Series: NOV 2016

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  • 20 Marks

QT – Nov 2016 – L1 – Q7 – Forecasting

Analyze absenteeism trends using time series and forecasting techniques for Dropper Ltd.

The personnel department of Dropper Ltd, a large cocoa processing company in DropperLand, is concerned about absenteeism among its shop floor workforce. The mean number of absentees per day for each quarter of the years 1999 to 2001 and Quarter 1 in 2002 is given in the table below:

Q1 Q2 Q3 Q4
1999 25.10 14.40 9.50 23.70
2000 27.90 16.90 12.40 26.10
2001 31.40 19.70 15.90 29.90
2002 34.50 – – –

Required:
a) Plot the data on a graph, leaving space for the remaining 2002 figures. (3 marks)

b) Using the method of 2-quarterly centered moving averages,
i) Determine the trend in the series and superimpose this on your graph in (a). (4 marks)
ii) Determine the equation of the trend line above by considering only the first and last centered moving average value on your graph in (i). (3 marks)

c) Using an appropriate decomposition model, determine the seasonal variations in the data. Give reasons for your choice of model. (5 marks)

d) Use your analysis above to roughly forecast the mean number of absentees for the remaining quarters of 2002. Comment on your forecast. (5 marks)

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  • 14 Marks

QT – Nov 2016 – L1 – Q6b – Elements of Calculus

Calculate the number of tons of low and high-grade steel to produce to maximize total revenue and determine the maximum total revenue.

Tema Steel Plant is capable of producing q1 tons per day of low-grade steel and q2 tons per day of high-grade steel, where:

If the fixed market price of low-grade steel is GH¢6.90 and the fixed market price of high-grade steel is GH¢13.80:

i) Determine the number of tons of low-grade steel and high-grade steel to be produced to maximize total revenue. (10 marks)

ii) Determine the maximum total revenue. (4 marks)

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  • 6 Marks

QT – Nov 2016 – L1 – Q6a – Elements of Calculus

Sketch the critical points on a cost or revenue function, including maximum, minimum, and inflexion points.

Sketch Graph(s) to show the following critical points on a cost or revenue function:

  • i) Local Maximum Point (1 mark)
  • ii) Absolute Maximum Point (1 mark)
  • iii) Local Minimum Point (1 mark)
  • iv) Absolute Minimum Point (1 mark)
  • v) Point of inflexion (2 marks)

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  • 20 Marks

QT – Nov 2016 – L1 – Q5 – Measures of Central Tendency

Analyze the returns on two investments using central tendency, dispersion, and provide a decision based on the results.

Suppose that Mr. Kuu, a retired chartered accountant, is facing a decision about where to invest the remaining small fortune after deducting the anticipated expenses for the next year from his consultancy earnings. An investment analyst has suggested two types of investments, and to help make the decision, he obtained some rates of return from each type. He would like to know what he can expect by way of the return on his investment, as well as other types of information, such as whether the rates are spread out over a wide range (making the investment risky) or are grouped tightly together (indicating a relatively low risk). The returns for the two types of investments are listed below:

If he decides to group the returns according to classes 19-10, 9-0, 1-10, 11-20, 21-30, 31-40 :

 

Required:

a) Draw histograms for each set of returns. (5 marks)
b) Compute the following measures of central tendency for the set of returns:
i) Mean (3 marks)
ii) Median (3 marks)
iii) Mode (3 marks)
c) Compute the following measures of spread for the set of returns:
i) Standard deviation (3 marks)
ii) Coefficient of variation (2 marks)
d) Based on (a), (b), and (c), which investment should Mr. Kuu choose and why? (1 mark)

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  • 5 Marks

QT – Nov 2016 – L1 – Q4c – Mathematics of Business Finance

Calculate the semi-annual sinking fund deposit required to repay a loan after 5 years.

