Philosophy - Kant Treatment of animals, Utilitarianism Vegetarianism Essay

Philosophy - Kant Treatment of animals, Utilitarianism Vegetarianism - Essay Example For instance, Immanuel Kant is opposed and condemned on the basis of his notion that only humans serve as the object of honor. The critics argue that Kant does not present anything in favor of displaying kindness towards animals, nor does he condemns exercising butcheries on the creature that is unable to speak or deliver a single word even. Kant does not give animals the status equal to man but is of the view that since the animals are unable to describe their pains and sufferings, they should be treated with kindness in the same manner as it is displayed towards the person. Hence, if Kantian philosophy is considered in its true prospect, it becomes crystal clear that the renowned philosopher lays stress upon the same moral values adopted by an overwhelming majority of the individuals belonging to various cultures and societies of the world. Moral values maintain the direct relationship with religious beliefs, social norms, and cultural values. All existing religions and culture preach kindness towards animals, and the same is emphasized upon by the philosophers. Neither religion, nor society allows harsh treatment of animals, but the life of the animals cannot be stated as honorable, precious and prestigious and that of the persons (i.e. humans) In his work under the title the Metaphysic of Morals, Kant declares that man is bound to pay his duties and obligations to himself and his fellow beings i.e. persons and nature of duties towards animals is surely different from those which are towards human beings.

Slapstick Comedy and Silent Films Essay Example | Topics and Well Written Essays - 2000 words

Slapstick Comedy and Silent Films - Essay Example Besides, enactment, the films also displayed certain captions which informed the audience about the theme of the film. The speedy actions enhanced the humor in the film. The actors who portrayed various characters were mostly shabbily or unconventionally dressed. Their funny attire supplemented by their clown like actions aroused laughter among the audiences. Thus the slapstick comedies consisted of absurd situations and vigorous actions, which had a comic tone and were performed by those actors who were highly energetic and good stuntmen. We find a detailed account on the comparative study of slapstick comedy and Commedia dell'arte in the book of David Madden, namely, -Harlequin's stick, Charlie's cane: a comparative study of commedia dell'arte and silent slapstick comedy. In his book, he gives the discrimination between the two art forms. Commedia dell'arte was performed directly in front of the audience, whereas the slapstick comedy was presented in an indirect form that is it was projected on the screen. The commedia plays were mostly for three hours whereas slapstick comedies were comparatively briefer. In commedia the actors were donned in masks and there was continuous verbal dexterity, slapstick noise, music and color, while the silent movies were devoid of sound and color as the films were Black and White. The commedia was not video graphed whereas the slapstick was video graphed and projected on the screen. (Harlequin's Stick, Charlie's Cane - David Madden, 1968) Actors like Charlie Chaplin, Buster Keaton and Harold Lloyd were considered the milestones in the world of silent cinema. Their powerful performances spell bounded... The researcher of this essay focuses mostly on presenting and discussing the slapstick comedies, that is a device in which, the characters have exaggerated and speedy physical activities backed up by accurate timing. They do this mainly to make people understand what kind of character they are portraying in that film. More emphasis is given on speed of actions and facial expressions. For example, the researcher states that in slapstick comedies we find scenes like a person slipping on the peel of banana skin, somebody hitting a person with frying pan, a person hitting his head against a suddenly opened door, etc. The central character enacts certain scene, which seems to be normal initially but suddenly the situation becomes chaotic, with all the characters running helter-skelter creating confusion. And it is during this time that the actor has to show presence of mind and has to take some action, which will make the audience laugh and also he has to do something brilliant to come ou t of that chaotic situation. The actor performs all sorts of actions like leaping, running, tumbling down etc. And for all these purposes he uses props like buckets, shovel, ladder, sea-saw, sticks, roller skates etc., which generates comedy. The researcher then presents a study on the silent films actors of early 20th century, such as Chaplin, Buster Keaton and Harold Lloyd, who were considered the milestones in the world of silent cinema and used the slapstick comedy in their films in a creative way that made their art memorable.

Mobile Phone And Battery Recycling In Mauritius Environmental Sciences Essay

Mobile Phone And Battery Recycling In Mauritius Environmental Sciences Essay The mobile phone industry, because of its desire to maintain high environmental standards, has voluntarily developed the Mobile Phone Industry Recycling Program. The program aims to ensure that potentially toxic components in mobile phones and batteries do not end up in landfill, but rather are recycled. Orange (Mauritius) and Mission Verte joint green initiative has launched a collection recycling campaign for old phones and wasted batteries. The aim was to reduce noxious liquid that may be released from the battery and cause harm to the environment for example contaminating the water in Mauritius while other parts of the phone will be recycled. Collection or disposable points will be situated in all Orange shop outlets across the island. For the period year 2007, according to the Central Statistics, Mauritius has imported a whopping   175,000 cellular phones while batteries 25 million batteries. In Mauritius, Orange has launched a national program to develop the recycling of mobile phones and batteries in partnership with BEM Enterprises Ltd, the Port Louis Citadelle Rotary Club and the Mission Verte association. Some 15 collection points have been set up at Orange stores. The collected equipment is grouped together and then transported to the BEM Enterprises sorting centre. Plastics and metals are routed to local recycling centres. Batteries, chargers and other electronic circuits for which there is no local processing channel are sent to Europe for recovery at approved recycling centres. BATTERY RECYCLING Most batteries contain heavy metals which is the main cause for environmental concern. Disposed of incorrectly, the heavy metals may leak into the ground when the battery erodes. This contributes to soil and water pollution and endangers wildlife. Some components in batteries can be toxic to fish and make them unfit for human consumption. Batteries contain a range of metals which can be reused as a secondary raw material. There are well-established methods for the recycling of most batteries containing lead, nickel-cadmium, nickel hydride and mercury. For some, such as newer nickel-hydride and lithium systems, recycling is still in the early stages. Mobile phone Battery recycling in UK It is estimated that in 2000, almost 19,000 tonnes of waste general purpose batteries and 113,000 tonnes of waste automotive batteries required disposal in the UK.    Currently, only a very small percentage of consumer disposable batteries are recycled (less than 2%) and most waste batteries are disposed of in landfill sites. The rate for recycling of consumer rechargeable batteries is estimated to be 5%.   The average household uses 21 batteries a year. The UK generates 20,000 30,000 tonnes of waste general purpose batteries every year, but less than 1,000 tonnes are recycled. Automotive batteries, on the other hand, are more routinely recycled in the UK, with a current recycling rate of approximately 90%.   They are collected at garages, scrap metal facilities and many civic amenity and recycling centres. Whilst the exact chemical make-up varies from type to type (see below), most batteries contain heavy metals, which are the main cause for environmental concern. When disposed of incorrectly, these heavy metals may leak into the ground when the battery casing corrodes.   This can contribute to soil and water pollution and endanger wildlife. Cadmium, for example, can be toxic to aquatic invertebrates and can bio-accumulate in fish, which damages ecosystems and makes them unfit for human consumption. Some batteries, such as button cell batteries, also contain mercury, which has similarly hazardous properties.   