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CMA JANUARY-2022 EXAMINATION BUSINESS LEVEL
SUBJECT: GE 03. FUNDAMENTALS OF BUSINESS MATHEMATICS
Time Allocated: Three hours Total Marks: 100
Instructions to Candidates
You are required to answer ALL questions.
Answers should be properly structured, relevant and computations need to be shown.
You are strongly advised to carefully read ALL the question requirements before attempting the question concerned (that is all parts and/or sub-questions).
ALL answers must be written in the answer book. Answers written on the question paper will not be submitted for marking.
Start answering each question from a fresh sheet. Your answers should be clearly numbered with the sub-question number then ruled off, so that the markers know which sub-question you are answering.
No of questions No of sub-questions Marks allocation
10 Maximum 03 10 per each question
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You are advised to spend no longer than 18 minutes on each question. Each question will carry 10 marks.
QUESTION 1
(a) An item sells for $3.99 when it includes Value Added Tax (VAT) at 17.5%. Due to the reduction of the VAT rate, the new selling price stands to $3.91. What is the new VAT rate?
(b) At the low price of $14, sales volume of a product in a week was 525 units. On the other hand, at the high price of $18, its sales volume was 475 units. Applying the High-Low method of establishing a relationship between the price (Y) and the demand (X), it was assumed that the relationship was like Y = a + bX. Find the values of a and b and hence the relationship.
[Marks: (3+7) = 10]
QUESTION 2
(a) A sample of 100 companies has been analysed by size and whether they pay invoices promptly. The sample has been cross-tabulated into large/small against fast payers/slow payers. 60 of the companies are classified as large of which 40 are slow payers. In total, 30 of all the companies are fast payers.
Find the probability that a company chosen at random is a fast paying small company.
(b) A company must decide between two projects: Project A and Project B. The profits that might be generated from each project are as follows.
Project A Project B
Probability Profit Probability Profit/(loss)
0.45 $ 4,000 0.64 $ 8,000
0.55 2,000 0.36 (1,000)
Which project should be chosen and what is the associated expected value of profit?
(c) The Net Present Value of an interest at 10% is 12,000 Taka and at 18% is -4,000 Taka.
What would be the IRR?
[Marks: (3+3+4) = 10]
QUESTION 3
(a) Draw a Normal Probability Distribution Curve and write down its characteristics. Let x be a continuous random variable that has a normal distribution with μ = 50 and σ = 8. Find the probability P(30≤x≤ 39).
(b) A racing car is one of the many toys manufactured by Mack Corporation. The assembly times for this toy follow a normal distribution with a mean of 55 minutes and a standard deviation of 4 minutes. The company closes at 5 P.M. every day. If one worker starts to assemble a racing car at 4 P.M., what is the probability that she will finish this job before the company closes for the day?
[Marks: (3+7) =10]
QUESTION 4
(a) Mr. A, Mr. B and Mr. C share the profits from their business so that Mr. A receives twice as much as Mr. B. On the other hand, Mr. C receives half as much as Mr. B. The total profit of the business last year was Tk. 91,000. Calculate the amounts of profits for Mr. A, Mr. B and Mr. C.
(b) A Machine depreciates by 20% in first year, then by 10% p. a. for next 5 years and by 2% p.
a. thereafter. Find out its value after 7 years if its initial price is Tk. 7,20,000.
[Marks: (5+5) =10]
QUESTION 5
(a) If the following data is to be illustrated by means of a histogram and if the standard interval is taken to be 5 kg, calculate the heights of the bars of the histogram (to the nearest whole number):
Weight Frequency
0–5 83
5–10 105
10–20 160
20–40 96
40–100 108
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(b) The director of a medium-sized company has decided to analyse the salaries that are paid to staff. The frequency distribution of salaries that are currently being paid is as follows.
Salary (£’000) Number of staff
Under 10 16
10–under 20 28
20–under 30 36
30–under 40 20
40–under 50 12
50–under 70 4
70 and over 4
From the above data, it was calculated that ∑f = 120, ∑fx = 3140 and ∑fx2 = 112,800. Some more information revels that the mean and standard deviation salaries now and 5 years ago are as follows:
5 years ago now
Mean £11,950 £25,000
Standard Deviation £10,600 £15,000
You are required to calculate the mean (to the nearest £), standard deviation (to the nearest £100) of salary and co-efficient of variation from the above data and also to make comments on the changes of mean salary and standard deviation in comparison to those of 5 years ago.
