ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management
|
|
- Natalie Newton
- 8 years ago
- Views:
Transcription
1 ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces ranged from $4 to $15 per MM BTU s n calendar years 2005 through Future prces are uncertan but are lkely to retan a hgh level of volatlty. Ths volatlty complcates analyss of potental plant captal nvestments to reduce energy usage, n partcular those that nvolve consderaton of alternate energy sources, snce tradtonal fnancal nvestment valuaton assumes that future cash flows are known exactly. Yet, ths s clearly not the case for many energy savng nvestments. In addton, future prce probablty functons may be best characterzed as non symmetrc and economc objectve functons as non-lnear further complcatng nvestment analyss. Falure to recognze these effects can result n ncorrectly valung the potental fnancal return of the nvestment. In ths paper, approprate technques to evaluate such nvestments are presented along wth case studes llustratng the approach. Keywords Energy Savng Project Investment Analyss; Rsk; Uncertanty; Monte Carlo Analyss Introducton For most plants n the process ndustres, energy s the second largest operatng cost component after the cost of raw materals. The rsng cost of energy has ncreased the nterest n process nvestments to reduce energy usage. However, evaluaton of the potental fnancal return of these nvestments s complcated by the volatlty n energy prces whch makes t dffcult to determne what prce or prces to use a bass for the fnancal analyss. Natural gas s the sngle largest type of external purchased fuel for the process ndustres and fgure 1 shows natural gas prcng n dollars per mllon BTU s ($/MMBTU) (EIA, 2011) for the perod 1993 to nvestment analyss, whch sgnfcantly ncreases project rsk. It can also be observed that the prce volatlty tends to be non-symmetrc wth a skew toward postve devatons. Wth the volatlty n prcng t s attractve to consder nvestments that wll allow use of multple energy sources so that usage can swtch perodcally from a more expensve to a cheaper source. The graph below shows natural gas and fuel ol prcng on equvalent bass for the same perod as the prevous graph. Fgure 2 Comparson Natural Gas and Fuel Ol Prce, 2000 to 2011 Fgure1- Natural Gas Prces, 2000 to 2011 The volatlty s apparent as s the assocated dffculty n forecastng future prcng to be used as the bass for It can be seen that there have been perods when natural gas s cheaper and perods when fuel ol s cheaper. A smlar skewness toward postve devatons s apparent n the fuel ol prcng as wth the natural gas prcng.
2 The subject of ths paper s then analyss of energy nvestments when there s sgnfcant uncertanty n the fuel prces wth the uncertanty best represented by nonsymmetrc dstrbutons and cases where there s potental swtchng between fuels. Background and Prevous Work A corporaton always has more potental nvestments than captal and t s necessary to rank the possble nvestments n terms of attractveness, generally n terms of fnancal return. The fnancal analyss requres valuaton models of the nvestment whch are based on a comparson of the tme based ncome stream generated by the nvestment wth ts cost. There are varous metrcs to use for ths comparson ncludng payback perod and Internal Rate of Return (IRR). From a rgorous fnancal pont of vew the preferred approach s to use the net present value (NPV) of the future sequence of after tax cash flows (ATCF) generated, dscounted back to the present tme (Brealey and Myers, 2003) compared wth the dscounted NPV of the nvestment. If the ATCF evoluton wth tme s known exactly ths can be expressed as: NPV(ATCF) = ATCF CoV = n n+ 1 + n + 1 = 1 rc+ r r) rc+ r r) Where: ATCF = ncremental after tax cash flow n perod (year) due to the nvestment n perod (year) 0 n = number fnancal evaluaton perods for the nvestment CoV n+1 = contnung value of the nvestment n perod n+1 r c = corporate weghted average after tax cost of captal r r = rsk premum to be appled to the expected returns from a partcular nvestment. The NPV of the cash flows s compared wth the NPV of the nvestment sequence IC to rank relatve nvestments. = = n IC NPV(IC) (2) = 0 rc) If NPV(ATCF) s greater than