Overview of Sociologys Conflict Theory

Conflict theory states that tensions and conflicts arise when resources, status, and power are unevenly distributed between groups in society  and that these conflicts become the engine for social change. In this context, power can be understood as control of material resources and accumulated wealth, control of politics and the institutions that make up society, and ones social status relative to others (determined not just by class but by race, gender, sexuality, culture, and religion, among other things). Karl Marx A house may be large or small; as long as the neighboring houses are likewise small, it satisfies all social requirement for a residence. But let there arise next to the little house a palace, and the little house shrinks to a hut. Wage Labour and Capital (1847) Marxs Conflict Theory Conflict theory originated in the work of Karl Marx, who focused on the causes and consequences of class conflict between the bourgeoisie (the owners of the means of production and the capitalists) and the proletariat (the working class and the poor). Focusing on the economic, social, and political implications of the rise of capitalism in Europe, Marx theorized that this system, premised on the existence of a powerful minority class (the bourgeoisie) and an oppressed majority class (the proletariat), created class conflict because the interests of the two were at odds, and resources were unjustly distributed among them. Within this system an unequal social order was maintained through ideological coercion which created consensus--and acceptance of the values, expectations, and conditions as determined by the bourgeoisie.  Marx theorized that the work of producing consensus was done in the superstructure of society, which is composed of social  institutions, political structures, and culture, and what it produced consensus for was the base, the economic relations of production.   Marx reasoned that as the socio-economic conditions worsened for the proletariat, they would develop a class consciousness that revealed their exploitation at the hands of the wealthy capitalist class of bourgeoisie, and then they would revolt, demanding changes to smooth the conflict. According to Marx, if the changes made to appease conflict maintained a capitalist system, then the cycle of conflict would repeat. However, if the changes made created a new system, like socialism, then peace and stability would be achieved. Evolution of Conflict Theory Many social theorists have built on Marxs conflict theory to bolster it, grow it, and refine it over the years. Explaining why Marxs theory of revolution did not manifest in his lifetime,  Italian scholar and activist  Antonio Gramsci  argued that the power of ideology was stronger than Marx had realized  and that more work needed to be done to overcome cultural hegemony, or  rule through common sense. Max Horkheimer and Theodor Adorno, critical theorists who were part of The Frankfurt School, focused their work on how the rise of mass culture--mass produced art, music, and media--contributed to the maintenance of cultural hegemony. More recently, C. Wright Mills drew on conflict theory to describe the rise of a tiny power elite composed of military, economic, and political figures who have ruled America from the mid-twentieth century. Many others have drawn on conflict theory to develop other types of theory within the social sciences, including feminist theory, critical race theory, postmodern and postcolonial theory, queer theory, post-structural theory, and theories of globalization and world systems. So, while initially conflict theory described class conflicts specifically, it has lent itself over the years to studies of how other kinds of conflicts, like those premised on race, gender, sexuality, religion, culture, and nationality, among others, are a part of contemporary social structures, and how they affect our lives. Applying Conflict Theory Conflict theory and its variants are used by many sociologists today to study a wide range of social problems. Examples include: How todays global capitalism creates a global system of power and inequality.How words play a role in reproducing and justifying conflict.The causes and consequences of the gender pay gap between men and women. Updated  by Nicki Lisa Cole, Ph.D.

Exploring the Mexican Independence from Spain Essay

Introduction To what extent was Mexico’s independence from Spain a â€Å"full-scale assault on dependency†? This essay will investigate how the Mexican independence from Spain was only slightly a â€Å"full-scale assault on dependency†, due to several political and social conflicts. Firstly, Mexico remained a monarchy (but not under the control of Spain) after the insurgency. Secondly, there was still an official state religion in Mexico. Another reason is because social conflicts reduced the desire for independence .On the other hand, it assaulted dependency because there were some changes within the social hierarchy, and because Mexico was free from Spain. Narrative Before the Mexican insurgency, a mass famine struck the Bajio, or lowland†¦show more content†¦For example, some of his reforms were the following: 1. That America is free and independent of all nations; 8. The salaries of the representatives will be enough for sustenance; 13. That the general laws apply to everyone, without excepting priviledged bodies, along with other radical reforms (Morelos). Unfortunately, none of them were actually implemented, as Morelos’ guerilla warfare tactic, resulting in many defeats. Finally, his movement ended as he was executed in 1815 by the Spanish Inquisition (Father Hidalgo Proclaims Grito de Dolores†). Towards the year 1820, desire for independence within Mexico decreased, as there was an inner conflict between the peninsulares, creoles, and the lower classes, as the aspirations of the lower castes would reduce the political and economic power of those classes (Keen 169; Huck 51). But then there was a new leader of the ind ependence movement: Agustin de Iturbide. Instead of continuing the legacies of Morelos and Hidalgo, he changed sides, fighting only for the independence of Spain (Huck 53-54) His conservative plan, the Plan of Iguala, consisted of creating a constitutional monarchy, establishing Roman Catholicism as the official religion of Mexico, and giving equality to only peninsulares and creoles (Kirkwood). Despite establishing independence, the Plan of Iguala created a long line of dictators, only to makeShow MoreRelatedReginald Lewis II EVALUATION OF SOURCES: Gonzales, Michael J.. The Mexican Revolution, 1910-1940.1600 Words   |  7 PagesEVALUATION OF SOURCES: Gonzales, Michael J.. The Mexican Revolution, 1910-1940. Albuquerque: University of New Mexico Press, 2002. Michael J. Gonzales, noted Peruvianist and author of two articles on copper mining in northern Mexico, in this latest book describes the revolution and provides extensive coverage (nearly one-third of the text) of the Porfiriato. Lucid, engaging, and containing interesting anecdotes, this political survey of the Mexican Revolution makes liberal use of relevant photographsRead MoreManifest Destiny Essay1346 Words   |  6 PagesFrom the time European colonists and settlers first set foot on this continent, they brought with them the beliefs, the ideas, that would evolve into the American ideology known today as Manifest Destiny. Still, it was not until 1834 that the newspaper editor, John L. OSullivan, is believed to have first coined the phrase â€Å"Manifest Destiny† when he said in his article Annexation, ...our manifest destiny to overspread the continent allotted by Providence for the free development of our yearlyRead MoreIndependence Movement of Brazil and Mexico.1943 W ords   |  8 Pagesorganizational structures by an independence movement, and if most is defined as greatest, successful as a desired outcome and original rationale and/or purpose is defined as an fundamental intentional reason, then between the countries of Brazil and Mexico, Brazil had the most successful revolutionary movement in terms of its original rationale and/or purpose because Brazil, unlike the Mexican independence movement, had a greater universal agreement about independence between every social classRead MoreThe United States Of America1490 Words   |  6 Pagesstill speaks Spanish, and the environmental pressures that affect peoples choices in when they use Spanish. a) How did the community come to be where it is today? The Spanish language first arrived at the U.S. in 1513, by Ponce de Leon. He was exploring the Florida peninsula. In 1565, Pedro Menendez de Aviles established the first Spanish speaking settlement in San Agustin Florida. Throughout 1520 to 1570 the Spanish continued to explore sand produce flourishing colonies along the Atlantic coastRead MoreEssay on Africans in Colonial Mexico5451 Words   |  22 Pagesof bozales, criollos, mulattoes, and zambos is far-reaching. The colonial period provides an excellent starting place for an examination of the significance of these groups not only because the institution of African slavery was introduced to New Spain at that time, but also because the regular influx of native Africans combined with the close attention paid to color-based castas in official records allows historians to trace the influence of African culture more readily during that period. TheRead MoreMexican Culture : Mexican American Culture1857 Words   |  8 Pages Mexican-American Culture Many immigrants come to the United States from all over the world. Some bring their families, some their prized possessions, others come with nothing but determination and the goal of a better life. One thing that