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**22 Real Options McGraw-Hill/Irwin**

Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

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**22-1 Value of follow-on investment opportunities**

Four Types of Real Opinions Opportunity to expand, make follow-up investments Opportunity to wait, invest later Opportunity to shrink or abandon project Opportunity to vary firm’s output or production methods Value of real option = NPV with option − NPV without option Types of options include option to expand, option to wait, option to trim down or abandon, and option to vary the mix of output or the firm’s production methods. Value of a real option = NPV with option – NPV without option

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**Table 22.1 cash flow and Financial Analysis of Mark I microcomputer**

Mark I Microcomputer in Millions NPV analysis for the Mark I Microcomputer Project is given. It has negative (-46 million) NPV.

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**Table 22.2a Mark ii microcomputer**

Here the option to expand to Mark II Microcomputer is evaluated. The option to expand is a call option. The value of the call option is + $55.1 million.

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**Table 22.2b Mark ii microcomputer**

Here the option to expand to Mark II Microcomputer is evaluated. The option to expand is a call option. The value of the call option is + $55 million.

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**Table 22.3 Cash flow of mark ii microcomputer**

The NPV of the Mark II project is negative (–$209 million). Forecasted from 1982 in millions

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**Figure 22.1 possible present values for mark ii in 1985**

Distribution shows range of possible present values for Mark II project 1985 Expected value roughly $800 million (less than required investment of $900 million) Option to invest pays off in shaded area above $900 million The next slide shows the distribution of possible present values. It is assumed to be lognormal distribution. Lognormal distributions are skewed to the right, therefore the expected outcome is greater than the most likely outcome. The most likely outcome is the highest point on the probability distribution.

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**Figure 22.1 possible present values for mark ii in 1985**

This shows the distribution of possible present values. It is assumed to be lognormal distribution. Lognormal distributions are skewed to the right, therefore the expected outcome is greater than the most likely outcome. The most likely outcome is the highest point on the probability distribution.

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**22-2 timing option Option to Wait Intrinsic value Option price**

Stock price The longer the wait, the more valuable the option is. It is a call option. An important point to note: if competition catches up with the idea, then the option value would be diminished.

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22-2 timing option Intrinsic value plus time premium equals option value Time premium equals value of being able to wait Option price Stock price Option value = intrinsic value + time premium Time premium = value of being able to wait

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**22-2 timing option Option to Wait More time equals more value**

Stock price Option price Option to Wait More time equals more value The longer the wait, the higher the value.

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**FIGURE 22.2 timing option example**

Possible cash flow and end-of-period values for malted herring project shown in black Project costs $180 million Red figures in parentheses show payoffs from option to wait and invest later in project, now positive-NPV at year 1 Waiting means loss of first year cash flow; figuring out current value of option is difficult This slide explains the timing options displayed in the graph on the next slide.

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**FIGURE 22.2 timing option example**

NPV if invested today is $20 million. Option to wait and invest later only if there is high demand.

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22-2 Timing Option High demand generates $25 million, $250 million value at end of year Low demand generates $16 million with no value High Demand Low Demand Total return if demand is high: [(25+250)/200 ] –1 = 0.375 Total return if demand is low: [( )/200] – 1 = –0.12 Risk-free rate = 5% Risk neutral return

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22-2 Timing Option Calculate probability of high demand for malted herring project Option value Expected return = (prob. of high demand) × (0.375) + (1 – prob. of high demand) × (–0.12) = 0.05 Prob of high demand = 0.343 Option value = [(0.343)(70) + (0.675)(0)]/1.05 = $22.9 million

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**Figure 22.3 development option for vacant land**

Option to wait: Choice of office building versus hotel, it is a difficult choice. This analysis does not consider the possibility that someone else might build a competing hotel or office building in the neighborhood. In that case, the area under wait would reduce drastically.

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**22-3 abandonment option Example**

Mrs. Mulla gives nonretractable offer to buy company for $150 million at anytime within next year Given possible outcomes What is value of offer? What is most Mrs. Mulla could charge for that option? Use discount rate of 10% You would sell for $150 million if the outcome were $50 million at the end of the year. Option to abandon is a put option.

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**22-3 abandonment option Example Year 0 Year 1 Year 2 120 (.6) 100 (.6)**

90 (.4) NPV = 145 70 (.6) 50 (.4) 40 (.4) 120(0.6) + 90(0.4)] / 1.1 = 98; If the outcome at the end of the year is 100, you would not sell because the value of the firm is 198. If the outcome is 50 at the end of the year, then you would sell.

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**22-3 abandonment option Option value = 162 − 145 = $17 Million**

Year 0 Year 1 Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 162 150 (.4) Option value = 162 − 145 = $17 Million [120(0.6) + 90(0.4)] / 1.1 = 98; If the outcome at the end of the year is 100, you would not sell as the value of the firm is 198. If the outcome is 50 at the end of the year, then you would sell.

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Figure 22.4 Value of Tanker This is an example of temporary abandonment. If the tanker rate is > R, reactivate the tanker If the tanker rate is < M, mothball the tanker

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**FIGURE 22.5 price of electricity in U.K.**

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**FIGURE 22.5 Price of electricity in U.K.**

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**Figure 22.6 aircraft purchase option**

If implemented at year 3, option guarantees fixed price and delivery at year 4 Without option, plane can still be ordered at year 3 but with uncertain price and delivery The option to purchase an aircraft gives the holder both the ability to get a lower price and also get the delivery of the aircraft.

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**Figure 22.7 aircraft purchase option**

The purchase option is worth most when NPV of purchase now is about zero and the forecasted wait for delivery is long.

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**Figure 22.8 Decision Tree for Figure 22.6**

If phase II trials are successful there is a recall option to invest $130 million. If exercised, there is 80% chance of launching approved drug. PV of drug, forecasted at $350 million in year 5, is underlying asset of call option.

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**22-6 conceptual problem Real options are not always feasible to use**

Options can be complex; it is sometimes impossible to arrive at “perfect” answer No clear structure to path and cash flows Competitors have real options, which alter option values by altering underlying assumptions and environment that serves as basis of valuation Valuation of real options can be complex. Real options do not always have a clear structure of the path and cash flows. Competition can alter the value of the option you are holding by altering the underlying assumptions and environment.

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