NPV(IC) then the nvestment has a postve return. The rato of ths dfference to the nvestment requred s known as the Proftablty Index and can be used to rank dfferent nvestments. However, ths famlar result s, n fact, only applcable when the projected cash flows are known wth very hgh probablty,.e. f the nvestment s essentally equvalent to a bond (Luenberger, 1998). Some energy nvestments n the past were made wth guaranteed fuel costs and guaranteed demands. The equatons above would be sutable for analyss of such stuatons. For most nvestments today n the process ndustres and most (1) partcularly for energy savng nvestments, ths s not the case. Energy projects have many rsk factors that lead to uncertanty n the calculaton of expected return both nternal n terms of equpment techncal performance, project executon effcency and user acceptance; and external n terms of demand, materal and labor costs, fnancng costs and energy prces. Of these, prces are typcally the largest rsk factor and are the subject of ths paper. To perform an analyss t s necessary to quantfy the rsk. For prcng, and other varables that can be consdered to be contnuous n nature, rsk s represented n the statstcal dstrbuton that s used for the future predcton of the varable evoluton over the lfe of the nvestment. At the same projected future mean value for the varable, a projecton wth hgher varance s consdered to be rsker or more uncertan than one wth a lower varance. In fnancal markets, t s desred to arrve at a sngle number whch values an nvestment, even wth the nvestment has hgh rsk. For example, t s desred to calculate the prce that would be approprate to purchase an opton. There are two generally accepted ways of arrvng at a sngle number whch s the value for such nvestments the rsk adjusted dscount rate and the certanty equvalence method. In the rsk adjusted dscount rate approach, the expected value of the cash flows s dscounted at a rate whch ncludes a rsk premum. The hgher the rsk, the hgher the rsk premum. In the certanty equvalence method, the expected cash flow s reduced by a penalty amount dependent agan on the rskness of the cash flow. It should not be surprsng that these two methods, f performed consstently, gve the same result (Obermaer, 2002) However, for project nvestment analyss, management s not just nterested n the most lkely value for the expected return but also n the dstrbuton. Even f the mean s postve, what s the probablty of a negatve return? If the prce dstrbuton s normal there s an analytc soluton for the mean and the varance of the NPV formula. For more general dstrbutons there s no analytc soluton. Evaluatng swtchng between fuels ntroduces a non-lnear element nto the objectve functon further complcatng the analyss. When there s no analytc soluton, the most common forms of project rsk analyss are senstvty analyss and Monte Carlo smulaton. In senstvty analyss the end ponts (hgh, low) of the ranges of possble outcomes s used as the bass for specfc fnancal case evaluaton. If the worst case stll has an adequate return then the nvestment can be approved. However, for many stuatons ths wll not be the result and t s of nterest to evaluate the probablty dstrbuton. Hertz (1968) s an early reference to the use of Monte Carlo smulaton for project nvestment evaluaton. The book by Dxt and Pendyck (1994) s an examnaton of nvestment analyss
3 when the tmng of the nvestment s one of the prmary uncertantes. The paper by Mlls et al (2006) dscusses performance rsk evaluaton for energy projects and quanttatvely settng the approprate project rsk premum. Van Groenendaal (1998) presents an analyss of the rsk n energy projects va senstvty analyss. Kulatlaka (1993) presented an analyss of the expected return for nvestments usng multple fuels when there was uncertanty n the tmng of the nvestment. Sngle Fuel, Prce Volatlty The ntal case evaluated was that for an nvestment n a new heater that would utlze a sngle fuel,.e. natural gas, wth a hgher effcency than that of the heater t replaced. The frst step was then to model natural gas prces from fgure 1. Consstent wth the Brce and Yucel (2005) prce modelng assumptons, the seres s splt nto two regons, one before January 1, 2000 and one after. The least square lnear trend lne for the post 2000 seres s calculated (see fgure 3) and the resduals from the trend lne used for dstrbuton analyss as shown n fgure 4 below. Fgure 3, Natural Gas Prcng Trend Lne, 2000 to 2011 The postve skewness s apparent from the hstogram and from the lack of ft of the normal dstrbuton. Varous standard non-symmetrc statstcal dstrbutons, ncludng lognormal, nverse normal and Gumbel, were evaluated on the bass of mnmzng the weghted least square error of the predcted versus actual cumulatve dstrbuton functon of the resduals. The lowest mean square error was produced by the Gumbel dstrbuton (Kotz and Nandarajah (2000)) and t was used for subsequent evaluaton. The sample mean square error for the Gumbel dstrbutons was approxmately 40% of the equvalent measure for the Normal dstrbuton. Fgure 4- Natural Gas Prce Volatlty - Resduals From Trend, 2000 to 2011 As a specfc case study to llustrate the ssues, consder nvestment n a new heater whch has a hgher effcency than the heater t replaces. Table 1 below gves the parameters used for the case study. Table 1- Assumptons For Investment Analyss Table 1 - Assumptons Assumptons Process Demand MMBTU/ Hr New Heater Investment Cost $ 13,000,000 Mantenance Costs Per Year, % Investment 2% Gas Prce Intal Gas Prce, $/ MMBTU $ 7 Increase Per Year, $ Old Equpment, Equpment Effcency, % 75 Lfe, Years 15 New Equpment, Effcency, % Operatng 90 Days/ Year Fxed Costs/ Yr $ 15,000 Cost of Capta 10% Deprecaton/Yr $ 866,667 Tax Rate 33% The base case analyss assumes an nvestment cost of $13, 000,000 and a gas cost of $7 per MMBTU s n the frst year ncreasng lnearly on the same trend lne as found for the 2000 to 2011 perod. It can be seen n Fgure 5 that the expected cash flow generates a postve net value compared wth the nvestment.
4 stuatons s more complcated. Flexblty requres nvestment now for an uncertan future payout. There are defnte costs but only potental benefts. As an extenson of the prevous case, purchase of equpment that can process a second fuel, for example fuel ol. In the analyss of ths case, t s necessary to develop a model of fuel ol prcng. A quadratc curve was ft to the prce data for the perod 2000 to 2011 as shown n fgure 7 below. Fgure 5 Investment Analyss, No Prce Volatlty The same case s then analyzed wth prce uncertanty. The natural gas prce statstcal dstrbuton s modeled wth the Gumbel dstrbuton wth a mean equal to the same value as the base case shown,.e. one that ncreases lnearly wth the year. The predcted future statstcal varance can then be adjusted and the resultng dstrbuton of the expected NPV examned. For example, the dstrbuton at the observed value for the varance for the perod 2000 to 2011 s shown below. Fgure 7- Fuel Ol Prcng Trend Lne, 2000 to 2011 The resduals from the trend lne were analyzed and agan found to be best modeled by the Gumbel non symmetrc dstrbuton wth a postve skewness as shown n Fgure 8. Fgure 6 NPV Dstrbuton, Prce Volatlty The smulaton ndcates an expected net NPV of $ However, ths s not the only nformaton receved. From a rsk management vewpont t s mportant to observe that the probablty of a negatve return for the nvestment s approxmately 22% and conversely the probablty of a return greater than $200,000 s 10%. These are mportant consderatons for comparatve nvestment analyss. Two Fuels, Uncorrelated Prce Volatlty As mentoned prevously, wth the volatlty n natural gas prcng t s desrable to consder nvestments that can use multple fuels, allowng the equpment to swtch and always use the cheaper fuel. Investment analyss of such Fgure 8 Ol Prce Resduals From Trend, 2000 to 2011 The fnancal model for the replacement heater was modfed to have two fuel optons, natural gas and fuel ol. The base fuel cost lne was assumed to be the lnear natural gas relatonshp from the prevous secton. The varance of the natural gas and the fuel prce around the trend lne was modeled wth ndependent and uncorrelated Gumbel statstcal dstrbutons wth the varance of the fuel ol dstrbuton at ten tmes that of the fuel gas. Agan the mean value for both fuel costs was the same for each perod. It was assumed that an ncreased nvestment of approxmately $300,000 was requred to add the dual-
