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Assessing the risks in acquisitions—The risk-chance analysis
0024-6301/86 $3.00 + .OO Pergamon Journals Ltd.
Long Range Planning, Vol. 19, No. 3, pp. 41 to 45, 1986 Printed in Great Britain
41
Assessing the Risks in The Risk-Chance Acquisitions Analysis Klaus Neubiirger
Every company encounters a dangerous gap of information by evaluating various decision alternatives on the base of objective achievement alone. It is at least as important to assert and quantify the expected risk of the chosen alternative. The Risk-Chance Analysis described in this article provides a goalrelated and risk-related evaluation of alternatives without additional expenditures for providing information, and with the convenience of data processing. It is more comprehensive than risk analysis, which only calculates the probability of risk.
Introduction The management of company A is going to decide on the acquisition of one out of two companies B or C. The management will decide based on qualitative information as well as on quantitative calculations of the probable value of the company. In this case this value accounts within the next 5 years for’
alternative might have been found that would not have yielded maximum profit but would have avoided losses in high cost environment. By using a comprehensive more information processing, management is able to consider in advance the potential risk that is related with every decision. Otherwise it is condemned only to react or to accept an unwanted development. Management is very often unwisely advised to adopt this narrow evaluation of alternatives. How can one meet the demand for an evaluation of alternatives that is related to all the objectives and the risks involved in a specific decision problem? And strictly speaking what do we mean by ‘risk’?
Confusion
About the Word ‘Risk’
If the management of company A decided on these figures (and the assumed objective of profit maximization) only, presumably it would acquire company C, which has the higher probable value. It would have gone systematically through a process of rational decision-making but this process would have been dangerously limited in respect to the investment of company A, as no information has been supplied about the involved risk.
Every writer who uses the word ‘risk’ seems to have a different definition. This confusion makes it necessary to deal with the meaning of risk. In the example quoted above it had been assumed that company A has examined the alternatives in ‘the most probable’ situation only. In checking the impact of the pessimistic situation too it may be possible to visualize in advance a probable loss. Having this additional information management can answer the question whether (a) it is willing to run this risk of possible loss, which has been quantified, in order to have a chance of making the largest profit or (b) it is content with the lower profit at a lower risk of loss.
This dangerous lack of information exists quite often in reality, a fact that is hard to understand since risk related information can be obtained from the available data. Management has restricted its decision-making process by only considering a ‘probable’ scenario. In considering all the alternatives in a ‘pessimistic’ scenario, for instance with a high increase in labour or factory supply costs, an
Looking at the alternative of company B in more detail (Table 2) as the ‘amount of risk’ we define the difference between the expected highest profit (or maximal value) $12,803,000 and the lowest profit (or highest loss) fl1,388,000, in this case this equals $1,415,000. Management is not only interested in knowing the potential risk amount but also the probability of this risk of $1,415,000. These proba-
Company
B = US $12,803,000
Company
C = US $12,871,000.
42
J une
Long Range Planning Vol. 19
1986
bilities related to the amount of risk are called ‘riskprobability’. In considering the optimistic scenario their logical counterparts are ‘chance’, ‘chance amount’ and ‘chance probability’. Therefore, the answer to the question which risk the management is willing to take for which achievement of objectives depends on: *
The amount of risk;
*
The probability of risk that is combined with the amount of risk;
*
The decision maker’s attitude to risk and
*
The achievement
Requirements of a Practical Risk Information Technique
*
Evaluation of alternatives as high-risk or highchance relative to all relevant objectives.
*
Stability of the above mentioned variables relative to all parameters and determination of the most essential parameter.
of the Risk-Chance
Table 1 shows in column E,, the pessimistic, in the column E,, the optimistic future profits of company B (company C) from 1987 to 1991. The criterion of ‘availability of the input information’ is the way that the risk-chance analysis obtains its information about achievement of objectives, amount of risk and probability of risk from the available data in Table 1. This is done by calculation as shown in Figure 1.2
To be convenient a risk-calculation technique has to fulfill two requirements: (1) Availability of the required data and (2) Availability of the required mathematical know-how.
