2.4. Formation of a rational project complex
The second most important problem of system evaluation of projects is the formation of their rational set and the optimal allocation of financial resources between them. We introduce the notion of rationing investment. By this term we mean the formation of a rational set of investment projects for priority financing and long-term financial planning based on the chosen optimization criterion and taking into account objective organizational, technological and financial constraints.
a) Simple rationing
The easiest way to jointly evaluate relatively simple projects that require investment only in the 1st unit period of time is simple rationing of capital investments. It consists in the fact that all projects are ranked in descending order of profitability index (see Chapter 4, § 1), and then included in a rational set in accordance with the rank. The formation of a set ends when the entire amount of the fund allocated for investment is distributed.
Although this method is widely considered in the literature and is popular in practice, it has very serious shortcomings.
• Does not consider the problems of project interaction. Projects can be mutually exclusive, complementary and independent. The action of one project can weaken or strengthen the action of the other. The distribution of capital between projects under P1 or MP1 will not allow the creation of an internally consistent project complex subject to a single ultimate goal;
• can result in a non-diversified set of them, which will not reduce, but, conversely, increase the risk for the organization that is financing;
• does not include consideration of the liquidity problem for projects with unequal validity.
Finally, if it can be applied, it can only be applied with very large restrictions (the investment terms should not exceed one year, the investments in each individual project should be significantly less than the total budget for financing all projects).
b) Linear programming
A more substantiated approach, as many authors believe, is the use of methods of mathematical programming for the formation of an optimal budget.
Most often it is proposed to use linear programming problems in the form
where n is the number of projects; ni - NPV by of the 7th project;
b $ - cash outflow (modulo) on the 7th project in the & pound; -st period of time;
C, - the maximum amount of the capital budget in the & pound; -th period of time.
The required vector A = (x , x2, xn} represents the share of funding for each of the n projects.
In order to get closer to reality, resource constraints (for example, the company does not have the opportunity to get all the raw materials needed for the project in full) and the possibility of financial investments (ie, borrowing or placement in government securities part of the funds). This problem is solved by the standard algorithm using the simplex method.
Situation 5.3. Optimization of a set of investment projects of a construction company
The construction company is considering three projects: the construction of a residential house (project A), an office center (project B) and a food store (project B).
The cash flows of these projects are presented below.
Cash flows, $, by year
Dwelling house (project A)
Office Center (Project B)
Shop (project B)
The cost of capital corporation - 15% per annum. Limitations:
1. Budgetary: The company's capital investment budget for the next three years provides for investments from the centralized funds of the company 850 cu. in the zero period. All subsequent investments are carried out at the expense of the profits of the projects themselves.
2. Resource: Projects 1 and 2 require special finishing materials for a total of $ 110 and $ 95, respectively. In the next two years for the corporation it is realistic to conclude contracts for a total of $ 150. In the years to come, this restriction will not be significant.
3. Financial: any additional funds a company can deposit into a bank C deposit at 10% per annum. For the company, a credit line is opened at a rate of 20% per annum for an amount not exceeding 200 USD. By experience, the term of deposit of money into a deposit does not exceed one year, and the maturity of loans is usually two years.
It is required to compile an optimal investment program for the corporation.
We will proceed from the fact that each of the projects can be partially funded and, thus, it is possible to vary the scale of each project without affecting its effectiveness per unit of invested capital. In addition, to simplify the model, suppose that you can get a loan or invest money in a deposit only during the zero period.
At a rate of 15% per annum, the net present value of each of the projects, subject to its 100% financing, is $:
Project A 100.15
Project B 160.93
Project B -14.74
We introduce two more conditional projects:
project D - an investment of one monetary unit in a bank deposit With a period of one year at 10% per annum. The cash flow of such a project in cu by years:
CF -1 +1,1, a NPV = -0,04 per one monetary unit of the invested funds;
project D - receiving a loan for two years at 20% per annum. The cash flow of this project:
CF +1 -0.2 -1.2,
a NPV = -0.08 per one monetary unit of the invested funds at a discount rate of 15% per annum.
Denoting by X the share of funding for each project in relation to its overall investment needs, we get the following formalized record of the conditions of this task:
optimization criterion (objective function):
100.15 ХА + 160.93 ХБ - 14.74 Хв - 0,04 X, - - 0,08 Хл - & gt; max restrictions:
500 ХА + 650 ХБ + 400 Хв + ХТ = 850 + Хд - budgetary;
100 ХА + 230 ХБ + 0,2 Хд = 330 ХБ + 1,1 X, - - financial;
50 XB + 1.2 XD & lt; 300 ХА + 130 Хв - financial;
200 & gt; Хд - financial;
150 & gt; 110 ХЛ + 95 ХБ - resource;
1 & gt; ХА, ХБ, Хв - natural;
XA, XB, XB, Xp, XD & gt; 0 are natural.
We have obtained the linear programming problem written in the standard form: a linear objective function, the value of which must be reduced to a maximum or to a minimum, and a number of linear constraints expressed as equalities or inequalities.
The standard algorithm for solving similar problems (simplex method) allows to obtain the following solution.
The maximum NPV value for a collection of projects under given circumstances is 155,023 cu
XA = 0.894; ХБ = 0,565; XB = 0; Xr = 235.76; XD = 200.
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