Mercury is no longer being used in the manufacture of non-rechargeable batteries, except button cells where it is a functional component, and the major European battery suppliers have been offering mercury-free disposable batteries since 1994. A number of valuable materials are used in the construction of mobile phones, and they contain components which, if carefully removed, can be used again, for example in electronic devices. Perhaps more importantly, some cell phones and their accessories contain substances that are amongst the 10 most dangerous known to man including Cadmium, Rhodium, Palladium, Beryllium and Lead Solder (Ref: Cellular Reclamation Ltd, Nov 2004) and most of this ends up in a land fill site or the sea. Now with so many convenient mobile phone recycling schemes around, theres no need for this and no excuse for not recycling your old phone % of material recycled all over the worldg-waste_recyc_material-m.gif Paper recycling Paper recycling is the process of recovering waste paper and remaking it into new paper products. There are three categories of paper that can be used as feedstocks for making recycled paper: mill broke, pre-consumer waste, and post-consumer waste. Mill broke is paper trimmings and other paper scrap from the manufacture of paper, and is recycled internally in a paper mill. Pre-consumer waste is material which left the paper mill but was discarded before it was ready for consumer use. Post-consumer waste is material discarded after consumer use, such as old corrugated containers (OCC), old magazines, old newspapers (ONP), office paper, old telephone directories, and residential mixed paper (RMP). Paper suitable for recycling is called scrap paper. The industrial process of removing printing ink from paperfibers of recycled paper to make deinked pulp is called deinking, an invention of the German jurist Justus Claproth. Water and air pollution The United States Environmental Protection Agencyà ¢Ã¢â€š ¬Ã… ½ (EPA) has found that recycling causes 35% less water pollution and 74% less air pollution than making virgin paper. Pulp mills can be sources of both air and water pollution, especially if they are producing bleached pulp. Modern mills produce considerably less pollution than those of a few decades ago. Recycling paper decreases the demand for virgin pulp and thus reduces the overall amount of air and water pollution associated with paper manufacture. Recycled pulp can be bleached with the same chemicals used to bleach virgin pulp, but hydrogen peroxide and sodium hydrosulfite are the most common bleaching agents. Recycled pulp, or paper made from it, is known as PCF (process chlorine free) if no chlorine-containing compounds were used in the recycling process. However, recycling mills may have polluting by-products, such as sludge. De-inking at Cross Pointes Miami, Ohio mill results in sludge weighing 22% of the weight of wastepaper recycled. Recycling facts and figures In the mid-19th century, there was an increased demand for books and writing material. Up to that time, paper manufacturers had used discarded linen rags for paper, but supply could not keep up with the increased demand. Books were bought at auctions for the purpose of recycling fiber content into new paper, at least in the United Kingdom, by the beginning of the 19th century. Internationally, about half of all recovered paper comes from converting losses (pre-consumer recycling), such as shavings and unsold periodicals; approximately one third comes from household or post-consumer waste. Some statistics on paper consumption: The average per capita paper use worldwide was 110  pounds (50  kg). It is estimated that 95% of business information is still stored on paper. [Source: International Institute for Environment and Development (IIED) Discussion Paper (IIED, London, September 1996)] Recycling 1  short ton (0.91  t) of paper saves 17 mature trees, 7 thousand US gallons (26  m3) of water, 3  cubic yards (2.3  m3) of landfill space, 2 barrels of oil (84 US gal or 320  l), and 4,100  kilowatt-hours (15  GJ) of electricity enough energy to power the average American home for six months. Although paper is traditionally identified with reading and writing, communications has now been replaced by packaging as the single largest category of paper use at 41% of all paper used. 115 billion sheets of paper are used annually for personal computers. The average web user prints 28 pages daily. Most corrugated fiberboard boxes have over 25% recycled fibers. Some are 100% recycled fiber. This articles factual accuracy may be compromised because of out-of-date information. Paper recycling by region European Union Paper recovery in Europe has a long history and has grown into a mature organization. The European papermakers and converters work together to meet the requirements of the European Commission and national governments. Their aim is the reduction of the environmental impact of waste during manufacturing, converting/printing, collecting, sorting and recycling processes to ensure the optimal and environmentally sound recycling of used paper and board products. In 2004 the paper recycling rate in Europe was 54.6% or 45.5  million short tons (41.3  Mt). The recycling rate in Europe reached 64.5% in 2007, which confirms that the industry is on the path to meeting its voluntary target of 66% by 2010. Japan Municipal collections of paper for recycling are in place. However, according to the Yomiuri Shimbun (Japanese newspaper published in Tokyo, Osaka, Fukuoka, and other major Japanese cities), in 2008, eight paper manufacturers in Japan have admitted to intentionally mislabeling recycled paper products, exaggerating the amount of recycled paper used. United States of America Recycling has long been practiced in the United States. The history of paper recycling has several dates of importance: 1690: The first paper mill to use recycled linen was established by the Rittenhouse family. 1896: The first major recycling center was started by the Benedetto family in New York City, where they collected rags, newspaper, and trash with a pushcart. 1993: The first year when more paper was recycled than was buried in landfills. Today, over half of the material used to make paper is recovered waste. Paper products are the largest component of municipal solid waste, making up more than 40% of the composition of landfills. In 2006, a record 53.4% of the paper used in the US (or 53.5 million tons) was recovered for recycling. This is up from a 1990 recovery rate of 33.5%. The US paper industry has set a goal to recover 55 percent of all the paper used in the US by 2012. Paper packaging recovery, specific to paper products used by the packaging industry, was responsible for about 77% of packaging materials recycled with more than 24 million pounds recovered in 2005. By 1998, some 9,000 curbside programs and 12,000 recyclable drop-off centers had sprouted up across the US for recycles collection. As of 1999, 480 materials recovery facilities had been established to process the collected materials. In 2008, the global financial crisis resulted in the price of old newspapers to drop in the US from $130 to $40 per short ton ($140/t to $45/t) in October. Recycling Plastic Bottles ( UK ) Plastic bottles can be found almost anywhere on Earth. This attests to the fact of their usefulness and to the ease and low cost in making these items. Indeed plastic bottles are so useful that almost any liquid beverage or food product can be found being sold in plastic bottles. So why do we recycle? The practice of recovering scraps and waste plastic and reprocessing these materials into new products is called recycling. Recycling makes use of materials that are at the end of their useful lives which otherwise would be added to the waste stream and end up in landfills or (sadly) in the ocean and on our shores. Recycled plastic bottles are an indispensable and ubiquitous part of our lives. They are light in weight and almost unbreakable when used for their designed purpose. This is also the reason why plastics and plastic bottles account for a large part of the waste generated by our throwaway society. Plastic bottles are the most recycled plastic items but still the recycle rate is only about 24 percent.    What are the benefits to recycling plastic bottles? Conservation of Oil. When a ton of plastic bottles are recycled approximately 3.8 barrels of petroleum is saved.   Reduction of Greenhouse Gas emissions. The substitution of recycled materials reduces the emission of greenhouse gases that are produced in the manufacturing of virgin materials. Saving of Landfill Space. Not having millions of plastic bottles in the landfill results in a saving of 6.7 cubic meters of landfill space that is at a premium right now. Plastic bottles also take an average of 500 years to biodegrade. Conservation of Energy. Water and soft drink bottles are made of polyethylene terephthalate or PET.   Recycling of one pound of PET results in a saving of approximately 12,000 BTUs (British Thermal Units). Benefits of Reuse. Recycled bottles can provide an environmentally friendly source of materials for the manufacture of new products and substitutes recycle materials for virgin materials. Recycling Plastic Bottles / Is the Recycling of Plastic Bottles Economically Feasible? Up to the present there is still continuing discussion and debate over whether the recycling of plastic bottles is economically feasible. Local government units and municipalities largely see the fiscal benefits of recycling plastic bottles because of the savings in landfill space and reduced landfill costs. Statistics from a Technical University of Denmark study show that recycling is still the most efficient method to dispose of household waste in 83 percent of all cases. Critics of recycling often claim that more resources are wasted in recycling than is saved. However municipal recycling is still worthwhile if the net costs do not exceed the landfill or other disposal costs.

