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Chapter 09 - CHAPTER 9 REVIEW QUESTIONS R1 An ability to...

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Unformatted text preview: CHAPTER 9 REVIEW QUESTIONS R1. An ability to make one or more future decisions involving real assets after information is received that can affect the financial outcomes. R2. The right to abandon allows the decision maker the ability to remove some potential negative outcomes. Who would dare open a new business such as a restaurant if they would never be allowed to close the business and would therefore be forced to keep it open forever even if it was losing money every day? R3. Decision trees begin with a single node on the left side that represents a current decision. As the diagram moves from left to right to model the passage of time, two types of nodes can be used: decision nodes and information nodes. Each node allows for the creation of two or more paths that indicate different sets of outcomes. Every meaningful potential pathway of the future is modeled. R4. In a decision tree, decision nodes represent points in time (under the conditions necessary to arrive at that node) at which the decision maker can make a meaningful decision that will alter the economic outcome of the project being analyzed. Examples of decisions would be to expand, to abandon, to switch to new technology and so forth. Information nodes are points in time (under the conditions necessary to arrive at that node) at which meaningful information is revealed such that it will be revealed which of two or more outcomes or pathways will be realized. Examples of information would be whether a technology is successful, whether the economy recovers, whether the market price of a particular good rises or falls and so forth. R5. The goal of backward induction is to solve the current decision. The current decision is solved by beginning with the final decisions and moving ”backward in time" one period at a time until the current time period and current decision are reached. R6. New information inside a decision tree is modeled as an information node. Infor— mation nodes reveal which of two or more outcomes or pathways are realized. Exam— ples of information that would reveal outcomes or pathways could include whether a prototype succeeds, whether a test is successful, whether a merger is approved, whether a regulation is changed, whether tax rates change, how market values change, etc. R7. Traditional NPV utilizes unconditional expected values. In terms of the math of NPV, traditional analysis places the expected net cash flows into the numerator of the formula. Real options allow decision makers to revise decisions and prevent many undesirable outcomes. For example, the option to shut down a convenience store would allow the entrepreneur the right to stop losing money if highly negative outcomes were realized such as a major loss of potential customers or if numerous competitors entered the market resulting in too many stores for the demand. 60 CHAPTER 9 PROBLEMS 1a. Undeveloped land allows the owner the real option of how to develop the land. If there are multiple potential uses that vary through time in relative attractiveness, the land owner may find it beneficial to wait and see which possible use of the land provides the best value. 1b. Factories that can run on multiple inputs offer the owner the real option of which input to use. If these multiple inputs vary through time in relative cost, the factory owner may find it beneficial at future points in time to switch to an input that affords the best value. 1c. Lines of credit allow borrowers the financial option of whether or not to borrow at some point in the future. If the credit risk of the borrower or the prevailing interest rates change, the borrower may find it beneficial to utilize the line of credit, but is not forced to use the line of credit if it is not advantageous to do so. 1d. Cancellable leases allow tenants the real option of whether or not to continue to rent at one or more points in the future. If the rental rates in the area vary or if the usefulness of remaining at the property varies through time, then the renter may find it beneficial to continue or cancel the lease — whichever path is more valuable to the renter. 1e. Payment alternatives allow borrowers the financial option of whether or not to delay payment (in effect, borrow money) and pay a greater amount of money at some point in the future. Consumers typically have these options on bills ranging from utility bills to credit card bills. Like the lines of credit discussed above, these options can be valuable if the credit risk of the borrower or the prevailing interest rates change. 1f. A long term employment contract allows the employer the real option of continuing to employ the radio personality if it is advantageous and fire the person if the person is not worth the salary. The value of the option comes from uncertainty with regard to the future worth of the radio personalities work — which could depend on changes in his or her popularity or changes in the marketplace (or perhaps even FCC rules). 1g. Producers with equipment that can generate more than one product offer the equipment owner the real option of changing the output being produced. If these different products vary through time in profit potential, the owner may find it beneficial at future points in time to switch to output that generates the best profit. An example might be a bottling line that can bottle various beverages. lh. Some actual gold coins have both a metallic value and value as legal currency. The owner of the coin has the real option of using the coin for its gold value or spending it with its currency value. The value of the option depends on the variability of the price of gold expressed in the currency of the coin. 61 1i. Some securities cause tax liabilities each year whether they are sold or not (e.g., many pure discount bonds). Owning an appreciated security usually means that some day the security will be sold and a tax liability will come due. However, by being able to chose the sales date, the owner of the security has the financial option of paying taxes when they wish to pay them — perhaps in a year in which their particular tax rate is low (a year of low income and/or a year of residency in a low tax jurisdiction). 2. If Ms. Lemsly sells all of her apartments now she will receive $110,000 each. But if she waits, the market price of condos may rise or fall. If the market value of condos falls below $100,000, Ms. Lemsly can continue to hold the apartments and earn cash flows with a present value of $100,000. If the market values of Condos rise above $110,000, Ms. Lemsly might find it worthwhile to sell the condos. If condo prices have reasonable chances of rising or falling by large amounts, Ms. Lemsly has a valuable real option. 3. This property provides Mr. South the real option of marketing the building as offering whichever of the three uses generate the highest value. If the prices per foot of each of the three uses are volatile and if they often move in different directions, then the odds are good that at least one of the three potential uses will soar in value, perhaps well above the current best value of $150 per foot. At some point one of the uses might rise so far in value above the other uses that it would make sense to exercise the option. 4. On the one hand it seems that there are two reasons that the high toll path is useless to Mr. Michaels: (1) on an average day it is not worth the higher tolls, and (2) it requires an electronic pass. However, the problem notes that on some days the toll free route might have a huge traffic delay due to an accident at the same time that the higher toll route is moving smoothly. On those days the toll route might generate benefits (saved time) greatly in excess of the tolls. Therefore, the electronic pass is a real option that may be worth the price. 5a. The probability of the three tests being successful is found by multiplying the three individual probabilities of success together: .2x.25X.5= > .025. A 2.5% chance at $100,000,000 is worth $2,500,000. The combined cost of the three tests is $3,500,000. Thus, ignoring risk and time value (using a discount rate of 0%) the NPV is negative and the project should be rejected (abandoned). 5b. Node A refers to the information revealed by the first test, node B the second test and node C the third test. Success = > Sell rights Success = > Node C < Success = > Node B< Failure = > Abandon Node A < Failure = > Abandon Failure 2 > Abandon 62 5.c. Start by inserting $100,000,000 cash if all three projects succeed $100,000,000 Success = > Node C < Success = > Node B< Failure = > Abandon Node A < Failure = > Abandon Failure = > Abandon Next, analyze whether it would be worth it to conduct the third test (Node C) if the previous two tests had succeeded. The third test costs $2,000,000 and has a 50% chance of paying nothing. The NPV is therefore $48,000,000 found by using a discount rate of 0% and computing the expected value of the inflows ($50,000,000) and subtracting out the cost of the test ($2,000,000). Insert the result into the tree as shown: Success = > $48,000,000 Success = > Node B< Node A < Failure = > Abandon Failure = > Abandon Next, analyze whether it would be worth it to conduct the second test (Node B) if the first test had succeeded. The second test costs $1,000,000 and has a 25% chance of paying off with $48,000,000 (the NPV if successful) and a 75% chance of paying nothing. The NPV is therefore $11,000,000 found by using a discount rate of 0% and computing the expected value of the inflows ($12,000,000) and subtracting out the cost of the test ($1,000,000). Insert the result into the tree as shown: Success = > $11,000,000 Node A < Failure = > Abandon Finally, analyze whether it would be worth it to conduct the first test (Node A) given the information from above. The first test costs $500,000 and has a 20% chance of paying off with $11,000,000 (the NPV if successful) and an 80% chance of paying nothing. The NPV is therefore $1,700,000 found by using a discount rate of 0% and computing the expected value of the inflows ($2,200,000) and subtracting out the cost of the test ($500,000). 