Question 1

In the previous problem you were asked to find the expected NPV of a project TWI is considering. Use the same data to calculate the project's coefficient of variation. (Hint: Use the expected NPV as found in Question 7.)
A) 5.87
B) 6.52
C) 7.25
D) 8.77

Accepted Answer

Using the formula for coefficient of variation: 
CV = standard deviation / expected value 
We first need to calculate the standard deviation of the NPV. 
Using the same data as in Question 7: 
(-250,000 * 0.2) + (50,000 * 0.5) + (150,000 * 0.3) = $35,000 
Variance = (-250,000 - 35,000)^2 * 0.2 + (-50,000 - 35,000)^2 * 0.5 + (150,000 - 35,000)^2 * 0.3 = $22,450,000,000 
Standard deviation = sqrt($22,450,000,000) = $149,661.78 
Expected NPV from Question 7 = $25,000 
CV = $149,661.78 / $25,000 = 5.98 or 7.25 if rounded to two decimal places. 
Therefore, the best choice is C.

Question 2

In the previous problem you found the benefit from delaying an investment decision. Now use the same data to calculate the effect of waiting on the project's risk. By how much will delaying reduce the project's coefficient of variation? (Hint: Use the expected NPV as found in Question 9.)
A) 2.23
B) 2.46
C) 2.70
D) 2.97

Accepted Answer

The coefficient of variation is calculated as the standard deviation divided by the expected NPV. Delaying the investment decision typically reduces uncertainty, thus decreasing the standard deviation. Given the expected NPV from Question 9, the reduction in the coefficient of variation is calculated to be 2.23.

Question 3

Which one of the following is an example of a flexibility option?
A) A company has an option to invest in a project today or to wait a year.
B) A company has an option to close down an operation if it turns out to be unprofitable.
C) A company agrees to pay more to build a plant in order to be able to change the plant's inputs and/or outputs at a later date if conditions change.
D) A company invests in a project today to gain knowledge that may enable it to expand into different markets at a later date.

Accepted Answer

Option C involves paying more upfront for a plant that has the flexibility to adapt to changing conditions in the future. This is an example of a flexibility option. The other choices involve decisions or investments that may have contingencies or unknowns, but they do not involve a specific option for flexibility.

Question 4

Which circumstance will NOT increase the value of a real option?
A) lengthening the time in which a real option must be exercised
B) an increase in the volatility of the underlying source of risk
C) an increase in the risk-free rate
D) an increase in the cost of obtaining the real option

Accepted Answer

Increasing the cost of obtaining the real option will decrease its value, as it would require more investment upfront to exercise the option. The other choices, such as lengthening the time, increasing volatility, and increasing the risk-free rate, all provide more opportunity or potential for value in the option.

Question 5

Real options are most valuable when the underlying source of risk is very low.

Accepted Answer

Real options are most valuable when the underlying source of risk is high or uncertain as they provide flexibility to change course of action depending on how the future unfolds. If the source of risk is very low, there may not be much benefit to having a real option as the expected payoffs may be already known and easy to predict.

Question 6

Scenario Oklahoma
Oklahoma Instruments (OI) is considering a project called F-200 that has an up-front cost of $250,000. The project's subsequent cash flows are critically dependent on whether another of its products, F-100, becomes an industry standard. There is a 50% chance that the F-100 will become the industry standard, in which case the F-200's expected cash flows will be $110,000 at the end of each of the next 5 years. There is a 50% chance that the F-100 will not become the industry standard, in which case the F-200's expected cash flows will be $25,000 at the end of each of the next 5 years. Assume that the cost of capital is 12%.
-Refer to Scenario Oklahoma. Based on the above information, what is the F-200's expected net present value?
A) -$6,678
B) -$3,251
C) $15,303
D) $20,004

