Abstract
We extend risk-value models for valuing streams of risky cash flows by establishing the well-known concept of terminal value in this context. For a constant growth assumption we are able to derive upper and lower bounds for the terminal value in the case of a translation-invariant and in the case of a position-invariant risk measure. For both cases we also obtain an exact formula under a special growth assumption for the future cash flows. Furthermore, we provide results on the applicability of the general findings for the case that the log-return of the risky investment follows a Brownian motion.
Highlights
The terminal value concept has a long-standing tradition in equity valuation and in the DCF methods used for company or project valuation (Massari et al 2016, ch. 11)
Considering a position invariance (PI) risk measure, we begin our considerations with the constant growth assumption (Assumption 1 from above), in which case we can prove a slightly different theorem when compared with the case of a translation invariance (TI) risk measure
We extend risk-value models for valuing streams of risky cash flows by introducing the concept of terminal value to this framework
Summary
The terminal value concept has a long-standing tradition in equity valuation (see e.g. Penman 1998; Courteau et al 2001) and in the DCF methods used for company or project valuation (Massari et al 2016, ch. 11). Dorfleitner and Gleißner (2018) have introduced a new valuation concept, called the risk-value-model valuation1 This concept is based on certainty equivalents derived from risk measures and accounts for the risk by subtracting a (time dependent) risk premium from the expected cash flow in the numerator. Our research implies a large step forward for valuation practitioners, who prefer to model some periods explicitly and make some simplifying assumptions for the rest In this regard the model is very useful as it brings the terminal value concept into risk-value models. The remainder of the paper is structured as follows: we derive general results on upper and lower bounds for the terminal value if the cash flows and their risk are expected to grow constantly.
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