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Ch 3:

Forecasting:Techniques and Routes

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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.

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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.

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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.

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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.

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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

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Forecasting Techniques and Routes

Techniques

Routes

Top-down routeBottom-up route

Quantitative

Qualitative

Simple regressionsMultiple regressionsTime trendsMoving averages

Delphi methodNominal group techniqueJury of executive opinionScenario projection

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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.

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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.

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Quantitative Forecasting Quantitative: Regression with related variable

Data set of Desk ‘Sales’ as related to both time and the number of households.

YEAR HOUSEHOLDS SALES1991 815 21091992 927 25301993 1020 22871994 987 31941995 1213 37851996 1149 33721997 1027 36981998 1324 39081999 1400 37252000 1295 41292001 1348 45322002 1422 4487

HISTORICAL DATA

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Quantitative ForecastingQuantitative: Sales plotted related to households.

SalesUnits Related to Number of Households

0

1000

2000

3000

4000

5000

0 500 1000 1500

Number of Households

Sa

les

Un

its

Sales

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Quantitative ForecastingSUMMARY OUTPUTSALES REGRESSED AS A FUNCTION

OF HOUSEHOLDSSUMMARY OUTPUT

Regression StatisticsMultiple R 0.874692094R Square 0.76508626 <== "Strength" of the regressionAdjusted R Square0.741594886Standard Error 411.9646302Observations 12

ANOVAdf SS MS F Significance F

Regression 1 5527412 5527412 32.56882 0.000196Residual 10 1697149 169714.9Total 11 7224561

Coefficients Standard Errort Stat P-value Lower 95%Intercept -587.111 722.4612 -0.812654 0.435336 -2196.855X Variable 1 3.504 0.614007 5.70691 0.000196 2.135989

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Quantitative ForecastingQuantitative: 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.

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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

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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:

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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

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Quantitative Forecasting Multiple Regression

HISTORICAL DATA

YEAR SALES HOUSEHOLDS INCOME

1991 50,010 26,500 39,300

1992 47,500 26,600 36,600

1993 53,410 27,000 40,000

1994 56,005 27,800 40,500

1995 52,605 28,300 41,450

1996 58,015 29,010 43,500

1997 61,900 31,500 42,500

1998 66,005 32,300 47,200

1999 72,200 32,900 51,400

2000 68,000 33,100 49,000

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Multiple Regression

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.983915573R Square 0.968089856Adjusted R Square 0.958972672Standard Error 1662.054711Observations 10

ANOVAdf SS MS F

Regression 2 586645269 293322634 106.1829888Residual 7 19336981.04 2762425.9Total 9 605982250

Coefficients Standard Error t Stat P-valueIntercept -24237.63048 6265.223546 -3.868598 0.006142807HOUSEHOLDS 1.425923969 0.533977813 2.6703806 0.03198204INCOME 0.944175397 0.305915979 3.086388 0.017656284

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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

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Multiple Regression

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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 valuesfor the explanatory variables