Question

The table below shows the quarterly revenue. in millions of euro, for a large German multinational company for the years 2018, 2019 and 2020

(a) calculate the trend, using a centered 4-point moving average
(B) compute the seasonal variations for the revenue
(c) if the trend for the quarter 1 of 2021 is predicted to be 350. what revenue would you predict for the company in quarter 1 of 2021

------- Q1 Q2 Q3 Q4
2018 276 388 301 325
2019 290 399 310 326
2020 298 407 315 330

Answer 1

[AI-generated answer — Explain Bot]

To calculate the trend using a centered 4-point moving average, follow these steps:

Step 1: Calculate the centered 4-point moving average for each quarter by taking the average of the two preceding quarters, the current quarter, and the following quarter. Do this for each year.

Year 2018:
Q1: (276 + 388 + 290 + 301) / 4 = 314.75
Q2: (388 + 301 + 325 + 310) / 4 = 331
Q3: (301 + 325 + 326 + 315) / 4 = 316.75
Q4: (325 + 326 + 298 + 330) / 4 = 319.75

Year 2019:
Q1: (290 + 310 + 298 + 399) / 4 = 324.25
Q2: (310 + 326 + 399 + 407) / 4 = 360.5
Q3: (326 + 315 + 407 + 315) / 4 = 340.75
Q4: (315 + 330 + 315 + 407) / 4 = 341.75

Year 2020:
Q1: (298 + 330 + 315 + 325) / 4 = 317
Q2: (330 + 315 + 325 + 330) / 4 = 322.5
Q3: (315 + 325 + 330 + 330) / 4 = 325
Q4: (325 + 330 + 330 + 315) / 4 = 325

Step 2: Calculate the trend for each year by taking the average of the centered 4-point moving averages.

Average for 2018: (314.75 + 331 + 316.75 + 319.75) / 4 = 320.5625
Average for 2019: (324.25 + 360.5 + 340.75 + 341.75) / 4 = 341.3125
Average for 2020: (317 + 322.5 + 325 + 325) / 4 = 322.625

So, the trend for the given data using a centered 4-point moving average is approximately 320.5625, 341.3125, and 322.625 for the years 2018, 2019, and 2020, respectively.

To compute the seasonal variations for the revenue, subtract the trend from each quarterly revenue.

Year 2018:
Q1: 276 - 320.5625 = -44.5625
Q2: 388 - 320.5625 = 67.4375
Q3: 301 - 320.5625 = -19.5625
Q4: 325 - 320.5625 = 4.4375

Year 2019:
Q1: 290 - 341.3125 = -51.3125
Q2: 399 - 341.3125 = 57.6875
Q3: 310 - 341.3125 = -31.3125
Q4: 326 - 341.3125 = -15.3125

Year 2020:
Q1: 298 - 322.625 = -24.625
Q2: 407 - 322.625 = 84.375
Q3: 315 - 322.625 = -7.625
Q4: 330 - 322.625 = 7.375

The seasonal variations for each quarter of each year are as follows:
2018: -44.5625, 67.4375, -19.5625, 4.4375
2019: -51.3125, 57.6875, -31.3125, -15.3125
2020: -24.625, 84.375, -7.625, 7.375

To predict the revenue for the company in Q1 of 2021, add the predicted trend (350) to the average seasonal variation for Q1 (computed from the data) of the past years.

Average seasonal variation for Q1: (-44.5625 + -51.3125 + -24.625) / 3 = -40.8333

Predicted revenue for Q1 2021: 350 + (-40.8333) = 309.1667 million euro.