Problem 312 The following equation summarizes the trend port

Problem 3-12

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

t = 0 at the first quarter of last year

B.) 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.)

Solution

Since the first quarter of the previous year is origin,

t=0 for the first quarter

t=1 for the second quarter

t=2 for the third quarter

t=3 for the fourth quarter

and hence for current year

t=4 for the first quarter

t=5 for the second quarter

t=6 for the third quarter

t=7 for the fourth quarter

and hence for the next year,

t=8 for the first quarter

t=9 for the second quarter

t=106 for the third quarter

t=11 for the fourth quarter

For 1^st quarter of the following year, t=12

Using Multiplication Model,

F= T_{t X} S_t X C_t X I_t

Estimation for the next year are

                For 1st quarter F   = 40 - 6.5 x 8 +2 x 8² = 116

For 2nd quarter F = 40 - 6.5 x 9 +2 x 9² = 143.5

For 3rd quarter F   = 40 - 6.5 x 10 +2 x 10² = 175

For 4th quarter F = 40 - 6.5 x 11 +2 x 11² = 210.5

For 1^st quarter of the following year, t=12

Then F = 40 - 6.5 x 12 +2 x 12² = 250

Since Seasonal Indices are given, the actual estimated sales should be

                For 1st quarter F   =   116 x1.1     =    127.6

For 2nd quarter F = 143.5 x1.0   =    143.5

For 3rd quarter F   = 175 x0.6      =    105

For 4th quarter F = 210.5x1.3    =    273.65

For the next year,

For 1st quarter F   =   250 x1.1     =    275