5 frng capabltes. Trals were then run wth ncreasng varance assumed for the prcng. The results are llustrated n fgure 9. At the case of low uncertanty n the prcng the NPV of the nvestment s negatve and t s not justfed. However, as the assumed prce volatlty ncreases the expected NPV ncreases. The concluson s then that expectatons of ncreased prce volatlty at the same mean ncrease the expected payback of the nvestment. Ths effect of varance on the mean s not normally consdered n nvestment analyss. Increased prce volatlty s consdered to be a negatve factor for an nvestment. Yet t can be seen that n the case of potental fuel swtchng t actually ncreases the expected return. Fgure 9 Effect of Assumed Prce Varance on Expected Investment NPV Dxt, A. K. and R. S. Pndyck (1994); Investment Under Uncertanty; Prnceton Unversty Press (EIA); Energy Informaton Agency; US Department of Energy; Short Term Energy Outlook; webste Table 2. US Energy Prces ; December 11, 2011 release Hertz, D.B.(1968) Investment Polces That Pay Off, Harvard Busness Revew; 46; pp (January February, 1968) S. Kotz, S. Nadarajah (1999); Extreme Value Dstrbutons; Imperal College Press Kulatlaka, N. (1993); The Value of Flexblty: The Case of a Dual Fred Industral Steam Boler, Fnancal Management: 22(3); pp (1993) Luenberger, D. G. (1998); Investment Scence; Oxford Unversty Press, 1998 Mlls, E.; et al (2006); From volatlty To value: analyzng and managng performance rsk n energy savng projects; Energy Polcy; (34); pp Obermaer, R.(2002); Comment on Rsk analyss n nvestment apprasal based on the Monte Carlo smulaton technque by A. Hacura, M. Jadamus-Hacura and A. Kocot; European Physcs Journal (B); (30); pp ; (2002) van Groenendaal, W.J.H. (1998); Estmatng NPV varablty for determnstc models; European Journal of Operatonal Research; (107), pp ; Concluson In ths paper, prce data for natural gas and fuel ol are analyzed for the perod 2000 to 2011 and found to be best modeled by non-symmetrc statstcal dstrbuton wth a postve skewness. Prce dstrbutons are often assumed to be symmetrc Normal or Gaussan dstrbutons for the purpose of analyss and ths assumpton s not supported by ths data. Volatlty of the fuel prces ncreases the rsk of potental energy savng nvestments and the postve skewness further complcates the analyss. Monte Carlo analyss s used to provde a more complete analyss of the nvestment rsk profle. Addng flexblty to the potental nvestment to permt burnng alternate fuels ncreases the nvestment cost and adds non-lnearty to the nvestment objectve functon. By case study t s shown that ncreasng the predcted volatlty of the fuel prces at the same mean prce value ncreases the expected payout of the nvestment an effect that s not generally recognzed n nvestment analyss n ths area. References Brealey, R. A. and S.C. Myers (2003); Prncples of Corporate Fnance, 7 th Ed.; McGraw-Hll Irwn Brown, S.PA. and M.K. Yucel; (2005) What Drves Natural Gas Prces; Federal Reserve Bank of Dallas; Research Note; February, 2005
An Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationRisk Model of Long-Term Production Scheduling in Open Pit Gold Mining
Rsk Model of Long-Term Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationA Model of Private Equity Fund Compensation
A Model of Prvate Equty Fund Compensaton Wonho Wlson Cho Andrew Metrck Ayako Yasuda KAIST Yale School of Management Unversty of Calforna at Davs June 26, 2011 Abstract: Ths paper analyzes the economcs
More informationIntra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intra-year Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationHow To Calculate The Accountng Perod Of Nequalty
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 2005-02 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 14853-7801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationCredit Limit Optimization (CLO) for Credit Cards
Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationA DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION. Michael E. Kuhl Radhamés A. Tolentino-Peña
Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATION-BASED OPTIMIZATION
More informationMultiple-Period Attribution: Residuals and Compounding
Multple-Perod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.
