dev 567 project and program analysis lecture 2: forecasting cash flows

Dev 567Project and Program Analysis

Lecture 2: Forecasting Cash Flows

Dr. M. Fouzul Kabir KhanProfessor of Economics and Finance

North South University

• Quantitative forecasting

• using univariate regression model

• using multivariate regression model

• Forecasting using smoothing models

• Time series forecasting methods

• Steps in quantitative forecasting

• Qualitative forecasting

• Forecasting routes

• Mini quiz and review

Forecasting techniques and routes

• Forecasting is the establishment of future expectations

by the analysis of past data, or the formation of opinions.

• Forecasting expected cash flows is an essential element

of capital budgeting.

• 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.

Forecasting: Techniques and Routes

Forecasting Techniques and Routes

Techniques Routes

Top-down routeBottom-up routeQuantitativ

eQualitative

•Simple regressions•Multiple regressions•Time trends•Moving averages

•Delphi method•Nominal group technique•Jury of executive opinion•Scenario projection

Four stages:

◦ Forecasting the capital outlays and operating cash inflows and outflows of the proposed project

◦ Adjusting these estimates for tax factors and calculating after tax cash flows

◦ Conducting sensitivity analysis◦ Allocating further resources, if necessary

Cash Flow Estimation for Project Appraisal

Quantitative Techniques•Use of quantitative techniques is possible, when

–Past information about the variable being forecast is

available; and

–Information can be quantified•Use quantitative data and 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 to make

the forecasts.

Data types

Dependent and independent (or explanatory) variables

Car sales, personal income, the price, price of its close

substitute brand, advertising

Identify and collect historical values of the variables

OLS techniques

◦ Two-variable regression model, one explanatory variable

explaining the behavior of the dependent variable

◦ Multiple regression model, two or more variables

explaining the behavior of the dependent variable

Forecasting with Regression Analysis


Original Data SetYear Desks Number of

Sold Households[Y Axis] [X Axis]

1992 50,010 26,5001993 47,500 26,6001994 53,410 27,0001995 56,005 27,8001996 52,605 28,3001997 58,015 29,0101998 61,900 31,5001999 66,005 32,3002000 72,200 32,9002001 68,000 33,100

Y = α + βX + μ

Where:

Y= the dependent variable, desks sold

X= The independent or explanatory variable, number of

households

α = a parameter of the regression equation called the regression

intercept

Β = a parameter of the regression equation called the slope or

regression coefficient

μ = stochastic disturbance or the error term

The Two Variable Regression Model

Two variable regression modelWorkbook3.2.xls


Two Variable Regression Results

Two-Variable Regression ResultsSUMMARY OUTPUT Regression Statistics

Regression StatisticsMultiple R 0.961595373R Square 0.924665662Adjusted R Square0.91524887Standard Error 2388.809108Observations 10

ANOVAdf SS MS F Significance F

Regression 1 560330978 5.6E+08 98.19327 9.0856E-06Residual 8 45651271.6 5706409Total 9 605982250

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0%Upper 95.0%Intercept -28326.26291 8801.17891 -3.218462 0.012267 -48621.831 -8030.695 -48621.83 -8030.695X1 2.945366696 0.29723401 9.909252 9.09E-06 2.2599434 3.63079 2.259943 3.63079

Given the regression estimateY = -28,326 + 2.945 X, R2

= 0.92

(-3.2) (9.9)Calculate desk sales for the year 2002.

Exercise I


Given Household and Income Projections Calculated Forecast Desk SalesFrom Two-Variable Regression

ForecastYear Households Income Year Desk

Sales2002 35,000 52,000 2002 74,7492003 35,990 54,100 2003 77,6642004 37,000 55,000 2004 80,6392005 38,500 56,970 2005 85,0562006 39,800 58,000 2006 88,885

Quantitative: Sales regressed on households.

Predicting with the regression output.

Regression equation is:Sales(for year) = -28,326 + 2.945 ( households).

Assuming that a separate data set forecasts the number of households at 1795 for the year 2002, then:

Sales(year 2002) = -28,326 + 2.945(35,000)

= 74,749 units.

