Selezione degli investimenti e costo del denaro

Abstract

Alcuni Autori ritengono che non abbia senso il costo del denaro, in uno schema lineare in cui si può ripartire il proprio denaro in tutte e sole le operazioni che determinano il tasso di sconto. La conclusione di tali Autori appare azzardata: infatti il loro risultato discende da una ipotesi estranea al modello lineare.

In questo lavoro io interpreto lo stesso modello, mostro che in esso ha senso il costo del denaro e propongo delle impostazioni alternative.

Abstract

An interesting economic problem consist in the search of the optimal allocation of one’s monetary resources in different financial transactions. We often consider as “optimal” the allocation which makes the sum of the actual values of investiments the highest possible, within the limits of all feasible operations. These values are reckoned according to the discount rates established by the financial market.

This type of abstraction can be acceptable when we can split our capital into a number of operations that are on the whole negligible, if compared with the movement of the market.

In case of a considerable turn over that may therefore affect the cost of money, it follows that we can’t determine an appropriate discount rate before establishing the distribution policy; on the other hand we cannot determine the distribution policy before defining the discount rate. As a border-line case we have that of an “enclosed” economy, where funds can be rationed into all and only those operations which determine the cost of capital. That is the case of “pure capital rationing”.

To solve the problem of reckoning the cost of capital under pure capital rationing, some Authors have formulated the two dual linear programs (1) and (2) and have deduced that f is the vector of market prices if and only if the optimal dual solution$\bar \lambda$ is equal to f. As that happens if and only if f=0, Burton and Damon [2] consider their “main result a rigorous proof that there does not exist a meaningful solution for the pure capital rationing problem” and conclude “that if there exist a solution to the problem it is not to be found by the traditional linear programming formulations”.

On the contrary I demonstrate that f=0 is the only possible capital cost because of the hypotesis$\bar \lambda$=f, which is not related to the linear pattern and is not acceptable from an economic-financial point of view.

Then I demonstrate that the market prices are all and only those based on which the actual values of the operations considered are 0. Nor was it right to expect more sophisticated conclusions of such an elementary scheme. Finally I express an alternative linear formulation, where the dual optimal solutions are exactly the market prices.