More informationOn the Optimal Control of a Cascade of Hydro-Electric Power Stations
On the Optmal Control of a Cascade of Hydro-Electrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy S-curve Regresson Cheng-Wu Chen, Morrs H. L. Wang and Tng-Ya Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationTraffic-light a stress test for life insurance provisions
MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money
Ch. 6 - The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21- Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationThe Development of Web Log Mining Based on Improve-K-Means Clustering Analysis
The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationHedging Interest-Rate Risk with Duration
FIXED-INCOME SECURITIES Chapter 5 Hedgng Interest-Rate Rsk wth Duraton Outlne Prcng and Hedgng Prcng certan cash-flows Interest rate rsk Hedgng prncples Duraton-Based Hedgng Technques Defnton of duraton
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationRisk-based Fatigue Estimate of Deep Water Risers -- Course Project for EM388F: Fracture Mechanics, Spring 2008
Rsk-based Fatgue Estmate of Deep Water Rsers -- Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More information) of the Cell class is created containing information about events associated with the cell. Events are added to the Cell instance
Calbraton Method Instances of the Cell class (one nstance for each FMS cell) contan ADC raw data and methods assocated wth each partcular FMS cell. The calbraton method ncludes event selecton (Class Cell
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 73-8 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qng-xn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationThe impact of hard discount control mechanism on the discount volatility of UK closed-end funds
Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closed-end funds Abstract The mpact
More informationSUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.
SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976-76-10-00
More informationUnderwriting Risk. Glenn Meyers. Insurance Services Office, Inc.
Underwrtng Rsk By Glenn Meyers Insurance Servces Offce, Inc. Abstract In a compettve nsurance market, nsurers have lmted nfluence on the premum charged for an nsurance contract. hey must decde whether
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 357-5200 Fax: (617) 357-5250 www.ersa-lawyers.com
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationAbstract # 015-0399 Working Capital Exposure: A Methodology to Control Economic Performance in Production Environment Projects
Abstract # 015-0399 Workng Captal Exposure: A Methodology to Control Economc Performance n Producton Envronment Projects Dego F. Manotas. School of Industral Engneerng and Statstcs, Unversdad del Valle.
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationDepreciation of Business R&D Capital
Deprecaton of Busness R&D Captal U.S. Bureau of Economc Analyss Abstract R&D deprecaton rates are crtcal to calculatng the rates of return to R&D nvestments and captal servce costs, whch are mportant for
More informationHOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*
HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, Perre-Andre
More informationThursday, December 10, 2009 Noon - 1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationAn Analysis of Central Processor Scheduling in Multiprogrammed Computer Systems
STAN-CS-73-355 I SU-SE-73-013 An Analyss of Central Processor Schedulng n Multprogrammed Computer Systems (Dgest Edton) by Thomas G. Prce October 1972 Techncal Report No. 57 Reproducton n whole or n part
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and
More informationCharacterization of Assembly. Variation Analysis Methods. A Thesis. Presented to the. Department of Mechanical Engineering. Brigham Young University
Characterzaton of Assembly Varaton Analyss Methods A Thess Presented to the Department of Mechancal Engneerng Brgham Young Unversty In Partal Fulfllment of the Requrements for the Degree Master of Scence
More informationAn Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services
An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsn-yng Wu b a Professor (Management Scence), Natonal Chao
More informationChapter 15 Debt and Taxes
hapter 15 Debt and Taxes 15-1. Pelamed Pharmaceutcals has EBIT of $325 mllon n 2006. In addton, Pelamed has nterest expenses of $125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationFuzzy Regression and the Term Structure of Interest Rates Revisited
