Introduction to Financial Mathematics - Math Problem Example

Financial Mathematics Student’s Name Institution Question One. In making a decision on which of the projects I will invest in, I will calculate the present value of the value of the cash flows then less the cost (Ross, 2006). However, in this case there is no need to less initial cost because the three projects have the same costs. Calculation of net present value  PROJECT I- PERTH YEAR 1 2 3 4 5 $ $ $ $ $ CASH FLOWS 300000 500000 500000 600000 600000 PVIF 5%n 0.9524 0.9070 0.8638 0.8227 0.7835 present value 285,714.29 453,514.74 431,918.80 493,621.48 470,115.70 Net present value 2,134,885.01 PROJECT TWO-ROCKHAMPTON YEAR 1 2 3 4 5 $ $ $ $ $ cash flows 580000 480000 480000 480000 480000 PVIF 5% 0.9524 0.9070 0.8638 0.8227 0.7835 Present values 552,380.95 435,374.15 414,642.05 394,897.19 376,092.56 Net present cash flows 2,173,386.90 PROJECT THREE-ADELAIDE YEAR 1 2 3 4 5 $ $ $ $ $ cash flows 450000 450000 500000 500000 620000 PVIF 5% 0.9524 0.9070 0.8638 0.8227 0.7835 Present values 428,571.43 408,163.27 431,918.80 411,351.24 485,786.22 Net present cash flows 2,165,790.95 From the calculation of the net present values, the project with the highest returns is project two-Rockhampton. This project should be chosen because the benefits in terms of the level of returns among the three projects will be the highest. One advantage about the cash flows in project two is that they are constant. If the discount rate changes to 4% The results of the cash flows when using 4% illustrate that the project with the highest level of returns will still be project two. In the case, the projects were being discount by 7%. The calculation of net present value would result  PROJECT I- PERTH YEAR 1 2 3 4 5 $ $ $ $ $ CASH FLOWS 300000 500000 500000 600000 600000 PVIF 5%n 0.9346 0.8734 0.8163 0.7629 0.7130 present value 280,373.83 436,719.36 408,148.94 457,737.13 427,791.71 Net present value 2,010,770.97 PROJECT TWO-ROCKHAMPTON YEAR 1 2 3 4 5 $ $ $ $ $ cash flows 580000 480000 480000 480000 480000 PVIF 5% 0.9346 0.8734 0.8163 0.7629 0.7130 Present values 542,056.07 419,250.59 391,822.98 366,189.70 342,233.37 Net present cash flows 2,061,552.71 PROJECT THREE-ADELAIDE YEAR 1 2 3 4 5 $ $ $ $ $ cash flows 450000 450000 500000 500000 620000 PVIF 5% 0.9346 0.8734 0.8163 0.7629 0.7130 Present values 420,560.75 393,047.43 408,148.94 381,447.61 442,051.43 Net present cash flows 2,045,256.15 A change to 7% does not change the project to be selected, project two still has the highest level of Net present cash flows and thus will have the highest returns. Graphical illustration of the effects of changes in interest rates Project one-PERTH Project two- ROCKHAMPTON Project three-ADELAIDE Question Two The Difference between Discounting and Compounding Discounting is a process of looking at the future payments or a series of income and calculating the value of such future payments to today’s value/ present value. This is possible given a discount rate/ rate of return of the incomes. The future payments may be different in nature; some of the cash flows will be the equal while others will be different. Some will be earned at the end of the year while others will be earned at the beginning of the year (Buchanan, 2006). In case the future payments do not have a fixed time period and occur in perpetuity the Gordon formula 5will be used in discounting. This formula calculates the present value in perpetuity of the ending year’s cash flows. The present value calculated in then discounted using the given discount rate. The present value in Gordon formula= PV= NCF (1+g)/ (k-g) Compounding Compounding is used in respect to the interest rates. Compounding involves the calculation of different forms of returns or cash flows. In the calculation, of interest in the first period involves the calculation multiplication of the interest with the principal amount. However, the second and other periods the amount of interest is calculated by multiplying the interest rate by the principal amount and interest values of the previous periods (Cartledge, 2000). An annuity is a series of returns/ incomes/ payments/ cash flows through a time period. The uniqueness of these cash flows is that they equal for in all the periods. The annuities can be classified into ordinary annuity and annuity due Ordinary annuity, results from the occurrence of cash flows at the end of the of the give years. We calculate the ordinary annuity value at present and in the future. The formula of the calculation of ordinary annuity present value is given by; PVAN n (years) r%=PAYMENTS*[[(1-1/(1+r)n]/r The payments are the same for all the years. The results will be the present value of future equal payments. The formula for the calculation of the future value is given as FVAN n (years)r%= PAYMENTS*[[(1+r)n -1]/r The results will be the value of future value given payments. An annuity due is the value of payments made at the beginning of a given period. Present value calculation is as follows; PVAN n (years) r%=PAYMENTS*[[(1-1/(1+r)n] /r](1+r) the effect of payments being made at the beginning of the period is illustrated through the multiplication with (1+r). future value of the annuity; FVAND n(years)r%= PAYMENTS*[[(1+r)n -1]/r]*(1+r). (r)- Is the discounting rate. Question Three The first goal is to earn $10000 per annum after her retirement 30 years from now for a period of 25 years. The payment will begin at the first year of her retirement. Her second goal needs $450000, 10 years from now. The last goal is to have $500,000 to bequest her son. The nearest goal will be to buy the house. As such; Future value= $450,000, r=15% Future value formula-FVAN nr= PMT*[[(1+r) n -1]/r Payments necessary each period = 450,000/[[ (1+0.15)^10-1]/ 0.15 =$22,163.43 Remainder of the savings 24,000-22,163.43=$ 1,836.57 After buying the house the achievement of the other goals requires; The payments present value is given by; given the r=10% and n=25 years. PVAN =PMT*[[(1-1/(1+r)n] /r](1+r) Present value = 10,000[[1-(1/1.10^25)]/0.10]*(1+0.10) =$ 