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Dms 101 Management Mathematics I Question Paper
Dms 101 Management Mathematics I
Course:Diploma In Business Management
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
STAGE II ORDINARY EXAMINATION FOR THE DIPLOMA IN
BUSINESS MANAGEMENT
DMS 101 MANAGEMENT MATHEMATICS I
DATE: AUGUST 2014
TIME: 1 1/2 Hours
INSTRUCTION: Answer any THREE questions
QUESTION ONE: (20 MARKS)
(a)
An investor intends to invest in a project whose cash flows are as given below:
Year Cash flows
1 - 10 5,000,000
11 - 20 9,000,000
21 - 40 4,000,000
Determine the present value of the total cash flows if the discounting rate is 10% p.a.
(4 Marks)
(b)
Given the first term and the common difference of an AP are 2 and 5 respectively, obtain
the 7th term and the sum of the first 15 terms
(c)
Given the first term and the common ratio of a GP are 3 and 2 respectively, find the 5th
term and the sum of the first 8 terms.
(d)
(4 Marks)
(4 Marks)
A saleslady earns a fixed monthly basic salary and a commission that is directly
proportional to the total sales made. For the months of January and February 2014, the
saleslady’s total earnings were Shs 31,200 and Shs 39,000 respectively. Her total sales
for the months of January and February 2014 were Shs 405,000 and Shs 600,000
respectively.
Required;
1
i) The saleslady’s rate of commission (2 Marks)
ii) The saleslady’s monthly basic salary (2 Marks)
iii) The total sales the saleslady has to make in order to receive a total
monthly earning of shs 34,500
(2 Marks)
QUESTION TWO: (20 MARKS)
(a) State any three assumptions made in cost-volume-and-profit (c-v-p) analysis. (3 Marks)
(b) A manufacturing company incurs Shs 100 to produce a unit of its product and a further
Shs 50 per unit to market the product. The fixed costs of production amount to shs
1,200,000 per month. The selling price per unit is shs 200.
Required;
i) (3 Marks)
ii)
(c)
The monthly cost function and revenue function The break-even number of units (4 Marks)
Kitale Electronics sells all its products on credit. Data gathered over time indicate that the
collection percentage for credit sales (debts) issued in any month is an exponential
function of the time since the sales were made. Specifically, the function approximating
this relationship is:
= 0.94 (1-e-0.08t) for t > 0
Where
is the percentage of debts (in shillings) collected months after the sales were
made.
When = 0, the total debtors is Sh.1,000,000.
Required:
Determine the following:
i)
The amount in shillings that is expected to be collected after 4 months.
(3 Marks)
ii)
The eventual or long-term amount in shillings which is expected to be collected
(3 Marks)
iii)
The number of months when 75% of the debts will have been collected.
(4 Marks)
2
QUESTION THREE: (20 MARKS)
a)
Mjengo Building Company purchased a hydraulic crane on 1st January 2009 at a cost of
sh. 300,000. The crane is expected to have a useful life of 10 years and a scrap value of
sh. 100,000. The company intends to use the reducing balance method to depreciate the
crane.
Required:
Calculate;
i) (4 Marks)
ii)
b)
The annual depreciation rate The value of the crane after the fifth year (2 Marks)
Grace is a money lender operating at Mlolongo Township. She lends money to her
customers at an interest of 5% compounded monthly. Justus borrows sh. 20,000 from
Grace to repair his “tuk tuk” taxi that operates in Mlolongo. He is to repay the money in 5
equal monthly installments of sh. 4,000 plus the accrued interest
Required:
i) the total amount of money Justus pays to Grace at the end of the 5 months period.
(4 Marks)
ii) the amount of money Justus pays to Grace each month for the 5 months. (4 Marks)
iii) the percentage profit that Grace makes from Justus at the end of the 5 months period
(5 Marks)
QUESTION FOUR: (20 MARKS)
a)
Using appropriate diagrams, distinguish between set union and set intersection.
(4 Marks)
b)
A criminal investigating officer conducted a research on three types of offences that
criminals jailed at Kazi Ngumu maximum prison had committed to warrant their jail
terms.
From a sample of 800 criminals, 230 were convicted for murder, 245 were convicted for
robbery and 325 were convicted for rape. 30 had engaged in all the three criminal
activities, 70 had engaged in murder and robbery, 110 had engaged in murder only and
185 engaged in rape only.
Required;
3
i)
Present the above information on a Venn diagram
(6 Marks)
The number of criminals who engaged in;
ii) Robbery only (2 Marks)
iii) Murder and robbery only (2 Marks)
iv) Robbery or rape but not murder (2 Marks)
v) One criminal activity only (2 Marks)
vi) At least two of the three criminal activities (2 Marks)
QUESTION FIVE: (20 MARKS)
a)
The total cost of producing x units of a product is estimated by the function:
C = f(x) = 60x + 0.2x2 + 25,000
Where C equals the total cost measured in Shs.
Required;
i) This is an example of what class of functions?
(1 Mark)
ii) What is the cost associated with producing 25,000 units?
What is the average cost at this level of output?
b)
(2 Marks)
KK Ltd is considering the importation of a new machine for a newly launched project at a
cost of sh. 4.2 millions. The machine is expected to have a useful life of 6 years and is
expected to raise the company’s cash flows as follows;
Year
1 2 3 4 5 6
1442 1162 945 840 798 735
Increase in
cash flows
(sh. “000”)
The company finds the straight line depreciation to be the best fit for the book value of
the machine through its lifespan.
Calculate;
i) The Accounting Rate of Return (ARR) (4 Marks)
ii) The Net Present Value (NPV) (4 Marks)
iii) The Internal Rate of Return (IRR) (6 Marks)
iv) The profitability Index (PI) and advice the management whether to proceed with
the importation of the machine or not.
4
(3 Marks)
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