Fuzzy Regresson and the Term Structure of Interest Rates Revsted Arnold F. Shapro Penn State Unversty Smeal College of Busness, Unversty Park, PA 68, USA Phone: -84-865-396, Fax: -84-865-684, E-mal: afs@psu.edu
More informationThe Current Employment Statistics (CES) survey,
Busness Brths and Deaths Impact of busness brths and deaths n the payroll survey The CES probablty-based sample redesgn accounts for most busness brth employment through the mputaton of busness deaths,
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationANALYSIS OF FINANCIAL FLOWS
ANALYSIS OF FINANCIAL FLOWS AND INVESTMENTS II 4 Annutes Only rarely wll one encounter an nvestment or loan where the underlyng fnancal arrangement s as smple as the lump sum, sngle cash flow problems
More informationPortfolio Loss Distribution
Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets hold-to-maturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationChapter 15: Debt and Taxes
Chapter 15: Debt and Taxes-1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More informationBrigid Mullany, Ph.D University of North Carolina, Charlotte
Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationAbstract. 260 Business Intelligence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING
260 Busness Intellgence Journal July IDENTIFICATION OF DEMAND THROUGH STATISTICAL DISTRIBUTION MODELING FOR IMPROVED DEMAND FORECASTING Murphy Choy Mchelle L.F. Cheong School of Informaton Systems, Sngapore
More informationDiscount Rate for Workout Recoveries: An Empirical Study*
Dscount Rate for Workout Recoveres: An Emprcal Study* Brooks Brady Amercan Express Peter Chang Standard & Poor s Peter Mu** McMaster Unversty Boge Ozdemr Standard & Poor s Davd Schwartz Federal Reserve
More informationA Critical Note on MCEV Calculations Used in the Life Insurance Industry
A Crtcal Note on MCEV Calculatons Used n the Lfe Insurance Industry Faban Suarez 1 and Steven Vanduffel 2 Abstract. Snce the begnnng of the development of the socalled embedded value methodology, actuares
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationKiel Institute for World Economics Duesternbrooker Weg 120 24105 Kiel (Germany) Kiel Working Paper No. 1120
Kel Insttute for World Economcs Duesternbrooker Weg 45 Kel (Germany) Kel Workng Paper No. Path Dependences n enture Captal Markets by Andrea Schertler July The responsblty for the contents of the workng
More informationEfficient Project Portfolio as a tool for Enterprise Risk Management
Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse
More informationSPECIALIZED DAY TRADING - A NEW VIEW ON AN OLD GAME
August 7 - August 12, 2006 n Baden-Baden, Germany SPECIALIZED DAY TRADING - A NEW VIEW ON AN OLD GAME Vladmr Šmovć 1, and Vladmr Šmovć 2, PhD 1 Faculty of Electrcal Engneerng and Computng, Unska 3, 10000
More informationWhen Talk is Free : The Effect of Tariff Structure on Usage under Two- and Three-Part Tariffs
0 When Talk s Free : The Effect of Tarff Structure on Usage under Two- and Three-Part Tarffs Eva Ascarza Ana Lambrecht Naufel Vlcassm July 2012 (Forthcomng at Journal of Marketng Research) Eva Ascarza
More informationStress test for measuring insurance risks in non-life insurance
PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n non-lfe nsurance Summary Ths memo descrbes stress testng of nsurance
More informationTraffic-light extended with stress test for insurance and expense risks in life insurance
PROMEMORIA Datum 0 July 007 FI Dnr 07-1171-30 Fnansnspetonen Författare Bengt von Bahr, Göran Ronge Traffc-lght extended wth stress test for nsurance and expense rss n lfe nsurance Summary Ths memorandum
More informationTrade Adjustment and Productivity in Large Crises. Online Appendix May 2013. Appendix A: Derivation of Equations for Productivity
Trade Adjustment Productvty n Large Crses Gta Gopnath Department of Economcs Harvard Unversty NBER Brent Neman Booth School of Busness Unversty of Chcago NBER Onlne Appendx May 2013 Appendx A: Dervaton
More informationESTIMATING THE MARKET VALUE OF FRANKING CREDITS: EMPIRICAL EVIDENCE FROM AUSTRALIA
ESTIMATING THE MARKET VALUE OF FRANKING CREDITS: EMPIRICAL EVIDENCE FROM AUSTRALIA Duc Vo Beauden Gellard Stefan Mero Economc Regulaton Authorty 469 Wellngton Street, Perth, WA 6000, Australa Phone: (08)
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 610-519-4390,
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationADVA FINAN QUAN ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS VAULT GUIDE TO. Customized for: Jason (jason.barquero@cgu.edu) 2002 Vault Inc.