Farewell to the One-Reelers :: essays research papers

The plot of Big Red Riding Hood is as thin as you can get, but that is usually the case with most one-reelers. Charley plays Jimmy Jump as in all of his one-reel shorts. A title describes Charley's character, "Jimmy Jump -- An intellectual giant, but a financial dwarf." Charley's task in this film is to translate the story "Little Red Riding Hood" into Swedish. So, in the entire film, Charley tries to finish reading the story. When a man buys the book and puts it in the back seat of his car, Jimmy rides alongside the car with his bicycle. He is so absorbed in his reading that he doesn't realize that a couple of gangsters have stolen the car and are being chased by the police. After a car-to-car shootout, with Jimmy oblivious to any action that takes place around him, he and his bicycle fall off the dock and into the sea where he manages to finish the story. Despite the simple plot, it is quite original, and many good gags stem from it. One memorable gag is when Jimmy tries to read the story from above a sunshade using binoculars. A policeman, persuing a thief, shoots his gun in the air hitting the sunshade, which falls to the ground along with Jimmy. There are many slapstick incidents that Jimmy gets into, like getting pricked with a sharp object in his rear and trying to avoid a suspicious cop, but many gags are quite inspired. The elaborate shootout as well as Jimmy's drop into the water at the end serve as the film's most exciting moments. The part when Jimmy falls into the water is quite memorable, in fact. Right after he descends into the sea, he finishes the story and a wide smile goes over his face, but just as quickly fear registers on his mug as he realizes where he is. Another memorable, yet quite surreal, scene in the film is the dream sequence. In it, Jimmy is an inept woodsman and Helen Gilmore plays Little Red Riding Hood.

A General Definition of Financial Reporting

Fiscal coverage in authorities can be seen as a sum-up of the authoritiess public presentation, or capacity, in raising, managing, and utilizing public money. Another manner of showing the function of fiscal coverage is to state it goes manus in manus with answerability. Accountability is frequently considered one of the basiss of good democratic authoritiess. Officials are given authorization and duty and it is the undertaking of the functionaries to clearly convey actions taken and whether these actions fall within the prescriptions of jurisprudence and community wants. Measuring public presentation or accounting with regard to raising, managing, and utilizing public money is a complex issue. The standards are many, diverse, and sometimes conflicting. In some instances there is a accepted regulation or criterions doing organic structure that can cover selected facets of fiscal answerability. In general, nevertheless, there may be more than one regulation doing organic structure. For case, there can be governmental and private regulation doing organic structures. Residents of the affected legal power may hold their ain positions or inadvertence commissions. More by and large, in a democratic society there are frequently norms that provide counsel on answerability. These norms, excessively, may diverge. As an illustration, see the dissension that can originate over a revenue enhancement determination. Is it equal to cover current and future duties made by determination shapers ; does it associate payments to benefits received ; does it enforce greater loads on one group as opposed to others ; and is it hard to roll up? Fiscal studies can be generated on all these issues. This text focuses more on the collectivity of fiscal determinations made by authorities, province and local authorities in peculiar. How does money raised screen disbursement and duties? What is the current and future fiscal wellness of the legal power or subentities covered. How make these determinations comply with the outlooks of regulation or criterion doing organic structures? Governments issue many types of fiscal studies, but the most across-the-board and seeable at the province and local degree is the Comprehensive Annual Financial Report ( see this chapter, lesson 2 ) ( CAFR ) . The CAFR includes the fiscal statements. In this text the fiscal statements provide the chief focal point and therefore the term fiscal statement is sometimes used interchangeably with the phrase fiscal study. Fiscal statements are reasonably demanding in format and supply a quantitative expression at the operating success, fiscal wellness, and conformity of the authorities describing units. The fiscal statements are frequently referred to as the GPFS ( General Purpose Financial Statements ) and can on occasion be taken out of the CAFR and shown individually. The signifier of these statements and the definitions of what they seek to measure are germinating. One signifier or definition may do success, wellness, and conformity appear adequate while another, less so. For case, wit h some signifiers and definitions adoption can be used to hike opportunities for reported success ; in others, it can non. As a consequence, this text will look critically at the current signifier and definitions and examine options. Another of import issue is that historically, the focal point of governmental fiscal coverage is on how good the authorities did in transporting out lawfully authorised maps for the different subentities and financess of authorities. In general, fiscal studies for authorities do non cover the authorities as a whole, but instead the studies screen separate subentities and financess such as all the money raised and spent for diversion or all the money raised and spent for a parking garage or all the fiscal activity for a constituent of the authorities such as school territory. Subentities and financess are at a degree below the full authorities organic structure or legal power. Subsequently, more attending will be given to the separate subentities and financess that are the soon the cardinal unit for governmental accounting. The chief private regulation doing organic structure, the Governmental Accounting Standards Board ( GASB ) , is sing many alterations for describing, such as a stu dy for the authorities as a whole which will probably be called the entity broad position to possibly supplement the fund position. Theoretical contentions aside, at a given point in clip, fiscal studies are based in portion on accounting regulations and other types of regulations or criterions that frequently capture the daily pecuniary minutess and events of authorities. The minutess are are so summarized into fiscal studies. These studies typically make direct appraisals of fiscal public presentation and many affairs that impinge on fiscal public presentation. Technically, one of the major ends of fiscal studies is to measure fiscal success, conditions, and conformity of the financess and other accounting subentities. With such information, one possible benefit of fiscal studies is to assist people make better determinations about their community, their authorities, and their economic system. These determinations may associate to the election of functionaries, ballots on new undertakings, and even the determination to remain in or travel off from a community. Further, the coverage may supply information so that determinations that make the legal power better off. Considerable systematic and official work on governmental fiscal coverage has been done for province and local authoritiess. This text focuses on the work done for province and local authoritiess. This text besides concentrates chiefly on the CAFR ( this chapter, lesson 2 ) and the fiscal statements ( this chapter, lessor 4 ) in the CAFR. Elementss of