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Risk analysis and investment appraisal in marketing
Risk Ana ysis and Investment in Marketing Appraisa D. A. Cameron Technical Beecham
Planning Research
and Development Department, Laboratories. London
The author is employed in Pharmaceutical Development and is concerned with the introduction of methods designed to integrate new products and technologies with the often conflicting objectives of production, marketing, and finance. This article outlines an approach to quantifying risk in investment appraisal and considers a marketing project although the technique has been used to appraise plant investment associated with uncertain technology and sales forecasts and also to investigate the optimal participation and financing for joint venture proposals. In addition, it is suggested that the organization of investment appraisal work may be more important than the techniques employed.
I
NVESTMI;NT
APPRAISAL.
COMMONLY
AIMS
to investigate three related areas which concern proposals to invest in projects. The questions asked are: (a) Has the project a satisfactory DCF return? (b) What will the payback period be? (c) What confidence can be expressed about the purported levels of investment and earning power? Line managers responsible for recommending a project for investment are usually motivated to oversell a proposal so long as it can be shown (sometimes by any means possible) that the project satisfies a specified return on investment. On the other hand general management responsible for authorizing capital investment are usually more concerned with the risk aspects of the project assuming that the proposal is compatible with company strategy. The behavioural aspects of the two groups in this common situation are basically antagonistic and it is therefore
DECEwlBER,
1972
often useful to establish a third group who can carry out a more objective investment appraisal in collaboration with line management for submission to general management. This role is perhaps best carried out by a planning function. INVESTMENT APPRAISAL OUTLINE By selecting and agreeing with line management the necessary data included in the project proposal, a base case can be specified which is used to calculate the return on investment, the net present value, and the payback period. The base case is usually an overview of the most likely investment, cost, and profit levels. Return on Investment The discounted cash flow (DCF) return for the project can be judged against an internal pass mark and gives an initial appreciation of how the proposal measures up to the general yardstick for allocating capital. Net Present Value The net present value (NPV) is calculated by discounting the project cash flows at the required company pass mark and this value is useful since it can indicate the additional amount which could be spent at the beginning of the project and still achieve the minimum DCF pass mark or alternatively can be considered as a contingency fund which might be available for further investment in the project should the need arise. Yet another way of considering NPV is the approximate gross loss of earnings which a project could withstand before failing the specified cut off rate. Conversely, a negative NPV can be used to budget the necessary pruning of investment, cutting of costs, or raising of prices which may be necessary to justify a project which has failed the pass mark but is nevertheless strategically or politically favoured.
Payback Period T-he payback period for the project (which is the elapsed time after which the cumulative cash flows become positive) provides a yardstick against which to judge any risk identified in the project. ASSESSMENT OF RISK The NPV and payback period are essentially elements which attempt to highlight the robustness and riskiness of new investments. Generally there are three attitudes towards risk : (a) ignore it; (b) express it verbally; (c) express it mathematically. The verbal expression is probably the most frequently applied and this is usually expressed as follows: “This investment is in a high risk political area, therefore, we will apply a DCF cut off rate of 30 per cent instead of I5 per cent.” This approach essentially expresses the desire to reduce the payback period but loading the DCF rate so as to achieve this objective is unfair to the project and to the company for two reasons. First, it assumes that the risk is the same for all years of the project and second, it assumes that all aspects of the project are equally risky. There is also a further important consideration. Attitudes to risk are influenced by basic personality characteristics and the chances are that the person responsible for authorizing capital investment in new projects will be different from the person(s) making the proposal. The decision takers may frequently wish to apply their own judgement to some of the claims made for the project. The considerations outlined above suggest that some mathematical expression of risk may provide a more meaningful base for assessing project proposals. For projects which are associated with powerful vested interests and which at the same time may just fail or achieve the required DCF pass mark, a
43
r
Investment
-----------
Appraisal
I
Project
Proposal
Project Sanction
Presentation
Figure
1. Progress
more rigorous analysis of risk might not only be particularly advantageous but it may also serve to reduce the inevitahle level of conflict. A mathematical expression of risk is not only feasible but it can be quite easily accomplished. This is illustrated by the accompanying case study which reports on a routine investment appraisal for a project where a risk analysis was also carried out because of the particular considerations which were present. This analysis was done using the Monte Carlo sampling technique on probabilities which line management wished to attach to specific variables in the project. Monte Carlo sampling can loosely be described as a method for choosing the most likely possibles and most of the major computer companies have standard investment analysis programmes which incorporate some variation on this routine. The problem can easily be processed by any competent O.R. department if the necessary input data is specified by line management. In this instance the ICL PROSPER package was used although one confident O.R. specialist informed the author that he could have written and tested a simpler and less expensive programme in a couple of days ! ORGANIZATION FOR INVESTMENT APPRAISAL In the author’s experience investment appraisal studies should be undertaken by a planning function since this is usually more able than line management or the accounting function to provide the neces\ary technical expertise and objectivity. Consistency of approach is also more likely to be maintained, especially in the larger organization. It may from time to
44
of Project
from
Proposal
of
Project
to Capital
Sanction.
