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**Real Options in Project Evaluation**

Stephen Gray Campbell R. Harvey

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**NPV and Real Options NPV: Real Option Valuation: Often misapplied**

Ignores strategic values if misapplied Real Option Valuation: Values contingencies in project outcomes (i.e., alternative future uses of the asset).

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**NPV and Real Options Many Types of Real Options Key is to identify**

Often they are difficult to value – however, even using judgment one can tell if they add or subtract value to the project

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**NPV and Real Options Input Mix Options or Process Flexibility**

The option to use different inputs to produce the same output is known as an input mix option or process flexibility. Examples: Agriculture: A beef producer will value the option to switch between various feed sources, preferring to use the cheapest acceptable alternative

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**NPV and Real Options Input Mix Options or Process Flexibility**

Examples: Utility industry. An electric utility may have the option to switch between various fuel sources to produce electricity. In particular, consider an electric utility that has the choice of building a coal-fired plant or a plant that burns either coal or gas.

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**NPV and Real Options Output Mix Options or Product Flexibility**

The option to produce different outputs from the same facility is known as an output mix option or product flexibility. Examples: Toy industry. A manufacturer's ability to cease producing a style of toy that has become unfashionable and quickly begin producing a popular new style of toy.

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**NPV and Real Options Abandonment or Termination Options**

Whereas traditional capital budgeting analysis assumes that a project will operate in each year of its lifetime, the firm may have the option to cease a project during its life. This option is known as an abandonment or termination option. Abandonment options, which are the right to sell the cash flows over the remainder of the project's life for some salvage value, are like American put options. When the present value of the remaining cash flows falls below the liquidation value, the asset may be sold.

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**NPV and Real Options Abandonment or Termination Options Examples**

These options are particularly important for large capital intensive projects such as nuclear plants, airlines, and railroads. They are also important for projects involving new products where their acceptance in the market is uncertain.

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NPV and Real Options Abandonment or Termination Options

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**NPV and Real Options Temporary-Stop or Shutdown Options Examples:**

For projects with production facilities, it may not be optimal to operate a plant for a given period if revenues will not cover variable costs. Examples: If the price of oil falls below the cost of extraction, for example, it may be optimal to temporarily shut down the oil well until the oil price recovers.

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**NPV and Real Options Temporary-Stop or Shutdown Options Examples:**

Farming: May be exercised if the cost of fertilizing, watering and harvesting exceeds the sale price of the product. Real-estate development: May be exercised if the cost of construction exceeds rent revenues.

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**NPV and Real Options Intensity or Operating Scale Options**

Intensity or operating scale options involve the flexibility to expand or contract the scale of the project. Management may have the option to change the output rate per unit of time or to change the total length of production run time.

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**NPV and Real Options Intensity or Operating Scale Options**

In order to obtain the option to expand production if demand increases suddenly, a firm may build production capacity in excess of the expected level of output. In this case, management has the right, but not the obligation to expand, and will exercise the option only if project conditions turn out to be favorable.

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**NPV and Real Options Intensity or Operating Scale Options**

Whereas the excess capacity will have an initial cost, the project with the option to expand is worth more than the project without the possibility of expansion, in which case the extra cost may be justified. Also, a firm may build a plant whose physical life exceeds the expected duration of use, thereby providing the firm with the option of producing more by extending the life of the project.

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**NPV and Real Options Option to Expand Example**

Build production capacity or the infrastructure for the capacity in excess of expected level of output (so it can produce at higher rate if needed). Management has the right (not the obligation to expand). If project conditions turn out to be favorable, management will exercise this option. Example Mozal Project

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NPV and Real Options Option to Expand

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**NPV and Real Options Option to Contract Example:**

This is the equivalent to a put option. Many projects can be engineered in such a way that output can be contracted in future. Forgoing future expenditures is equivalent to exercising the put option. Example: Modularization of project.

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NPV and Real Options Option to Contract

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**NPV and Real Options Option to Expand or Contract (Switching Option)**

It is equivalent to the firm having a portfolio of call and put options. Restarting operations when project currently shut down is a call option. Shutting down is a put option.

