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Questions and Answers
What is the exercise price K of the option?
What is the exercise price K of the option?
- 100
- 90
- 85
- 95 (correct)
What is the value of d1 as calculated in the expression?
What is the value of d1 as calculated in the expression?
- 0.25
- 0.50
- 0.60
- 0.43 (correct)
What is the risk-free rate r per year indicated in the content?
What is the risk-free rate r per year indicated in the content?
- 0.3
- 0.4
- 0.1 (correct)
- 0.5
Which value corresponds to N(0.18) from the cumulative standard normal distribution table?
Which value corresponds to N(0.18) from the cumulative standard normal distribution table?
What is the expiration time T of the option in years?
What is the expiration time T of the option in years?
What is the NPV if the company decides not to invest today?
What is the NPV if the company decides not to invest today?
What is the expected benefit of conducting the field study?
What is the expected benefit of conducting the field study?
What is the formula used to calculate the option value?
What is the formula used to calculate the option value?
If consumers do not like the computers, what will be the NPV loss when investing today?
If consumers do not like the computers, what will be the NPV loss when investing today?
What happens to cash flows if the field study is conducted?
What happens to cash flows if the field study is conducted?
What is the value of NPV1 when the investment is made today and consumers like the computers?
What is the value of NPV1 when the investment is made today and consumers like the computers?
What is the impact of investing immediately versus waiting in terms of NPV?
What is the impact of investing immediately versus waiting in terms of NPV?
How is NPV affected by consumer preferences in this scenario?
How is NPV affected by consumer preferences in this scenario?
What is the risk-neutral probability of an up movement derived from the calculations?
What is the risk-neutral probability of an up movement derived from the calculations?
What is the return in the good state of the world as per the calculations?
What is the return in the good state of the world as per the calculations?
What is the immediate value of the call option if exercised immediately?
What is the immediate value of the call option if exercised immediately?
If the revenues are 50 during a positive market state, what must the project's value today still equal?
If the revenues are 50 during a positive market state, what must the project's value today still equal?
What will the value of the option be if it is exercised in one year according to the calculations?
What will the value of the option be if it is exercised in one year according to the calculations?
Which pricing model is specifically noted for its ease of application?
Which pricing model is specifically noted for its ease of application?
What is a key limitation of the Black-Scholes formula mentioned?
What is a key limitation of the Black-Scholes formula mentioned?
In the Black-Scholes formula, what does $S_0$ represent?
In the Black-Scholes formula, what does $S_0$ represent?
Which variable is used in the calculation of $d_1$ in the Black-Scholes formula?
Which variable is used in the calculation of $d_1$ in the Black-Scholes formula?
What does $N(d)$ signify in the context of the Black-Scholes formula?
What does $N(d)$ signify in the context of the Black-Scholes formula?
What type of option is not adequately priced by the Black-Scholes formula?
What type of option is not adequately priced by the Black-Scholes formula?
What is the formula for calculating $d_2$ in the Black-Scholes model?
What is the formula for calculating $d_2$ in the Black-Scholes model?
What does the variable $K$ stand for in the context of option pricing?
What does the variable $K$ stand for in the context of option pricing?
What is the maximum amount Company X should be willing to pay for the field study?
What is the maximum amount Company X should be willing to pay for the field study?
What is the expected cost when investing at t=1?
What is the expected cost when investing at t=1?
If Company X decides not to invest, what will be the NPV?
If Company X decides not to invest, what will be the NPV?
Which scenario gives a NPV of 6.349 if Company X decides to invest?
Which scenario gives a NPV of 6.349 if Company X decides to invest?
How is the option value calculated based on the given data?
How is the option value calculated based on the given data?
What is the net benefit if the expected cost is 0.21?
What is the net benefit if the expected cost is 0.21?
Why is the option value larger than the NPV if investing at t=0?
Why is the option value larger than the NPV if investing at t=0?
What is the NPV when investing at t=0?
What is the NPV when investing at t=0?
