Transversality and the Stochastic Nature of Cash Flows

Abstract

We show that a transversality condition is necessary when it comes to valuing a company with an infinite lifespan. Without transversality the firm value cannot be uniquely determined. Also, an assumption on a lower bound of cash flows is necessary to achieve the desired result. We discuss four different stochastic cash flow processes and analyze to what extent the processes associated with these enterprise values satisfy the transversality condition.

Basic Elements: Cash Flow, Tax, Expectation, Cost of Capital, Value

“…12 See in particular Kruschwitz and Löffler (2013). 13 Convergence can be pointwise, almost-everywhere, in L 2 or in probability, etc.…”

“…We believe that this assumption is of technical nature that is not an important economic restriction. The following considerations are-in parts literally-taken from Kruschwitz and Löffler (2013). In that sense transversality includes the condition (2.9) for an almost-everywhere convergence.…”

“…In Husmann et al (2006) it is shown how several national tax codes can be implemented into our model. Transversality is extensively discussed in Kruschwitz and Löffler (2013). A lot of examples, counterexamples as well as proofs can be found there.…”

Stochastic Discounted Cash Flow

“…Transversality is extensively discussed in Kruschwitz and Löffler (2013). A lot of examples, counterexamples as well as proofs can be found there.…”