every immigrant brings with them is their culture. One of the most dominant minority cultures in the United States is the Mexican culture. The US shares a border with Mexico making it easier for immigrants to stay in contact with their families in their homeRead MoreImportance Of Geography On The History1848 Words   |  8 Pagesland was given to them by their God and no one is the rightful owner of any land in America. The native tribes would move from place one to another and other tribes would come and take live in that land. But when Europeans came to The new world they would ask natives to give them the little land that they can use and slowly they started tricking or forcibly taking the land away from the natives. The natives were simple minded people who were aston ished by the new things like weapons, cloths, alcoholRead MoreInfluence of Immigration on the American Culture and Language14362 Words   |  58 PagesSources †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. Appendix †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. INTRODUCTION The United States is a society of immigrants. Ever since its formation in 1776, and even before that, the United States has attracted immigrants from around the world. Since its early days, the country has admitted more than 50 million newcomers, a larger number of immigrants than any country in history. For over two centuries, people have flocked under this nations protective wings as opportunistsRead MoreBohlander/Snell-Managing Hr24425 Words   |  98 Pagessize you are, you’re suddenly competing against companies you’ve never heard of all around the world that make a very similar widget or provide a very similar service,† as one global manager put it. In fact, nearly threequarters of HR professionals from companies large and small in a wide range of industries and countries say they expect their company’s international business to grow in the coming years.1 Some of these companies are handling the challenge well. Others are failing miserably as theyRead MoreVolkswagen20284 Words   |  82 Pageswas to find out which particular modes did VW use to enter Chinese market and what are the rationales behind such choice. It was found that it is the macro environment (political, economic, social and technological) and micro environment (threat from five forces) of China lends itself to a particular entry mode: joint venture. It also presented the challenges and directions of the company in its future development in China -1- MA MANAGEMENT DISSERTATION XIAOFENG WEN Acknowledgements

Snapshot Of Main Scenario Company Profile Essay - 2864 Words

Contents Synopsis 2 Main Case 6 Snapshot of main scenario 6 Company Profile 6 Technology behind confirmtkt.com 7 Business Model 8 SWOT Analysis 10 Strengths: 10 Weaknesses: 10 Opportunities: 10 Threats: 10 Regulatory Framework 10 Porter Five Competitive Forces Analysis 11 a) Bargaining power of buyers 11 b) Bargaining power of suppliers 11 c) Threat of new entrants 11 d) Threat of substitutes 11 e) Intensity of Competition 11 Competitor Analysis 11 Trainman.com 12 Pnr.me 12 Indiarailinfo.com 12 Main case central issue 12 References 14 TEACHING NOTE 15 Synopsis Subject Area Confirmtkt.com (Confirm ticket) is a travel website which predicts the chances of a railway ticket getting confirmed. It uses a set of algorithm and past data to calculate the results. It is slowly growing in popularity evident from the fact that it has received till date over 10 million queries on seat availability and over 750,000 queries on ticket confirmation. It has received significant coverage from media channels like Aaj Tak, RailNews etc. The company also has over 10,000 followers on Facebook reflects the healthy growth that the company is registering among the youth of the nation. The company of late wants to find sources of revenue generation. The various sources available include advertisement on its website, collaboration with various travel agencies offering tour packages (individual and institutional) and partnership deals with hotel and motels. The case dwells into the revenueShow MoreRelatedSlot Sharing Model For Campus Placements1380 Words   |  6 Pagesperforming student in the class. This is one major issue in the campus placement scenario. In view of the fact that all major companies would demand for the first day for the campus recruitment, it is a challenge to decide which company should be given the first day. Once the first day slot is committed to a company it deprives the students the opportunity of attending the campus of the dream company and many times the company given the first slot might not end up in recruiting as many numbers as expectedRead More Transaction Management Techniques of Concurrency and Recovery2847 Words   |  11 Page stransactions. Deadlock is a vicious circle where one transaction needs a resource being held by another which will not release it until it receives the resource being held by the next, and so on. Starvation is similar to deadlock. When the queueing scenario for a lock is unfair and one or more transactions have to wait indefinitely to acquire the needed lock starvation occurs. Serialization is the idea of isolating, or appearing to isolate a transaction, so it acts like the only transaction happeningRead MoreIterative Process Of Design Thinking Essay2111 Words   |  9 PagesCase) Describe Lackner’s Dilemma Lacker was the head for invocation and technology. His dilemma was should open innovation at Siemens be in practice or discontinued. He was sanctioned with an annual budget of 3 billion euros when compared to other companies in the market for innovation this was small budget for open innovation. Lacker decided to came up with some his strategies and later decided to present it so the to the board. The response was After presenting the strategy to high level staff,Read MoreNestle Swot1886 Words   |  8 PagesIntroduction: Nestlà ©Ã¢â‚¬â„¢s lineage dates back to 1867 when Henri Nestle founded the company Ste Henri Nestle and was responsible for producing infant food composed of milk, grain, and carbohydrates. 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And hence is the Iterative Methodology the best approach for such Projects, becauseRead MoreSample of Ieee Test Plan for P2V Conversion5702 Words   |  23 PagesTest Deliverables 16 8. Testing Tasks 16 Tasks necessary to prepare for : 16 a. Systems Testing 16 DIVSS160.beerdivision.africa.gcn.local (SQL Server Instance) 17 b. Functional Testing 18 8.1 FUNCTIONAL TESTING: Subject Area Test Scenarios 19 a. DailySales 19 b. CICIntraday 19 c. BBBEE (Investec) 19 Risks and Contingencies 29 High-risk assumptions of the test plan 29 Contingency Plans 29 x. BACKOUT PLAN 29 9. Approvals 30 * 1. Introduction BriefRead MorePreventing Violence in the Workplace2255 Words   |  10 Pagesthese types of scenarios. To get a better understanding of some of the factors that lead up to a case of workplace violence, one must have a grasp of highly publicized incidents that have occurred in the past. By far, the most popular case of workplace violence that many can remember is the incident the coined the term â€Å"going postal.† The Oklahoma Historical Society described the events as such, â€Å"USPS letter carrier Patrick H. Sherrill, a â€Å"disgruntled postal worker† fit the profile of a potentialRead MoreEsquel Group14861 Words   |  60 Pages20 20 21-22 22-23 23-24 24-25 25-26 †¢ †¢ †¢ †¢ †¢ †¢ †¢ †¢ †¢ †¢ †¢ †¢ †¢ †¢ Study Aims Civic Exchange Aims Methodology Limitations Sustainable Development Measuring Sustainability Global Reporting Initiative A Sustainability ‘Snapshot’ - The Esquel Group Introduction to the ‘Snapshot’ Introduction to EG Introduction to EG What does EG do? Where is EG located? What is EG’s Mission? Who are EG’s customers? How does EG operate? EG and Sustainable Development †¢ †¢ †¢ †¢ †¢ †¢ EG’s Sustainable DevelopmentRead MoreSwots: Strategic Management and Swot Analysis10122 Words   |  41 Pagesfit between a commercial venture and its environment. 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Purpose of the research paper While SWOT is a pervasive

Examine the reasons for the changes in the patterns of marriage and cohabitation in the last 40 years or so free essay sample

In the last 40 years, Society in Britain has experienced many changes that have affected the family. There have been changes in attitudes to and expectations of family life, as well as official changes such as government laws. These changes have been induced by the rise of feminism; they have increased awareness of women’s rights and freedoms. Another change that has affected family is postmodernism, which has promoted freedom, choice and diversity. Secularisation has also affected the family, which has taken away stigmas attached to aspects of family life. The changes resulting have affected marriage rates, which are decreasing, and more people are now marrying later in life and more than once. More people are choosing to cohabit, either before or instead of marrying, and this is becoming increasingly common in young couples. Divorce rates have also increased in the last 40 years, following the changes in the law and attitudes. As society’s view of a ‘conventional family’ has changed over the last 40 years, the variety of acceptable norms has increased drastically. We will write a custom essay sample on Examine the reasons for the changes in the patterns of marriage and cohabitation in the last 40 years or so or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page In the past, an unmarried woman or spinster would be looked down on in society ,as it was a norm that a woman should be married with children. If they didn’t they would be judged as there was a problem with them so that they couldn’t have kids or a husband. The average age for a women first getting married in 1961 was 23.1 this has risen to 30 by June 2009. This shows that women are now waiting longer for their first marriage. This is down to many different reasons. Single women aren’t looked down on by the majority of people today, they are viewed as strong, independent women. This means that there is next to no pressure for women to get married quickly. This has resulted in the rise in cohabitation. Marriage is no longer seen as the definition of a proper relationship by society. 