Group MembersAfaq Ali Siddiqui Aisha Siddiqua Bajwa Abdul Wadood Maria Rabbani Sara Tahir Shahid Iqbal Atif Hussain Badar Siddiqui Faisal Javed Siddiqui Ghazala Rehman Hasan Muiz Waqas Mehmood.

Points for PresentationIntroduction Methodology Outlier Considerations Decomposing the Sales Data De-Seasonalizing the Sales Data Measuring the Sales Trend Measuring the Cyclic Effects Making the Sales Forecast Summary and Final Remarks

IntroductionThis case discusses the practical role of sales forecasting for the small business concern. We have discussed an actual business case from a realistic perspective by noting circumstances which do come up in the real world. Selection and implementation of the proper sales forecast methodology is important in planning and control issue for most profit maximizing firms and agencies.

Introduction Cont.Over or-under sales forecast error may cause the firm to be with excess inventory carrying cost resulting in lost sales. Most qualified departments are assigned the forecasting task. Accuracy of forecast is most significant. Stable demand means easier forecasting Our forecasting approach can be used by any size firm.

MethodologyTwo main methods:

Explanatory method Extrapolation method

Our focus on extrapolation method-easier and accurate Scientifically valid, easy-to-follow and implement procedure

WOMETCO CorporationNot having much financial and technical expertise But having control and better communication Considering recent three years sales data for 1982, 1983 and 1984 that reflects the current business situation. Sales time unit divided into 4 week periods

CCC=DSO+DSI-DPO

Sales Time Series DataPeriod 1 2 3 4 5 6 7 8 9 10 11 12 13 1982 sales 171 422 191 033 193 991 207 399 205 494 197 367 208 396 214 413 200 260 187 900 182 203 180 789 171 892 1983 sales 170 006 196 112 200 181 211 874 219 528 215 573 232 726 236 883 221 034 216 940 206 932 198 068 189 484 1984 sales 189 863 205 745 213 248 228 480 231 781 237 120 254 384 253 862 232 810 226 728 223 668 218 328 209 008

WOMETCO Vending Machine Sales300 250 200 150 100 50 0 1 14 27

Original Sales

Analysis of the DataWithin each year, an initial period of sales growth. Followed by a decline. Between years, a general increase in sales. Mid-1982 sales data differs from 1983 and 1984.

Outlier ConsiderationThe sharp decline in period 6 of 1982 is a unique occurrence. Similar sales levels too high or too low are called Outliers. Outliers are not considered when making new forecasts. For it we have 2-choices: 1) To replace the outlier by taking average of immediate values on both sides of it(if outlier in middle or recent part). 2)Throw away sales data up to and including the Outlier (Period 1-6 sales)- (if in early oldest part).

Decomposing Sales DataFOR A PROPER FORECAST We must first understand and measure the components influencing sales !!

Decomposing Sales DataFour sale components in time series analysis influencing sales (fluctuations): Seasonalities repeat from year to year with same timing and level of intensity Growth or Decay TRENDS increase or decrease steadily over time Cyclic Oscillations due to overall economic environment(independent of seasonal effect) Irregularities other than above.

Decomposing Sales DataSale components must initially be removed from raw data (decomposition) Then effects are measured. Finally, putting them back on new sales estimates(re-composition).

Steps for ForecastingWe will proceed with the following steps before forecasting and future values.STEP # 01: Computing the seasonal effects on sales values. STEP # 02: De-Seasonalizing the sales values. STEP # 03: Computing/Calculating the overall sales trend. STEP # 04: Computing the Cyclical effects on sales. STEP # 05: Forecasting for Future values.

01- Measuring Seasonal EffectsSTEP # 01: Computing a centered 13-period moving average for all possible periods for all given years. STEP # 02: Compute the ratio of actual sales in each period to the moving average in Step#01. STEP # 03: Average above ratios for 1-13 for all given periods. STEP # 04: Correct the averaged ratios from step # 03 for possible round-off error to get the 13 period seasonal index set.

02- De-Seasonalizing the DataSTEP # 01: Divide the original sales by the seasonal indexes (as in step # 04 previously) to get the de-seasonalized sales level.

Data After De-Seasonalizing.

De-Seasonalized Sales Data on Forecasting Graph.

03- Measuring the Sales TrendUsing the de-seasonalized data, we can consider the growth trend by making the trend line. This sales trend line will represent the overall linear trend of sales growth over time

03- Measuring the sales trendTrend line equation: Y=A+BX where Y=predicted sales level A=vertical intercept of trend line equation B=sales growth rate per period (ie slope of the trend line equation) The trend line equation for WOMETCO case is: Y=186731.2+1450.74(X) . where X = Period - 6

Sales Trend Data

Sales Trend Graph

04- Cyclic Effects Calculations:STEP # 01: Divide the De-Seasonalized sales with the sales trend. The cyclic index thus obtained will be the percentage of sales greater or less than the sales of the same period. STEP # 02: Calculate 3-period moving average to balance out the larger variations in the index. This is also known as index smoothening.

Cyclic Effects Data

and so on

Cyclic Effects on Forecasting Graph.Plotting of Cyclic Indexes(For All Periods): As the Business Cycle is longer than Seasonal Cycle, understanding of Cyclic Analysis is not expected as accurate as Seasonal Analysis. Due to Economic Factors A General Approximation of Cyclic Sales factor is more realistic aim.

Cyclic Effects on Forecasting Graph.

Cyclic Effects on Forecasting Graph.Evaluating the Individuality of the Index Plot:Similar MagnitudeAccruing of Cyclic peaks in period 12 & 33, and 4 & 27. But parts of different business cycle. Much of index plot lies between 100-103%.

Cyclic Effects on Forecasting Graph.Conclusion:The cycle repeats itself i.e. the Cyclic Length is about 24 periods. After stable period between 100-103%, a cyclic decline starting in about the 16th period of the cycle. In order to make Sales Forecast, we project the Approximate Continuation of this cycle curve into the next few periods of 1985.

05- Making the sales forecastNow we can make sales forecast for the next few periods after studying all the sales components. The following steps are included in this procedure: Compute the future sales trend level using the trend line equation Multiply the sales trend level from step 1 by the period seasonal index to include seasonal index. Multiply the result of step 2 by the projected cyclic index to include cyclic effects and get the final forecast result.

Making the Sales ForecastSales Forecast for next three periodsPeriod 1985 a Period (X) b Predicted (trend ) sales c Seasonal index (%) (From column e of table 3) 1 2 3 34 35 36 236056.36 237507.10 238957.84 86.1 95.7 97.9 d= b.c Estimate d sales with trend & seasonal effects 203244.5 2 227294.2 9 233939.7 2 e Projecte d cyclic index (%) f= d.e Sales forecast for next period

102.5 101.5 101.0

208326 230704 236279

Making the sales forecastSales Forecast for next three periods

Predicted (Trend) salesY=186731.2+1450.74(x)

Y= 1836731.2+1450.74(34)=236056.36 Y= 1836731.2+1450.74(35)=237507.10 Y= 1836731.2+1450.74(36)=238957.84

Summary and Final RemarksOutset statement Alternative method of relevant components of sales variation. Sales forecasts by recombining these components . Mathematical calculations plus managements firsthand knowledge can lead to logical and justified new sales estimates. Based on the relative complexity of more inclusive but very sophisticated forecasting techniques, we recommend that management go through an evolutionary progression in adopting new forecasting techniques. This is to say, a simple forecast method well understood is better implemented than one with all inclusive features but unclear in certain facets.

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