Principles of Finance - Lecture 11
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Questions and Answers

What is the abandonment value if the project is abandoned?

  • $190 (correct)
  • $50
  • $70
  • $100

    • Which option allows for a reduction in the project's value by 20%?

  • Expansion option
  • Contraction option (correct)
  • Abandonment option
  • Investment option

    • What is the cost associated with expanding the value of the project by 30%?

  • $70 (correct)
  • $190
  • $100
  • $50

    • How many real options are available for the project mentioned?

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

    Which option provides $50 in cash for the project?

    <p>Contraction option</p> Signup and view all the answers

    Which of the following best describes the Real Options Analysis (ROA)?

    <p>An approach used for multi-period investment decisions under uncertainty.</p> Signup and view all the answers

    What does the option to 'defer' in real options analysis entail?

    <p>Delaying the start of a project until later.</p> Signup and view all the answers

    Which assumption is NOT part of the Real Options Analysis (ROA)?

    <p>Arbitrage opportunities are always present.</p> Signup and view all the answers

    What is the role of binomial trees in Real Options Analysis?

    <p>To model the fluctuations and evolution of project value.</p> Signup and view all the answers

    Which option best defines the 'expand' flexibility in Real Options?

    <p>Increasing investment for an additional cost.</p> Signup and view all the answers

    What is the expression for the value of the option at time t = 1 for an upward movement?

    <p>$V_u = (1 + r_f)^{-1} qV_{uu} + (1 - q)V_{ud}$</p> Signup and view all the answers

    What calculation needs to be made to determine the value of an American option at time t = T?

    <p>The maximum of the option value and the intrinsic value.</p> Signup and view all the answers

    If $rf$ is assumed constant over time, what does this imply about the parameter q?

    <p>q remains constant throughout the options' life.</p> Signup and view all the answers

    Which of the following best describes the value of the option today at time t = 0?

    <p>$V_0 = (1 + r_f)^{-1} (q^2 V_{uu} + 2(1 - q)V_{ud} + (1 - q)^2 V_{dd})$</p> Signup and view all the answers

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

    <p>$V_T = max[ST - K, 0]$</p> Signup and view all the answers

    What is the formula used to calculate the expected return on the underlying asset in one year?

    <p>E[S1] = qSu + (1 − q)Sd</p> Signup and view all the answers

    In the context of option valuation, what is the value of a call option at terminal date, T?

    <p>VT = max[ST - K; 0]</p> Signup and view all the answers

    Which method is suggested for determining the option value in the two-period model?

    <p>Backward induction</p> Signup and view all the answers

    What assumption is made regarding the risk-free rate (rf) in the option valuation model?

    <p>rf is constant over time</p> Signup and view all the answers

    What does the variable q represent in the formula for expected return on the underlying asset?

    <p>The probability of an upward movement</p> Signup and view all the answers

    What is the definition of the value of the option at terminal date for a put option?

    <p>max[K - ST; 0]</p> Signup and view all the answers

    In the two-period option valuation model, what is implied by the term 'recombining decision trees'?

    <p>The possible price movements merge back into common outcomes</p> Signup and view all the answers

    What does the equation E[ST] = (1 + rf)∆t S0 represent in the context of expected returns?

    <p>The expected price of the asset after time period τ</p> Signup and view all the answers

    What is the value of a call option at time t = 1 if the stock price is at its maximum compared to the strike price K?

    <p>max $S_u - K$</p> Signup and view all the answers

    At time t = 0, the value of a put option is calculated using which of the following formulas?

    <p>$max K - S_0 + (1 + r_f)^{-1} qV_u + (1 - q)V_d$</p> Signup and view all the answers

    What does the term $r_f$ represent in option valuation?

    <p>Risk-free return rate</p> Signup and view all the answers

    In the context of American option valuation, what is the significance of the formula involving $V_{uu}$ and $V_{ud}$?

    <p>They represent the potential future values of the option.</p> Signup and view all the answers

    For the given deferral option example with $K = 125$ and $r_f = 5\%$, what does the term 'deferral option' imply?

    <p>The option can be delayed before exercise.</p> Signup and view all the answers

    What does the expression $max K - S_{0}$ refer to in the valuation of put options?