40 years ago, living together outside of marriage was a rarity; however cohabitation can now be seen as a socially acceptable alternative to marriage. This is partly due to the changing attitudes to sexual relationships mean that sex is no longer seen as only legitimate within marriage, this has also resulted in far fewer members of my generation viewing cohabitation as morally wrong. More and more people are also seeing that the legal papers of marriage are just legal papers it  doesn’t add to the relationship. For people in today’s society a happy relationship is much more important than the papers that come with getting married, people see that a couple that cohabit and are happy have as much of a valid relationship than those who are married. Divorce rates have also increased as a result of the change in attitudes. In the past there was a stigma attached to getting divorced, however It is now much more acceptable and ‘normal’ for divorce to happen, 40% of marriages end in divorce. The attitude to marriage has changed from it being a lifelong contract to a serious relationship, and it is far more acceptable for a relationship to end than a contract to be broken, so divorce becomes more acceptable, and more people feel able to end a relationship in which they are not happy. When another wave of Feminism started in the 60’s, their views have been impacting society’s values and the pattern of family life. Feminists believe in the independence of women, both financially and socially, and that marriage is oppressive to females because it is dominated by males. They also reject the idea that women should become the housewife giving up her career to bear children. They welcome the rise in cohabitation. They do agree with the postmodernists in that family life should be down to choice and is diverse. They say that women should have the freedom to choose whether they marry, cohabit or divorce or whether they raise children alone or in a relationship all dependent on their choice. They have also encouraged women to focus on a career rather than starting a family and getting married, thus the marriage rate has decreased. Feminist have also given positive responses to the government that have made laws making divorce easier. Before these laws it was ridiculously difficult for women to get a divorce. These laws give women more freedom for women to abusive and oppressive marriages. Judith Stacey has argued how that greater choice has benefitted women because it enables them to be free from patriarchal oppression and shape their family to their needs. Marxist-Feminists have gone as far as linking gender inequality to class inequality, they would say that the falling rates in marriage and raising rates of divorce are showing that society is becoming less controlled by the capitalist men. Feminist say that as women take on a more equal role in society as they are able to support themselves financially and can afford to be free from male oppression. Laws over the When laws relating to marriage and divorce  have changed in the last 30 years, they have both helped to shape and influence social attitudes, and also reflected the changes in attitudes that have taken place. The Civil Partnerships Act in 2004 enabled people of the same sex to enter in to a civil partnership, or gay marriage. This has meant that the concept of marriage has been widened beyond previous definition, and provides another option for people who may otherwise have felt forced in to a heterosexual marriage in order to conform to societies expectations. This could have an impact on patterns of heterosexual marriage because people no longer feel they need to fit a certain mould, because the law has changed to be more inclusive. Legislation has also made divorce a lot easier than before and more of an option for many people. In 1984, the law said that rather than being married for 3 years before a couple were allowed to divorce, the time was reduced to one year. The Family Law Act in 1996 said that there did not have to be any fault involved with divorce for it to be done quickly and promoting mediation to make the process easier. This turned the idea of divorce from being that of a failed marriage, and the result of someone’s mistakes or failures, to be being just another part of normal life, an acceptable next step after being married for a while. The decline in religious people in Britain has also been a factor in the patterns of cohabitation and divorce. As the country becomes more and more secular, values that are traditionally associated with religion are declining gradually. Younger generations no longer viewing sex outside of marriage as sinful is just one of these religious traditions that are declining, it is also less likely to be taken into consideration for couples choosing to cohabit instead of marrying. The church has always been supportive of marriage it’s a tradition of religion, but as the decline in the churches influence over society’s values, marriage could be seen as declining in value too. Most religions still uphold the importance of marriage in a person’s life so they therefore discredit divorce, so in the past couples would have tried at all accounts to stay together and make it work. The divorce rates have increased because people are less likely to be considering religious views when making their decisions. In the UK there has been a vast increase over the last 40 years in the variety of different faith influences in the UK. Due to society becoming more multicultural, there has been an increase in marriages where the partners have different  faiths, or one person has no faith. This can lead to difficulties in the Childs upbringing. Another difficulty could be the conflict caused by two families of different faiths. Divorce is more likely in inter-faith marriages than those of the same faith; this has also helped in the increase of the divorce rate. . Postmodernism can also help to explain trends in marriage, divorce and cohabitation in the last 40 years. Postmodernist ideas say that choice for every individual is the most important thing, and puts personal freedom and satisfaction above all else. Postmodernists say that unlike frogs or butterflies we us people don’t go through a fixed life cycle, instead we follow a life course where at many points we go either one way or another. This means that there is no right or ideal way to have a relationship or raise a family, so people are free to live however be most convenient for them, which may include cohabitation rather than marriage. Postmodernist views also say that our identity is no longer defined by our family background, and instead centres on material possessions, which means families are less important to who we are. This could mean that people are less inclined to see marriage as a vital part of adulthood and so choose cohabitation because it is more flexible, or to remain single. With an emphasis on self-fulfilment means that people will become less focused on commitment to anything outside of themselves, from party politics to relationships, this has also made marriage rates suffered. by putting priority on yourself means that if they aren’t fulfilled by their partner, whether this is their wife/husband or boyfriend/girlfriend. They can leave to find a new one. This would also explain the higher divorce rate. Beck has argued that we now live in a ‘risk society’ where tradition has less influence and people have more choice. He says that as a result of this we make choices by calculating the risk and reward factors involved. He also says how it contrasts from earlier years where both partners had fixed roles and had less choice for example, people were expected to marry. Once married men were expected to be the breadwinner and disciplinarian and make the important financial decisions, whilst women took care of children and the house. British society’s understanding of the form and function of a family has been changing over the last 30 years, and this has been shown in the rates of marriage falling, divorce and remarriage increasing, and cohabitation becoming a more popular lifestyle choice. Society’s values  have been affected by a greater emphasis on individualism and personal fulfilment, as opposed to the traditional values of the Church, which have had more of a role in defining the family in the past. There has been an increase in awareness of equality issues too, particularly with the rise of feminism and gay rights, which have lead to changes in the law such as the Civil Partnerships Act, and legislation to increase ease of divorce. Various sociological theories have attempted to explain these changes, particularly postmodernism, but the fact that 95.1% of British women still choose to marry before the age of 49 shows that while our views on marriage and family life becoming more flexible, they still remain an important part of our society. In my opinion the reason for the increase in marriage is because Britain has become a throwaway society, we can dispose of anything we choose including marriage, a marriage can end up in divorce after six weeks.