What is the reason for not investing immediately, despite a positive NPV?
What is the reason for not investing immediately, despite a positive NPV?
How does the volatility of cash flows affect the value of the option to postpone investment?
How does the volatility of cash flows affect the value of the option to postpone investment?
Which scenario is analogous to American call options regarding early exercise?
Which scenario is analogous to American call options regarding early exercise?
What does the NPV of the project at time 0 signify?
What does the NPV of the project at time 0 signify?
How is the investment opportunity with an option to wait similar to a call option?
How is the investment opportunity with an option to wait similar to a call option?
Given the possible future values of 160 or 250, how is the expected payout of the option calculated?
Given the possible future values of 160 or 250, how is the expected payout of the option calculated?
What financial concept exemplifies that the option is worth more than being exercised immediately?
What financial concept exemplifies that the option is worth more than being exercised immediately?
What can conclude about the two possible cash flows of 250 and 160 based on the project value?
What can conclude about the two possible cash flows of 250 and 160 based on the project value?
Flashcards
Exercise Price (K)
Exercise Price (K)
The price at which an option can be exercised.
Expiration Time (T)
Expiration Time (T)
The time remaining until the option expires. In this example, the option expires in three months.
Risk-Free Rate (r)
Risk-Free Rate (r)
The annual interest rate on a risk-free investment.
Cumulative Standard Normal Distribution Table
Cumulative Standard Normal Distribution Table
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Black-Scholes Model
Black-Scholes Model
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Black-Scholes Formula
Black-Scholes Formula
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European Option
European Option
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American Option
American Option
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Binomial Model
Binomial Model
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Risk-Neutral Pricing
Risk-Neutral Pricing
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Limitations of Black-Scholes
Limitations of Black-Scholes
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Advantages of Binomial Model
Advantages of Binomial Model
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Net Present Value (NPV)
Net Present Value (NPV)
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Expected Value
Expected Value
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Option Value
Option Value
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Scenario Analysis
Scenario Analysis
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Probability of Success
Probability of Success
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Expected Value Approach
Expected Value Approach
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Maximum Willingness to Pay
Maximum Willingness to Pay
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Investment Valuation
Investment Valuation
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Option to Wait
Option to Wait
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Positive Option Value
Positive Option Value
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NPV without Option
NPV without Option
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Volatility and Option Value
Volatility and Option Value
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Early Cash Flow and Option Value
Early Cash Flow and Option Value
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Call Option
Call Option
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Option to Wait as a Call Option
Option to Wait as a Call Option
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Benefit of Field Study (Avoid Loss)
Benefit of Field Study (Avoid Loss)
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Cost of Field Study (Delay of Cash Flows)
Cost of Field Study (Delay of Cash Flows)
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NPV with Consumer Acceptance
NPV with Consumer Acceptance
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NPV with Consumer Rejection
NPV with Consumer Rejection
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Initial Investment Cost
Initial Investment Cost
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Future Cash Flows
Future Cash Flows
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Discount Rate
Discount Rate
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Risk-Neutral Probability
Risk-Neutral Probability
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Expected Value (Risk-Neutral)
Expected Value (Risk-Neutral)
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Revenue and Option Value
Revenue and Option Value
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Study Notes
University of St. Gallen Corporate Finance - Lecture 4: Options and Real Options
- Course Instructor: Marc Arnold
- Course Focus: Options and Real Options within Corporate Finance.
Objectives
- Understanding Standard NPV Analysis Limitations: Traditional NPV analysis doesn't account for real options.
- Option Pricing Fundamentals: Gain a foundational understanding of option pricing principles.
- Exploring Option Pricing Models: Learning about the Black-Scholes model and the Binomial model, which are key models for option pricing.
- Recognizing Real Options: Improving the ability to identify and assess various real options for informed business decision-making.
Projects with Real Options
- Company Projects: Projects may include embedded choices, such as the option to invest or not, to shut down or expand.
- Real Options: These are similar to financial options except usually not tradable.
