Present Value with Random Stopping Times

Abstract

Discounting an income stream with a random stopping time produces a formula similar to one for a perpetuity, except that a risk premium is added to the discount rate. This results in a valuation equation that is convenient to apply to complex multi-phase income streams. It suggests a framework for empirical research that includes, for example, bankruptcy rates derived from company fundamentals to estimate the expected stopping time of a business, and offers an additional perspective on the role of interest rates in the economy.

Keywords: present value, stopping time, risk premium

JEL Classification: G12