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  • 20 Marks

BMF – May 2015 – L1 – SB – Q6 – Basics of Business Finance and Financial Markets

Describe the Boston Consulting Group (BCG) matrix used for business portfolio management.

Describe the Boston Consulting Group (BCG) matrix.

The Boston Consulting Group (BCG) matrix is a model by which businesses are
classified in relation to market growth and relative market share.
The strategy of each business is determined on the basis of the following factors:
(i) The growth rate of its market
(ii) The market share it enjoys

The matrix can be depicted by the following quadrant:

b. Product-Market Strategies:

i. Stars:
Stars operate in high-growth markets and dominate their sectors. They require substantial investment to maintain market position but promise high returns. The recommended product-market strategy is to continue heavy investment in advertising, promotion, and product development to ensure growth in market share and revenue.

ii. Question Marks (Problem Children):
These products operate in high-growth markets but have low market share. They create opportunities for long-term growth but need significant cash investments. The suggested strategy is to either invest heavily to turn them into stars or divest if the market position does not improve. This may involve strategic decisions like harvesting or liquidation.

iii. Cash Cows:
These products have high market share in low-growth markets. They generate consistent cash flows but offer limited growth opportunities. The strategy is to maintain or consolidate their position, using their revenue to fund other areas of the business that require investment (such as Stars or Question Marks).

iv. Dogs:
Dogs have low market share in low-growth markets, providing little to no profit potential. The strategy is often to divest or liquidate these products, as they are not worth the continued investment given their bleak future.

c. Weaknesses of the BCG Matrix:

  1. The model ignores the synergies between different business units, which can affect overall profitability.
  2. High market share does not always guarantee profitability, as it depends on other factors such as cost structure and competitive advantage.

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  • 20 Marks

BMF – May 2015 – L1 – SB – Q6 – Basics of Business Finance and Financial Markets

Describe the Boston Consulting Group (BCG) matrix used for business portfolio management.

Describe the Boston Consulting Group (BCG) matrix.

The Boston Consulting Group (BCG) matrix is a model by which businesses are
classified in relation to market growth and relative market share.
The strategy of each business is determined on the basis of the following factors:
(i) The growth rate of its market
(ii) The market share it enjoys

The matrix can be depicted by the following quadrant:

b. Product-Market Strategies:

i. Stars:
Stars operate in high-growth markets and dominate their sectors. They require substantial investment to maintain market position but promise high returns. The recommended product-market strategy is to continue heavy investment in advertising, promotion, and product development to ensure growth in market share and revenue.

ii. Question Marks (Problem Children):
These products operate in high-growth markets but have low market share. They create opportunities for long-term growth but need significant cash investments. The suggested strategy is to either invest heavily to turn them into stars or divest if the market position does not improve. This may involve strategic decisions like harvesting or liquidation.

iii. Cash Cows:
These products have high market share in low-growth markets. They generate consistent cash flows but offer limited growth opportunities. The strategy is to maintain or consolidate their position, using their revenue to fund other areas of the business that require investment (such as Stars or Question Marks).

iv. Dogs:
Dogs have low market share in low-growth markets, providing little to no profit potential. The strategy is often to divest or liquidate these products, as they are not worth the continued investment given their bleak future.

c. Weaknesses of the BCG Matrix:

  1. The model ignores the synergies between different business units, which can affect overall profitability.
  2. High market share does not always guarantee profitability, as it depends on other factors such as cost structure and competitive advantage.

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  • 5 Marks

BMF – May 2015 – L1 – SB – Q5b – Management, Individual, and Organisational Behaviour

Discuss hygiene factors and motivators in Herzberg’s two-factor theory.

Write briefly on the following:
i. Hygiene factors
ii. Motivators

i. Hygiene Factors: These are factors that can lead to dissatisfaction in the workplace if they are absent or inadequate, but their presence does not necessarily create satisfaction. They include aspects like working conditions, salary, company policies, job security, and relationships with supervisors and colleagues. Inadequate hygiene factors result in employee dissatisfaction, but improving these factors alone will not boost job satisfaction.

ii. Motivators: These are factors that positively influence job satisfaction and encourage employees to improve performance. They include recognition, responsibility, opportunities for advancement, achievement, and personal growth. Unlike hygiene factors, motivators directly impact an employee’s level of job satisfaction and contribute to higher levels of performance and motivation.

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  • 5 Marks

BMF – May 2015 – L1 – SB – Q5b – Management, Individual, and Organisational Behaviour

Discuss hygiene factors and motivators in Herzberg’s two-factor theory.

Write briefly on the following:
i. Hygiene factors
ii. Motivators

i. Hygiene Factors: These are factors that can lead to dissatisfaction in the workplace if they are absent or inadequate, but their presence does not necessarily create satisfaction. They include aspects like working conditions, salary, company policies, job security, and relationships with supervisors and colleagues. Inadequate hygiene factors result in employee dissatisfaction, but improving these factors alone will not boost job satisfaction.

ii. Motivators: These are factors that positively influence job satisfaction and encourage employees to improve performance. They include recognition, responsibility, opportunities for advancement, achievement, and personal growth. Unlike hygiene factors, motivators directly impact an employee’s level of job satisfaction and contribute to higher levels of performance and motivation.