*
The top-box of Figure 1 asks for the pessimistic value W,, the optimistic W, and the probable W,. To determine W, for instance this value is calculated by using the pessimistic E,, for 1987-1991 only. Having calculated Wr and I%‘, in the same way the additional information in Table 2 can be provided. From this the management can see that the alternative ‘buying company C’ shows a higher amount of risk ($3,566,000) than alternative B, but offers the higher amount of chance, too ($3,096,000). If ‘buying company B’ is more of a chance or of a risk it has to be considered how much the probable figures E,, of both alternatives are
the method
Amount of risk related to all relevant objectiveand controlling-figures, such as profit, liquidity, share of long-term liabilities and so on.
‘Chance equals opportunity.
Table 1. Data for an acquisition decision Future profits of company B (company C) us $ ‘000’S)
to the
First criterion for the convenience of such a calculation has been the availability of the required data. To provide the information about the value of the companies B and C, some data are already available (Table 1). By these figures it is already expected that company B in 1987 (t= l), pessimistically seen, will have a future profit of $500,000 (E,,), in 1988 (t= 2) for instance, optimistically seen, a future profit of $l,OOO,OOO(E3J and in 1991 (t = 5) a future profit, probably, of $l,lOO,OOO (E&.
Independent of different attitudes towards risk, people do accept risk as the counterpart to chance* but they are more afraid of a non-calculated risk than of a incalculable risk.
To make best use of the information should provide the following data:
Probabilities of risk that are related amount of risk.
Suitability Analysis
of objectives.
The requirements of a practical risk-information technique have been explained above. We outlined what information about objectives and risks is necessary for a decision and has therefore to be provided by the technique. But such a calculation has to be checked for its usefulness within the company. That means a methodology has to fulfill two equally important criteria: (1) convenience and (2) best use of available information.
*
t
Pessimistic E1t
Probable
Year
E2t
Optimistic E31
1987
1
500
600
700
1988
2
w&x
- 1989
3
(;y (700) 600
1990
4
(“9cg)
1991
5
‘l”o”o”o’ (800)
yJ (1100) 1100 (1100)
WJ
58ooooo) (900) 900 \9lE? (1140) 1200 (1400)
Assessing the Risks in Acquisitions-The
w,= ;
43
uss
Company B
Company C
12,803,OOO
12,871,OOO
w, Pessimistic value
14,053,000
15,967,OOO
% Amount of risk w, - wp Amount of chance
11.388.000
9.305.000
1,415,000
3.566.000
1,250,OOO
3.096.000
risky
risky
high stability
low stability
E5 +
r-1(1.08)'
Analysis
Table 2. Risks and chance* calculated from Table 1
Calculation of value W, by E,,, E,, E3t
Et
Risk-Chance
Probable value
0.08 (1.085)
T Optimistic value
Arithmetic* for
w, - w, Evaluation of the alternative3 Stability of“ w,
*Chance equals opportunityfor benefit.
(residual balance $100,000) (see Table 1). However in the same year the future profit figures of company C were reduced from $900,000 to $500,000 (residual balance $400,000), respectively increased to $950,000 (residual balance $50,000). Such differences in the input data (subject to different sensitivities of the acquisition alternatives towards changed assumptions of the company’s environment) also have to be considered in assessing whether the acquisition of company B is a high risk or not, -e.g. by 1ook’mg~aKiG variation in values.3 The same procedure can be applied to answer the question how changes in the objective IV,, are influenced by changes in the future profit data? (i.e. how sensitive is WV.4)
“Multivail = multi-interval arithmetic.
