Inter-Temporal Resolution of Risk: The Case of the Tax Shield
30 Pages Posted: 5 May 2002
Date Written: April 2002
There are two ways to view the inter-temporal risk profile of a finite stream of cash flows that is represented by a binomial process. We can examine the risk profile of the cash flow process or the value process that is derived from the cash flow process. First, with respect to a given year n, we can assess the individual risks of the annual cash flows by specifying a set of annual risk-adjusted discount rates, where rho(ni) is the discount rate for the cash flow in year i with reference to year n. In the second view on the inter-temporal risk profile for a finite stream of cash flows, we construct the value process from the cash flow process and with respect to a given point in time n, we assess the risk of the "present value" of the cash flow stream and summarize the collective risk of the cash flow stream with rho(nV) a single risk-adjusted discount rate for year n.
In this paper, we illustrate and compare the two views on the inter-temporal risk profile by using a five-period binomial process to represent the finite stream of tax shields. In particular, we examine the inter-temporal evolution of the "cash flow discount rates" and the "present value discount rates" for the tax shields, and the relationships between them. In Section One, we briefly discuss the two different ways to characterize the risk profile. In Section Two, to illustrate the two descriptions of the risk profile, we present the tax shield process based on the M & E formulation.
Keywords: Inter-temporal resolution of risk, tax shield
JEL Classification: D61, G31, H43,
Suggested Citation: Suggested Citation