Real Options Analysis in Capital Budgeting
39 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the primary focus of Real Options Analysis (ROA) in capital budgeting?

The primary focus of ROA is to evaluate investment decisions over multiple periods under uncertainty by incorporating flexibility options.

Name two key assumptions of Real Options Analysis (ROA) based on the binomial model.

Two key assumptions are the no arbitrage condition and the efficient capital market hypothesis.

What does the marketed asset disclaimer (MAD) imply in the context of Real Options Analysis?

MAD implies that the underlying risky asset for valuing the project is the project itself.

How does Real Options Analysis allow for project flexibility in investment decisions?

<p>It allows investors to adapt their decisions by expanding, contracting, abandoning, extending, or deferring projects.</p> Signup and view all the answers

Explain the role of the replicating portfolio approach in Real Options Analysis.

<p>The replicating portfolio approach is used to value real options by creating a portfolio that mimics the project's cash flows and risks.</p> Signup and view all the answers

What is the formula for the value of an option after j ups at time s = t for t not equal to T?

<p>The formula is $V_{s,j} = (1 + r_f)^{- riangle t} qV_{s+1,j+1} + (1 - q)V_{s+1,j}$.</p> Signup and view all the answers

How is the value of a European call option at time t = 1 expressed?

<p>It is expressed as $V_u = (1 + r_f)^{-1} qV_{uu} + (1 - q)V_{ud}$ for the upward movement.</p> Signup and view all the answers

Describe how the value of a European option at time t = 0 is calculated.

<p>The value is calculated as $V_0 = (1 + r_f)^{-1} qV_u + (1 - q)V_d$.</p> Signup and view all the answers

What is the terminal value of an American call option at time T?

<p>The terminal value is $V_T = ext{max}[S_T - K, 0]$.</p> Signup and view all the answers

What must be determined at every time t for American options?

<p>It must be determined whether it is optimal to exercise the option or continue holding it.</p> Signup and view all the answers

What is the abandonment value of the project mentioned in the real option analysis example?

<p>$190</p> Signup and view all the answers

What percentage reduction in value occurs if the contraction option is exercised, and what cash amount is received?

<p>20% reduction, $50 cash</p> Signup and view all the answers

What cost is associated with the expansion option for increasing the project's value?

<p>$70</p> Signup and view all the answers

In the context of real options, how do the options for abandoning, contracting, and expanding affect each other?

<p>They do not affect each other.</p> Signup and view all the answers

What is the approximate value of $q$ used in the example for the real options analysis?

<p>0.56</p> Signup and view all the answers

What is the purpose of a replicating portfolio in option valuation?

<p>A replicating portfolio aims to match the price of an option through a combination of shares and risk-free bonds.</p> Signup and view all the answers

How do you determine the risk-neutral probability, q?

<p>The risk-neutral probability, q, is determined using the formula $q = \frac{(1 + r_f)^{\Delta t} - d}{u - d}$.</p> Signup and view all the answers

What does the option value at terminal date, $V_T$, represent for a call option?

<p>For a call option, $V_T = \max[S_T - K, 0]$, representing the maximum payoff if the option is exercised.</p> Signup and view all the answers

In the context of option pricing, what do $V_u$ and $V_d$ represent?

<p>$V_u$ and $V_d$ represent the option values at the upper and lower possible stock prices at time T, respectively.</p> Signup and view all the answers

What condition is implied by no arbitrage regarding option and portfolio pricing?

<p>The condition of no arbitrage implies that the price of the option, $V_0$, must equal the value of the replicating portfolio.</p> Signup and view all the answers

What role does the risk-free return, $r_f$, play in option valuation?

<p>The risk-free return, $r_f$, is used to discount future cash flows to present value and gauge the expected returns.</p> Signup and view all the answers

What does $S_0$ represent in option valuation formulas?

<p>$S_0$ represents the current price of the underlying asset at time t = 0.</p> Signup and view all the answers

Define the terms $u$ and $d$ in the option pricing framework.

