THE INSTITUTE OF COST AND MANAGEMENT ACCOUNTANTS OF BANGLADESH

CMA JUNE, 2018 EXAMINATION

BUSINESS LEVEL
SUBJECT: GE 03. FUNDAMENTALS OF BUSINESS MATHEMATICS.
Time: Three hours Full Marks: 100
❖ Answer any FIVE questions. All questions carry equal marks.
❖ Answer must be brief, relevant, neat and clean.
❖ Use fresh sheet for answering each question.
Q. No. 1
(a) Find the value of X in terms of a, b, c and Y, from: Y = 2√(𝑎𝑏𝑋 ÷ 𝑐)
(b) Solve for X from: − 3x + 10 > 40
(c) A person pays no tax on the first Tk.2,50,000 of earnings and then 10% tax on the
remainder of earnings. If s/he wishes to have Tk.6,10,000 net of tax earnings, what gross
earnings does s/he need?
(d) A small company produces specialized posters. The total cost is made up of three
elements – materials, labor and administration as follows:

Materials Tk.0.50 per poster

Labor Tk.15 per hour
Administration Tk.10 per 100 plus Tk.50

The set up time for printing takes two hours and the posters are run off at the rate of 300
per hour. If the number of posters produced is denoted by N, write down the formulae for
the following in Tk.:
(i) the total cost of materials,
(ii) the time taken to produce the posters,
(iii) the total labor cost of production,
(iv) the administration cost.

(e) For statistical data, mention various types of the measure of dispersion. Which one is the
best measure and why?
[Marks: (3+2+5+6+4) = 20]
Q. No. 2.
(a) State at least four characteristics of quality data.
(b) A firm has the workforce with the following age structure:
Age-group (years) 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65
Number of persons 5 10 13 28 21 12 8 3
Calculate the mean, median, mode, standard deviation and coefficient of variation.
(c) Calculate Laspeyre's price index and Paasche's price index for the following data:
Meal Type Meals for 2010 Meals for 2011
Price per meal in Tk. Quantity Price per meal in Tk. Quantity
Fish & Chips 1800 20 2000 18
Pizza 1600 22 1800 17
Rice & Curry 2200 18 2400 20
Roast Lunch 2400 15 2600 11
(d) A pie chart is used to display the following data:
(i) Sales of product J 43
(ii) Sales of product V 25
(iii) Sales of product C 27
What angle in degrees on the pie chart would represent product C’s share of sales?
[Marks: 2+(3+3+3+3+1)+3+2 = 20]

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CMA JUNE, 2018 EXAMINATION
BUSINESS LEVEL
SUBJECT: GE 03. FUNDAMENTALS OF BUSINESS MATHEMATICS.

Q. No. 3
(a) An investor is considering three options, only one of which h/se can afford. All three have
the same initial outlay, but there are different income patterns available from each.
Investment A pays Tk.20,000 each year at the end of the next five years. Investment B
pays Tk.10,000 at the end of the first year, Tk.15,000 at the end of the second year, and
so on until the final payment of Tk.30,000 at the end of the fifth year. Investment C pays
Tk.40,000 at the end of the first year, Tk.30,000 at the end of the second year, and
Tk.20,000 at the end of the third. The investor estimates a constant rate of interest of 10%
throughout the next 5 years. Which investment should s/he choose?
(b) For project C above, if the initial outlay is Tk.70,000, then find the IRR for C. What is the
profitability index of this project?
(c) In project financial analysis, write down the accept-reject criterion for pay-back period,
NPV, IRR and Profitability Index.
[Marks: (10+5+5) = 20]
Q. No. 4
(a) Carefully study the following spread-sheet and answer the questions below:
A B C D
1 Unit selling price Tk.65 Annual volume 10,000
2
3 Seasonal
Variation
4 Quarter-1 -20%
5 Quarter-2 -35%
6 Quarter-3 10%
7 Quarter-4 45%
8
9 Sales budget Seasonal variation Quarterly Quarterly
(units) volume turnover
10 Quarter-1
11 Quarter-2
12 Quarter-3
13 Quarter-4

(i) The cell B10 shows the seasonal variation in units for quarter-1. Write a suitable
formula for this cell so that it can be copied for cells B11, B12 and B13.
(ii) The cell C10 shows the sales volume in units for quarter-1. Write a suitable formula
for this cell so that it can be copied for cells C11, C12 and C13.
(iii) The cell D10 shows the turnover in quarter-1. Write a suitable formula for this cell so
that it can be copied for cells D11, D12 and D13.
(b) The table below shows the demand for a particular brand of razor in a shop for each of
the last nine months.

