problem set 4
15 Describe the following situation in the language of options: Air France negotiates a purchase option for 10 Boeing 787s. Air France must confirm the order by 2014. Otherwise Boeing will be free to sell the aircraft to other airlines.
A call option that allows Air France to fix the delivery date and price.
13 Describe the following situation in the language of options: A paper mill can be shut down in periods of low demand and restarted if demand improves sufficiently. The costs of closing and reopening the mill are fixed.
A complex option that allows the company to abandon temporarily (an American put) and (if the put is exercised) to subsequently restart (an American call).
10 Describe the following situation in the language of options: Drilling rights to undeveloped heavy crude oil in Northern Alberta. Development and production of the oil is a negative- NPV endeavor. (Assume a break-even oil price is C$90 per barrel, versus a spot price of C$80.) However, the decision to develop can be put off for up to five years. Development costs are expected to increase by 5% per year.
A five-year American call option on oil. The initial exercise price is C$90 a barrel, but the exercise price rises by 5% per year.
12 1. (A variation on question 11) Describe the following situation in the language of options: Assume the restaurant faces known fixed costs of $300,000 per year, incurred as long as the restaurant is operating. Thus, (image) The annual standard deviation of the forecast error of revenue less variable costs is 10.5%. The interest rate is 10%. Ignore taxes.
A put option, as in question 11, except that the exercise price should be interpreted as $5 million in real estate value plus the present value of the future fixed costs avoided by closing down the restaurant. Thus, the exercise price is: $5,000,000 + ($300,000/0.10) = $8,000,000 Note: The underlying asset is now PV(revenue - variable cost), with annual standard deviation of 10.5%.
14 Describe the following situation in the language of options: A real estate developer uses a parcel of urban land as a parking lot, although construction of either a hotel or an apartment building on the land would be a positive-NPV investment.
An in-the-money American option to choose between two assets; that is, the developer can defer exercise and then determine whether it is more profitable to build a hotel or an apartment building. By waiting, however, the developer loses the cash flows from immediate development.
6 Gas turbines are among the least efficient ways to produce electricity, much less thermally efficient than coal or nuclear plants. Why do gas-turbine generating stations exist? What's the option?
Gas turbines can be started up on short notice when spark spreads, or the difference between the price of electricity and the cost of the natural gas used as fuel, are high. The turbines' value comes from flexibility in production. The option is the ability to run or not run the turbine.
1 Explain the difference between the net present value approach and the risk-neutral valuation approach for valuing a new capital investment opportunity. What are the advantages of the risk-neutral valuation approach for valuing real options?
In the net present value approach, cash flows are estimated in the real world and discounted at a risk-adjusted discount rate. In the risk-neutral valuation approach, cash flows are estimated in the risk-neutral world and discounted at the risk-free interest rate. The risk- neutral valuation approach is arguably more appropriate for valuing real options because it is very difficult to determine the appropriate risk-adjusted discount rate when options are valued.
9 Alert financial managers can create real options. Give three or four possible examples.
Potential ways that financial managers can create real options include: Designing the initial investment project to create inexpensive options for later expansion; investing in a series of modular production facilities rather than committing to a single large plant; using standardized equipment with good salvage values; waiting and gathering information before investing (the timing option)
7 Why is quantitative valuation of real options often difficult in practice? List the reasons briefly.
Real options can be complex. Many real-options problems are not well structured, and it can be difficult to lay out a roadmap of future events and decisions. Competitive interactions can generate further complications.
18 (A variation on Problem 17): Suppose the land is occupied by a warehouse generating rents in one year of $150,000 after real estate taxes and all other out-of-pocket costs. The present value of the land plus warehouse is again $1.7 million. Other facts are as in Problem 17. You have a European call option. What is it worth?
The asset value from Problem 17 is now reduced by the present value of the rents: PV(rents) = 0.15/1.12 = 0.133 Therefore, the asset value is now (1.7 - 0.133) = 1.567.
4 Suppose that you are evaluating the potential construction of a new plant for Hoya Enterprises. You have assumed an economic life of ten years for the plant and have estimated the NPV of this plant based off of this economic life and other cash flow assumptions. What might be wrong with the ten-year economic life assumption? How would you undertake a more complete analysis?
