Public Policy on Business Competition Essay

Synopsis American organizations have been off guard from their remote rivals because of the imperfect financial framework and the entrepreneur economy of the nation. The outside organizations have been persistently improving their proficiency and viability corresponding to their American partners which implies that they have now gotten increasingly serious and can even outperform that of the American items. The severe government guidelines and taxes intended to ensure the American economy is presently the reason for the lesser occupations accessible for American laborers. Re-appropriating had certainly diminished the quantity of employments and some way or another the industrialist society that America has depended on re-appropriating as a method of reducing expenses. Free enterprise has its own wrongs when contrasted with communism. Communism is something contrary to private enterprise, in communism the legislature needs to make sure that riches is dispensed to all citizenry. Despite the fact that, communism has given to the entirety of its individuals it additionally carried the economy of the nation to its ruin. The guideline of similar favorable position is the way to guaranteeing that countries exist together and get related on each other. Near favorable position implies that every nation delivers a specific item which is turns into the financial quality of the nation. It might have it’s own inconveniences however every nation will have their own near bit of leeway and disservice.  Public Policy on Business Competition  â â â â â â â â â â For over four decades now, American organizations have been losing ground to remote contenders. While 24.8 percent of all vehicles sold everywhere throughout the world were made in the United States in 1986, by 1992 the U.S. share had declined to 20.7 percent. Presently, this number goes further down to a little more than 16 percent (OICA). Various elements have added to the loss of the United States’ producing intensity. To start with, outside contenders have put resources into progressively proficient hardware and forms and have established different projects that have raised laborer efficiency comparative with the United States. Second, legislatures of some outside assembling businesses have given arranging, budgetary sponsorships, positive assessment rates, and other mechanical strategies intended to sustain and bolster their modern base. In any case, maybe the best motivation behind why the United States is slipping as far as worldwide intensity is a result of open strategies dependent on indulging.  â â â â â â â â â â Arbitrary exchange boundaries, unreasonable shares, and excessively prohibitive levies are the standard with regards to the government’s current remain on business rivalry. American specialists and organizations are in a consistent condition of cognizance wherein a feeling of privilege plagues. They continually campaign since they feel that the legislature should shield them from the downpour of rivalry from abroad. The thing is, Americans will keep on losing their business to the Indians and the Chinese. Organizations intend to reduce expenses any place and at whatever point they can. Given a decision, they will redistribute to whomever can give them the best worth. Rather than crying and campaigning, Americans should search for approaches to change. They ought to get rid of needing to do humble assignments and begin looking towards employments that require more aptitude and mental sharpness. Not having any desire to improve and rather requesting insurance from the tides of progress won't advance society at all and rather debases it. Actually, it is the premise of an idea that was demonstrated inadequate and impracticable.  â â â â â â â â â â Socialism depends on the imperfect thought that citizenry ought to be rises to and the legislature must make sure that everybody is being thought about. One of the significant objections imposed by communists has been that private enterprise licenses surplus incentive to stream to industrialists, making free enterprise an exceptionally inconsistent, class-ridden society. On the other hand, a communist society would share the arrival to capital among the laborers, in this manner advancing a lot more prominent fairness than a market economy. This â€Å"strength† as communists put it, end up being socialism’s ruin.  â â â â â â â â â â Indeed, the experience of communist nations represents how endeavors to level wages by seizing property from the rich can wind up harming everybody. By forbidding private responsibility for, communist governments reduced the disparities that emerged from huge property earnings. Be that as it may, the diminished motivations to work, gather capital, and improve †on the grounds that the legislature will accommodate each man †disabled this framework and ruined whole nations.  â â â â â â â â â â The guideline of similar preferred position holds that every nation will spend significant time in the creation and fare of those merchandise or administrations that it can deliver at moderately ease since it is more proficient in delivering them than different nations. On the other hand, every nation will import those merchandise which it produces at generally significant expense or those that it is unequipped for delivering by any means. This straightforward guideline gives the unflinching premise to worldwide exchange (Samuelson and Nordhaus 663). The most proficient and profitable example of specialization is that countries should focus on exercises in which they are moderately or nearly more productive than others. What's more, despite the fact that nations might be totally less or more proficient than every single other nation, every single nation will have an unmistakable near preferred position in certain territories while having a clear relative drawback in others. End The worldwide financial circle is mind boggling and it is essentially represented by the most impressive nation. The American economy had been one of the most grounded financial players in worldwide exchange. At the point when a nation turns out to be excessively reliant on different nations for their financial items and administrations, similar to the American culture, it tends to be accepted that they are putting their monetary government assistance because of different countries. This can tremendously affect American economy as the most essential administrations keep on being re-appropriated, money related quality is decreased. It is like a nursery worker who is watering the neighbor’s yard. The American culture is pouring their cash to outside economies without considering whether that remote nation will work with American organizations as end purchasers. So as to switch things around, the American government should seek after and receive the rule of similar bit of leeway, rather than depending on private enterprise or communism alone. With near preferred position every nation spends significant time in a couple of items and administrations, in this manner balancing force and impact in the universal economy. American businesses should investigate the perils of re-appropriating, the disservices of reducing expenses in the cost of joblessness and the evil impacts of over reliance on remote nations. Thusly, the administration ought to practically look at the current situation of the nation in universal exchange. Relative preferred position holds the key for financial security and progress.  Reference: Hitt, Michael An., Ireland, R. Duane and Hoskisson, Robert E. South-Western College Publishing, 1999. Association Internationale des Constructeurs d’Automobiles. Accessible: http://oica.net/wp-content/transfers/2007/06/worldprod_country-revised.pdf., January 19, 2008. Samuelsson, Paul A. furthermore, Nordhaus, William D.2.