Month 1 2 3 4 5 6 7 8 9
Demand 10 12 13 17 15 19 20 21 20
(i) Calculate a three month moving average for months three to nine. What would be your
forecast for the demand in month ten?
(ii) Apply exponential smoothing with a smoothing constant of 0.3 to derive a forecast for the
demand in month ten.
(iii) Which of the two forecasts for month ten do you prefer and why?

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CMA JUNE, 2018 EXAMINATION
BUSINESS LEVEL
SUBJECT: GE 03. FUNDAMENTALS OF BUSINESS MATHEMATICS.

Q. No. 4 (cont’d…)

(c) Carefully study the following spread-sheet and answer the questions below:
A B C D E
1
2
3
4 5 6 8 =B4+C4*D4
5 3 1 2 =(B5+C5)*2
6 9 7 2 =B6-C6/2
7 4 5 10 =(B7+C7)/D7
8 5 7 8 =B8+C8*D8-2
9 6 6 =(B9-1)*(C9+4)
10
11 9 7 -2 =B14-C14*D14
12 5 8 -6 =(B15-C15)^2
13 12 8 -4 =(B16^2)+(C16)
14 4 16 -2 =(B16/C17)*D17^2
15 17 8 =(B18+C18)/0.5
16 7 20 6 =C19/(B19+C19)

From the above spreadsheet find the values of E4, E5, E6, E7, E8, E9, E11, E12, E13,
E14, E15, and E16.

(d) Mrs. Sifat wants to plan a trip to Hawaii with her husband on their 10th wedding
anniversary in two years. She anticipates that the all-inclusive trip will cost $9500 for both
of them and wants to start saving. How much should she deposit at the end of each
month into her account that pays 12% compounded monthly to pay for the trip in two
years?
[Marks: 5+(2+2+2)+5+4 = 20]
Q. No. 5
(a) A pet food company has developed a low-fat dog food designed to make overweight dogs
loss weight. In field tests on 1,000 pet dogs, some dogs ate the new food and some a
normal dog food. The results of these tests were as follows:

Given low-fat food Given normal food

Lost weight 200 250
No weight loss 300 250
Find:
(i) The probability that a dog has lost weight.
(ii) The conditional probability that a dog has lost weight, given that it received low-fat
food.
(iii) The conditional probability that a dog was given the normal food, given that it lost
weight.
(b) A salesman is known to sell a product in 3 out of 5 attempts while another salesman is 2
out of 5 attempts. Find the probability that
(i) No sale will be effected when they both try to sell the product and
(ii) Either of them will succeed in selling the product.

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CMA JUNE, 2018 EXAMINATION
BUSINESS LEVEL
SUBJECT: GE 03. FUNDAMENTALS OF BUSINESS MATHEMATICS.

Q. No. 5 (cont’d…)

(c) A West Coast Publishing Company keeps accurate records of its monthly expenditure for
advertising and its total monthly sales. For the first ten months of 2017, the records
showed the following (note that units are in dollars):
Advertising (in thousands) 43 44 36 38 47 40 41 54 37 46
Sales (in millions) 74 76 60 68 79 70 71 94 65 78

(i) Find the least-squares prediction equation appropriate for the data.
(ii) If the company plans to spend $80,000 for advertising next month, what is their
predicted sale? (Assume that all other factors can be neglected).
[Marks: 5+8+(4+3) = 20]
Q. No. 6
(a) Solve the following simultaneous equations graphically and algebraically:
4x + 3y = 24
7x + 5y = 35
(b) You have been supplied with the following data regarding the grades of candidates in an
interview presentation and their written exam scores:

Candidate Grade awarded Exam score

Mr. A A 70
Mr. B B 76
Mr. C A 58
Mr. D C 88
Mr. E D 81

What is the Spearman’s correlation coefficient?

(c) What is the difference between “risk” and “uncertainty”?

(d) Write a short note on annuity.
(e) In the analysis of inter-relationship of variables, the obtained coefficient of determination is
0.49. What do you mean by this figure?
(f) In order of mathematical operations, what is meant by BEDMAS? How the sequence of
the letters can be explained?
(g) In the model of time series, Y = T × S × C × R, which letter represents the seasonal
variation? How this seasonal variation affects business decision? Explain shortly.

[Marks: 5+5+2+2+2+2+2 = 20]

= THE END =

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