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  • 15 Marks

BMF – May 2015 – L1 – SB – Q5a – Management, Individual, and Organisational Behaviour

List and explain the five levels of human needs as per Maslow’s hierarchy.

List and explain the FIVE general types of human needs in ascending order.

  1. Physiological Needs: These are the basic survival needs for human life, such as food, water, shelter, air, and clothing. In an organizational context, these are equated to adequate salary, heat, and air to ensure employees’ survival and well-being.
  2. Safety Needs: Once physiological needs are met, individuals seek protection and security, both physically and psychologically. In the workplace, this relates to job security, safe working conditions, and a stable environment free from physical harm.
  3. Belongingness/Social Needs: After safety, individuals look for social connections, love, and belonging. In an organization, this refers to forming relationships with colleagues and feeling accepted as part of a team. Employees value a friendly work environment and camaraderie among coworkers.
  4. Esteem Needs: These involve the need for recognition, respect, and self-esteem. Employees strive to achieve recognition for their work, which can be fulfilled through awards, promotions, or being acknowledged as valuable team members.
  5. Self-Actualization Needs: The highest level, where individuals strive to realize their full potential. In the workplace, this involves opportunities for personal growth, creativity, and achieving career goals. Managers can help employees meet these needs by providing challenging tasks and encouraging innovation.

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  • 15 Marks

BMF – May 2015 – L1 – SB – Q5a – Management, Individual, and Organisational Behaviour

List and explain the five levels of human needs as per Maslow’s hierarchy.

List and explain the FIVE general types of human needs in ascending order.

  1. Physiological Needs: These are the basic survival needs for human life, such as food, water, shelter, air, and clothing. In an organizational context, these are equated to adequate salary, heat, and air to ensure employees’ survival and well-being.
  2. Safety Needs: Once physiological needs are met, individuals seek protection and security, both physically and psychologically. In the workplace, this relates to job security, safe working conditions, and a stable environment free from physical harm.
  3. Belongingness/Social Needs: After safety, individuals look for social connections, love, and belonging. In an organization, this refers to forming relationships with colleagues and feeling accepted as part of a team. Employees value a friendly work environment and camaraderie among coworkers.
  4. Esteem Needs: These involve the need for recognition, respect, and self-esteem. Employees strive to achieve recognition for their work, which can be fulfilled through awards, promotions, or being acknowledged as valuable team members.
  5. Self-Actualization Needs: The highest level, where individuals strive to realize their full potential. In the workplace, this involves opportunities for personal growth, creativity, and achieving career goals. Managers can help employees meet these needs by providing challenging tasks and encouraging innovation.

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  • 20 Marks

BMF – May 2015 – L1 – SB – Q4 – Basics of Business Finance and Financial Markets

Discuss major cash flow items in capital investment projects and explain the payback period investment appraisal method.

a. List and explain FOUR major cashflow items to be included in a capital investment project. (8 Marks)
b.
i. Explain the payback period technique of investment appraisal. (4 Marks)
ii. State TWO advantages and TWO disadvantages of payback period. (8 Marks)

a. Major cashflow items to be included in a capital investment project:

  1. Initial capital outlay: This is the cash expenditure required at the beginning of the project, usually spent on fixed assets.
  2. Operating cash flows: These include cash inflows from sales and cash outflows for operating expenses like wages, utilities, and materials.
  3. Terminal cash flows: These are the cash flows at the end of the project, such as salvage value or disposal of assets.
  4. Incremental cash flows: These refer to the additional cash flows generated directly by the investment, which wouldn’t have been earned otherwise.

b. i. Payback Period Investment Appraisal Technique:
This technique calculates the time needed for the cash inflows generated by a project to recover the initial investment. It emphasizes liquidity by focusing on the period over which the project will generate enough cash inflows to cover the initial outlay. It does not take into account the time value of money or cash flows beyond the payback period.

ii. Advantages of Payback Period:

  1. Simple to calculate and understand.
  2. It is useful for projects where liquidity is important because it focuses on recovering the initial investment quickly.

Disadvantages of Payback Period:

  1. It ignores cash flows that occur after the payback period, potentially overlooking the profitability of longer-term projects.
  2. It does not consider the time value of money.

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  • 20 Marks

BMF – May 2015 – L1 – SB – Q4 – Basics of Business Finance and Financial Markets

Discuss major cash flow items in capital investment projects and explain the payback period investment appraisal method.

a. List and explain FOUR major cashflow items to be included in a capital investment project. (8 Marks)
b.
i. Explain the payback period technique of investment appraisal. (4 Marks)
ii. State TWO advantages and TWO disadvantages of payback period. (8 Marks)

a. Major cashflow items to be included in a capital investment project:

  1. Initial capital outlay: This is the cash expenditure required at the beginning of the project, usually spent on fixed assets.
  2. Operating cash flows: These include cash inflows from sales and cash outflows for operating expenses like wages, utilities, and materials.
  3. Terminal cash flows: These are the cash flows at the end of the project, such as salvage value or disposal of assets.
  4. Incremental cash flows: These refer to the additional cash flows generated directly by the investment, which wouldn’t have been earned otherwise.

b. i. Payback Period Investment Appraisal Technique:
This technique calculates the time needed for the cash inflows generated by a project to recover the initial investment. It emphasizes liquidity by focusing on the period over which the project will generate enough cash inflows to cover the initial outlay. It does not take into account the time value of money or cash flows beyond the payback period.

ii. Advantages of Payback Period:

  1. Simple to calculate and understand.
  2. It is useful for projects where liquidity is important because it focuses on recovering the initial investment quickly.

Disadvantages of Payback Period:

  1. It ignores cash flows that occur after the payback period, potentially overlooking the profitability of longer-term projects.
  2. It does not consider the time value of money.

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  • 20 Marks

BMF – May 2015 – L1 – SB – Q3 – The Role of Professional Accountants in Business and Society

Discuss reasons for government involvement in the Nigerian financial system and mechanisms for intervention.

a. State FIVE reasons for the increasing role of Government in the Nigerian Financial System.
(10 Marks)

b. State FIVE mechanisms for government intervention in the financial system.
(10 Marks)

a. Reasons for the Increasing Role of Government in the Nigerian Financial System:

  1. To maintain monetary stability: The government needs to ensure that the financial system remains stable to control inflation and manage the economy effectively.
  2. To promote economic growth: Government interventions are essential to stimulate growth and support the development of various sectors of the economy.
  3. To ensure healthy competition: By regulating the financial system, the government prevents monopolies and ensures fair competition, both domestically and internationally.
  4. To protect the public from fraud and exploitation: Government policies are crucial to safeguarding the public from unethical financial practices.
  5. To attract foreign investment: A stable financial system encourages international investors, contributing to the growth of the economy.

b. Mechanisms for Government Intervention in the Financial System:

  1. Open Market Operations (OMO): The government buys and sells treasury bills and bonds to control the money supply.
  2. Changes in monetary policy rates (MPR): Adjusting the MPR influences interest rates, which in turn affects borrowing and investment levels in the economy.
  3. Liquidity ratio adjustments: The government can change the liquidity ratio to control the amount of cash that banks must hold as reserves, impacting the availability of credit.
  4. Fiscal policy (taxation and spending): The government uses taxes and public spending to influence the financial system and stimulate or slow down the economy.
  5. Recapitalization of banks: To maintain stability, the government may require banks to recapitalize, ensuring that they have enough funds to meet their obligations.

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  • 20 Marks

BMF – May 2015 – L1 – SB – Q3 – The Role of Professional Accountants in Business and Society

Discuss reasons for government involvement in the Nigerian financial system and mechanisms for intervention.

a. State FIVE reasons for the increasing role of Government in the Nigerian Financial System.
(10 Marks)

b. State FIVE mechanisms for government intervention in the financial system.
(10 Marks)

a. Reasons for the Increasing Role of Government in the Nigerian Financial System:

  1. To maintain monetary stability: The government needs to ensure that the financial system remains stable to control inflation and manage the economy effectively.
  2. To promote economic growth: Government interventions are essential to stimulate growth and support the development of various sectors of the economy.
  3. To ensure healthy competition: By regulating the financial system, the government prevents monopolies and ensures fair competition, both domestically and internationally.
  4. To protect the public from fraud and exploitation: Government policies are crucial to safeguarding the public from unethical financial practices.
  5. To attract foreign investment: A stable financial system encourages international investors, contributing to the growth of the economy.

b. Mechanisms for Government Intervention in the Financial System:

  1. Open Market Operations (OMO): The government buys and sells treasury bills and bonds to control the money supply.
  2. Changes in monetary policy rates (MPR): Adjusting the MPR influences interest rates, which in turn affects borrowing and investment levels in the economy.
  3. Liquidity ratio adjustments: The government can change the liquidity ratio to control the amount of cash that banks must hold as reserves, impacting the availability of credit.
  4. Fiscal policy (taxation and spending): The government uses taxes and public spending to influence the financial system and stimulate or slow down the economy.
  5. Recapitalization of banks: To maintain stability, the government may require banks to recapitalize, ensuring that they have enough funds to meet their obligations.

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  • 20 Marks

BMF – May 2015 – L1 – SB – Q2 – The Business Environment

Discuss four external environmental factors that impact business operations.

Businesses do not operate in a vacuum. There is a combination of internal and external factors that affect how businesses function.
State and explain any FOUR external environmental factors that affect a business.

  1. Political Factors:
    Political factors affect the level of opportunities and threats within the business environment. Factors such as the stability of the political system, government policies, and regulations have a major influence on how businesses operate. A change in government or political instability can affect market conditions and disrupt business operations.
  2. Economic Factors:
    Economic conditions, including inflation rates, interest rates, economic growth, and exchange rates, play a crucial role in business performance. A strong economy encourages businesses to expand, whereas a weak economy may force businesses to downsize or halt operations.
  3. Socio-Cultural Factors:
    Socio-cultural aspects include the beliefs, values, attitudes, and lifestyles of people. These factors influence consumer behavior and market demand. A business must understand these cultural nuances to tailor products and services that meet the expectations of its customers.
  4. Technological Factors:
    The level of technological advancement within a country or industry determines the efficiency of production processes and service delivery. Businesses must keep up with technological changes to remain competitive. This includes automation, internet usage, and new software or tools that improve operational efficiency.

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  • 20 Marks

BMF – May 2015 – L1 – SB – Q2 – The Business Environment

Discuss four external environmental factors that impact business operations.

Businesses do not operate in a vacuum. There is a combination of internal and external factors that affect how businesses function.
State and explain any FOUR external environmental factors that affect a business.

  1. Political Factors:
    Political factors affect the level of opportunities and threats within the business environment. Factors such as the stability of the political system, government policies, and regulations have a major influence on how businesses operate. A change in government or political instability can affect market conditions and disrupt business operations.
  2. Economic Factors:
    Economic conditions, including inflation rates, interest rates, economic growth, and exchange rates, play a crucial role in business performance. A strong economy encourages businesses to expand, whereas a weak economy may force businesses to downsize or halt operations.
  3. Socio-Cultural Factors:
    Socio-cultural aspects include the beliefs, values, attitudes, and lifestyles of people. These factors influence consumer behavior and market demand. A business must understand these cultural nuances to tailor products and services that meet the expectations of its customers.
  4. Technological Factors:
    The level of technological advancement within a country or industry determines the efficiency of production processes and service delivery. Businesses must keep up with technological changes to remain competitive. This includes automation, internet usage, and new software or tools that improve operational efficiency.

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  • 5 Marks

BMF – May 2015 – L1 – SB – Q1b – Business and Organizational Structures and Choices

Identifying the advantages of a partnership business.

Identify FIVE advantages of a partnership business.

  1. Shared management and pooled knowledge: Partners bring in varied expertise and skills to manage the business.
  2. Attraction of more financial resources: Partnerships can attract more capital compared to sole proprietorships.
  3. Continuity in comparison with sole proprietorship: Unlike sole proprietorships, partnerships can continue even when one partner exits.
  4. Division of labor: Partners can divide work based on their strengths, leading to more efficient management.
  5. Sharing of risks and losses: The risks and financial losses are shared among partners, reducing the burden on a single individual.

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  • 5 Marks

BMF – May 2015 – L1 – SB – Q1b – Business and Organizational Structures and Choices

Identifying the advantages of a partnership business.

Identify FIVE advantages of a partnership business.

  1. Shared management and pooled knowledge: Partners bring in varied expertise and skills to manage the business.
  2. Attraction of more financial resources: Partnerships can attract more capital compared to sole proprietorships.
  3. Continuity in comparison with sole proprietorship: Unlike sole proprietorships, partnerships can continue even when one partner exits.
  4. Division of labor: Partners can divide work based on their strengths, leading to more efficient management.
  5. Sharing of risks and losses: The risks and financial losses are shared among partners, reducing the burden on a single individual.

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  • 15 Marks

BMF – May 2015 – L1 – SB – Q1a – Business and Organizational Structures and Choices

Features of the Memorandum of Association, Articles of Association, and Public Sector Entities.

State FIVE features of each of the following:
i. Memorandum of Association (5 Marks)
ii. Articles of Association (5 Marks)
iii. Public Sector Entity (5 Marks)

i. Features of Memorandum of Association:

  • The name of the company.
  • The names and addresses of the shareholders.
  • The number of shares held by each shareholder.
  • The location of the registered office.
  • The objectives of the company.

ii. Features of Articles of Association:

  • The internal relations of the company.
  • The rights of shareholders.
  • How meetings are convened.
  • Appointment and renewal of directors and other officers.
  • Power and duties of directors.

iii. Features of Public Sector Entity:

  • It is owned by the government.
  • It is created by an Act of Parliament.
  • It is managed by a board of directors appointed by the government.
  • It renders essential services.
  • It is not established for profit.

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  • 15 Marks

BMF – May 2015 – L1 – SB – Q1a – Business and Organizational Structures and Choices

Features of the Memorandum of Association, Articles of Association, and Public Sector Entities.

State FIVE features of each of the following:
i. Memorandum of Association (5 Marks)
ii. Articles of Association (5 Marks)
iii. Public Sector Entity (5 Marks)

i. Features of Memorandum of Association:

  • The name of the company.
  • The names and addresses of the shareholders.
  • The number of shares held by each shareholder.
  • The location of the registered office.
  • The objectives of the company.

ii. Features of Articles of Association:

  • The internal relations of the company.
  • The rights of shareholders.
  • How meetings are convened.
  • Appointment and renewal of directors and other officers.
  • Power and duties of directors.

iii. Features of Public Sector Entity:

  • It is owned by the government.
  • It is created by an Act of Parliament.
  • It is managed by a board of directors appointed by the government.
  • It renders essential services.
  • It is not established for profit.

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  • 1 Marks

BMF – MAY 2015 – L1 – SA – Q20 – Communications in Business

Defining the process of information transmission in business contexts.

The process of transmission of information from one person, group or organisation to another is called:

A. Decoding
B. Communication
C. Globalization
D. Presentation
E. Translation

Answer: B. Communication

Explanation:
Communication refers to the process of transmitting information from one entity to another, encompassing various methods and channels. It is essential for effective interaction within and between organizations.

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  • 1 Marks

BMF – MAY 2015 – L1 – SA – Q20 – Communications in Business

Defining the process of information transmission in business contexts.

The process of transmission of information from one person, group or organisation to another is called:

A. Decoding
B. Communication
C. Globalization
D. Presentation
E. Translation

Answer: B. Communication

Explanation:
Communication refers to the process of transmitting information from one entity to another, encompassing various methods and channels. It is essential for effective interaction within and between organizations.

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  • 1 Marks

BMF – MAY 2015 – L1 – SA – Q19 – Management, Individual, and Organisational Behaviour

Identifying the leadership style based on authority and control over rewards.

A leadership style in which the leader has the authority to withhold or give reward and punishment is referred to as ………………. style.

A. Democratic leadership
B. Participative leadership
C. Contingency leadership
D. Autocratic leadership
E. Laissez faire leadership

Answer: D. Autocratic leadership

Explanation:
Autocratic leadership is characterized by a leader who has significant control over decision-making and the authority to reward or punish subordinates. This style does not typically involve team input or collaboration, focusing instead on the leader’s authority and directives.

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  • 1 Marks

BMF – MAY 2015 – L1 – SA – Q19 – Management, Individual, and Organisational Behaviour

Identifying the leadership style based on authority and control over rewards.

A leadership style in which the leader has the authority to withhold or give reward and punishment is referred to as ………………. style.

A. Democratic leadership
B. Participative leadership
C. Contingency leadership
D. Autocratic leadership
E. Laissez faire leadership

Answer: D. Autocratic leadership

Explanation:
Autocratic leadership is characterized by a leader who has significant control over decision-making and the authority to reward or punish subordinates. This style does not typically involve team input or collaboration, focusing instead on the leader’s authority and directives.

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  • 10 Marks

QTB – May 2015 – L1 – SB – Q5a – Statistics

This question involves calculating the probabilities of various scenarios of success for two independent businesses using probability theory.

a. The probability that business A succeeds is 0.65 while the probability that business B
succeeds is 0.75. If the successes of the two events are independent, obtain the
probability that
i. either business A or business B or both businesses succeed (4 Marks)
ii. only one of the businesses succeeds (3 Marks)
iii. none of the two businesses succeed (3 Marks)

i. Probability that either business A or business B or both succeed:

P(A or B) = P(A) +P(B)−P (A and B)

Substituting the values:

P(A or B )= 0.65+0.75 − 0.4875 = 1.40 − 0.4875 = 0.9125

Thus, the probability that either business A or business B or both succeed is 0.9125 or 91.25%.

ii) Probability that only one of the businesses succeeds:

This is the probability that either A succeeds and B fails, or B succeeds and A fails. The formula is:

P(only one succeeds)=P(A and not B)+P(B and not A)

Where:

P(A and not

B) = P (A) × (1−P(B)) = 0.6 5× (1−0.75) = 0.65 × 0.25 = 0.1625

P (B and not A) = P (B) × (1−P(A)) = 0.75 × (1−0.65) =0.75 × 0.35 = 0.2625

Adding these together: P(only one succeeds) = 0.1625 + 0.2625 = 0.425

Thus, the probability that only one of the businesses succeeds is 0.425 or 42.5%.

iii. Probability that none of the two businesses succeed:

This is the probability that both A and B fail:

P (none succeed) = (1−P(A)) ×(1−P(B)) = (1−0.65) × (1−0.75) = 0.35×0.25 = 0.0875

Thus, the probability that none of the two businesses succeed is 0.0875 or 8.75%.