<p>$u$ and $d$ are the factors by which the underlying asset's price increases or decreases in the next time period, respectively.</p> Signup and view all the answers

What does the term E[ST] represent in relation to the underlying asset?

<p>E[ST] represents the expected value of the underlying asset at time T.</p> Signup and view all the answers

Explain the significance of the parameters u and d in option valuation.

<p>The parameters u and d represent the up and down factors, respectively, which are constant and indicate potential price movements of the underlying asset.</p> Signup and view all the answers

What is meant by 'backwards induction' in the context of option valuation?

<p>Backwards induction is a method used to determine the value of an option by calculating its value at expiration and then working backwards to the present.</p> Signup and view all the answers

Define the value of a European call option at the terminal date t = T.

<p>The value of a European call option at t = T is given by max[ST - K, 0], where ST is the stock price at time T and K is the strike price.</p> Signup and view all the answers

What does the term rf represent in the valuation model?

<p>The term rf represents the risk-free rate, assumed to be constant in the option valuation model.</p> Signup and view all the answers

How does the expected return formula E[S1] - S0 = rf S0 illustrate the relationship between future and present values?

<p>The formula illustrates that the expected return on the underlying asset is equal to the risk-free return on the initial investment S0.</p> Signup and view all the answers

What is meant by a 'recombining decision tree' in the context of option pricing?

<p>A recombining decision tree allows for price paths that converge back to the same node, simplifying the calculations for multiple scenarios.</p> Signup and view all the answers

What is the value of a put option at the terminal date t = T?

<p>The value of a put option at t = T is max[K - ST, 0], indicating the payoff when the stock price is below the strike price.</p> Signup and view all the answers

What does the value of an option depend on when using the formula for American options?

<p>The value of an option depends on the exercise value and the continuation value.</p> Signup and view all the answers

Define the term 'continuation value' as used in the context of option pricing.

<p>Continuation value is the expected value of holding the option for the next period, discounted back to the present.</p> Signup and view all the answers

What does 'rf' represent in the formulas for option valuation?

<p>'rf' represents the risk-free rate of return used to discount future cash flows.</p> Signup and view all the answers

In the two-period model, what does a call option's value depend on at time t=1?

<p>A call option's value depends on the maximum of the difference between the stock price and the strike price, or the discounted continuation value.</p> Signup and view all the answers

Explain how the value of a put option is calculated when the stock price decreases.

<p>The value of a put option is calculated as the maximum of the strike price minus the stock price, or the discounted continuation value.</p> Signup and view all the answers

What is the significance of the parameter 'K' in the option valuation formulas?

<p>'K' is the strike price of the option, which determines the exercise value.</p> Signup and view all the answers

In the example provided, what is the value of K and the risk-free return, rf?

<p>In the example, K = $125 and the risk-free return, rf = 5%.</p> Signup and view all the answers

How does the calculation differ for an option at time t = 0 compared to later times?

<p>At time t = 0, the option's value includes expected values from both up and down movements, discounted to present value.</p> Signup and view all the answers

Flashcards

Multiperiod Capital Budgeting

The process of evaluating investment decisions that span multiple periods and involve uncertainty.

Real Options Analysis (ROA)

An approach to valuing investments that considers the flexibility to adjust investment plans based on future circumstances.

Marketed Asset Disclaimer (MAD)

The assumption that the value of the project being evaluated is the underlying asset for valuation.

Efficient Capital Market

The assumption that financial markets are efficient and reflect all available information.

Signup and view all the flashcards

Recombining Binomial Trees

A model that uses a series of branching paths to represent possible future outcomes of an investment.

Signup and view all the flashcards

Vs,j (Value of option at time 's = t' for scenario 'j')

The value of an option at time 's = t' for a specific scenario 'j' before the option's maturity date 'T'. It is calculated using a risk-neutral probability 'q' and the discounted expected value of the option in the next period for both possible scenarios (j+1 and j).

