## Assume You Have Been Given The Following Information On Purcell Industries Current Stock Price 15 Exercise Price Of Option 15 Time To Maturity Of Option 6 Months Risk-free Rate 10 Variance Of Stock Price 0.12

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17-1 Assume you have been given the following information on Purcell Industries: BLACK-SCHOLES MODEL

Current stock price = \$15 Exercise price of option = \$15

Time to maturity of option = 6 months Risk-free rate = 10%

Variance of stock price = 0.12 d1 = 0.32660

Using the Black-Scholes Option Pricing Model, what would be the value of the option?

17-2 The exercise price on one of Flanagan Company's options is \$15, its exercise value is \$22, and options its premium is \$5. What are the option's market value and the price of the stock?

17-3 Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the INVESTMENT TIMING OpTION: hotel would require an initial investment of \$20 million. Kim expects that the hotel will produce positive cash flows of \$3 million a year at the end of each of the next 20 years. The project's cost of capital is 13 percent.

a. What is the project's net present value?

b. While Kim expects the cash flows to be \$3 million a year, it recognizes that the cash flows could, in fact, be much higher or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a 50 percent chance that the tax will be imposed, in which case the yearly cash flows will be only \$2.2 million. At the same time, there is a 50 percent chance that the tax will not be imposed, in which case the yearly cash flows will be \$3.8 million. Kim is deciding whether to proceed with the hotel today or to wait 1 year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at \$20 million. Assume that all cash flows are discounted at 13 percent. Using decision tree analysis, should Kim proceed with the project today or should it wait a year before deciding?

DECISION TREE ANALYSIS

17-4

INVESTMENT TIMING OPTION: DECISION TREE ANALYSIS

17-5

INVESTMENT TIMING OPTION: DECISION TREE ANALYSIS

17-6

REAL OPTIONS: DECISION TREE ANALYSIS

17-7

INVESTMENT TIMING OPTION: OPTION ANALYSIS

The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates that the project would cost \$8 million today. Karns estimates that once drilled, the oil will generate positive net cash flows of \$4 million a year at the end of each of the next 4 years. While the company is fairly confident about its cash flow forecast, it recognizes that if it waits 2 years, it would have more information about the local geology as well as the price of oil. Karns estimates that if it waits 2 years, the project would cost \$9 million. Moreover, if it waits 2 years, there is a 90 percent chance that the net cash flows would be \$4.2 million a year for 4 years, and there is a 10 percent chance that the cash flows will be \$2.2 million a year for 4 years. Assume that all cash flows are discounted at 10 percent.

a. If the company chooses to drill today, what is the project's net present value?

b. Using decision tree analysis, would it make sense to wait 2 years before deciding whether to drill?

Hart Lumber is considering the purchase of a paper company. Purchasing the company would require an initial investment of \$300 million. Hart estimates that the paper company would provide net cash flows of \$40 million at the end of each of the next 20 years. The cost of capital for the paper company is 13 percent.

a. Should Hart purchase the paper company?

b. While Hart's best guess is that cash flows will be \$40 million a year, it recognizes that there is a 50 percent chance the cash flows will be \$50 million a year, and a 50 percent chance that the cash flows will be \$30 million a year. One year from now, it will find out whether the cash flows will be \$30 million or \$50 million. In addition, Hart also recognizes that if it wanted, it could sell the company at Year 3 for \$280 million. Given this additional information, does using decision tree analysis indicate that it makes sense to purchase the paper company? Again, assume that all cash flows are discounted at 13 percent.

Utah Enterprises is considering buying a vacant lot that sells for \$1.2 million. If the property is purchased, the company's plan is to spend another \$5 million today (t = 0) to build a hotel on the property. The after-tax cash flows from the hotel will depend critically on whether the state imposes a tourism tax in this year's legislative session. If the tax is imposed, the hotel is expected to produce after-tax cash inflows of \$600,000 at the end of each of the next 15 years. If the tax is not imposed, the hotel is expected to produce after-tax cash inflows of \$1,200,000 at the end of each of the next 15 years. The project has a 12 percent cost of capital. Assume at the outset that the company does not have the option to delay the project. Use decision tree analysis to answer the following questions.

a. What is the project's expected NPV if the tax is imposed?

b. What is the project's expected NPV if the tax is not imposed?

c. Given that there is a 50 percent chance that the tax will be imposed, what is the project's expected NPV if they proceed with it today?

d. While the company does not have an option to delay construction, it does have the option to abandon the project 1 year from now if the tax is imposed. If it abandons the project, it would sell the complete property 1 year from now at an expected price of \$6 million. Once the project is abandoned the company would no longer receive any cash inflows from it. Assuming that all cash flows are discounted at 12 percent, would the existence of this abandonment option affect the company's decision to proceed with the project today?

e. Finally, assume that there is no option to abandon or delay the project, but that the company has an option to purchase an adjacent property in 1 year at a price of \$1.5 million. If the tourism tax is imposed, the net present value of developing this property (as of t = 1) is only \$300,000 (so it wouldn't make sense to purchase the property for \$1.5 million). However, if the tax is not imposed, the net present value of the future opportunities from developing the property would be \$4 million (as of t = 1). Thus, under this scenario it would make sense to purchase the property for \$1.5 million. Assume that these cash flows are discounted at 12 percent, and the probability that the tax will be imposed is still 50 percent. How much would the company pay today for the option to purchase this property 1 year from now for \$1.5 million?

Rework Problem 17-3 using the Black-Scholes model to estimate the value of the option. (Hint: Assume the variance of the project's rate of return is 6.87 percent and the risk-free rate is 8 percent.)

17-8

INVESTMENT TIMING OPTION: OPTION ANALYSIS

Rework Problem 17-4 using the Black-Scholes model to estimate the value of the option: The risk-free rate is 6 percent. (Hint: Assume the variance of the project's rate of return is 1.11 percent.)

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### Responses

• NATALINO
What is the project’s expected NPV if the tax is imposed?
7 years ago