 

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  • 10 Marks

QTB – May 2015 – L1 – SB – Q5a – Statistics

This question involves calculating the probabilities of various scenarios of success for two independent businesses using probability theory.

a. The probability that business A succeeds is 0.65 while the probability that business B
succeeds is 0.75. If the successes of the two events are independent, obtain the
probability that
i. either business A or business B or both businesses succeed (4 Marks)
ii. only one of the businesses succeeds (3 Marks)
iii. none of the two businesses succeed (3 Marks)

i. Probability that either business A or business B or both succeed:

P(A or B) = P(A) +P(B)−P (A and B)

Substituting the values:

P(A or B )= 0.65+0.75 − 0.4875 = 1.40 − 0.4875 = 0.9125

Thus, the probability that either business A or business B or both succeed is 0.9125 or 91.25%.

ii) Probability that only one of the businesses succeeds:

This is the probability that either A succeeds and B fails, or B succeeds and A fails. The formula is:

P(only one succeeds)=P(A and not B)+P(B and not A)

Where:

P(A and not

B) = P (A) × (1−P(B)) = 0.6 5× (1−0.75) = 0.65 × 0.25 = 0.1625

P (B and not A) = P (B) × (1−P(A)) = 0.75 × (1−0.65) =0.75 × 0.35 = 0.2625

Adding these together: P(only one succeeds) = 0.1625 + 0.2625 = 0.425

Thus, the probability that only one of the businesses succeeds is 0.425 or 42.5%.

iii. Probability that none of the two businesses succeed:

This is the probability that both A and B fail:

P (none succeed) = (1−P(A)) ×(1−P(B)) = (1−0.65) × (1−0.75) = 0.35×0.25 = 0.0875

Thus, the probability that none of the two businesses succeed is 0.0875 or 8.75%.

 

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  • 20 Marks

QTB – May 2015 – L1 – SB – Q4 – Operations Research

This question requires calculating the average machine life, replacement costs, and determining the best replacement strategy for ATM machines in a bank.

The management of a bank observed that the disruption of the bank ATM services was due to the age of the machines. Data on ATM failure is as follows:

Year after replacement 1 2 3
Cumulative % of failures 30% 75% 100%

It was further observed that 1,000 units of these machines are in use nationwide and they can be replaced collectively for N5 million per machine. If replaced individually, they cost N30 million per machine.

You are required to calculate:
a.
i. Average machine life (2 Marks)
ii. Average number of replacements per year (2 Marks)
iii. Cost of individual replacement per year (2 Marks)
iv. Cost of mass replacement at the end of the year (12 Marks)

b. Determine the best replacement strategy (2 Marks)

Calculation of percentage of failure

a (i) Average machine life

The total cost of group replacement is therefore:

Since the lowest average cost of N14,000 million is obtained in the first year of mass
replacement, it is optimal to have a mass replacement at the end of year one.
The best replacement strategy is the mass replacement since the cost of mass replacement (that is
N14,000 million relatively lower than the cost of individual replacement (that is N15,390
million)

 

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  • 20 Marks

QTB – May 2015 – L1 – SB – Q4 – Operations Research

This question requires calculating the average machine life, replacement costs, and determining the best replacement strategy for ATM machines in a bank.

The management of a bank observed that the disruption of the bank ATM services was due to the age of the machines. Data on ATM failure is as follows:

Year after replacement 1 2 3
Cumulative % of failures 30% 75% 100%

It was further observed that 1,000 units of these machines are in use nationwide and they can be replaced collectively for N5 million per machine. If replaced individually, they cost N30 million per machine.

You are required to calculate:
a.
i. Average machine life (2 Marks)
ii. Average number of replacements per year (2 Marks)
iii. Cost of individual replacement per year (2 Marks)
iv. Cost of mass replacement at the end of the year (12 Marks)

b. Determine the best replacement strategy (2 Marks)

Calculation of percentage of failure

a (i) Average machine life

The total cost of group replacement is therefore:

Since the lowest average cost of N14,000 million is obtained in the first year of mass
replacement, it is optimal to have a mass replacement at the end of year one.
The best replacement strategy is the mass replacement since the cost of mass replacement (that is
N14,000 million relatively lower than the cost of individual replacement (that is N15,390
million)

 

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  • 5 Marks

QTB – May 2015 – L1 – SB – Q3b – Mathematics

This question involves expressing the interest rate in terms of future value and principal investment for a 3-year investment.

Mr. Taiwo invested a certain amount of money P, at an annual interest rate r, for a period
of 3 years. The future value of this investment is given by

Express r in terms of S and P

 

 

To express r in terms of S and P, follow these steps:

 

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  • 5 Marks

QTB – May 2015 – L1 – SB – Q3b – Mathematics

This question involves expressing the interest rate in terms of future value and principal investment for a 3-year investment.

Mr. Taiwo invested a certain amount of money P, at an annual interest rate r, for a period
of 3 years. The future value of this investment is given by

Express r in terms of S and P

 

 

To express r in terms of S and P, follow these steps:

 

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  • 15 Marks

QTB – May 2015 – L1 – SB – Q3a – Operations Research

Determining the equilibrium price and quantity from demand and supply functions.