Quantitative Forecasting


Enhanced Data SetDesks Number of Income

Sold Households[Y Axis] [X Axis] [X Axis 2nd Var.]50,010 26,500 39,30047,500 26,600 36,60053,410 27,000 40,00056,005 27,800 40,50052,605 28,300 41,45058,015 29,010 43,50061,900 31,500 42,50066,005 32,300 47,20072,200 32,900 51,40068,000 33,100 49,000

Y = α + β1X1 + β2X2 + μ

Where:

Y= the dependent variable, desks sold

X1= The independent or explanatory variable, number of

households

X2 = The independent or explanatory variable, income

α = a parameter of the regression equation called the regression intercept

β1, β2 = parameters of the regression equation called the slope or

regression coefficient

μ = stochastic disturbance or the error term

The Multiple Regression Model

Multiple Regression Results

Multiple Regression ResultsSUMMARY OUTPUT

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


Regression 2 586645269 2.93E+08 106.183 5.8E-06Residual 7 19336981.04 2762426Total 9 605982250

Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept -24237.63048 6265.223546 -3.868598 0.006143 -39052.52 -9422.742 -39052.52 -9422.742X1 1.425923969 0.533977813 2.670381 0.031982 0.163268 2.68858 0.163268 2.68858X2 0.944175397 0.305915979 3.086388 0.017656 0.2208 1.667551 0.2208 1.667551

The multiple regression modelWorkbook3.2.xls


Given the regression estimateY = -24,237 + 1.426 X1+0.944X2,R2

= 0.96

(-3.86) (2.67) (3.09)X1 and X2 are number of households and

income respectivelyCalculate desk sales for the year 2002.

Exercise II


Given Household and Income Projections Calculated Forecast Desk SalesFrom Multiple Regression

ForecastYear Households Income Year Desk

Sales2002 35,000 52,000 2002 74,7612003 35,990 54,100 2003 78,1552004 37,000 55,000 2004 80,4452005 38,500 56,970 2005 84,4442006 39,800 58,000 2006 87,270

Quantitative Forecasting: Using Multiple Regression

Multiple regression equation is:

Sales in year = -24,237 +1.426 (households) + 0.944(Income)

Forecast of sales for the year 2002 is:Sales in year 2002 = -24,237 + 1.426(35,000)+

+ 0.944(52,000) = 74,761 Units

Forecasting using regression results(Workbook 3.3)



Original Data SetYear Time Desks

Counter Sold"T" [X Axis] [Y Axis]

1992 1 50,0101993 2 47,5001994 3 53,4101995 4 56,0051996 5 52,6051997 6 58,0151998 7 61,9001999 8 66,0052000 9 72,2002001 10 68,000

Forecasting with time-trend projections


Forecasting with time-trend projectionsSUMMARY OUTPUT Regression Results: Top Desk Inc, Using Time as the Independent Variable

Regression StatisticsMultiple R 0.941177R Square 0.885814Adjusted R Square0.871541Standard Error2940.97Observations 10


Regression 1 5.37E+08 5.37E+08 62.06137 4.88E-05Residual 8 69194449 8649306Total 9 6.06E+08

CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept 44535.67 2009.065 22.16736 1.81E-08 39902.75 49168.58 39902.75 49168.58X Variable 1 2550.788 323.7902 7.877904 4.88E-05 1804.126 3297.45 1804.126 3297.45

Given the regression estimate

Y = 44,535.67 + 2,550.788 T, R2 = 0.87

Where T is the explanatory variable, time.

Calculate desk sales for the year 2005.

Exercise III

Equation for the regression line is:Sales in year = -44,535.67 + 2,550.788(Year)

Forecast of sales for the year 2005 is:

Sales in 2005 = -44,535.67 + (2,550.788*14) = 80,247 Units

Quantitative Forecasting: Regression Line Use


Forecasting with time-trend projections

Five Year Forecast Desk SalesUsing Regression Equation

Actual Year ForecastYear Ahead Sales11 1 72,59412 2 75,14513 3 77,69614 4 80,24715 5 82,797

Forecasting with time-trend projections(Workbook 3.3)


Forecasting Using Smoothing Models

CALCULATIONSGIVEN DATA 3- Year Errors Squared

Year Sales Units SMA Errors

1 39,0002 30,5003 45,000 38,167 6,833 46,694,4444 50,000 41,833 8,167 66,694,4445 59,000 51,333 7,667 58,777,7786 40,000 49,667 -9,667 93,444,4447 38,000 45,667 -7,667 58,777,7788 35,000 37,667 -2,667 7,111,1119 45,000 39,333 5,667 32,111,11110 50,000 43,333 6,667 44,444,44411 41,000 45,333 -4,333 18,777,77812 49,000 46,667 2,333 5,444,444

46,667 Sum Sq Err = 432,277,77845,556 MSE = 43,227,77847,074 Root MSE = 6,575

• Simple moving average:

First three year SMA =

(39,000+30,500+45,000)/3 = 38,167

Second three year SMA =

(30,500+45,000+50,000)/3 = 41,833

Calculated by dropping year 1 and adding

year 4

Last three year SMA =

(50,000+41,000+49,000)/3 = 46,667


Weighted moving average In SMA each observation in the calculation receives

equal weight In WMA different weights are assigned to each

observation in the time series. For example, more

weight may be assigned to recent data. The weights

must add up to 1 Three year WMA for years 1-12 is WMA = 50,000(0.1) 41,000(0.3)+49,000(0.6)=

