The Fencing Problem | Mathematics Problem

The Fencing Problem | Mathematics Problem The Fencing Problem. A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. She is not concerned about the shape of the plot, but it must have a perimeter of 1000m. Which shape, with a perimeter of 1000m has the maximum possible area? Let us start off with a isosceles triangles. The area of an isosceles triangle can be computed by using the Area=  ½ base x height formula.   Let us start of with the equilateral triangle. Then each side has length 1000/3=333.4. We need to calculate the height. For this we use trigonometry. The height(h) divides the triangle in two identical right angles. All the angles are equal and add up to 180 ° so angle C is 60 °. Then,   since, tan C= height/adjacent we have that height=tanC x adjacent So area of triangle is  ½ x 166.67 x 333.34 x tan 60 = 48114.4 Next suppose we shorten the base so that it’s 300 m in length. Then the other two sides are 350 m each.   Here we don’t know the angles but we can use Pythagoras’ theorem to obtain the height. We get 150^2+h^2=350^2 which means h^2= 350^2-150^2=100000 and h=316.2 So area of triangle is  ½ x 300 x 316.2=47434.2 Next we shorten the base consecutively another four times and perform the same calculation. The results are displayed in the table below. Base m Side m Area m^2 334.34 333.34 48114.4 300 350 47434.2 250 375 44194.2 200 400 38729.8 150 425 31374.8 100 450 22360.7 It is clear from the table that the area decreases and that the equilateral triangle has the largest area. Next we consider rectangles. A square with a perimeter of 1000 m has sides of length 250 m and thus the area   250250=62 500 squared meters. Let us stretch the square by 25 meters to 275. To keep the 1000 m perimeter the horizontal sides shorten to 225. The area is 275225=61875. We repeat this procedure and show the results in the table below. Hight m Width m Area m^2 250 250 62000 275 225 61875 300 200 60000 325 175 56875 350 150 52500 375 125 46875    We can see that the squre has the greatest area and that the area decrases as the square is stretched. We can see that the area would eventually be zero as the wiidth gets smaller and smaller and close to zero. Also we see that the the square has a greater area than the triangle. Let us examine shapes with more sides to see if the area increases. Thus we should calculate the agrea of a   regular pentagon.   It can be divided into 5 isosceles triangles with each of the sides as a base. Using the same procedure as when we calculated the area of the equilateral triangle we can calculte the area of the triangle in the pentagon. Multiplying by 5 we get the area of the pentagon. Each side has length 1000/5= 200. The angle at the centre is 360/5=72. As this is an isosceles triangle we get that the other two angles are (180-72)/2=54. So height=tan54 x 100 and the area of the triangle is  ½ 200 x tan 54 x 100=13763.8. Now we need to multiply by 5 to get the area of the triangle. We get Area= 68819.1 m This is bigger than the square. Let us construct a formula for the general n-sided polygon. The length od each side is 1000/n. The central angle is 360/n. So the other two angles are (180-360/n)/2 which simplifies to   90 –180/n. That gives the formula for the height h=tan(90 –180/n) x (1000/2n) and the area of triangle is    ½ 1000/n x tan(90 –180/n) x (1000/2n). We need to multiply the number of sides which gives Area=500 x tan(90 –180/n) x 500/n. Using this formula we calculate areas for a n sided polygon as n increases. The results are shown in the table below. Number of sides Side length Area 5 200 68819.1 6 166.7 72168.8 7 142.9 74161.5 8 125 75444.2 9 111.1 76318.8 10 100 76942.1 11 90.1 77401.9 15 66 78410.5 30 33.3 79286.4 1000 1 79577.2 It is clear that as the number of sides increases so does the area. But as the number of sides increases we get closer and closer to the shape of a circle which can be thought of as the an infinitely sided polygon. Thus the shape with the largest area is the ciscle. What is the area of a circle with perimeter of 1000m? 2x Pi x radius=1000 so radius=159.2. From the formula for the area of a circle, Pi x r^2, we get the area 79622.53 The Sarbanes–Oxley Act of 2002: Overview and Impact The Sarbanes–Oxley Act of 2002: Overview and Impact Sarbanes Oxley Companies Abstract The Sarbanes–Oxley Act of 2002 was passed on July 30, 2002 and only the public companies are now feeling its impact. This act frequently called the â€Å"most significant accounting or auditing legislation since the securities exchange Act of 1934†. After the implementation it has established its demands to the companies for proper management and disclosure of risk. Nortel networks is a giant corporate in telecom industry and as it is expected they also have faced the challenges come from the SOX act. Some of them are in favor and some are against the Nortel. ‘SOX’ has manipulated a larger impact on Nortel internal employee and external customers as well as their financial statement. The outcome of the Nortel is clearly different from before implementing the SOX. This paper is to develop a deeper understanding of the SOX, how it governs the public corporate, financial disclosure and