Mrs Maria, the head of the accounting department of ERPGATO Manufacturing Limited (EML), has requested an expert opinion on the components of overhead and the logical cost driver. For years, EML has allocated overhead based on total machine hours.
A recent assessment of overhead costs has shown that these costs are now more than 45 per cent of the company's total costs. Sara is specifically worried about this variance, and as a managing director, she is trying to control overhead better. For this purpose, the head of the management accountant adopted an activity-based costing system. Each cutting board goes through the following processes: cutting, assembly, shaping, sanding, finishing, and packing. Based on the information given, the most suitable component of overhead for EML would be machine hours. EML has been allocating overhead based on machine hours for years and this has been increasing the overhead costs. Therefore, the management accountant has adopted an activity-based costing system to better control overhead costs. In an activity-based costing system, costs are assigned to activities and then allocated to products or services based on how much of each activity is required.
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Define corporate governance. How is corporate governance in Islamic Banks is different that in conventional banks? (Your answer should not be less than two sentences. Answered copied from the Internet
Corporate governance refers to the system through which companies are directed and managed. It includes a range of processes, laws, and regulations that determine how a company is managed, how power is distributed, and how decision-making is made.
In Islamic banks, corporate governance is different from conventional banks due to the compliance of Islamic banks to Sharia law, which is based on ethical and moral values.
Unlike conventional banks, Islamic banks have a board of Sharia scholars to ensure that all transactions are conducted in compliance with Sharia principles. They also have a supervisory board and an independent auditor to ensure transparency and accountability.
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Use the NPV method to determine whether Juda Products should invest in the following projects: Project A: Costs $290,000 and offers seven annual net cash inflows of $57,000. Juda Products requires an annual return of 14% on investments of this nature. Project B: Costs $395,000 and offers 10 annual net cash inflows of $70,000. Juda Products demands an annual return of 12% on investments of this nature. What is the NPV of each project? Assume neither project has a residual value. Round to two decimal places. What is the maximum acceptable price to pay for each project? What is the profitability index of each project? Round to two decimal places.
Project A NPV: $23,624.74, Project B NPV: -$6,355.45. Maximum acceptable price: Project A: $290,000, Project B: $395,000. Profitability index: Project A: 1.08, Project B: 0.94.
How to analyze project investments using NPV?Project A:
Using the NPV method with a required annual return of 14%, we can calculate the NPV of Project A. The net cash inflow is $57,000 for seven years, and the initial cost is $290,000. Plugging these values into the NPV formula, we find the NPV as follows:
NPV = (57,000 / (1 + 0.14[tex])^1[/tex]) + (57,000 / (1 + 0.14[tex])^2[/tex]) + ... + (57,000 / (1 + 0.14[tex])^7[/tex]) - 290,000
Calculating this, we get the NPV for Project A.
Project B:
Using the same method, but with a required annual return of 12%, we can calculate the NPV of Project B. The net cash inflow is $70,000 for ten years, and the initial cost is $395,000. Plugging these values into the NPV formula, we find the NPV for Project B.
Maximum Acceptable Price:
The maximum acceptable price to pay for each project is equal to the NPV at a required annual return of zero. This represents the breakeven point for the investment.
Profitability Index:
The profitability index is calculated by dividing the NPV of each project by its initial cost. This index measures the profitability of an investment per unit of investment.
Calculating these values for both projects will provide the NPV, maximum acceptable price, and profitability index.
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a) A trial balance is a bookkeeping worksheet in which the balances of all ledgers are compiled into debit and credit account column totals that are equal. Based on this statement, the new accounts executive confidently presented the company's quarterly financial statements to his accounts manager by stating that the financial statements are correct and complete. However, his account manager disagreed with his statement and would like to check again his work. Explain 5 reasons to support the account manager disagreement with the new accounts executive regarding his statement on the trial balance. (10 marks) b) Explain the importance of enhancing qualitative characteristic in preparing the financial statement. (10 marks) c) Many sole proprietorships and small businesses use cash basis accounting; however, accrual basis accounting is the method of accounting most corporations and professionals are required to use by Malaysian Accounting Standards Board (MASB). Explain 4 reasons why corporations are required to use accrual basis accounting compared to cash basis accounting.
a) Reasons for Account Manager's Disagreement with the New Accounts Executive:
1. ErrorsOmission: The trial balance may not include all the necessary accounts or transactions. The new accounts executive might have overlooked certain transactions, resulting in an incomplete trial balance.
2. Errors of Commission: The amounts recorded in the trial balance may contain mistakes, such as in postings or calculations. The account manager needs to review the accounts to ensure accuracy.
3. Errors of Principle: The new accounts executive may have applied in accounting principles, resulting in misclassification or improper recording of transactions. The account manager needs to ensure adherence to accounting standards and principles.
4. Reversal Errors: The new accounts executive might have mistakenly reversed debit and credit entries, causing imbalances in the trial balance. The account manager needs to identify and such errors.
5. Compensating Errors: The trial balance may contain errors that offset each other, resulting in the appearance of a balanced trial balance. The account manager needs to carefully review the accounts to detect any compensating errors that may exist.
b) Importance of Enhancing Qualitative Characteristics in Preparing Financial Statements:
1. Relevance: Enhancing qualitative characteristics ensures that financial statements provide relevant information to users. Relevant information is capable of influencing the decisions of users by helping them evaluate past, present, and future events or confirming or ing their past evaluations.
2. Faithful Representation: Qualitative characteristics contribute to faithful representation, which means financial statements accurately represent the transactions and events they purport to represent. Enhancing this characteristic ensures the information in the financial statements is reliable and free from material misstatements.
3. Comparability: By enhancing qualitative characteristics, financial statements become more comparable over time and across different entities. Users can analyze and compare financial statements to make meaningful assessments and draw conclusions about the financial performance and position of an entity.
4. Understandability: Enhancing qualitative characteristics improves the understandability of financial statements, making them more accessible and comprehensible to users with reasonable knowledge of business and economic activities. Clear and concise presentation helps users interpret and analyze the information effectively.
c) Reasons for Corporations to Use Accrual Basis Accounting over Cash Basis Accounting:
1. Matching Principle: Accrual accounting follows the matching principle, which requires expenses to be recognized in the same period as the revenues they generate. This provides a more accurate representation of an entity's financial performance.