46,700


Simple moving average(Workbook 3.4)


Exponential smoothing is a special case of WMA in which one weight-the weight for the most recent observation is selected. Weight assigned to the most recent observation is call the smoothing constant α

Ft+1= αYt+(1- α)Ft

Where:

Ft+1= forecast value for period t+1

Ft= forecast value for period t

Yt= actual value for period t

α =the smoothing constant(0< α<1)



Alpha = 0.2

CALCULATIONS

Smoothed Year Sales Units Sales Units

1 39,0002 30,500 36,7503 45,000 35,5004 50,000 37,4005 59,000 39,9206 40,000 43,7367 38,000 42,9898 35,000 41,9919 45,000 40,593

10 50,000 41,47411 41,000 43,17912 49,000 42,74413 43,99514 44,99615 45,797

GIVEN DATA

Exponential smoothing(Workbook3.5)


• Classical time series approach separates an observed series for a variable into the components of trend, cyclical variation, seasonal movements and random variation

▫ Y=T+C+S+I or Y=TxCxSxI• Modern time series analysis techniques

▫ ARCH-Autoregressive conditional heteroscedasticity

▫ GARCH- Generalized autoregressive conditional heteroscedasticity

▫ ARIMA- Autoregressive integrated moving average

▫ VAL-Vector autoregressive lag

▫ ADL- Autoregressive distributed lag • Mechanical approach to forecasting

More Complex Time Series Forecasting Methods

• Top-Down Where international and national events affect the future

behaviour of local variables.• Project dealing with internationally traded commodity

• Global macro level-international economic conditions- forecasts for the proposed project at the micro level

• International RMG price trend, project output price• Production of RMG by the project• Operational expenditure forecast• Tax factors• Net after tax operating cash flows

• Bottom-up• Small project dealing with local market

Forecasting Routes

Qualitative Forecasting

Using expert opinion and collective experience to unlock the secrets of the future.

The keys to employing qualitative forecasting are:

Data as an historical series is not available, or is not relevant to future needs.

¨ An unusual product or a unique project is being contemplated.

• Even when quantitative techniques are used, estimates may be combined with qualitative judgments

• People may be better able to detect random variation.

• People might be able to integrate external (non-time series) information in the forecasting process.

Why use human judgement?

Qualitative Forecasting:

By Survey-• Data can be gathered by phone or in

writing.• Data comes in three categories:

1. Highly valuable2. Absolutely essential3. Supporting material.

• The survey group is known as the ‘reference population’.

Data from expert opinion

• Obtaining information from individuals

• Using groups to make forecasts

• Jury of executive opinion senior managers draw upon their collective wisdom

to map out future events. These discussions are

carried out in open meeting, and may be subject to

the drawbacks of group think and personality

dominance.


Forward Links

Backward Links

Major Steps in the SurveyIdentify Information

Needs

Sampling Design

Develop Questionnaire

Analyze Data

Write Report

Collect Data

Using groups-• The Delphi Method: drawing upon the group’s expertise by getting individual submissions, without

the drawback of face to face meetings


Data From Expert Opinion

The Delphi Method is named after a famous Oracle who prophesied in the ancient Greek city of Delphi. An Oracle (wise person) interceded between men and gods.

Qualitative Forecasting: Data From Expert Opinion

Using groups -

Qualitative Forecasting: Data From Expert Opinion

• The Nominal Group Technique is a face to face Delphi method, allowing group discussion.

The Devils Advocate method poses sub-groups to question the group’s findings. The Dialectical Inquiry method poses sub-groups to challenge the group’s findings with alternative scenarios.

Qualitative Forecasting: Using Expert Opinion

1.Output from the group techniques is sorted into scenarios.2.These scenarios are further reviewed by the group.

3.A final ‘consensus of opinion’ forecast is accepted by the group.

• Qualitative forecasting is used when historical

data is not available, or when the planning

horizon is very long.

• Qualitative forecasting uses expert opinion,

collected in a variety of ways.

Collected expert wisdom has to be carefully managed.

Research shows that both the Delphi Method, and the

Nominal Group technique, are reliable forecast methods.

Qualitative Forecasting: Summary

• Sophisticated forecasting is essential for capital budgeting

decisions

• Quantitative forecasting uses historical data to establish

relationships and trends which can be projected into the

future

• Qualitative forecasting uses experience and judgment to

establish future behaviours

• Forecasts can be made by either the ‘top down’ or ‘bottom

up’ routes.

Forecasting: Summary

Back to the Future!

dev 567 project and program analysis lecture 2: forecasting cash flows

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