More practice problems on Real Option Valuation
Note: (Questions 3-5 are from “Intermediate Financial Management, 8th ed., by Brigham and Daves)
Solutions 1& 2 are in white font (change font color to reveal solutions)
1) You are considering a project to open Homer’s Doughnut Shop. You estimate the following potential cash flows will occur:
Event / probability / NPV of project (t=0)apartments built next to strip mall / 0.6 / 12000
no apartments built next to strip mall / 0.4 / -15000
If you wait a year to open Homer’s Doughnut shop, you will know, with certainty, whether the apartments will be built on the adjacent piece of land or not, before you need to make the decision to invest in the shop, or not. However, the cost of the doughnut shop lease will go up if the apartments are built and you wait a year to invest. The NPVs of the investment if you wait a year & invest become:
Event / probability / NPV (@t=1) / NPV (@t=0)apartments built next to strip mall / 0.6 / 8000 / 7273
no apartments built next to strip mall / 0.4 / -15000 / -13636
1a) What is the NPV of the decision to invest NOW?_____1200______(Write answer on line)
.6(12000) + .4(-15,000)
1b) What is the NPV of the decision to wait a year to invest, given that you have the option not to invest at that time?__4363.8______(Write answer on line)
.6(7273) + .4 (0)
1c) ______What should the investor do? Wait to invest
a) Invest NOWb) Wait a year to investc) Don’t invest NOW or LATER
Mmmm…donuts!
2)______You are considering a project to build a Jimmy-John’s Sandwich shop on a vacant piece of land. The NPV of your sandwich shop will depend on the type of development on the adjacent property. The possibilities for adjacent property development are given below, along with their respective probabilities.
You can build the shop today or wait a year. If you wait a year to invest in your sandwich shop, you will know, WITH CERTAINTY, what will be built on the adjacent property. At that time, you can also decide not to invest. Also, if you build the shop in one year, you can contract to sell it after one year (i.e., two-years from now), for varying amounts, depending on the development on the adjacent property. You estimate the NPVs (discounted back to t=0) in the following table.
Adjacent property / Probability / Course of action / NPV (t=0)Nothing is built / .25 / Sell shop / -50,000
Keep shop / -200,000
Office complex is built / .50 / Sell shop / -10,000
Keep shop / 100,000
Strip mall is built / .25 / Sell shop / 150,000
Keep shop / 100,000
What is the NPV of the option to wait a year to build a Jimmy-John’s Sandwich shop, also considering that you have the option to sell it?
a) $87,500b) $75,000c) $100,000d) 0e) None of these
Build or wait:
0 (.25 ) + 100 (.5) + 150 (.25) = 87,500
Solutions for 3-5 are in Excel (separate file)
3) KimHotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require a positive investment of $20 million. Kim expects that the hotel will produce positive cash flows of $3 million a year at the end of the next 20 years. The project’s cost of capital is 13%.
a)What is the project’s NPV?
b)While Kim expects that the cash flows will be $3 million per year, they recognize that the cash flows could, in fact, be much higher or lower, depending on whether the Korean government imposes a large hotel tax. There is a 50% chance the new tax will be imposed. One year from now, Kim will know whether the tax is imposed. If the tax is imposed, the annual after tax cash flow will be only $2.2 million. If the tax is not imposed, the after tax cash flows will be $3.8 million. Kim is deciding whether to proceed with the project TODAY, or whether to wait a year. If Kim waits a year, the cost of the project will remain $20 million. What is the NPV of the project, if Kim waits a year to invest? What should Kim do…invest today, or wait a year to invest?
4) Karns Oil Co is deciding whether to drill for oil on a tract of land that the company owns. Karns estimates that the project will cost $8 million today, and will generate after tax cash flows of $4 million a year at the end of each of the next 4 years.
While Karns is fairly confident about its cash flow estimates, it recognizes that if it waits 2 years, it will have more information about the local geology, as well as the price of oil. If Karns waits 2 years, the project’s cost will increase to $9 million. Moreover, if Karns waits 2 years, there is a 90% chance that the net cash flows will be $4.2 million for each of the next four years, and a 10% chance that the net cash flows will be $2.2 million a year for 4 years.
The discount rate for all cash flows is 10%.
a)What is the NPV of the project if Karns decides to invest today?
b)What is the NPV of the project if Karns decides to invest in two years? What should Karns do – invest today or wait two years?
5) Hart Lumber is considering the purchase of the White Paper Co. Purchase of White Paper would require an initial investment of $300 million. Hart estimates that White Paper would provide net cash flows of $40 million at the end of each of the next 20 years. The cost of capital is 13%.
a) What is the NPV of the project to purchase White Paper today?
b) While Hart’s best guess is that the cash flows of White Paper will be $40 million a year, it recognizes that there is a 50% chance that the cash flows will be $50 million a year and a 50% chance that the cash flows will be $30 million a year for 20 subsequent years. One year from now, Hart will find out whether White Paper’s cash flows will be $30 or $50 million. Additionally, Hart recognizes that, if it wanted, it could sell White Paper 3 years from now for $280 million.
What is Hart’s best course of action if they wait, and the $30 million cash flow occurs? What is Hart’s best course of action if they wait, and the $50 million cash flow occurs? What is the NPV of the decision to wait to invest, and (potentially) sell White Paper?
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