Project Appraisal - Multiple Projects

Multiple Projects and Constraints Introduction: When investment proposals are considered individually, any of the DCF criteria- NPV, IRR, or BCR – may be applied for obtaining a correct “accept or reject” signal. However, in the existing organization, capital investment projects often cannot be considered individually or in isolation as project independence, lack of rationing and project divisibility are rarely fulfilled. So it is proposed to discuss the problems with the method of ranking, and other techniques to be employed to select the capital budget in face of constraints. 13. Constraints: Projects are economically independent, if the acceptance or rejection of one does not change the cash flow stream or does not affect the acceptance or rejection of the other. But, the projects are dependent, if these conditions are not fulfilled. Mutually exclusive projects substitutes for each other.

Even though the projects are not mutually exclusive, they influence negatively each other’s cash flows if they are accepted together. Positive economic dependency occurs when there is complementarity between projects. These can be asymmetric or symmetric. Capital Rationing: When funds available for investment are inadequate to undertake all projects which are otherwise acceptable, capital rationing exists. Reasons are: i ) Internal limitation or external limitation ii) Set a limit to the capital expenditure outlays iii) A choice of hurdle rate higher than the cost of capital of the firm iv) Inability to raise sufficient amounts of funds at a given cost of capital. The implication of rising capital supply is that some projects would be postponed or abandoned if the cost of capital tends to increase.

Behaviour of Cost of Capital Cost of Capital

Quantum of Funds raised Project Indivisibility: A capital project has to be accepted or rejected in toto- a project cannot be accepted or rejected partially. Given the indivisibility of capital projects and the existence of capital rationing, the need arises for comparing projects. An example will illustrate the indivisibility. Example: A firm is evaluating three projects A, B, and C which have the following data. The funds available to the firm for investment are Rs. 0.7 million.

Project Capital Outlay NPV A Rs. 0.5 million Rs. 0.2 million B Rs. 0.4 million Rs. 0.15 million C Rs. 0.3 million Rs. 0.1 million In this situation, acceptance of project A which yields a NPV of Rs. 0.2 million results in rejection of projects B and C which together would yield a combined NPV of Rs. 0.25 million. Hence, because of the indivisibility of projects, there is a need for the comparison of projects before the acceptance/rejection decisions are taken. 2. Methods of Ranking Because of economic dependency, capital rationing, or project indivisibility, a need arises for comparing projects in order to take a decision of acceptance or rejection. Basically two approaches are available: (i) the method of ranking, and (ii) the method of mathematical programming

The method of ranking consists of two steps: (i) Rank all projects in a decreasing order according to their individual NPV’s , IRR’s, or BCR’s. (ii) Accept projects in that order until the capital budget is exhausted. The method of ranking, originally proposed by Joel Dean is seriously impaired by two problems: (i) conflict in ranking as per DCF criteria, and (ii) project indivisibility. Conflict in Ranking: Consider a set of five projects, A, B, C, D, and E, for which the following information is available. Project A B C D E

Investment (Rs.) 10,000 25,000 30,000 38,000 35,000

Annual Cash Flow Project life (Rs.) (years) 4,000 12 10,000 4 6,000 20 12,000 16 12,000 9

The NPV, IRR, and BCR for the five projects and the ranking along these dimensions are shown below: Project A B C D E

NPV NPV IRR (Rs.) Ranking % 14,776 4 39 5,370 5 22 14,814 3 19 45,688 1 30 28,936 2 29

IRR BCR Ranking 1 2.48 4 1.21 5 1.49 2 2.20 3 1.83

BCR Ranking 1 5 4 2 3

It is clear that the three criteria rank the projects differently. If there is no capital rationing, all the projects would be accepted under all the three criteria though internal ranking may differ across criteria. However, if the funds available are limited, the set of projects accepted would depend on the criteria adopted. What causes ranking conflicts? Ranking conflicts are traceable to differing assumptions made about the rate of return at which intermediate cash flows are re-invested.

