The central theme of this thesis is the nature, impact and
Steuer reports that a sample of 25 constraints, 50 variable problems with three objective functions had an average of 605 extreme efficient vertices and required 152 seconds of CPU time on an IBM 370/165
computer. However, the time required appears to increase exponentially with the size of the problem and he was unable to obtain complete sets of solutions in any reasonable time to problems*much larger than this.
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resolution of the interdependencies that arise between the
investment and the financing decision. In previous sections various aspects of these interdependencies have been introduced, though most of the subsequent discussion of necessity has centred around
fairly simple models. Thus in section 1.3 it was suggested that models which consist only of a cash constraint and a debt capacity constraint (nay be 'solved' by a relatively straight forward
application of discounting principles, though it is certainly far from clear how such discounting approaches might behave in more complex models. Section 1.4 introduced some of the problems that arose out of interdependencies between the form of the valuation model, the financing options and the constraint 3et. In particular it concentrated upon the effect of a finite horizon time. The extent to which this poses a problem in practice for large scale planning models remains unknown. A similar question emerges in the theory of lease valuation. While analytical methods suffice far the development of valuation formulae in most of the models mentioned
so far, such methods have proved inadequate when it comes to dealing with more elaborate models. This is of course a major weakness in the analysis since the leasing decision appears to be a result
of a complex interaction of tax laws and debt availability determined largely by reporting standards. Finally the work of the last section
suggests that the firm operates in an environment where its courses of action are constrained by consideration of the impact that they might have on a whole multiplicity of criteria. An exploration of
this idea requires a model rich in detail but much less rigid in structure than the conventional linear programming models hitherto discussed.
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Unfortunately, many of the models which have been used to illustrate the various aspects of the above problems are relatively trivial in nature and fail to provide adequate test material.
In order to provide for a more comprehensive examination of the ideas developed in this thesis a realistically sized* programming model of the firm was developed.
The model was developed in two distinct forms. The first of these follows the traditional economic valuation approach where the objective js the maximisation of shareholder wealth. In this model all the constraints are hard constraints in that a plan is
infeasible unless it simultaneously satisfies all the constraints.
The same data and basic structure is also used to generate a parallel version which takes the form of a 'goal' programming model. In this model all the financial restrictions or constraints are 'soft' constraints and hence it is possible that all or any of these restrictions may not be net in an acceptable plan.
The model provides a central test bed for the computational evaluation of the main ideas of this thesis and despite its size and complexity it plays a contributing rather than leading role in this thesis. In order to emphasise the nature of this role and avoid breaking up the theoretical arguments, a detailed statement of the model is reserved for the appendices with a discussion of the structure of the objective function in the appropriate chapters.
A short summary of the main features of the model should suffice at this point, while a detailed mathematical statement can be found in appendix I.
The final form of the model had over 360 variables with over 180 constraining and defining equations excluding simple bounds.
As already stated, the model is a linear programming representation of the investment opportunities over time facing an organisation together with corresponding a set of financing alternatives. Briefly, it contains four groups of variables representing accounting quantities, financing and investment opportunities and variables associated with goals and targets.
The accounting variables have been chosen at a level of detail that gives sufficient richness for the purpose in hand without an excessive amount of detail. Hence, while current assets are included at an aggregate level, capital assets are grouped into two categories to allow for different tax treatments. Also overdraft, dividends and tax payable are identified as
separate elements composing the short term liabilities because of their importance as financing elements. For the same reason long term capital and shareholders capital are separately identified also. The modal has two main groups of constraints.
(a) A technological set consisting of the cash balance equations and accounting definitions.
(b) A financial policy set associated with the performances on certain key financial criteria such as return on capital, times interest covered, earnings and dividend per share.
Apart from the financing alternatives the firm is faced with a series of decisions to be made about investments in projects.
There are 16 different projects in all, though since some of these projects are available in more than one year there are in fact up to 45 projects available over the eight year planning period.
The projects are specified in terms of their contribution to sales, earnings, current assets and liabilities together with a statement
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of their capital requirements in both building and land and plant and equipment. The internal rate of return of these projects varies between 7.5% and 15.5%. A complete summary of the projects occurs in appendix IV.
It is further assumed that the organisation at the start has already a series cf on-going operations and future financing commitments such as planned long term debt requirements. Apart from these projections resulting from its current operations, the firm has a series of policy targets, for instance a minimum return dividend payout and capital in each year, and sales targets which it hopes to achieve over the planning period. A statement of these targets together with the other base data appears in appendix III. Also contained in appendix III is a statement of the taxation allowances which the organisation may claim and details of the assumptions made about the timing of the cash inflows and outflows during a year.
It will be seen that the model in itself is not original, indeed it would be difficult to generate a model which is completely different from all the many other models produced in this field. Clearly,
the antecendents in the literature on whose ideas the model is based can be found in the pioneering work of Heingartner (621, the work of Chambers (67,71) on the incorporation of financial
constraints and equity issues, the share price valuation approach of Carleton(70) and the complexity and output procedures by
Hamilton and Moses (73) . The model is little more than a synthesis and extension of the features considered best in these models.
Any unique nature lies in the use and emphasis of the model and the structure of the objective functions necessary for goal programming.
Interdependencies, Hlrschleifer, Baumol and Quandt,
2.1 Introduction.
In this chapter the nature of the interdependencies that arise between the set of investment decisions and the discount rate at the optimum in capital budgeting models is examined in detail. As-was indicated in section 1.2 Baumol and Quandt (65) suggested that the dual values gave the correct discount rate or opportunity cost of funds to use in the formulation of the
problem. The subsequent attempt to solve the problem reformulated in this way led them to suggest that there was no solution other than the null solution. The following section shows how it is possible by paying particular attention to the assumptions and by careful definition of the mathematical variables to cite numerical counter examples with non-trivial solutions in which the discount rate is consistent with the dual value. Section 2.3 then,
provides a formal mathematical treatment of the problem in which it is shown that in general there exists many consistent solutions and the numerical example is merely one of a particular subset of these solutions. Section 2.4 identifies the economic meaning of these solutions and the implications for discount methodology by relating the solutions to the fundamental paper by Hirschleifer
(58) on the theory of optimal investment decisions. It is argued in conclusion that this paper forms a basis for the development of mathematical programming approaches to the capital investment problem.
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