Traditional approaches to address uncertainty - such as increasing the discount rates, applying risk premiums, adjusting CAPM/WACC models, and incorporating scenario analysis with probability overlays - are typically static, ex-ante adjustments. However, long-term risks, such as the carbon dioxide emitted today persisting for centuries and nuclear waste like plutonium having half-lives spanning tens of thousands of years, highlight the inadequacy of conventional financial markets in guiding investments to mitigate such enduring threats. Financial instruments with maturities beyond 30 years are rare; even the widely traded 30-year U.S. Treasury represents the practical upper bound of most liquid markets, leaving economic models as the primary tool for valuing more distant futures. Yet, models projecting long-term outcomes over such extended periods face exponentially increasing uncertainty, resulting in non-deterministic cash flows that conflict with the deterministic assumptions of traditional NPV models. To address this uncertainty, academic research strongly supports the adoption of a declining discount rate, a more flexible and realistic approach for valuing long-term investments. When the future path of discount rates is uncertain, taking expectations over a range of possible scenarios implies that the certainty-equivalent discount rate declines as the time horizon lengthens. While declining rates are often justified on ethical grounds, such as intergenerational equity, demonstrate that no normative assumption is required: declining effective rates emerge endogenously from uncertainty about future r . Costanza 28 highlights arguments put forward by Weitzman (1998, 2001, 2007) 29 and Newell & Pizer (2003) 30 , stating that discount rates themselves are uncertain and because of this, their average value should decline over time, highlighting that: Future rates decline in our model because of dynamic uncertainty about future events, not static disagreement over the correct rate, nor an underlying belief or preference for deterministic declines in the discount rate . 31
When we include a static r this further underestimates compounding, path-dependent impacts based on this underlying choice.
A further limitation arises from the circularity embedded in WACC and CAPM, where the cost of equity is derived from market valuations that themselves depend on discounting future cash flows at the very rate being estimated. The dependence on WACC and CAPM calculations to arrive at a given discount rate, however, contains an inherent flaw due to its somewhat tautological underpinning argument. The discount rate, used to value future cash flows, depends on the cost of equity, which is influenced by the market value of equity. However, the market value itself is derived from the present value of cash flows discounted by the same rate, creating a feedback loop. With regards to the terminal value component, given that this represents a perpetuity, its contribution to Net Present Value (NPV) can be substantial, depending on the length of the forecasted period, the growth rate ( g ), and discount rate ( r ). TV often dominates NPV calculations, as financial models typically use relatively short forecast horizons (10 years), assume constant long- term growth ( g ) , and value assets on a long-term basis. In such cases, TV can account for over 50% of total NPV, making valuations highly sensitive to small changes in g and r . While extending the forecast horizon reduces the TV’s weight, enhancing valuation accuracy and reducing reliance on 28 Costanza, R., Kubiszewski, I., Stoeckl, N. & Kompas, T., 2021. Pluralistic discounting recognizing different capital contributions: an example estimating the net present value of global ecosystem services, p. 2. 29 Weitzman, M.L., 1998. Recombinant growth. The quarterly journal of economics , 113 (2), pp.331-360, Weitzman, M.L., 2001. Gamma discounting. American Economic Review , 91 (1), pp.260-271, Weitzman, M.L., 2007. A review of the Stern Review on the economics of climate change. Journal of economic literature , 45 (3), pp.703-724. 30 Newell, R.G. and Pizer, W.A., 2003. Regulating stock externalities under uncertainty. Journal of environmental economics and management, 45(2), pp.416-432. 31 Costanza, R., Kubiszewski, I., Stoeckl, N. & Kompas, T., 2021. Pluralistic discounting recognizing different capital contributions: an example estimating the net present value of global ecosystem services, p.2.
8
Powered by FlippingBook