5.d. The NPV is $1,700,000 and the first test should be begun! The recognition of the real options demonstrated the positive NPV and may lead to saving the world from the incredible global warming that some have argued seems to have already raised the earth’s temperature by almost 1 degree Centigrade in the last 100 years combined (a portion of which might even be man—made!) 63 5.6. The problem inferred that the firm had searched for bidders and that nobody in world was willing to pay more than $100,000,000 for the technology if successful. Pre— sumably that value included all of the potential benefits that anybody perceived as being worthwhile. There were no consortiums of for profit corporations, not for profit corporations and government agencies that together valued the technology at more than $100,000,000. Thus, it is difficult to argue that the NPV should be adjusted. 6. There are two decision points in time: (1) which of the three tests to conduct first, and (2) given the first test being successful, which test to conduct second. The other test would be conducted if the first two succeeded. The decision tree could be drawn like this (the test numbers refer to the order of the tests as listed in the text): Do Test #2 Second = > Do Test #3 Last Do Test #1 First < / Do Test #3 Second = > Do Test #2 Last / Do Test #1 Second = > Do Test #3 Last < — — Do Test #2 First < \ Do Test #3 Second = > Do Test #1 Last \ Do Test #1 Second = > Do Test #2 Last Do Test #3 First < Do Test #2 Second = > Do Test #1 Last Using backward induction, let’s start with the value of performing the final test: If final test is #1: NPV = (.2x$100,000,000) — $500,000 = > $19,500,000 If final test is #2: NPV = (.25x$100,000,000) — $1,000,000 = > $24,000,000 If final test is #3: NPV = (.5x$100,000,000) — $2,000,000 = > $48,000,000 Now, the NPV of each of the second tests can be calculated given the NPVs of the final tests (above) and the probabilities and costs of the second tests (in textbook). There are six pathways corresponding to the six paths on the right hand side of the original tree (shown in millions of dollars): Do Test #2 Second = > Do Test #3 Last: NPV = (.25x$48) — 1.0 = > $11.0 Do Test #3 Second = > Do Test #2 Last: NPV = (.5x$24) —— 2.0 = > $10.0 Do Test #1 Second = > Do Test #3 Last: NPV = (.2x$48) — 0.5 = > $9.1 Do Test #3 Second = > Do Test #1 Last: NPV = (.5x$19.5) — 2.0 = > $7.75 Do Test #1 Second = > Do Test #2 Last: NPV = (.2x$24) -— 0.5 = > $4.3 Do Test #2 Second = > Do Test #1 Last: NPV = (.25x$19.5) — 1.0 = > $3.875 @SAPP’N?‘ Note that path #1 is better than path #2, so since they come from the same starting point (doing test #1 first) we can eliminate path #2. Similarly path #3 eliminates path #4, and path #5 eliminates path #6. Placing the results into the diagram: 64 Do Test #1 First: NPV = (.20x $11.0) — $0.5 => $1.7 / < ———— Do Test #2 First: NPV = (.25 X $9.1) — $1.0 => $1.275 \ Do Test #3 First: NPV = (.50 X $4.3) - $2.0 = > $0.150 The sequence valued in problem #5 is best, valued at $1,700,000. The "Isolate Alage" test (test #1) should be done first. 7 .a. Since the three story hotel does not change value whether the airport is built or not, the tree is simplified. The three story hotel creates a cumulative profit of $50 million found as the total revenue (20 years x $4 million) less the cost of $30 million. / Airport Approved Build 5 Story < Airport Approved / \ Airport First Denied < / Airport Denied < ——————— Build 3 Story = > +$50M \ / Airport Approved Build 5 Story < Airport Approved \ Airport First Denied < Airport Denied 7b. The five story hotel costs $20M more. If the airport is built after five years it produces $30M more in revenues. If after ten years it produces $20M more in reven— ues, there would be no subsequent decision —the value simply depends on probabilities The flexible use hotel costs $3M more, involves the real option to expand the hotel if the airport is improved for $20M more. If the airport is never improved then the hotel should not be expanded. If the airport is built in the tenth year, it turns out that it is irrelevant whether the hotel is expanded because the ten years of +$2M revenue matches the $20M cost. However, if the airport is built after fives years, the fifteen years of +$2M revenue exceeds the $20M cost by $10M: / Airport Approved +$60M Build 5 Story < Airport Approved +$50M / \ Airport First Denied < / Airport Denied +30M < ——————— Build 3 Story = > +$50M \ / Airport Approved +$57 Build 5 Story < Airport Approved +$47M \ Airport First Denied < Airport Denied +$47M 65 In the above diagram all final decision are made and valued. Now the probabilities (50% airport for fifteen years, 25% airport for 10 years and 25% no airport) can be used to find the expected values of the three paths of the original decision. Build 5 Story = (50%x$60M)+(25%x$50M)+(25%x$30M) = $50M Build 3 Story = (50%X$50M)+(25%x$50M)+(25%x$50M) = $50M Build Flexible = (50%x$57M)+(25%x$47M)+(25%x$47M) = $52M The flexible use hotel produces a long term cumulative expected profit of $52 million, exceeding by $2 million the value of the other two alternative which just happen to be equal. 