Engineering Economic free essay sample

The final section expands on the principles of benefit-cost analysis. An in-depth treatment of the practices and techniques covered in this compilation is available in the ASTM compilation of standards on building economics. 2 The ASTM compilation also includes case illustrations showing how to apply the practices and techniques to investment decisions. A broader perspective on the application of engineering economics to fire protection engineering can be found in The Economics of Fire Protection by Ramachandran. This work is intended as a textbook for fire protection engineers and includes material and references that expand on several other chapters of this section of the SFPE handbook. Time Value of Money The following are reasons why $1000 today is â€Å"worth† more than $1000 one year from today: 1. Inflation 2. Risk 3. Cost of money Of these, the cost of money is the most predictable, and, hence, it is the essential component of economic analysis. Cost of money is repres ented by (1) money paid for the use of borrowed money, or (2) return on investment. Cost of money is determined by an interest rate. Time value of money is defined as the time-dependent value of money stemming both from changes in the purchasing power of money (inflation or deflation) and from the real earning potential of alternative investments over time. Cash-Flow Diagrams It is difficult to solve a problem if you cannot see it. The easiest way to approach problems in economic analysis is to draw a picture. The picture should show three things: 1. A time interval divided into an appropriate number of equal periods 2. All cash outflows (deposits, expenditures, etc. ) in each period 3. All cash inflows (withdrawals, income, etc. ) for each period Unless otherwise indicated, all such cash flows are considered to occur at the end of their respective periods. Figure 5-7. 1 is a cash-flow diagram showing an outflow or disbursement of $1000 at the beginning of year 1 and an inflow or return of $2000 at the end of year 5. Cash-Flow Concepts Cash flow is the stream of monetary (dollar) values— costs (inputs) and benefits (outputs)—resulting from a project investment. Dr. John M. Watts, Jr. , holds degrees in fire protection engineering, industrial engineering, and operations research. He is director of the Fire Safety Institute, a not-for-profit information, research, and educational corporation located in Middlebury, Vermont. Dr. Watts also serves as editor of NFPA’s Fire Technology. Dr. Robert E. Chapman is an economist in the Office of Applied Economics, Building and Fire Research Laboratory, National Institute of Standards and Technology. Notation To simplify the subject of economic analysis, symbols are introduced to represent types of cash flows and 5–93 5–94 Fire Risk Analysis $2000 F(2) C F(1) = F(1)(i) Interest is applied to the new sum: 0 1 2 3 4 5 C (F)(1)(1 = i) C P(1 = i)2 F (3) C F (2)(1 = i) C P(1 = i)3 and by mathematical induction, F(N) C P(1 = i)N Figure 5-7. 1. $1000 Cash-flow diagram. EXAMPLE: $100 at 10 percent per year for 5 yr yields F(5) C 100(1 = 0. 1)5 C 100(1. 1)5 C 100(1. 61051) C $161. 05 which is over 7 percent greater than with simple interest. EXAMPLE: In 1626 Willem Verhulst bought Manhattan Island from the Canarsie Indians for 60 florins ($24) worth of merchandise (a price of about 0. 5 cents per hectare [0. 2 cents per acre]). At an average interest rate of 6 percent, what is the present value (2001) of the Canarsies’ $24? F C P(1 = i)N C $24(1 = 0. 06)375 C $7. 4 ? 1010 Seventy-four billion dollars is a reasonable approximation of the present land value of the island of Manhattan. interest factors. The symbols used in this chapter conform to ANSI Z94;4 however, not all practitioners follow this standard convention, and care must be taken to avoid confusion when reading the literature. The following symbols will be used here: PC FC NC iC Present sum of money ($) Future sum of money ($) Number of interest periods Interest rate per period (%) A complete list of the ANSI Z94 symbols is given in Appendix A to this chapter. Interest Calculations Interest is the money paid for the use of borrowed money or the return on invested capital. The economic cost of construction, installation, ownership, or operation can be estimated correctly only by including a factor for the economic cost of money. Simple interest: To illustrate the basic concepts of interest, an additional notation will be used: F(N) C Future sum of money after N periods Then, for simple interest, F(1) C P = (P)(i) C P(1 = i) and F(N) C P = (N)(P)(i) C P(1 = Ni) For example: $100 at 10 percent per year for 5 yr yields F(5) C 100[1 = (5)(0. )] C 100(1. 5) C $150 However, interest is almost universally compounded to include interest on the interest. Compound interest F(1) C P = (P)(i) C P(1 = i) is the same as simple interest, Interest Factors Interest factors are multiplicative numbers calculated from interest formulas for given interest rates and periods. They are used to convert cash flows occurring at different times to a common time. The f unctional formats used to represent these factors are taken from ANSI Z94, and they are summarized in Appendix B to this chapter. Compound Amount Factor In the formula for finding the future value of a sum of money with compound interest, the mathematical expression (1 = i)N is referred to as the compound amount factor, represented by the functional format (F/P, i, N). Thus, F C P(F/P, i, N) Interest tables: Values of the compound amount, present worth, and other factors that will be discussed shortly, are tabulated for a variety of interest rates and number of periods in most texts on engineering economy. Example tables are presented in Appendix C to this chapter. Although calculators and computers have greatly reduced the need for such tables, they are often still useful for interpolations. Engineering Economics 5–95 Present Worth Present worth is the value found by discounting future cash flows to the present or base time. Discounting: The inverse of compounding is determining a present amount which will yield a specified future sum. This process is referred to as discounting. The equation for discounting is found readily by using the compounding equation to solve for P in terms of F: P C F(1 = i)gt;N EXAMPLE: What present sum will yield $1000 in 5 yr at 10 percent? P C 1000(1. 1)gt;5 C 1000(0. 62092) C $620. 92 This result means that $620. 92 â€Å"deposited† today at 10 percent compounded annually will yield $1000 in 5 yr. Present worth factor: In the discounting equation, the expression (1 = i)gt;N is called the present worth factor and is represented by the symbol (P/F, i, N). Thus, for the present worth of a future sum at i percent interest for N periods, P C F(P/F, i, N) Note that the present worth factor is the reciprocal of the compound amount factor. Also note that (P/F, i, N) C 1 (F/P, i, N) Nominal versus effective interest: It is generally assumed that interest is compounded annually. However, interest may be compounded more frequently. When this occurs, there is a nominal interest or annual percentage rate and an effective interest, which is the figure used in calculations. For example, a savings bank may offer 5 percent interest compounded quarterly, which is not the same as 5 percent per year. A nominal rate of 5 percent compounded quarterly is the same as 1. 25 percent every three months or an effective rate of 5. 1 percent per year. If r C Nominal interest rate, and M C Number of subperiods per year then the effective interest rate is †¹ ? M r gt;1 iC 1= M EXAMPLE: Credit cards usually charge interest at a rate of 1. 5 percent per month. This amount is a nominal rate of 18 percent. What is the effective rate? i C (1 = 0. 