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The use of financial models in long range planning
The Use ofFinancial Models in Long Range Plannin P. J. Dohrn
and G. R. Salkin
The authors explain the concept of a model and outline the ways in which modelling techniques may be used to answer some of the financial questions which arise in long range planning. The article is concerned with the use of cash flow models, decision trees, linear programming and other mathematical techniques, to explore the financial implications of alternative strategies.
ONG
RANGE
PLANNING
IS GROWING
rapidly in importance as increasing numbers of managers realize that it gives them an edge over their competitors. However it is a complex and difficult activity to which the modern manager must devote a large part of his time and effort, for decisions made now on the size of plant to build or which new markets to enter will strongly influence the future or even survival of the company. When carrying out Long-Range Planning the manager wants answers to many questions, two groups of which will concern us here. The first group is typified by: “What will be the financial results of the plan if all my assumptions are correct ?” The second group, less obvious but just as significant, are those which refer to contingencies for which he must plan if some of his assumptions break down. One such question is: “How would profit be affected if competition forced us to drop the price of a certain product?” The planner may be faced with a bewildering variety of alternatives and possibilities whose consequences must be calculated. It is with growing recognition of the vital and complex nature of these decisions that managers are turning to management scientists for aid in making them. As a result new techniques have been devised and adapted to give a clear statement of the consequences of a plan. the possible outcomes of alternatives and the effects of uncertainty or risk. One approach which uses these techniques is called financial modelling. Finan-
DECEMBER,
1969
cial models are powerful aids to the financial side of planning. They provide assessments of the consequences of alternative policies or chance events. and in certain forms will automatically calculate the best policy. This paper explains the concept of a model and outlines the ways in which modelling techniques may be used to answer some of the financial questions which arise in long range planning. THE
IDEA
OF A MODEL
“Model” is used in the same sense as the model employed by an aircraft designer, on which aspects of design are tested. and decisions made before production starts. The designer has performance criteria such as speed. length of take-off. carrying capacity to satisfy. He must alter variables such as power and dimensions to suit these and at the same time take account of atmospheric turbulence and other chance events. There are three sides to his problem : (a) criteria to be satisfied: (b) variables which can be altered within certain limits; (c) chance occurrences outside the control of the pilot. A manager deciding about the future is in a similar position. He has criteria to satisfy, factors which he can alter, and chance occurrences which may upset his plans. Like the designer, he can build a model of the business on which the effects of chance and of changes in the variables may be tested. Hiscriteriamay.forexample, be net profit or the values of key financial
ratios; the variables perhaps capital investment and selling price; and the chance occurrences could be intensity of competition or changes in wage rates. A financial model consists of relationships between criteria and variables, taking chance events into account. It must reflect the relative importance of the variables, the extent to which they can be controlled, and any limitations or restrictions on their values. Therefore the purpose of a model is to experiment with changes in variables so that their effects can be calculated. STEPS
IN
MODEL
BUILDING
There are four key steps in building and working with financial models: Definition qf the problem, selection of criteria, and identification of alternatives. The information on which this phase is based may come from customer demand, marketing studies, management intuition, research, or a variety of other sources. Formulation of the structure qf the model. Determining at this early stage the technique to be used and the form of the relationships between the factors, puts the alternatives into perspective, helping to identify others, and points to the data required. Collection of data. Some details of the information required are given below. Substitution on the model, evaluation of the alternative courses of action and possible outcomes of chance events, relative to the criteria selected.
27
Our experience shows that there is a tremendous upsurge in understanding of the problem as the model is formulated and analysed, leading to restatement, new alternatives, and restructuring of the model itself. The whole process is a dynamic one with continual development, changes in criteria. and recognition of other alternatives. One crucial aspect is the information on which the model is based. The well known maxim, “garbage in-garbage out”, applies here at least as much as it applies anywhere, and if managers are to get useful results from their model they must be prepared to invest in information. Financial, operating, and marketing data are required, including investment needed. life of facilities, residual value. operating and fixed costs. market size, market share, and growth rate. In addition, any available knowledge about the uncertainty in the data should be gathered. We might say that a market is expected to be worth f90.000 per annum by 1973, but there is a 30 per cent chance that this could be less than E65,000, or we could go further and associate a probability with each of the possible sales incomes. It is also important to know the objectives of the business over the period contemplated and to express these quantitatively, perhaps in terms of return on investment and time. A corporate objective to gain a major share of a market must be brought down to the actual share desired, say 60 per cent, and the time over which growth is to take place, followed by translation of these figures into year-by-year sales incomes. In the next section we examine the ways in which this information is built up into a model and the techniques which are available to help answer the many questions posed by planners. METHODS The available techniques for building and analysing financial models may be divided into three groups as follows: (a) Simultation; (b) Decision trees and probability; (c) Mathematical programming, particularly linear programming. The choice of technique for a specific application depends on the problem and on the people and resources available. Simulation and mathematical programming models are almost invariably operated on a computer. The relative advantages and disadvantages of each one are compared in the descriptions below. Simulation Simulation models can range from simple models of a project in which variables are altered one by one, to complex systems based on control theory, In practice two
