REAL OPTION ANALYSIS EXAMPLE 1

[Pages:50]REAL OPTION ANALYSIS EXAMPLE 1

A company is considering investing in a project. The present value (PV) of future discounted expected cash flows is either 3000 if the market goes up or 500 if the market goes down next year. The objective probability the market will go up is 20%. The appropriate risk-adjusted rate of return (cost of capital) is 25%. The initial capital investment required at time 0 is 1200. The risk-free rate is 10% per year. a. Determine the PV of the project at time 0. b. Determine the NPV of the project at time 0. c. Should the company invest in this project? d. Upon closer inspection the CFO realizes the company actually has some flexibility in managing this project. Specifically, if the market goes down, the company can abandon the project, and liquidate its original capital investment for 75% of its original value. If, however, the market should go up, the company could expand operations, which would result in twice the original PV. To expand the company will have to make an additional capital expenditure of 800. The CFO wants to know if the company should now proceed with the project with the added flexibilities, and asks for you advice. Use the original project without flexibility as the traded underlying security.

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REAL OPTION ANALYSIS EXAMPLE 2

A company is considering investing in a project. The present value (PV) of future discounted expected cash flows is either 8000 if the market goes up or 3000 if the market goes down next year. The objective probability the market will go up is 30%. The appropriate risk-adjusted rate of return (cost of capital) is 25%. The initial capital investment required at time 0 is 4000. The risk-free rate is 5% per year. a. Determine the PV of the project without flexibility at time 0. b. Determine the NPV of the project without flexibility at time 0. c. Should the company invest in this project without flexibility? d. Suppose the company has some flexibility in managing this project. Specifically, if the market goes down, the company can abandon the project, and liquidate its original capital investment (at time 0) for 50% of its original value. If, however, the market should go up, the company could expand operations. With expansion the PV (as seen at the end of next year) will be 50% larger than the original PV forecast. To expand the company will have to make an additional capital expenditure of 1000. Using the original project without flexibility as the traded underlying security, determine the ROA value of this project with flexibility.

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REAL OPTION ANALYSIS EXAMPLE 3

A company is considering investing in a project. The present value (PV) of future discounted expected cash flows is either 10,000 if the market goes up or 5,000 if the market goes down next year. The objective probability the market will go up is 60%. The appropriate risk-adjusted rate of return (cost of capital) is 25%. The initial capital investment required at time 0 is 8,000. The risk-free rate is 10% per year. a. Determine the PV of the project at time 0. b. Determine the NPV of the project at time 0. c. Should the company invest in this project? d. The company has some flexibility in managing this project. Specifically, if the market goes down, the company can abandon the project, and liquidate its original capital investment for 50% of its original value. If, however, the market should go up, the company could expand operations, which would result in twice the original PV. To expand the company will have to make an additional capital expenditure of 4,000. Determine the ROA value of this project with flexibility. Use the original project without flexibility as the traded underlying security. e. What is the cost of capital that will yield the correct value if the objective probabilities are used?

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A DELAY OPTION EXAMPLE

The real-estate price for a one-unit condominium, P, is currently $100 thousand. Next year the price will, with equal probability, rise to either $150 thousand, if the market moves favorably, or decline to $90 thousand, if the market moves unfavorably.

The construction cost (both now and next year) for a 6-unit building is $80 thousand per unit, and $90 thousand for a 9-unit building. Construction is instantaneous, and rent covers operating expenses, so no free cash flow is generated now or next year. The risk-free rate is 10%. Questions: 1. Should the company invest in this real estate construction project? 2. What is the value of this real estate construction project? 3. Let St denote the price of a non-dividend paying stock. The price process of S follows a binomial lattice with U = 1.5 and D = 0.90. S0 = 100 and R = 1.1. Let C(T, K) denote a European call option on S with a maturity of T years and strike price of K. a. Determine the time 0 price of C(1, 80). b. Determine the time 0 price of C(1, 110). c. Determine the cost of the portfolio of 6C(1, 80) +3C(1, 110). d. Compare the answers to questions 2 and 3(c). e. Let V1(P1) denote the final payoffs of this real estate construction project. Write a formula for V1(P1). Here, we consider the general case P1 0. f. Graphically depict the function V1( ? ). (Label the x-axis P1 and the y-axis V1(P1).) g. Use (f) to explain (d).

4. What is the value of this real estate construction project if the delay option last for two years?

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A REDEVELOPMENT OPTION EXAMPLE

A real estate developer has the opportunity to redevelop a parcel of land over the next 5 years. Here is the relevant information:

The project is valued today at 12.5 million. The project's (yearly) value follows a binomial lattice with U = 1.5 and D = 2/3. The project pays no dividends. The cost to develop the land today is 10 million. The development cost increases 10% each year. At the beginning of each year it costs 0.5 million to maintain the land if it is not developed for the

upcoming year. If the land is developed, then there is no maintenance cost. During any year the developer may abandon the project and receive 1.2 million. The objective probability of the market going up is 70%. The risk-free rate is 10%. The real estate developer sees this redevelopment project as a great opportunity. In fact, she is ready to develop the land today, as she has calculated its NPV at 2.5 million. She asks your consulting company for advice on what to do.

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