Signup and view all the flashcards

q (Risk-neutral probability)

The risk-neutral probability of the asset price going up in the next period. It is calculated using the risk-free rate and the expected return of the underlying asset.

Signup and view all the flashcards

VT (Value of option at maturity)

The value of an American option at the maturity date 'T'. It is the maximum of either the intrinsic value of the option (exercising it immediately) or zero (not exercising it). For a call option, the intrinsic value is the difference between the underlying asset price and the strike price.

Signup and view all the flashcards

Option valuation

The process of determining the value of an option by considering all possible future scenarios and their probabilities, and discounting the expected value back to the present using the risk-free rate.

Signup and view all the flashcards

Value of an option at a specific time 't' (before the expiration of the option)

The value of an option at time 't' is calculated using the risk-neutral probability 'q' and the discounted expected value of the option in the next period for both possible scenarios.

Signup and view all the flashcards

Expected Return on Underlying Asset

The expected return on an underlying asset over a certain period of time, typically calculated using the risk-free rate and probabilities of upward and downward movements.

Signup and view all the flashcards

Probability of Upward Movement (q)

A constant value representing the probability of an upward movement in the underlying asset's price in a binomial tree model.

Signup and view all the flashcards

Option Value at Expiration (VT)

The value of an option at the expiration date, determined by the difference between the underlying asset's price and the strike price, depending on whether it's a call or put option.

Signup and view all the flashcards

Backward Induction

The process of calculating the value of a financial instrument, such as an option, by working backward from the expiration date to the present, using a binomial tree model.

Signup and view all the flashcards

Option Value (V)

The value of an option at any point in time before its expiration, calculated using backward induction and considering the probability of different future outcomes.

Signup and view all the flashcards

European Options

An options contract that can only be exercised on the expiration date, not before.

Signup and view all the flashcards

Replicating Portfolio

A theoretical portfolio that perfectly replicates the payoff of an option. It consists of a specific number of shares of the underlying asset (m) and a risk-free bond (B).

Signup and view all the flashcards

Number of Shares (m)

The number of shares of the underlying asset in a replicating portfolio, calculated by the difference in the option's value in the up and down states divided by the difference in the underlying asset's price in these states.

Signup and view all the flashcards

Amount Invested in Bonds (B)

The amount invested in risk-free bonds in a replicating portfolio, calculated to match the option's payoff in both up and down states.

Signup and view all the flashcards

Risk-Free Return (rf)

The risk-free return on bonds over a specific period (∆t) is used to calculate the bond component of the replicating portfolio.

Signup and view all the flashcards

Risk-Neutral Probability (q)

The probability that the underlying asset's price will move up (u) in the next period, calculated based on the risk-free rate and the potential price movements of the asset.

Signup and view all the flashcards

Option Valuation at Time Zero (V0)

The value of an option at time zero (V0) is equal to the value of the replicating portfolio, which consists of the number of shares (m) multiplied by the current asset price (S0) plus the value of the bonds (B).

Signup and view all the flashcards

Risk-Neutral Valuation

The expected return on the underlying asset is equal to the risk-free rate when using risk-neutral probabilities, implying that investors are indifferent to risk.

Signup and view all the flashcards

Option Value at Time t (t ̸= T)

The value of an option at a specific time (t) before maturity, calculated by considering the potential future values of the underlying asset, exercise price, risk-free rate, and time to maturity. It involves comparing the payoff of immediate exercise with the expected value of holding the option.

Signup and view all the flashcards

Option Valuation: Maximizing Value

The highest possible value between the immediate exercise of an option and holding onto it with the hope for a more profitable outcome in the future. This value is determined by considering current asset price, strike price, risk-free rate, future price expectations, and time to maturity.

Signup and view all the flashcards

Exercise Value of an Option

The payoff received from exercising an option immediately. This is the difference between the current underlying asset price and the strike price, limited to zero if it results in a loss.

