Topic: Forecasting

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  • 20 Marks

QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

The sales of PQR Nigeria Plc. in thousands of Naira are listed in the table below for each quarter for years 2005 – 2008.

Sales of PQR in N’000s

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4
2005 22 35 82 37
2006 24 46 81 44
2007 25 40 87 49
2008 29 42 100 55

Required:

a. Calculate the trend in the above data using the Least Squares Method. (12 Marks)
b. Estimate the sales for each quarter using the trend line. (4 Marks)
c. Calculate the percentage variation for each quarter’s actual sales from the estimate obtained in (b) above. (4 Marks)

(Total: 20 Marks)

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  • 1 Marks

QTB – Nov 2014 – L1 – SA – Q6 – Forecasting

Identifies the method that is not considered a quantitative forecasting technique.

The following are quantitative techniques of forecasting in business analysis EXCEPT:
A. Regression analysis
B. Delphi method
C. Moving average
D. Exponential smoothing
E. Time series analysis

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  • 20 Marks

QT – Nov 2017 – L1 – Q3 – Forecasting

Analyze the relationship between website hits and promotions using correlation and regression analysis.

A small business is interested in the relationship between the number of hits on its website (measured by the number of visitors that have used the main menu) and the level of website promotion (in GH¢ 00s). The table below gives the figures for the last six months:

Month Web Site Hits Web Site Promotion (GH¢ 00s)
1 25 1.0
2 24 1.2
3 56 1.6
4 54 1.4
5 55 1.2
6 58 1.8

Required:
a) Graph the number of website hits against website promotion. (2 marks)
b) Comment on any possible relationship in (a) above. (2 marks)
c) Calculate the correlation coefficient and give an interpretation to its value. (5 marks)
d) Determine the regression line. (5 marks)
e) Using the regression line found in part (d) above, predict the number of website hits if the level of monthly promotion were increased to GH¢200. (2 marks)
f) Comment on the reliability of your prediction in (e) above. (1 mark)
g) Comment on the simple forecasting model you have developed above. (3 marks)

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  • 15 Marks

QT – May 2019 – L1 – Q5b – Forecasting

Compute 5-period moving averages, weighted moving averages, and comment on their suitability for forecasting

The number of enquiries being made to a mail order business during a Monday to Friday working week is given as:

Week Monday Tuesday Wednesday Thursday Friday
1 34 36 24 25 41
2 33 34 24 23 43
3 35 37 25 25 47

Required: i) Plot the data on a graph.
ii) Compute a 5-period moving average for the data.
iii) Compute a ‘weighted’ moving average for the data if the smoothing constant is α=0.5.
iv) Superimpose the graphs of (ii) and (iii) on your graph in (i) above.
v) Comment on the suitability of the two smoothing methods above. (16 marks)

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  • 4 Marks

QT – May 2019 – L1 – Q5a – Forecasting

Explain the concepts of moving averages and exponential smoothing in time series forecasting.

The objective of smoothing methods is to smooth out the random variations due to irregular components of the time series and provide an overall impression of the pattern of movement in the data over time.

Required:
Explain the following smoothing methods:

i) Moving averages (2 marks)
ii) Exponential smoothing (2 marks)

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  • 20 Marks

QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

The number of clients who consulted Tsoo Consult within a period of three years were recorded as follows:

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4
1 75 70 75 80
2 95 85 80 65
3 100 105 115 90

Required:
a) Assuming a 4 quarterly cycle, calculate the centred trend values for the data by moving average method. (4 marks)

b) Using (a) above and the multiplicative model, calculate the average seasonal variations. (5 marks)

c) Using (b) above, calculate the adjusted average seasonal variations for the data. (5 marks)

d) Using the trend and the adjusted average seasonal variation, forecast the number of clients for Year 4 based on the multiplicative model. (6 marks)

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  • 20 Marks

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

The following data gives how much 10 students of ICAG spend on TroTro to the Institute and food weekly:

Food (x) 10 12 14 16 18 20 22 24 26 28
TroTro (y) 25 24 22 20 19 17 13 12 11 10

Required:

a) Using a graph paper, construct a scatter diagram of the data.
(4 marks)

b) Determine the correlation coefficient.
(4 marks)

c) Calculate the coefficient of determination of the data and interpret its value.
(4 marks)

d) Determine the regression line of y on x, and interpret the coefficient.
(8 marks)

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  • 20 Marks

QT – May 2016 – L1 – Q2 – Forecasting

This question asks for the creation of a linear regression trend equation, seasonal components, and forecasts for chocolate sales.

Countess Company trades in bars of Golden Tree Chocolate from Tema Cocoa Processing Company Limited. The number of bars of chocolate sold per quarter over a four-year period by Countess Company is:

YEAR QUARTER 1 QUARTER 2 QUARTER 3 QUARTER 4
1 20 10 4 11
2 33 17 9 18
3 45 23 11 25
4 60 30 13 29

Required:

i) Plot the data on a graph (3 marks)

ii) Calculate a linear regression trend equation for the data (5 marks)

iii) Calculate the four seasonal components using a multiplicative model (5 marks)

iv) Forecast the number of bars of chocolate for the next two years (5 marks)

v) Comment on the reliability of the forecasts in iv) above (2 marks)

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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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  • 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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  • 4 Marks

QT – Nov 2015 – L1 – Q1a – Forecasting

State the four factors commonly found in time series data.