time be necessary to draw on the services of Operational Researchers or Management Scientists for specialist work involving the use ofcomputers but thejob is more likely to succeed if meetings between them and line management are avoided: a meaningful dialogue is rarely. if ever, established and the resultant fear and mistrust often generated can in extreme cases destroy a pro.ject proposal. CASE
analysis showed that the return on inve\tment was likely to lie in 111~ DC‘F range 22-30 per cent and that the most I~hcly return would be 26 per cent with a standard deviation of & I per cent. In other word\ the analysis showed that even though the base case return of 30 per cent appeared to be optimistic the proposal nevertheless seemed to be very robust since the chance of significantly deviating from the indicated 26 per cent return was small. The total investment analysis including the necessary discussions and meetings was completed in under 2 weeks and computer time cost about f2OO.
STUDY
Summary A proposal was put forward which requested a f2 million franchise investment in 34 hotels for Eastern Europe. The hotels were to be constructed over a period of IO years and the capital would be repaid by a guaranteed I5 per cent of gross room revenue. The base case showed a DCF return of 30 per cent, a N.P.V. of f5 million (assessed against a pass mark of I5 per cent), and a payback period of 6 years. Doubt was expressed about some of the financial input to the base case and a risk analysis was carried out by attaching probabilities to some of the base case assumptions. The results of the risk
Table
Country
1. Projected
Method Table I shows the projected completion schedule for the hotels and Table 2 shows the anticipated earning power for each hotel assuming a range of occupancy rates. These two tables incorporate the base case which assumed an X0 per cent annual occupancy. Table 3 shows the probabilities which were attached to such factors as hotel completion dates, occupancy rates, room prices and seasonal variations and also the alternative values which were
Completion
Schedule
of Hotels.
1972
1973
1974
1975
1976
1977
1978
1979
1980
Yugoslavia Hungary Poland Romania USSR
0 3 0 0 2
3 2 0 1 1
2 0 1 1 0
1 0 2 2 0
0 0 3 1 1
0 0 0 1 1
0 0 0 1 1
0 0 0 1 1
0 0 0 1 1
a
Total each year
5
7
4
5
5
2
2
2
2
34
Cumulation
5
12
16
21
26
26
30
32
34
Total
6 5 6 9
LONG RANGE PLANNING
Table (Calculation
2. Proposed
based on proposed
Earning
standard
Power
specitied
of Investment.
600 bed hotel:
120 singles
and 480 doubles.)
60% 600 360 120 60 180 -
Percentage 70% 600 420 120 90 210 -
360 -
420 -
480 -
540 -
Busy Season (152 Days) Single at E6.00 Single Double at E12.00* Double at f6.50
E 720 720 1200 -
E 720 1100 1400 -
E 720 1400 1600 -
E 720 1800 1700
Daily revenue Season total at 152 days Off Season (213 Days) Corresponding calculation season total at 213 days Gross Room Revenue Guaranteed Gross Income at 15 per cent
2640 400,000
3220 490,000
3720 560,000
4220 640,000
380,000 780,000
460,000 950,000
530,000 1,090,000
117,000
143,000
164,000
Total beds Total occupied Distribution: Single beds Single doubles* Doubles
“Double
2.
3.
3. Probabilities
Inn completion dates Chance of inns being completed Chance of inns being completed Chance of inns being completed Occupancy Chance of 85% occupancy Chance of 80% occupancy Chance of 75%. occupancy Room Prices Busy season Single room
Double,
used as single
Double
0 ff season Single
Double,
room
used as single
Double
4.
5.
90% 600 540 120 150 270 -
610,000 1,250,OOO 188,000
bed with single occupancy.