28
types of simulation model are frequently encountered. One is the model of an individual project which uses Monte-Carlo methods to carry out risk analysis. The other is the simple model of accounting and financial processes called cash flow simulation. The latter group of models will be desribed here. Figure I shows a simplified flow diagram of a computer program named the Cash Flow Simulator. It uses projected sales and production data to generate a set of monthly and year-end accounts, printing out the items listed in Table 1. A sample of the questions which this approach is most helpful in answering is given below: (a) What is the effect on profit if sales TABLE 1. CASH SIMULATION
FLOW
Month TRADING ACCOUNT Opening W.I.P. Mat. purchases Var. mfg. costs Total Closing W.I.P. Net F.G. prod. Opening F.G. Net F.G. prod. Total -Closing stock Cost of sales Sales -Cost of sales Gross profit PROFIT
AND LOSS ACCOUNT Expenses Fixed costs Marketing cost Total expenses Net orofit Gross profit
BALANCE SHEET Fixed assets Current assets Stock W.I.P. Debtors Cash Current liabilities Creditors Current expenses Net assets Ownership interest Capital Profit Previous profit Total ANALYSIS
AND RATIOS Sales.‘Stock Sales/Debtors Stock/Debtors Profit,‘Sales Profit /Capital Sales/Assets Working capital
are 10 per cent below forecast’! sales-production pattern cause any key financial ratios to move out of control? (c) If a large increase in sales volume by promotion is intended, what are the working capital requirements? (4 How far can price be lowered before reaching the break-even point at various sales volumes? (e, How do varying material costs affect the accounts? (0 In what way does a change in the rules for calculating production reorder quantities and stock levels affect the accounts‘? The Cash Flow Simulator Program is really a device which allows easy re-calculation of accounts on a computer after the quantities which make them up have been altered. For instance, the procedure in studying answers to the first question above would be: enter the sales forecast along with all the other data and calculate accounts including net profit; next enter the reduced forecast, re-calculate profit, and compare results. As many sales patterns as desired could be tried. Working capital would be studied by entering the forecast sales pattern and noting working capital requirements during the period of high production rate. This might be followed by a study in which sales volumes were varied and different prices tried with each level of sales to determine break-even points and profit levels. The effects of changes in material costs and in production-inventory rules may be investigated in a similar fashion. Financial ratios such as those shown at the bottom of Table 1. or others which may be preferred. would be monitored at all stages in order to be sure that they were not moving out of control. Any number of products or factories may be handled. The programme gives a trading account for each and a full set of accounts at the end. The user may choose from two types of production-inventory rule, programme his own rule or enter his own data. as required. The model has been programmed to mode”. This operate in “conversational means that the computer asks a series of questions through the console printer and the user answers these by the typewriter keyboard on the console. The sequence of questions regarding fixed assets, capital. and cash is illustrated below, with questions in italics and the user’s answers in bold type.
(b) Does the projected
Enter initial levels of: Fixed assets Capital Cash 180,000 85,000 15.000
LONG
RANGE
PLANNING
Will there be am’ change in the levels qf Fixed Assets, Capital or Cash during the course of the simulation . . Yes (I) No (2) 1 Month ( ) Change in level of Fixed Assets ( ) Month ( ) Change in level of Capital ( ) Month ( ) Change in level of Cash ( ) 6 20,000 6 12,000 0 0 Are there any ,further changes Yes (1) No (2) 2 Subsequent questions request stock, cost and demand data and production-inventory rules, down to the final question which is: Would you like to begin again
ITees(I)
THE CASH FLOW SIMULATOR IN PRACTICE For practical application, the programme always has to be extensively modified to suit the particular problem. Because of this it has been written as a series of blocks or sub-routines, allowing the user to rewrite those parts which have to be changed without upsetting the remainder of the programme. One application concerned a Company owning a number of factories with limited capacity, making only one product. The main objective was to increase the market share over a six year period.
&ii2 Start
lnitialise accounts
-
_
1
T
Enter cost data & sales forecast f Select prod. inv. control rule
t Carry out accounting calculations
DECEMBER,
1969
0.50 0.99 0.98
6350,990 &289,999 ~175,000
Write trading account 1
This could be done in three ways: raise the output of existing factories, establish new ones. or acquire other companies. Within these possibilities there were a number of variables, such as pricing policy, sales volumes, timing of expansion and acquisitions, purchase prices, and establishment costs. A modified form of the model described above was used to help management to reach their decision. The model was most effective in determining the followinz asnects of nlannine: (4 Elects on long term irofitability of changes in pricing policy and sales volume. (b) Profitability of factories available for acquisition over a range of purchase prices and product selling prices. Cc)The way in which profitability of new factories varied with timing and product price. (4 Comparison of a range of combinations of the three types of expansion. One important result was that acquisition and establishment of new factories were only economic with relatively high prices. The rewriting of the programme, and the computations, were carried out at a tota cost of under f5000 including computer time. Our next method is more efficient in the presence of risk and uncertainty. DECIStON TREES AND PROBABtLtTY The use of probability, with or without the decision tree technique is particularly useful where uncertainty plays a large part in planning. A “probability” is assigned to chance events which the manager cannot control, as illustrated below:
~v~~~~~~~~,
1
$0 (2)
The “conversational mode” is very helpful in teaching. but is inefficient for practical applications, where punched cards are normally used.
