Real Option Problem

Assume that a firm's investment project once completed, will produce a fixed flow of output forever. For convenience you can choose the units so that the quantity of output from the project is equal to one unit per year. Suppose the inverse demand function, giving price P in terms of quantity Qis P YD(Q), where Y is a stochastic shift variable. Assume that the variable cost of production are assumed to be zero, so the firm's profit flow is just P YD). Hence we can assume, without loss of generality, that the P itself is a stochastic variable. Therefore, assume that P follows the stochastic process: where dz is the increment of a standard Brownian motion, ? is the drift rate, and ? the volatility. The future revenues are discounted at the rate ?. a. What is the expected present value V of the project, when the current price is P2 b. Derive the optimal investment strategy in this project given the investment is irreversible implying a sunk investment cost I c. Derive the value of the option to invest. Note: Follow the contingent claims analysis method of Chapter 5 in Dixit and Pindyck (1994) Assume that a firm's investment project once completed, will produce a fixed flow of output forever. For convenience you can choose the units so that the quantity of output from the project is equal to one unit per year. Suppose the inverse demand function, giving price P in terms of quantity Qis P YD(Q), where Y is a stochastic shift variable. Assume that the variable cost of production are assumed to be zero, so the firm's profit flow is just P YD). Hence we can assume, without loss of generality, that the P itself is a stochastic variable. Therefore, assume that P follows the stochastic process: where dz is the increment of a standard Brownian motion, ? is the drift rate, and ? the volatility. The future revenues are discounted at the rate ?. a. What is the expected present value V of the project, when the current price is P2 b. Derive the optimal investment strategy in this project given the investment is irreversible implying a sunk investment cost I c. Derive the value of the option to invest. Note: Follow the contingent claims analysis method of Chapter 5 in Dixit and Pindyck (1994)