State the four (4) factors which may be present in a Time Series Data. (4 Marks)

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  • 20 Marks

IMAC – MAR 2024 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Calculate daily variations using moving averages and explain interrelationships between material price and usage variances, and labor rate and efficiency variances.

a) BB Importers Ltd has been importing electrical gadgets through the port of Takoradi over the past ten years. Management is aware that the business has been facing seasonal fluctuations but there is no scientific basis for the determination of such variations that can be used to predict future revenue. As a newly recruited Cost Accountant, you have been provided with some past daily sales performance over a three-week period. Details of the sales performance are shown below:

Sales Monday Tuesday Wednesday Thursday Friday
Week 1 780 830 890 850 850
Week 2 880 930 990 950 950
Week 3 980 1030 1090 1050 1050

Required:
Using daily moving averages, calculate the daily variation for the company. (15 marks)

b) The reasons for variances might be connected, and two or more variances may arise from the same cause. For example, a favorable variance and an adverse variance might have the same cause.

Required:
Explain the interrelationships between:
i) Material price and usage variances (2.5 marks)
ii) Labor rate and efficiency variances (2.5 marks)

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  • 20 Marks

IMAC – NOV 2023 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Determine the trend and seasonal variation in sales using moving averages and calculate factors for estimating direct material costs.

a) A company operates from Monday to Friday. Sales data for the most recent three weeks as well as the moving total are as follows:

Day Sales Moving Total
Day 1 78
Day 2 83
Day 3 89 420
Day 4 85 430
Day 5 85 440
Day 6 88 450
Day 7 93 460
Day 8 99 470
Day 9 95 480
Day 10 95 490
Day 11 98 500
Day 12 103 510
Day 13 109 520
Day 14 105
Day 15 105

Required:
i) State the length of the cycle. (2 marks)
ii) Using the moving averages, establish the trend of the historical data above. (6 marks)
iii) Calculate the seasonal variation for each day of the week. (7 marks)

b) The value of variances as a control technique for management depends on the reliability and accuracy of the standard costs. If the standard costs are inaccurate, comparisons between actual cost and standard cost will have no meaning.

Required:
Explain TWO (2) factors to be considered by the purchasing department in estimating the direct material costs per unit of raw material. (5 marks)

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  • 20 Marks

IMAC – JULY 2023 – L1 – Q5 – Budgeting | Forecasting

Prepare seasonally adjusted sales forecast and production overheads budget, and explain key components of time series analysis.

Question:
a) Balan Ltd is engaged in manufacturing and selling a single product and is in the process of preparing its budget for 2024. The following information is available:

Sales:
Balan Ltd has developed the linear relationship Y = 20,000 + 4,000X, where X represents the time period (X = 1 for the 1st quarter of 2024) and Y represents the sales trend in units.

The following seasonal variations are required to be adjusted to the sales trend in order to arrive at the sales forecast:

Quarter Jan-Mar Apr-Jun Jul-Sep Oct-Dec
Index value 110 90 80 120

A unit of product can be sold at GH¢1,000 during the first three quarters, and this price will be increased by 10% in the fourth quarter of 2024.

Production Overheads:
Based on the past 6 quarters’ results, the following statistical data has been gathered:
n = 6 (where ‘n’ is the number of quarters considered)
∑X = 306 (where ‘X’ is the production quantity in thousands of units)
∑Y = 146,400 (where ‘Y’ is the total production overheads in GH¢ thousands)
∑XY = 7,578,400
∑X² = 15,886

Balan Ltd estimates a linear relationship between output (X) and production overheads (Y), and the total production overheads can be expressed as Y = a + bX.

Balan Ltd does not maintain finished goods inventories. You are one of the Management Accounting executives of Balan Ltd and have been requested to assist in compiling budget figures.

Required:
i) Prepare the seasonally adjusted quarterly sales forecast in unit and in value for the calendar year 2024. (4 marks)
ii) Prepare the quarterly production overheads budget for the calendar year 2024. (5 marks)

b) Explain the following terms:
i) Trend-Cycle (C) (2 marks)
ii) Seasonal Components (S) (2 marks)
iii) Irregular Components (I) (2 marks)

c) The purpose of Management Accounting is to provide information for planning, control, and decision making. Information for control of the performance is an important management task.

Required:
Outline THREE (3) activities involved in providing information for control purposes. (5 marks)

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  • 20 Marks

IMAC – Nov 2021 – L1 – Q5 – Budgeting | Forecasting

Analysis of a regression equation related to absenteeism, seasonal variation in production output, and variance analysis for overheads.

a) A large manufacturing company is investigating the cost of sickness amongst production workers who the company has employed for more than one year. The following regression equation, based on a random sample of 50 for such production workers, was derived for 2018:

y=15.6−1.2xy = 15.6 – 1.2x

where yy represents the number of days absent in a year because of sickness and xx represents the number of years’ employment with the company.