A producer wishes to determine the equilibrium price and quantity of his goods in the
market. He estimated the market demand and supply functions as follows:

where P is the price in thousands of naira and q is quantity in thousands of units, calculate
the equilibrium price and quantity for the producer

 

 

 

 

 

 

At equilibrium, Demand = Supply
Thus

ALITER
Therefore, the equilibrium price is N286,000 while the equilibrium quantity is 12,000 unit

 

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  • 15 Marks

QTB – May 2015 – L1 – SB – Q3a – Operations Research

Determining the equilibrium price and quantity from demand and supply functions.

A producer wishes to determine the equilibrium price and quantity of his goods in the
market. He estimated the market demand and supply functions as follows:

where P is the price in thousands of naira and q is quantity in thousands of units, calculate
the equilibrium price and quantity for the producer

 

 

 

 

 

 

At equilibrium, Demand = Supply
Thus

ALITER
Therefore, the equilibrium price is N286,000 while the equilibrium quantity is 12,000 unit

 

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  • 20 Marks

QTB – May 2015 – L1 – SB – Q2 – Statistics

Calculating probabilities related to household expenditure on mobile phones.

A research was conducted to know the average monthly household expenditure on mobile phones in DETOTAR Estate.
The research shows the average monthly household expenditure to be N5,200. Assume that the monthly household expenditure on mobile phones in the Estate is normally distributed with a standard deviation of N1,800. Determine the probability of a randomly selected household in DETOTAR Estate if the monthly expenditure on mobile phone is:

a. more than N8,700 (5 Marks)
b. between N2,600 and N9,000 (6 Marks)
c. between N7,600 and N10,200 (6 Marks)
d. less than N8,800 (3 Marks)

a) Required probability (shaded area) is

0.5 – 0.4738 = 0.026

b) Required probability (shaded area) is

 

c) Required probability (shaded area) is

 

d) Required probability (shaded area) is

 

Summary of Answers:

  • a. More than N8,700: 0.0256
  • b. Between N2,600 and N9,000: 0.9081
  • c. Between N7,600 and N10,200: 0.0890
  • d. Less than N8,800: 0.9772

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  • 20 Marks

QTB – May 2015 – L1 – SB – Q2 – Statistics

Calculating probabilities related to household expenditure on mobile phones.

A research was conducted to know the average monthly household expenditure on mobile phones in DETOTAR Estate.
The research shows the average monthly household expenditure to be N5,200. Assume that the monthly household expenditure on mobile phones in the Estate is normally distributed with a standard deviation of N1,800. Determine the probability of a randomly selected household in DETOTAR Estate if the monthly expenditure on mobile phone is:

a. more than N8,700 (5 Marks)
b. between N2,600 and N9,000 (6 Marks)
c. between N7,600 and N10,200 (6 Marks)
d. less than N8,800 (3 Marks)

a) Required probability (shaded area) is

0.5 – 0.4738 = 0.026

b) Required probability (shaded area) is

 

c) Required probability (shaded area) is

 

d) Required probability (shaded area) is

 

Summary of Answers:

  • a. More than N8,700: 0.0256
  • b. Between N2,600 and N9,000: 0.9081
  • c. Between N7,600 and N10,200: 0.0890
  • d. Less than N8,800: 0.9772

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  • 20 Marks

QTB – May 2015 – L1 – SB – Q1 – Data Collection Analysis

Analyzing average daily sales data to compute frequency, median, and mode.

The table below shows average daily sales of Rice Krispies in the month of August 2014 in Flavour Restaurant:

Sales Sales Sales Sales Sales Sales Sales Sales Sales Sales
32 8 12 18 26 18 32 28 15 14
22 44 24 18 32 46 52 62 72 78
29 32 10 14 16 24 32 40 24 42
17 20 23 13 16 17 19 36 25 60
25 15 20 42 32 16 20 25 24 50
10 9 11 21 19 12 48 32 32 30

You are required to:
a. Use tally method to prepare a frequency table starting from 1 – 10, 11 – 20, etc. (8 Marks)
b. Compute:
(i) The median (6 Marks)
(ii) The mode (6 Marks)
(Total 20 Marks)

a. Preparation of frequency table using tally method with range (1 – 10, 11 – 20, etc

b (i)

Median = 24.07

(ii) 10.5 + (0.708) 10

= 10.5 + 7.08

Mode = 17.58

 

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  • 20 Marks

QTB – May 2015 – L1 – SB – Q1 – Data Collection Analysis

Analyzing average daily sales data to compute frequency, median, and mode.

The table below shows average daily sales of Rice Krispies in the month of August 2014 in Flavour Restaurant:

Sales Sales Sales Sales Sales Sales Sales Sales Sales Sales
32 8 12 18 26 18 32 28 15 14
22 44 24 18 32 46 52 62 72 78
29 32 10 14 16 24 32 40 24 42
17 20 23 13 16 17 19 36 25 60
25 15 20 42 32 16 20 25 24 50
10 9 11 21 19 12 48 32 32 30

You are required to:
a. Use tally method to prepare a frequency table starting from 1 – 10, 11 – 20, etc. (8 Marks)
b. Compute:
(i) The median (6 Marks)
(ii) The mode (6 Marks)
(Total 20 Marks)

a. Preparation of frequency table using tally method with range (1 – 10, 11 – 20, etc

b (i)

Median = 24.07

(ii) 10.5 + (0.708) 10

= 10.5 + 7.08

Mode = 17.58

 

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q20 – Statistics

Calculating the inter-quartile range for the weekly wages of employees.

