Question

New car sales for a dealer in Cook County, Illinois, for the past year are shown in the following table, along with monthly indexes (seasonal relatives), which are supplied to the dealer by the regional distributor.

Month	Units Sold	Index
Jan.	640	0.80
Feb.	648	0.80
Mar.	630	0.70
Apr.	761	0.94
May.	735	0.89
Jun.	850	1.00
Jul.	765	0.90
Aug.	805	1.15
Sept.	840	1.20
Oct.	828	1.20
Nov.	840	1.25
Dec.	800	1.25

1. Plot the data. Does there seem to be a trend?

2. Deseasonalize car sales.

3. Plot the deseasonalized data on the same graph as the original data. Comment on the two graphs.

4. Assuming no proactive approach on the part of management, discuss (no calculations necessary) how you would forecast sales for the first three months of the next year.

5. What action might management consider based on your findings in part b?

question 4 and 5

Answer 1

Question:- Plot the data. Does there seem to be a trend?

Answer:- If we look at the plotted graph there seems to be an increasing trend in the unit sold of the car.

900 800 Units Sold 700 600 500 400 300 200 100 0 Jan Feb. Mar Apr Мay. Jun. Jul Aug. Units Sold Oct Nov Dec Sept

Question- Deseasonalize car sales.

Answer:- The following formula will be sued for the deseasonalization of car sales

Deseasonalize car sales=unit sold/ index

Month	Units Sold	Index	Deseasonaled sale	Deseasonaled sale
Jan.	640	0.8	640/0.8	800
Feb.	648	0.8	648/0.8	810
Mar.	630	0.7	630/0.7	900
Apr.	761	0.94	761/0.94	809.5745
May.	735	0.89	735/0.89	825.8427
Jun.	850	1	850/1	850
Jul.	765	0.9	765/0.9	850
Aug.	805	1.15	805/1.15	700
Sept.	840	1.2	840/1.2	700
Oct.	828	1.2	828/1.2	690
Nov.	840	1.25	840/1.25	672
Dec.	800	1.25	800/1.25	640

Question:- Plot the deseasonalized data on the same graph as the original data. Comment on the two graphs

Answer:-

1000 900 800 700 600 500 Units Sold 400 - Deseasonaled sale 300 200 100 0 'uer Feb. Mar dvw May 'unr Jul any Sept AON Dec.

Once the deseasonalized data is plotted on the same graph, we will find a totally different pattern. In the case of deseasonalized data, there seems to be a decline in the number of units sold of cars.

Question:- Assuming no proactive approach on the part of management, discuss (no calculations necessary) how you would forecast sales for the first three months of the next year.

Answer:- As there was a decreasing trend in the sales of the car, thus in order to forecast the sales for the first three months of the next year, we can fit a monthly trend line to the deseasonalized values by assuming t=0 in the last month of the previous year. Then in order to find out the trend values for the next year’s first month i.e. January, we will put the value of t=13. Then we will multiply the trend value with the suitable monthly season relative. Similarly, the calculation can be done for the next two months by putting the values as t=14, and t=15

Question:- What action might management consider based on your findings in part b?

Answer:- As there is a downward trend in the findings of part b, the management must try something to boost the sales of the car. This can be done with the help of advertisement, sales promotion activities.