- Flexibility in Management: Management's ability to react to changing market conditions has value.
- Real Option Valuation: Standard NPV analysis does not account for real options. Thus, specialized tools are necessary.
Types of Real Options
- Option to Expand: A pilot program is used to assess the market and design before full-scale production.
- Option to Wait: Companies can delay investment and reassess conditions, reducing costly mistakes from premature decisions.
- Option to Abandon: An option to cancel a project if it doesn't meet expectations or is becoming unprofitable.
- Option to Switch: An option to change production methods, inputs, or products.
How to Value Real Options
- NPV & Real Options: NPV analysis does not inherently accommodate real options; it often is a preliminary step to real option evaluations.
- Real Option Valuation: Deciding trees or option pricing methodologies may be required to evaluate situations involving real options
Basics of Option Pricing
- Discounting Cash Flows: Discounting cash flows is not appropriate for valuing options; the risk of an option changes over time.
Black-Scholes(-Merton) Formula for European Options
- The formula is shown to determine call and put options values.
- The formulas include variables like the current underlying price, exercise price, risk-free rate, time to expiration, and standard deviation.
Black-Scholes Option Valuation
- Formulas and an example of pricing an option when using the Black Scholes Model are presented.
More Flexible: Binomial Model
- Tree Construction: Building a tree representing potential future values of the underlying asset to perform option valuation.
- Time Steps: Increments in time used in option pricing or decision trees become progressively smaller.
- Up/Down Movements: Defining up/down movements of the underlying in a binomial pricing tree is crucial.
Risk-Neutral Valuation
- Risk-Free Approach: The approach assumes investors do not care about risk, allowing risk-free rate to be used for discounting.
- Option Pricing: Option pricing is simplified by discounting expected cash flows of options.
- Risk-Neutral Probabilities: Risk-neutral probabilities are used in calculations.
Option Pricing via Replication
- Replication Strategy: Options can be priced by creating a portfolio that replicates the option's payoff.
- Same Value: Both the option and the replicating portfolio have the same payoffs at the option expiration date.
Investment Opportunity (Projects with Real Options)
- Project Details: Information is presented on possible investments for an R&D project for a new drug. This includes timelines and financial details.
- DCF Analysis: Discounted cash flow approach is used to determine expected return of an investment.
- NPV Calculation: Investment NPV is calculated to evaluate whether the investment should proceed despite cost of capital.
Option to Expand
- Mark I Project Description: A description of the project and the opportunity to invest.
- Information about investment requirements and project success probabilities are presented.
Option to Wait
- Decision Tree Analysis: A method to evaluate decisions in scenarios with uncertainty is demonstrated.
- Option value: The option to wait adds value to the negative NPV project (at times).
- Detailed explanation: How the decision tree is formed and analyzed.
- Field Study: A field study scenario may be one component in evaluating an option to wait.
Option to Wait and Risk-Neutral Pricing
- Project Description: A project description is presented to determine market conditions.
- Option Valuation: The option value (using the Risk-Neutral approach) is calculated.
Discussion & Examination Task
- Discussion Topics: Questions that may come up in discussions are given, as well as questions that address examination material and how to approach problem analyses from an option pricing/ valuation perspective. Additional detail on approaches and problem resolution method are presented on these questions.
Key Takeaways
- Real Options Significance: Real options are central to many impactful business decisions. This is a key insight of the material.
- Valuation Importance in Startups: Startup businesses often involve real options in their valuation.
- Option Recognition Importance: Recognition of valuable real options is critical for creating more profitable decisions..
- Traditional Methods: Traditional methods can negatively impact investment decisions if they do not factor in real options.
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Description
This quiz covers Lecture 4 of the Corporate Finance course at the University of St. Gallen, focusing on the concepts of options and real options. It emphasizes the limitations of standard NPV analysis and introduces key option pricing models, including Black-Scholes and Binomial. Additionally, it explores the application of real options in business decision-making.