Table
1.
gives
of Occupancy 80% 600 480 120 120 240 -
Season Variation Busy season
Joint
Venture
DECEMBER, 1972
Net Income
Used for Hotel
Project
Analysis.
compared with I~O\C ubcd 1.01.111~’ This data wab provided h> marketing management who intended IO propose the pro.iect. The representation. the approach, and the values specified 111Table 3 evolved from joint discussions betueen base
marketing management. niarhet plannliq. and real estate consultants. The concepts
were readily accepted and assimilated b> marketing management and real estate consultants who had not used the technique before. A sensitivity analysis carried out by market-planning highlighted which financial inputs had the greatest effect on the project return and these formed the basis for choosing Table 3.
40% 40% 20%
were optional; any have been specified.
E7.00 L6.00 25.00 f14.00 fl2.00 E1O.OO f7.00 E6.50 f5.00
30% 60% 10% 30% 60% 10% 30% 50% 20%
25.00 24.00 f3.00 flO.00 f8.00 L6.00 E5.00 L4.50 L4.00
10% 60% 30% 10% 60% 30% 30% 50% 20%
152 days 136 days 120 days 15%
20% 60% 20% 100%
shown
in
other
number
(Base case) COMPUTER Sensitivity
10% 60% 30%
the variable5
The data were programmed into the ICL PROSPER package and (for the technic:)” 400 calculations (called iterations by the OR people) were performed by the computer. The computer selected a random sample of the variables shown in Table 3 for each Iteration (this is Monte Carlo sampling) and the appropriate DCF return was calculated. The ri3k analysis option in PROSPER is designed to print out two graphs: one i!, a histogram which shows the distribution of the DCF returns determined by the 400 calculations and other is a cumulative histogram which shows the probability of achieving a minimum DCF return. The 400 calculations could
on time 1 year late 2 years late
case.
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
PRINT of DCF
OUT Return
Figure 2 shows the results of the calculations expressed as a distribution of the DCF returns. Point (a) shows the mean return to be 26 per cent DCF achieved by 140. or 35 per cent. of the 400 calculations. Line (b) shows that for 30 per cent of the calculations the deviation about the 26 per cent DCF return is -I per cent DCF and 7 I per cent DCF. Line (c) shows that for 10 per cent of the calculations the deviation about the 26 per cent DCF return is -4 per cent and +5 per cent. The standard deviation about the mean 26 per cent DCF return was f I per cent DCF which is indicative of a very stable project. For a more unstable project the histogram would have been ‘fatter’ which would have meant the chance of much greater variations about the mean DCF return. In general this representation provides two pieces of descriptive information. These are the most likely project returns after taking account of a possible range of financial inputs and the shape of the histogram which indicates the robustness of the project.
45
46
LONG
RANGE
PLANNING
Probability of Achieving DCF Return
a Minimum
Figure 3 gives the probability of achieving at least the DCF returns-shown. Point (d) shows that there is a 0 per cent chance of exceeding 30 per cent DCF return. Point (e) shows that there is a 65 per cent chance of achieving or exceeding a 26 per cent DCF return. Point (f) shows that there is a 100 per cent chance of the DCF return being greater than 22 per cent. It can be seen that the chance of the DCF occuring falls in the relatively narrow band of 2230 per cent. This again indicates the ‘good risk’ characteristic of the project. It may at first appear naive for a computer programme to print that there is absolutely no chance of a DCF return being less than 22 per cent or more than 30 per cent. However if this is interpreted with the input from Table 3 in mind, the results are shown to be logical. For example there is no indication in the input data of a zero
DECEMBER,
1972
return on investment which might be the case if all the hotels burnt down as soon as they were built. The input data is only representative of the normal decision variables requiring discretion.
SCOPE
OF RISK
ANALYSIS
The example used is a simple application of the technique since the only variations which could arise were included in the hotel completion schedule and the projected revenue plan. The capital investment and percentage take of gross revenue were guaranteed. In different circumstances the appraisal could have been expanded to include variations in the investment required, operating costs, fixed costs, and the useful life of the facilities. In fact the approach can be used for any decision which requires capital investment in the presence of uncertainty. It is particularly useful for projects where more than one function is implicated (for example
marketing and production) since separarc variables can be specified by the respective line managements and combined to gauge the joint effect on the investment proposal. A useful check list of areas where uncertainty can usually be found is: 1. 2. 3. 4. 5. 6. 7. 8.
9. 10.
Il. 12. 13.