practice of public accounting in general sense. Besides this it will focus on the outcomes of Nortel network after implementation of SOX and its financial statement. Introduction There have been found a number of corporate financial scandals (e.g. Tyco International) that provides various type of weakness in the governance and auditing practice in the organization. It represents the failures in controlling the reliability and integrity to the stock markets. The scandals cost billions of dollars for the investors when the affected companies were collapsed. As a result, these scandals make upset the public confidence in the nation’s security markets. The Sarbanes–Oxley Act was passed in positive response by the American congress on July 30, 2002 in response to a number of major corporate and accounting scandals and these scandals in result of decreasing the investors or shareholders confident on investing on the share market. To restore their confident, a new regulation from SEC (Security and Exchange Commission) is implemented. The act was granted by a vote of 423-3 by the House and by the Senate 99-0. So, it can be said that the act had not to face approving challenges. The Sarbanes–Oxley Act gives the government a strong control. This act is commonly known as Sox or Sarbox act and it consist of eleven titles. Each title contains different sections and setting from further corporate board tasks to criminal penalties. The Sarbanes–Oxley Act was named after senator Paul Sarbanes and Representative Michael G. Oxley. President George W. Bush signed it into law, stating it included, â€Å"the most far reaching reforms of American business practice since the time of Franklin D. Roosevelt†. The established legislation is applicable for all U.S. public company boards, management and public accounting firms. This new legislation is an enhancement to standardize the process for all US public companies; the companies will become more transparent on company board, Management and public accounting firms. For example, the Tyco International case reduced the confidence and shocked the investors in the listed companies in the share market and the liable reporting authorities. So, the purpose of the act was to recover the confidence and make tight the government rules and regulations on the companies to keep them under control. The consistent financial reporting process is ensured by this act. Consequently, the reliability to the public in accordance with disclosure is increased. The telecom professionals found themselves under the force to fulfill the regulation within a short time. By doing this they can keep away from any criminal accusations. The most important provisions of  the  Sarbanes–Oxley Act include: Accelerated reporting of trades by insiders Public reporting of CEO and CFO compensation and profits. Auditor independence and a prohibition on audit firms offering value-added services. Companies are now required to have an internal audit function, which must be certified by external auditors Certification of financial reports by CEOs and CFOs. This paper presents a real understanding on the Sarbanes–Oxley Act and its impact on the telecom industry. It also provides the controls adopted by the authority to maximize the financial reporting process. Besides these, it would give a clear idea that will act as a guideline on what possible interface control may need to implement to the telecom governance and accounting process. Literature review From a number of financial scandals the act Sarbanes Oxley has been evolved. This act provides some important and practical provisions for the public companies. There are eleven titles under the Sarbanes–Oxley Act of 2002 and these are: Public Company Accounting Oversight Board (PCAOB), Auditor independence, Corporate responsibility, Enhanced financial disclosures, Analyst conflicts of interest, Commissions resources and authority, Studies and reports, Corporate and criminal fraud accountability, White collar crime penalty enhancement, Corporate tax returns, Corporate fraud accountability. All these titles provide fifty seven sections overall. The public accounting, public corporate or financial disclosure, all these are the boundary of Sarbanes–Oxley Act. The impact of Sarbanes Oxley 2002 on the Nortel networks in the telecom industry in regarding to its internal employee and external customer. Moreover, the outcomes of the Nortel telecom after the implementation of Sarbanes–Oxley Act. Some implied recommendations from this act and also some limitations of different sections. An overview of SOX act Public company accounting oversight board (PCAOB) Title one has nine section and it establishes public company accounting oversight board. This public company accounting oversight board is to provide independent oversight of public accounting firms providing audit services. It also deals with the auditors registering, defining the specific process, subject to the securities laws, and related matters. It is to ensure the public confidence in the preparation of informative, accurate and independent audit reports. The board will be termed as a body corporate, operated as a nonprofit organization. Auditor independence Title two also consists