I 1 Write out accounts and financial ratios
An event with probability 1 is certain to occur, whereas one with probability zero is certain not to occur. Where the probability lies between 0 and 1, the larger the probability the more likely the event; for example a probability of 0.50 means a “fifty-fifty” chance, and 0.98 means nearly certain. If he adopts this approach. the user must obtain estimates of probabilities as illustrated above-not always an easy task, One way in which these are employed to give a better basis for decisions is illustrated in the discussion of decision trees below.
29
We have now seen how simulation may be used to study the effects of different alternatives and how this may be extended by means of probabilities to encompass an analysis of the risks involved. None of these methods however, will automatically find the best policy. To do this we must turn to mathematical programming techniques. Mathematical
KEY:
<>
Decision
Point
0 Chance
Event
FIGURE 2. DECISION TREE (First stage of a Decision Tree for a manufacturer deciding whether to commence production of a new product on a large or small scale) Decision
Trees
Consider now the case of a manager who has a new product ready to be manufactured and marketed. Some limited market research data has been obtained, along with capital and operating costs. and he is trying to decide how big a plant to build. Two questions which he might want to answer are : (a) How do returns on a large plant built now compare with those on a small plant extended to meet increases in demand? (b) What happens if we build a very large factory and sales do not come up to expectation ? There are a number of possible sequences of decisions and chance events hidden in these questions. Problems such as this are best handled with the aid of a Decision Tree. Figure 2 illustrates a decision tree for just such a problem. The decision facing the manager now is whether or not to build a large plant, and the chance possibilities are that the market may be either large (national) or small (local) and that a competitor may introduce a substitute if the product is successful. An explanation of the theory of decision trees would be out of place here, and we must confine ourselves to an example of the steps in the solution and the results. Costs and expected revenue have already been determined, so that the planner is able to calculate the return from any of the
30
many possible final outcomes traced along the branches of the tree. This in itself ii very useful because he is then able to see all of the possibilities which may range from a high return to a heavy loss. In Table 2 some results are illustrated for a case in which there were seven possible outcomes. If, however, the planner has also been able to estimate the probability of a large or a small market and whether or not the competitor will introduce a substitute, he can calculate a measure of probability for each outcome as in the third column of Table 2. The use of probabilities may be extended, for example probabilities may be assigned to each of a range of sales volumes. The results may be taken a stage further by the use of Utility Theory. A “utility” can be determined for each of the immediate alternatives, so that they may be ranked in order of preference. TABLE
2. DECISION
Decision
Build
Large
Plant BuildPlant Small ’ This
may for example
be the net present
Programming
Mathematical Programming is one of the more powerful techniques available to the financial model builder. It is concerned with allocating the company’s activities to its resources so as to gain the objective in the best possible way. The resources might be machine hours, working capital and markets; the activities might be making screws or motor cars; and the objective might be to achieve the maximum profit. In other words, mathematical programming is a way of finding the optimum use of resources. It is the oprirmrm which dismathematical programming tinguishes from the other methods discussed above which, while allowing the user to try the effects of policies which he has chosen himself, will not automatically find the optimum policy. However, this is not all that mathematical programming achieves. It also shows clearly which resources are critical by valuing them in terms of the contribution they would make to profit if they were increased. Thus resources not wholly used up have “value” zero because an increase would not bring about any changes in profit, whereas a resource which is fully used is assigned a value related to the rate of improvement in profit if the amount of the resource were increased. Therefore the critical resources are sorted out and the effect on profit of increasing them easily calculated. In addition, mathematical programming can be adapted to find the results of allocating the resources in ways other than the optimum, and how sensitive profit is to such changes. These two additional facilities-to value the company’s resources in terms of their contribution to profit. and to produce statements of the TREE
*Return a 500,000 200,000 -100,000 -300,000 300,000 150,000 100.000 value of all cash flows
RESULTS Probability of the return shown after the decision is made 0.6 0.1 8:: ;:; 0.3 over the life of the project.