Financial Reports — Government and Business In general, authorities has significantly different accounting regulations for developing fiscal studies than does concern. Government relies more on a hard currency footing or liquidness and one-year logic to measure one-year activities, whereas concern relies more on an accrual logic to incorporate appraisal of both one-year and long term events. Besides accounting regulations, authorities Torahs and ordinances play a big function in the these governmental fiscal studies. Therefore, the frequent refer to conformity. The lawfully authorised budget of the legal power is critical to fiscal coverage in authorities. That is, the fiscal studies assess the grade to which the authorities disposal, peculiarly fiscal direction, was in conformity with the budget. Because of the importance of the importance of the one-year budget in answerability, authoritiess soon make a clear differentiation between current or one-year points and long term points in their fiscal studies, with accent on current points. Similarly, authoritiess differentiate between liquid assets and fixed assets, with more attending to liquid assets. For the most portion, fiscal studies are intended to supply information for people outside the direction of the authorities. These people are frequently referred to as external users. Because these external users do non hold direct control over the content of fiscal studies, parts of the studies are audited, for illustration, the hearer seeks to certify that the fiscal statements are soon reasonably in agreement with by and large accepted accounting rules ( GAAP ) . Regardless of where or how accounting criterions are developed for fiscal coverage, the standard scene procedure is extremely controversial since a good trade can be at interest in describing fiscal success, conditions, and conformity. A study exudating hapless consequences, conditions, or conformity can upset users. Therefore, the standard scene procedure is sometimes shaped by values and political force per unit areas to obtain favourable fiscal screenings. Many of the alterations in accounting and coverage that have shaped concern accounting criterions have merely begun to come in or be discussed in authorities. The attempt to mensurate current and long term economic chances and convey that information in a blunt manner so external users can apportion resources to those concern they feel will gain has non made a important impact of province and local fiscal coverage. Some of the grounds have to make with the legal nature of province and local authorities. Some have to make with political reserve to publically expose hapless consequences. Some have to make with the questionable rightness of an accent on economic sciences instead than a balance toward economic sciences, societal equity, involvement group political relations, and conformity. Recent proposal by GASB suggest as greater involvement in economic success and chances. A List of Important Footings Associated with Financial Reports — A Expression at single points. accounting regulations Called by and large accepted accounting rules ( GAAP ) , accounting regulations are developed through a due-process system or became accepted with common usage. one-year budget The legislative assembly yearly ( some biannually ) authorizes what grosss to raise, what money to borrow, what promises to do, and what activities to pay for. one-year or current points v. long term Government fiscal studies emphasize and by and large have more stiff accounting regulations for fiscal minutess that involve money raised, spent, or due during the current twelvemonth. Long term points are set aside or de-emphasized until they come due. audited In general, audits effort to find whether the presentation of fiscal information conforms to a set of standards, with the standards in authorities including both accounting regulations and authorities Torahs and ordinances. authorized Given authoritiess ‘ heavy trust on legality, fiscal studies focal point well on whether money was raised, handled, and spent harmonizing to legal mandates. The word conformity becomes really important. better determinations Fiscal studies are intended to better determination devising. These determination can be economic such as a good return on investing or political such as how to vote on a campaigner or issue. capacity

Engineering Economics

Eng ineeri ng Economy Third Edition Leland T. Blank, P. E. Department of Industrial Engineering Assistant Dean of Engineering Texas A & M University Anthony J. Tarquin, P. E. Department of Civil Engineering Assistant Dean of Engineering The University of Texas at EI Paso McGraw-Hill Book Company New York S1. Louis San Francisco Auckland Bogota Caracas Colorado Springs Hamburg Lisbon London Madrid Mexico Milan Montreal New Delhi Oklahoma City Panama Paris San Juan Silo Paulo Singapore Sydney Tokyo Toronto 4 Level One 1. Define and recognize in a problem statement the economy symbols P, F, A, n, and i. 1. 6 Define cash flow, state what is meant by end-of-period convention, and construct a cash-flow diagram, given a statement describing the amount and times of the cash flows. Study Guide 1. 1 Basic Terminology Before we begin to develop the terminology and fundamental concepts upon which engineering economy is based, it would be appropriate to define what is meant by engineering economy . In the simplest terms, engineering economy is a collection of mathematical techniques which simplify economic comparisons. With these techniques, a rational, meaningful approach to evaluating the economic aspects of different methods of accomplishing a given objective can be developed. Engineering economy is, therefore, a decision assistance tool by which one method will be chosen as the most economical one. In order for you to be able to apply the techniques, however, it is necessary for you to understand the basic terminology and fundamental concepts that form the foundation for engineering-economy studies. Some of these terms and concepts are described below. An alternative is a stand-alone solution for a give situation. We are faced with alternatives in virtually everything we do, from selecting the method of transportation we use to get to work every day to deciding between buying a house or renting one. Similarly, in engineering practice, there are always seveffl ways of accomplishing a given task, and it is necessary to be able to compare them in a rational manner so that the most economical alternative can be selected. The alternatives in engineering considerations usually involve such items as purchase cost (first cost), the anticipated life of the asset, the yearly costs of maintaining the asset (annual maintenance and operating cost), the anticipated resale value (salvage value), and the interest rate (rate of return). After the facts and all the relevant estimates have been collected, an engineering-economy analysis can be conducted to determine which is best from an economic point of view. However, it should be pointed out that the procedures developed in this book will enable you to make accurate economic decisions only about those alternatives which have been recognized as alternatives; these procedures will not help you identify what the alternatives are. That is, if alternatives ,4, B, C, D, and E have been identified as the only possible methods to solve a Particular problem when method F, which was never recognized as an alternative, is really the most attractive method, the wrong decision is certain to be made because alternative F could never be chosen, no matter what analytical techniques are used. Thus, the importance of alternative identification in the decision-making process cannot be overemphasized, because it is only when this aspect