Corporate Finance Lecture 4: Options and Real Options

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Questions and Answers

What is the exercise price K of the option?

100

95 (correct)

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?

0.3

0.4

0.1 (correct)

0.5

Which value corresponds to N(0.18) from the cumulative standard normal distribution table?

0.5714 Signup and view all the answers

What is the expiration time T of the option in years?

0.25 Signup and view all the answers

What is the NPV if the company decides not to invest today?

0 Signup and view all the answers

What is the expected benefit of conducting the field study?

0.2 × 4.048 Signup and view all the answers

What is the formula used to calculate the option value?

4.17 − 3.57 Signup and view all the answers

If consumers do not like the computers, what will be the NPV loss when investing today?

−4.048 Signup and view all the answers

What happens to cash flows if the field study is conducted?

They are delayed. Signup and view all the answers

What is the value of NPV1 when the investment is made today and consumers like the computers?

5.476 Signup and view all the answers

What is the impact of investing immediately versus waiting in terms of NPV?

Immediate investment can lead to NPV loss. Signup and view all the answers

How is NPV affected by consumer preferences in this scenario?

It changes based on whether consumers like or dislike the product. Signup and view all the answers

What is the risk-neutral probability of an up movement derived from the calculations?

0.343 Signup and view all the answers

What is the return in the good state of the world as per the calculations?

37.5% Signup and view all the answers

What is the immediate value of the call option if exercised immediately?

USD 20m Signup and view all the answers

If the revenues are 50 during a positive market state, what must the project's value today still equal?

200 Signup and view all the answers

What will the value of the option be if it is exercised in one year according to the calculations?

USD 22.9m Signup and view all the answers

Which pricing model is specifically noted for its ease of application?

Black-Scholes formula Signup and view all the answers

What is a key limitation of the Black-Scholes formula mentioned?

Accuracy for American options Signup and view all the answers

In the Black-Scholes formula, what does $S_0$ represent?

Current price of the underlying Signup and view all the answers

Which variable is used in the calculation of $d_1$ in the Black-Scholes formula?

Annual standard deviation of the underlying Signup and view all the answers

What does $N(d)$ signify in the context of the Black-Scholes formula?

Cumulative probability from the normal distribution Signup and view all the answers

What type of option is not adequately priced by the Black-Scholes formula?

American options Signup and view all the answers

What is the formula for calculating $d_2$ in the Black-Scholes model?

$d_2 = d_1 - ext{σ} imes T$ Signup and view all the answers

What does the variable $K$ stand for in the context of option pricing?

Exercise price of the option Signup and view all the answers

What is the maximum amount Company X should be willing to pay for the field study?

0.6 Signup and view all the answers

What is the expected cost when investing at t=1?

0.21 Signup and view all the answers

If Company X decides not to invest, what will be the NPV?

0 Signup and view all the answers

Which scenario gives a NPV of 6.349 if Company X decides to invest?

Cash flow of USD 35m Signup and view all the answers

How is the option value calculated based on the given data?

NPV1 when investing minus the NPV when not investing Signup and view all the answers

What is the net benefit if the expected cost is 0.21?

0.6 Signup and view all the answers

Why is the option value larger than the NPV if investing at t=0?

Increased cash flow variability Signup and view all the answers

What is the NPV when investing at t=0?

3.5714 Signup and view all the answers

What is the reason for not investing immediately, despite a positive NPV?

The option to wait has a positive value. Signup and view all the answers

How does the volatility of cash flows affect the value of the option to postpone investment?

It increases the value of the option. Signup and view all the answers

Which scenario is analogous to American call options regarding early exercise?

If dividends are large, early exercise might be rational. Signup and view all the answers

What does the NPV of the project at time 0 signify?

The net benefit of the investment after accounting for costs. Signup and view all the answers

How is the investment opportunity with an option to wait similar to a call option?

Investing means exercising the option and losing additional potential value. Signup and view all the answers

Given the possible future values of 160 or 250, how is the expected payout of the option calculated?

Using a weighted average based on market conditions. Signup and view all the answers

What financial concept exemplifies that the option is worth more than being exercised immediately?

Risk-neutral pricing. Signup and view all the answers

What can conclude about the two possible cash flows of 250 and 160 based on the project value?

The project's value is uncertain, depending on market dynamics. Signup and view all the answers

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.