[Marks: (3+7) = 10]
QUESTION 6
(a) A project requires an investment of $10,000 and will generate returns of $7,000 in the first year and $5,000 in the second year. Calculate the IRR for the project.
(b) You have been supplied with the following data regarding the grades (A for excellent and E for unsatisfactory) of candidates in an interview presentation and their written exam scores:
Candidate Grade awarded Exam score
Mr. K A 70
Mr. L B 76
Mr. M A 58
Mr. N C 88
Mr. O D 81
What is the Spearman’s correlation co-efficient? Comment on its value.
[Marks: (5+5) = 10]
QUESTION 7
(a) A health and fitness center has to buy one of two types machine A or B. A would cost Taka 2,00,000 half of which would be due on delivery, the remainder a year later. Machine B would cost Taka 2,40,000 with payment due in the same way as for Machine A. Both Machines last for 6 years and have an expected scrap value of 10% of their original cost price. Taking into account operating cost of maintenance, Machine A would produce year end net operational cash flows of Taka 40,000 and Machine B year end net operational cash flows of Taka 50,000. In both cases the relevant Cost of Capital is 10% p. a. throughout the period. Find out the NPV of Machine A.
(b) If r = 0.6 and N = 64, find out the probable error of the coefficient of correlation and determine the limit for r.
[Marks: (5+5) = 10]
QUESTION 8
(a) A diabetic is interested in determining how the amount of aerobic exercise impacts his blood sugar. When his blood sugar reaches 170 mg/dL, he goes out for a run at a pace of 10 minutes per mile. On different days, he runs different distances and measures his blood sugar after completing his run. Note that the preferred blood sugar level is in the range of 80 to 120 mg/dL. Levels that are too low or too high are extremely dangerous. The data generated are given in the following table.
Distance (miles) 2 2 2.5 2.5 3 3 3.5 3.5 4 4 4.5 4.5 Blood sugar (mg/dL) 136 146 131 125 120 116 104 95 85 94 83 75
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(i) Find the predictive regression equation of blood sugar level on the distance run.
(ii) Give a brief interpretation of the values of a and b calculated in part (i).
(iii) Calculate the predicted blood sugar level count after a run of 3.1 miles.
(iv) Estimate the blood sugar level after a 10-mile run. Comment on this finding.
(b) Explain the meaning of the words simple and linear as used in simple linear regression. Also, explain the meaning of independent and dependent variables for a regression model.
[Marks: (8+2) = 10]
QUESTION 9
(a) The examples in this chapter all relate to the following table:
Sales of article B (‘000 units)
Q1 Q2 Q3 Q4 (Q = Quarter) 2001 24.8 36.3 38.1 47.5
2002 31.2 42.0 43.4 55.9 2003 40.0 48.8 54.0 69.1 2004 54.7 57.8 60.3 68.9
Use the above data and the regression line T=28.54 + 2.3244t to find the seasonal component (S) as the arithmetic mean of Y =T for each quarter, where Y denotes the actual sales and T the trend given by the regression equation. Adjust your average seasonal variations so that they add to 4.
(b) Write short notes on the components of a time series.
[Marks: (8+2) =10]
QUESTION 10
(a) Write two advantages and two disadvantages of using spreadsheet.
(b) The following spreadsheet can be used to investigate the inter-relationship between advertising expenditure and sales.
A B C D E
1 Monthly Advertising Sales ($’000)
2 Expenditure ($’000)
3 X Y X2 Y2 XY
4 1.2 132.5 1.44 17556.25 159.00
5 0.9 98.5 0.81 9702.25 88.65
6 1.6 154.3 2.56 23808.49 246.88
7 2.1 201.4 4.41 40561.96 422.94
8 1.6 161 2.56 25921.00 257.60
9 7.4 747.7 11.78 117549.95 1175.07
Write the formula in excel format for cell C7, D4, E6, A9 and E9. Also, calculate the Pearson’s correlation coefficient taking appropriate figures from the table.
[Marks: (4+6) =10]
*END OF QUESTION PAPER*
