Question 3
ICAN
•
2021
•
PERFORMANCE MANAGEMENT
•
mixed
Case Stimulus
Some time ago, Robert launched a new product. At first, sales were good but now the figures are causing concern. Robert wants a more accurate sales forecast to produce detailed cash forecasts. Since there are some seasonality present in the raw data, the series for sales shown below represents the underlying trend based on an averaging process:
Year Quarter Trend point (Cartons)
2016 3rd 1 10,000
2016 4th 2 10,760
2017 1st 3 10,920
2017 2nd 4 11,000
2017 3rd 5 11,050
2017 4th 6 11,080
2018 1st 7 11,085
2018 2nd 8 11,095
2018 3rd 9 11,120
2018 4th 10 11,130
On average, quarters 1 and 3 are 5% and 6% respectively above trend whilst quarters 2 and 4 are respectively 2% and 9% below trend. Some preliminary calculations on the above ten observations have been carried out and the results are summarised below:
Results from ten periods’ observations:
Linear regression y = a + bx
Slope = 82.67
Intercept = 10,472.33
Coefficient of determination = 0.535
It is required to make forecasts of sales for quarters 3 and 4 in 2019 and for quarters 1 and 2 in 2020 but there is some discussion on whether the ten-period data shown above are suitable for forecasting or whether only the last five periods would provide a better basis for forecasting. Linear analysis of the last five periods only gives the following intermediate results:
Results of last five periods’ observations:
Σy = 555.10
Σx² = 330
Σy² = 61,627.40
Σxy = 4,442.15
Note: the y values have been scaled down by 100 times for ease of calculation.
Additional Information
{
"label": "Supporting information",
"content": "| Year | Quarter | Trend point | Sales (Cartons) |\n|------|---------|-------------|-----------------|\n| 2016 | 3rd | 1 | 10,000 |\n| 2016 | 4th | 2 | 10,760 |\n| 2017 | 1st | 3 | 10,920 |\n| 2017 | 2nd | 4 | 11,000 |\n| 2017 | 3rd | 5 | 11,050 |\n| 2017 | 4th | 6 | 11,080 |\n| 2018 | 1st | 7 | 11,085 |\n| 2018 | 2nd | 8 | 11,095 |\n| 2018 | 3rd | 9 | 11,120 |\n| 2018 | 4th | 10 | 11,130 |"
}
{
"label": "Supporting information",
"content": "| Results of last five periods' observations: |\n|-------------------------------------------|\n| Σy = 555.10 |\n| Σx² = 330 |\n| Σy² = 61,627.40 |\n| Σxy = 4,442.15 |"
}
{
"label": "Supporting information",
"content": "| Probability | No of pupils joining late |\n|------------|--------------------------|\n| 0.2 | 80 |\n| 0.3 | 30 |\n| 0.5 | 52 |"
}
Requirements
(
a
)
Forecast the sales of the four quarters required using the ten-period observations results.
(
b
)
Prepare similar forecasts based on the last five periods’ observations.
(
c
)
Explain which forecasting bases produce the better forecast.
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About This Question
This is
Ican
2021
Performance Management
Question 3.
It is one of the
mixed
questions from the
2021
Ican
Performance Management
examination.