Question

In: Finance

The following equation summarizes the trend portion of quarterly sales of condominiums over a long cycle....

The following equation summarizes the trend portion of quarterly sales of condominiums over a long cycle. Sales also exhibit seasonal variations.

Ft = 53 − 4.3t + 3.3t 2
  

where
Ft = Unit sales
t = 0 at the first quarter of last year

Quarter Relative
1 1.05
2 1.05
3 .55
4 1.35


Using the information given, prepare a forecast of sales for each quarter of next year (not this year), and the first quarter of the year following that. (Round intermediate calculations and final answers to 2 decimal places.)

Quarter Forecast
1
2
3
4
1

Solutions

Expert Solution

t = 0 represents Q1 of last year. Please see the table below. Please see the second row that explains the mathematics. We have to forecast Ft for 4 quarters of next year and 1 quarter of the following year. "t" corresponding to these periods is from t = 8 to t = 12.

Your answers are:

Quarter Forecast
                  1       293.55
                  2       342.00
                  3       207.00
                  4       658.80
                  1       614.65

Please see the sequence below for further understanding. Cells highlighted in yellow are your answer.

Year Quarter t Forecast Without Seasonality Relative/Seasonal Index Forecast With Seasonality
Ft= 53 − 4.3 x t + 3.3 x t2 R R x Ft
Last year 1 0 53.00 0.95 61.75
2 1 52.00 0.9 57.60
3 2 57.60 0.45 32.40
4 3 69.80 1.2 106.80
This year 1 4 88.60 0.95 109.25
2 5 114.00 0.9 135.00
3 6 146.00 0.45 87.30
4 7 184.60 1.2 296.40
Next Year 1 8 229.80 0.95 293.55
2 9 281.60 0.9 342.00
3 10 340.00 0.45 207.00
4 11 405.00 1.2 658.80
Year after 1 12 476.60 0.95 614.65

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