Figure 1. The method of calculating risk and chance
Looking again at the requirements for a riskinformation technique you realize that the riskchance analysis has to be expanded with respect to the probability of risk and has to be judged with regard to the mathematical knowledge and ability
changed towards the optimistic or the pessimistic end. The future profit E,, of company B in 1989 changed from $800,000 to $600,000 (residual balance $200,000), respectively changed to $900,000
--
i--
-5
Company 8 -
Company C
__, I
I
Y-a
1
L__-
i
30 20 t
10 It 0
I
I
Ii
L-m
1 L-1 L___,
i__,
I
II I II
~ 7
L
I/
I
LB_
t
II
1234567
11
11
8
9
10
1
II
11
12
Classof Risk
Figure 2. Risk profiles for two acequisition
candidates
L_ 1
“I If 13
14
I
15
16
1 I
I
I
17
18
19
44
Long Range Planning Vol. 19
June 1986
of the user. This has to be decided by the potential user.
or not. So a detailed description of the procedure for calculating probabilities is not required.5
In stage I the user could work with estimates instead of the formula which has been used here to make it easier to understand. If the amount of risk is matched with a probability of risk, the formula is required to calculate (Figure 1).
Table 3 and Figure 2 show additional information to be developed for the example of company acquisition. Figure 2 shows graphically the cumulative probabilities in Table 3. One recognizes that the spread of the figures of alternative C is wider than that of alternative B. This has already been shown in the evaluation of stability (Table 2).
Risk-Probability To calculate probabilities for the amount of risk the risk-chance analysis does not need any further information beyond those in Table 1. By finetuning the procedure, the interval from pessimistic to optimistic future profit can be subdivided into several smaller equal intervals (see Figure 1 for subdivision into 19 equal intervals). This provides relative frequencies and the required probabilities. In practice, the amounts of risk are more important and the decision-maker can make an assessment based on his experience whether they are probable
Management will most likely decide for alternative B if it is willing to risk less and alternative C if it is willing to risk more. These decisions were already obvious from the information gained in stage I (compare Table 2). Looking at the risk profile of Figure 2 management can determine the value of W, if it is willing to accept a 10 per cent riskprobability that the value will be too high. For the company C Figure 2 shows the corresponding figures in class 3, e.g. the value must not exceed $10,400,000.
Table 3. Risk profiles for two acquisition candidates Company B Value ($) 16,000-15,650 class19 15,650-15,300 class18 15.300-14.950 class17 14.950-14.600 class16 14,600-14,250 class15 14.250-13.900 class14 13.900-13,550 class13 13,550-13,200 class12 13,200-12,850 class11 12.850-12.500 class10 12.500-12.150 class9 12.150-11.800 class8 11,800-11,450 class7 11,450-11,100 class6 11,100-10,750 class5 10.750-10.400 class4 10.400-10.050 class3 10.050-9700 class2 9700-9350 class1
Relative probabilities
CompanyC
Cumulative probabilities
Relative probabilities
Cumulative probabilities
-
-
5.55
5.55
-
-
5.55
11.1
-
-
5,55
16.6
-
-
5.55
22.2
-
-
5.55
27.8
IO,5
10.5
5,55
33.3
IO,5
21,o
5.55
38.8
15,7
36,8
5,55
44.4
IO,5
47.3
11.1
55.5
IO,5
57.8
0
55.5
15,7
73,6
5.55
61.1
10.5
84,1
5.55
66.7
10.5
94,6
5,55
72,22
5,3
100
5.55
77.7
-
100
5,55
83.3
-
100
5,55
88.8
-
100
5.55
94.4
-
100
-
100
0 5.55
94,4 100
Assessing the Risks in Acquisitions-The
The gap of information in evaluating chances and risks can be bridged by this practical method. By using the risk-chance analysis you can produce information for systematic and consistent management of risk without additional expenditure and with the added convenience of using data processing. The risk-chance analysis permits a decision based on both objectives and risks. As management are more likely to be worried about an uncalculated risk than of an incalculable risk the method offers the chance to make a higher profit by consciously accepting a calculated risk. This helps to extend the options available to the management in making strategic decisions.