of the process has been thoroughly completed that the analysis techniques presented in this book can be of greatest value. In order to be able to compare different methods for accomplishing a given objective, it is necessary to have an evaluation criterion that can be used as a basis Terminology and Cash-Flow Diagrams 5 for judging the alternatives. That is, the evaluation criterion is that which is used to answer the question â€Å"How will I know which one is best? Whether we are aware of it or not, this question is asked of us many times each day. For example, when we drive to work, we subconsciously think that we are taking the â€Å"best† route. But how did we define best? Was the best route the safest, shortest, fastest, cheapest, most scenic, or what? Obviously, depending upon which criterion is used to identify the best, a dif ferent route might be selected each time! (Many arguments could have been avoided if the decision makers had simply stated the criteria they were using in determining the best). In economic analysis, dollars are generally used as the basis for comparison. Thus, when there are several ways of accomplishing a given objective, the method that has the lowest overall cost is usually selected. However, in most cases the alternatives involve intangible factors, such as the effect of a process change on employee morale, which cannot readily be expressed in terms of dollars. When the alternatives available have approximately the same equivalent cost, the nonquantifiable, or intangible, factors may be used as the basis for selecting the best alternative, For items of an alternative which can be quantified in terms of dollars, it is important to recognize the concept of the time value of money. It is often said that money makes money. The statement is indeed true, for if we elect to invest money today (for example, in a bank or savings and loan association), by tomorrow we will have accumulated more money than we had originally invested. This change in the amount of money over a given time period is called the time value of money; it is the most important concept in engineering economy. You should also realize that if a person or company finds it necessary to borrow money today, by tomorrow more money than the original loan will be owed. This fact is also explained by the time value of money. The manifestation of the time value of money is termed interest, which is a measure of the increase between the original sum borrowed or invested and the final amount owed or accrued. Thus, if you invested money at some time in the past, the interest would be Interest = total amount accumulated – original investment (1. 1) On the other hand, if you borrowed would be Interest money at some time in the past, the interest (1. 2) = present amount owed – original loan In either case, there is an increase in the amount of money that was originally invested or borrowed, and the increase over the original amount is the interest. The original investment or loan is referred to as principal. Probs. 1. 1 to 1. 4 1. 2 Interest Calculations When interest is expressed as a percentage of the original amount per unit time, the result is an interest rate. This rate is calculated as follows: . Percent interest rate = interest accrued per unit time 00% .. I x 1 0 origma amount (1. 3) 6 Level One By far the most common time period used for expressing interest rates is 1 year. However, since interest rates are often expressed over periods of time shorter than 1 year (i. e. 1% per month), the time unit used in expressing an interest rate must also be identified and is termed an interest period. The following two examples illustrate the computation of interest rate. Example 1. 1 The Get-Rich-Quick (GRQ) Company invested $100,000 on May 1 and withdrew a total of $106,000 exactly one year later. Compute (a) the interest gained from the original investment and (b) the interest rate from the investment. Solution (a) Using Eq. ( 1. 1), Interest = 106,000 – 100,000 = $6000 (b) Equation (1. 3) is used to obtain Percent interest rate = 6000 per year 100,000 x 100% = 6% per year Comment For borrowed money, computations are similar to those shown above except that interest is computed by Eq. (1. 2). For example, if GRQ borrowed $100,000 now and repaid $110,000 in 1 year, using Eq. (1. 2) we find that interest is $10,000, and the interest rate from Eq. (1. 3) is 10% per year. Example 1. 2 Joe Bilder plans to borrow $20,000 for 1 year at 15% interest. Compute (a) the interest and (b) the total amount due after 1 year. Solution (a) Equation (1. 3) may be solved for the interest accrued to obtain Interest = 20,000(0. 15) = $3000 (b) Total amount due is the sum of principal and interest or Total due Comment = 0,000 + 3000 = $23,000 Note that in part (b) above, the total amount due may also be computed as Total due = principal(l + interest rate) = 20,000(1. 15) = $23,000 In each example the interest period was 1 year and the interest was calculated at the end of one period. When more than one yearly interest period is involved (for example, if we had wanted to know the amount of interest Joe Bilder would owe on Terminology and Cash-Flow Diagrams 7 the above loan after 3 years), it becomes necessary to determine whether the interest . payable on a simple or compound basis. The concepts of simple and compound interest are discussed in Sec. . 4. Additional Examples 1. 12 and 1. 13 Probs. 1. 5 to 1. 7 1. 3 Equivalence The time value of money and interest rate utilized together generate the concept of equivalence, which means that different sums of money at different times can be equal in economic value. For example, if the interest rate is 12% per year, $100 today (i. e. , at present) would be equivalent to $112 one year from today, since mount accrued = 100 =$112 Thus, if someone offered you a gift of $100 today or $112 one year from today, it would make no difference which offer you accepted, since in either case you would have $112 one year from today. The two sums of money are therefore equivalent to each other when the interest rate is 12% per year. At either a higher or a lower interest rate, however, $100 today is not equivalent to $112 one year from today. In addition to considering future equivalence, one can apply the same concepts for determining equivalence in previous years. Thus, $100 now would be equivalent to 100/1. 12 = $89. 29 one year ago if the interest rate is 12% per year. From these examples, it should be clear that $89. 29 last year, $100 now, and 112 one year from now are equivalent when the interest rate is 12% per year. The fact that these sums are equivalent can be established by computing the interest rate as follows: 112 100 = 1. 12, or 12% per year and 8~~~9 = 1. 12, or 12% per year The concept of equivalence can be further illustrated by considering different loan-repayment schemes. Each scheme represents repayment of a $5000 loan in 5 years at 15%-per-year interest. Table 1. 1 presents the details for the four repayment methods described below. (The methods for determining the amount of the payments are presented in Chaps. 2 and 3. ) †¢ Plan 1 a interest or principal is recovered until the fifth year. Interest accumulates each year on the total of principal and all accumulated interest. †¢ Plan 2 The accrued interest is paid each year and the principal is recovered at the end of 5 years. †¢ Plan 3 The accrued interest and 20% of the principal, that is, $1000, is paid each year. Since the remaining loan balance decreases each year, the accrued interest decreases each year. + 100(0. 12) = 100(1 + 0. 12) = 100(1. 12) 8 Level One Table 1. 1 Different repayment schedules of $5,000 at 15% for 5 years (1) End of year (2) = 0. 