Biography of the Wealthy Painter Peter Paul Rubens

Life story of the Wealthy Painter Peter Paul Rubens Dwindle Paul Rubens was a Flemish Baroque painter, most popular for his unrestrained European style of painting. He figured out how to integrate various variables, from the experts of the Renaissance and the early Baroque. He had an enchanted existence. He was alluring, knowledgeable, a conceived squire and, by dint of ability, had a virtual lock on the picture showcase in northern Europe. He was knighted, feted, became impressively well off from commissions and kicked the bucket before he outlasted his ability. Early Life Rubens was conceived on June 28, 1577, in Siegen, a German territory of Westphalia, where his Protestant-inclining legal advisor father had moved the family during the Counter-Reformation. Taking note of the young men vivacious knowledge, his dad actually observed that youthful Peter got an old style training. Rubens mother, who might not have shared a liking for the Reformation, moved her family back to Antwerp (where she possessed an unobtrusive property) in 1567 after her spouses troublesome passing. At 13 years old, when the familys remaining assets went to furnish his senior sister with a marriage share, Rubens was sent to be a page in the home of the Countess of Lalaing. The cleaned habits he got there served him well in the years ahead, however after a few (despondent) months he got his mom to student him to a painter. By 1598, he had joined the painters society. His Art From 1600 to 1608, Rubens lived in Italy, at the administration of the Duke of Mantua. During this time he deliberately considered crafted by the Renaissance experts. Upon his arrival to Antwerp, he turned into the court painter to the Spanish governors of Flanders and therefore to Charles I of England (who, actually, knighted Rubens for strategic work) and Marie de Medici, Queen of France. The more notable works he turned out during the following 30 years incorporated The Elevation of the Cross (1610), The Lion Hunt (1617-18), and Rape of the Daughters of Leucippus (1617). His court representations were in extraordinary interest, as he as often as possible set their subjects in juxtaposition with divine beings and goddesses of folklore to all the more likely recognize the elevated places of respectability and sovereignty. He painted strict and chasing subjects, just as scenes, yet is most popular for his oft-unclothed figures who appeared to twirl in development. He adored depicting young ladies with meat on their bones, and moderately aged ladies wherever express gratitude toward him right up 'til today. Rubens broadly said, My ability is to such an extent that no endeavor, anyway huge in size...has ever outperformed my boldness. Rubens, who had a greater number of solicitations for work than time, became well off, amassed an assortment of workmanship and claimed a house in Antwerp and a nation home. In 1630, he wedded his subsequent spouse (the first had passed on certain years prior to), a 16-year-old young lady. They spent a glad decade together before gout welcomed on cardiovascular breakdown and finished Rubens life on May 30, 1640, in the Spanish Netherlands (present day Belgium). The Flemish Baroque continued with his replacements, the vast majority of whom (especially Anthony van Dyke) he had prepared. Significant Works The Massacre of the Innocents, 1611The Hippopotamus Hunt, 1616The Rape of the Daughters of Leucippus, 1617Diana and Callisto, 1628The Judgment of Paris, 1639Self Portrait, 1639