Comments
(3) To find this relative evaluation of an alternative as being more of a risk or of a chance the procedure is as follows: The percentage difference of the pessimistic to the probable future profit figure is calculated for each year. They are added and the mean of them is calculated for each year. The same happens with the optimistic future profit figure. They are added and the mean of them is calculated. The percentage difference between the probable and the optimistic figures is called D, and the difference between the probable and the pessimistic figures is called Dr. By comparing these figures to the percentage deviation of the pessimistic or optimistic overall value of the probable (they are called d,, respectively d,) one gets figures that always comply with one of nine possible criterions of a criterion-matrix (compare Table 4). In this example one calculates: 1 > 0.88 > = 0.81 that means the case
This case has been called R C = chance, N = neuter).
(1) The basis of the calculation are not estimated figures but, to make it easier to understand, calculated figures which are determined by the following formula (compare Figure 1): IV, value of company B (C), E,, future profits of company B (C), t=l, 2, 3, 4, 5; 1=1987, 2=1988, 3=1989, 4=1990,5=1991 K= 1, 2, 3; 1 = pessimistic figures, 2 = probable figures, 3 = optimistic figures.
in (R=risk,
(4) When then stability of the alternatives is checked, information of Table 2 is confirmed, e.g. the amount of chance and the amount of risk of alternative B is less than of C. (5) Detailed information can be found in: Neuburger, K. W. ‘Risikobeurteilung bei strategisthen Untemehmensentscheidungen’, Stuttgart 1980, West Germany.
Do do Do do -_1 dp=-4) c do_ -l=Dp dp dp
II>&>% I I R
45
use of multi-interval-arithmetic (multivall) and the method of calculation only occurs because of the need to find probabilities for risks.
Conclusion
4
Analysis
(2) The
In stage II which requires more mathematical knowledge of the user, relative frequencies can be determined as probabilities for the amounts of risk or chance without having to provide the input of probabilities. The risk-chance analysis makes it possible to gain information in one or two stages which depends on the importance of the decision.
DP
Risk-Chance
N
%I<+$ dp
c
Long Range Planning, Vol. 19, No. 3, pp. 41 to 45, 1986 Printed in Great Britain
41
Assessing the Risks in The Risk-Chance Acquisitions Analysis Klaus Neubiirger
Every company encounters a dangerous gap of information by evaluating various decision alternatives on the base of objective achievement alone. It is at least as important to assert and quantify the expected risk of the chosen alternative. The Risk-Chance Analysis described in this article provides a goalrelated and risk-related evaluation of alternatives without additional expenditures for providing information, and with the convenience of data processing. It is more comprehensive than risk analysis, which only calculates the probability of risk.
Introduction The management of company A is going to decide on the acquisition of one out of two companies B or C. The management will decide based on qualitative information as well as on quantitative calculations of the probable value of the company. In this case this value accounts within the next 5 years for’
alternative might have been found that would not have yielded maximum profit but would have avoided losses in high cost environment. By using a comprehensive more information processing, management is able to consider in advance the potential risk that is related with every decision. Otherwise it is condemned only to react or to accept an unwanted development. Management is very often unwisely advised to adopt this narrow evaluation of alternatives. How can one meet the demand for an evaluation of alternatives that is related to all the objectives and the risks involved in a specific decision problem? And strictly speaking what do we mean by ‘risk’?
Confusion
About the Word ‘Risk’
If the management of company A decided on these figures (and the assumed objective of profit maximization) only, presumably it would acquire company C, which has the higher probable value. It would have gone systematically through a process of rational decision-making but this process would have been dangerously limited in respect to the investment of company A, as no information has been supplied about the involved risk.
Every writer who uses the word ‘risk’ seems to have a different definition. This confusion makes it necessary to deal with the meaning of risk. In the example quoted above it had been assumed that company A has examined the alternatives in ‘the most probable’ situation only. In checking the impact of the pessimistic situation too it may be possible to visualize in advance a probable loss. Having this additional information management can answer the question whether (a) it is willing to run this risk of possible loss, which has been quantified, in order to have a chance of making the largest profit or (b) it is content with the lower profit at a lower risk of loss.