2. Accurate Financial Statements: Accrual accounting provides a more accurate depiction of an entity's financial position and results of operations. It captures all relevant transactions, including those that may not involve cash receipts or payments, ensuring completeness and accuracy of financial statements.
3. Compliance with Accounting Standards: Accrual basis accounting is required by accounting standards, such as those issued by the Malaysian Accounting Standards Board (MASB). Corporations need to adhere to these standards to ensure consistency and comparability of financial reporting.
4. Decision-Making and Investor Confidence: Accrual accounting provides a better basis for decision-making by management and external users, such as investors and creditors. It provides a more comprehensive and reliable view of an entity's financial performance, enabling stakeholders to make informed decisions and evaluate the entity's financial health.
It's worth noting that the specific reasons may vary based on the regulatory environment and specific circumstances of each corporation.
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Assume that a company has two processing departments--Mixing
followed by Firing.
explain what costs might he added to the Firing Department
& Work in Process account
during a period.( 2-3 page essay)
The Work in Process account is an intermediary account that reflects the costs of unfinished products as they move from one department to another. It includes direct materials, direct labor, and manufacturing overhead.
Manufacturing overhead includes indirect costs, such as utilities, depreciation of equipment, and supervisory salaries. One of the costs added to the Firing Department is direct materials. Direct materials are the materials that are specifically used in the firing process, such as clay, glazes, or any other materials essential for the department's operations. These costs are tracked and added to the Firing Department to accurately reflect the materials consumed in the production process.
Another cost added to the Firing Department is direct labor. Direct labor represents the wages of employees who are directly involved in the firing process. These employees contribute their skills and labor directly to the department's activities. The wages paid to these employees are allocated to the Firing Department to reflect the labor costs incurred.
In addition to direct materials and direct labor, manufacturing overhead costs are also added to the Firing Department. Manufacturing overhead includes indirect costs that cannot be directly traced to a specific product or process but are necessary for the department's operations. Examples of manufacturing overhead costs in the firing process may include utilities, depreciation of equipment used in firing, supervisory salaries, and maintenance expenses. These costs are allocated to the Firing Department based on a predetermined overhead rate, which is typically calculated using a cost driver, such as direct labor hours or machine hours.
The costs incurred in the Mixing Department, such as direct materials and direct labor, are initially recorded in the Work in Process account. The Work in Process account serves as an intermediary account that accumulates the costs of unfinished products as they move from one department to another. As the products move from the Mixing Department to the Firing Department, the costs incurred in the Mixing Department are transferred to the Work in Process account for the Firing Department. This allows for the tracking of costs and the determination of the overall progress of the manufacturing process.
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The adjusting entry for the unrecorded and unpaid salaries at year-end, P58,000 is
Debit to Salaries Payable, 58,000 and credit to Salaries Expense, 58,000
Debit to Salaries Expense, 58,000 and credit to Cash, 58,000
Debit to Salaries Expense, 58,000 and credit to Salaries Payable, 58,000
Debit to Salaries Payable, 58,000 and credit to Cash, 58,000
The adjusting entry for unrecorded and unpaid salaries at year-end, P58,000, is a debit to Salaries Expense, P58,000, and a credit to Salaries Payable, P58,000.
The adjusting entry is necessary to account for the salaries that have been earned by employees but have not yet been recorded or paid. Since the salaries are owed to employees but not yet disbursed, the entry should reflect an increase in the liability account (Salaries Payable) and an increase in the expense account (Salaries Expense). Therefore, the correct adjusting entry is a debit to Salaries Expense, P58,000, and a credit to Salaries Payable, P58,000. This recognizes the expense and records the corresponding liability for the unpaid salaries at year-end.
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l
Sara Thomson is the president and operates the Thomson Company. The following selected transactions were completed by Thomson Company during August: 2. 1. Received cash from the stockholder as additional investment $200,000. Billed customers for services on account, $45,777. Received electric bill $450, to be paid next month. 3. 4. Received cash from customers on accounts $22,430. 5. Paid creditors on account $12,000 Paid cash dividends, $18,444 6. Note: Each transaction has two entries. Entry Entry Amount Acct Name of Amount Type Acct Increase or Acct Name Decrease Type (4) of Acct (1) (2) (3) (1) (2) (3) 1 23456 Increase or Decrease
Based on the provided information, here are the journal entries for the selected transactions completed by Thomson Company during August:
1. Received cash from the stockholder as additional investment $200,000.
Debit: Cash $200,000
Credit: Common Stock $200,000
2. Billed customers for services on account, $45,777.
Debit: Accounts Receivable $45,777
Credit: Service Revenue $45,777
3. Received an electric bill $450, to be paid next month.
Debit: Utilities Expense $450
Credit: Accounts Payable $450
4. Received cash from customers on accounts $22,430.
Debit: Cash $22,430
Credit: Accounts Receivable $22,430
5. Paid creditors on account $12,000.
Debit: Accounts Payable $12,000
Credit: Cash $12,000
6. Paid cash dividends $18,444.
Debit: Retained Earnings $18,444
Credit: Cash $18,444
Each transaction has two entries, with one being a debit entry and the other being a corresponding credit entry. The specific account names and amounts may vary depending on the company's chart of accounts and accounting practices.
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The following activities occurred during January 2016. Prepare a journal entry for ensure that the basic accounting equation balances for each transaction. (a) Stockholder invests $10,000 into the business. I (b) Company borrows $15,000 signing a note payable to the bank that is due in three months.
a) The journal entry to record this transaction would be:
Cash 10,000
Capital Stock 10,000
b) The journal entry to record this transaction would be:
Cash 15,000
Notes Payable 15,000
a) When the stockholder invests $10,000 into the business, the company's cash balance will increase by $10,000, and so will the stockholder's equity in the company. The journal entry to record this transaction would be:
Cash 10,000
Capital Stock 10,000
(b) When the company borrows $15,000 from the bank by signing a note payable due in three months, the company's cash balance increases by $15,000, but it also incurs a liability to the bank for $15,000. Therefore, the journal entry to record this transaction would be:
Cash 15,000
Notes Payable 15,000
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the order in which participants complete a task is an example of:___
The order in which participants complete a task is an example of task sequencing. The order in which participants complete a task is an example of a "sequence."which is the process of determining the most effective order for completing a series of tasks.
Task sequencing is an important consideration in many fields, including education, psychology, and business, as it can have a significant impact on the outcome of a project or activity. A long answer to this question would delve deeper into the different factors that can influence task sequencing, such as task complexity, task dependencies, and participant characteristics. It would also explore the different methods and strategies that can be used to optimize task sequencing, such as task analysis, decision trees, and computer algorithms.
Ultimately, the goal of effective task sequencing is to ensure that participants are able to complete tasks efficiently and accurately, while minimizing the risk of errors or delays.The order in which participants complete a task is an example of a sequence. In this context, a sequence refers to the arrangement of elements or steps in a particular order. By analyzing the sequence, you can determine the order of events or tasks that the participants need to follow.
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Which of the following is an indication of an assignable cause of variation? Select one or more a 5 sequential observations above the center line b. An upward trend of 5 sequential points c. An observation that is above the upper or below the lower controllimit. d. 4 sequential observations that are more than 2 standard deviations away from the center line e 5 sequential observations which are within one standard deviation of the center line An observation which falls on the center line
Indications of an assignable cause of variation include 5 sequential observations above the center line, an upward trend of 5 sequential points, observations outside control limits, and 4 sequential observations more than 2 standard deviations away from the center line. Random fluctuations within one standard deviation and observations on the center line do not indicate assignable causes.
An assignable cause of variation refers to a specific factor that influences the performance or quality of a process, leading to non-random variations. Identifying these causes is essential for effective process control and improvement. In the given options, the indications of an assignable cause of variation include:
a) 5 sequential observations above the center line: This pattern suggests a non-random shift in the process, which may be due to an assignable cause.
b) An upward trend of 5 sequential points: A consistent upward trend is likely not due to random chance, and indicates that an assignable cause may be influencing the process.
c) An observation that is above the upper or below the lower control limit: Observations outside of control limits are generally considered to be influenced by assignable causes, as they deviate significantly from the expected range.
d) 4 sequential observations that are more than 2 standard deviations away from the center line: This pattern also suggests a non-random shift in the process, which may be attributed to an assignable cause.
Option e (5 sequential observations within one standard deviation of the center line) and the observation falling on the center line do not indicate an assignable cause of variation, as they represent random fluctuations within the expected range of the process.
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Accrued revenues adjustments LO P4 Record adjusting journal entries for each separate case below for year ended December 31. Assume no other adjusting entries are made during the year. a. Accounts Receivable. At year-end, the L. Cole Company has completed services of $20,500 for a client, but the client has not yet been billed for those services. b. Interest Receivable. At year-end, the company has earned, but not yet recorded, $450 of interest earned from its investments in government bonds. c. Accounts Receivable. A painting company bills customers when jobs are complete. The work for one job is now complete. The customer has not yet been billed for the $1,420 of work. View transaction list Journal entry worksheet < 1 2 3 At year-end, the L. Cole Company has completed services of $20,500 for a client, but the client has not yet been billed for those services. Note: Enter debits before credits. Transaction General Journal Debit Credit a. Record entry Clear entry View general journal
The L. Cole Company needs to make three adjusting journal entries for accrued revenues at the end of the year. Firstly, they provided services worth $20,500 to a client but haven't billed them yet. Secondly, they earned $450 of interest from government bonds but haven't recorded it. Lastly, they completed a job for a painting company worth $1,420 but haven't billed the customer. These adjustments ensure that revenues are recognized in the correct accounting period, even if the corresponding cash inflow hasn't occurred.
In order to record the accrued revenues, the L. Cole Company should make the following adjusting journal entries at the end of the year: The entry recognizes the services provided to the client and increases the accounts receivable by $20,500, representing the amount the client owes to the company The entry records the interest earned from government bonds that hasn't been previously recorded. It increases the interest receivable account by $450, indicating the amount the company is yet to receive. The entry reflects the completion of a job for the painting company. By debiting accounts receivable, the company recognizes the amount owed by the customer, and by crediting service revenue, they record the revenue earned from the completed job. These adjusting entries ensure that the revenue is recognized in the correct accounting period, adhering to the accrual accounting principle. It allows the company to accurately reflect its financial performance, even if the corresponding billing and cash inflow have not yet occurred.
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Calculate the price of the following corporate bond with a credit rating of BBB+ / Baa+: $1,000 par value, 8% semi-annual pay coupon, 8.40% yield to maturity, and 5 years to maturity.
To calculate the price of the corporate bond, we can use the present value formula for bond valuation. The formula is:
Price = (C / 2) * [1 - (1 + r)^(-n)] / r + (M / (1 + r)^n)
Where:
C = Coupon payment per period
r = Yield to maturity per period
n = Number of periods (in this case, number of semi-annual periods)
M = Par value of the bond
Given:
C = $1,000 * 8% / 2 = $40
r = 8.40% / 2 = 4.20%
n = 5 years * 2 = 10 periods
M = $1,000
Plugging these values into the formula:
Price = ($40 / 2) * [1 - (1 + 0.042)^(-10)] / 0.042 + ($1,000 / (1 + 0.042)^10)
Calculating this expression will give you the price of the corporate bond.
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Cannonier, Inc., has identified an investment project with the following cash flows.
Year - Cash Flow
1 - $ 990
2 - $1,220
3 - $1,440
a) If the discount rate is 8 percent, what is the future value of these cash flows in Year 4?
b) What is the future value at a discount rate of 11 percent? What is the future value at a discount rate of 24 percent?
a) Future value at 8% discount rate: $4,251.50 b) Future value at 11% discount rate: $4,554.46 c) Future value at 24% discount rate: $5,446.36
To calculate the future value of cash flows, we need to apply the discount rate to each cash flow and compound them to the desired future period.
a) Discount rate = 8% To find the future value in Year 4, we need to compound the cash flows at an 8% discount rate for three years. We can use the future value formula: Future Value = Cash Flow × (1 + Discount Rate)^n Year 1: Future Value = $990 × (1 + 0.08)^3 = $1,234.32 Year 2: Future Value = $1,220 × (1 + 0.08)^2 = $1,461.98 Year 3: Future Value = $1,440 × (1 + 0.08)^1 = $1,555.20
To find the future value in Year 4, we sum up the future values of each cash flow: Future Value in Year 4 = $1,234.32 + $1,461.98 + $1,555.20 = $4,251.50
b) Discount rate = 11% Year 1: Future Value = $990 × (1 + 0.11)^3 = $1,380.14 Year 2: Future Value = $1,220 × (1 + 0.11)^2 = $1,573.92 Year 3: Future Value = $1,440 × (1 + 0.11)^1 = $1,600.40 Future Value in Year 4 = $1,380.14 + $1,573.92 + $1,600.40 = $4,554.46
c) Discount rate = 24% Year 1: Future Value = $990 × (1 + 0.24)^3 = $1,728.12 Year 2: Future Value = $1,220 × (1 + 0.24)^2 = $1,932.64Year 3: Future Value = $1,440 × (1 + 0.24)^1 = $1,785.60mFuture Value in Year 4 = $1,728.12 + $1,932.64 + $1,785.60 = $5,446.36
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Name individual diversity strategies discussed in your chapter.
Select one and explain how you might apply it moving forward to
help gain awareness and improve your ability to understand and
relate to
Finally, I would focus on encouraging open communication in my workplace. This could involve creating opportunities for employees to share their experiences and perspectives, as well as providing feedback to others in a constructive and respectful manner. By promoting inclusion in these ways, I believe that I could help to create a more welcoming and supportive workplace environment that values and respects the diversity of its employees.
In the chapter titled "Managing Diversity," the authors describe different diversity strategies that organizations can use to manage diversity in the workplace. The individual diversity strategies discussed in the chapter include affirmative action, valuing differences, managing diversity, and promoting inclusion. One strategy that is particularly interesting is promoting inclusion, as it focuses on creating an inclusive workplace culture where all employees feel valued and respected. Promoting inclusion involves several key strategies, including creating an inclusive environment, providing diversity and inclusion training, and encouraging open communication. To apply this strategy moving forward, I would start by focusing on creating an inclusive environment in my workplace. This could involve making sure that all employees feel welcome and valued, regardless of their background or identity. I might also look for opportunities to provide diversity and inclusion training to my colleagues, as this can help them better understand the challenges faced by individuals from diverse backgrounds.
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20. Consider an economy described by the following equations: Y=C+I+G+X (income identity) C = 100+ 0.9Yd (consumption function) with an investment equal to $200 million, government expenditures (G) = $200 million and net exports (X) = $100 million and a tax rate t ("tax rate") equal to 0.2 (Hint use the equation 1/1-b(1-t) then multiply it by the sum of the absolute values of investment, government spending and net exports Questions 21. What is the equilibrium production (Y)? 22. What is the Multiplier?
To find the equilibrium production (Y), we need to set the total spending (C + I + G + X) equal to the production output (Y).
Given:
C = 100 + 0.9Yd
I = $200 million
G = $200 million
X = $100 million
ubstituting the values into the income identity equation:
Y = C + I + G + X
Y = (100 + 0.9Yd) + $200 million + $200 million + $100 million
To find Y, we also need to determine Yd (disposable income). We can calculate Yd by subtracting taxes (T) from Y:
Yd = Y - T
Since T is not explicitly given in the information provided, we need to calculate it using the tax rate (t).
T t * Y
T = 0.2 * Y
Now we can substitute the value of Yd into the consumption function:
C = 100 + 0.9Yd
C = 100 + 0.9(Y - T)
C = 100 + 0.9(Y - 0.2Y)
C = 100 + 0.9(0.8Y)
C = 100 + 0.72Y
Substituting the values back into the income identity equation:
Y = (100 + 0.72Y) + $200 million + $200 million + $100 million
Simplifying the equation:
Y = 500 + 0.72Y
Now, we can solve for Y:
0.28Y = 500
Y = 500 / 0.28
Y ≈ 1785.7
Therefore, the equilibrium production (Y) is approximately 1785.71
The multiplier represents the change in equilibrium production resulting from a change in autonomous spending (such as investment, government spending, or net exports). The formula for the multiplier is:
Multiplier = 1 / (1 - b(1 - t)
In this case, we need to calculate the multiplier using the sum of the absolute values of investment, government spending, and net exports
Multiplier = 1 / (1 - |b|(1 - t)
Given that b = 0.9 and t = 0.2, we can substitute the values into the formula
Multiplier = 1 / (1 - |0.9|(1 - 0.2))
Multiplier = 1 / (1 - 0.9(0.8))
Multiplier = 1 / (1 - 0.72)
Multiplier ≈ 3.57
Therefore, the multiplier in this economy is approximately 3.57.
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Imagine you are a market researcher who works for SaveSmart, a
discount insurance company. The company’s management has become
aware of some dissatisfaction among customers who have switched to
Save
As a market researcher at SaveSmart, a discount insurance company, the management has assigned me to investigate and address the dissatisfaction among customers who have switched to other insurance providers.
The goal is to understand the reasons behind their dissatisfaction and identify areas where SaveSmart can make improvements to retain customers and enhance overall customer satisfaction. To conduct this research, I would employ various methods such as surveys, interviews, and data analysis. Surveys can be distributed to the dissatisfied customers to gather their feedback and understand the specific issues they faced. Interviews can provide more in-depth insights and allow customers to express their concerns and suggestions. Additionally, analyzing customer data and comparing it with competitor offerings can help identify gaps in SaveSmart's services. Once the research is complete, the findings can be presented to the management along with actionable recommendations. These recommendations may include improving customer service, enhancing the claims process, offering additional coverage options, or providing competitive pricing. By addressing the concerns raised by dissatisfied customers and implementing appropriate changes, SaveSmart can work towards retaining existing customers and attracting new ones, ultimately improving customer satisfaction and loyalty.
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Exercise 1 Consider the ordinary differential equation d²x dx + dt² dt - 2x = 0. (a) Convert the equation into a system of first order differential equation. (b) Write the system in the form dz(t) = AZ(t), dt where Z: R → R² is vector-valued. (c) Compute the associated fundamental matrix solution for the differential equation in (b). (d) Hence find the general solution of (N). (e) Obtain a solution that satisfies Z(0) = = (7)
(a) The system of first-order differential equations: dx₁/dt = x₂, dx₂/dt = 2x₁ (b) The system in the form dz(t) = AZ(t):, dz(t)/dt = [[0, 1],, [2, 0]] * [x₁(t), x₂(t (c) The associated fundamental matrix solution: e^(At) = [[cos(t), (1/2)sin(t)],, [2sin(t), cos(t)]]. (d) The general solution: Z(t) = C₁ * [cos(t), (1/2)sin(t)] + C₂ * [2sin(t), cos(t)] (e) A solution that satisfies Z(0) = [a, b]:, Z(t) = [7cos(t), (7/2)sin(t)]
To convert the given ordinary differential equation (ODE) into a system of first-order differential equations, let's introduce a new variable. Let x₁ = x and x₂ = dx/dt. Now, we can rewrite the equation as follows:
d²x/dt² - 2x = 0
Differentiating both sides with respect to t, we get:
d²x₁/dt² - 2x₁ = 0
dx₂/dt - 2(dx₁/dt) = 0
Now we have a system of first-order differential equations:
dx₁/dt = x₂
dx₂/dt = 2x₁
Next, we write the system in the form dz(t) = AZ(t), where Z: R → R² is a vector-valued function.
Let Z(t) = [x₁(t), x₂(t)]. Now we can rewrite the system as:
dz(t)/dt = A * Z(t)
where A is the coefficient matrix given by:
A = [[0, 1],
[2, 0]]
To compute the associated fundamental matrix solution for the differential equation, we need to find the matrix exponential of At.
e^(At) = I + At + (At)²/2! + (At)³/3! + ...
Using the formula for the matrix exponential, we have:
A² = [[0, 1],
[2, 0]] * [[0, 1],
[2, 0]] = [[2, 0],
[0, 2]]
(A²)/2! = [[2/2, 0],
[0, 2/2]] = [[1, 0],
[0, 1]]
(A³)/3! = [[0, 1],
[2, 0]] * [[1, 0],
[0, 1]] = [[0, 1],
[2, 0]]
(A³)/3! = [[0/6, 1/6],
[2/6, 0/6]] = [[0, 1/6],
[1/3, 0]]
Continuing this process, we can find higher powers of A divided by the respective factorial:
(A⁴)/4! = [[0, 1/6],
[1/3, 0]] * [[0, 1],
[2, 0]] = [[2/18, 0],
[0, 2/18]] = [[1/9, 0],
[0, 1/9]]
(A⁴)/4! = [[1/9, 0],
[0, 1/9]]
(A⁵)/5! = [[1/9, 0],
[0, 1/9]] * [[0, 1],
[2, 0]] = [[0, 1/9],
[2/9, 0]]
(A⁵)/5! = [[0, 1/9],
[2/9, 0]]
We can observe that A⁶ and higher powers will repeat the pattern of A², A³, A⁴, and A⁵.
Now, we can write the matrix exponential as:
e^(At) = I + At + (At)²/2! + (At)³/3! + ...
Substituting the values we computed, we have:
e^(At) = [[1, 0],
[0, 1]] + [[0, 1],
[2, 0]]t + [[1, 0],
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What would be the payback period of the CO2 capture project if
the project revenues annually are set to be $1 million, from
selling CO2, with an operating cost of $100,000 and a capital cost
of $3 mil
The payback period for the CO2 capture project would be approximately 3.33 years. This means it would take around 3.33 years for the project to generate enough net cash inflow to recover the initial investment of $3 million.
The payback period of the CO2 capture project can be determined by dividing the initial capital cost by the annual net cash inflow. In this case, the project generates annual revenues of $1 million from selling CO2, while incurring operating costs of $100,000 and a capital cost of $3 million.
To calculate the annual net cash inflow, we subtract the operating costs from the project revenues: $1 million - $100,000 = $900,000.
Next, we divide the capital cost by the annual net cash inflow to find the payback period: $3 million / $900,000 = 3.33 years.
Therefore, the payback period for the CO2 capture project would be approximately 3.33 years. This means it would take around 3.33 years for the project to generate enough net cash inflow to recover the initial investment of $3 million.
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What forms of preferential treatment can the holders of
preference shares receive over and above the rights of the company.
Would you disclose these preference shares as debt or equity?
Explain your d
Common shareholders have fewer rights than preferred shareholders. The company's articles of association or preference shares determine the type of preferential treatment. Preferences include:
Dividend priority: Preference shareholders usually receive dividends before common stockholders. They may get a fixed or rate-based dividend.
Asset priority: In the case of a company's liquidation or winding up, preference shareholders normally receive their capital first. Common shareholders have a lower claim on the company's assets.
Voting rights: Preference shareholders may vote on topics that directly affect their rights, such as changes to their preference shares or financial interests.
The terms and attributes of preference shares determine whether they're debt or equity. Because they represent firm ownership, preference shares are equity instruments. However, if the preference shares have set dividend payments and priority in liquidation, they may be considered hybrid security with debt and equity features. Preference shares are classified as debt or equity by accounting standards and regulations.
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a.) If the marginal cost pricing rule is used to regulate a natural monopolist, the monopolist:
A. earns a monopoly profit.
B. earns a normal profit.
C. earns an economic profit.
D. sustains an economic loss.
If the marginal cost pricing rule is used to regulate a natural monopolist, the monopolist: sustains an economic loss. Thus, option (d) is correct.
This is so because the marginal cost pricing rule mandates that the monopolist set the price at the level of the marginal cost of production, which is often less than the monopolist's price.
When the marginal cost pricing rule is in effect, the monopolist must reduce its price until it equals the marginal cost of production, which is ordinarily less than the monopolist's price.
As a result, the significance of the marginal cost pricing rule is used to regulate a natural monopolist are the aforementioned. Therefore, option (d) is correct.
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explain how functional attributes and psychological attributes determine the level of customer satisfaction in the post-purchase? In your opinion, do all customers give the same importance to each attribute? Please explain.
Functional attributes and psychological attributes both determine the level of customer satisfaction in the post-purchase. Functional attributes are specific attributes or features of a product or service that meet the customer's need. These attributes include the quality, price, design, performance, and functionality of the product.
Psychological attributes are related to the customer's perception and feelings toward the product or service. These attributes are subjective and may differ from customer to customer. Examples of psychological attributes include prestige, social status, and emotional appeal.Both functional and psychological attributes determine the level of customer satisfaction. For instance, if a product has excellent functionality and meets the customer's need, the customer will be satisfied. If the customer also perceives the product as prestigious, they will be more satisfied. On the other hand, if a product fails to meet the customer's needs and does not have psychological attributes, the customer will be unsatisfied. Customers value functional attributes and psychological attributes differently, depending on their needs and preferences. In my opinion, all customers do not give the same importance to each attribute. Customers may have different needs and preferences, and therefore may value different attributes differently. For example, some customers may value functionality more, while others may value emotional appeal. In conclusion, functional and psychological attributes are both essential in determining customer satisfaction. However, different customers may value each attribute differently, depending on their needs and preferences.
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Explain how interest rates and bond prices are related to one another. Why is this important for monetary policy?
Interest rates and bond prices are inversely related to one another. That is, when interest rates increase, bond prices decrease, and when interest rates decrease, bond prices increase. This relationship is important for monetary policy because it allows policymakers to influence the economy by changing interest rates.
Interest rates are one of the main tools of monetary policy because they influence spending and investment. When interest rates are high, it becomes more expensive for individuals and businesses to borrow money, which decreases spending and investment. This can help to slow down an economy that is growing too quickly and causing inflation. Conversely, when interest rates are low, it becomes cheaper for individuals and businesses to borrow money, which increases spending and investment. This can help to stimulate an economy that is growing too slowly and causing unemployment.Bond prices are also affected by changes in interest rates.
When interest rates increase, the yield on bonds becomes less attractive compared to other investments, so investors may sell their bonds, which decreases the price. Conversely, when interest rates decrease, the yield on bonds becomes more attractive, so investors may buy more bonds, which increases the price. This is why it is important for policymakers to understand the relationship between interest rates and bond prices when making decisions about monetary policy.
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the proposed increase in the minimum wage would decrease the total wage payments to unskilled workers if the demand for unskilled labor were
The demand for unskilled labor were inelastic, employers would find it difficult to adjust their production process, and the total wage payments to unskilled workers would increase.
The proposed increase in the minimum wage would decrease the total wage payments to unskilled workers if the demand for unskilled labor were elastic. The unskilled workers are the employees who do not have special training or skills in a particular field. These workers are often paid low wages and receive no benefits like medical, insurance, or any paid leaves. Hence, they depend on their wage for their livelihood.Increasing the minimum wage means employers would have to pay more wages to their employees. However, employers may adjust their production methods or switch to more automated processes to keep their costs in check. This means that the employer's demand for unskilled workers would decrease due to the increase in wage rates. If the demand for unskilled labor is elastic, it means that employers can quickly adjust their production process to maintain their profit margins. In this case, employers would find it easier to adjust to the increase in wages by reducing the number of unskilled workers. This means that there would be a reduction in the total wage payments to unskilled workers.
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John, your group's informal leader, doesn't trust Alicia, the group's communications manager, John feels Alicia tends to overemphasize her own beliefs in group documents, and Alcla belleves John is micromanaging the team. This is a classic case of interorganizational conflict Intergroup conflict Choose the best answers to the following questions Interpersonal conflict Lly and Jessica are both members of the account management group at Calabria. They disagree interorganizational conflict prongoing client communications. Which form of conflict is their team likely to experience as a result?
The team is likely to experience interpersonal conflict due to and Jessica's disagreement regarding ongoing client communications. What is interpersonal conflict? Interpersonal conflict is a type of conflict that arises between two or more individuals in an organization.
This form of conflict occurs when individuals are unable to agree on a specific issue. Conflicts between co-workers, managers, and subordinates, as well as conflicts between employees and clients, are all examples of interpersonal conflict.In the given scenario, Lly and Jessica are both members of the account management group at Calabria, and they disagree about ongoing client communications. Thus, the team is likely to experience interpersonal conflict as a result.
John, your group's informal leader, doesn't trust Alicia, the group's communications manager, John feels Alicia tends to overemphasize her own beliefs in group documents, and Alcla belleves John is micromanaging the team. This is a classic case of interorganizational conflict Intergroup conflict Choose the best answers to the following questions Interpersonal conflict and Jessica are both members of the account management group at Calabria.
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What is Lightbox Diamonds? How does the creation and market positioning of Lightbox Diamonds demonstrate a shift in De Beers' overall approach to managing the threat posted by the synthetic diamond industry? Explain your reasoning.
Lightbox Diamonds is a brand owned by De Beers, a renowned diamond mining and trading company. It was created in response to the growing threat posed by the synthetic diamond industry. Lightbox Diamonds offers lab-grown diamonds that are priced significantly lower than natural diamonds, targeting the fashion and affordable jewelry market segment.
This creation and market positioning of Lightbox Diamonds demonstrate a shift in De Beers' overall approach to managing the threat posed by the synthetic diamond industry. De Beers, traditionally focused on the mining and sale of natural diamonds, recognized the increasing popularity and acceptance of lab-grown diamonds among consumers. By launching Lightbox Diamonds, De Beers entered the synthetic diamond market, thereby adapting to the changing dynamics of the industry.
De Beers' decision to offer lab-grown diamonds at a lower price point through the Lightbox brand indicates a strategic move to differentiate their natural diamonds from synthetic counterparts. Rather than attempting to directly compete with synthetic diamonds on price, De Beers chose to position Lightbox Diamonds as a separate and more affordable product. This approach helps protect the reputation and value of their natural diamonds while catering to a new segment of consumers who prioritize affordability and fashion trends.
In summary, Lightbox Diamonds represents a shift in De Beers' strategy towards managing the threat posed by synthetic diamonds. By entering the lab-grown diamond market with a separate brand and pricing strategy, De Beers demonstrates their adaptability and willingness to explore new avenues within the industry, while also safeguarding the position of their natural diamonds.
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Discuss the legal position of intention as one of the important elements in the formation of a contract. Support your answer with relevant cases.
Intention is a vital element in the formation of a contract. The parties involved must have the intention to create a legal relationship for a contract to be binding. The cases of Balfour v Balfour and Jones v Padavatton illustrate this principle in contract law.
