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9609 · 8.1.3

Sales forecasting — practice questions

Practice and worked examples for 9609 Sales forecasting. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

Quarterly sales (units): Q1 400, Q2 450, Q3 500, Q4 480. Calculate a 3-quarter moving average for Q4 and comment on trend.

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3-period MA for Q4 = (450 + 500 + 480) ÷ 3 = 476.7 units

Trend: Generally rising from Q1–Q3, slight dip in Q4 (480 vs 500).

Use: Forecast Q1 next year ≈ 477 if trend stable — plan production and inventory.

Limitation: If new competitor launches in Q1, historical MA overstates demand — supplement with qualitative Delphi or scenario planning.

Worked example 2

A retailer's quarterly sales revenue ($'000) for the last two years are as follows:

  • Year 1: Q1 80, Q2 100, Q3 120, Q4 90
  • Year 2: Q1 90, Q2 115, Q3 135, Q4 105

Calculate: a) The 4-quarter centered moving average (trend) for Year 2, Quarter 1. b) The seasonal variation for Year 1, Quarter 3.

Show solution outline

To solve this, we will calculate the 4-quarter moving averages and then the centered moving average (trend).

Step 1: Calculate 4-Quarter Moving Averages (Uncentered) A 4-quarter moving average is the sum of sales for four consecutive quarters, divided by 4. This value is placed between the quarters it covers.

  • MA (for Y1 Q2-Y2 Q1): (100 + 120 + 90 + 90) / 4 = 100.0 (placed between Y1 Q3 & Q4)
  • MA (for Y1 Q3-Y2 Q2): (120 + 90 + 90 + 115) / 4 = 103.75 (placed between Y1 Q4 & Y2 Q1)
  • MA (for Y1 Q4-Y2 Q3): (90 + 90 + 115 + 135) / 4 = 107.5 (placed between Y2 Q1 & Y2 Q2)

Step 2: Calculate the Centered Moving Average (Trend) To get a trend value for a specific quarter, we average the two adjacent uncentered moving averages.

a) For Year 2, Quarter 1: The trend value for Y2 Q1 is the average of the MA between Y1 Q4/Y2 Q1 and the MA between Y2 Q1/Y2 Q2.

  • Trend (Y2 Q1) = (103.75 + 107.5) / 2 = 211.25 / 2 = 105.625 **Answer (a): The trend for Y2 Q1 is 105,625.∗∗105,625.**

b) For Year 1, Quarter 3: First, find the trend value for Y1 Q3. We need the first MA (for Y1 Q1-Q4): (80 + 100 + 120 + 90) / 4 = 97.5.

  • Trend (Y1 Q3) = (97.5 + 100.0) / 2 = 197.5 / 2 = 98.75 Now, calculate the seasonal variation.
  • Seasonal Variation = Actual Sales - Trend Value
  • Seasonal Variation (Y1 Q3) = 120 - 98.75 = +21.25 Answer (b): The seasonal variation for Y1 Q3 is +$21,250. This indicates that sales in Q3 are typically $21,250 higher than the underlying trend.
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