If the weekly wages of 5 employees at XYZ company are N10,000, N8,500, N7,500, N6,000, and N5,200, the inter-quartile range for the weekly wages is:

A. N3,450
B. N3,650
C. N3,850
D. N4,050
E. N4,250

Answer:
B. N3,650

Explanation:
To find the inter-quartile range (IQR), first arrange the wages in ascending order: N5,200, N6,000, N7,500, N8,500, N10,000.

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q20 – Statistics

Calculating the inter-quartile range for the weekly wages of employees.

If the weekly wages of 5 employees at XYZ company are N10,000, N8,500, N7,500, N6,000, and N5,200, the inter-quartile range for the weekly wages is:

A. N3,450
B. N3,650
C. N3,850
D. N4,050
E. N4,250

Answer:
B. N3,650

Explanation:
To find the inter-quartile range (IQR), first arrange the wages in ascending order: N5,200, N6,000, N7,500, N8,500, N10,000.

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q19 – Statistics

Identifying the components separated during the deseasonalisation of business data.

Deseasonalisation of business data is a process of separating two components of a time series which are:

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer:
C. Trend and seasonal variation

Explanation:
Deseasonalisation is the process of removing the seasonal component from a time series to analyze the underlying trend and cyclical variations more effectively. This helps in understanding the non-seasonal fluctuations in the data.

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q19 – Statistics

Identifying the components separated during the deseasonalisation of business data.

Deseasonalisation of business data is a process of separating two components of a time series which are:

A. Trend and cyclical variation
B. Irregular and cyclical variation
C. Trend and seasonal variation
D. Cyclical and seasonal variation
E. Seasonal and irregular variations

Answer:
C. Trend and seasonal variation

Explanation:
Deseasonalisation is the process of removing the seasonal component from a time series to analyze the underlying trend and cyclical variations more effectively. This helps in understanding the non-seasonal fluctuations in the data.

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q18 – Statistics

Identifying the term for the locus of mid-points of a histogram.

The locus of the mid-points of the tops of the rectangles in the constructed histogram by a straight line is known as:

A. Ogive
B. Frequency polygon
C. Component bar chart
D. Pictogram
E. Histogram

Answer:
B. Frequency polygon

Explanation:
The locus of the mid-points of the tops of the rectangles in a histogram forms what is called a frequency polygon. This graphical representation allows for the visualization of the distribution of data and can be constructed by connecting the mid-points of the histogram bars with straight lines.

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q18 – Statistics

Identifying the term for the locus of mid-points of a histogram.

The locus of the mid-points of the tops of the rectangles in the constructed histogram by a straight line is known as:

A. Ogive
B. Frequency polygon
C. Component bar chart
D. Pictogram
E. Histogram

Answer:
B. Frequency polygon

Explanation:
The locus of the mid-points of the tops of the rectangles in a histogram forms what is called a frequency polygon. This graphical representation allows for the visualization of the distribution of data and can be constructed by connecting the mid-points of the histogram bars with straight lines.

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q17 – Statistics

Identifying the incorrect statement regarding properties of standard deviation.

The following are properties of standard deviation EXCEPT:

A. The greater the spread of the data, the larger the value of the standard deviation
B. The value of standard deviation equals zero seems unlikely except when all observations take the same value
C. Standard deviation takes into account all items in the data set
D. Standard deviation cannot be used for further statistical analysis
E. Standard deviation is not influenced by the size and unit of measurement

Answer:
D. Standard deviation cannot be used for further statistical analysis

Explanation:
Standard deviation is a crucial measure in statistics that indicates the dispersion or spread of a dataset. It can certainly be used for further statistical analysis, including hypothesis testing and constructing confidence intervals. The other statements regarding the properties of standard deviation are true.

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  • 1 Marks

QTB – May 2015 – L1 – SA – Q17 – Statistics

Identifying the incorrect statement regarding properties of standard deviation.

The following are properties of standard deviation EXCEPT:

A. The greater the spread of the data, the larger the value of the standard deviation
B. The value of standard deviation equals zero seems unlikely except when all observations take the same value
C. Standard deviation takes into account all items in the data set
D. Standard deviation cannot be used for further statistical analysis
E. Standard deviation is not influenced by the size and unit of measurement

Answer:
D. Standard deviation cannot be used for further statistical analysis

Explanation:
Standard deviation is a crucial measure in statistics that indicates the dispersion or spread of a dataset. It can certainly be used for further statistical analysis, including hypothesis testing and constructing confidence intervals. The other statements regarding the properties of standard deviation are true.

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