FIN 650: Project Appraisal
Lecture 2
Forecasting Cash Flows
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.
2
Forecasting Techniques and Routes
Techniques
Quantitative
•Simple regressions
•Multiple
regressions
•Time trends
•Moving averages
Qualitative
Routes
Top-down route
Bottom-up route
•Delphi method
•Nominal group
technique
•Jury of executive
opinion
•Scenario projection
3
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.
4
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.

5
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
6
Forecasting with Regression Analysis
Original Data Set
Year
Desks
Sold
[Y Axis]
1992
50,010
1993
47,500
1994
53,410
1995
56,005
1996
52,605
1997
58,015
1998
61,900
1999
66,005
2000
72,200
2001
68,000
Number of
Households
[X Axis]
26,500
26,600
27,000
27,800
28,300
29,010
31,500
32,300
32,900
33,100
7
The Two Variable Regression Model
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
8
Forecasting with Regression Analysis
Two variable regression model
(Workbook 3.2)

9
Two Variable Regression Results
Two-Variable Regression Results
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.961595373
R Square
0.924665662
Adjusted R Square0.91524887
Standard Error 2388.809108
Observations
10
ANOVA
df
Regression
Residual
Total
Intercept
X1
SS
MS
F
Significance F
1 560330978 5.6E+08 98.19327 9.0856E-06
8 45651271.6 5706409
9 605982250
Coefficients Standard Error t Stat
P-value Lower 95% Upper 95%Lower 95.0%
Upper 95.0%
-28326.26291 8801.17891 -3.218462 0.012267 -48621.831 -8030.695 -48621.83 -8030.695
2.945366696 0.29723401 9.909252 9.09E-06 2.2599434 3.63079 2.259943 3.63079
10
Class Exercise I
Given the regression estimate
Y = -28,326 + 2.945 X, R2 = 0.92
(-3.2)
(9.9)
Calculate desk sales for the year 2002.

11
Forecasting with Regression Analysis
Given Household and Income Projections
Year
Households
Income
2002
2003
2004
2005
2006
35,000
35,990
37,000
38,500
39,800
52,000
54,100
55,000
56,970
58,000
Calculated Forecast Desk Sales
From Two-Variable Regression
Forecast
Year
Desk
Sales
2002
74,749
2003
77,664
2004
80,639
2005
85,056
2006
88,885
12
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.
13
Forecasting with Regression Analysis
Enhanced Data Set
Desks
Number of
Sold
Households
[Y Axis]
[X Axis]
50,010
26,500
47,500
26,600
53,410
27,000
56,005
27,800
52,605
28,300
58,015
29,010
61,900
31,500
66,005
32,300
72,200
32,900
68,000
33,100
Income
[X Axis 2nd Var.]
39,300
36,600
40,000
40,500
41,450
43,500
42,500
47,200
51,400
49,000
14
The Multiple Regression Model
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
15
Multiple Regression Results
Multiple Regression Results
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.983915573
R Square
0.968089856
Adjusted R Square 0.958972672
Standard Error
1662.054711
Observations
10
ANOVA
df
Regression
Residual
Total
Intercept
X1
X2
2
7
9
SS
MS
586645269 2.93E+08
19336981.04 2762426
605982250
F Significance F
106.183 5.8E-06
Coefficients
Standard Error
t Stat
P-value Lower 95%Upper 95%Lower 95.0%
Upper 95.0%
-24237.63048
6265.223546 -3.868598 0.006143 -39052.52 -9422.742 -39052.52 -9422.742
1.425923969
0.533977813 2.670381 0.031982 0.163268 2.68858 0.163268 2.68858
0.944175397
0.305915979 3.086388 0.017656 0.2208 1.667551 0.2208 1.667551
16
Forecasting with Regression Analysis
The multiple regression model
(Workbook 3.2)

17
Class Exercise II
Given the regression estimate
Y = -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 respectively
Calculate desk sales for the year 2002.

