5. TARIFAS ELÉCTRICAS
5.2 ESTRUCTURA GENERAL DE LAS TARIFAS ELÉCTRICAS
and routes
Forecasting is important in all facets of business. A supermarket needs to forecast the demand for different types of cleaning agents, soft drinks and meat products. A car manufacturer has to forecast the demand for the different types of cars it produces. A farmer must forecast the demand for a variety of crops when deciding what to plant next spring. A government must forecast its tax revenue in order to design its budget each year. A business corporation needs to forecast the future requirement of different types of labour inputs, raw materials, machines and buildings as an integral part of its business processes. All business firms have to plan for the future. The success of a business firm is closely related to how well management is able to anticipate the future and develop suitable strategies. No business organization can function effectively without forecasts for the goods and services it provides and the inputs it purchases.
In project evaluation, the ‘cash flows’ of a proposed project refer to expected future cash flows of that project. The reference is not to past or historical data, but to future data expected from the proposed project. Perhaps the most critically important task in project appraisal is the forecasting of expected cash flows. The cash flows form the basis of project appraisal. If the cash flow estimates are not reliable, the detailed investment analyses can easily lead, regardless of the sophisticated project appraisal techniques used, to poor business decisions. Therefore, reliable estimates of cash flows by careful and diligent forecasting are critically important.
The estimation of cash flows for project appraisal may be viewed as having four main stages:
r forecasting the capital outlays and operating cash inflows (e.g. cash proceeds from product sales) and outflows (e.g. expenses) of the proposed project;
r adjusting these estimates for tax factors, and calculating the after-tax cashflows; r determining the variables which have the greatest impact on the project’s net present value
(sensitivity analysis); and
r allocating further resources, if necessary, to improve the reliability of the critical variables identified in the preceding stage.
Capital outlays of the project may be relatively easy to estimate. In many cases, they are made during the first year or the first few years of the project in its establishment stages.
Sales and operating expenses normally occur throughout the planning period for the project analysis. From the sales and operating expenses, net operating cash flows can be derived. By adjusting these estimates for tax factors, the after-tax cash flows can be calculated.
It is also important to identify all the variables that determine the cash flows and to assess which of those variables have the greatest influence on cash flows. These variables (which have the greatest influence on cash flows and hence on the project’s net present value) are usually called critical variables, because the values of these variables are critical to the project’s success or failure. An unexpected change in values of these variables can considerably affect the project’s expected NPV, turning a viable project into a non-viable one. Sensitivity analysis, which will be discussed in Chapter 8, is used to determine which variables have a pronounced effect on the project’s NPV.
Once these critical variables are identified, further resources may, if warranted, be allo- cated to obtaining more reliable forecasts of their future values. These variables require close monitoring both during the data acquisition process and after the project’s implementation, with a view to early intervention if necessary.
Managers can use sound judgement, 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. However, translating this feeling into numbers which can be used to represent the next five years’ sales, the next years’ raw material requirements, or the next ten years’ cash flows is often difficult. Knowledge of suitable forecasting methods and the ability to apply them can help managers to estimate future values now. Since the interest in capital budgeting is in medium- to long-term investment projects, the focus is on annual cash flow forecasts (and not on weekly, monthly or quarterly forecasts).
Forecasting is a highly complex and detailed subject. Some forecasting techniques involve a rigorous, formal methodology while some are more informal and subjective. Entire books have been written about forecasting, and a large number of forecasting techniques are available.
An analyst, who will use a selected technique or combination of techniques, may (depending upon the nature of the project) use different routes (or paths or procedures) to arrive at a set of forecasts. Selected techniques and routes which are widely used in capital budgeting forecasts are sketched in Figure 3.1.
Selected techniques (or methods) have been classified into two main groups, namely, quantitative and qualitative. As the ways of thinking for forecasting, two routes have been identified, i.e. top-down and bottom-up. This chapter will discuss the quantitative tech- niques and routes listed in Figure 3.1. Chapter 4 will discuss qualitative (or judgemental) techniques, examples of which are again listed in Figure 3.1. Given the special features associated with forestry projects and property investments, cash flow forecasts will be re- visited in the specific contexts of forestry project evaluation, in Chapters 10 and 13, and property investment analysis, in Chapter 15.
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
Figure 3.1. Forecasting techniques and routes
Study objectives
After studying this chapter the reader should be able to:
r evaluate the suitability of several quantitative forecasting techniques for a given project r employ a selected technique or combination of techniques to forecast cash flows for a
given project
r identify a suitable forecasting route for estimating cash flows for a given project.
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 behaviour of a single variable over a period of time. These relationships or behaviours are then used for making forecasts.
Forecasting with regression analysis
Regression equations attempt to explain the behaviour of a selected dependent variable by the behaviour of one or more independent (or explanatory) variables. For example, the behaviour of sales (units) of a particular brand of car may be dependent on four explanatory variables – personal income, the price and advertising expenditure of that brand and the price of its closest substitute brand.