LONG
RANGE
PLANNING
consequences of alternative courses of action-are as important in practice as the ability to calculate the optimum. In order to make these statements clear, let us look at a typical list of questions which can be answered by mathematical programming: Q.1 How can we best use our resources to achieve maximum profit? 4.2 What is the optimum amount of storage space in three years’ time? 4~3 Is machine capacity limiting the firm’s ability to earn more? 4.4 How would the optimum change under different pricing policies? Q.5 How sensitive is our profit to the sales volume of particular products ? Q.6 If we phase out a certain product how will profit be affected ? Questions 1 and 2 concern the optimum. Question 3 the valuing of resources, and Questions 4, 5 and 6 alternative policies. The branch of mathematical programming most often used in company modelbuilding is called Linear Programming. Setting-up a linear programming model is a fairly complex operation because all relevant relationships between activities, resources and the chosen objective must be stated in detail as algebraic equations. This means first of all making a list of the company’s resources and all constraints on its activities including machine hours, subcontractors, cash, and markets. Some possible resources and constraints are shown in Table 3. All possible activities, such as products which can be manufactured, are then listed. The next step is to determine the relationships between activities and resources, which means finding out how much of each resource is used by each activity. and then writing this as an equation. The example in the Appendix will explain the process. The result is a number of equations-in some cases perhaps two or three thousand-and possibly many thousands of activities arranged in a “tableau” for computation. Computation is carried out on a computer, probably using an adaptation of the computer manufacturer’s standard linear programming package. We realize that the idea of using equaTABLE Financial working capital cash investment capital receivables collection period money borrowed money repaid prices Listed
3. RESOURCES
1969
SUCCESSFUL FINANCIAL
AND
CONSTRAINTS Marketing
machine hours labour hours storage space subcontracted work raw materials time
constraints
USE OF MODELS
Keys to successful use of models are the same no matter which method is adopted, indeed they are very like a list of conditions for an effective long range plan. At the beginning objectives must be set and variables identified. The model must be (a) practical, and only as complex as required by the programme and as allowed by the quality of data and
Physical
above are some of the typical
DECEMBER,
to find an optimum company policy might give rise to scepticism in the minds of some readers. However, linear programming has proved in a great number of applications over the last twenty or so years, that it is a practical and effective technique. These applications have covered for example, company and financial modelling, blending, transportation, and allocation of production facilities. We have been concerned in a recent application to a light engineering company manufacturing a number of products, some of which have a seasonal demand. The programme is designed to cover twelve quarterly periods giving optimum levels of production and storage of each product in each period in response to sales forecasts. It takes account of limitations on time, storage facilities, cash, machine labour, raw material supply and so on. The cost of developing a linear programming model depends largely on the complexity required. It can be as little as f10,OOO but may range up to f50,OOO and beyond. In spite of its power, linear programming has limitations and the technique has been extended in a number of ways. One of these is called integer programming. Integer programming allows the user to include activities which must be treated as a whole, such as major capital projects. Thus the financial model can help to select the best group of projects from all those available, where capital is rationed, and will schedule annual expenditure on those selected. Another new development worthy of note, called “goal programming”, allows more than one objective to be considered in the same programme. tions
maximum minimum
on company
sales
of each
product
sales of each product
available facilities;
(b) built with the close co-aperation
of the managers and accountants who are to use it; (cl readily convertible into working budgets; Cd)updated regularly and subject to continual development. Close co-operation of managers and accountants is vital, for this helps to ensure that the other conditions above are obeyed. There is no need for them to carry out the whole operation, but they must commit some time to assisting with it so that they fully understand the use and limitations of the model. Probably the greatest danger lies in accepting the output as gospel. Financial models are merely aids to planning, which help in understanding the relevant alternatives and in identifying critical variables. They do not substitute for the manager, but assist him in making better decisions. CONCLUSION
A manager’s most important and challening decisions are those concerned with planning. Financial models provide managers with a way of experimenting with the future, of determining the likely consequences of their plans, and discovering what they must plan for in order to cover the likelihood of their assumptions breaking down. As business grows more complex the managements of many companies are successfully applying financial models to long range planning. l APPENDIX Construction Programming
of Linear Tableau
Suppose a work centre is available for 410 hours per month and that three products are made on it; product 1 taking 2 hours per unit, product 2 taking 3 hours and product 3 taking 5 hours. If XI, X2, X3 are respectively the quantities, of oroducts 1, 2 and 3 manufactured on this work centre during the month, the number of hours per monthly for which the work centre is used is: 2x1 i This that:
total
cannot 2x1
(the sign
‘-’
3x2 -
be greater
5x3 than
410 hours,
so
- 3x2 -- 5x3-410 means
‘is not greater
than’).
This inequality is one of those which go to make up the tableau. It relates the resource of machine hours to the rate at which it is used up by each of the three products. It is also expressed as the constraint which availability of only 410 machine hours exerts on the quantities of products 1,2 and 3 manufactured by this method. Other inequalities will express constraints due to availability of raw material, working capital, cash, markets, transport facilities, storage space and others. The inequalities are converted to equations for the solution of the problem. The objective must also be stated in terms of variables like X1, XZ, X3, showing the profit derived from one unit of each of them. Thus if X1 and XZ each gained E2 per unit and X3 fl, total profit earned by them would be:
activities.
Profit
= 2x1 + 2x2 A x3
31
and G. R. Salkin
The authors explain the concept of a model and outline the ways in which modelling techniques may be used to answer some of the financial questions which arise in long range planning. The article is concerned with the use of cash flow models, decision trees, linear programming and other mathematical techniques, to explore the financial implications of alternative strategies.
ONG
RANGE
PLANNING
IS GROWING
rapidly in importance as increasing numbers of managers realize that it gives them an edge over their competitors. However it is a complex and difficult activity to which the modern manager must devote a large part of his time and effort, for decisions made now on the size of plant to build or which new markets to enter will strongly influence the future or even survival of the company. When carrying out Long-Range Planning the manager wants answers to many questions, two groups of which will concern us here. The first group is typified by: “What will be the financial results of the plan if all my assumptions are correct ?” The second group, less obvious but just as significant, are those which refer to contingencies for which he must plan if some of his assumptions break down. One such question is: “How would profit be affected if competition forced us to drop the price of a certain product?” The planner may be faced with a bewildering variety of alternatives and possibilities whose consequences must be calculated. It is with growing recognition of the vital and complex nature of these decisions that managers are turning to management scientists for aid in making them. As a result new techniques have been devised and adapted to give a clear statement of the consequences of a plan. the possible outcomes of alternatives and the effects of uncertainty or risk. One approach which uses these techniques is called financial modelling. Finan-
DECEMBER,
1969
cial models are powerful aids to the financial side of planning. They provide assessments of the consequences of alternative policies or chance events. and in certain forms will automatically calculate the best policy. This paper explains the concept of a model and outlines the ways in which modelling techniques may be used to answer some of the financial questions which arise in long range planning. THE
IDEA
OF A MODEL
“Model” is used in the same sense as the model employed by an aircraft designer, on which aspects of design are tested. and decisions made before production starts. The designer has performance criteria such as speed. length of take-off. carrying capacity to satisfy. He must alter variables such as power and dimensions to suit these and at the same time take account of atmospheric turbulence and other chance events. There are three sides to his problem : (a) criteria to be satisfied: (b) variables which can be altered within certain limits; (c) chance occurrences outside the control of the pilot. A manager deciding about the future is in a similar position. He has criteria to satisfy, factors which he can alter, and chance occurrences which may upset his plans. Like the designer, he can build a model of the business on which the effects of chance and of changes in the variables may be tested. Hiscriteriamay.forexample, be net profit or the values of key financial
ratios; the variables perhaps capital investment and selling price; and the chance occurrences could be intensity of competition or changes in wage rates. A financial model consists of relationships between criteria and variables, taking chance events into account. It must reflect the relative importance of the variables, the extent to which they can be controlled, and any limitations or restrictions on their values. Therefore the purpose of a model is to experiment with changes in variables so that their effects can be calculated. STEPS
IN
MODEL
BUILDING
There are four key steps in building and working with financial models: Definition qf the problem, selection of criteria, and identification of alternatives. The information on which this phase is based may come from customer demand, marketing studies, management intuition, research, or a variety of other sources. Formulation of the structure qf the model. Determining at this early stage the technique to be used and the form of the relationships between the factors, puts the alternatives into perspective, helping to identify others, and points to the data required. Collection of data. Some details of the information required are given below. Substitution on the model, evaluation of the alternative courses of action and possible outcomes of chance events, relative to the criteria selected.
27
Our experience shows that there is a tremendous upsurge in understanding of the problem as the model is formulated and analysed, leading to restatement, new alternatives, and restructuring of the model itself. The whole process is a dynamic one with continual development, changes in criteria. and recognition of other alternatives. One crucial aspect is the information on which the model is based. The well known maxim, “garbage in-garbage out”, applies here at least as much as it applies anywhere, and if managers are to get useful results from their model they must be prepared to invest in information. Financial, operating, and marketing data are required, including investment needed. life of facilities, residual value. operating and fixed costs. market size, market share, and growth rate. In addition, any available knowledge about the uncertainty in the data should be gathered. We might say that a market is expected to be worth f90.000 per annum by 1973, but there is a 30 per cent chance that this could be less than E65,000, or we could go further and associate a probability with each of the possible sales incomes. It is also important to know the objectives of the business over the period contemplated and to express these quantitatively, perhaps in terms of return on investment and time. A corporate objective to gain a major share of a market must be brought down to the actual share desired, say 60 per cent, and the time over which growth is to take place, followed by translation of these figures into year-by-year sales incomes. In the next section we examine the ways in which this information is built up into a model and the techniques which are available to help answer the many questions posed by planners. METHODS The available techniques for building and analysing financial models may be divided into three groups as follows: (a) Simultation; (b) Decision trees and probability; (c) Mathematical programming, particularly linear programming. The choice of technique for a specific application depends on the problem and on the people and resources available. Simulation and mathematical programming models are almost invariably operated on a computer. The relative advantages and disadvantages of each one are compared in the descriptions below. Simulation Simulation models can range from simple models of a project in which variables are altered one by one, to complex systems based on control theory, In practice two
