Real Options Analysis in Capital Budgeting

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

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

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

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

<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

<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

<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

<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

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

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

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

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

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

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

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

<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

<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

<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

<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

<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

<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

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

<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

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

<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

<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

<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

<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

<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

<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

<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

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

<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

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

<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

<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

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

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

<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