18
Forecasting with Regression Analysis
Given Household and Income Projections
Year
Households
Income
2002
2003
2004
2005
2006
35,000
35,990
37,000
38,500
39,800
52,000
54,100
55,000
56,970
58,000
Calculated Forecast Desk Sales
From Multiple Regression
Forecast
Year Desk
Sales
2002 74,761
2003 78,155
2004 80,445
2005 84,444
2006 87,270
19
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
20
Forecasting with Regression Analysis
Forecasting using regression results
(Workbook 3.2)

21
Forecasting with Regression Analysis
Forecasting
with time-trend projections
Original Data Set
Year
Time
Desks
Counter
Sold
"T" [X Axis]
[Y Axis]
1
50,010
1992
2
47,500
1993
3
53,410
1994
4
56,005
1995
5
52,605
1996
6
58,015
1997
7
61,900
1998
8
66,005
1999
9
72,200
2000
10
68,000
2001
22
Forecasting with Regression Analysis
Forecasting
SUMMARY OUTPUT
with time-trend projections
Regression Results: Top Desk Inc, Using Time as the Independent Variable
Regression Statistics
Multiple R 0.941177
R Square 0.885814
Adjusted R Square
0.871541
Standard Error2940.97
Observations
10
ANOVA
df
Regression
Residual
Total
SS
MS
F Significance F
1 5.37E+08 5.37E+08 62.06137 4.88E-05
8 69194449 8649306
9 6.06E+08
Coefficients
Standard 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 49168.58
X Variable 1 2550.788 323.7902 7.877904 4.88E-05 1804.126 3297.45 1804.126 3297.45
23
Class Exercise III
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.
24
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
25
Forecasting with Regression Analysis
Forecasting
Actual
Year
11
12
13
14
15
with time-trend projections
Five Year Forecast Desk Sales
Using Regression Equation
Year
Forecast
Ahead
Sales
1
72,594
2
75,145
3
77,696
4
80,247
5
82,797
26
Forecasting with Regression Analysis
Forecasting with time-trend projections
(Workbook 3.3)

27
Forecasting Using Smoothing Models
GIVEN
Year
DATA
Sales Units
1
2
3
4
5
6
7
8
9
10
11
12
39,000
30,500
45,000
50,000
59,000
40,000
38,000
35,000
45,000
50,000
41,000
49,000
3- Year
SMA
38,167
41,833
51,333
49,667
45,667
37,667
39,333
43,333
45,333
46,667
46,667
45,556
47,074
CALCULATIONS
Errors
6,833
8,167
7,667
-9,667
-7,667
-2,667
5,667
6,667
-4,333
2,333
Sum Sq Err =
MSE =
Root MSE =
Squared
Errors
46,694,444
66,694,444
58,777,778
93,444,444
58,777,778
7,111,111
32,111,111
44,444,444
18,777,778
5,444,444
432,277,778
43,227,778
6,575
28
Forecasting Using Smoothing Models
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

29
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

30
Forecasting Using Smoothing Models
Simple moving average
(Workbook 3.4)

31
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)
32
Forecasting Using Smoothing Models
Alpha =
0.2
GIVEN DATA
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Sales Units
39,000
30,500
45,000
50,000
59,000
40,000
38,000
35,000
45,000
50,000
41,000
49,000
CALCULATIONS
Smoothed
Sales Units
36,750
35,500
37,400
39,920
43,736
42,989
41,991
40,593
41,474
43,179
42,744
43,995
44,996
45,797
33
Forecasting Using Smoothing Models
Exponential smoothing
(Workbook3.5)

34
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


Modern time series analysis techniques






Y=T+C+S+I or Y=TxCxSxI
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
35
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
36
Qualitative Forecasting
Using expert opinion and
collective experience to
unlock the secrets of the
future.
37
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
38
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.
39
Qualitative Forecasting:
Data From Expert Opinion
By Survey


Data can be gathered by phone or in
writing.
Data comes in three categories:
1.
Highly valuable
2.
Absolutely essential
3.
Supporting material.
The survey group is known as the
‘reference population’.
40
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.
41
Major Steps in the Survey
`
Forward links
Identify Information Needs
Sampling design
Develop questionnaire
Collect data
Backward links
Analyze data
Write report
42
Qualitative Forecasting:
Data From Expert Opinion
Using groups
The Delphi Method: drawing upon the
group’s expertise by getting
individual submissions, without the
drawback of face to face meetings.
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.
43
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.
44
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.
45
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.
46
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.
47