Explanation
According to the PMBOK Guide, return of investment (ROI) is a financial analysis technique that calculates the ratio of the net benefits to the total costs of a project or an investment. ROI helps to evaluate the profitability and feasibility of a project or an investment by comparing the expected benefits with the required costs. A higher ROI indicates that the project is more profitable and worth pursuing, while a lower ROI indicates that the project is less profitable and should be rejected. ROI can also be used to compare different project options and select the one that has the highest ROI, as it represents the most value for the organization.
In this question, the project manager is preparing the business case for a project in a not for profit organization.
The project manager justifies the cost of the project to a group of sponsors. The business case is a document that describes the rationale and justification for initiating a project or an investment, and how it aligns with the organizational strategy, objectives, and values. The business case also includes the expected benefits and costs of the project or the investment, and the analysis and evaluation of the alternatives and options. The business case helps the project manager and the sponsors to make informed decisions about the project initiation and selection.
To justify the cost of the project, the project manager should use ROI as a benefits realization metric. Benefits realization is the process of identifying, planning, managing, and measuring the benefits and value that a project or an investment delivers to the organization and the stakeholders. Benefits realization metrics are tools and techniques that help to quantify and evaluate the benefits and value of a project or an investment, and to compare them with the baseline values. ROI is a common and widely used benefits realization metric, as it helps to demonstrate the financial value and impact of a project or an investment, and to justify its cost and feasibility. ROI can be calculated as follows:
ROI = (Net Benefits / Total Costs) x 100%
Net Benefits = Total Benefits - Total Costs
Total Benefits = The sum of all the monetary and non-monetary benefits that the project or the investment will generate over its life cycle.
Total Costs = The sum of all the monetary and non-monetary costs that the project or the investment will incur over its life cycle.
The project manager should estimate the total benefits and costs of the project, and calculate the net benefits and the ROI. The project manager should also compare the ROI of the project with the ROI of the other alternatives or options, and select the one that has the highest ROI. The project manager should present the ROI of the project to the sponsors, and explain how it reflects the value and benefit of the project, and how it outweighs the cost of the project.
The other options are not correct because they do not provide a valid benefits realization metric to justify the cost of the project. Option A is wrong because it refers to the total value of ownership, which is a concept that considers the total costs and benefits of owning and using a product, service, or asset over its life cycle. It is not a benefits realization metric, but rather a way of estimating the total benefits and costs of a project or an investment. Option B is wrong because it refers to the budget at completion (BAC), which is the total amount of money that is planned to be spent on a project or a work breakdown structure component. It is not a benefits realization metric, but rather a cost baseline value that is used to measure and control the project cost performance. Option C is wrong because it refers to the payback period, which is a financial analysis technique that calculates the time required to recover the initial investment of a project or an investment. It is not a sufficient benefits realization metric, as it does not consider the benefits and costs after the payback period, the time value of money, or the profitability of the project or the investment. References:
PMBOK Guide, 6th edition, pages 33-34, 333-334, 440-441
Return on Investment (ROI) - Project Management Knowledge
Return on Investment (ROI) - Project Management Institute
Benefits Realization Management: A Practice Guide | PMI
Benefits Realization Management - ProjectEngineer

Explanation
A hybrid project management approach is a combination of two or more project management methodologies, such as waterfall and agile, that best suit the project's needs. A hybrid approach allows the project manager to plan some phases in detail, while leaving other phases more flexible and adaptable to changes. A hybrid approach can also balance the sponsor's expectations of following the project objectives, while incorporating new information and feedback as the project progresses. According to the PMBOK Guide, a hybrid approach can be used when the project has both predictive and adaptive elements, or when the project environment is complex and uncertain. References:
PMBOK Guide, 7th edition, page 271
What Is Hybrid Project Management?2
Ultimate Guide To Hybrid Project Methodologies & How To Make Them3

Explanation
The project manager should discuss the issue with the virtual team members and revise the communications management plan as an immediate corrective action. This is because the project manager needs to understand the reasons why the virtual team members are unable to join the regular project update meetings and find a solution that works for them. The project manager should also update the communications management plan to reflect the changes in the communication requirements, methods, frequency, and tools for the virtual team members. The project manager should ensure that the communication plan is aligned with the project objectives, stakeholder expectations, and organizational culture.
Option B is not a good action, as escalating this issue to the virtual team members' supervisors may not be appropriate or effective. It may also create conflict, resentment, and distrust among the team members. The project manager should try to resolve the issue directly with the virtual team members and not involve their supervisors without their consent or agreement.
Option C is not a good action, as adding this issue to the risk management plan and taking action if it persists is a passive and delayed approach. The project manager should try to prevent or mitigate the issue as soon as possible and not wait until it becomes a risk that affects the project performance. The project manager should also not treat the issue as a risk, but as a problem that needs to be solved.
Option D is not a good action, as discussing the issue with the project sponsors and adding this as an issue in the issue log is a reactive and formal approach. The project manager should try to solve the issue informally and collaboratively with the virtual team members and not escalate it to the project sponsors unless necessary. The project manager should also not document the issue in the issue log, but in the communication plan. References:
[PMBOK Guide], 6th edition, page 368, section 10.1
[PMP Exam Content Outline], page 10, task 5 under domain 2

Explanation
A trend analysis is a technique that examines project performance over time to determine if performance is improving or deteriorating. A trend analysis of risks can help the project manager and the sponsor to identify the patterns and causes of risks, and to take appropriate actions to mitigate or avoid them. In an agile project, the project manager should use the project risk register tracking tool and the issues log to perform a trend analysis of risks. The project risk register tracking tool is a tool that records the identified risks, their probability, impact, response strategies, and status. The issues log is a document that records the issues that arise during the project, their resolution, and their impact on the project. By extracting the data from these two sources, the project manager can provide the sponsor with a comprehensive and accurate trend analysis of risks. Option B is the best answer because it uses the most relevant and reliable sources of information for the trend analysis of risks. Option A is not a good answer because it does not address the sponsor's request for a trend analysis of risks, and it may waste time and resources by brainstorming on general risks that are not specific to the project. Option C is not a good answer because it does not provide a trend analysis of risks, and it may notinclude the latest information on the risks that the project has monitored. Option D is not a good answer because it does not provide a trend analysis of risks, and it may not be relevant or helpful to the sponsor's decision-making process. References: [Agile Practice Guide], page 62; [A Guide to the Project Management Body of Knowledge (PMBOK Guide)], Seventh Edition, pages 74-75, 78-79.