In order to forecast the future values using an estimated regression equation, it is first necessary to identify the variables which explain the historical behaviour of the depen- dent variable. If the historical values for the relevant variables can be collected, an appro- priate regression equation can be estimated using, for example, the ordinary least squares (OLS) technique. If the future values of the explanatory (or independent) variables of
Table 3.1. Desk sales and number of households
Desks sold Number of households
Year Y X 1992 50,010 26,500 1993 47,500 26,600 1994 53,410 27,000 1995 56,005 27,800 1996 52,605 28,300 1997 58,015 29,010 1998 61,900 31,500 1999 66,005 32,300 2000 72,200 32,900 2001 68,000 33,100
this regression equation can be predicted, those values can then be used to forecast the future values of the dependent variable. For example, car sales can be forecast by substi- tuting the future values of the explanatory variables into the estimated car sales regression equation.
When the dependent variable being forecast is largely influenced by a single explana- tory variable, the two-variable regression model – one explanatory variable explaining the behaviour of the dependent variable – is used. When the variable being forecast is influ- enced by two or more explanatory variables, the multiple regression model – two or more variables explaining the behaviour of the dependent variable – is used.
The two-variable regression model
Two-variable (or simple) regression analysis is best explained using an example. A desk- manufacturing company, Top Desk Inc., has experienced, over the last decade or so, a gradual increase in demand for its desks. The company finds that this increase is caused by the gradual increase in the number of households in the region over time. Desk sales and number of households for the period 1992–2001 are presented in Table 3.1. Top Desk’s research and development department has access to a set of reliable population projections for the next five years and believes that the past pattern of increase in the number of house- holds in the region will continue over the next five years. Research also suggests that no (desk-manufacturing) competitor is expected to enter this particular market for at least the next five years provided Top Desk continues to satisfy the market. The company is considering expanding its capacity to meet the increasing demand by investing a consid- erable sum of capital. This is the proposed project for which cash flow forecasts are being sought. As a first step, Top Desk wants to forecast the demand for its desks for the next five years.
Since the past trend is expected to continue in the future and one single variable (the number of households) seems to influence the desk sales, the project analyst would use
simple regression analysis. In this case, the form of the regression equation is: Y =α+βX+U
where:
Y = the dependent variable, which is Top Desk’s annual desk sales
X = the independent (or explanatory) variable, which is the number of house- holds in the region.
α= a parameter of the regression equation called the regression intercept β = a parameter of the regression equation called the regression slope or
regression coefficient
U = stochastic disturbance, or error term.
The error term U is also called the random (or stochastic) disturbance since it disturbs an otherwise deterministic relation. This error term is a surrogate for all those variables which may have negative and positive influences on Y. The expected (or average) value of these influences is assumed to be zero.
The values of the two parameters in the above regression equation can be estimated using the ordinary least squares (OLS) regression technique, which is widely used in statistical estimation and forecasting. The data set in Table 3.1 is used for illustration.
Workbook 3.1
The regression function in Excel is used for estimating the regression equation with the data in Table 3.1. This function is found in Excel under the Tools, Data Analysis menu. Following the insertion of appropriate data for input Y and input X, regression analysis can be performed. The Excel regression output is held in Workbook 3.1. Using selected data from the Excel output, the regression equation (along with relevant test statistics) can be written as:
ˆ
Y= −28,326+2.945 X R2=0.92 (−3.2) (9.9)
The values in parentheses are t values, which are used to test whether the coefficient estimates are statistically significant. R2is a measure of overall ‘goodness of fit’ of the regression
equation.
The estimated value ofα, the regression intercept, is −28,326, andβ, the regression slope is 2.945.
The details pertaining to various statistical significance tests of regression models are found in most statistics and econometric textbooks. Two examples are Kmenta (1990) and Gujarati (1995). In this capital budgeting textbook, it is not intended to go into the details of statistics. As a rule of thumb, for samples of more than ten observations, it is quite safe to assume that if the t value is greater than two, the coefficient is statistically significant, and if it is less than two, the relevant coefficient is not statistically significant (meaning it cannot
be declared different from zero).1For example, the t value for the coefficient estimate 2.945 is 9.9, suggesting the estimate is strongly (statistically) significant.
The t value for the intercept estimate−28,326 is−3.2, indicating that the estimate is statistically significant. The value of the intercept indicates the average level of desk sales when the number of households is zero. However, this is a mechanical interpretation of the intercept term and, in regression analysis, such literal interpretation of the intercept term may not always be meaningful. Very often we cannot attach any physical meaning to the intercept (Gujarati, 1995, pp. 82–4). Except in cases where the regression analysis is deliberately set up to emphasize the intercept value, statistical significance tests on the intercept or interpretation of its value are not generally important or relevant. In our example, it does not make much sense to interpret the intercept value. The sample range of the explanatory variable (number of households) does not include zero as one of the observed values.
For the purpose of forecasting, the statistical significance of individual coefficients is not as important as the regression equation as a whole. To test the statistical significance of the regression equation as a whole, we can look at the value of R2, the coefficient of determination. A regression with an R2 value close to 1 is preferred. As a rough guide,
regressions with R2greater than 0.6 are accepted as reasonable for forecasting purposes in
industrial research.
