1. 1 Ch 3: Forecasting: Techniques and Routes

2. 2 Study objectives After studying this chapter the reader should be able to: Evaluate the suitability of several quantitative forecasting techniques for a given project Employ a selected technique or combination of techniques to forecast cash flows for a given project Identify a suitable forecasting route for estimating cash flows for a given project.

3. 3 Introduction The cash flows form the basis of project appraisal. The most critically important task in project appraisal is the forecasting of expected cash flows. Forecasting is the establishment of future expectations by the analysis of past data, or the formation of opinions.

4. 4 Capital budgeting requires the commitment of significant funds today in the hope of long term benefits. The role of forecasting is the estimation of these benefits. Introduction Managers can use sound judgment, intuition and awareness of the state of the economy to obtain an idea or a ‘gut feeling’ of what is likely to happen in the future Forecasting is a highly complex and detailed subject.

5. 5 Introduction The estimation of cash flows for project appraisal may be viewed as having four main stages: 1. Forecasting the capital outlays and operating cash inflows (e.g. cash proceeds from product sales) and outflows (e.g. expenses) of the proposed project; 2. Adjusting these estimates for tax factors, and calculating the after-tax cashflows; 3. Determining the variables which have the greatest impact on the project’s net present value (sensitivity analysis); and 4. Allocating further resources, if necessary, to improve the reliability of the critical variables identified in the preceding stage.

6. 6 Introduction It is important to identify all the variables that determine the cash flows and to assess which of those variables are critical variables (have the greatest influence on cash flows) because the values of these variables are critical to the project’s success or failure

7. 7 Forecasting Techniques and Routes Techniques Routes Top-down route Bottom-up route Quantitative Qualitative Simple regressions Multiple regressions Time trends Moving averages Delphi method Nominal group technique Jury of executive opinion Scenario projection

8. 8 Quantitative techniques Quantitative techniques can be used when:- 1. Past information about the variable being forecast is available, and 2. Information can be quantified. These techniques use quantitative data and quantitative methods to estimate relationships between variables or to identify the behavior of a single variable over a period of time. These relationships or behaviors are then used for making forecasts.

9. 9 Forecasting with regression analysis Regression equations attempt to explain the behavior of a selected dependent variable by the behavior of one or more independent (or explanatory) variables. For example, the behavior of sales (units) of a particular brand of car may be dependent on four explanatory variables:- Personal income The price of that brand Advertising expenditure of that brand The Price of its closest substitute brand.

10. 10 Quantitative Forecasting Quantitative: Regression with related variable Data set of Desk ‘Sales’ as related to both time and the number of households.

11. 11 Quantitative Forecasting Quantitative: Sales plotted related to households.

12. 12 Quantitative Forecasting

13. 13 Quantitative Forecasting Quantitative: Sales regressed on households. Predicting with the regression output. Regression equation is: Sales(for year) = 587.11 + ( 3.316 x households). Assuming that a separate data set forecasts the number of households at 1795 for the year 2006, then: Sales(year 2006) = -587.11 + ( 3.316 x 1795) = 5365.11units.

14. 14 Quantitative Forecasting The multiple regression model In the two-variable regression model, there was only one independent (or explanatory) variable. In many situations, the behavior of a given variable is explained not by a single independent variable but by a number of variables

15. 15 Quantitative Forecasting The multiple regression model A multiple regression equation has one dependent variable (Y) and two or more explanatory variables. For example, a multiple regression equation with two explanatory variables may be written in the form: A multiple regression equation with three explanatory variables may be written in the form:

16. 16 Let us now estimate a three-variable multiple regression (which has one dependent variable and two explanatory variables). Sales as a function of both Income and the number of households. Quantitative Forecasting Multiple Regression

17. 17 Quantitative Forecasting Multiple Regression HISTORICAL DATA YEAR SALESHOUSEHOLDSINCOME 1991 50,01026,50039,300 1992 47,50026,60036,600 1993 53,41027,00040,000 1994 56,00527,80040,500 1995 52,60528,30041,450 1996 58,01529,01043,500 1997 61,90031,50042,500 1998 66,00532,30047,200 1999 72,20032,90051,400 2000 68,00033,10049,000

18. 18 Multiple Regression

19. 19 Quantitative Forecasting Multiple Regression Predicting with the regression output. Regression equation is: Sales (for year) = - 24237 + ( 1.43 x households) + ( 0.94 x Income).. Assume that the company wants to forecast desk sales for the next five years, 2002–2006, and the relevant household and income projections are available. These data are presented

20. 20 Multiple Regression

21. 21 Quantitative Forecasting Multiple Regression Predicting with the regression output. Regression equation is: Sales (for year) = - 24237 + ( 1.43 x households) + ( 0.94 x Income).. The reliability of the forecast values depends on the reliability of the predicted values for the explanatory variables

22. 22 Forecasting with time-trend projections One basic requirement when using regression analysis for forecasting is the availability of predictions for the explanatory variable or variables. When such predictions are not available and when the time series exhibits a long-term trend, time-trend projections can be used for forecasting The time-trend method may be viewed as a special case of simple regression analysis where the independent variable is ‘time’.

23. 23 Time-trend projections

24. 24 Time-trend projections

25. 25 Time-trend projections

26. 26 Forecasting using smoothing models The earlier discussion of regression and time-trend models applies to situations where the historical time series exhibits a trend. When the historical time series does not exhibit a significant trend, smoothing models can be used for forecasting because these models adapt well to changes in the level of the time series. These models are particularly suitable for situations where the more recent observations are more indicative of future values

27. 27 Advantages Easy to use Provide reasonable forecasts for the short- to medium-term forecasting periods Disadvantages They will not catch turning points since the basis of the forecast is nothing but a weighted average of the historical data. They are not suitable for a project concerned with a new product Forecasting using smoothing models

28. 28 smoothing models Simple moving average (SMA) Consider the hypothetical sales data for the past twelve years in Table 3.6, There is no trend apparent in these data. The simple moving average (SMA) uses the average of the n most recent values in the time series as the forecast for the next period. Choosing n = 3, three-year moving averages have been calculated using Excel and are shown in Table 3.6

29. 29 Table 3.6. Hypothetical sales data and calculation of simple moving average

30. 30 smoothing models Simple moving average (SMA) How to choose the value of n? If four-year moving averages are used, different forecasts will be obtained. In practice, values of n in the range three to five are often used. The Excel spreadsheet makes it easy to obtain sets of moving averages using different values for n. Then, the n which yields the minimum MSE can be selected for calculating the moving averages

31. 31 smoothing models Simple moving average (SMA)

32. 32 smoothing models Weighted moving average (WMA) In SMA, each observation in the calculation receives equal weight. In the weighted moving average (WMA), different weights are assigned to the values in the time series. For example, if the decision-maker believes that recent values are more important than less recent ones in arriving at forecasts, greater weight can be given to these.

33. 33 For example, using the sales data set in Table 3.6, the sales for year 13 could be forecast by taking the three-year WMA. The allocation of weights is as follows: A weight of 0.6 for the most recent observation (which is 49,000), 0.3 for the next older observation (which is 41,000) and 0.1 for the oldest observation (which is 50,000). Then the three-year WMA for the period of years 10–12 is: smoothing models Weighted moving average (WMA)

34. 34 Exponential smoothing The basic exponential smoothing model is: