Annuity Factor Research Articles

A Comparative Study of Immediate Annuities and Ordinary Annuities in establishing the Phantom of Zero Liability Under the Trusteeship Pension Valuation Structure

Background: The liabilities of a pension scheme define the financial value to be paid at a definite period in the future. The underlying goal of pension plans is to provide retirees with sufficient stream of income to enable them to live a decent financially independent life post-employment period. The regulatory framework for occupational pension schemes necessitates the services of trustees as administrators who assume legal administrative responsibilities on the scheme and saddled to oversee actuarial valuations of the scheme's liabilities at definite points in time. Objectives: The objective of this paper is (i) to empirically examine the drivers of pension liability and how they are evaluated by the trustee’s model. (ii) Specifically, the study intends to use input parameters of the trustee model to establish the conditions for which the value of liability is zero under trusteeship annuity factor. Methods: This study applies trustees’ valuation model, the present values together with infinitesimal calculus. Salary data as well as demographic data were obtained from an agricultural production services company located in Jos-South, Nigeria. Results: Computational evidence from our results proves that the total service liability under the conditions of the current model is vanishingly zero. However, when the annuity factor is replaced by life table annuity, the service liability does not vanish. Conclusion: The total service liability obtained as zero therefore initiates inquiry as to whether this current valuation framework causes potential uncertainties for the pension trustees who are responsibly saddled with both administration and core decision-making responsibilities of the system.

THERMODYNAMIC AND ECONOMIC ANALYSIS OF A BIOGAS -FUELED MICRO GAS TURBINE WITH COMPRESSOR PHOTOVOLTAIC DRIVE

The increase in global and Brazilian energy demand plus environmental concern due to pollutant emissions are motivating investigation and development of sustainable energy sources and the interaction between them. In this context, electricity generation through solar and solid urban waste energy harnessing has become an effective option for Brazilian energy matrix diversification. Therefore, in order to ratify this trend, a thermodynamic analysis of a 200 kWe micro gas turbine using biogas as fuel and photovoltaic panels to drive compressor shaft is presented in this paper. In terms of methodology, Engineering Equation Solver (EES) Demo was used to run a classic steady state thermodynamic model and a parametric analysis to evaluate MGT performance with a PV system integrated in order to assess specific fuel consumption reduction (SFC) at Belo Horizonte, Minas Gerais, Brazil, operation. Radiasol 2 was the software used to acquire solar insolation data over the year. The fuel economy occurs since power produced in turbine does not need to be discounted to drive compressor shaft during periods when solar insolation is present or when energy generation during the day is sufficient to be credited as Brazilian legislation allows grid integrated systems. In cases that solar energy is not enough or absent, a transmission mechanism similar to a clutch should be considered as well as proposed in other studies to guarantee uninterrupted system operation. Futhermore, an economic analysis was performed to evaluate kWh cost for conventional and hybrid systems. Interest rate, inflation, construction period and amortization period are important parameters taken into account to calculated annuity factor that must be evaluated to predict energy cost. The thermodynamic results showed that SFC=0,718 kg/kWh for conventional operation and SFC=0,266 kg/kWh for hybrid operation for the best operating compressor pressures ratio. The economic results showed that payback time for MGT and MGT with compressor photovoltaic drive are lower than lifetime systems, and hybrid MGT electricity cost is lower when compared to paid ones nowadays.

Development of Design Method for River Water Source Heat Pump System Using an Optimization Algorithm

River water source heat pump (RWSHP) systems are being proposed to reduce the energy consumption and carbon emissions of buildings. The RWSHP system is actively applied to large-scale buildings due to its stable performance. The application of RWSHP in large-scale facilities requires an accurate capacity design with considerations of building load, heat source, and environment conditions. However, most RWSHP systems are over-designed based on peak load of buildings. These design methods, based on peak loads, are economically and environmentally disadvantageous. Therefore, this paper aims to development an optimal design method, both economically and environmentally, for the RWSHP system. To develop this optimal design method, a simulation model was created with an optimization algorithm. The economics of the RWSHP system were calculated bases on present worth of annuity factor. Moreover, CO2 emissions were estimated using the life cycle climate performance proposed by the International Institute of Refrigeration. The total cost of the proposed RWSHP system that apply the optimum design method decreased by 24% compared to conventional RWSHP systems. Moreover, CO2 emissions of the proposed RWSHP system reduced by 4% compared to conventional RWSHP systems.

