Question

The following table provides monthly sales ($1000) at a college bookstore. The sales show a seasonal pattern, with the greatest number when the college is in session and decrease during the summer months.

Calculate all seasonal factors? Then calculate the forecasted sales per month for year 5 - third quarter only. Given that a fiscal year starts in January and ends in December. In year 5 the expected to be a total of $3,600,000

M T	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1	196	188	192	164	140	120	112	140	160	168	192	200
2	200	188	192	164	140	122	132	144	176	168	196	194
3	196	212	202	180	150	140	156	144	164	186	200	230
4	242	240	196	220	200	192	176	184	204	228	250	260

Answer 1

Months	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec	Total
T
1	196	188	192	164	140	120	112	140	160	168	192	200	1972
2	200	188	192	164	140	122	132	144	176	168	196	194	2016
3	196	212	202	180	150	140	156	144	164	186	200	230	2160
4	242	240	196	220	200	192	176	184	204	228	250	260	2592
Mean	208.5	207	195.5	182	157.5	143.5	144	153	176	187.5	209.5	221	2185
Factor	1.14508	1.136842	1.073684	0.999542	0.864989	0.788101	0.790847	0.840275	0.96659	1.029748	1.150572	1.21373	12

Above table shows the seasonal factors in the last row.

Steps to calculate :

1. Calculating the mean of a month for four years. Ex - For Jan, Mean = (196+200+196+242)/4 = 208.5 = D(Jan)

2. Calculate the grand mean ie., D = (D(Jan)+D(Feb)+....+D(Dec))/12 = 182.08

3. Seasonality Factor for January is = D(Jan)/D = 208.5/182.08 = 1.14508 (Note: Calculated in the last row of the table)

4. Similarly it can be calculated for all other Months.

Part b:

Now given that expected sales for Year 5 = $3600000... Let us calculate using $3,600

Hence average monthly sales of Year 5 = 3600/12 = 300

Forecast for month of July = Average monthly sales in year 5 X Seasonality factor of July = 300 * 0.79 = 237

Forecast for July in year 5 = $2,37,000