The (adjusted) R2 value of 0.92 says that 92% of the variation in the dependent (or
explained) variable Y is explained by the independent (or explanatory) variable X, number of households.
The estimated equation (presented above) can be used to forecast sales of desks. This will be illustrated later in this section.
The multiple regression model
In the two-variable regression model, there was only one independent (or explanatory) variable. In many situations, the behaviour of a given variable is explained not by a single independent variable but by a number of variables. An example is the sales of a particular brand of car, mentioned earlier. Also in the Top Desk example, the desk sales may be influenced not only by the number of households but also by household income.
Here we consider the multiple regression model which enables the incorporation of more than one explanatory variable in the regression. 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:
Y=α+β1X1+β2X2+U
A multiple regression equation with three explanatory variables may be written in the form: Y =α+β1X1+β2X2+β3X3+U
1 More precisely, the critical value of the t-statistic for rejecting the null hypothesis that a parameter differs from
zero (in a two-tailed test) approaches 1.96 as the sample size approaches infinity. If the null hypothesis is rejected, it may be concluded (though some uncertainty still remains) that the coefficient in the underlying time series ‘population’ is not zero.
Table 3.2. Desk sales, number of households and average household income
Desks sold Number of households Income ($)
Year Y X1 X2 1992 50,010 26,500 39,300 1993 47,500 26,600 36,600 1994 53,410 27,000 40,000 1995 56,005 27,800 40,500 1996 52,605 28,300 41,450 1997 58,015 29,010 43,500 1998 61,900 31,500 42,500 1999 66,005 32,300 47,200 2000 72,200 32,900 51,400 2001 68,000 33,100 49,000
Let us now estimate a three-variable multiple regression (which has one dependent vari- able and two explanatory variables). To illustrate a multiple regression and, at the same time, to show how the regression coefficient values change when another variable is added, another variable, household income, is added as X2to the data in Table 3.1. The new data
set is presented in Table 3.2. Workbook
3.2
Again, Excel’s regression function is used to estimate the regression. The full Excel regression output can be viewed in Workbook 3.2.
Using selected Excel output, the regression equation (along with the relevant test statis- tics) can be written as:
ˆ
Y= −24,237+1.426 X1+0.944 X2 R2=0.96
(−3.86) (2.67) (3.09)
Notice the change in the X1slope coefficient (from 2.945 to 1.426). Compared to the two-
variable regression estimate, the multiple regression seems to improve slightly the R2(from
0.92 to 0.96) as a result of the addition of another explanatory variable. Both regression estimates are highly statistically significant. In this case, either of the two equations can be used for forecasting purposes. The assumption, of course, is that population and income projections are available.
Forecasting using regression results
Assume that the company wants to forecast desk sales for the next five years, 2002–2006, and the relevant household and income projections are available. These data are presented in Table 3.3.
Table 3.3. Household and income projections, 2002–2006
Number of households Income ($)
Year X1 X2 2002 35,000 52,000 2003 35,990 54,100 2004 37,000 55,000 2005 38,500 56,970 2006 39,800 58,000
Table 3.4. Desk sales forecasts using two-variable and multiple regressions
Sales forecasts using
Household projections Household and income projections
Year X1 X1and X2 2002 74,749 74,761 2003 77,665 78,155 2004 80,639 80,445 2005 85,057 84,444 2006 88,885 87,270
Using either the two-variable or the multiple regression analysis, the expected number of desk sales can be forecast. The results from Workbook 3.2 are reproduced in Table 3.4. As an illustration of the mechanics of producing these forecasts, the estimation of the first figure using both one-variable and multiple regressions is shown below:
Workbook 3.2
Forecast for year 2002 using two-variable regression: ˆ
Y = −28,326+2.945 (35,000)=74,749 Forecast for year 2002 using multiple regression:
ˆ
Y = −24,237+1.426 (35,000)+0.944 (52,000)=74,761
The two forecasting models provide similar estimates in this particular case and, there- fore, either set of forecasts can be chosen. In reality, however, forecasts produced from two models can vary considerably. In such situations, the two sets of forecasts can be used in two alternative scenarios of the project when a project is analysed under different scenarios.
The reliability of the forecast values depends on the reliability of the predicted values for the explanatory variables. Often, the values for the predictors are readily available. For example, population and household income projections as well as other leading statistical indicators of the economy or industrial performance are readily available from reliable sources for most of the countries in the world.
If the past pattern is expected to continue into the future, regression models can provide reasonable forecasts for the key cash flow variables. It is also worth noting here that if turning points in the predictors can be foreseen, then turning points in cash flow variables can also be predicted.
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. In the preceding example, predictions were available for both the number of households and income. When such predictions are not available and when the time series exhibits a long-term trend, time-trend projections can be used for forecasting. Time-trend projections are flexible and may be used both for short-term or long-term forecasts. Time-trend forecasts are particularly suitable for time series which exhibit a consistent increase or decrease over time and where the past pattern is expected to continue in the future.
The time-trend method may be viewed as a special case of simple regression analysis