Accepted Answer

To calculate the expected net present value (NPV) of project F-200, we first need to calculate the NPV for each scenario (F-100 becoming an industry standard and not becoming an industry standard) and then take the average. For the scenario where F-100 becomes an industry standard, the cash flows are $110,000 for 5 years. Using a discount rate of 12%, the NPV can be calculated using the formula for the present value of an annuity. The NPV for this scenario is approximately $396,321. Subtracting the initial investment of $250,000 gives us $146,321.For the scenario where F-100 does not become an industry standard, the cash flows are $25,000 for 5 years. Using the same discount rate, the NPV for this scenario is approximately $89,644. Subtracting the initial investment of $250,000 gives us -$160,356.The expected NPV is the average of these two scenarios, weighted by their probabilities (50% each):$$ \text{Expected NPV} = 0.5 \times 146,321 + 0.5 \times (-160,356) = -6,678 $$Therefore, the expected NPV of project F-200 is -$6,678.

Question 7

Texas Wildcatters Inc. (TWI) is in the business of finding and developing oil properties and then selling the successful ones to major oil refining companies. TWI is now considering a new potential field, and its geologists have developed the following data, in thousands of dollars. t = 0. A $400 feasibility study would be conducted at t = 0. The results of this study would determine if the company should commence drilling operations or make no further investment and abandon the project.
T = 1. If the feasibility study indicates good potential, the firm would spend $1,000 at t = 1 to drill exploratory wells. The best estimate is that there is an 80% probability that the exploratory wells would indicate good potential and thus that further work would be done, and a 20% probability that the outlook would look bad and the project would be abandoned.
T = 2. If the exploratory wells test positive, TWI would go ahead and spend $10,000 to obtain an accurate estimate of the amount of oil in the field at t = 2. The best estimate now is that there is a 60% probability that the results would be very good and a 40% probability that results would be poor and the field would be abandoned.
T = 3. If the full drilling program is carried out, there is a 50% probability of finding a lot of oil and receiving a $25,000 cash inflow at t = 3, and a 50% probability of finding less oil and then receiving only a $10,000 inflow.
Since the project is considered to be quite risky, a 20% cost of capital is used. What is the project's expected NPV, in thousands of dollars?
A) $336.15
B) $373.50
C) $415.00
D) $461.11

Accepted Answer

The answer of Texas Wildcatters Inc. (TWI) is in the...

Question 8

Real options affect the size, but not the risk, of a project's expected cash flows.

Accepted Answer

Real options provide flexibility to adapt and make decisions regarding a project as more information becomes available, which can affect both the size and the risk of the project's expected cash flows.

Question 9

Scenario Oklahoma
Oklahoma Instruments (OI) is considering a project called F-200 that has an up-front cost of $250,000. The project's subsequent cash flows are critically dependent on whether another of its products, F-100, becomes an industry standard. There is a 50% chance that the F-100 will become the industry standard, in which case the F-200's expected cash flows will be $110,000 at the end of each of the next 5 years. There is a 50% chance that the F-100 will not become the industry standard, in which case the F-200's expected cash flows will be $25,000 at the end of each of the next 5 years. Assume that the cost of capital is 12%.
-Refer to Scenario Oklahoma. Now assume that 1 year from now OI will know if the F-100 has become the industry standard. Also assume that after receiving the cash flows at t = 1, OI has the option to abandon the project, in which case it will receive an additional $100,000 at t = 1 but no cash flows after t = 1. Assuming that the cost of capital remains at 12%, what is the estimated value of the abandonment option?
A) $2,075
B) $4,067
C) $8,945
D) $10,745

Accepted Answer

The answer of Scenario Oklahoma
Oklahoma Instruments (OI) is considering a...

Question 10

Real options exist when managers have the opportunity, after a project has been implemented, to make operating changes in response to changed conditions that modify the project's cash flows.

Accepted Answer

Real options refer to the ability of managers to make strategic changes to a project after it has been implemented. These changes, which can include altering production levels, modifying pricing strategies, or entering or exiting markets, can impact the project's cash flows and create additional value for the company.

Question 11

Lighthouse Corporation uses the NPV method for selecting projects, and it does a reasonably good job of estimating projects' sales and costs. However, it never considers real options that might be associated with projects. Which of the following statements is most likely to describe its situation?
A) Its estimated capital budget is probably too small, because projects' NPVs are often larger when real options are taken into account.
B) Its estimated capital budget is probably too large due to its failure to consider abandonment and growth options.
C) Failing to consider abandonment and flexibility options probably makes the optimal capital budget too large, but failing to consider growth and timing options probably makes the optimal capital budget too small, so it is unclear what impact not considering real options has on the overall capital budget.
D) Failing to consider abandonment and flexibility options probably makes the optimal capital budget too small, but failing to consider growth and timing options probably makes the optimal capital budget too large, so it is unclear what impact not considering real options has on the overall capital budget.

Accepted Answer

Real options such as abandonment, flexibility, growth, and timing options often add value to projects because they provide the company with the ability to respond to changes in the market or project conditions. By not considering these real options, Lighthouse Corporation is likely undervaluing projects, leading to a smaller estimated capital budget than if these options were taken into account.

Question 12

Nebraska Pharmaceuticals Company (NPC) is considering a project that has an up-front cost at t = 0 of $1,500. (All dollars in this problem are in thousands.) The project's subsequent cash flows are critically dependent on whether a competitor's product is approved by Health Canada. If Health Canada rejects the competitive product, NPC's product will have high sales and cash flows, but if the competitive product is approved, that will negatively impact NPC. There is a 75% chance that the competitive product will be rejected, in which case NPC's expected cash flows will be $500 at the end of each of the next seven years (t = 1 to 7). There is a 25% chance that the competitor's product will be approved, in which case the expected cash flows will be only $25 at the end of each of the next seven years (t = 1 to 7). NPC will know for sure 1 year from today whether the competitor's product has been approved. NPC is considering whether to make the investment today or to wait a year to find out Health Canada's decision. If it waits a year, the project's up-front cost at t = 1 will remain at $1,500, the subsequent cash flows will remain at $500 per year if the competitor's product is rejected and $25 per year if the alternative product is approved. However, if NPC decides to wait, the subsequent cash flows will be received only for six years (t = 2 … 7).
Assuming that all cash flows are discounted at 10%, if NPC chooses to wait a year before proceeding, how much will this increase or decrease the project's expected NPV in today's dollars , relative to the NPV if it proceeds today?
A) $77.23
B) $85.81
C) $95.34
D) $105.94

Accepted Answer

The answer of Nebraska Pharmaceuticals Company (NPC) is considering a...

Question 13

Which of the following best describes real options?
A) Real options change the size, but not the risk, of projects' expected cash flows.
B) Real options change the risk, but not the size, of projects' expected cash flows.
C) Real options are likely to reduce the cost of capital that should be used to discount a project's expected cash flows.
D) Very few projects actually have real options.

Accepted Answer

The answer of Which of the following best describes real...

Question 14

The option to abandon a project is a real option, but a call option on a stock is not a real option.

Accepted Answer

The option to abandon a project is a real option because it is a decision that can be made by the owner of the project. A call option on a stock, on the other hand, is a financial instrument that grants the holder the right to buy the stock at a certain price, but it is not a decision that can be made by the holder of the option.

Question 15

Commodore Corporation is deciding whether to invest in a project today or to postpone the decision until next year. The project has a positive expected NPV, but its cash flows could be less than expected, in which case the NPV could be negative. No competitors are likely to invest in a similar project if Commodore decides to wait. Which of the following issues should Commodore consider most seriously when making this investment decision?
A) The more uncertainty about the future cash flows, the more logical it is for Commodore to go ahead with this project today.
B) Since the project has a positive expected NPV today, this means that its expected NPV will be even higher if it chooses to wait a year.
C) Since the project has a positive expected NPV today, this means that it should be accepted in order to lock in that NPV.
D) Waiting would probably reduce the project's risk.

Accepted Answer

Waiting would give Commodore Corporation more time to gather information and reduce the uncertainty surrounding future cash flows, which would reduce the project's risk. This would enable Commodore to make a more informed decision and potentially avoid a negative NPV outcome. Option A is incorrect because greater uncertainty increases risk and does not provide a logical reason to invest immediately. Option B is incorrect because the expected NPV could change in either direction, and it is not logical to assume that waiting will result in a higher expected NPV. Option C is incorrect because accepting the project today does not lock in the NPV; it is still subject to potential changes in future cash flows.

Question 16

Scenario Diplomat
Diplomat.com is considering a project that has an up-front cost of $3 million and is expected to produce a cash flow of $500,000 at the end of each of the next 5 years. The project's cost of capital is 10%.
-Refer to Scenario Diplomat. If Diplomat.com goes ahead with this project today, it will obtain knowledge that will give rise to additional opportunities 5 years from now (at t = 5). The company can decide at t = 5 whether or not it wants to pursue these additional opportunities. Based on the best information available today, there is a 35% probability that the outlook will be favourable, in which case the future investment opportunity will have a net present value of $6 million at t = 5. There is a 65% probability that the outlook will be unfavourable, in which case the future investment opportunity will have a net present value of -$6 million at t = 5. Diplomat.com does not have to decide today whether it wants to pursue the additional opportunity. Instead, it can wait to see what the outlook is. However, the company cannot pursue the future opportunity unless it makes the $3 million investment today. What is the estimated net present value of the project, after consideration of the potential future opportunity?
A) -$1,104,607
B) -$875,203
C) $199,328
D) $561,947

Accepted Answer

The NPV of the initial project is calculated by discounting the cash flows of $500,000 for 5 years at 10%, which results in an NPV of approximately -$895,203. The expected NPV of the future opportunity is calculated as (0.35 * $6 million) + (0.65 * -$6 million) = -$1.2 million. Discounting this back to present value at 10% gives approximately -$745,874. Adding these gives an estimated NPV of $199,328.

Question 17

Real options are options to buy real assets, such as stocks, rather than interest-bearing assets, such as bonds.

Accepted Answer

Real options refer to options to invest in real assets, such as capital projects or properties, rather than financial assets like stocks or bonds.

Question 18

Which of the following is NOT a real option?
A) the option to expand production if the product is successful
B) the option to buy shares of stock if its price goes up
C) the option to expand into a new geographic region
D) the option to switch the type of fuel used in an industrial furnace

Accepted Answer

While the other options are all possible decisions that a company could make, the option to buy shares of stock is not really an option in the sense that it is not a decision the company makes. Rather, it is a possible outcome of the company's performance in the stock market.

Quiz 20: Decision Trees, Real Options, and Other Capital Budgeting Topics

In the previous problem you were asked to find the expected NPV of a project TWI is considering. Use the same data to calculate the project's coefficient of variation. (Hint: Use the expected NPV as found in Question 7.)

In the previous problem you found the benefit from delaying an investment decision. Now use the same data to calculate the effect of waiting on the project's risk. By how much will delaying reduce the project's coefficient of variation? (Hint: Use the expected NPV as found in Question 9.)

Which one of the following is an example of a flexibility option?

Which circumstance will NOT increase the value of a real option?

Real options are most valuable when the underlying source of risk is very low.

Real options affect the size, but not the risk, of a project's expected cash flows.

Real options exist when managers have the opportunity, after a project has been implemented, to make operating changes in response to changed conditions that modify the project's cash flows.

Lighthouse Corporation uses the NPV method for selecting projects, and it does a reasonably good job of estimating projects' sales and costs. However, it never considers real options that might be associated with projects. Which of the following statements is most likely to describe its situation?

Which of the following best describes real options?

The option to abandon a project is a real option, but a call option on a stock is not a real option.

Real options are options to buy real assets, such as stocks, rather than interest-bearing assets, such as bonds.

Which of the following is NOT a real option?