The effect of parameters and irradiance estimation techniques on PV potential quantification: The case of Mexico

The impact of some irradiance estimation techniques and model parameters in the assessment of solar potential has not yet been clarified, therefore, the case of Mexico is used in this work is to reduce such a gap. Firstly, a universe of 1629 weather stations and 108 models were used to study the effect of model-based and interpolation techniques on the estimation of the resource potential. Secondly, a centralized and two decentralized geographic potential scenarios were analyzed. Thirdly, the effect of parameters related to PV solar harvesting and production costs was evaluated. Our results revealed dramatic differences in the resource potential when heuristics models were used; differences up to 10% were found for the same location; in contrast, the evaluated interpolation techniques provided very close results with sensibility indexes (SI) below of 2.11%. Differences up to 15% were found in the average daily irradiance when the available area for PV installation is considered, which revealed the importance of the determination of suitable areas for harvesting. Changes up to %27 in the technical potential were found for different c Si-Poly modules. The parameters affecting most significantly the cost were the annuity factor (SI = 75.89%), the balance of the system (SI = 56.95%) and the PV module investment cost (39.28%). Our results provide reasonable results when compared with actual prices and provide evidence of the role of government policies to lower the costs.

Analysis of Mortality Improvement on the Pension Cost Due to Aging Population

Aging is a good indicator in demographic and health areas as the lifespanof the elderly population increases. Based on the government’s Economic Outlook 2019,it was found that an aging population would increase the government pension paymentsas the pensioners and their beneficiaries have longer life expectancy. Due to mortalityrates decreasing over time, the life expectancy tends to increase in the future. Theaims of this study are to forecast the mortality rates in the years 2020 and 2025 usingthe Heligman-Pollard model and then analyse the effect of mortality improvement onthe pension cost (annuity factor) for the Malaysian population. However, this studyonly focuses on estimating the annuity factor using life annuities through the forecastedmortality rates. The findings indicated that the pension cost is expected to increase ifthe life expectancy of the Malaysian population increases due to the aging population inthe near future. Thus, to reduce pension costs and help the pensioners from insufficientfinancial income, the government needs to consider an extension of the retirement age infuture.

What is the Return Rate of a Corporate Pension Scheme? Generalized Annuity Factors Simplify Calculation

Corporate pension schemes are widely spread especially in Northern Europe, North America, Japan. Often the major portion of defined contributions to the scheme is shouldered by the employer. A crucial question for an employee is, whether the return from his/her corporate pension plan - taking into account the corporate engagement and eventually governmental savings promotion - is favourable in comparison to other capital products for the time of retirement. This question is not answered by the absolute return in form of the future pension amount. Additionally, the employee must know the relative return, the Pension Rate of Return (PRR), in relation to what he/she has invested in form of employee contributions into the pension plan during his/her work life. Focussing on better pension information and also on counteraction to melting interest return, two current topics will be addressed. A very useful evaluation instrument for this task is the Generalized Annuity Factor (GAF). It is a generalization of the well-known Annuity Factor, which is restricted to constant payments only. With GAF any time dependent payments, e.g. linear or more complex nonlinear payments over time can be valued by a compressed closed-form formula in the same manner as constant payments by the classic Annuity Factor. Pension payments regarding mortality are such complex payments depending systematically on age. Because of its computational efficiency the new instrument simplifies calculations to be done also in smaller funds, firms or public services with common spreadsheet programs.

Generalization of the Annuity Factor

The well-known Annuity Factor, restricted to constant payments only, can be generalized for time dependent payments. A Generalized Annuity Factor (GAF) broadens the application potential considerably as is shown exemplarily for the valuation of loans and pension obligations. For the first time for such linear and nonlinear payments over time, compressed closed-form formulae for important financial key numbers such as present value, duration, convexity or value at risk can be derived. Moreover, easy computation makes General Annuity Factors a useful valuation tool especially in the field of finance and accounting. As General Annuity Factors can be implemented as User Defined Functions in a spreadsheet program, calculations can also be done in smaller firms or public services. Because of its computational efficiency the new instrument is also suitable for far-sighted economical models such as Asset Liability Management models (ALM) or life-cycle valuation models concerning products or investments.