28
types of simulation model are frequently encountered. One is the model of an individual project which uses Monte-Carlo methods to carry out risk analysis. The other is the simple model of accounting and financial processes called cash flow simulation. The latter group of models will be desribed here. Figure I shows a simplified flow diagram of a computer program named the Cash Flow Simulator. It uses projected sales and production data to generate a set of monthly and year-end accounts, printing out the items listed in Table 1. A sample of the questions which this approach is most helpful in answering is given below: (a) What is the effect on profit if sales TABLE 1. CASH SIMULATION
FLOW
Month TRADING ACCOUNT Opening W.I.P. Mat. purchases Var. mfg. costs Total Closing W.I.P. Net F.G. prod. Opening F.G. Net F.G. prod. Total -Closing stock Cost of sales Sales -Cost of sales Gross profit PROFIT
AND LOSS ACCOUNT Expenses Fixed costs Marketing cost Total expenses Net orofit Gross profit
BALANCE SHEET Fixed assets Current assets Stock W.I.P. Debtors Cash Current liabilities Creditors Current expenses Net assets Ownership interest Capital Profit Previous profit Total ANALYSIS
AND RATIOS Sales.‘Stock Sales/Debtors Stock/Debtors Profit,‘Sales Profit /Capital Sales/Assets Working capital
are 10 per cent below forecast’! sales-production pattern cause any key financial ratios to move out of control? (c) If a large increase in sales volume by promotion is intended, what are the working capital requirements? (4 How far can price be lowered before reaching the break-even point at various sales volumes? (e, How do varying material costs affect the accounts? (0 In what way does a change in the rules for calculating production reorder quantities and stock levels affect the accounts‘? The Cash Flow Simulator Program is really a device which allows easy re-calculation of accounts on a computer after the quantities which make them up have been altered. For instance, the procedure in studying answers to the first question above would be: enter the sales forecast along with all the other data and calculate accounts including net profit; next enter the reduced forecast, re-calculate profit, and compare results. As many sales patterns as desired could be tried. Working capital would be studied by entering the forecast sales pattern and noting working capital requirements during the period of high production rate. This might be followed by a study in which sales volumes were varied and different prices tried with each level of sales to determine break-even points and profit levels. The effects of changes in material costs and in production-inventory rules may be investigated in a similar fashion. Financial ratios such as those shown at the bottom of Table 1. or others which may be preferred. would be monitored at all stages in order to be sure that they were not moving out of control. Any number of products or factories may be handled. The programme gives a trading account for each and a full set of accounts at the end. The user may choose from two types of production-inventory rule, programme his own rule or enter his own data. as required. The model has been programmed to mode”. This operate in “conversational means that the computer asks a series of questions through the console printer and the user answers these by the typewriter keyboard on the console. The sequence of questions regarding fixed assets, capital. and cash is illustrated below, with questions in italics and the user’s answers in bold type.
(b) Does the projected
Enter initial levels of: Fixed assets Capital Cash 180,000 85,000 15.000
LONG
RANGE
PLANNING
Will there be am’ change in the levels qf Fixed Assets, Capital or Cash during the course of the simulation . . Yes (I) No (2) 1 Month ( ) Change in level of Fixed Assets ( ) Month ( ) Change in level of Capital ( ) Month ( ) Change in level of Cash ( ) 6 20,000 6 12,000 0 0 Are there any ,further changes Yes (1) No (2) 2 Subsequent questions request stock, cost and demand data and production-inventory rules, down to the final question which is: Would you like to begin again
ITees(I)
THE CASH FLOW SIMULATOR IN PRACTICE For practical application, the programme always has to be extensively modified to suit the particular problem. Because of this it has been written as a series of blocks or sub-routines, allowing the user to rewrite those parts which have to be changed without upsetting the remainder of the programme. One application concerned a Company owning a number of factories with limited capacity, making only one product. The main objective was to increase the market share over a six year period.
&ii2 Start
lnitialise accounts
-
_
1
T
Enter cost data & sales forecast f Select prod. inv. control rule
t Carry out accounting calculations
DECEMBER,
1969
0.50 0.99 0.98
6350,990 &289,999 ~175,000
Write trading account 1
This could be done in three ways: raise the output of existing factories, establish new ones. or acquire other companies. Within these possibilities there were a number of variables, such as pricing policy, sales volumes, timing of expansion and acquisitions, purchase prices, and establishment costs. A modified form of the model described above was used to help management to reach their decision. The model was most effective in determining the followinz asnects of nlannine: (4 Elects on long term irofitability of changes in pricing policy and sales volume. (b) Profitability of factories available for acquisition over a range of purchase prices and product selling prices. Cc)The way in which profitability of new factories varied with timing and product price. (4 Comparison of a range of combinations of the three types of expansion. One important result was that acquisition and establishment of new factories were only economic with relatively high prices. The rewriting of the programme, and the computations, were carried out at a tota cost of under f5000 including computer time. Our next method is more efficient in the presence of risk and uncertainty. DECIStON TREES AND PROBABtLtTY The use of probability, with or without the decision tree technique is particularly useful where uncertainty plays a large part in planning. A “probability” is assigned to chance events which the manager cannot control, as illustrated below:
~v~~~~~~~~,
1
$0 (2)
The “conversational mode” is very helpful in teaching. but is inefficient for practical applications, where punched cards are normally used.
