Chapter 13, Real Options Video Solutions, Financial Management: Theory and Practice

Problem 1

Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the 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 $13 \%$.
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 $50 \%$ 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 $50 \%$ chance that the tax will not be imposed, in which case the yearly cash flows will be 5.3 .8 million. Kim is deciding whether to proceed with the hotel today or to wait 1 year to find cut whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $\$ 20$ million. Assume that all cash flaws are discounted at $13 \%$. Using decision tree analysis, should Kim proceed with the project today or should it wait a year before deciding?

Nick Johnson

Numerade Educator

05:17

Problem 2

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 $90 \%$ chance that the net cash flows would be $\$ 4.2$ million a year for 4 years, and there is a $10 \%$ chance that the cash flows will be $\$ 2.2$ million a year for 4 years. Assume that all cash flows are discounted at $10 \%$.
a. If the company chooses to drill today, what is the project's net present value?
b. Using decision tree analysis, does it make sense to wait 2 years before deciding whether to drill?

Aishwarya Krishnakumar

Numerade Educator

03:59

Problem 3

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 $13 \%$
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 $50 \%$ chance the cash flows will be $\$ 50$ million a year, and a $50 \%$ 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 $13 \%$.

Julie Silva

Numerade Educator

00:00

Problem 4

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 $12 \%$ cost of capital. Assume at the out set 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 $50 \%$ chance that the tax will be imposed, what is the project's expected NTV if they proceed with it today?
d. While the company does nut 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 $12 \%$, 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 $12 \%$, and the probability that the tax will be imposed is still $50 \%$. How much would the company pay today for the option to purchase this property 1 year from now for $\$ 1.5$ million?

Oluwadamilola Ameobi

Numerade Educator

04:06

Problem 5

Fethe's Funny Hats is considering selling trademarked curly orange-haired wigs for University of Tennessee football games. The purchase cost for a 2-year franchise to sell the wigs is $\$ 20,000$. If demand is good $(40 \%$ probability), then the net cash flows will be $\$ 25,000$ per year for 2 years. If demand is bad $(60 \% \text { probability })$, then the net cash flows will be $\$ 5,000$ per year for 2 years. Fethe's cost of capital is $10 \%$
a. What is the expected NPV of the project?
b. If Fethe makes the investment today, then it will have the option to renew the franchise fee for 2 more years at the end of Year 2 for an additional payment of $\$ 20,000 .$ In this case, the cash flows that occurred in Years 1 and 2 will be repeated (so if demand was good in Years 1 and 2 , then it will continue to be good in Years 3 and 4 ). Write out the decision tree and use decision tree analysis to calculate the expected NPV of this project including the option to continue on for an additional 2 years. Note: The franchise fee payment at the end of Year 2 is known, so it should be discounted at the risk-free rate, which is $6 \%$.

Julie Silva

Numerade Educator

04:02

Problem 6

Rework Problem $13-1$ using the Black-Scholes model to estimate the value of the option. (Hint: Assume the variance of the project's rate of return is $6.87 \%$ and the risk-free rate is $8 \% .$ )

Willis James

Numerade Educator

01:03

Problem 7

Rework Problem $13-2$ using the Black-Scholes model to estimate the value of the option: The risk-free rate is $6 \%$. (Hint: Assume the variance of the project's rate of return is $1.11 \% .$ )

Breanna Ollech

Numerade Educator

01:03

Problem 8

Rework Problem $13-5$ using the Black-Scholes model to estimate the value of the option. The risk-free rate is $6 \%$. (Hint: Assume the variance of the project's rate of return is $20.25 \% .$)

Breanna Ollech

Numerade Educator

02:30

Problem 9

Start with the partial model in the file $F M 12 \mathrm{Ch} 13 \mathrm{PO} 9$ Build a Model.xls from the textbook's Web site. Bradford Services Inc. (BSI) is considering a project that has a cost of $\$ 10$ million and an expected life of 3 years. There is a $30 \%$ probability of good conditions, in which case the project will provide a cash flow of $\$ 9$ million at the end of each year for 3 years. There is a $40 \%$ probability of medium conditions, in which case the annual cash flows will be $\$ 4$ million, and there is a $30 \%$ probability of bad conditions and a cash flow of $-\$ 1$ million per year. BSI uses a $12 \%$ cost of capital to evaluate projects like this.
a. Find the project's expected present value, $\mathrm{NPV}$, and the coefficient of variation of the present value.
b. Now suppose that BSI can abandon the project at the end of the first year by selling it for $\$ 6$ million. BSI will still receive the Year 1 cash flows, but will receive no cash flows in subsequent years.
c. Now assume that the project cannot be shut down. However, expertise gained by taking it on would lead to an opportunity at the end of Year 3 to undertake a venture that would have the same cost as the original project, and the new project's cash flows would follow whichever branch resulted for the original project. In other words, there would be a second $\$ 10$ million cost at the end of Year 3 , and then cash flows of either $\$ 9$ million, $\$ 4$ million, or $-\$ 1$ million for the following 3 years. Use decision tree analysis to estimate the value of the project, including the opportunity to implement the new project at Year 3 Assume the $\$ 10$ million cost at Year 3 is known with certainty and should be discounted at the risk-free rate of $6 \%$.
d. Now suppose the original (no abandonment and no additional growth) project could be delayed a year. All the cash flows would remain unchanged, but information obtained during that year would tell the company exactly which set of demand conditions existed. Use decision tree analysis to estimate the value of the project if it is delayed by 1 year. (Hint: Discount the $\$ 10$ million cost at the risk-free rate of $6 \%$ since it is known with certainty.
e. Go back to part c. Instead of using decision tree analysis, use the Black-Scholes model to estimate the value of the growth option. The risk-free rate is $6 \%,$ and the variance of the project's rate of return is $22 \%$.

M Hassan Anwar

Numerade Educator