15(5) Interest for year (3) = (2) + (5) Total owed at end of year (4) Payment per plan (3) – (4) Balance after payment (5) Plan 1 0 1 2 3 4 5 Plan 2 0 1 2 3 4 5 Plan 3 0 1 2 3 4 5 Plan 4 0 1 2 3 4 5 $ 750. 00 862. 50 991. 88 1,140. 66 1,311. 76 5,750. 00 6,612. 50 7,604. 38 8,745. 04 10,056. 80 0 0 0 0 10,056. 80 $10,056. 80 $ $5,000. 00 5,750. 00 6,612. 50 7,604. 38 8,745. 04 0 $750. 00 750. 00 750. 00 750. 00 750. 00 $5,750. 00 5,750. 00 5,750. 00 5,750. 00 5,750. 00 $ 750. 00 750. 00 750. 00 750. 00 5,750. 00 $8,750. 00 $5,000. 00 5,000. 00 5,000. 00 5,000. 00 5,000. 00 0 $750. 00 600. 00 450. 00 300. 00 150. 00 $5,750. 00 4,600. 00 3,450. 00 2,300. 00 1,150. 00 $1,750. 00 1,600. 00 1,450. 0 1,300. 00 1,150. 00 $7,250. 00 5,000. 00 4,000. 00 3,000. 00 2,000. 00 1,000. 00 0 $750. 00 638. 76 510. 84 363. 73 194. 57 $5,750. 00 4,897. 18 3,916. 44 2,788. 59 1,491. 58 $1,491. 58 1,491. 58 1,491. 58 1,491. 58 1,491. 58 $7,457. 90 $5,000. 00 4,258. 42 3,405. 60 2,424. 86 1,297. 01 0 †¢ Plan 4 Equal payments are made each year with a portion going toward princi- pal recovery and the remainder covering the accrued interest. Since the loan balance decreases at a rate which is slower than in plan 3 because of the equal end-of-year payments, the interest decreases, but at a rate slower than in plan 3. te that the total amount repaid in each case would be different, even though each repayment scheme would require exactly 5 years to repay the loan. The difference in the total amounts repaid can of course be explained by the time value of money, since the amount of the payments is different for each plan. With respect to equivalence, the table shows that when the interest rate is 15% per year, $5000 at time 0 is equivalent to $10,056. 80 at the end of year 5 (plan 1), or $750 per year for 4 years and $5750 at the end of year 5 (plan 2), or the decreasing amounts shown in years 1 through 5 (plan 3), or $1,491. 8 per year for 5 years (plan 4). Using the formulas developed in Chaps. 2 and 3, we could easily show that if the payments in Terminology and Cash-Flow Diagrams 9 each plan (column 4) were reinvested at 15% per year when received, the total amount of money available at the end of year 5 would be $10,056. 80 from each repayment plan. Additional Examples 1. 14 and 1. 15 Probs. 1. 8 and 1. 9 1. 4 Simple and Compound Interest The concepts of interest and interest rate were introduced in Sees. 1. 1 and 1. 2 and ed in Sec. 1. 3 to calculate for one interest period past and future sums of money equivalent to a present sum (principal). When more than one interest period is involved, the terms simple and compound interest must be considered. Simple interest is calculated using the principal only, ignoring any interest that was accrued in preceding interest periods. The total interest can be computed using the relation Interest = (principal)(number of periods)(interest rate) = Pni (1. 4) Example 1. 3 If you borrow $1000 for 3 years at 14%-per-year simple interest, how much money will you owe at the end of 3 years? Solution The interest for each of the 3 years is = Interest per year 1000(0. 14) = $140 Total interest for 3 years from Eq. (1. 4) is Total interest = 1000(3)(0. 4)= $420 Finally, the amount due after 3 years is 1000 + 420 Comment = $1420 The $140 interest accrued in the first year and the $140 accrued in the second year did not earn interest. The interest due was calculated on the principal only. The results of this loan are tabulated in Table 1. 2. The end-of-year figure of zero represents th~ present, th at is, when the money is borrowed. Note that no payment is made by the borrower until the end of year 3. Thus, the amount owed each year increases uniformly by $140, since interest is figured only on the principal of $1000. Table 1. 2 Simple-interest (1) (2) computation (3) (4) (2) + (3) Amount owed (5) End of year 0 1 2 Amount borrowed $1,000 Interest Amount paid 3 $140 140 140 $1,140 1,280 1,420 $ 0 0 1,420 10 Level One In calculations of compound interest, the interest for an interest period is calculated on the principal plus the total amount of interest accumulated in previous periods. Thus, compound interest means â€Å"interest on top of interest† (i. e. , it reflects the effect of the time value of money on the interest too). Example 1. 4 If you borrow $1000 at 14%-per-year compound interest, instead of simple interest as in the preceding example, compute the total amount due after a 3-year period. Solution The interest and total amount due for each year is computed as follows: Interest, year 1 = 1000(0. 14) = $140 Total amount due after year 1 = 1000 + 140 = $1140 Interest, year 2 = 1140(0. 14) = $159. 60 Total amount due after year 2 = 1140 + 159. 60 = $1299. 60 Interest, year 3 = 1299. 60(0. 14)= $181. 94 Total amount due after year 3 = 1299. 60 + 181. 94 = $1481. 54 Comment The details are shown in Table 1. 3. The repayment scheme is the same as that for the simple-interest example; that is, no amount is repaid until the principal plus all interest is due at the end of year 3. The time value of money is especially recognized in compound interest. Thus, with compound interest, the original $1000 would accumulate an extra $1481. 54 – $1420 = $61. 54 compared with simple interest in the 3-year period. If $61. 54 does not seem like a significant difference, remember that the beginning amount here was only $1000. Make these same calculations for an initial amount of $10 million, and then look at the size of the difference! The power of compounding can further be illustrated through another interesting exercise called â€Å"Pay Now, Play Later†. It can be shown (by using the equations that will be developed in Chap. ) that at an interest rate of 12% per year, approximately $1,000,000 will be accumulated at the end of a 40-year time period by either of the Table 1. 3 Compound-interest (1) (2) computation (3) (4) = (2) + (3) (5) End of year 0 1 2 3 Amount borrowed $1,000 Interest Amount owed $1,140. 00 1,299. 60 1,481. 54 Amount paid $140. 00 159. 60 181. 94 $ 0 0 1,481. 54 Terminology and Cash-Flow Diagrams 11 – llowing investment schemes: †¢ Plan 1 Invest $2610 each year for the first 6 years and then nothing for the next 34 years, or †¢ Plan 2 Invest nothing for the first 6 years, and then $2600 each year for the next 34 years!! ‘ote that the total investment in plan 1 is $15,660 while the total required in plan _ to accumulate the same amount of money is nearly six times greater at $88,400. Both the power of compounding and the wisdom of planning for your retirement at he earliest possible time should be quite evident from this example. An interesting observation pertaining to compound-interest calculations in-olves the estimation of the length of time required for a single initial investment to double in value. The so-called rule of 72 can be used to estimate this time. The rule i based on the fact that the time required for an initial lump-sum investment to double in value when interest is compounded is approximately equal to 72 divided by the interest rate that applies. For example, at an interest rate of 5% per year, it would take approximately 14. 4 years (i. e. , 72/5 = 14. 4) for an initial sum of money to double in value. (The actual time required is 14. 3 years, as will be shown in Chap. 2. ) In Table 1. 4, the times estimated from the rule of 72 are compared to the actual times required for doubling at various interest rates and, as you can see, very good estimates are obtained. Conversely, the interest rate that would be required in order for money to double in a specified period of time could be estimated by dividing 72 by the specified time period. Thus, in order for money to double in a time period of 12 years, an interest rate of approximately 6% per year would be required (i. e. , 72/12 = 6). It should be obvious that for simple-interest situations, the â€Å"rule of 100† would apply, except that the answers obtained will always be exact. In Chap. 2, formulas are developed which simplify compound-interest calculations. The same concepts are involved when the interest period is less than a year. A discussion of this case is deferred until Chap. 3, however. Since real-world calculations almost always involve compound interest, the interest rates specified herein refer to compound interest rates unless specified otherwise. Additional Example 1. 