Human sexuality Essay Example | Topics and Well Written Essays - 1250 words

Human sexuality - Essay Example The old Greeks are famous for their obsession with the male genitalia, making it the point of convergence of different kinds of craftsmanship and display (â€Å"History of Sex†, 2004). This has persuaded that they were basically a race of gay people, who possibly had sexual relations with their spouses when important with the end goal of multiplication. To a limited degree, particularly as it applies to the life of the spouse, this is very evident. At the point when the spouses are thought of by any stretch of the imagination, it’s normally with regards to, â€Å"gee, I wonder why those ladies set up with their men out celebrating with their person companions all the time?† Very little thought is ever given to the idea of a sexual coexistence for the ladies of old Greece. â€Å"The male thought of female sexuality was that Greek men accepted that ladies begrudged their penises† (â€Å"History of Sex†, 2004). In spite of this somewhat slanted perspec tive on female sexuality, there is a wide assemblage of data with respect to the fairly formalized perspectives this general public held seeing their ladies as they became sexual creatures. Fundamentally, these ladies were consigned to two extremely unmistakable general classifications †they were either spouses or they were whores (Thompson, 2005). It was in the job of a whore that a lady had the best cultural adaptability, however this didn't mean they had the option to live preferable lives over the spouses, who were basically overlooked other than to have youngsters (Thompson, 2005).

EU law Assignment Example | Topics and Well Written Essays - 2750 words

EU law - Assignment Example The scientist expresses that in European Union, the most significant authoritative instruments are guidelines and mandates. A guideline is a general principle that is committing upon part countries in entire and is straightforwardly appropriate to all part states. Committing in entire indicates that the part states has no inclination as to strategy and structure. Then again, mandates are general principle, however they are authoritative concerning their outcome. For every part state, it is normal, an order is committing regarding the result to be cultivated. With regards to the decision to strategy and structure, the establishments of the part states can practice their capacity. There is less lucidity about their immediate effect because of the more extensive arrangement opportunity given to part states in transposing EU mandates. In any case, one ought not underestimate the effect of orders, and the national guidelines will must be translated in such a style, that is most in agreeme nt with the mandate under reference. On account of its own breakdown to complete the responsibilities which the order requires, a Member Nation which has not embraced the sanctioning activities as requested by the mandate inside the specified time may not bank upon it as against such people. In line with a person who has followed with the specifications of a mandate, may demand a civil court not to direct to actualize a city rule which is in opposition to the order not executed into the local authority arrangement of a repudiating Member Nation. Further, it must support that request if the responsibility in issue is adequately exact and unconditional.2. S2 European Communities Act 1972 specifies that â€Å"all such benefits, specialists, obligations, responsibilities and restrictions ... emerging by or made under the Treaties ... as in concurrence with the Treaties are without further approval to be agreed authority sway or utilized in the UK, will be ... forced so ... â€Å" Furt her, any assigned Minister, Her Majesty may by Order in Council, or potentially division may by rules, make arrangement ... to execute any Community duty of the United Kingdom. Orders fall under auxiliary enactment of the wellspring of EU law. A mandate is a most huge authoritative instrument together with the EU guideline. Its principle point is to unite the double points of both guaranteeing the required consistency of Union law and respecting the assorted variety of national structures and customs. It is to be recollected that order primarily focuses on the harmonization and not for the unification of the law. The justification is to dispose of contentions and logical inconsistencies between national guidelines and laws or continuously to sob out inconsistencies, so that, a uniform specification exists in all the part countries. It is to be noticed that a mandate is compulsory on all the part countries concerning the objective to be cultivated, however it appoints it to the natio nal authorities to fix it on how the agreed network objective is to be actualized into their residential legitimate structures. Particularly, the part countries can take into the image of exceptional residential situations while actualizing the network rules. What is significant that an EU order doesn't outperform the laws of part countries however puts a dedication on the part countries to fine - tune their national law in congruity with Community guidelines? Thus, there will be two â€phases of law-production practice win in EU3. Source - eur-lex.europa.eu †º EUR-Lex Home †º Help In UK, the â€Å"General Product Safety Regulations 2005 â€Å"is in power and these guidelines are established in similarity with the â€Å"section 2(2) of the European Communities Act and transpose the Directive 2001/95/EC on general Product Safety† into UK law. The fundamental point of the General Product Safety Directive (GPSD) is to ensure that all merchandise focused on or plaus ible to be utilized by UK inhabitants under everything being equal and typical unsurprising specifications are protected. In the event of cell phones, the GPS Regulations will reach out to those-parts of wellbeing in UK. The GPSD is pertinent to

