A Model for the Optimal Selection of Lenders

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Most private placements are offered to a small number of select investors, at a fixed rate that can
be set by the issuer. In this paper, a model is developed that enables the estimation of the interest rate to be
offered to each investor, in the two styles of solicitation of investors (simultaneous and sequential), so that
the issuer can obtain the desired financing at minimum cost. Specifically, in the simultaneous case, we
provide the subgroup of investors that supply sufficient funds and the common optimal rate to be offered to
all investors; in the sequential case, we determine the preference order under which the negotiation should
be carried out and the particular optimal rate to be offered to each investor. As a conclusion, it is found that
not only does the sequential solicitation imply a financing cost that is lower than or equal to the
simultaneous solicitation but it also implies a greater or equal number of investors.

Alberto Augusto Álvarez López decano Facultad de Ciencias Económicas y Empresariales, UNED