Required: i) Explain the meaning of each component of the regression equation. (2 marks)
ii) Predict the number of days of absence through sickness to be expected of an employee who has been with the company for eight years. (2 marks)
iii) Explain TWO (2) limitations or problems of using this equation in practice. (4 marks)

b) A statistician is carrying out an analysis of a company’s production output. The output varies according to the year’s season, and, from the data, she has calculated the following seasonal variations in units of production:

QUARTER 1 2 3 4
Year 1 +11.2 +23.5
Year 2 -9.8 -28.1 +12.5 +23.7
Year 3 -7.4 -26.3 +11.7

Required: i) Calculate and explain the average quarterly variation for each quarter. (5 marks)
ii) If the trend output in the 4th Quarter of Year 3 is expected to be 10,536 units, what is the forecast output? (2 marks)

c) KK Ltd operates a standard absorption costing system and has provided the following costs data in relation to its prime product, Qwikpass:

Standard Cost Card:

GH¢
Direct Material 4kg @ GH¢3/kg 12
Direct Labour 3hrs @ GH¢5/hr 15
Variable Overheads 3hrs @ GH¢3/hr 9
Fixed Overheads 3hrs @ GH¢2 6
Total Cost per Unit 42

Budgeted Units: 6,000

Actual Results:

GH¢
Units produced 6,400
Direct Materials Purchased and used 32,000kg 144,000
Direct Labour 30,720hrs 199,680
Variable Overheads 138,240
Fixed Overheads 45,000
Total costs 526,920

Required: i) Compute the Variable Overheads Expenditure Variance. (1 mark)
ii) Compute the Fixed Overheads Expenditure Variance. (2 marks)
iii) Compute the Fixed Overheads Volume Variance. (2 marks)

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  • 20 Marks

IMAC – MAY 2021 – L1 – Q5 – Cost Segregation and Estimation | Forecasting | Standard Costing and Variance Analysis

Apportionment of service center costs to production departments and calculation of direct materials price variance.

a) A company is preparing its annual budget and it is estimating the number of units of Product W that would be sold in each quarter of year 2. Past experience has shown that the trend for sales of the product is represented by the following relationship:

y = a + bx where: y = quantity of sales units in the quarter a = 15,000 b = 3,000 x = the quarter number where 1 = quarter 1 of year 1

Actual sales of Product W in year 1 were affected by seasonal variations and were as follows:

Quarter Actual Sales Units
1 20,250
2 19,425
3 25,200
4 24,300

Required: Calculate the expected unit sales of Product W for each quarter of year 2, after adjusting for seasonal variations using the multiplicative model. (6 marks)

b) The records of direct labour hours and total factory overhead cost of Cooper Limited over the first six months of its operations are given below:

Month Direct Labour Hours Total Factory Overheads (GH¢000)
September 50,000 14,800
October 80,000 17,000
November 120,000 23,800
December 40,000 11,900
January 100,000 22,100
February 60,000 16,150

Management is interested in distinguishing between the fixed and variable portions of the overheads.

Required: Using the least square regression method, estimate the variable cost per direct labour hour and the total fixed cost per month. (9 marks)

c) State and explain the methods used in setting: i) Direct Material Cost Standard. (2.5 marks) ii) Direct Labour Cost Standard. (2.5 marks)

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  • 20 Marks

IMAC – NOV 2020 – L1 – Q5 – Forecasting

Explain features of time series; prepare a histogram and analyze sales trends; explain overhead accounting terminologies.

a) Explain in brief the following features of time series:
i) Trend.
ii) Seasonal variation.
iii) Random variation.
(6 marks)

b) The following table relates to sales of Emefa Ltd for a three-year period:

Year 1st Quarter (GH¢’000) 2nd Quarter (GH¢’000) 3rd Quarter (GH¢’000) 4th Quarter (GH¢’000)
Year 1 200 150 180 260
Year 2 220 190 210 280
Year 3 240 200 220 300

Required:
i) Prepare a histogram using the above sales figures. (7 marks)
ii) Describe the trend of performance of the company. (2 marks)

c) Explain the following terminologies as used in accounting for overheads in management accounting:
i) Apportionment
ii) Allocation
iii) Allotment
iv) Absorption
v) Over/(under) absorption
(5 marks)

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  • 20 Marks

IMAC – MAY 2020 – L1 – Q5 – Forecasting | Standard Costing and Variance Analysis

Calculate sales trend using moving average and line of best fit; identify sources of information for standard prices.

a) The monthly sales of Danamo Company Limited have been given as follows:

Monthly Sales (GH¢’000) Moving Total (GH¢’000)
April 150
May 140
June 160
July 180
August 200
September 190
October 220
November 230
December 250

Required:
i) Using the three-month moving average, calculate the trend. (3 marks)

ii) Using the line of best fit, estimate the sales of January, February, and March of the following year. (12 marks)

b) State and explain FIVE (5) sources of information that may be considered in setting standard prices for materials in Management Accounting. (5 marks)

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