Interplant heat exchanger network synthesis using nanofluids for interplant heat exchange

Heat transfer between different processes or inter-plant heat integration can be seen as an efficient way to cost-efficiently improve the energy efficiency of a system of different processes. Nanofluids are a new type of heat transfer fluids, in which particles with size of 1–100 nm are suspended in a liquid. Nanosized particles can cause considerable enhancement in convective heat transfer performance of the base fluid, although at the same time they increase the viscosity of the fluid, thus enhancing the needed pumping power. In this work we study the effect of using nanofluids in streams transferring heat from different processes by optimizing the total annual cost of a heat exchanger network. These costs include the cost of hot and cold utilities, heat exchanger investment costs and pumping costs. A modified version of the well-known Synheat superstructure is used as the optimization model in comparing the different fluids (water and five nanofluids) in two examples. Some key parameters (electricity price and annuity factor) are varied in these two examples. The results show that nanofluids can in some cases save total annual costs and especially if electricity prices are low compared to other factors. This is true especially for MgO1.0% which outperformed water and the other nanofluids in normal price conditions. But altogether it is evident that most, and in some cases all, of the benefits provided by nanofluids to improved heat transfer is canceled out by the increased pressure drops.

Interest Rate Swaptions - A Review & Derivation of Swaption Pricing Formulae

In this paper we outline the European interest rate swaption pricing formula from first principles using the Martingale Representation Theorem and the annuity measure. This leads to an expression that allows us to apply the generalized Black-Scholes result. We show that a swaption pricing formula is nothing more than the Black-76 formula scaled by the underlying swap annuity factor. Firstly we review the Martingale Representation Theorem for pricing options, which allows us to price options under a numeraire of our choice. We also highlight and consider European call and put option pricing payoffs. Next we discuss how to evaluate and price an interest swap, which is the swaption underlying instrument. We proceed to examine how to price interest rate swaptions using the martingale representation theorem with the annuity measure to simplify the calculation. Finally applying the Radon-Nikodym derivative to change measure from the annuity measure to the savings account measure we arrive at the swaption pricing formula expressed in terms of the Black-76 formula. We also provide a full derivation of the generalized Black-Scholes formula for completeness.

Managing Longevity Risk by Implementing Sustainable Full Retirement Age Policies

AbstractIn this article, we investigate the effect of five policies to link the retirement age to (forecasted) survival probabilities. We investigate the effect of these policies on the distribution of the (future) full retirement age and on longevity risk in the discounted future payments. Our investigated policies effectively hedge longevity risk, but do lead to substantial uncertainty in the retirement age and the expected number of years in retirement. We find that policies based on present values lead to a higher annuity factor than policies based on expected remaining years in retirement. Our results can explain the differences between the proposed automatic rule to adjust the full retirement age in the United Kingdom (defined contribution pension schemes) and the Netherlands (defined benefit pension schemes).

Transportation fuel production from gasified biomass integrated with a pulp and paper mill - Part B: Analysis of economic performance and greenhouse gas emissions

This paper presents a comparison between four gasification-based biorefineries integrated with a pulp and paper mill. It is a continuation of 'Transportation fuel production from gasified biomass integrated with a pulp and paper mill - Part A: Heat integration and system performance'. Synthesis into methanol, Fischer-Tropsch crude or synthetic natural gas, or electricity generation in a gas turbine combined cycle, were evaluated. The concepts were assessed in terms of GHG (greenhouse gas) emissions and economic performance. Net annual profits were positive for all biofuel cases for an annuity factor of 0.1 in the year 2030; however, the results are sensitive to biofuel selling prices and CO2,eq charge. Additionally, GHG emissions from grid electricity are highly influential on the results since all biofuel processes require external power. Credits for stored CO2 might be necessary for processes to be competitive, i.e. storage of separated CO2 from the syngas conditioning has an important role to play. Without CO2 storage, the gas turbine case is better than, or equal to, biofuels regarding GHG emissions. Efficiency measures at the host mill prior to heat integration of a gasification process are beneficial from the perspective of GHG emissions, while having a negative impact on the economy.

Industrial waste heat recovery technologies: An economic analysis of heat transformation technologies

Abstract In this paper, the potential of industrial waste heat for heating and cooling applications is investigated. Therefore, heat transformation technologies are presented and their technical and economic potential are discussed. First, different industrial processes and their operating temperatures are presented as possible waste heat sources as well as low temperature processes, which can be supplied with waste heat. Then, a general economic analysis is performed for three different cases of waste heat use: an absorption chiller producing cold and heat production with a compression and an absorption heat pump. The maximum acceptable investment cost for each technology is estimated and compared with the current investment cost depending on the operating hours of the system. For this, three different consumer types, Enthusiast, Real Estate and Industry, are defined to represent different expectations in interest rate, payback period and the resulting annuity factor. Instead of judging if a technology is profitable or not, it is calculated how much the system is allowed to cost in order to be competitive for certain operating hours. Combined with present day cost of the technology, this serves as a rough judgment of the market deployment process. Finally, a sensitivity analysis of the initial assumptions for the economic analysis is performed, revealing a strong influence of the annuity factor. For the present day technology cost, absorption chillers were found to be profitable for two of the three consumer types when operated for at least 2500 h per year. Electric heat pumps are profitable for all consumer types when exceeding 4000 operating hours per year while absorption heat pumps start at 3000 h of operation per year to be profitable for all consumer types.

