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**Real Options Traditional capital budgeting analysis:**

estimates cashflows each period discounts to get NPV firm decides to invest/not invest BIG PROBLEM: Traditional analysis assumes that a firm’s only choice is accept/reject the project. THIS IS NOT TRUE!!

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**In a real business situation, firms face many choices with**

respect to how to operate a project, both before it starts and after it is underway. Eg. Flexibility: use a production technology that is adaptable can produce more than one product if market for one product goes down, can switch production to the other the option to change production if the firm wants to (the flexibility) is valuable makes the project worth more traditional NPV analysis assumes cashflows fixed, will not change with future business conditions – ignores the value of this option

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Eg. Abandonment firm invests in project after a time the firm may be able to shut down production if things are not going well option to abandon traditional analysis assumes that the firm either takes the project and runs it for its life, or rejects it But…the ability to start a project and shut it down (perhaps temporarily) if conditions warrant is valuable

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Eg. Option to Delay traditional analysis assumes firm accepts project now or never invests But…what if firm has choice to delay making decision? Wait and see how things develop and then decide to invest or not The choice to delay if the firm wants is valuable Other examples of valuable options (choices) a firm may have include: option to expand/shrink production option to move into new market R&D gives the option to develop new products if they become viable development options on natural resources et cetera

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Real Options Any time a firm has the ability to make choices, there is a value added to the project in question traditional NPV analysis ignores this value the study of real options attempts to put a dollar value on the ability to make choices

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**How are real options valued? Three major ways:**

Use methods developed for pricing financial options We look at financial options later in the course Black-Scholes Model May be problems 2) Decision trees look at this method here 3) Stochastic optimization problems like (2) but using far more complicated (and realistic) models for the probability of different events occurring

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Option to Delay simple example from “Irreversibility, Uncertainty and Investment”, Robert Pindyck [Journal of Economic Literature, 1991] for $800 a firm can build widget factory makes 1 widget per year factory is built instantly investment is irreversible if factory built, first widget produced immediately no costs of manufacturing no taxes appropriate discount rate is 10%

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**Option to Delay the price of widgets is currently $100**

next year the price will be either $150 (50% probability) or $50 (50% probability) whatever price holds next year will hold forever after

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**year 2 year 0 year 1 Price = $150 Price = $150 Price = $100**

prob. = 0.5 Price = $100 prob. = 0.5 Price = $50 Price = $50

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**Traditional NPV Analysis**

Expected year 1 price = E[price] = 0.5($150) + 0.5($50) = $100 Standard analysis says NPV > 0, so start project.

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Option to Delay BUT… firm has another option. Delay the choice of whether to invest or not. Wait until next year to decide. Can see what price turns out to be before making decision. If you delay, you lose on the year 0 sales ($100). The bad part of delaying – lost sales. But, you get to see what price will be before making irreversible investment. The good part of delaying, reduced uncertainty.

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CASE 1: If delay and price turns out to be $50: NPV < 0 , so firm will not invest. From today’s perspective, NPV = 0 if price turns out to be $50.

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CASE 2: If delay and price turns out to be $150: Firm will invest if the price goes to $150.

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**the essence of the option to delay is that it allows the firm to avoid **

the “bad” outcome delay deciding until you see what the state of the world is: you lose some sales on delay if the market turns out to be bad, you do not invest and do not take the loss does the avoided loss make the foregone sales worthwhile? Price = $150 NPV = NPV = ?? Price = $50 NPV = 0

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**NPV in year 0 of delaying project**

= (0.5)(772.73) + (0.5)(0) = $386.36 the NPV of delaying ($386.36) is more than the NPV of starting immediately ($300) therefore, firm should delay start of project the flexibility of being able to wait another year to decide whether to invest or not is worth an additional $86.36 Does this mean that firms should always delay projects? No, if probability of high price in this example was 90% it would be best to start immediately

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Option to Abandon ability to abandon a project if things are not going well is valuable allows firm to avoid bad outcomes value of the option to abandon can be calculated in similar way to option to delay see example handout

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1 CHAPTER 12 Real Options Real options Decision trees Application of financial options to real options.

1 CHAPTER 12 Real Options Real options Decision trees Application of financial options to real options.

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