ADVA FINAN QUAN 00 Vault Inc. VAULT GUIDE TO ADVANCED FINANCE AND QUANTITATIVE INTERVIEWS Copyrght 00 by Vault Inc. All rghts reserved. All nformaton n ths book s subject to change wthout notce. Vault
More informationTransition Matrix Models of Consumer Credit Ratings
Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationENTERPRISE RISK MANAGEMENT IN INSURANCE GROUPS: MEASURING RISK CONCENTRATION AND DEFAULT RISK
ETERPRISE RISK MAAGEMET I ISURACE GROUPS: MEASURIG RISK COCETRATIO AD DEFAULT RISK ADIE GATZERT HATO SCHMEISER STEFA SCHUCKMA WORKIG PAPERS O RISK MAAGEMET AD ISURACE O. 35 EDITED BY HATO SCHMEISER CHAIR
More informationStudy on Model of Risks Assessment of Standard Operation in Rural Power Network
Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationGeneral Iteration Algorithm for Classification Ratemaking
General Iteraton Algorthm for Classfcaton Ratemakng by Luyang Fu and Cheng-sheng eter Wu ABSTRACT In ths study, we propose a flexble and comprehensve teraton algorthm called general teraton algorthm (GIA)
More informationEstimating Total Claim Size in the Auto Insurance Industry: a Comparison between Tweedie and Zero-Adjusted Inverse Gaussian Distribution
Estmatng otal Clam Sze n the Auto Insurance Industry: a Comparson between weede and Zero-Adjusted Inverse Gaussan Dstrbuton Autora: Adrana Bruscato Bortoluzzo, Italo De Paula Franca, Marco Antono Leonel
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER Revsed May 2003 ABSTRACT In ths paper, we nvestgate
More informationInterest Rate Forwards and Swaps
Interest Rate Forwards and Swaps Forward rate agreement (FRA) mxn FRA = agreement that fxes desgnated nterest rate coverng a perod of (n-m) months, startng n m months: Example: Depostor wants to fx rate
More informationPower-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts
Power-of-wo Polces for Sngle- Warehouse Mult-Retaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationReturn decomposing of absolute-performance multi-asset class portfolios. Working Paper - Nummer: 16
Return decomposng of absolute-performance mult-asset class portfolos Workng Paper - Nummer: 16 2007 by Dr. Stefan J. Illmer und Wolfgang Marty; n: Fnancal Markets and Portfolo Management; March 2007; Volume
More informationEarthquake Vulnerability Reduction Program in Colombia A Probabilistic Cost-benefit Analysis
Publc Dsclosure Authorzed Earthquake Vulnerablty Reducton Program n Colomba A Probablstc Cost-beneft Analyss WPS3939 Publc Dsclosure Authorzed Abstract Francs Ghesquere, World Bank Lus Jamn, Unversty of
More informationSTATISTICAL DATA ANALYSIS IN EXCEL
Mcroarray Center STATISTICAL DATA ANALYSIS IN EXCEL Lecture 6 Some Advanced Topcs Dr. Petr Nazarov 14-01-013 petr.nazarov@crp-sante.lu Statstcal data analyss n Ecel. 6. Some advanced topcs Correcton for
More informationApplication of Quasi Monte Carlo methods and Global Sensitivity Analysis in finance
Applcaton of Quas Monte Carlo methods and Global Senstvty Analyss n fnance Serge Kucherenko, Nlay Shah Imperal College London, UK skucherenko@mperalacuk Daro Czraky Barclays Captal DaroCzraky@barclayscaptalcom
More informationHigh Correlation between Net Promoter Score and the Development of Consumers' Willingness to Pay (Empirical Evidence from European Mobile Markets)
Hgh Correlaton between et Promoter Score and the Development of Consumers' Wllngness to Pay (Emprcal Evdence from European Moble Marets Ths paper shows that the correlaton between the et Promoter Score
More informationAllocating Time and Resources in Project Management Under Uncertainty
Proceedngs of the 36th Hawa Internatonal Conference on System Scences - 23 Allocatng Tme and Resources n Project Management Under Uncertanty Mark A. Turnqust School of Cvl and Envronmental Eng. Cornell
More informationProject Networks With Mixed-Time Constraints
Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationOptimal Customized Pricing in Competitive Settings
Optmal Customzed Prcng n Compettve Settngs Vshal Agrawal Industral & Systems Engneerng, Georga Insttute of Technology, Atlanta, Georga 30332 vshalagrawal@gatech.edu Mark Ferguson College of Management,
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More information