Project Indivisibility A problem in choosing the capital budget on the basis of individual ranking arises because of indivisibility of capital expenditure projects. To illustrate, consider the following set of projects ( ranked according to their NPV ) being evaluated by a firm which has a capital constraint of Rs. 2,500,000. Project A B C D E

Outlay (Rs.) 1,500,000 1,000,000 800,000 700,000 600,000

NPV (Rs.) 400,000 350,000 300,000 300,000 250,000

If the selection is based on individual NPV ranking, projects A and B would be included in the capital budget – these projects exhaust the capital budget. A cursory examination, however, would suggest that it is more desirable to select projects B, C, and D. These three projects can be

accommodated within the capital budget and have a combined NPV of Rs. 850,000 which is greater than the combined NPV of A and B. Feasible Combination Approach: The above example suggests that the following procedure may be used for selecting the set of investments under capital rationing. (This procedure can also take care of project interdependency) 1. Define all combinations of projects which are feasible, given the capital restriction and project interdependencies. 2. Choose the feasible combination that has the highest NPV Illustration Project Outlay(Rs.) NPV(Rs.) A 1,800,000 750,000 B 1,500,000 600,000 C 1,200,000 500,000 D 750,000 360,000 E 600,000 300,000

Projects B and C are mutually exclusive. Other projects are independent. Given the above information, the feasible combinations and their NPV s are shown below: Feasible combination A and B A and D A and E B and D B and E C and D C and E B, D and E C, D and E

Outlay (Rs.) 3,000,000 2,550,000 2,400,000 2,250,000 2,100,000 1,950,000 1,800,000 2,850,000 2,550,000

NPV (Rs.) 1,250,000 1,110,000 1,050,000 960,000 900,000 860,000 800,000 1,260,000 1,160,000

The most desirable feasible combination consist of projects B, D and E as it has the highest NPV.

3. Mathematical Programming Approach The feasible combinations described above becomes increasingly cumbersome as the number of projects increases and as the number of years in planning horizon increases. To cope with a problem of this kind, it is helpful to use mathematical programming models. The advantage of mathematical programming models is that they help in determining the optimal solution without explicitly evaluating all feasible combinations. A mathematical programming model is formulated in terms of two broad categories of equations: ( i ) the objective function (ii) the constraint equations. Both are defined in terms of parameters and decision variables. Parameters represent the characteristics of the decision environment which are given. Decision variable represents what is to control by decision makers. Out of wide variety of mathematical programming models, three types are usually used.

 Linear programming model  Integer programming model  Goal programming model 4. Linear Programming Model Assumptions: • The objective function and the constraint equations are linear. • All the coefficients in the objective function and constraint equations are defined with certainty. • The objective function is unidimensional. • The decision variables are considered to be continuous. • Resources are homogeneous. 5. Integer Linear Programming Model The principal motivation for the use of integer linear programming approach are: a) It overcomes the problem of partial projects which besets the linear programming model as it permits only 0 or 1 value for the decision variables.

b) It is capable of handling virtually any kind of project interdependency. It may be noted that the only difference between the linear integer programming model and the basic linear programming model is that the first one ensures that a project is either completely accepted or completely rejected. The following kinds of project interdependencies can be incorporated in the integer linear programming model: o Mutual exclusiveness o Contingency o Complementariness 6. Goal programming Model The goal programming approach, a kind of mathematical programming approach, provides a methodology for solving an optimization problem that involves multiple goals. To use the goal programming model, the decision makers must:

1. State an absolute priority order among his goals. 2. Provide a target value for each of his goal. It seeks to solve the programming problem by minimizing the absolute deviations from the specific goals in order of the priority structure established. Goals at priority level one are sought to be optimized first. Only when this is done will the goals at priority level two be considered ; so on and so forth. At a given priority level, the relative importance of two or more goals is reflected in the weights assigned to them.