The life of a project is not fixed ahead of time. Hoya has the option to abandon the plant after a certain number of years if performance is poor. If performance is great, exercise of the abandonment option could be delayed well beyond the estimated ten-year life.
3 A start-up company is moving into its first offices and needs desks, chairs, filing cabinets, and other furniture. It can buy the furniture for $25,000 or rent it for $1,500 per month. The founders are of course confident in their new venture, but nevertheless they rent. Why? What's the option?
The option is the abandonment value of the used furniture. The company can buy furniture and resell (abandon) if the start-up fails, but the abandonment value of used furniture is not great. It's often better to retain flexibility by renting.
21 Josh Kidding, who has only read part of Chapter 10 of the BMA text, decides to value a real option by (1) setting out a decision tree, with cash flows and probabilities forecasted for each future outcome; (2) deciding what to do at each decision point in the tree; and (3) discounting the resulting expected cash flows at the company cost of capital. Will this procedure give the right answer? Why or why not?
The valuation approach proposed by Josh Kidding will not give the right answer because it ignores the fact that the discount rate within the tree changes as time passes and the value of the project changes.
2 Look again at the valuation in Table 22.2 of the BMA text for the option to invest in the Mark II project. Consider a change in each of the following inputs. Would the change increase or decrease the value of the expansion option? a. Increased uncertainty (higher standard deviation). b. More optimistic forecast (higher expected value) of the Mark II in 1985. c. Increase in the required investment in 1985.
a. Increases the value of the expansion option (unless the cash flows from the Mark II needed to be discounted at a higher rate) b. Increases the value of the expansion option as the expected cash flows are higher Reduces the value of the expansion option as the expected cash flows arelower
8 True or false? a. Real-options analysis sometimes tells firms to make seemingly negative-NPV investments to secure future growth opportunities. b. Using the Black-Scholes formula to value options to invest is dangerous when the investment project would generate significant immediate cash flows. c. Binomial trees can be used to evaluate options to acquire or abandon an asset. It's OK to use risk-neutral probabilities in the trees even when the asset beta is 1.0 or higher. d. It's OK to use the Black-Scholes formula or binomial trees to value real options, even though the options are not traded. A real-options valuation will sometimes reveal that it's better to invest in a singlelarge plant than a series of smallerplants.
a. True. Negative-NPV projects may have call options on follow-on projects. b. True. Options are more attractive when uncertainty is great and immediate project cash flows—which are lost or postponed by waiting—are small. c. True. Shareholders accept any capital investment whose market value if traded exceeds its cost, as long as they can buy traded securities with the same risk characteristics as the project. d. True. Using the risk-neutral method values the option as if it could be traded. e. True. The series of smaller plants generates real options, but the large plant may nevertheless be more efficient.
5 You own a parcel of vacant land. You can develop it now, or wait. a. What is the advantage of waiting? b. Why might you decide to develop the property immediately?
a. While you wait, you learn more about land prices and best use of the land. This is a call option, whose value could be substantial. By developing immediately, you capture rents immediately, which might offset some costs of maintaining the property (to meet local land use restrictions) and propertytaxes.
20 Respond to the following comments. a. "You don't need option pricing theories to value flexibility. Just use a decision tree. Discount the cash flows in the tree at the company cost of capital." b. "These option pricing methods are just plain nutty. They say that real options on risky assets are worth more than options on safe assets." "Real-options methods eliminate the need for DCF valuation of investmentprojects."
a. You can't use any one discount rate for the option payoffs. The risk of an option changes as asset price changes and time passes. b. The risky asset may be worth less as a consequence of its riskiness, but the option on the risky asset is more valuable because the option owner can capitalize from up moves while not losing due to down moves. The value of an option depends on the value of the underlying asset. DCF valuation of investment projects is necessary in order to determine the value of the underlyingasset.
16 1. Look again at Table 22.2 of the BMA text. (Note that using our model, the valuation would be $56.8 million. This is due to the BMA text using an approximation of the more accepted model.) How does the value in 1982 of the option to invest in the Mark II change if: a. The investment required for the Mark II is $800 million (vs. $900 million)? b. The present value of the Mark II in 1982 is $500 million (vs. $467 million)? The standard deviation of the Mark II's present value is only 20% (vs.35%)?
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