The following equation summarizes the trend portion of quarterly sales of condom
ID: 3042753 • Letter: T
Question
The following equation summarizes the trend portion of quarterly sales of condominiums over a long cycle. Sales also exhibit seasonal variations. Ft = 50 4t + 3t 2 where Ft = Unit sales t = 0 at the first quarter of last year Quarter Relative 1 .90 2 .90 3 .40 4 1.20 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
Explanation / Answer
Trend line: Ft = 50 4t + 3t2
t = 0 for first quarter of last year, the values of t will be 8, 9, 10, 11, 12 for the first 4 quartes of next year
t = 8, 9, 10, 11 for the I, II, III, and IVth quarter of next year
Trend forecast for the next year is given as follows:
Quarter
Period (t)
Unseasonalized Forecast
Seasonal Indices
Seasonalized forecast
Next year
Ft = 50 4t + 3t2
SI
Ft * SI
1
8
50 – 4(8) + 3(8)2
= 210
0.9
210*0.9
= 189
2
9
257
0.9
231.3
3
10
310
0.4
124
4
11
369
1.2
442.8
1
12
434
0.9
390.6
Quarter
Period (t)
Unseasonalized Forecast
Seasonal Indices
Seasonalized forecast
Next year
Ft = 50 4t + 3t2
SI
Ft * SI
1
8
50 – 4(8) + 3(8)2
= 210
0.9
210*0.9
= 189
2
9
257
0.9
231.3
3
10
310
0.4
124
4
11
369
1.2
442.8
1
12
434
0.9
390.6
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