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

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Finance

The following equation summarizes the trend portion of quarterlysales of condominiums over a long cycle. Sales also exhibitseasonal variations.

F_t = 53 ? 4.3t + 3.3t²
where
F_t = 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 eachquarter of next year (not this year), and the first quarter of theyear following that. (Round intermediate calculations and finalanswers to 2 decimal places.)
Quarter Forecast
1
2
3
4
1

Answer & Explanation Solved by verified expert

3.9 Ratings (669 Votes)

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 F_t 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
			F_t= 53 ? 4.3 x t + 3.3 x t²	R	R x F_t
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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