This dangerous lack of information exists quite often in reality, a fact that is hard to understand since risk related information can be obtained from the available data. Management has restricted its decision-making process by only considering a ‘probable’ scenario. In considering all the alternatives in a ‘pessimistic’ scenario, for instance with a high increase in labour or factory supply costs, an
Looking at the alternative of company B in more detail (Table 2) as the ‘amount of risk’ we define the difference between the expected highest profit (or maximal value) $12,803,000 and the lowest profit (or highest loss) fl1,388,000, in this case this equals $1,415,000. Management is not only interested in knowing the potential risk amount but also the probability of this risk of $1,415,000. These proba-
Company
B = US $12,803,000
Company
C = US $12,871,000.
42
J une
Long Range Planning Vol. 19
1986
bilities related to the amount of risk are called ‘riskprobability’. In considering the optimistic scenario their logical counterparts are ‘chance’, ‘chance amount’ and ‘chance probability’. Therefore, the answer to the question which risk the management is willing to take for which achievement of objectives depends on: *
The amount of risk;
*
The probability of risk that is combined with the amount of risk;
*
The decision maker’s attitude to risk and
*
The achievement
Requirements of a Practical Risk Information Technique
*
Evaluation of alternatives as high-risk or highchance relative to all relevant objectives.
*
Stability of the above mentioned variables relative to all parameters and determination of the most essential parameter.
of the Risk-Chance
Table 1 shows in column E,, the pessimistic, in the column E,, the optimistic future profits of company B (company C) from 1987 to 1991. The criterion of ‘availability of the input information’ is the way that the risk-chance analysis obtains its information about achievement of objectives, amount of risk and probability of risk from the available data in Table 1. This is done by calculation as shown in Figure 1.2
To be convenient a risk-calculation technique has to fulfill two requirements: (1) Availability of the required data and (2) Availability of the required mathematical know-how.
*
The top-box of Figure 1 asks for the pessimistic value W,, the optimistic W, and the probable W,. To determine W, for instance this value is calculated by using the pessimistic E,, for 1987-1991 only. Having calculated Wr and I%‘, in the same way the additional information in Table 2 can be provided. From this the management can see that the alternative ‘buying company C’ shows a higher amount of risk ($3,566,000) than alternative B, but offers the higher amount of chance, too ($3,096,000). If ‘buying company B’ is more of a chance or of a risk it has to be considered how much the probable figures E,, of both alternatives are
the method
Amount of risk related to all relevant objectiveand controlling-figures, such as profit, liquidity, share of long-term liabilities and so on.
‘Chance equals opportunity.
Table 1. Data for an acquisition decision Future profits of company B (company C) us $ ‘000’S)
to the
First criterion for the convenience of such a calculation has been the availability of the required data. To provide the information about the value of the companies B and C, some data are already available (Table 1). By these figures it is already expected that company B in 1987 (t= l), pessimistically seen, will have a future profit of $500,000 (E,,), in 1988 (t= 2) for instance, optimistically seen, a future profit of $l,OOO,OOO(E3J and in 1991 (t = 5) a future profit, probably, of $l,lOO,OOO (E&.
Independent of different attitudes towards risk, people do accept risk as the counterpart to chance* but they are more afraid of a non-calculated risk than of a incalculable risk.
To make best use of the information should provide the following data:
Probabilities of risk that are related amount of risk.
Suitability Analysis
of objectives.
The requirements of a practical risk-information technique have been explained above. We outlined what information about objectives and risks is necessary for a decision and has therefore to be provided by the technique. But such a calculation has to be checked for its usefulness within the company. That means a methodology has to fulfill two equally important criteria: (1) convenience and (2) best use of available information.