Market size Selling prices Market growth rate Market share investment required (Marketing and ProducEon) Phasing of capital expenditure Working capital Residual value of expenditure Operating costs (Marketing and Production) Fixed costs (Marketing and Production) Useful life of facilities (Marketing and Production) Process variables (Production) Inflation. n
47
Planning Research
and Development Department, Laboratories. London
The author is employed in Pharmaceutical Development and is concerned with the introduction of methods designed to integrate new products and technologies with the often conflicting objectives of production, marketing, and finance. This article outlines an approach to quantifying risk in investment appraisal and considers a marketing project although the technique has been used to appraise plant investment associated with uncertain technology and sales forecasts and also to investigate the optimal participation and financing for joint venture proposals. In addition, it is suggested that the organization of investment appraisal work may be more important than the techniques employed.
I
NVESTMI;NT
APPRAISAL.
COMMONLY
AIMS
to investigate three related areas which concern proposals to invest in projects. The questions asked are: (a) Has the project a satisfactory DCF return? (b) What will the payback period be? (c) What confidence can be expressed about the purported levels of investment and earning power? Line managers responsible for recommending a project for investment are usually motivated to oversell a proposal so long as it can be shown (sometimes by any means possible) that the project satisfies a specified return on investment. On the other hand general management responsible for authorizing capital investment are usually more concerned with the risk aspects of the project assuming that the proposal is compatible with company strategy. The behavioural aspects of the two groups in this common situation are basically antagonistic and it is therefore
DECEwlBER,
1972
often useful to establish a third group who can carry out a more objective investment appraisal in collaboration with line management for submission to general management. This role is perhaps best carried out by a planning function. INVESTMENT APPRAISAL OUTLINE By selecting and agreeing with line management the necessary data included in the project proposal, a base case can be specified which is used to calculate the return on investment, the net present value, and the payback period. The base case is usually an overview of the most likely investment, cost, and profit levels. Return on Investment The discounted cash flow (DCF) return for the project can be judged against an internal pass mark and gives an initial appreciation of how the proposal measures up to the general yardstick for allocating capital. Net Present Value The net present value (NPV) is calculated by discounting the project cash flows at the required company pass mark and this value is useful since it can indicate the additional amount which could be spent at the beginning of the project and still achieve the minimum DCF pass mark or alternatively can be considered as a contingency fund which might be available for further investment in the project should the need arise. Yet another way of considering NPV is the approximate gross loss of earnings which a project could withstand before failing the specified cut off rate. Conversely, a negative NPV can be used to budget the necessary pruning of investment, cutting of costs, or raising of prices which may be necessary to justify a project which has failed the pass mark but is nevertheless strategically or politically favoured.
Payback Period T-he payback period for the project (which is the elapsed time after which the cumulative cash flows become positive) provides a yardstick against which to judge any risk identified in the project. ASSESSMENT OF RISK The NPV and payback period are essentially elements which attempt to highlight the robustness and riskiness of new investments. Generally there are three attitudes towards risk : (a) ignore it; (b) express it verbally; (c) express it mathematically. The verbal expression is probably the most frequently applied and this is usually expressed as follows: “This investment is in a high risk political area, therefore, we will apply a DCF cut off rate of 30 per cent instead of I5 per cent.” This approach essentially expresses the desire to reduce the payback period but loading the DCF rate so as to achieve this objective is unfair to the project and to the company for two reasons. First, it assumes that the risk is the same for all years of the project and second, it assumes that all aspects of the project are equally risky. There is also a further important consideration. Attitudes to risk are influenced by basic personality characteristics and the chances are that the person responsible for authorizing capital investment in new projects will be different from the person(s) making the proposal. The decision takers may frequently wish to apply their own judgement to some of the claims made for the project. The considerations outlined above suggest that some mathematical expression of risk may provide a more meaningful base for assessing project proposals. For projects which are associated with powerful vested interests and which at the same time may just fail or achieve the required DCF pass mark, a
43
r
Investment
-----------
Appraisal
I
Project
Proposal
Project Sanction
Presentation
Figure
1. Progress
more rigorous analysis of risk might not only be particularly advantageous but it may also serve to reduce the inevitahle level of conflict. A mathematical expression of risk is not only feasible but it can be quite easily accomplished. This is illustrated by the accompanying case study which reports on a routine investment appraisal for a project where a risk analysis was also carried out because of the particular considerations which were present. This analysis was done using the Monte Carlo sampling technique on probabilities which line management wished to attach to specific variables in the project. Monte Carlo sampling can loosely be described as a method for choosing the most likely possibles and most of the major computer companies have standard investment analysis programmes which incorporate some variation on this routine. The problem can easily be processed by any competent O.R. department if the necessary input data is specified by line management. In this instance the ICL PROSPER package was used although one confident O.R. specialist informed the author that he could have written and tested a simpler and less expensive programme in a couple of days ! ORGANIZATION FOR INVESTMENT APPRAISAL In the author’s experience investment appraisal studies should be undertaken by a planning function since this is usually more able than line management or the accounting function to provide the neces\ary technical expertise and objectivity. Consistency of approach is also more likely to be maintained, especially in the larger organization. It may from time to
44
of Project
from
Proposal
of
Project
to Capital
Sanction.