Maame TorTor borrows GH¢3,000.00 and agrees to pay interest quarterly at an annual rate of 8%. At the same time, she sets up a sinking fund in order to repay the loan at the end of 5 years. The sinking fund earns interest at the rate of 6% compounded semi-annually.

Required:
Determine the size of each semi-annual sinking fund deposit. (5 marks)

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  • 10 Marks

QT – Nov 2016 – L1 – Q4b – Mathematics of Business Finance

Calculate the monthly amortization payments, total interest, and equity for a house loan at 9% interest over 25 years.

Maame TorTor has just purchased a GH¢70,000.00 house and made a down payment of GH¢15,000.00.

Required:
i) Determine how much money is needed to amortize (i.e., pay monthly) the balance at a 9% interest rate compounded annually for 25 years. (5 marks)
ii) Determine the total interest for the 25 years. (2 marks)
iii) Determine after 20 years the equity she has in the house. (3 marks)

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  • 5 Marks

QT – Nov 2016 – L1 – Q4a – Mathematics of Business Finance

Explain the terms annuities, sinking fund, and amortization related to loan repayment.

One of the most important applications of annuities is the repayment of interest-bearing debts. These debts can be paid by making periodic deposits into a sinking fund, which is used at a future date to pay the principal of the debt, or by making periodic payments that cover the outstanding interest and the principal. This second method is called amortization.

Required:
i) Explain the term annuities as used in the statement above. (2 marks)
ii) What is a sinking fund? (2 marks)
iii) When is a loan with a fixed rate of interest said to be amortized? (1 mark)

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  • 20 Marks

QT – Nov 2016 – L1 – Q3 – Forecasting

Derive a regression forecasting equation for iron rod demand based on construction permits and analyze the results.

The Branch Manager of a building material production plant feels that the demand for iron rod shipments may be related to the number of construction permits issued in the country during the previous quarter. The Manager has collected the data shown in the table below:

Construction Permits Iron Rods
15 6
9 4
40 16
20 6
25 13
25 9
15 10
35 16

Required:

i) Use the normal equations of the least square regression method to derive a regression forecasting equation for the data. (9 marks)
ii) Interpret your regression coefficient in (i) above. (1 mark)
iii) Using the regression line in (a) above, determine a point estimate for Iron Rods when the number of construction permits is 30. (2 marks)
iv) Is your estimate in (iii) above reliable? Give reason(s) for your answer. (2 marks)
v) Calculate the coefficient of determination and interpret it. (6 marks)

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  • 20 Marks

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

JinJin Company Limited makes two types of leather belts: Type Superior and Type Standard. Type Superior is of high quality, and Type Standard is of lower quality. The respective profits are GHp 40 and GHp 30 per belt. The production of each Type Superior requires twice as much time as a Type Standard belt, and if all belts were of Type Standard, the company could make 1,000 belts per day. The supply of leather is sufficient for only 800 belts per day (both types combined). Belt Type Superior requires a fancy buckle, and only 400 of these are available per day. There are only 700 buckles a day available for Type Standard.

Required:
a) Formulate this problem as a Linear Programming Model. (4 marks)

b) Set up the initial Simplex Tableau. (4 marks)

c) Solve your Tableau in (b) above. (8 marks)

d) Interpret your final Simplex Tableau. (4 marks)

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  • 5 Marks

QT – Nov 2016 – L1 – Q1c – Probability

This question deals with calculating the conditional probability of earning more than GHC 5,000 given that an ICAG-qualified individual stays at a university.

If selected by the panel, the probability that an ICAG-qualified member will remain with the Private University is 0.6, and the probability that a Chartered Accountant earns more than GHC 5,000 per month in the university is 0.5. If the probability that Mr. Agbagba will remain with the university or earn more than GHC 5,000 per month is 0.7:

Required:
Calculate the probability that he will earn more than GHC 5,000 per month given that he is a Chartered Accountant who will stay with the university.