015)12 gt; 1 C 1. 1956 gt; 1 C 19. 56% Continuous interest: A special case of effective interest occurs when the number of periods per year is infinite. This represents a situation of continuous interest, also referred to as continuous compounding. Formulas for continuous interest can be derived by examining limits as M approaches infinity. Formulas for interest factors using continuous compounding are included in Appendix B. Continuous interest is compared to monthly interest in Table 5-7. 1. EXAMPLE: Compare the future amounts obtained under various compounding periods at a nominal interest rate of 12 percent for 5 yr, if P C $10,000. (See Table 5-7. 2. ) EXAMPLE: What interest rate is required to triple $1000 in 10 years? PC therefore, (P/F, i, 10) C From Appendix C, (P/F, 10%, 10) C 0. 3855 and (P/F, 12%, 10) C 0. 220 By linear interpolation, i C 11. 6% 1 3 F C (P/F, i, 10) 3 Series Payments Life would be simpler if all financial transactions were in single lump-sum payments, now or at some time in the Table 5-7. 1 Continuous Interest (%) Effective Nominal % 5 10 15 20 Monthly 5. 1 10. 5 16. 1 21. 9 Continuous 5. 1 10. 5 16. 2 22. 1 Interest Periods Normally, but not always, the interest period is taken as 1 yr. There may b e subperiods of quarters, months, weeks, and so forth. 5–96 Table 5-7. 2 Compounding Annual Semi-annual Quarterly Monthly Weekly Daily Hourly Instantaneously aF/P Fire Risk Analysis Example of Continuous Interest N C 5 yr, r C 12% M 1 2 4 12 52 365 8760 a i 12. 000 12. 360 12. 551 12. 683 12. 734 12. 747 12. 749 12. 750 NM 5 10 20 60 260 1825 43,800 a F/P 1. 76234 1. 79085 1. 80611 1. 81670 1. 820860 1. 821938 1. 822061 1. 822119a F 17,623. 40 17,908. 50 18,061. 10 18,167. 00 18,208. 60 18,219. 38 18,220. 61 18,221. 19 (instantaneous) C e Ni C e 5(0. 12) C e 0. 6. future. However, most situations involve a series of regular payments, for example, car loans and mortgages. Series compound amount factor: Given a series of regular payments, what will they be worth at some future time? Let A C the amount of a regular end-of-period payment Then, note that each payment, A, is compounded for a different period of time. The first payment will be compounded for N gt; 1 periods (yr): F C A(1 = i)Ngt;1 and the second payment for N gt; 2 periods: F C A(1 = i)Ngt;2 and so forth. Thus, the total future value is F C A(1 = i)Ngt;1 = A(1 = i)Ngt;2 = ? = A(1 = i) = A or FC A[(1 = i)N gt; 1] i Capital recovery factor: It is also important to be able to relate regular periodic payments to their present worth; for example, what monthly installments will pay for a $10,000 car in 3 yr at 15 percent? Substituting the compounding equation F C P(F/P, i, N) in the sinking fund equation, A C F(A/F, i, N), yields A C P(F/P, i, N)(A/F, i, N) And, substituting the corresponding interest factors gives AC P [i(1 = i)N ] [(1 = i)N gt; 1] In this equation, the interest expression is known as the capital recovery factor, since the equation defines a regular income necessary to recover a capital investment. The symbolic equation is A C P(A/P, i, N) Series present worth factor: As with the other factors, there is a corresponding inverse to the capital recovery factor. The series present worth factor is found by solving the capital recovery equation for P. PCA or, symbolically P C A(P/A, i, N) [(1 = i)N gt; 1] [i(1 = i)N ] The interest expression in this equation is known as the series compound amount factor, (F/A, i, N), thus F C A(F/A, i, N) Sinking fund factor: The process corresponding to the inverse of series compounding is referred to as a sinking fund; that is, what size regular series payments are necessary to acquire a given future amount? Solving the series compound amount equation for A, 8 4 i AC F [(1 = i)N gt; 1] Or, using the symbol (A/F, i, N) for the sinking fund factor A C F(A/F, i, N) Here, note that the sinking fund factor is the reciprocal of the series compound amount factor, that is, (A/F, i, N) C 1/(F/A, i, N). Other Interest Calculation Concepts Additional concepts involved in interest calculations include continuous cash flow, capitalized costs, beginning of period payments, and gradients. Continuous cash flow: Perhaps the most useful function of continuous interest is its application to situations where the flow of money is of a continuous nature. Continuous cash flow is representative for 1. A series of regular payments for which the interval between payments is very short 2. A disbursement at some unknown time (which is then considered to be spread out over the economic period) Engineering Economics 5–97 Factors for calculating present or future worth of a series of annual amounts, representing the total of a continuous cash flow throughout the year, may be derived by integrating corresponding continuous interest factors over the number of years the flow is maintained. Continuous cash flow is an appropriate way to handle economic evaluations of risk, for example, the present value of an annual expected loss. Formulas for interest factors representing continuous, uniform cash flows are included in Appendix B. Capitalized costs: Sometimes there are considerations, such as some public works projects, which are considered to last indefinitely and thereby provide perpetual service. For example, how much should a community be willing to invest in a reservoir which will reduce fire insurance costs by some annual amount, A? Taking the limit of the series present worth factor as the number of periods goes to infinity gives the reciprocal of the interest rate. Thus, capitalized costs are just the annual amount divided by the interest rate. When expressed as an amount required to produce a fixed yield in perpetuity, it is sometimes referred to as an annuity. Beginning-of-period payments: Most returns on investment (cash inflows) occur at the end of the period during which they accrued. For example, a bank computes and pays interest at the end of the interest period. Accordingly, interest tables, such as those in Appendix C, are computed for end-of-year payments. For example, the values of the capital recovery factor (A/P, i, N) assume that the regular payments, A, occur at the end of each period. On the other hand, most disbursements (cash outflows) occur at the beginning of the period (e. g. , insurance premiums). When dealing with beginning-of-period payments, it is necessary to make adjustments. One method of adjustment for beginning-of-period payments is to calculate a separate set of factors. Another way is to logically interpret the effect of beginning-of-period payments for a particular problem, for example, treating the first payment as a present value. The important thing is to recognize that such variations can affect economic analysis. Gradients: It occasionally becomes necessary to treat the case of a cash flow which regularly increases or decreases at each period. Such patterned changes in cash flow are called gradients. They may be a constant amount (linear or arithmetic progression), or they may be a constant percentage (exponential or geometric progression). Various equations for dealing with gradient series may be found in Appendix B. Fire protection engineering economic analysis is primarily concerned with cost-reduction decisions, finding the least expensive way to fulfill certain requirements, or minimizing the sum of expected fire losses plus investment in fire protection. There are four common methods of comparing alternative investments: (1) present worth, (2) annual cost, (3) rate of return, and (4) benefit-cost analysis. Each of these is dependent on a selected interest rate or discount rate to adjust cash flows at different points in time. Discount Rate The term discount rate is often used for the interest rate when comparing alternative projects or strategies. Selection of discount rate: If costs and benefits accrue equally over the life of a project or strategy, the selection of discount rate will have little impact on the estimated benefit-cost ratios. However, most benefits and costs occur at different times over the project life cycle. Thus, costs of constructing a fire-resistive building will be incurred early in contrast to benefits, which will accrue over the life of the building. The discount rate then has a significant impact on measures such as benefit-cost ratios, since the higher the discount rate, the lower the present value of future benefits. In view of the uncertainty concerning appropriate discount rate, analysts frequently use a range of discount rates. This procedure indicates the sensitivity of the analysis to variations in the discount rate. In some instances, project rankings based on present values may be affected by the discount rate as shown in Figure 5-7. 