of nine sections and it establishes the independence of the auditors. This act provides a standard for the external auditors which limit the conflicts of interest. Furthermore, it also refers the approval requirements for the new auditors. Partner rotation policy, conflict interest issues, auditor reporting programs are in this boundary. According to the section 201, it is not approved to do other kind of business for the auditing companies, which are apart from with the same clients. Corporate responsibility Title three consists of eight sections and it emphasizes on the responsibility of the senior executives. The senior executives will be responsible for the accuracy and validity of corporate financial reports. It also establishes the responsibility by the corporate officers about the accuracy and completeness of the corporate financial reports. Besides this, the interaction between external auditors and corporate audit committees has been specified through this act. There would be no improper manipulation on conduct of audits. Forfeiture of certain bonuses and profits, officer and director bars and penalties, insider trades during pension funds blackout periods, fair funds for investors, all these will be treated as the corporate responsibility. For example, according to the section 302, it is implied that the company should be responsible for approving the integrity of their company financial reports. Enhanced financial disclosures There are nine sections in the title four and it mandates the requirements for financial transactions, such as off balance transaction. In addition, pro-forma figures and stock transactions of corporate officers are described under this act. The accuracy and validity of financial reports and disclosures is dependent on the internal controls to be ensured. There is the possibility of material change in financial condition. It enhanced conflict of interest provisions of personal loans to executives. This act provides the disclosures of transactions involving management and principal stockholders. Management assessment of internal controls, exemption, code of ethics for senior financial officers, disclosure of audit committee financial expert, enhanced review of periodic disclosures by issuers, real time issuer disclosures are the section included in this title. Analyst conflicts of interest This title consist only one section and it emphasizes on to restore the confidence of the investors in the reporting of securities analyst. This title defines the code of conduct that is applicable for the securities analyst and it emphasis the disclosure of knowable conflict of interest. Commissions resources and authority This title six consists of four sections and provides practices to recover the confidence in securities analysts. It also defines the authority of Security Exchange Commission to censure or bar securities professionals from practice. It also provides the information about which person can and cannot be barred from practicing as a broker, advisor or dealer. Studies and reports Title seven consists of five sections and enhances the conducting research to prevent the violence that may occur by the SEC registrants and auditors. Effects of consolidation of public accounting firms or role of credit rating agencies in the operation of securities market or securities violations and enforcement actions, and whether investment banks assisted and others to influence earnings and obfuscate of true financial condition are the boundary of this title. Corporate and criminal fraud accountability Title eight ‘corporate and criminal fraud accountability’ consists of seven sections and it is referred to as the â€Å"corporate and criminal fraud act of 2002†. Specific criminal penalties for fraud manipulation and destruction or alteration of financial records or other interference with investigation all these are provided by this act. White collar crime penalty enhancement Title nine â€Å"white collar crime penalty enhancement† consist of two sections and this section is also known as â€Å"white collar crime penalty enhancement act of 2002†. This section of title nine defines the criminal penalties that associated with white collar crimes and conspiracies. It provides the more reliable guidelines and specially adds failure to certify corporate financial reports as a criminal offense. Corporate tax returns Title ten â€Å"corporate tax returns† consists of only one section which states that the chief executive officer should sign the company tax return. Corporate fraud accountability Title eleven â€Å"corporate fraud accountability† consists of sevens sections. According to the section 1101 it has been recommended that this title can be named as â€Å"corporate fraud accountability act of 2002†. This act is to find out the corporate fraud and records which could temper the criminal offenses. It identifies these offenses and joins those offenses to specific penalties. This not only provides this description but also revises sentencing guidelines and strengthens their penalties. Conceptual framework of this study This paper conducts a study about the impact of SOX act on the telecom company. The Sarbanes Oxley 2002 act is to present a detailed report