Fermina Daza A Strong Independent Woman - Literature Essay Samples

The idea of equality of the sexes in Latin America is a relatively new phenomena. Until the late nineteenth century and early twentieth century, the time period of Love in the Time of Cholera, women were predominantly treated as the inferior sex. Therefore, women were also often excluded from taking part in public life like their male counterparts in areas such as those pertaining to politics, economics, and education. Although women of the time period do not enjoy the same social freedom of their male counterparts, Gabriel Garcà ­a Mà ¡rquez in his novel Love in the Time of Cholera does not portray women as oppressed. Rather, Mà ¡rquez portrays several of his female characters as strong, resourceful, and independent individuals. This is particularly evident in how the novel presents Fermina Daza in her marriage to Dr. Juvenal Urbino as a strong, independent woman who is the intellectual equal of her husband. Despite not having received the same level of education as her husband, Fermina demonstrates that she is still the intellectual equal of her husband by outsmarting his rules. Unlike Fermina, who never finishes her studies nor receives her baccalaureate degree, Urbino had completed advanced studies in medicine and surgery to the point that none of his contemporaries seemed as rigorous and as learned as he in his science (Mà ¡rquez 105). Yet, Urbino comes to appreciate his wifes abundant domestic knowledge and skills after she becomes tired of his lack of understanding and asked him for an unusual birthday gift: that for one day he would take care of the domestic chores (Mà ¡rquez 222). Through the course of her birthday, Urbino demonstrates himself to be completely helpless regarding domestic knowledge and skills so that Fermina must resume command of the house prior to lunch. Regardless of his claims that Fermina would equally struggle to cure the sick, both Urbino and Fermina learn from this experience that each must appreciate the others unique knowledge and skills. Similarly, after discovering a discrepancy in Urbinos proclamation that nothing that does not speak will come into [their] house, resourcefully Fermina discovers and then buys a royal Paramaribo parrot, who speaks in a voice seemingly human (Mà ¡rquez 23). Thus, Urbino bowed to the ingenuity of his wife and recognizes that she is capable of outsmarting him and his rules (Mà ¡rquez 23). Therefore, by outsmarting Urbinos rules Fermina demonstrates that despite her lacking as advanced tutelage as her husband received, she is still his intellectual equal and he should appreciate her as such. Ferminas strong character and resolve is most evident in her determination and refusal to let others, particularly her husband, influence her choices or make decisions for her. This is clearly seen when she decides to leave and go live with her cousin Hildebranda after she becomes aware that Urbino is having an affair. Since Urbino knew the strength of her character very well, he simply accepted her decision with humility (Mà ¡rquez 235). However, this does not prevent Urbino from seeking to persuade Fermina in her decisions, especially using the intervention of religious authority figures. However, instead of swaying her in favor of Urbino and his ideas, the involvement of religious authority figures in Urbinos and Ferminas relationship makes her even more adamant in her own opinions and choices. This is particularly evident prior to their courtship, when Urbinos last resort in wooing Fermina was the mediation of Sister Franca de la Luz, Superior of the Academy (Mà ¡rq uez 125). Since Fermina hates her, she becomes outraged and becomes increasingly more vehement in her refusal to speak with Urbino. Similarly, this occurs when Urbino sends the Bishop of Riohacha on a pastoral visit to Fermina while she is living with Hildebranda in order to convince her to return home to him (Mà ¡rquez 236). Rather than give Urbino the satisfaction of her giving in to his request, Fermina refused in an amiable but firm manner when the Bishop asks to hear her