I 1 Write out accounts and financial ratios
An event with probability 1 is certain to occur, whereas one with probability zero is certain not to occur. Where the probability lies between 0 and 1, the larger the probability the more likely the event; for example a probability of 0.50 means a “fifty-fifty” chance, and 0.98 means nearly certain. If he adopts this approach. the user must obtain estimates of probabilities as illustrated above-not always an easy task, One way in which these are employed to give a better basis for decisions is illustrated in the discussion of decision trees below.
29
We have now seen how simulation may be used to study the effects of different alternatives and how this may be extended by means of probabilities to encompass an analysis of the risks involved. None of these methods however, will automatically find the best policy. To do this we must turn to mathematical programming techniques. Mathematical
KEY:
<>
Decision
Point
0 Chance
Event
FIGURE 2. DECISION TREE (First stage of a Decision Tree for a manufacturer deciding whether to commence production of a new product on a large or small scale) Decision
Trees
Consider now the case of a manager who has a new product ready to be manufactured and marketed. Some limited market research data has been obtained, along with capital and operating costs. and he is trying to decide how big a plant to build. Two questions which he might want to answer are : (a) How do returns on a large plant built now compare with those on a small plant extended to meet increases in demand? (b) What happens if we build a very large factory and sales do not come up to expectation ? There are a number of possible sequences of decisions and chance events hidden in these questions. Problems such as this are best handled with the aid of a Decision Tree. Figure 2 illustrates a decision tree for just such a problem. The decision facing the manager now is whether or not to build a large plant, and the chance possibilities are that the market may be either large (national) or small (local) and that a competitor may introduce a substitute if the product is successful. An explanation of the theory of decision trees would be out of place here, and we must confine ourselves to an example of the steps in the solution and the results. Costs and expected revenue have already been determined, so that the planner is able to calculate the return from any of the
30
many possible final outcomes traced along the branches of the tree. This in itself ii very useful because he is then able to see all of the possibilities which may range from a high return to a heavy loss. In Table 2 some results are illustrated for a case in which there were seven possible outcomes. If, however, the planner has also been able to estimate the probability of a large or a small market and whether or not the competitor will introduce a substitute, he can calculate a measure of probability for each outcome as in the third column of Table 2. The use of probabilities may be extended, for example probabilities may be assigned to each of a range of sales volumes. The results may be taken a stage further by the use of Utility Theory. A “utility” can be determined for each of the immediate alternatives, so that they may be ranked in order of preference. TABLE
2. DECISION
Decision
Build
Large
Plant BuildPlant Small ’ This
may for example
be the net present
Programming
Mathematical Programming is one of the more powerful techniques available to the financial model builder. It is concerned with allocating the company’s activities to its resources so as to gain the objective in the best possible way. The resources might be machine hours, working capital and markets; the activities might be making screws or motor cars; and the objective might be to achieve the maximum profit. In other words, mathematical programming is a way of finding the optimum use of resources. It is the oprirmrm which dismathematical programming tinguishes from the other methods discussed above which, while allowing the user to try the effects of policies which he has chosen himself, will not automatically find the optimum policy. However, this is not all that mathematical programming achieves. It also shows clearly which resources are critical by valuing them in terms of the contribution they would make to profit if they were increased. Thus resources not wholly used up have “value” zero because an increase would not bring about any changes in profit, whereas a resource which is fully used is assigned a value related to the rate of improvement in profit if the amount of the resource were increased. Therefore the critical resources are sorted out and the effect on profit of increasing them easily calculated. In addition, mathematical programming can be adapted to find the results of allocating the resources in ways other than the optimum, and how sensitive profit is to such changes. These two additional facilities-to value the company’s resources in terms of their contribution to profit. and to produce statements of the TREE
*Return a 500,000 200,000 -100,000 -300,000 300,000 150,000 100.000 value of all cash flows
RESULTS Probability of the return shown after the decision is made 0.6 0.1 8:: ;:; 0.3 over the life of the project.
