Sales Forecast
Transcript: SALES FORECAST By : WIDAD EL HAMDI INTRODUCTION In this table, Company X presents its quarterly sales statistics for the last 4 years. It is requested to provide sales forecasts for the following year. INTRODUCTION Graphical Representation => The graphical representation of sales let appear: -A general sales growth trend -A marked seasonality of sales => Sales forecasting process is based on the determination of the general trend as well as the seasonality phenomenon. Graphical Representation of Sales Determination of the General Sales Trend General Sales Trend Methods used to research the general sales trend: Manual adjustment: very simple process but not very precise. Double Moving Average (DMA): Slightly more sophisticated but still very simple method. Calculation of centered moving average Centered Moving Average Graphical Representation of the Evolution of Moving Averages Graphical Representation The graph clearly shows that the evolution of sales follows a linear trend. Determination of the linear regression line To adjust sales by a linear regression line, we have an equation of the form Y = a X+ b, where y represents sales, x the rank of the quarter, and a and b the coefficients to be determined by the following equations: Linear Regression Line The following table summarizes the data required for this calculation: CALCULATION By applying the formulas, we find: linear regression line y = 9.6 x+437.4 => If the trend does not follow a linear pattern, it becomes necessary to use another model or at least to reduce the model to a linear pattern if possible. Exponential Trends & Power Trends Non-Linear Trend Exponential Trends : e.g: the following table shows the sales of a product for the last 6 quarters. Exponential Trends The graphical representation of sales: An acceleration in sales growth is clearly visible. => Calculation of the logarithmic base 10 of sales. CONFIRMATION => The curve corresponds fairly well to a linear model. RESULT The sales equation as a function of time is expressed as: This sales equation can be written as: log y = log b + x log a We put : Log y = Y Log b = B Log a = A It becomes then: Y = B + Ax So Y = Ax + B => Which leads us back to a linear form. Power trends: Power Trends The power function is of the form: The use of logarithms lets writing: log y = log b + a log x We put: Log y = Y Log b = B Log x = X It becomes then: Y = a X + B => Which leads us back to a linear form. Forecast Seasonal Phenomenon & Forecast - The seasonal phenomenon: Seasonal Phenomenon Methods for determining seasonal coefficients : The method of periodic averages The trend ratio method => The seasonal coefficients are slightly different depending on the methodology followed. Quarter 1 : Sales average of Q1 Q1 = (524 +532 + 556 + 660) / 4 = 568 Coef Q1 = 568 / 519 = 1.095. Quarter 1 therefore represents 109.4% of an "average" quarter. In the same way, we obtain the coefficients for the other three quarters: Q2 = 426/519 = 0.821 Q3 = 390/519 = 0.751 Q4 = 692/519 = 1.333 The sum of the coefficients is equal to 4. Method of Periodic Averages Method of Periodic Averages We will calculate for each observation the ratio between the observed value and the value determined according to the linear adjustment, i.e. Trend Ratio Method Trend Ratio Method Example: For the first quarter of N-4, the value given by the adjustment is equal to: yˆ= (9.6 x1) + 437.4 = 447 The seasonal index is therefore equal to : I= 524/447 = 1.17 Forecast Quarterly forecasts will be given by the following calculations. Fi = (axi + b) x Ci Example: For the first quarter of year N (quarter 17), we will have: P17 = ((9.6 *17)+437.4)*1.13 = 676.23 Overall, we obtain the following sales forecasts for the four quarters: Q1 I 676,23 Q2 I 505,54 Q3 I 461,83 Q4 I 818,73 Forecast