7c. The cost of the real option was the added $3 million construction costs. Since the hotel turned out to be worth $2 million more, including that cost, the value of the real option must be +$5 million. The $5 million of expected profit comes from the 50% chance that the airport will be constructed early and allow the $20 million expansion that produces $30 million in revenue. Building the five story hotel risks the regret that the added space will not be used if the airport is never built. 8. In the super hot real estate market of the later 1990’s and early 2000’s, many speculators placed small deposits on condominium purchases as soon as the projects announced. The idea was that if the real estate market stayed hot, by the time the was finished the market value could greatly exceed the purchase price that they locked in with their deposit. The speculator could buy the condo and sell it at the market price, or perhaps even sell the option to a prospective condo buyer. The key was to find projects with small deposits on long term constructions that would have volatile prices and would allow the buyer to walk away from the deal if they so desired with no loss other than forfeiture of the deposit. Developers responded by raising deposits. 66 CHAPTER 9 DISCUSSION QUESTIONS 1. When you think about it life is full of real options — involved in virtually every decision we make. College students discover real options in job offers, extra credit projects, cancellable agreements to get together, flex dollar meal plans, returnable textbook purchases, party invitations and so forth. The key is to find alternatives in which at least some meaningful decision does not need to be made until after informa— tion is revealed. A party invitation might turn out to be valuable if no better offers are received prior to the time of the party. 2. In the case of financial options, there is typically another side to the option that suffers to the extent that the option owner benefits when the option is used (or exercised). These situations are called zero sum games because wealth is being transferred rather than created. Of course the seller of that financial option demands a payment (or premium) when the option is sold and enters into the deal in the hopes of receiving a net benefit. In the case of real options it is often not as clear that there is ”another side" to the option that must suffer to whatever extent the option owner benefits. For example, if we review the options discussed in problem #1 of this chapter, we see that often the use of the option by the option holder does not create an offsetting loss to someone else. The owners of the undeveloped land or the multiple use equipment may clearly benefit from some market movements, but the option does not have to derive its value from the loss of others — it could be a net gain in wealth — such as better use of land and better use of energey resources. Regarding whether it is ethical to exercise an option that hurts someone else (e.g., using a line of credit after one’s credit worthiness has seriously declined), most would argue that the option must have been legally obtained, with no fraud or deception involved. It is important to recognize that in life, like in sports, many of our efforts are designed to create benefits for us at the cost to others. We try to win a game while knowing that the other person would prefer to win. Similarly, we often shop for discounts, search for the best jobs, ask for salary increases, file for insurance claims, take the closest parking spots, select the nicest bench at a park or table at a restaurant, return bottles for deposits, avoid toll roads, try to avoid paying for parking, sell our old books, try to avoid some taxes and on and on and on. We do so many things that can be viewed quite simply as efforts to benefit financially or otherwise at the cost of others. For the last few centuries economists have begun understanding how these apprently selfish actions can work to the benefit of all ——~ as noted by Adam Smith as the famous "invisible hand". 3. In the technology boom and internet bubble of the 1990’s, some firms had enormous wait times for their products, but allowed orders to be placed with no penalty for cancellation. Frustrated buyers soon learned that they were better off ordering far 67 more products than they expected to use and then cancelling t...
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