2. Project A is preferred to project B for discount rates below 15 percent, while the converse is true for discount rates greater than 15 percent. In this instance, the decision to adopt project A in preference to project B will reflect the belief that the appropriate discount rate is less than or equal to 15 percent. A Net present value 0 B Comparison of Alternatives Most decisions are based on economic criteria. Investments are unattractive, unless it seems likely they will be recovered with interest. Economic decisions can be divided into two classes: 1. Income-expansion—that is, the objective of capitalism 2. Cost-reduction—the basis of profitability 5 10 15 20 Discount rate (%) Figure 5-7. 2. Impact of discount rate on project selection. 5–98 Fire Risk Analysis A comparison of benefits and costs may also be used to determine the payback period for a particular project or strategy. However, it is important to discount future costs or benefits in such analyses. For example, an analysis of the Beverly Hills Supper Club fire compared annual savings from a reduction in insurance premiums to the costs of sprinkler installation. Annual savings were estimated at $11,000, while costs of sprinkler installation ranged from $42,000 to $68,000. It was concluded that the installation would have been paid back in four to seven years (depending on the cost of the sprinklers). However, this analysis did not discount future benefits, so that $11,000 received at the end of four years was deemed equivalent to $11,000 received in the first year. Once future benefits are discounted, the payback period ranges from five to eleven years with a discount rate of 10 percent. Inflation and the discount rate: Provision for inflation may be made in two ways: (1) estimate all future costs and benefits in constant prices, and use a discount rate which represents the opportunity cost of capital in the absence of inflation; or (2) estimate all future benefits and costs in current or inflated prices, and use a discount rate which includes an allowance for inflation. The discount rate in the first instance may be considered the real discount rate, while the discount rate in the second instance is the nominal discount rate. The use of current or inflated prices with the real discount rate, or constant prices with the nominal discount rate, will result in serious distortions in economic analysis. Present worth (Plan A) C P = A(P/A, 12%, 40) C $1,000,000 = $1000(8. 24378) C $1,008,244 Present worth (Plan B) C P = A(P/A, 12%, 40) = F(P/F, 12%, 20) C $200,000 = $50,000(8. 24378) = $75,000(0. 0367) C $619,964 Thus, plan B is the least-cost alternative. A significant limitation of present worth analysis is that it cannot be used to compare alternatives with unequal economic lives. That is, a ten-year plan and a twenty-year plan should not be compared by discounting their costs to a present worth. A better method of comparison is annual cost. Annual Cost To compare alternatives by annual cost, all cash flows are changed to a series of uniform payments. C urrent expenditures, future costs or receipts, and gradients must be converted to annual costs. If a lump-sum cash flow occurs at some time other than the beginning or end of the economic life, it must be converted in a two-step process: first moving it to the present and then spreading it uniformly over the life of the project. Alternatives with unequal economic lives may be compared by assuming replacement in kind at the end of the shorter life, thus maintaining the same level of uniform payment. System Cost Partial system Full system $ 8000 $15,000 Insurance Premium $1000 $250 Life 15 yr 20 yr Present Worth In a present worth comparison of alternatives, the costs associated with each alternative investment are all converted to a present sum of money, and the least of these values represents the best alternative. Annual costs, future payments, and gradients must be brought to the present. Converting all cash flows to present worth is often referred to as discounting. EXAMPLE: Two alternate plans are available for increasing the capacity of existing water transmission lines between an unlimited source and a reservoir. The unlimited source is at a higher elevation than the reservoir. Plan A calls for the construction of a parallel pipeline and for flow by gravity. Plan B specifies construction of a booster pumping station. Estimated cost data for the two plans are as follows: Plan A Pipeline Construction cost Life Cost of replacing equipment at the end of 20 yr Operating costs $1,000,000 40 years Plan B Pumping Station $200,000 40 years (structure) 20 years (equipment) EXAMPLE: Compare the value of a partial or full sprinkler system purchased at 10 percent interest. Annual cost (partial system) C A = P(A/P, 10%, 15) C $1000 = $8000(0. 3147) C $2051. 75 Annual cost (full system) C A = P(A/P, 10%, 20) C $250 = $15,000(0. 11746) C $2011. 90 The full system is slightly more economically desirable. When costs are this comparable, it is especially important to consider other relevant decision criteria, for example, uninsured losses. 0 $1000/yr $75,000 $50,000/yr Rate of Return Rate of return is, by definition, the interest rate at which the present worth of the net cas h flow is zero. Computationally, this method is the most complex method of comparison. If more than one interest factor is involved, If money is worth 12 percent, which plan is more economical? (Assume annual compounding, zero salvage value, and all other costs equal for both plans. ) Engineering Economics 5–99 the solution is by trial and error. Microcomputer programs are most useful with this method. The calculated interest rate may be compared to a discount rate identified as the â€Å"minimum attractive rate of return† or to the interest rate yielded by alternatives. Rate-of-return analysis is useful when the selection of a number of projects is to be undertaken within a fixed or limited capital budget. EXAMPLE: An industrial fire fighting truck costs $100,000. Savings in insurance premiums and uninsured losses from the acquisition and operation of this equipment is estimated at $60,000/yr. Salvage value of the apparatus after 5 yr is expected to be $20,000. A full-time driver during operating hours will accrue an added cost of $10,000/yr. What would the rate of return be on this investment? @ 40% present worth C P = F(P/F , 40%, 5) = A(P/A, 40%, 5) C gt;$100,000 = $20,000(0. 18593) = ($60,000 gt; 10,000)(2. 352) C $5,478. 60 @ 50% present worth C P = F(P/F, 50%, 5) = A(P/A, 50%, 5) C gt;$100,000 = $20,000(0. 13169) = ($60,000 gt; $10,000)(1. 7366) C gt;$10,536. 