16 Probs. 1. 10 to 1. 26 Table 1. 4 Doubling time estimated actual time from rule of 72 versus Doubling lime, no. of periods Interest rate, % per period 1 Estimated from rule 72 Actual 70 35. 3 14. 3 7. 5 2 5 10 20 40 36 14. 4 7. 2 3. 6 1. 8 3. 9 2. 0 12 Level One 1. 5 Symbols and Their Meaning The mathematical symbols: relations sed in engmeenng economy employ the following P = value or sum of money at a time denoted as the present; dollars, pesos, etc. F A n i = value or sum of money at some future time; dollars, pesos, etc. = a series of consecutive, equal, end-of-period month, dollars per year, etc. amounts of money; dollars per = number of interest periods; months, years, etc. = interest rate per interest period; percent per month, percent per year, etc. The symbols P and F represent single-time occurrence values: A occurs at each interest period for a specified number of periods with the same value. It should be understood that a present sum P represents a single sum of money at some time prior to a future sum or uniform series amount and therefore does not necessarily have to be located at time t = O. Example 1. 11 shows a P value at a time other than t = O. The units of the symbols aid in clarifying their meaning. The present sum P and future sum F are expressed in dollars; A is referred to in dollars per interest period. It is important to note here that in order for a series to be represented by the symbol A, it must be uniform (i. e. the dollar value must be the same for each period) and the uniform dollar amounts must extend through consecutive interest periods. Both conditions must exist before the dollar value can be represented by A. Since n is commonly expressed in years or months, A is usually expressed in units of dollars per year or dollars per month, respectively. The compound-interest rate i is expressed in percent per interest period, for example, 5% per year. Ex cept where noted otherwise, this rate applies throughout the entire n years or n interest periods. The i value is often the minimum attractive rate of return (MARR). All engineering-economy problems must involve at least four of the symbols listed above, with at least three of the values known. The following four examples illustrate the use of the symbols. Example 1. 5. If you borrow $2000 now and must repay the loan plus interest at a rate of 12% per year in 5 years, what is the total amount you must pay? List the values of P, F, n, and i. Solution In this situation P and F, but not A, are involved, since all transactions are single payments. The values are as follows: P = $2000 Example 1. 6 i = 12% per year n = 5 years If you borrow $2000 now at 17% per year for 5 years and must repay the loan in equal yearly payments, what will you be required to pay? Determine the value of the symbols involved. Terminology and Cash-Flow Diagrams 13 ~- ution = S2000 = ? per year for 5 years = 17% per year = 5 years – ere is no F value involved. – 1 In both examples, the P value of $2000 is a receipt and F or A is a disbursement. equally correct to use these symbols in reverse roles, as in the examples below. Example 1. 7 T you deposit $500 into an account on May 1, 1988, which pays interest at 17% per year, hat annual amount can you withdraw for the following 10 years? List the symbol values. Solution p = $500 A =? per year i = 17% per year n= 10 years Comment The value for the $500 disbursement P and receipt A are given the same symbol names as before, but they are considered in a different context. Thus, a P value may be a receipt (Examples 1. 5 and 1. 6) or a disbursement (this example). Example 1. 8 If you deposit $100 into an account each year for 7 years at an interest rate of 16% per year, what single amount will you be able to withdraw after 7 years? Define the symbols and their roles. Solution In this example, the equal annual deposits are in a series A and the withdrawal is a future sum, or F value. There is no P value here. A = $100 per year for 7 years F =? i = 16% per year n = 7 years Additional Example 1. 17 Probs. 1. 27 to 1. 29 14 Level One 1. 6 Cash-Flow Diagrams Every person or company has cash receipts (income) and cash disbursements (costs) which occur over a particular time span. These receipts and disbursements in a given time interval are referred to as cash flow, with positive cash flows usually representing receipts and negative cash flows representing disbursements. At any point in time, the net cash flow would be represented as Net cash flow = receipts – disbursements (1. 5) Since cash flow normally takes place at frequent and varying time intervals within an interest period, a simplifying assumption is made that all cash flow occurs at the end of the interest period. This is known as the end-of-period convention. Thus, when several receipts and disbursements occur within a given interest period, the net cash flow is assumed to occur at the end of the interest period. However, it should be understood that although the dollar amounts of F or A are always considered to occur at the end of the interest period, this does not mean that the end of the period is December 31. In the situation of Example 1. 7, since investment took place on May 1, 1988, the withdrawals will take place on May 1, 1989 and each succeeding May 1 for 10 years (the last withdrawal will be on May 1, 1998, not 1999). Thus, end of the period means one time period from the date of the transaction (whether it be receipt or disbursement). In the next chapter you will learn how to determine the equivalent relations between P, F, and A values at different times. A cash-flow diagram is simply a graphical representation of cash flows drawn on a time scale. The diagram should represent the statement of the problem and should include what is given and what is to be found. That is, after the cash-flow diagram has been drawn, an outside observer should be able to work the problem by looking at only the diagram. Time is considered to be the present and time 1 is the end of time period 1. (We will assume that the periods are in years until Chap. . ) The time scale of Fig. 1. 1 is set up for 5 years. Since it is assumed that cash flows occur only at the end of the year, we will be concerned only with the times marked 0, 1, 2, †¦ , 5. The direction of the arrows on the cash-flow diagram is important to problem solution. Therefore, in this text, a vertical arrow pointing up will indicate a positive cash flow. Conversely, an a rrow pointing down will indicate a negative cash flow. The cash-flow diagram in Fig. 1. 2 illustrates a receipt (income) at the end of year 1 and a disbursement at the end of year 2. It is important that you thoroughly understand the meaning and construction of the cash-flow diagram, since it is a valuable tool in problem solution. The three examples below illustrate the construction of cash-flow diagrams.  ° Figure 1. 1 A typical cash-flow time scale. Year 1 Year 5 r=;:;; r+;:;. I 1 2 Time o I I 3 4 I 5 Terminology and Cash-Flow Diagrams 15 + Figure 1. 2 Example of positive and negative cash flows. 2 3 Time Example 1. 9 Consider the situation presented in Example 1. 5, where P = $2000 is borrowed and F is to be found after 5 years. Construct the cash-flow diagram for this case, assuming an interest rate of 12% per year. Solution Figure 1. 