Mid Term Question
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Charizma is one of the leading affordable clothing brands in Pakistan, known for its wide range of unique and high-quality products in both ready- to-wear and unstitched clothing, as well as accessories. Over the past few decades, this brand has experienced remarkable growth, expanding its business exponentially. The brand consistently meets its annual targets and continues to thrive. Consider the quarterly data on sales of this brand for the years 2021 and 2022 as given in the table below.
You are required to answer the following questions using the available information.
(i) Find the forecast value of sales and forecast error for each quarter of Year 2021 and Year 2022 by using Naïve technique of forecasting. Provide the answer in the format given in table.
(ii) By using the moving average method of forecasting, calculate two quarter moving average for all available quarterly data for the year 2021 and year 2022. Provide the answer in the format given in the table.
(iii) Consider the data given in this part and calculate the smoothed/predicted value of sales for the fourth quarter of the year 2022 using the exponential smoothing method of forecasting. Predicted value of sales for third quarter (Y3) of year 2022 = Rs. 825,000
Actual value of sales for third quarter (Y3) of year 2022 = Rs. 775,000 Smoothing constant= 0.4
To find the forecast value of sales and forecast error for each quarter of Year 2021 and Year 2022 using the Naïve technique of forecasting, we simply use the actual sales value of the previous quarter as the forecast for the current quarter.
1st Quarter Forecast Value of Sales = 700,000 (same as actual sales) 1st Quarter Forecast Error = Actual Sales - Forecast Value = 700,000 - 700,000 = 0
2nd Quarter Forecast Value of Sales = 700,000 (same as actual sales of the 1st quarter) 2nd Quarter Forecast Error = Actual Sales - Forecast Value = 750,000 - 700,000 = 50,000
3rd Quarter Forecast Value of Sales = 750,000 (same as actual sales of the 2nd quarter) 3rd Quarter Forecast Error = Actual Sales - Forecast Value = 800,000 - 750,000 = 50,000
4th Quarter Forecast Value of Sales = 800,000 (same as actual sales of the 3rd quarter) 4th Quarter Forecast Error = Actual Sales - Forecast Value = 725,000 - 800,000 = -75,000
2nd Quarter Forecast Value of Sales = 800,000 (same as actual sales of the 1st quarter) 2nd Quarter Forecast Error = Actual Sales - Forecast Value = 825,000 - 800,000 = 25,000
3rd Quarter Forecast Value of Sales = 825,000 (same as actual sales of the 2nd quarter) 3rd Quarter Forecast Error = Actual Sales - Forecast Value = 775,000 - 825,000 = -50,000
4th Quarter Forecast Value of Sales = 775,000 (same as actual sales of the 3rd quarter) 4th Quarter Forecast Error = Actual Sales - Forecast Value = 820,000 - 775,000 = 45,000
Moving on to the moving average method of forecasting, we calculate the two-quarter moving average for all available quarterly data.
1st Quarter 2-Quarter Moving Average = (700,000 + 750,000) / 2 = 725,000
2nd Quarter 2-Quarter Moving Average = (750,000 + 800,000) / 2 = 775,000
3rd Quarter 2-Quarter Moving Average = (800,000 + 725,000) / 2 = 762,500
4th Quarter 2-Quarter Moving Average = (725,000 + 800,000) / 2 = 762,500
2nd Quarter 2-Quarter Moving Average = (725,000 + 800,000) / 2 = 762,500
3rd Quarter 2-Quarter Moving Average = (800,000 + 825,000) / 2 = 812,500
4th Quarter 2-Quarter Moving Average = (825,000 + 775,000) / 2 = 800,000
Lastly, to calculate the smoothed/predicted value of sales for the fourth quarter of 2022 using the exponential smoothing method of forecasting, we use the formula:
Smoothed Value = (1 - Smoothing Constant) * (Previous Smoothed Value) + (Smoothing Constant) * (Actual Value)
Predicted value of sales for third quarter (Y3) of year 2022 = Rs. 825,000 Actual value of sales for third quarter (Y3) of year 2022 = Rs. 775,000 Smoothing constant = 0.4
Previous Smoothed Value = Predicted value for Y3 = 825,000 Actual Value = Actual sales for Y3 = 775,000 Smoothing Constant = 0.4
Smoothed Value for the fourth quarter (Y4) of 2022: Smoothed Value = (1 - 0.4) * (Predicted Value for Y3) + (0.4) * (Actual Value for Y3) Smoothed Value = 0.6 * 825,000 + 0.4 * 775,000 Smoothed Value = 495,000 + 310,000 Smoothed Value = 805,000
Therefore, the smoothed/predicted value of sales for the fourth quarter of 2022 using the exponential smoothing method is Rs. 805,000.
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