40 By linear interpolation, the rate of return is 43 percent. costs of operating fire departments. Indirect costs are more difficult to measure. They include items such as the constraints on choice due to fire protection requirements by state and local agencies. A major factor in the identification of relevant benefits and c osts pertains to the decision unit involved. Thus, if the decision maker is a property owner, the relevant benefits from fire protection are likely to be the reduction in fire insurance premiums and fire damage or business interruption losses not covered by insurance. In the case of a municipality, relevant benefits are the protection of members of the community, avoidance of tax and payroll losses, and costs associated with assisting fire victims. Potential benefits, in these instances, are considerably greater than those faced by a property owner. However, the community may ignore some external effects of fire incidents. For example, the 1954 automobile transmission plant fire in Livonia, Michigan, affected the automobile industry in Detroit and various automobile dealers throughout the United States. However, there was little incentive for the community to consider such potential losses in their evaluation of fire strategies, since they would pertain to persons outside the community. It might be concluded, therefore, that the more comprehensive the decision unit, the more likely the inclusion of all relevant costs and benefits, in particular, social costs and benefits. Measurement of Benefits and Costs Direct losses are measured or estimated statistically or by a priori judgment. Actuarial fire-loss data collected nationally or for a particular industry may be used, providing it is adequately specific and the collection mechanism is reliable. More often, an experienced judgment of potential losses is made, sometimes referred to as the maximum probable loss (MPL). Indirect losses, if considered, are much more difficult to appraise. A percentage or multiple of direct losses is sometimes used. However, when indirect loss is an important decision parameter, a great deal of research into monetary evaluation may be necessary. Procedures for valuing a human life and other indirect losses are discussed in Ramachandran. 3 In the measurement of benefits, it is appropriate to adjust for utility or disutility which may be associated with a fire loss. Costs may be divided into two major categories: (1) costs of private fire protection services, and (2) costs of public fire protection services. In either case, cost estimates will reflect the opportunity cost of providing the service. For example, the cost of building a fire-resistive structure is the production foregone due to the diversion of labor and resources to make such a structure. Similarly, the cost of a fire department is the loss of other community services which might have been provided with the resources allocated to the fire department. Benefit-Cost Analysis Benefit-cost analysis, also referred to as cost-benefit analysis, is a method of comparison in which the consequences of an investment are evaluated in monetary terms and divided into the separate categories of benefits and costs. The amounts are then converted to annual equivalents or present worths for comparison. The important steps of a benefit-cost analysis are 1. 2. 3. 4. Identification of relevant benefits and costs Measurement of these benefits and costs Selection of best alternative Treatment of uncertainty Identification of Relevant Benefits and Costs The identification of benefits and costs depends on the particular project under consideration. Thus, in the case of fire prevention or control activities, the benefits are based on fire losses prior to such activities. Fire losses may be classified as direct or indirect. Direct economic losses are property and contents losses. Indirect losses include such things as the costs of injuries and deaths, costs incurred by business or industry due to business interruption, losses to the community from interruption of services, loss of payroll or taxes, loss of market share, and loss of reputation. The direct costs of fire protection activities include the costs of constructing fire-resistive buildings, installation costs of fire protection systems, and the Selection of Best Alternative There are two considerations in determining benefitcost criteria. The first pertains to project acceptability, while the second pertains to project selection. Project acceptability may be based on benefit-cost difference or benefit-cost ratio. Benefit-cost ratio is a measure 5–100 Fire Risk Analysis of project worth in which the monetary equivalent benefits are divided by the monetary equivalent costs. The first criterion requires that the value of benefits less costs be greater than zero, while the second criterion requires that the benefit-cost ratio be greater than one. The issue is more complicated in the case of project selection, since several alternatives are involved. It is no longer a question of determining the acceptability of a single project, but rather selecting from among alternative projects. Consideration should be given to changes in costs and benefits as various strategies are considered. Project selection decisions are illustrated in Figure 5-7. 3. The degree of fire protection is given on the horizontal axis, while the marginal costs and benefits associated with various levels of fire safety are given on the vertical axis. As the diagram indicates, marginal costs are low initially and then increase. Less information is available concerning the marginal benefit curve, and it may, in fact, be horizontal. The economically optimum level of fire protection is given by the intersection of the marginal cost and marginal benefit curves. Beyond this point, benefits from increasing fire protection are exceeded by the costs of providing the additional safety. A numerical example is given in Table 5-7. 3. There are five possible strategies or programs possible. The first strategy, A, represents the initial situation, while the remaining four strategies represent various fire loss reduction activities, each with various costs. Strategies are arranged in ascending order of costs. Fire losses under each of the five strategies are given in the second row, while the sum of fire losses and fire reduction costs for each strategy is given in the third row. The sum of fire losses and fire reduction costs of each strategy is equivalent to the life-cycle cost of that strategy. Life-cycle cost analysis is an alternative to benefit-cost analysis when the outcomes of the investment decision are cost savings rather than benefits per se. Additional information on life-cycle cost analysis is found in Fuller and Petersen. 5 Table 5-7. 3 Use of Benefit-Cost Analyses in Strategy Selection Strategy Category Fire reduction costs Fire losses Sum of fire reduction costs and fire losses Marginal benefits Marginal costs Marginal benefits minus marginal costs Marginal benefit-cost ratio A 0 100 100 0 0 0 — B 10 70 80 30 10 20 3. 0 C 25 50 75 20 15 5 1. 33 D 45 40 85 10 20 –10 0. 5 E 70 35 105 5 25 –20 0. 