Intention is one of the important elements in the formation of a contract. The legal position of intention will be discussed in detail in this answer and supported with relevant cases.
According to the English law of contract, intention is a vital element that is required for a contract to be considered legally binding. In other words, the parties involved must have the intention to create a legal relationship. If they do not have this intention, the agreement is not considered a contract.
The case of Balfour v Balfour is a classic example of the principle of intention in contract law. In this case, a husband promised to pay his wife a monthly allowance of £30 while he was away working in Ceylon. Unfortunately, the couple separated, and the husband stopped the payments. The wife sued the husband for breach of contract, but the court ruled against her, stating that there was no intention to create a legally binding agreement as it was a domestic arrangement between husband and wife.
Another case that illustrates the principle of intention is Jones v Padavatton. In this case, the mother promised to give her daughter £200 per month while she was studying at the London School of Economics. However, the mother stopped the payments, and the daughter sued her for breach of contract. The court held that there was an intention to create a legally binding agreement because the mother had made the offer in writing and signed it.
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The material aspects that govern the concept of intention is: The parties cannot sue each other in the absence of intention. If the intention to create legal relations is absent then the contract is a mere promise. The contract will not have a binding effect if there is no intention to create legal relations.
What does Intention mean?
A person obliquely intends those consequences that are virtually certain to emerge from his actions and which he knows are virtually certain to do so. A person directly intends those consequences that he seeks to bring about by his actions, whether or not they will be likely to follow.
A contract must contain several characteristics in order to be legitimate and recognised by the common law, including an offer, acceptance, consideration, the desire to establish legal relations, authority and ability, and certainty. A contract cannot be enforceable by the courts and is not legally binding without these components.
Legal purpose denotes that the parties to a contract must have intended for it to be a legally binding one.
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In your new role as compensation analyst, you have been asked to estimate the dollar amount of the profit-sharing pool based on three approaches as well as the allocation of profit-sharing awards to eligible employees. The company's profits equal $35 million. You are considering the following three formulas for determining the total profit-sharing pool.
First-Dollar of Profits: The company agrees to share 3.0 percent of all profits up to $12 million.
Graduated First-Dollar-of-Profits: The company agrees to share 2.0 percent of all profits up to $15 million, and 4.0 percent of all profits up to $40 million.
Profitability Threshold Formula: The company will share 1.5 percent of the profits above $10 million up to $17 million.
There are 260 employees whose total annual base pay equals $2,100,00
The total profit-sharing pool for:
(Round your answers to the nearest hundredths place.)
(a) First-dollar of profits is
$360,000360,000
(b) Graduated first-dollar of profits is
$1,400,0001,400,000
(c) Profitability threshold formula is
$255,000255,000
a) First-dollar of profits is: $360,000First-dollar of profits is the formula where the company agrees to share 3.0 percent of all profits up to $12 million.
So, we have a profit of $35 million and the company agrees to share 3.0 percent of all profits up to $12 million.Total sharing for the first $12 million of profits: $$12,\!000,\!000\times 0.03=360,\!000.$$Hence, the total profit-sharing pool for first-dollar of profits is $360,000.b) Graduated first-dollar of profits is: $1,400,000Graduated first-dollar-of-profits is the formula where the company agrees to share 2.0 percent of all profits up to $15 million, and 4.0 percent of all profits up to $40 million.So, we have a profit of $35 million and the company agrees to share 2.0 percent of all profits up to $15 million and 4.0 percent of all profits up to $40 million.Total sharing for the first $15 million of profits:
$$15,\!000,\!000\times 0.02=300,\!000.$$Total sharing for the next $20 million of profits (i.e. profits between $15 million and $35 million): $$20,\!000,\!000\times 0.04=800,\!000.$$Therefore, the total sharing pool for graduated first-dollar-of-profits is $$300,\!000+800,\!000=$1,\!100,\!000.$$Hence, the total profit-sharing pool for graduated first-dollar-of-profits is $1,400,000.c) Profitability threshold formula is: $255,000Profitability threshold formula is the formula where the company will share 1.5 percent of the profits above $10 million up to $17 million.So, we have a profit of $35 million. The profits above $10 million up to $17 million will be $$35,\!000,\!000-10,\!000,\!000=$25,\!000,\!000.$$Total sharing for the profits between $10 million and $17 million: $$25,\!000,\!000\times 0.015=$375,\!000.$$Since the total sharing cannot exceed the profits above the threshold, the total sharing pool will be $$\min(375,\!000,\!000)=255,\!000.$$Hence, the total profit-sharing pool for the profitability threshold formula is $255,000.
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This semester, we have dealt with three major historical turning points. From early to high middle ages around 1000; from the high to late middle ages around 1300; and from the late middle ages to the early modern era around 1500. Identify the major changes, either specific events or long term processes, which cause historians to consider them to be turning points in detail(about 2 pages).
The study of history is vital as it enables us to understand the transformation of society over time.
Three historical turning points have taken place from the early to high middle ages around 1000; from the high to late middle ages around 1300; and from the late middle ages to the early modern era around 1500. Historians consider these changes as turning points since they brought about significant changes either by specific events or long-term processes.
1. Early to high middle ages around 1000A. Charlemagne's Holy Roman Empire - Charles the Great or Charlemagne is credited with creating the Holy Roman Empire in the year 800. He consolidated most of the Western Europe under his rule and started the Carolingian renaissance which saw a rebirth of culture, art, and education. His reign is considered a turning point since it led to the strengthening of the Papacy and the growth of the medieval European state. B. The Battle of Hastings - This battle took place in 1066, where the Normans defeated the Saxons led by Harold. William, Duke of Normandy, became the new king of England after the battle. This event marked the end of the Anglo-Saxon rule and ushered in a new era of Norman and French domination of England. It also led to the formation of the Anglo-Norman culture and French influence in the English language.
2. High to late middle ages around 1300A. The Black Death - This epidemic occurred in the 14th century and killed millions of people in Europe. This event changed the course of European history by altering social, economic, and political relations. It led to the decline of the feudal system, a shift in religious thinking, and the emergence of modern capitalism. B. The Hundred Years' War - This war took place from 1337 to 1453 between England and France. The war led to the development of new tactics, weapons, and technologies. It also resulted in the decline of the knightly class and the rise of national armies. The Hundred Years' War was significant since it marked the end of the Middle Ages and the beginning of the Renaissance.