time be necessary to draw on the services of Operational Researchers or Management Scientists for specialist work involving the use ofcomputers but thejob is more likely to succeed if meetings between them and line management are avoided: a meaningful dialogue is rarely. if ever, established and the resultant fear and mistrust often generated can in extreme cases destroy a pro.ject proposal. CASE
analysis showed that the return on inve\tment was likely to lie in 111~ DC‘F range 22-30 per cent and that the most I~hcly return would be 26 per cent with a standard deviation of & I per cent. In other word\ the analysis showed that even though the base case return of 30 per cent appeared to be optimistic the proposal nevertheless seemed to be very robust since the chance of significantly deviating from the indicated 26 per cent return was small. The total investment analysis including the necessary discussions and meetings was completed in under 2 weeks and computer time cost about f2OO.
STUDY
Summary A proposal was put forward which requested a f2 million franchise investment in 34 hotels for Eastern Europe. The hotels were to be constructed over a period of IO years and the capital would be repaid by a guaranteed I5 per cent of gross room revenue. The base case showed a DCF return of 30 per cent, a N.P.V. of f5 million (assessed against a pass mark of I5 per cent), and a payback period of 6 years. Doubt was expressed about some of the financial input to the base case and a risk analysis was carried out by attaching probabilities to some of the base case assumptions. The results of the risk
Table
Country
1. Projected
Method Table I shows the projected completion schedule for the hotels and Table 2 shows the anticipated earning power for each hotel assuming a range of occupancy rates. These two tables incorporate the base case which assumed an X0 per cent annual occupancy. Table 3 shows the probabilities which were attached to such factors as hotel completion dates, occupancy rates, room prices and seasonal variations and also the alternative values which were
Completion
Schedule
of Hotels.
1972
1973
1974
1975
1976
1977
1978
1979
1980
Yugoslavia Hungary Poland Romania USSR
0 3 0 0 2
3 2 0 1 1
2 0 1 1 0
1 0 2 2 0
0 0 3 1 1
0 0 0 1 1
0 0 0 1 1
0 0 0 1 1
0 0 0 1 1
a
Total each year
5
7
4
5
5
2
2
2
2
34
Cumulation
5
12
16
21
26
26
30
32
34
Total
6 5 6 9
LONG RANGE PLANNING
Table (Calculation
2. Proposed
based on proposed
Earning
standard
Power
specitied
of Investment.
600 bed hotel:
120 singles
and 480 doubles.)
60% 600 360 120 60 180 -
Percentage 70% 600 420 120 90 210 -
360 -
420 -
480 -
540 -
Busy Season (152 Days) Single at E6.00 Single Double at E12.00* Double at f6.50
E 720 720 1200 -
E 720 1100 1400 -
E 720 1400 1600 -
E 720 1800 1700
Daily revenue Season total at 152 days Off Season (213 Days) Corresponding calculation season total at 213 days Gross Room Revenue Guaranteed Gross Income at 15 per cent
2640 400,000
3220 490,000
3720 560,000
4220 640,000
380,000 780,000
460,000 950,000
530,000 1,090,000
117,000
143,000
164,000
Total beds Total occupied Distribution: Single beds Single doubles* Doubles
“Double
2.
3.
3. Probabilities
Inn completion dates Chance of inns being completed Chance of inns being completed Chance of inns being completed Occupancy Chance of 85% occupancy Chance of 80% occupancy Chance of 75%. occupancy Room Prices Busy season Single room
Double,
used as single
Double
0 ff season Single
Double,
room
used as single
Double
4.
5.
90% 600 540 120 150 270 -
610,000 1,250,OOO 188,000
bed with single occupancy.