LONG
RANGE
PLANNING
consequences of alternative courses of action-are as important in practice as the ability to calculate the optimum. In order to make these statements clear, let us look at a typical list of questions which can be answered by mathematical programming: Q.1 How can we best use our resources to achieve maximum profit? 4.2 What is the optimum amount of storage space in three years’ time? 4~3 Is machine capacity limiting the firm’s ability to earn more? 4.4 How would the optimum change under different pricing policies? Q.5 How sensitive is our profit to the sales volume of particular products ? Q.6 If we phase out a certain product how will profit be affected ? Questions 1 and 2 concern the optimum. Question 3 the valuing of resources, and Questions 4, 5 and 6 alternative policies. The branch of mathematical programming most often used in company modelbuilding is called Linear Programming. Setting-up a linear programming model is a fairly complex operation because all relevant relationships between activities, resources and the chosen objective must be stated in detail as algebraic equations. This means first of all making a list of the company’s resources and all constraints on its activities including machine hours, subcontractors, cash, and markets. Some possible resources and constraints are shown in Table 3. All possible activities, such as products which can be manufactured, are then listed. The next step is to determine the relationships between activities and resources, which means finding out how much of each resource is used by each activity. and then writing this as an equation. The example in the Appendix will explain the process. The result is a number of equations-in some cases perhaps two or three thousand-and possibly many thousands of activities arranged in a “tableau” for computation. Computation is carried out on a computer, probably using an adaptation of the computer manufacturer’s standard linear programming package. We realize that the idea of using equaTABLE Financial working capital cash investment capital receivables collection period money borrowed money repaid prices Listed
3. RESOURCES
1969
SUCCESSFUL FINANCIAL
AND
CONSTRAINTS Marketing
machine hours labour hours storage space subcontracted work raw materials time
constraints
USE OF MODELS
Keys to successful use of models are the same no matter which method is adopted, indeed they are very like a list of conditions for an effective long range plan. At the beginning objectives must be set and variables identified. The model must be (a) practical, and only as complex as required by the programme and as allowed by the quality of data and
Physical
above are some of the typical
DECEMBER,
to find an optimum company policy might give rise to scepticism in the minds of some readers. However, linear programming has proved in a great number of applications over the last twenty or so years, that it is a practical and effective technique. These applications have covered for example, company and financial modelling, blending, transportation, and allocation of production facilities. We have been concerned in a recent application to a light engineering company manufacturing a number of products, some of which have a seasonal demand. The programme is designed to cover twelve quarterly periods giving optimum levels of production and storage of each product in each period in response to sales forecasts. It takes account of limitations on time, storage facilities, cash, machine labour, raw material supply and so on. The cost of developing a linear programming model depends largely on the complexity required. It can be as little as f10,OOO but may range up to f50,OOO and beyond. In spite of its power, linear programming has limitations and the technique has been extended in a number of ways. One of these is called integer programming. Integer programming allows the user to include activities which must be treated as a whole, such as major capital projects. Thus the financial model can help to select the best group of projects from all those available, where capital is rationed, and will schedule annual expenditure on those selected. Another new development worthy of note, called “goal programming”, allows more than one objective to be considered in the same programme. tions
maximum minimum
on company
sales
of each
product
sales of each product
available facilities;
(b) built with the close co-aperation
of the managers and accountants who are to use it; (cl readily convertible into working budgets; Cd)updated regularly and subject to continual development. Close co-operation of managers and accountants is vital, for this helps to ensure that the other conditions above are obeyed. There is no need for them to carry out the whole operation, but they must commit some time to assisting with it so that they fully understand the use and limitations of the model. Probably the greatest danger lies in accepting the output as gospel. Financial models are merely aids to planning, which help in understanding the relevant alternatives and in identifying critical variables. They do not substitute for the manager, but assist him in making better decisions. CONCLUSION
A manager’s most important and challening decisions are those concerned with planning. Financial models provide managers with a way of experimenting with the future, of determining the likely consequences of their plans, and discovering what they must plan for in order to cover the likelihood of their assumptions breaking down. As business grows more complex the managements of many companies are successfully applying financial models to long range planning. l APPENDIX Construction Programming
of Linear Tableau
Suppose a work centre is available for 410 hours per month and that three products are made on it; product 1 taking 2 hours per unit, product 2 taking 3 hours and product 3 taking 5 hours. If XI, X2, X3 are respectively the quantities, of oroducts 1, 2 and 3 manufactured on this work centre during the month, the number of hours per monthly for which the work centre is used is: 2x1 i This that:
total
cannot 2x1
(the sign
‘-’
3x2 -
be greater
5x3 than
410 hours,
so
- 3x2 -- 5x3-410 means
‘is not greater
than’).
This inequality is one of those which go to make up the tableau. It relates the resource of machine hours to the rate at which it is used up by each of the three products. It is also expressed as the constraint which availability of only 410 machine hours exerts on the quantities of products 1,2 and 3 manufactured by this method. Other inequalities will express constraints due to availability of raw material, working capital, cash, markets, transport facilities, storage space and others. The inequalities are converted to equations for the solution of the problem. The objective must also be stated in terms of variables like X1, XZ, X3, showing the profit derived from one unit of each of them. Thus if X1 and XZ each gained E2 per unit and X3 fl, total profit earned by them would be:
activities.
Profit
= 2x1 + 2x2 A x3
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