*
t
Pessimistic E1t
Probable
Year
E2t
Optimistic E31
1987
1
500
600
700
1988
2
w&x
- 1989
3
(;y (700) 600
1990
4
(“9cg)
1991
5
‘l”o”o”o’ (800)
yJ (1100) 1100 (1100)
WJ
58ooooo) (900) 900 \9lE? (1140) 1200 (1400)
Assessing the Risks in Acquisitions-The
w,= ;
43
uss
Company B
Company C
12,803,OOO
12,871,OOO
w, Pessimistic value
14,053,000
15,967,OOO
% Amount of risk w, - wp Amount of chance
11.388.000
9.305.000
1,415,000
3.566.000
1,250,OOO
3.096.000
risky
risky
high stability
low stability
E5 +
r-1(1.08)'
Analysis
Table 2. Risks and chance* calculated from Table 1
Calculation of value W, by E,,, E,, E3t
Et
Risk-Chance
Probable value
0.08 (1.085)
T Optimistic value
Arithmetic* for
w, - w, Evaluation of the alternative3 Stability of“ w,
*Chance equals opportunityfor benefit.
(residual balance $100,000) (see Table 1). However in the same year the future profit figures of company C were reduced from $900,000 to $500,000 (residual balance $400,000), respectively increased to $950,000 (residual balance $50,000). Such differences in the input data (subject to different sensitivities of the acquisition alternatives towards changed assumptions of the company’s environment) also have to be considered in assessing whether the acquisition of company B is a high risk or not, -e.g. by 1ook’mg~aKiG variation in values.3 The same procedure can be applied to answer the question how changes in the objective IV,, are influenced by changes in the future profit data? (i.e. how sensitive is WV.4)
“Multivail = multi-interval arithmetic.
Figure 1. The method of calculating risk and chance
Looking again at the requirements for a riskinformation technique you realize that the riskchance analysis has to be expanded with respect to the probability of risk and has to be judged with regard to the mathematical knowledge and ability
changed towards the optimistic or the pessimistic end. The future profit E,, of company B in 1989 changed from $800,000 to $600,000 (residual balance $200,000), respectively changed to $900,000
--
i--
-5
Company 8 -
Company C
__, I
I
Y-a
1
L__-
i
30 20 t
10 It 0
I
I
Ii
L-m
1 L-1 L___,
i__,
I
II I II
~ 7
L
I/
I
LB_
t
II
1234567
11
11
8
9
10
1
II
11
12
Classof Risk
Figure 2. Risk profiles for two acequisition
candidates
L_ 1
“I If 13
14
I
15
16
1 I
I
I
17
18
19
44
Long Range Planning Vol. 19
June 1986
of the user. This has to be decided by the potential user.
or not. So a detailed description of the procedure for calculating probabilities is not required.5
In stage I the user could work with estimates instead of the formula which has been used here to make it easier to understand. If the amount of risk is matched with a probability of risk, the formula is required to calculate (Figure 1).
Table 3 and Figure 2 show additional information to be developed for the example of company acquisition. Figure 2 shows graphically the cumulative probabilities in Table 3. One recognizes that the spread of the figures of alternative C is wider than that of alternative B. This has already been shown in the evaluation of stability (Table 2).
Risk-Probability To calculate probabilities for the amount of risk the risk-chance analysis does not need any further information beyond those in Table 1. By finetuning the procedure, the interval from pessimistic to optimistic future profit can be subdivided into several smaller equal intervals (see Figure 1 for subdivision into 19 equal intervals). This provides relative frequencies and the required probabilities. In practice, the amounts of risk are more important and the decision-maker can make an assessment based on his experience whether they are probable
Management will most likely decide for alternative B if it is willing to risk less and alternative C if it is willing to risk more. These decisions were already obvious from the information gained in stage I (compare Table 2). Looking at the risk profile of Figure 2 management can determine the value of W, if it is willing to accept a 10 per cent riskprobability that the value will be too high. For the company C Figure 2 shows the corresponding figures in class 3, e.g. the value must not exceed $10,400,000.