Signup and view all the flashcards

Continuation Value of an Option

The expected future value of an option, calculated as the discounted value of the expected payoff from holding the option until a later time. This includes the probabilities of different future scenarios and the time value of money.

Signup and view all the flashcards

Time Value of an Option

The difference between the value of holding an option and exercising it immediately. It represents the potential future gains from holding the option, discounted back to the present.

Signup and view all the flashcards

Deferral Option

A real option that allows the holder to delay a project or investment decision until a later time. It reflects the flexibility to wait and learn more about the project or market conditions before making a commitment.

Signup and view all the flashcards

Risk-Free Rate (rf)

This refers to the risk-free rate of return that is used as a discount rate to calculate the present value of future cash flows. It represents the rate of return that can be earned with certainty in the market, usually based on government bonds or other risk-free securities.

Signup and view all the flashcards

Study Notes

Principles of Finance - Lecture 11: Multiperiod Capital Budgeting under Uncertainty: Real Options Analysis

  • This lecture covers multi-period capital budgeting under uncertainty using real options analysis (ROA).
  • Previous methods focused on one-period investment decisions using Net Present Value (NPV).
  • Real-world investments span multiple periods, offering flexibility options like expansion, contraction, abandonment, and deferral.
  • ROA values investment projects by considering these flexibility options.

Assumptions for Real Options Analysis (ROA)

  • Marketed Asset Disclaimer (MAD): The value of the project itself is used as the underlying risky asset.
  • No Arbitrage: A replicating portfolio approach is used for real option valuation.
  • Efficient Capital Market: Project value evolution over time is modeled using recombining binomial trees.

Option Valuation (One Period)

  • The present value of a project without flexibility is calculated.
  • Options have values derived depending on possible future project values (up or down).
  • Option values at terminal date (final period) depend on whether it's a call or put option, determined by the exercise price (K).
  • A replicating portfolio is composed of shares (m) of the underlying risky asset and an amount (B) invested in risk-free bonds.

Option Valuation (One Period) - Continued

  • The values of the option at the end of the period (Vu and Vd) are calculated based on the underlying asset price movement (up or down).
  • The risk-neutral probability (q) is calculated using the risk-free rate and the up and down movements of the underlying asset.
  • The option's present value is calculated using the risk-neutral probabilities and the values at the end of the period.

Option Valuation (Two Periods)

  • Assumptions include constant values for "u" (up movement) and "d" (down movement) and recombining decision trees.
  • Present value of the project without flexibility is calculated.
  • The option's value at the terminal date (T) is determined by whether it's a call or put option, using the exercise price (K).
  • Option values are calculated backward using the risk-neutral probability.
  • Calculating the values after j increases and at time s.

Option Valuation (Two Periods) - American Options

  • For American options, the option holder can exercise the option at any time up to the expiration date.
  • It is necessary to check at every point in time if exercising the option is optimal, or if it's better to keep the option for a future, favorable payoff.
  • Option value at terminal date and value after increases at time s are calculated.

Real Option Analysis (One Real Option)

  • An example of a deferral option is presented with an exercise price (K) of $125.
  • The value of the project without option and the risk-free return (rf = 5%) are given.

Real Option Analysis (Several Real Options)

  • Three real options (abandonment, contraction, and expansion) are presented for a project.

  • Option values are calculated using backward induction considering the impact of different decisions.

  • Abandonment value given.

  • Contraction option: 20% reduction in project value, and $50 in cash.

  • Expansion option: 30% increase in project value with $70 cost.

  • Real options are independent in impact.

  • Formulas to calculate values at different points in time and for different scenarios, or different options.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Principles of Finance: Real Options Analysis Lecture Notes PDF

Description

Test your understanding of Real Options Analysis (ROA) in the context of capital budgeting. This quiz covers key concepts, assumptions, and methods used in ROA, such as the binomial model and the valuation of options. Dive deep into the flexibility and strategic decision-making that ROA offers for investments.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser