FIN 650: Project Appraisal Lecture 2 Forecasting Cash Flows

FIN 650: Project Appraisal

Lecture 2

Forecasting Cash Flows

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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.

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Forecasting Techniques and Routes

Techniques

Routes

Top-down routeBottom-up route

Quantitative

Qualitative

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

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

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Cash Flow Estimation for Project Appraisal

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 to

improve the reliability of the initial variables identified in the preceding stage.

Long term investment – look at annual rather than weekly or monthly cash flows.

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.

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Forecasting with Regression Analysis 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

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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

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The Two Variable Regression Model

Y = α + βX + μ

Where:Y= the dependent variable, desks soldX= The independent or explanatory

variable, number of householdsα = a parameter of the regression equation

called the regression interceptΒ = a parameter of the regression equation

called the slope or regression coefficientμ = stochastic disturbance or the error term

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Forecasting with Regression Analysis

Two variable regression model(Workbook 3.2)

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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

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Class Exercise I

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

= 0.92

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

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Forecasting with Regression Analysis

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

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Quantitative Forecasting

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.

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Forecasting with Regression Analysis

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

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The Multiple Regression Model

Y = α + β1X1 + β2X2 + μ

Where:Y= the dependent variable, desks soldX1= The independent or explanatory variable,

number of householdsX2 = The independent or explanatory variable,

incomeα = a parameter of the regression equation called

the regression interceptβ1, β2 = parameters of the regression equation

called the slope or regression coefficientμ = stochastic disturbance or the error term

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Multiple Regression ResultsMultiple Regression ResultsSUMMARY OUTPUT

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

ANOVAdf SS MS F Significance F

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

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Forecasting with Regression Analysis

The multiple regression model(Workbook 3.2)

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Class Exercise II

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.

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Forecasting with Regression Analysis

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

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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

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Forecasting with Regression Analysis

Forecasting using regression results(Workbook 3.2)

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Forecasting with Regression Analysis

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

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Forecasting with Regression Analysis

Forecasting with time-trend projections

SUMMARY 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

ANOVAdf SS MS F Significance F

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

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Class Exercise III

Given the regression estimateY = 44,535.67 + 2,550.788 T, R2

= 0.87

Where T is the explanatory variable, timeCalculate desk sales for the year 2005.

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Quantitative Forecasting: Regression Line Use

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

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Forecasting with Regression Analysis

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

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Forecasting with Regression Analysis

Forecasting with time-trend projections(Workbook 3.3)

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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

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Forecasting Using Smoothing Models

Simple moving average:First three year SMA =

(39,000+30,500+45,000)/3 = 38,167Second three year SMA =

(30,500+45,000+50,000)/3 = 41,833Calculated by dropping year 1 and addingyear 4Last three year SMA =

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

Forecasting Using Smoothing Models

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

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Forecasting Using Smoothing Models

Simple moving average(Workbook 3.4)

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Forecasting Using Smoothing Models

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)

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Forecasting Using Smoothing Models

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

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Forecasting Using Smoothing Models

Exponential smoothing(Workbook3.5)

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More Complex Time Series Forecasting Methods

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

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Forecasting Routes•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

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Qualitative Forecasting

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

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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

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Why use human judgement?

People may be better able to detect random variation.

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

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Qualitative Forecasting:Data From Expert Opinion

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’.

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Qualitative Forecasting: 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.

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Major Steps in the Survey` Identify Information Needs

Sampling design

Develop questionnaire

Collect data

Analyze data

Write report

Backward links

Forward links

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Qualitative Forecasting: Data From Expert Opinion

The Delphi Method: drawing upon the group’s expertise by getting individual submissions, without the drawback of face to face meetings.

Using groups-

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.

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Qualitative Forecasting: Data From Expert Opinion

Using groups - 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.

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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.

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Qualitative Forecasting: Summary

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.

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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.