    <p>Intrinsic value at expiration</p> Signup and view all the answers

    What condition is necessary for a call option to be valuable at any given time?

    <p>$S_j &gt; K$</p> Signup and view all the answers

    The term $(1 - q)V_{j}$ in the option valuation formula reflects which scenario?

    <p>Probability of downward movement</p> Signup and view all the answers

    What formula represents the value of a call option at terminal date, t = T?

    <p>$max[S_T - K; 0]$</p> Signup and view all the answers

    In a replicating portfolio, which variable represents the number of shares of the underlying risky asset?

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

    What does the risk-neutral probability, q, depend on according to the given content?

    <p>The difference between the upward and downward future values</p> Signup and view all the answers

    In the context of option pricing, which statement about the no-arbitrage principle is correct?

    <p>The replicating portfolio and option must have the same price.</p> Signup and view all the answers

    What does the value of an option at time zero (V_0) equal in terms of m and B?

    <p>$mS_0 + B(1 + r_f)^{- riangle t}$</p> Signup and view all the answers

    What equation relates the values Vu and Vd to the shares m and the bonds B using the no-arbitrage condition?

    <p>$V_u - V_d = m(u - d)$</p> Signup and view all the answers

    What is the value of the option calculated at the terminal date for put options?

    <p>$max[K - S_T; 0]$</p> Signup and view all the answers

    Which of the following describes the relationship between the risk-neutral expected return on the underlying asset and the risk-free return?

    <p>The expected return equals the risk-free return.</p> Signup and view all the answers

    Study Notes

    Principles of Finance - Lecture 11

    • Lecture focuses on multi-period capital budgeting under uncertainty using real options analysis (CWS ch. 9)
    • Previous methods (NPV) only considered one-period investment decisions under uncertainty.
    • Real-world investments often span multiple time periods, offering flexibility in decision-making.
    • Flexibility options include expansion, contract, abandonment, extension, and deferral.

    Real Options Analysis (ROA)

    • ROA is based on the binomial model.
    • Marketed asset disclaimer (MAD): Underlying risky asset is the project value itself.
    • No arbitrage: Replicating portfolio approach used for real option valuation.
    • Efficient capital market: Models project value evolution with recombining binomial trees.

    Option Valuation (One Period)

    • Project's present value (without flexibility) is used as a base.
    • Options' value is determined based on future value of the project under different possible scenarios.
    • Option value at terminal date (t=T): calculated as maximum of [ST – K; 0] (call option) or [K - ST; 0] (put option).

    Option Valuation (One Period) - Continued

    • A replicating portfolio for an option includes shares of the underlying risky asset and an investment in default-free bonds.
    • Formula for values are given.

    Option Valuation: Risk-Neutral Probabilities

    • Risk-neutral probability(q) determines expected return on the underlying asset at risk free return.
    • Solving for q in equations

    Option Valuation (Two Periods)

    • Assumes constant "u" and "d" (up and down movements) and recombining decision trees.
    • Option value is determined via backwards induction.

    Option Valuation (Two Periods) - European Options

    • Assumes constant risk-free rate (rf), which implies a constant q.
    • Values calculated at the terminal date (t = T).
    • Option values calculated for various scenarios at intermediate dates based on possible upward or downward movements and calculated value at a later date

    Option Valuation (Two Periods) - American Options

    • Check if optimal to exercise option or continue at each point in time.
    • Option value determined for various scenarios at intermediate dates and based on possible upward/downward movements, potentially changing value at a later date if exercised.

    Real Option Analysis (One Real Option)

    • Example analysis of deferral option, using a numerical example.
    • Calculating intrinsic value of the underlying project without flexibility and demonstrating effect of flexibility options within given time period.

    Real Option Analysis (Several Real Options)

    • Examples of three real options (abandonment, contraction, and expansion) presented with numerical illustrations
    • Value of project in the different time periods assessed against the value of each option.

    References

    • CWS, ch. 9 (Core textbook for financial valuation)

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    Principles of Finance: Real Options Analysis Lecture Notes PDF

    Description

    This lecture focuses on multi-period capital budgeting using real options analysis. It explores how traditional methods like NPV fall short when considering investments spanning multiple time periods, introducing flexibility options such as expansion and abandonment. Additionally, the lecture covers the binomial model and the valuation of options in capital projects.

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