Extending Yagil exchange ratio determination model to the case of stochastic dividends

TL;DR

This paper generalizes the Yagil exchange ratio model to stochastic dividend growth, accounting for both expected values and variance, resulting in a more complex bargaining region in stock mergers.

Contribution

It extends the deterministic Yagil model to a stochastic setting, incorporating dividend growth variability into exchange ratio determination.

Findings

The bargaining region depends on dividend growth mean and standard deviation.

The model accounts for both expected values and variance of dividends.

It provides a more comprehensive framework for stock merger negotiations.

Abstract

This article extends, in a stochastic environment, the Yagil (1987) model which establishes, in a deterministic dividend discount model, a range for the exchange ratio in a stock-for-stock merger agreement. Here, we generalize Yagil's work letting both pre- and post-merger dividends grow randomly over time. If Yagil focuses only on changes in stock prices before and after the merger, our stochastic environment allows to keep in account both shares' expected values and variance, letting us to identify a more complex bargaining region whose shape depends on mean and standard deviation of the dividends' growth rate.