confession with the explicit argument that she had nothing to repent of (Mà ¡rquez 236). She does not allow her decision to be influenced by the Bishop, but does leave with Urbino when he visits only because she would be happy to leave with him (Mà ¡rquez 254). This can also be seen during their honeymoon in how, although Fermina wanted to turn on the light in their suite, she wanted to be the one to do it, without anyones ordering her to, and she had her way (Mà ¡rquez 158). Overall, Fermina is a strong ch aracter who does not allow others, especially her husband, to persuade her or make decisions for her, instead choosing what she wants or what is most beneficial to her. Although Fermina Daza is dependent upon her husband like most women of her time, her husband is equally if not more dependent upon her. This is particularly evident after their golden wedding anniversary, when both were not capable of living for an instant without the other and that capacity diminished as their age increased (Mà ¡rquez 26). However, neither Fermina nor Urbino could have said if their mutual dependence was based on love or convenience (Mà ¡rquez 26). Urbinos dependence on Fermina is best illustrated through his need for her to care for him in his old age. Since Urbino is ten years older than Fermina, as he grows older he continually becomes weaker leaving Fermina as the strongest of the pair. At first, Fermina simply assists her husband with tasks such as bathing and dressing out of love, but for the last five years of Urbinos life she had been obliged to do it regardless of the reason because he could not dress himself (Mà ¡rquez 26). As Urbino decline s in health with his increasing age, he increasingly comes to depend upon Fermina in order to live. Basically, Urbino depends on Fermina more than Fermina depends on him. Despite Ferminas seeming dependence on Urbino for stability and companionship, she is still very independent minded. Unlike many other women of her time, she is independent in how she does not necessarily rely on her husband for a place to live. This can be seen in how Fermina threatened to move back to her fathers old house, which still belonged to her during the escalating argument between herself Urbino over whether or not there is any soap in the bath (Mà ¡rquez 29). This is also demonstrated when she leaves and goes to live with her cousin Hildebranda after she becomes aware that Urbino is having an affair. However, her independence is most clearly illustrated in how Fermina continues living after Urbinos sudden death. Despite his fear of any possible pain associated with death, what worried Dr. Urbino most about dying was the solitary life Fermina Daza would lead without him (Mà ¡rquez 45). However, Urbinos fear is unfounded because from her first moment as a wid ow, it was obvious that Fermina Daza was not as helpless as her husband had feared (Mà ¡rquez 46). When Ferminas son suggests his wife should accompany her on her riverboat journey, Fermina says that she is too big to have anyone take care of [her] (Mà ¡rquez 325). Unlike her husband, Fermina is independent and does not need anyone to take care of nor provide for her. Ferminas marriage to Urbino reveals that she is a strong, independent woman who is the intellectual equal of her husband. Urbino depends on Fermina more than Fermina depends on him since she does not need anyone to take care of nor provide for her. Despite her lack of as advanced tutelage as her husband received, by outsmarting Urbinos rules Fermina demonstrates she is still his intellectual equal and that he should appreciate her as such. In addition, Fermina is a strong character since she does not allow others, especially her husband, to persuade her or make decisions for her, instead choosing what she wants or what is most beneficial to her. Overall, by presenting Fermina Daza in her marriage to Dr. Juvenal Urbino as a strong, independent woman who is the intellectual equal of her husband, Mà ¡rquez in his novel Love in the Time of Cholera does not portray women as oppressed but rather as quite equal to their male counterparts.