3 presents the cash-flow diagram. Comment While it is not necessary to use an exact scale on the cash-flow axes, you will probably avoid errors later on if you make a neat diagram. Note also that the present sum P is a receipt at year 0 and the future sum F is a disbursement at the end of year 5. Example 1. 10 If you start now and make five deposits of $1000 per year (A) in a 17%-per-year account, how much money will be accumulated (and can be withdrawn) immediately after you have made the last deposit? Construct the cash-flow diagram. Solution The cash flows are shown in Fig. 1. 4. Since you have decided to start now, the first deposit is at year 0 and the [lith Comment deposit and withdrawal occur at the end of year 4. Note that in this example, the amount accumulated after the fifth deposit is to be computed; thus, the future amount is represented by a question mark (i. e. , F = ? ) Figure 1. 3. Cash-flow diagram for Example 1. 9. + P = $2. 000 i = 12% o 2 3 4 5 Year F= ? 16 Figure 1. 4 Cashflow diagram for Example 1. 10. Level One F= ? i = 17†³10 2 0 3 4 Year A=$1. 000 Example 1. 11 Assume that you want to deposit an amount P into an account 2 years from now in order to be able to withdraw $400 per year for 5 years starting 3 years from now. Assume that the interest rate is 151% per year. Construct the cash-flow diagram. Figure 1. 5 presents the cash flows, where P is to be found. Note that the diagram shows what was given and what is to be found and that a P value is not necessarily located at time t = O. Solution Additional Examples 1. 18 to 1. 20 Probs. 1. 30 to 1. 46 Additional Examples Example 1. 12 Calculate the interest and total amount accrued after 1 year if $2000 is invested at an interest rate of 15% per year. Solution Interest earned = 2000(0. 15) = $300 Total amount accrued = 2000 + 2000(0. 15) = 2000(1 + 0. 15) = $2300 Figure 1. 5 Cashflow diagram for Example 1. 11. A = $400 o 2 3 4 5 6 7 Year p=? Terminology and Cash-Flow Diagrams 17 Example 1. 13 a) Calculate the amount of money that must have been deposited 1 year ago for you to have $lOQO now at an interest rate of 5% per year. b) Calculate the interest that was earned in the same time period. Solution a) Total amount accrued = original deposit + (original deposit)(interest rate). If X = original deposit, then 1000 = X + X(0. 5) = X(l + 0. 05) 1000 = 1. 05X 1000 X=-=952. 38 1. 05 Original deposit = $952. 38 (b) By using Eq. (1. 1), we have Interest = 1000 – 952. 38 = $47. 62 Example 1. 14 Calculate the amount of money that must have been deposited 1 year ago for the investment to earn $100 in interest in 1 year, if the interest rate is 6% Per year. Solution Let a = a = = total amount accrued and b = original deposit. Interest Since a Interest Interest b b + b (interest rate), interest can be expressed as + b (interest rate) b =b = b (interest rate) $100 = b(0. 06) b = 100 = $1666. 67 0. 06 Example 1. 5 Make the calculations necessary to show which of the statements below are true and which are false, if the interest rate is 5% per year: (a) $98 now is equivalent to $105. 60 one year from now. (b) $200 one year past is equivalent to $205 now. (c) $3000 now is equivalent to $3150 one year from now. (d) $3000 now is equivalent to $2887. 14 one year ago. (e) Interest accumulated in 1 year on an investment of $2000 is $100. Solution (a) Total amount accrued = 98(1. 05) = $102. 90 =P $105. 60; therefore false. Another way to solve this is as follows: Required investment = 105. 60/1. 05 = $100. 57 =P $9? Therefore false. b) Required investment = 205. 00/1. 05 = $195. 24 =p $200; therefore false. 18 Level One (e) Total amount accrued = 3000(1. 05) = $3150; therefore true. (d) Total amount accrued = 2887. 14(1. 05) = $3031. 50 â€Å"# $3000; therefore false. (e) Interest = 2000(0. 05) = $100; therefore true. Example 1. 16 Calculate the total amount due after 2 years if $2500 is borrowed now and the compoundinterest rate is 8% per year. Solution The results are presented in the table to obtain a total amount due of $2916. (1) (2) (3) (4) = (2) + (3) (5) End of year Amount borrowed $2,500 Interest Amount owed Amount paid o 1 2 Example 1. 17 $200 216 2,700 2,916 $0 2,916 Assume that 6% per year, starting next withdrawing Solution P = you plan to make a lump-sum deposit of $5000 now into an account that pays and you plan to withdraw an equal end-of-year amount of $1000 for 5 years year. At the end of the sixth year, you plan to close your account by the remaining money. Define the engineering-economy symbols involved. $5000 A = $1000 per year for 5 years F = ? at end of year 6 i = 6% per year n = 5 years for A Figure 1. 6 Cashflow diagram for Example 1. 18. $650 $625 $600 $575 $ 550 $525 $500 $625 t -7 -6 -5 -4 -3 -2 -1 t o Year P = $2,500 Terminology and Cash-Flow Diagrams 19 Example 1. 1B The Hot-Air Company invested $2500 in a new air compressor 7 years ago. Annual income â€Å"-om the compressor was $750. During the first year, $100 was spent on maintenance, _ cost that increased each year by $25. The company plans to sell the compressor for salvage at the end of next year for $150. Construct the cash-flow diagram for the piece f equipment. The income and cost for years – 7 through 1 (next year) are tabulated low with net cash flow computed using Eq. (1. 5). The cash flows are diagrammed . Fig. 1. 6. Solution End of year Net cash flow Income Cost -7 -6 -5 -4 -3 -2 -1 0 1 Example 0 750 750 750 750 750 750 750 750 + 150 $2,500 100 125 150 175 200 225 250 275 $-2,500 650 625 600 575 550 525 500 625 1. 19 Suppose that you want to make a deposit into your account now such that you can withdraw an equal annual amount of Ai = $200 per year for the first 5 years starting 1 year after your deposit and a different annual amount of A2 = $300 p er year for the following 3 years. How would the cash-flow diagram appear if i is 14! % per year? Solution The cash flows would appear as shown in Fig. 1. 7. Comment The first withdrawal (positive cash flow) occurs at the end of year 1, exactly one year after P is deposited. Figure 1. 7 Cash-flow diagram for two different A values, Example 1. 19. A2 = $300 A, = $200 0 1 2 3 4 i = 14+% 5 6 7 8 Year p=? 20 Level One p=? j = 12% per year Figure 1. 8 Cash-flow diagram for Example 1. 20. F2 1996 1995 A = $50 A = $150 = $50 F, = $900 Example 1. 20 If you buy a new television set in 1996 for $900,. maintain it for 3 years at a cost of $50 per year, and then sell it for $200, diagram your cash flows and label each arrow as P, F, or A with its respective dollar value so that you can find the single amount in 1995 that would be equivalent to all of the cash flows shown. Assume an interest rate of 12% per year. Solution Comment Figure 1. 8 presents the cash-flow diagram. The two $50 negative cash flows form a series of two equal end-of-year values. As long as the dollar values are equal and in two or more consecutive periods, they can be represented by A, regardless of where they begin or end. However, the $150 positive cash flow in 1999 is a single-occurrence value in the future and is therefore labeled an F value. It is possible, however, to view all of the individual cash flows as F values. The diagram could be drawn as shown in Fig. . 9. In general, however, if two or more equal end-of-period amounts occur consecutively, by the definition in Sec. 105 they should be labeled A values because, as is described in Chap. 2, the use of A values when possible simplifies calculations considerably. Thus, the interpretation pictured by the diagram of Fig. 1. 9 is discouraged and will not generally be used further in this text. p=? j = 12% per year F. = $150 1. 9 A cash flow for Example 1. 20 considering all values as future sums. Figure 1996 1995 1997 1998 1999 F2 = $50 F3 = $50 F, = $900