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  • 20 Marks

QT – Nov 2016 – L1 – Q7 – Forecasting

Analyze absenteeism trends using time series and forecasting techniques for Dropper Ltd.

The personnel department of Dropper Ltd, a large cocoa processing company in DropperLand, is concerned about absenteeism among its shop floor workforce. The mean number of absentees per day for each quarter of the years 1999 to 2001 and Quarter 1 in 2002 is given in the table below:

Q1 Q2 Q3 Q4
1999 25.10 14.40 9.50 23.70
2000 27.90 16.90 12.40 26.10
2001 31.40 19.70 15.90 29.90
2002 34.50 – – –

Required:
a) Plot the data on a graph, leaving space for the remaining 2002 figures. (3 marks)

b) Using the method of 2-quarterly centered moving averages,
i) Determine the trend in the series and superimpose this on your graph in (a). (4 marks)
ii) Determine the equation of the trend line above by considering only the first and last centered moving average value on your graph in (i). (3 marks)

c) Using an appropriate decomposition model, determine the seasonal variations in the data. Give reasons for your choice of model. (5 marks)

d) Use your analysis above to roughly forecast the mean number of absentees for the remaining quarters of 2002. Comment on your forecast. (5 marks)

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  • 14 Marks

QT – Nov 2016 – L1 – Q6b – Elements of Calculus

Calculate the number of tons of low and high-grade steel to produce to maximize total revenue and determine the maximum total revenue.

Tema Steel Plant is capable of producing q1 tons per day of low-grade steel and q2 tons per day of high-grade steel, where:

If the fixed market price of low-grade steel is GH¢6.90 and the fixed market price of high-grade steel is GH¢13.80:

i) Determine the number of tons of low-grade steel and high-grade steel to be produced to maximize total revenue. (10 marks)

ii) Determine the maximum total revenue. (4 marks)

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  • 6 Marks

QT – Nov 2016 – L1 – Q6a – Elements of Calculus

Sketch the critical points on a cost or revenue function, including maximum, minimum, and inflexion points.

Sketch Graph(s) to show the following critical points on a cost or revenue function:

  • i) Local Maximum Point (1 mark)
  • ii) Absolute Maximum Point (1 mark)
  • iii) Local Minimum Point (1 mark)
  • iv) Absolute Minimum Point (1 mark)
  • v) Point of inflexion (2 marks)

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  • 20 Marks

QT – Nov 2016 – L1 – Q5 – Measures of Central Tendency

Analyze the returns on two investments using central tendency, dispersion, and provide a decision based on the results.

Suppose that Mr. Kuu, a retired chartered accountant, is facing a decision about where to invest the remaining small fortune after deducting the anticipated expenses for the next year from his consultancy earnings. An investment analyst has suggested two types of investments, and to help make the decision, he obtained some rates of return from each type. He would like to know what he can expect by way of the return on his investment, as well as other types of information, such as whether the rates are spread out over a wide range (making the investment risky) or are grouped tightly together (indicating a relatively low risk). The returns for the two types of investments are listed below:

If he decides to group the returns according to classes 19-10, 9-0, 1-10, 11-20, 21-30, 31-40 :

 

Required:

a) Draw histograms for each set of returns. (5 marks)
b) Compute the following measures of central tendency for the set of returns:
i) Mean (3 marks)
ii) Median (3 marks)
iii) Mode (3 marks)
c) Compute the following measures of spread for the set of returns:
i) Standard deviation (3 marks)
ii) Coefficient of variation (2 marks)
d) Based on (a), (b), and (c), which investment should Mr. Kuu choose and why? (1 mark)

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  • 5 Marks

QT – Nov 2016 – L1 – Q4c – Mathematics of Business Finance

Calculate the semi-annual sinking fund deposit required to repay a loan after 5 years.

Maame TorTor borrows GH¢3,000.00 and agrees to pay interest quarterly at an annual rate of 8%. At the same time, she sets up a sinking fund in order to repay the loan at the end of 5 years. The sinking fund earns interest at the rate of 6% compounded semi-annually.