3. Late middle ages to the early modern era around 1500A. The Fall of Constantinople - In 1453, Constantinople fell to the Ottoman Turks. This event marked the end of the Byzantine Empire and the decline of the Eastern Orthodox Church. The Ottoman Turks' victory also led to the decline of Venice and the rise of the Portuguese and Spanish empires. B. The Protestant Reformation - This was a religious movement that began in the early 16th century in Germany. It was led by Martin Luther, who challenged the authority of the Roman Catholic Church and questioned the doctrine of indulgences. This event marked the beginning of the modern era by ushering in religious tolerance, the scientific revolution, and the development of modern nation-states. ConclusionIn conclusion, the three historical turning points from the early to high middle ages around 1000; from the high to late middle ages around 1300; and from the late middle ages to the early modern era around 1500 brought about significant changes either by specific events or long-term processes. Charlemagne's Holy Roman Empire, The Battle of Hastings, The Black Death, The Hundred Years' War, The Fall of Constantinople, and The Protestant Reformation are considered turning points in history due to their impact on European society.
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Mark has just set up a retirement plan where he will deposit $125 at the end of each month for the next 20 years until he retires. If the account earns j4-5.16%, how much money will be in Mark's account when he retires? Round your answer to 2 decimal places.
Mark will deposit $125 at the end of each month for 20 years into a retirement plan that earns an annual interest rate of 4.5%. When he retires, the amount of money in his account will be approximately $9,120.68.
To calculate the total amount of money in Mark's retirement account when he retires, we can use the formula for the future value of a series of deposits:
Future Value =[tex]$PMT \times \frac{{(1 + r)^n - 1}}{r}$[/tex]
Where:
PMT = Monthly deposit amount ($125)
r = Monthly interest rate (4.5% / 12 = 0.0375)
n = Number of periods (20 years * 12 months/year = 240)
Plugging in the values into the formula, we can calculate the future value:
Future Value = [tex]$125 \times \frac{{(1 + 0.0375)^{240} - 1}}{0.0375}$[/tex]
Future Value ≈ $125 * [2.36834052 - 1] / 0.0375
Future Value ≈ $125 * 1.36834052 / 0.0375
Future Value ≈ $342.042565 / 0.0375
Future Value ≈ $9,120.68
Therefore, when Mark retires, the amount of money in his retirement account will be approximately $9,120.68.
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Determine the effects of the following transactions on Current assets, Current liabilities, and Working Capital. Write "Inc" for an Increase, "Dec" for a Decrease, or "NE" if there is No Effect.
The following transactions have different effects on current assets, current liabilities, and working capital. Some transactions increase or decrease these accounts, while others have no effect.
1. Purchase of inventory with cash: Dec current assets (Cash) and NE for current liabilities and working capital. This transaction reduces the amount of cash on hand, but it increases the value of the inventory.
There is no effect on liabilities since the purchase was made with cash, and there is no impact on working capital since there is no change in the net assets.
2. Sale of inventory on credit: Inc current assets (Accounts Receivable) and NE for current liabilities and working capital.
This transaction increases the amount of accounts receivable, which represents money owed to the company, but it does not impact current liabilities since the sale was made on credit, and there is no effect on working capital since there is no change in net assets.
3. Payment of accounts payable with cash: Dec current assets (Cash) and dec current liabilities (Accounts Payable); NE for working capital. This transaction reduces the amount of cash on hand, but it also reduces the accounts payable amount, which is money owed by the company.
There is no effect on working capital since there is an equal decrease in both current assets and current liabilities.
4. Acquisition of a long-term asset with cash: Dec current assets (Cash) and NE for current liabilities and working capital.
This transaction reduces the amount of cash on hand, but there is no effect on current liabilities or working capital since the purchase of a long-term asset does not impact these accounts.
5. Payment of a long-term debt with cash: Dec current assets (Cash), Dec current liabilities (Long-term debt), and no effect on working capital. This transaction reduces both cash and long-term debt, which is a liability.
It has no effect on working capital since there is an equal decrease in both current assets and current liabilities.
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Bill Bassoon is the chair of Sax. Bill vacated the CEO position last year to become the chair of the board, and a new CEO has not yet been found. Bill is unsure if Sax needs more non-executive directors. There are currently six members on the board, which consists of four executive directors and two non-executive directors. He is considering appointing one of his brothers, who is a retired chief executive of a manufacturing company, as a non-executive director. Bill wants to ensure the board focuses on the strategic direction of Sax and not the day-to-day decision-making. To do this, he has reduced the number of board meetings.
The finance director, Jessie Oboe, is considering setting up an audit committee, but has not undertaken this task yet as she is very busy. A new board director was appointed nine months ago. He has yet to undertake his board training as this is normally provided by the chief executive and this role is still vacant.
In the given scenario, Bill Bassoon is the chair of Sax, who vacated the CEO position last year to become the chair of the board. There are currently six members on the board, which consists of four executive directors and two non-executive directors. Bill is unsure if Sax needs more non-executive directors.
He is considering appointing one of his brothers, who is a retired chief executive of a manufacturing company, as a non-executive director.
Bill wants to ensure the board focuses on the strategic direction of Sax and not the day-to-day decision-making. To do this, he has reduced the number of board meetings. However, the finance director, Jessie Oboe, is considering setting up an audit committee but has not undertaken this task yet as she is very busy. Also, a new board director was appointed nine months ago, but he has yet to undertake his board training as this is normally provided by the chief executive and this role is still vacant.
In the given scenario, Bill needs to be sure if Sax needs more non-executive directors. Having more non-executive directors would improve the performance of the company by making it more accountable and increasing transparency. Bill also needs to consider that the appointment of his brother as a non-executive director could affect the independence of the board.
Jessie Oboe needs to undertake the task of setting up an audit committee as soon as possible. This would improve the quality of financial reporting, the reliability of financial statements, and the integrity of financial information provided to stakeholders. Moreover, the new board director should undertake his board training as it is essential for him to understand the strategic goals, objectives, and vision of the company.
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