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**NPV and Real Options Option to Expand or Contract (Switching Option)**

Example: A project whose operation can be dynamically turned on and off (or switched to two distinct locations) is worth more than the same project without the flexibility to switch.

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NPV and Real Options Option to Expand or Contract (Switching Option)

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**NPV and Real Options Initiation or Deferment Options Examples:**

The option to choose when to start a project is an initiation or deferment option. Examples: The purchaser of an off-shore lease can choose when, if at all, to develop property.

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**NPV and Real Options Initiation or Deferment Options Examples:**

Initiation options are particularly valuable in natural resource exploration where a firm can delay mining a deposit until market conditions are favorable. If natural resource companies were committed to producing all resources discovered, they would never explore in areas where the estimated extraction cost exceeded the expected future price at which the resource could be sold.

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NPV and Real Options Initiation or Deferment Options

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**NPV and Real Options Intraproject vs. Interproject Options**

Interproject options arise when the development of one project creates value that attach to other projects. Sequencing options, for example, are interproject options because the sequencing of projects creates value for subsequent projects as the direct result of undertaking the initial project. Traditional capital budgeting analysis will miss this option because projects evaluated on stand-alone basis.

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**NPV and Real Options Growth Options**

The value of the firm can exceed the market value of the projects currently in place because the firm may have the opportunity to undertake positive NPV projects in the future. Standard capital budgeting techniques involve establishing the present value of these projects based on anticipated implementation dates. However, this implicitly assumes that the firm is committed to go ahead with the projects.

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**NPV and Real Options Growth Options Example:**

Since management need not make such a commitment, they retain the option to exercise only those projects that appear to be profitable at the time of initiation. Example: High-tech and software industries (where there are significant first-mover advantages)

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**NPV and Real Options Shadow Costs**

Standard valuation techniques may overvalue some projects by failing to recognize the losses in flexibility to the firm that result from implementation. The acceptance of one project may eliminate options that attach to other projects.

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**NPV and Real Options Shadow Costs Example:**

Building a plant in a particular city eliminates the options to expand the capacity of plants in nearby cities. Management time.

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**NPV and Real Options Financial Flexibility**

Choice of capital structure can affect value of project. Like operating flexibility, financial flexibility can be measured by the value of the financial options made available to the firm by its choice of capital structure. Interaction between financial and operating options can be strong -- especially for long-term investment projects with a lot of uncertainty

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**NPV and Real Options Identifying Real Options**

Why are there empty lots in prime commercial real estate areas in all major cities? Multipurpose real estate (hotel/apartment) Why to firms use a hurdle rate for project evaluation greater than their cost of capital?

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**NPV and Real Options Detailed Example: Abandonment**

Abbeytown Copper 2-yr lease over a known deposit. Deposit contains eight million pounds of copper Mining involves a one-year development phase, at a cost of $1.25 million immediately Extraction costs (outsourced) at $0.85 / pound at beginning of extraction phase (one year after development phase is initiated) Sale of copper would be at spot price of copper as of beginning of extraction phase

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**NPV and Real Options Detailed Example: Abandonment**

Current spot price of copper is $0.95 / pound Log change in copper prices are normally distributed with mean 7% and standard deviation 20% (p.a.) Abbeytown's required rate of return for this project is 10%, and the riskless rate is 5%

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**NPV and Real Options Traditional NPV analysis: Reject**

Expected NPV = (E[S1] ) 1.1 where E[S1] = Expected price of Copper in one year's time Current price of Copper, S0 = 0.95 Expected rate of return on copper, r = 7% Expected price of copper in one year, S1 = 0.95e0.07 = Hence E[NPV] = ( )/1.1 = Reject

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**NPV and Real Options Option Analysis S = 0.95 * 8 = 7.6**

K = * 8 = 6.8 r = 5% T = 1 year = 20%

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NPV and Real Options

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**NPV and Real Options Option Analysis Accept Call Value = 1.3**

Option Cost = Option-adjusted Present Value = 0.05 Accept

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**NPV and Real Options Why does the option to abandon have value?**

Can choose to abandon the project if the price of copper is low after one year.