2 Marginal costs Data in the first two rows may then be used to determine the marginal costs or marginal benefits from the replacement of one strategy by another. Thus, strategy B has a fire loss of $70 compared to $100 for strategy A, so the marginal benefit is $30. Similarly, the marginal benefit from strategy C is the reduction in fire losses from B to C or $20. The associated marginal cost of strategy C is $15. Declining marginal benefits and rising marginal costs result in the selection of strategy C as the optimum strategy. At this point, the difference between marginal benefits and marginal costs is still positive. Marginal benefit-cost ratios are given in the last row. It is worth noting that, while the highest marginal benefitcost ratio is reached at activity level B (as is the highest marginal benefit-cost difference), project C is still optimum, since it yields an additional net benefit of $5. This finding is reinforced by examining changes in the sum of fire losses and fire reduction costs (i. e. , life-cycle costs). Total cost plus loss first declines, reaching a minimum at point C, and then increases. This pattern is not surprising, since as long as marginal benefits exceed marginal costs, total losses should decrease. Thus, the two criteria— equating marginal costs and benefits, and minimizing the sum of fire losses and fire reduction costs—yield identical outcomes. Treatment of Uncertainty $ Marginal benefits A final issue concerns the treatment of uncertainty. One method for explicitly introducing risk considerations is to treat benefits and costs as random variables which may be described by probability distributions. For example, an estimate of fire losses might consider the following events: no fire, minor fire, intermediate fire, and major fire. Each event has a probability of occurrence and an associated damage loss. The total expected loss (EL) is given by EL C 3 } iC0 piDi 0 Degree of fire safety 100% Figure 5-7. 3. Project selection. where p0 C probability of no fire p1 C probability of a minor fire Engineering Economics 5–101 2 C probability of an intermediate fire p3 C probability of a major fire Dn C associated damage loss, n C 0,1,2,3 Expected losses may be computed for different fire protection strategies. Thus, a fire protection strategy that costs C3 and reduces damage losses of a major fire from D3 to D3 will result in an expected loss EL C p0D0 = p1D1 = p2D2 = p3D3 = C3 Similarly, a fire control strategy that costs C2 and reduces the probability of an intermediate fire from p2 to p2 has an expected loss EL C p0D0 = p1D1 = p2D2 = p3D3 = C2 A comparison of expected losses from alternative strategies may then be used to determine the optimal strategy. Use of expected value has a limitation in that only the average value of the probability distribution is considered. Discussion of other procedures for evaluating uncertain outcomes is given by Anderson and Settle. 6 5. S. K. Fuller and S. R. Petersen, â€Å"Life-Cycle Costing Manual for the Federal Energy Management Program,† NIST Handbook 135, National Institute of Standards and Technology, Gaithersburg, MD (1996). 6. L. G. Anderson and R. E. Settle, Benefit-Cost Analysis: A Practical Guide, Lexington Books, Lexington, MA (1977). Additional Readings R. E. Chapman, â€Å"A Cost-Conscious Guide to Fire Safety in Health Care Facilities,† NBSIR 82-2600, National Bureau of Standards, Washington, DC (1982). R. E. Chapman and W. G. Hall, â€Å"Code Compliance at Lower Costs: A Mathematical Programming Approach,† Fire Technology, 18, 1, pp. 77–89 (1982). L. P. Clark, â€Å"A Life-Cycle Cost Analysis Methodology for Fire Protection Systems in New Health Care Facilities,† NBSIR 822558, National Bureau of Standards, Washington, DC (1982). W. J. Fabrycky, G. J. Thuesen, and D. Verma, Economic Decision Analysis, 3rd ed. Prentice Hall International, London (1998). E. L. Grant, W. G. Ireson, and R. S. Leavenworth, Principles of Engineering Economy, 8th ed. , John Wiley and Sons, New York (1990). J. S. McConnaughey, â€Å"An Economic Analysis of Building Code Impacts: A Suggested Approach,† NBSIR 78-1528, National Bureau of Standards, Washington, DC (1978). D. G. Newnan and J. P. Lavelle, Engineering Economic Analysis, 7th ed. , Engineering Press, Austin, TX (1998). C. S. Park, Contemporary Engineering Economics, 2nd ed. , AddisonWesley, Menlo Park, CA (1997). J. L. Riggs, D. D. Bedworth, and S. U. Randhawa, Engineering Economics, 4th ed. , McGraw-Hill, New York (1996). R. T. Ruegg and H. E. Marshall, Building Economics: Theory and Practice, Van Nostrand Reinhold, New York (1990). R. T. Ruegg and S. K. Fuller, â€Å"A Benefit-Cost Model of Residential Fire Sprinkler Systems,† NBS Technical Note 1203, National Bureau of Standards, Washington, DC (1984). W. G. Sullivan, J. A. Bontadelli, and E. M. Wicks, Engineering Economy, 11th ed. , Prentice Hall, Upper Saddle River, NJ (2000). References Cited 1. ASTM E833, Definitions of Terms Relating to Building Economics, American Society for Testing and Materials, West Conshohocken, PA (1999). 2. ASTM Standards on Building Economics, 4th ed. , American Society for Testing and Materials, West Conshohocken, PA (1999). 3. G. Ramachandran, The Economics of Fire Protection, E FN Spon, London (1998). 4. American National Standards Institute Standard Z94. 0-1982, â€Å"Industrial Engineering Terminology,† Chapter 5, Engineering Economy, Industrial Engineering and Management Press, Atlanta, GA (1983). Appendix A: Symbols and Definitions of Economic Parameters Symbol Definition of Parameter Cash flow at end of period j End-of-period cash flows (or equivalent end-of-period values) in a uniform series continuing for a specified number of periods Amount of money (or equivalent value) flowing continuously and uniformly during each period, continuing for a specified number of periods Future sum of money—the letter F implies future (or equivalent future value) Uniform period-by-period increase or decrease in cash flows (or equivalent values); the arithmetic gradient Number of compounding periods per interest perioda Number of compounding eriods Present sum of money—the letter â€Å"P† implies present (or equivalent present value). Sometimes used to indicate initial capital investment. Salvage (residual) value of capital investment Rate of price level increase or decrease per period; an â€Å"inflation† of â€Å"escalation† rate Uniform rate of cash flow increase or decrease from period to period; the geometric gradient Effective interest rate per interest perioda (discount rate), expressed as a percent or decimal fraction Nominal interest rate per interest period,a expressed as a percent or decimal fraction Aj A – A F G M N P S f g i r Normally, but not always, the interest period is taken as 1 yr. Subperiods, then, would be quarters, months, weeks, and so forth. 5–102 Fire Risk Analysis Appendix B: Functional Forms of Compound Interest Factorsa Name of Factor Algebraic Formulation Functional Format Group A. All cash flows discrete: end-of-period compounding Compound amount (single payment) Present worth (single payment) Sinking fund Capital recovery (1 = i)N (1 = (F/P, i, N) (P/F, i, N) (A/F, i, N) (A/P, i, N) (F/A, i, N) (P/A, i, N) (A/G, i, N) (P/G, i, N) i)–N i (1 = i )N – 1 i(1 = i)N (1 = i )N – 1 1 = i )N – 1 i (1 = i )N – 1 i(1 = i )N (1 = i )N – iN – 1 i (1 = i )N – i (1 = i )N – iN – 1 i 2(1 = i ) N Compound amount (uniform series) Present worth (uniform series) Arithmetic gradient to uniform series Arithmetic gradient to present worth Group B. All cash flows discrete: continuous compounding at nominal rate r per period Continuous compounding compound amount (single payment) Continuous compounding present worth (single payment) Continuous compounding present worth (single payment) Continuous compounding sinking fund Continuous compounding capital recovery Continuous compounding compound amount (uniform series) rN e–rN erN – 1 erN(er – 1) er – 1 erN – 1 erN(er – 1) erN – 1 erN – 1 er – 1 (F/P, r, N) (P/F, r, N) (P/A, r, N) (A/F, r, N) (A/P, r, N) (F/A, r, N) Group C. Continuous, uniform cash flows: continuous compounding Continuous compounding sinking fund (continuous, uniform payments) Continuous compounding capital recovery (continuous, uniform payments) Continuous compounding compound amount (continuous, uniform payments) Continuous compounding present worth (continuous, uniform payments) aSee r erN – 1 rerN erN – 1 erN – 1 r erN – 1 rerN – A /F, r, N – A /P, r,N – F/A , r, N) – P/A , r, N)