QUESTION ONE Daniel obtains cash from an ATM

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QUESTION ONE

Daniel obtains cash from an ATM. He suspects that the rate at which he spends cash is affected by the amount of cash withdrawn during the previous visit to the ATM. To investigate this he deliberately varies the amount that he withdraws. He records for each visit to an ATM the amount withdrawn (x=SH'00') and the number of hours until his next visit(y=hours) to an ATM.

Withdrawal 1 2 3 4 5 6 7 8 9 10

X 40 10 100 110 120 150 20 90 80 130

y 56 62 195 330 94 270 48 196 214 286

 

Required:

a) Draw a scatter diagram for the above data and establish the equation for the line of best fit. (4 marks)

b) Calculate the equation of the regression line (6 marks)

c) Determine the sum of squared errors(SSE) for both the equation in (a) and (b) above. Does your analysis validate the OLS argument (8 Marks)

d) Interpret, in context, the gradient of the regression line. (2 marks)

 

QUESTION TWO

Q a new company, is being established to manufacture and sell an electronic tracking device: the Trackit. The owners are excited about the future profits that the business will generate. They have forecast that sales will grow to 2,600 Trackits per month within five months and will be at that level for the remainder of the first year. 

 

The owners will invest a total of shs. 250,000 in cash on the first day of operations (that is the first day of Month 1). They will also transfer non-current assets into the company. 

 

Extracts from the company's business plan are shown below. 

 

Sales 

The forecast sales for the first five months are: 

 

Month Trackits

1 1,000

2 1,500

3 2,000

4 2,400

5 2,600

 

The selling price has been set at shs. 140 per Trackit. 

 

Sales receipts 

Sales will be mainly through large retail outlets. The pattern for the receipt of payment is expected to be as follows: 

 

Time of payment % of sales value 

Immediately 15 * 

One month later 25 

Two months later 40 

Three months later 15 

 

 

Time of payment % of sales value 

Immediately 15 * 

One month later 25 

Two months later 40 

Three months later 15 

 

The balance represents anticipated bad debts. 

 

* A 4% discount will be given for immediate payment. 

 

Production 

The budget production volumes in units are: 

 

Month 1 Month 2 Month 3 Month 4 

1,450  1,650  2,120  2,460 

 

Variable production cost 

The budgeted variable production cost is shs. 90 per unit, comprising: 

  shs.  

Direct materials 60 

Direct wages 10 

Variable production overheads 20 

Total variable cost 90 

 

Direct materials: Payment for purchases will be made in the month following receipt. There will be no opening inventory of materials in Month 1. It will be company policy to hold inventory at the end of each month equal to 20% at of the following month's production requirements. The direct materials cost includes the cost of an essential component that will be bought in from a specialist manufacturer. 

 

Direct wages will be paid in the month in which the production occurs. 

 

Variable production overheads: 65% will be paid in the month in which production occurs and the remainder will be paid one month later. 

 

Fixed overhead costs 

Fixed overheads are estimated at shs. 840,000 per annum and are expected to be incurred in equal amounts each month. 60% of the fixed overhead costs will be paid in the month in which they are incurred and 15% in the following month. The balance represents depreciation of noncurrent assets. 

 

Ignore VAT and Tax 

Required 

(a) Prepare a cash budget for each of the first three months and for that three-month period in total.

(14 marks)

(b) There is some uncertainty about the cost of the specialist component (this is 

included in the direct material cost). It is thought that the cost of the component could range between shs. 32 and shs. 50 per Trackit. It is currently included in the cost estimates at shs. 40 per Trackit. 

 

  Calculate the budgeted total net cash flow for the three-month period in total if the cost of the component was 

(i) shs. 32 

(ii) shs. 50 

(6 marks)

 

 

QUESTION THREE

A restaurant in Kisumu City has recorded its weekly sales over a 5- month period as follows:

Sales in ksh'000'

Week-1 Week-2 Week-3 Week-4

JANUARY 2500 1750 1200 3100

FEBRUARY 2650 1800 1400 3350

MARCH 2800 2000 1500 3400

APRIL 2850 1950 1450 3650

MAY 2900 2050 1750 3800

 

Required: 

i) Calculate the seasonal indices for each week using multiplicative index (4 Marks)

 

ii) Establish the trend line using ordinary least square (OLS) method (4 Marks)

 

iii) Using the trend in (ii) above, forecast the sales that the restaurant should make in week 2 of June (2 Marks)

    (Total: 10 Marks)