which is $12,183 million. The profit-maximizing decision is to continue with the firm’s current level of operations at $12,183 million on that node (denoted G). Similarly, for the terminal node H, we see that the value of continuing existing operations at that time is $82 million from the underlying asset lattice. In comparison, by contracting its operations to 50 percent, the value is 0.5($82) + $400 = $441. Hence, the decision at that node is to contract operations by 50 percent and the profit-maximizing value on that node is $441 million. This result is intuitive, because if the underlying asset value of pursuing existing business operations is such that it is very high based on current good operating conditions (node G), then it is wise to continue its current levels of operation. Otherwise, if

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REAL OPTIONS BUSINESS CASES

circumstances force the value of the firm’s operations down to such a low level as specified by node H, then it is optimal to contract the existing business by 50 percent.

Moving on to the intermediate nodes, we see that node I is calculated as $2,734 million. At this particular node, the firm again has two options, to contract its operations at that point or not to contract, thereby keeping the option to contract available and open for the future in the hopes that when the market is up, the firm has the ability to execute the option and contract its existing operations. The value of contracting at that node is 0.5($2,718) + $400 = $1,759 million. The value of continuing is simply the discounted weighted average of potential future option values using the risk-neutral probability. As the risk adjustment is performed on the probabilities of future option cash flows, the discounting can be done using the risk-free rate. That is, for the value of keeping the option alive and open, we have

[(P)($l I) + (1 - P)($l |)1exp[(-| |)(| |)1 = $2,734 million

which is higher than the contraction value. This result assumes a 5 percent risk-free rate rf, and a time-step 81 of 1. Using the backward induction technique, the lattice is back-calculated to the starting point to obtain the value of $ ~~l million. Because the value obtained through a DCF is $1,000

million for current existing operations, the option value of being able to contract 50 percent of its operations is $ ~~l million. The $1,000 million

is the static NPV without flexibility, the $ ~~l million is the real options value, and the combined value of $ ~~l million is the ENPV (Ex-

panded NPV) value or NPV+O (NPV with real options flexibility value), the correct total value of this manufacturing initiative. The real options value is worth an additional I 1 percent of existing business operations. If

a real options approach is not used, the manufacturing initiative will be undervalued.

Option to Contract

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Option Valuation Lattice

Max(Contract, Open) Max($1759, $2734) Decision: Open at $2734

Max(Contiact, Open) Max($4095, $7389) Decision: Open at $7389

Max(Contiact, End) Max($6491, $12183) Decision: End at $12183

Max(Contiact, End) Max($2741, $4482) Decision: End at $4482

Max(Contiact, End) Max($441, $82) Decision: Contract at $441

(h)

Exercise: Contraction Option

Open the Excel file Workbook Exercise (Contraction Option).xls from the enclosed CD-ROM. Use the same input parameters provided in the example but add a 2 percent dividend rate that grows at a -5 percent rate annually. Solve this modified contraction option by completing these lattices.

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