Table 3. Risk profiles for two acquisition candidates Company B Value ($) 16,000-15,650 class19 15,650-15,300 class18 15.300-14.950 class17 14.950-14.600 class16 14,600-14,250 class15 14.250-13.900 class14 13.900-13,550 class13 13,550-13,200 class12 13,200-12,850 class11 12.850-12.500 class10 12.500-12.150 class9 12.150-11.800 class8 11,800-11,450 class7 11,450-11,100 class6 11,100-10,750 class5 10.750-10.400 class4 10.400-10.050 class3 10.050-9700 class2 9700-9350 class1
Relative probabilities
CompanyC
Cumulative probabilities
Relative probabilities
Cumulative probabilities
-
-
5.55
5.55
-
-
5.55
11.1
-
-
5,55
16.6
-
-
5.55
22.2
-
-
5.55
27.8
IO,5
10.5
5,55
33.3
IO,5
21,o
5.55
38.8
15,7
36,8
5,55
44.4
IO,5
47.3
11.1
55.5
IO,5
57.8
0
55.5
15,7
73,6
5.55
61.1
10.5
84,1
5.55
66.7
10.5
94,6
5,55
72,22
5,3
100
5.55
77.7
-
100
5,55
83.3
-
100
5,55
88.8
-
100
5.55
94.4
-
100
-
100
0 5.55
94,4 100
Assessing the Risks in Acquisitions-The
The gap of information in evaluating chances and risks can be bridged by this practical method. By using the risk-chance analysis you can produce information for systematic and consistent management of risk without additional expenditure and with the added convenience of using data processing. The risk-chance analysis permits a decision based on both objectives and risks. As management are more likely to be worried about an uncalculated risk than of an incalculable risk the method offers the chance to make a higher profit by consciously accepting a calculated risk. This helps to extend the options available to the management in making strategic decisions.
Comments
(3) To find this relative evaluation of an alternative as being more of a risk or of a chance the procedure is as follows: The percentage difference of the pessimistic to the probable future profit figure is calculated for each year. They are added and the mean of them is calculated for each year. The same happens with the optimistic future profit figure. They are added and the mean of them is calculated. The percentage difference between the probable and the optimistic figures is called D, and the difference between the probable and the pessimistic figures is called Dr. By comparing these figures to the percentage deviation of the pessimistic or optimistic overall value of the probable (they are called d,, respectively d,) one gets figures that always comply with one of nine possible criterions of a criterion-matrix (compare Table 4). In this example one calculates: 1 > 0.88 > = 0.81 that means the case
This case has been called R C = chance, N = neuter).
(1) The basis of the calculation are not estimated figures but, to make it easier to understand, calculated figures which are determined by the following formula (compare Figure 1): IV, value of company B (C), E,, future profits of company B (C), t=l, 2, 3, 4, 5; 1=1987, 2=1988, 3=1989, 4=1990,5=1991 K= 1, 2, 3; 1 = pessimistic figures, 2 = probable figures, 3 = optimistic figures.
in (R=risk,
(4) When then stability of the alternatives is checked, information of Table 2 is confirmed, e.g. the amount of chance and the amount of risk of alternative B is less than of C. (5) Detailed information can be found in: Neuburger, K. W. ‘Risikobeurteilung bei strategisthen Untemehmensentscheidungen’, Stuttgart 1980, West Germany.
Do do Do do -_1 dp=-4) c do_ -l=Dp dp dp
II>&>% I I R
45
use of multi-interval-arithmetic (multivall) and the method of calculation only occurs because of the need to find probabilities for risks.
Conclusion
4
Analysis
(2) The
In stage II which requires more mathematical knowledge of the user, relative frequencies can be determined as probabilities for the amounts of risk or chance without having to provide the input of probabilities. The risk-chance analysis makes it possible to gain information in one or two stages which depends on the importance of the decision.
DP
Risk-Chance
N
%I<+$ dp
c