Table
1.
gives
of Occupancy 80% 600 480 120 120 240 -
Season Variation Busy season
Joint
Venture
DECEMBER, 1972
Net Income
Used for Hotel
Project
Analysis.
compared with I~O\C ubcd 1.01.111~’ This data wab provided h> marketing management who intended IO propose the pro.iect. The representation. the approach, and the values specified 111Table 3 evolved from joint discussions betueen base
marketing management. niarhet plannliq. and real estate consultants. The concepts
were readily accepted and assimilated b> marketing management and real estate consultants who had not used the technique before. A sensitivity analysis carried out by market-planning highlighted which financial inputs had the greatest effect on the project return and these formed the basis for choosing Table 3.
40% 40% 20%
were optional; any have been specified.
E7.00 L6.00 25.00 f14.00 fl2.00 E1O.OO f7.00 E6.50 f5.00
30% 60% 10% 30% 60% 10% 30% 50% 20%
25.00 24.00 f3.00 flO.00 f8.00 L6.00 E5.00 L4.50 L4.00
10% 60% 30% 10% 60% 30% 30% 50% 20%
152 days 136 days 120 days 15%
20% 60% 20% 100%
shown
in
other
number
(Base case) COMPUTER Sensitivity
10% 60% 30%
the variable5
The data were programmed into the ICL PROSPER package and (for the technic:)” 400 calculations (called iterations by the OR people) were performed by the computer. The computer selected a random sample of the variables shown in Table 3 for each Iteration (this is Monte Carlo sampling) and the appropriate DCF return was calculated. The ri3k analysis option in PROSPER is designed to print out two graphs: one i!, a histogram which shows the distribution of the DCF returns determined by the 400 calculations and other is a cumulative histogram which shows the probability of achieving a minimum DCF return. The 400 calculations could
on time 1 year late 2 years late
case.
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
(Base case)
PRINT of DCF
OUT Return
Figure 2 shows the results of the calculations expressed as a distribution of the DCF returns. Point (a) shows the mean return to be 26 per cent DCF achieved by 140. or 35 per cent. of the 400 calculations. Line (b) shows that for 30 per cent of the calculations the deviation about the 26 per cent DCF return is -I per cent DCF and 7 I per cent DCF. Line (c) shows that for 10 per cent of the calculations the deviation about the 26 per cent DCF return is -4 per cent and +5 per cent. The standard deviation about the mean 26 per cent DCF return was f I per cent DCF which is indicative of a very stable project. For a more unstable project the histogram would have been ‘fatter’ which would have meant the chance of much greater variations about the mean DCF return. In general this representation provides two pieces of descriptive information. These are the most likely project returns after taking account of a possible range of financial inputs and the shape of the histogram which indicates the robustness of the project.
45
46
LONG
RANGE
PLANNING
Probability of Achieving DCF Return
a Minimum
Figure 3 gives the probability of achieving at least the DCF returns-shown. Point (d) shows that there is a 0 per cent chance of exceeding 30 per cent DCF return. Point (e) shows that there is a 65 per cent chance of achieving or exceeding a 26 per cent DCF return. Point (f) shows that there is a 100 per cent chance of the DCF return being greater than 22 per cent. It can be seen that the chance of the DCF occuring falls in the relatively narrow band of 2230 per cent. This again indicates the ‘good risk’ characteristic of the project. It may at first appear naive for a computer programme to print that there is absolutely no chance of a DCF return being less than 22 per cent or more than 30 per cent. However if this is interpreted with the input from Table 3 in mind, the results are shown to be logical. For example there is no indication in the input data of a zero
DECEMBER,
1972
return on investment which might be the case if all the hotels burnt down as soon as they were built. The input data is only representative of the normal decision variables requiring discretion.
SCOPE
OF RISK
ANALYSIS
The example used is a simple application of the technique since the only variations which could arise were included in the hotel completion schedule and the projected revenue plan. The capital investment and percentage take of gross revenue were guaranteed. In different circumstances the appraisal could have been expanded to include variations in the investment required, operating costs, fixed costs, and the useful life of the facilities. In fact the approach can be used for any decision which requires capital investment in the presence of uncertainty. It is particularly useful for projects where more than one function is implicated (for example
marketing and production) since separarc variables can be specified by the respective line managements and combined to gauge the joint effect on the investment proposal. A useful check list of areas where uncertainty can usually be found is: 1. 2. 3. 4. 5. 6. 7. 8.
9. 10.
Il. 12. 13.
Market size Selling prices Market growth rate Market share investment required (Marketing and ProducEon) Phasing of capital expenditure Working capital Residual value of expenditure Operating costs (Marketing and Production) Fixed costs (Marketing and Production) Useful life of facilities (Marketing and Production) Process variables (Production) Inflation. n
47