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**NPV and Real Options What is the probability that we will abandon?**

= 1 - Prob(exercise) = 1 - N(d2) = = 0.24

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NPV and Real Options What is the probability that we will abandon?

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**NPV and Real Options Detailed Example: Deferment Option**

A company has the opportunity to build a new power project in a foreign country. Net cash flows are $100mm in the first year of operation.

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NPV and Real Options Net cash flows in the second year of operation depend upon whether the government sponsors a link to bypass a transmission “bottleneck”. There is a 50% probability the government will intervene. This is an example of political risk.

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NPV and Real Options If the link goes ahead, demand for power from the new plant will be low and net cash flow will be $80 mm. If the link does not go ahead, demand for power from the new plant will be high and net cash flow will be $125 mm. Similar uncertainty surrounds Year 3 net cash flows. Cash flows beyond Year 3 are perpetual.

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... 156 0.5 125 0.5 0.5 ... 100 100 0.5 0.5 80 0.5 ... 64 Expected Net Cash Flow ... 100 103 105 ... 1 2 3

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Expected Net Cash Flow ... 100 103 105 ... 1 2 3

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**Scenario 1a Build now or never. Cost to build is 1,100.**

NPV=1, ,100 = -56. Negative NPV. Reject the project.

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**Scenario 1b Build now or never. Cost to build is reduced to 1,000.**

NPV=1, ,000 = +44. Positive NPV. Accept the project.

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**Scenario 2 Option to delay for one year.**

During this one-year delay, the generator learns whether or not the new entrepreneurial link will proceed. Based on this additional information, a “smarter” decision can be made. Cost to build is 1,100.

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**... 156 “up” state 125 ... 100 “down” state 80 ... 64**

0.5 “up” state 125 0.5 ... 100 0.5 “down” state 80 0.5 ... 64 Expected Net Cash Flow in “up” state ... 125 128 Expected Net Cash Flow in “down” state ... 80 82 ... 1 2 3

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Expected Net Cash Flow in “up” state ... 125 128 ... 1 2 3

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Expected Net Cash Flow in “down” state ... 80 82 ... 1 2 3

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**Scenario 2a (continued)**

Option to delay for one year. Cost to build is 1,100. Wait one year: proceed if “up state”, NPV=177. reject if “down state”, NPV=0. Expected NPV today is:

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**Scenario 2a (continued)**

Expected NPV today is: Compare with NPV without delay: NPV without delay = - 56 Difference: 136

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**Scenario 2b Option to delay for one year. Cost to build is 1,000.**

If we build now, NPV0 = 44. What if we wait one year?

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**Scenario 2b Wait one year: Expected NPV today is:**

proceed if “up state”, NPV=277. reject if “down state”, NPV=0. Expected NPV today is:

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**Scenario 2b Expected NPV today is:**

Compare with NPV without 1 yr delay: NPV without delay = 44 Difference: 82

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Remarks The option to delay can be valuable, even if the project has positive NPV if started immediately. The value of these options is ignored by standard DCF techniques. Proper analysis of these options is needed not just for project valuation, but also for project timing.

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**Scenario 3 – Add abandonment**

Plant can be abandoned at any time for 800. This option will be exercised whenever the PV of future cash flows falls below 800. This only happens at the lowest node, where perpetual cash flows are 64.

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... 156 Yearly Cash Flows 125 ... 100 100 80 One-time Liquidation Value 800

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Scenario 3 (continued) When the abandonment option is incorporated, the NPV of building the project now is +77. The NPV of waiting for one year is +126. It is still optimal to delay for one year in this case, although the incremental value of delaying has decreased. The value of the option to delay is lower if it is easy to exit a bad investment.

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**NPV and Real Options Only as good as the inputs**

Drift, variance, probabilities Beware of mean reversion Theory relies on availability of a replicating portfolio Equilibrium issues

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**NPV and Real Options How do real options impact discount rates?**

How far can we take real options theory in understanding major issues in corporate finance?

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