and declining discount rates in the long-term project appraisal. The results ... Source: own study based on A Social Time Preference Rate For Use In Long-.
The concept of time-declining discount rate in the appraisal of public projects with long-term effects Monika Foltyn-Zarychta, PhD, University of Economics in Katowice
Summary: Intergenerational public investments are difficult to appraise due to discounting process, which affects immensely present value of project’s effects. The paper identifies the concepts of long-term discounting and evaluates the impact of constant and declining discount rates in the long-term project appraisal. The results indicate that application of declining discount rate leads to a significant change in present value of project’s remote effects. Key words: discount rate, public investment, long-term
The aims and research hypothesis Research aims were formulated as follows: 1) identification of approaches defining time-declining discount rate on the basis of literature studies; 2) determining the impact of the approaches on project appraisal on the basis of results of modelling present value of effects. Research hypothesis: „application of discount factor that follows the assumptions of time declining discount rate in public project appraisal results in substantial change in present value of time-remote investment effects influencing considerably the outcome of investment decision process”.
Methodology The theoretical goals were achieved due to literature critical studies, while empirical aims were reached by using present value profiles calculated under the selected declining discount rate approaches. The profiles compared value of investment sample effect of 1000 monetary units appearing in the time frame of 1 to 300 years from present.
Selected results Literature studies reveal a number of approaches justifying the decline in discount rate value in time. Some presents Fig.1.
with h - “time perception” parameter and k - parameter determining the difference from exponential discounting.
DECLINING DISCOUNT RATE
Uncertainty (Weitzman)
Future fairness social choice (Li & Löfgren)
s=const
Observed Individual Choice (Loewenstein & Prelec)
Fig. 1. Selected approaches justifying time declining discount rate concept Source: own study based on A Social Time Preference Rate For Use In LongTerm Discounting, OXERA, UK 2002.
Uncertainty – calculating PV certainty equivalent with various levels of discount rate results in applying higher weights on low-discount-rate scenarios due to higher present value. As a result, Weitzman proposes the schedule of discount rates ranging from 4% (immediate future, 1-5 years) to 0% (far-distant future, more than 300 years). Intergenerational fairness (social choice) – the rights of future generations are defined and justify the decline in discount rate. Li and Löfgren propose to calculate utility discount rate as a weighted average of two individuals representing society, an utilitarian and a conservationist who decide upon intertemporal allocations, however they differ in preferences. Observed individual choice – deriving discount rate from individual decisions in real (experimental economics) or hypothetical markets (contingent valuation). Loewenstein and Prelec research showed the possibility to define discount rate
s L&P
s L&L
s MW
1000 900 800 700 600 500 400 300 200 100 0 1
51
101
151
201
251
301
Fig.2. Comparison of present value of 1000 monetary units time profiles according to selected approaches. Source: own study.
Testing the impact of the approaches indentified involved two steps: 1) calculating the values of discount rates for the assumed time frame of the analysis, and 2) comparing profiles of present value of future effect calculated with the declining discount rates and traditional approach – time-constant discount rate (continuous compounding). The value of the constant rate was assumed to be 4%. The results are presented in Fig. 2.
Conclusions The paper identifies three approaches justifying the use of time-declining discount rate for intergenerational project appraisal due to uncertainty, intragenerational fairness and individual preferences. The results of comparing present value of future effect show that the value under constant discount rate approach is the lowest of all as it drops to 0,01 unit for 300 years time frame. Under the declining discount rate assumption the highest present value has been found for Loewenstein and Prelec model (170 units for 300 years). The results suggest the usefulness of declining discount rate approach in intergenerational investment appraisal.
Koncepcja zmniejszającej się w czasie stopy dyskonta w ocenie efektywności inwestycji publicznych o oddziaływaniach długoterminowych Streszczenie: Artykuł dokonuje przeglądu podejść do problemu dyskontowania w długim terminie a także podejmuje próbę oceny możliwości zastosowania koncepcji zmniejszającej się w czasie stopy dyskonta w ocenie efektywności inwestycji publicznych o oddziaływaniach długoterminowych. Wnioski wskazują, że zastosowanie zmniejszającej się w czasie stopy dyskontowej w miejsce podejścia wykorzystującego stały poziom stopy powoduje istotne zmiany w wartości bieżącej długoterminowych efektów projektów.