Upgrading of wood pre-hydrolysis liquor for renewable barrier design: a techno-economic consideration

A techno-economic assessment of an upgrading procedure and outtake of a pre-hydrolysate in a presumed dissolving pulp mill was performed. Pre-hydrolysis of spruce wood chips in pilot scale produced input data for energy and mass balances and was performed with and without subsequent membrane filtration to produce hydrolysate fractions rich in galactoglucomannan and with some lignin. The hydrolysate is a viable raw material for the production of renewable thin oxygen barrier films as demonstrated herein in the formulation of free standing films with very low oxygen permeability at both moderate and high relative humidities. Approximately 50,000 ton dry solid upgraded pre-hydrolysate suitable for production of oxygen barriers could be produced according to the presumed dissolving pulp mill producing about 500,000 air dry ton dissolving pulp per year and applying a liquor to wood ratio of 4:1. Utilization of the pre-hydrolysis liquor hence adds value to and realizes the dissolving plant as a biorefinery. A sensitivity analysis indicates that the market price of the upgraded pre-hydrolysate has the largest positive effect on the return on investment for separation and upgrading of a pre-hydrolysate. Increased investment cost and increased annuity factor show negative effects.

Influence of dryer type on the performance of a biomass gasification combined cycle co-located with an integrated pulp and paper mill

Integration of biomass gasification with a pulp and paper mill is a possible route to create more value-added products. This route facilitates, for example, more advanced electricity generation and production of biomass based transportation fuels or chemical feedstock. Each unit operation in such a process affects overall efficiency as well as possibilities for process integration. In this paper, the impact of different dryer types in a biomass gasification combined cycle (BIGCC) has been evaluated in terms of efficiency and economic performance. The BIGCC was sized so that the excess heat would replace the current steam production from bark and oil. The results show that the dryer type can have a significant impact on economic performance and efficiencies. A BIGCC with an integrated belt dryer, utilizing excess heat to heat the drying air from the mill, can result in electrical efficiencies of up to around 40%, while e.g. a steam dryer can reach 36–37%. Choice of oxidant, air or oxygen, in the gasifier affects both capital and operational cost. Air was proven to be the most cost efficient solution for the cases evaluated in this study. The investment of around 100 to 140 million Euros for a BIGCC facility is profitable for most evaluated cases for an annuity factor of 0.1, while the net annual profit is negative for most cases when the annuity factor was increased to 0.2, even when including financial support for renewable electricity.

SOLAR 1.1 software: a case study of a chicken farm illumination project

The aim of this paper is to describe the use of SOLAR 1.1 software to de¬sign an illumination system for a chicken farm. This software version also helps carry out the economic analysis for grid-connected or stand-alone photovoltaic systems for choosing practical values of the investment rate and annuity factor and calculates the payback period of investment in the photovoltaic plant.

Influence of seasonal variations on energy-saving opportunities in a pulp mill

Significant energy savings can be achieved in the pulp and paper industry through process integration. The aim of this paper was to investigate how much seasonal variations in the process influence the potential for making energy savings. The hot and warm water system in a market pulp mill has been evaluated from an energy point of view, using pinch analysis. Considerable energy-saving potential was found, 40.7 MW, of which 16.5 MW was in the form of steam savings. The steam savings represent 7% of the total steam consumption at the mill. New heat exchanger networks were redesigned using different approaches. The influence of seasonal variations was estimated from the calculated energy savings when monthly averages were used in the new heat exchanger networks. When seasonal variations were taken into account, the energy-saving opportunities fell by 2.5–5.0 MW, depending on heat exchanger network design, compared with a steady-state scenario. Consequently, 88–94% of the theoretical energy savings could be realised. An economic evaluation indicates positive earnings from investment in a new heat exchanger network when seasonal variations were taken into account, even with low prices for the extracted steam and excess heat (5 €/MWh) and with an annuity factor of 0.2.