How Students Can Reduce Their Carbon Footprint

Simple Things Students Can Do to Go Green This Year Everyone should do their part to protect the planet, and for some students "going green" can also be a valuable opportunity to explore a pressing cause that has become a major focus in the US lately. Recent reports have found that the Earth is warming much faster than previously thought – raising concerns among teens around the globe. A recent survey found that a majority of US teens are worried about climate change and 1 in 4 have participated in some form of activism on the topic of the Earth's climate. When students are in the midst of preparing for college it can be easy to become totally consumed with SAT scores and personal statements. While preparing for college and making the most of their high school experience is certainly important, students can also remain mindful of their surroundings and find simple ways to reduce their carbon footprint. Especially for students where environmentalism is a particular topic of interest or specialty, it's important to lead by example. Whether you want to be the next Greta Thunberg – the teen climate activist making headlines – or you just want to do your part to help reduce your carbon footprint this semester, keep reading to learn some simple eco-friendly steps you can take. Rethink Your Plastic Bottle HabitBuying plastic water bottles may seem like a convenient solution, particularly for students on the go. However, constant plastic use is not doing the environment any favors. Instead of relying on single-use bottles to quench their thirst students should consider picking out a reusable bottle and carrying it with them throughout classes and extracurricular activities. Not only is this a far more eco-friendly option, it can also cut down on spending in the long run. There are plenty of innovative water bottle brands, so don’t be afraid to spend some time perusing options before settling on a brand and design that matches your personal style. Students can also encourage their schools to go plastic bottle-free and advocate for water filling stations on campus. Ditch the Plastic StrawsStraw use may seem pretty inconsequential, but constantly opting for plastic for your beverages can add up in a pretty negative way. Switching from plastic to paper or metal straws is a small step students can take to reduce their carbon footprint. Many coffee shops have made the switch to paper straws and metal options are easy to find online. If your local shops don’t offer non-plastic options, consider making the suggestion to a store manager or salesperson. This is also another area where students can advocate for their school to go green by suggesting alternatives to plastic straws in the cafeteria. Find Alternate TransportationBiking is more than a solid exercise option! It’s also a fun and easy way to reduce your carbon footprint. Constant car use is harmful to the environment, so students should consider looking into alternate modes of transportation including biking, walking, and public transit like buses and trains. Biking not your thing? Consider other options like skateboarding, scooters, or even inline skates! While it may not be feasible for some students to take alternative transportation to school everyday, replacing short car rides with cycling or other modes of transport can be a great way to reduce your carbon emissions while also upping your physical activity for the day. Put Down the HamburgersReducing your meat consumption is another relatively easy way for students to become more eco-friendly. Greenhouse gas emissions from the agriculture industry are a major concern for the environment, so consider incorporating more meatless meals into your diet. Students can get creative by exploring alternative protein sources such as tofu, tempeh, and seitan as well as opting for beans, nuts, and legumes. While there’s no need to forgo meat entirely, even cutting back can have a significant impact on your carbon footprint. Forgo Fast FashionWhile buying cheap and on-trend clothing from major fashion retailers is always tempting, it’s not always an eco-conscious choice. Buying fast fashion contributes to massive annual textile waste as well as major contamination issues due to the vast amount of pesticides used on the genetically modified cotton many clothing items are made of. Instead of buying in bulk, consider investing in a few ethically made wardrobe staples you can repurpose for years to come. Buying clothing second-hand at local thrift stores is also another eco-friendly option that can help students go green while also saving some green! Second-hand clothing tends to be more affordable and can help you reduce waste – not to mention you can often find some one-of-a-kind pieces! By making a few simple changes students can reduce their carbon footprint and feel empowered to take action against climate change. Whether it’s environmental advocacy or another cause, it’s important for students to make an impact within their local communities. If you are looking for more ideas on how to make a change and highlight it throughout the application process, our team of college admissions experts are here to help!

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? 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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. 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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)