on a company’s internal controls over the SEC. in addition, the overall review of SOX in a short way to understand deeply is the framework of this study. It would be difficult to get the right information from the respondents. The respondents may be unaware about the significance of the survey. Besides this, complexity in data collecting system may hamper the study paper. Multifaceted questions and difficult language is an obstacle to get the proper records. So, easy and understandable language will be used. Sarbanes–Oxley Act 2002 and the practice of public accounting According to the Sarbanes–Oxley Act 2002 all public accounting firms who wish to provide auditing function for the purpose of publicity traded companies need to register with the board. This act provides the scope of audit practice and reports, details investigation and defines conflict-of-interest prohibition. The SOX itself has changed or affect the practice of public accounting system of Nortel. Nortel believes that all adjustment is necessary for presenting a fair financial statement. It expected to everyone that the practice of public accounting will be fair in a manner. Before the Sarbanes–Oxley Act passage, the firms did not have to usually disclose stock-opinion grants to the Security and Exchange Commission unless the close of the business year. The firms had to disclose the stock-opinion within two business days after issuance. Sarbanes–Oxley Act has become now a law. Accounting, financial reporting and tracking of sales activities all these are affected by this act. Sarbanes Oxley is to be said as a mandatory which is applicable for all listed companies in the U.S. whether foreign or not and compliance is not an option. In case of Nortel the effects of SOX has begun. Like much of the business community, the public financial report is very crucial to present in a systematic way. The growing number of restatement and so many other certain public accounting practices which shake the public confidence in the financial reporting system has been seen for a long time. Although it is difficult to measure the effect of accounting issues on the investor confidence, various efforts to find out investor confidence have been made. For example, a survey based index provides the public opinion in regarding to the accounting practice. Public cite public accounting practice as a difficult and complex issue, which has negative impact on the stock market. Some surveys indicate that after implementation of Sarbanes–Oxley Act in July 2002. â€Å"Other sources such as empirical research studies and academic experts generally suggest accounting issues have negatively affected overall investor confidence and raised questions about the integrity of U.S. markets†. (GAO October, 2002). According to the Sarbanes–Oxley Act 2002 in the audit committee at least one member would be financially literate. The audit committee consists of minimum three members. However, SOX puts a strong emphasis on audit committee function with respect to the company’s relation with an external auditor. As a result the audit committee of each issuer becomes directly responsible appointment, compensation and oversight of the work of any registered public accounting company employed by that issuer. (Didenko Pavel) At first Sarbanes–Oxley Act creates a nonprofit corporation that is â€Å"public company accounting oversight board† or PCAOB. Its â€Å"five SEC-appointed members (of whom two will be CPAs), financed by new public company fees, will register, inspect and discipline public accounting firms, including foreign firms in certain cases, as well as establish and enforce auditing, quality control, and independence standards.†(McTamaney, Aug 9 2002). Because of the new Sarbanes–Oxley Act the audit firm itself now will turn around its guide audit partner every five years. Hence, the sec 103 of the Sarbanes Oxley enhances public accounting firms to prepare, maintain and continue a period of time which is not less than 7 years. Section 104 allows the advisory board to maintain and review all audit papers for a period of 5 years from the end of the fiscal period. The section 105 of SOX provides the authorization to the oversight board to perform a wide investigation of auditing firms. Besides the auditing firms associated persons are to be conducted through broad investigation and the act authorizes the board to â€Å"require the production of audit work papers and any other document or information in the possession of a registered public accounting firm or any associated person thereof.† (Patzakis John, 2003). Accounting did not cause the recent corporate scandals such as Enron and WorldCom. Unreliable financial statements were the results of management decisions, fraudulent or otherwise. To blame management’s misdeeds on fraudulent financial statements casts accountants as the scapegoats and misses the real issue. Reliable financial reports rely to a certain extent on effective internal controls, but effective internal controls rely to a large extent on a reliable management system coupled with strong corporate governance. (A management system is a process of planning, executing, and control for all business processes in an organization.)