Required:
Determine the size of each semi-annual sinking fund deposit. (5 marks)

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  • 10 Marks

QT – Nov 2016 – L1 – Q4b – Mathematics of Business Finance

Calculate the monthly amortization payments, total interest, and equity for a house loan at 9% interest over 25 years.

Maame TorTor has just purchased a GH¢70,000.00 house and made a down payment of GH¢15,000.00.

Required:
i) Determine how much money is needed to amortize (i.e., pay monthly) the balance at a 9% interest rate compounded annually for 25 years. (5 marks)
ii) Determine the total interest for the 25 years. (2 marks)
iii) Determine after 20 years the equity she has in the house. (3 marks)

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  • 5 Marks

QT – Nov 2016 – L1 – Q4a – Mathematics of Business Finance

Explain the terms annuities, sinking fund, and amortization related to loan repayment.

One of the most important applications of annuities is the repayment of interest-bearing debts. These debts can be paid by making periodic deposits into a sinking fund, which is used at a future date to pay the principal of the debt, or by making periodic payments that cover the outstanding interest and the principal. This second method is called amortization.

Required:
i) Explain the term annuities as used in the statement above. (2 marks)
ii) What is a sinking fund? (2 marks)
iii) When is a loan with a fixed rate of interest said to be amortized? (1 mark)

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  • 20 Marks

QT – Nov 2016 – L1 – Q3 – Forecasting

Derive a regression forecasting equation for iron rod demand based on construction permits and analyze the results.

The Branch Manager of a building material production plant feels that the demand for iron rod shipments may be related to the number of construction permits issued in the country during the previous quarter. The Manager has collected the data shown in the table below:

Construction Permits Iron Rods
15 6
9 4
40 16
20 6
25 13
25 9
15 10
35 16

Required:

i) Use the normal equations of the least square regression method to derive a regression forecasting equation for the data. (9 marks)
ii) Interpret your regression coefficient in (i) above. (1 mark)
iii) Using the regression line in (a) above, determine a point estimate for Iron Rods when the number of construction permits is 30. (2 marks)
iv) Is your estimate in (iii) above reliable? Give reason(s) for your answer. (2 marks)
v) Calculate the coefficient of determination and interpret it. (6 marks)

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  • 20 Marks

QT – Nov 2016 – L1 – Q2 – Linear Programming

This question involves formulating and solving a linear programming problem for maximizing profit in belt production.

JinJin Company Limited makes two types of leather belts: Type Superior and Type Standard. Type Superior is of high quality, and Type Standard is of lower quality. The respective profits are GHp 40 and GHp 30 per belt. The production of each Type Superior requires twice as much time as a Type Standard belt, and if all belts were of Type Standard, the company could make 1,000 belts per day. The supply of leather is sufficient for only 800 belts per day (both types combined). Belt Type Superior requires a fancy buckle, and only 400 of these are available per day. There are only 700 buckles a day available for Type Standard.

Required:
a) Formulate this problem as a Linear Programming Model. (4 marks)

b) Set up the initial Simplex Tableau. (4 marks)

c) Solve your Tableau in (b) above. (8 marks)

d) Interpret your final Simplex Tableau. (4 marks)

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  • 5 Marks

QT – Nov 2016 – L1 – Q1c – Probability

This question deals with calculating the conditional probability of earning more than GHC 5,000 given that an ICAG-qualified individual stays at a university.

If selected by the panel, the probability that an ICAG-qualified member will remain with the Private University is 0.6, and the probability that a Chartered Accountant earns more than GHC 5,000 per month in the university is 0.5. If the probability that Mr. Agbagba will remain with the university or earn more than GHC 5,000 per month is 0.7:

Required:
Calculate the probability that he will earn more than GHC 5,000 per month given that he is a Chartered Accountant who will stay with the university.

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