The Simple Analytics of a Pooled Annuity Fund

AbstractThis article provides a formal analysis of payout adjustments from a longevity risk‐pooling fund, an arrangement we refer to as group self‐annuitization (GSA). The distinguishing risk diffusion characteristic of GSAs in the family of longevity insurance instruments is that the annuitants bear their systematic risk, but the pool shares idiosyncratic risk. This obviates the need for an insurance company, although such instruments could be sold through a corporate insurer. We begin by deriving the payout adjustment for a single entry group with a single annuity factor and constant expectations. We then show that under weak requirements a unique solution to payout paths exists when multiple cohorts combine into a single pool. This relies on the harmonic mean of the ratio of realized to expected survivorship rates across cohorts. The case of evolving expectations is also analyzed. In all cases, we demonstrate that the periodic‐benefit payment in a pooled annuity fund is determined based on the previous payment adjusted for any deviations in mortality and interest from expectations. GSA may have considerable appeal in countries which have adopted national defined contribution schemes and/or in which the life insurance industry is noncompetitive or poorly developed.

Ruined moments in your life: how good are the approximations?

In this paper we implement numerical PDE solution techniques to compute the probability of lifetime ruin which is the probability that a fixed retirement consumption strategy will lead to financial insolvency under stochastic investment returns and lifetime distribution. This problem is a variant of the classical and illustrious ruin problem in insurance, but adapted to individual circumstances. Using equity market parameters derived from US-based financial data we conclude that a 65-year-old retiree requires 30 times their desired annual (real) consumption to generate a 95% probability of sustainability, which is equivalent to a 5% probability of lifetime ruin, if the funds are invested in a well-diversified portfolio. The 30-to-1 margin of safety contrasts with the relevant annuity factor for an inflation-linked pension which would generate a zero probability of lifetime ruin. Our paper then goes on to compare the PDE-based values with moment matching and comonotonic-based approximations that have been proposed in the literature. Our results indicate that the Reciprocal Gamma approximation provides an accurate fit as long as the volatility of the underlying investment return does not exceed σ=30% per annum, which is consistent with capital market history. At higher levels of volatility the moment matching approximations break down. We also confirm that the comonotonic-based lower bound approximation provides remarkably accurate results when the time steps are small though. Our results should be of interest to academics, practitioners and software developers who are interested in computing sustainable consumption and withdrawal rates towards the end of the human life-cycle, but without resorting to crude simulations.

Ruined Moments in Your Life: How Good are the Approximations?

In this paper we implement numerical PDE solution techniques to compute the probability of lifetime ruin which is the probability that a fixed retirement consumption strategy will lead to financial insolvency under stochastic investment returns and lifetime distribution. Using equity market parameters derived from US-based financial data we conclude that a 65-year-old retiree requires 30 times their desired annual (real) consumption to generate a 95% probability of sustainability, which is equivalent to a 5% probability of lifetime ruin, if the funds are invested in a well-diversified equity portfolio. The 30-to-1 margin of safety can be contrasted with the relevant annuity factor for an inflation-linked income which would generate a zero probability of lifetime ruin. Our paper then goes on to compare the numerical PDE values with various moment matching and other approximations that have been proposed in the literature to compute the lifetime probability of ruin. Our results indicate that the Reciprocal Gamma approximation provides an accurate fit as long as the volatility of the underlying investment return does not exceed three-fourths = 30% per annum, which is consistent with capital market history. At higher levels of volatility the moment matching approximations break down and we provide some theoretical reasons for this phenomena. Our numerical and methodological results should be of interest to both academics and practitioners who are interested in methods of approximating stochastic present values as well as methods for computing sustainable consumption and withdrawal rates towards the end of the human life cycle.

The Use of Utility Functions for Investment Channel Choice in Defined Contribution Retirement Funds. II: A Proposed System

ABSTRACTIn this paper a system for recommending investment channel choices to members of defined contribution retirement funds is proposed. The system is interactive, using a member's answers to a series of questions to derive a utility function. The observed values are interpolated by means of appropriate formulae to produce a smooth utility function over the whole positive range of benefits at retirement. The resulting function, together with stochastic models of the returns on the available channels and of the annuity factor at exit, is then used to recommend an optimum apportionment of the member's investment. The proposed system is applied to the observed values of utility functions of post-retirement income elicited from members of retirement funds. Difficulties in the application are discussed and the results are analysed. The sensitivity of the recommendations to the parameters of the stochastic model is discussed.