Toehold Purchase Problem: A comparative analysis of two strategies

TL;DR

This paper compares two strategic approaches for corporate takeovers, analyzing their expected profits and probabilities of success through mathematical models, revealing similar profit outcomes but differing in takeover likelihood.

Contribution

It introduces mathematical models for toehold and no-toehold strategies, providing a detailed comparison of their success probabilities and expected profits.

Findings

Expected profits are equal for both strategies.

Toehold strategy has a higher probability of successful takeover.

Mathematical analysis uses incomplete Beta functions and bounds for binomial coefficients.

Abstract

Toehold purchase, defined here as purchase of one share in a firm by an investor preparing a tender offer to acquire majority of shares in it, reduces by one the number of shares this investor needs for majority. In the paper we construct mathematical models for the toehold and no-toehold strategies and compare the expected profits of the investor and the probabilities of takeover the firm in both strategies. It turns out that the expected profits of the investor in both strategies coincide. On the other hand, the probability of takeover the firm using the toehold strategy is considerably higher comparing to the no-toehold strategy. In the analysis of the models we apply the apparatus of incomplete Beta functions and some refined bounds for central binomial coefficients.