74,337.71 The future value requirements are given by; FVAN nr= PMT*[[(1+r) n -1]/r Future value = 10000*25+500,000=750,000 Payments =750,000/[[1.15^20-1]/0.15]=7,321.10 She will require (7.321-918.285=6402.815) each year. The amount of savings she had remaining were $18,365.7. This amount if divided by 20 years gives $918.285. Question Four The national bank of Australia is the fourth largest banking the country. The ranking is based on number of customers and the market capitalization. The bank has branches in more than ten countries in the world. It has a total of 11 million customers worldwide; the numbers of ATMs are 4658 while the numbers of branches are 1810. It has been able to invest more than $33.51 in corporate responsibility. In the analysis of the company’s financial statements, the statement of comprehensive income for the year ended September 2011 indicates that the interest income was $34,270 million, the interest expense was $21,236. The total operating expenses were $8,365, the profit before tax was $6,728 and the Net profit for the period was $5,220. The company had a very high basic earnings ratio per share of 233.60 and diluted earnings per share of 231.50. The total comprehensive income for the period was 5,243. The statement of cash flows showed that the net operating cash flows were $9,165 while the net cash flows from the investing activities were $-5,490. The net cash flows from financing activities were $7,303, the cash and cash equivalents for the period ended September was $36,006. The bank is governed by a group twelve board of directors, the Michael Chaney is the group chairman while the group CEO, Cameron Clyne led the group’s executive committee. He is an executive director. FAR Limited This company deals with production of oil of gas through exploration in different counties, in America and Africa. It has acquired various agreements on huge oil deposits in the world. The company’s statement of comprehensive income for the year ended December 2011 shows that the company’s revenue was ($2,385,214) the exploration costs were ($8,848,376). The acquisition costs were ($ 1,319,507). The company made a loss before income tax of ($ 12154417). The total comprehensive income for the year was ($ 1,216,664). The earnings per share were -0.90 while the diluted earnings were -0.90. The cash flow statements indicate that the receipts from the customers were $851,680. The net operating cash flows were ($ 3,353,697). The payments from oil and gas were -11,072,161. The net cash flows from investing activities were -10,309,890. The repayments of borrowings were $-154,510 while the cash flows from the financing activities were ($-173,085). The cash and cash equivalents at the end of the year were 23,803,920. The board of director of directors is composed of four members; three are non-executive while one is the managing director. The largest shareholder is the JP Morgan Nominees Australia limited followed by HSBC custody Nominees. The FAR limited nominees do not form part of the 20 largest shareholders. The managing director Ms. Catherine is compensated an amount of $22.91k annually; the exploration manager earns $23.91k while the administration manager receives $125.32k. The use of financial statements by external and internal users Manager The financial statements assist the manager to make strategic decisions relating to the company. The statements are historic in nature thus are able to give results of a past period analyzing the various conditions in the same period. Cash flows are presented in the form of financing, operating and investing activities. The income statement evaluates the profit that the management has generated throughout the year (Giroux, 2003). These financial statements are valuable in evaluating the performance of the management over a given period of time. Divided to be awarded to the shareholders is determined through the profits calculated in the statement of comprehensive income. Employee Employees of a company need to know how secure their job is, this is possible through evaluation of the company’s financial statements. The employees use the financial information during negotiation of better packages or seek promotions. They use these financial statements to analyze different companies and evaluate the best company to work for. As an external user The shareholder of a company evaluates the performance of the management through the financial statements. The shareholder is able to understand the functionality of the company through the financial statements. In addition, the shareholder evaluates the returns from the given investments in a company. As a prospective investor, I would analyze the risks of the company through the amount of cash flows to creditors and other debtors. The statement of comprehensive income would assist me in determining the level of returns I expect from the company. A supplier of commodities to any of the two companies would use the financial statements to consider the credit worthiness of the companies. The amount of cash flows to the creditors in relation to the amount of cash flows from the assets would assist in assessing the level of risks in supplying goods to the company. A competitor would analyze the financial statements to determine the strategies the companies are using in the market (Kimmel, 2007). The government uses the financial statement for verification of whether the amount of tax paid to the tallies with the amount of profit of the companies. The financial statements are used to evaluate whether the companies have followed the necessary regulations in reporting of the annual results. The Agency Problem This is the conflict between the shareholders and the management. It arises whereby the principle has delegated some authority to an agent. However, instead of the agent fulfilling the principle goals the agent maximizes his own goals. The issuance of incentives to the management is a way of reducing the agency problem. The agency problem can still persist even if the managers are given extraordinary incentives. The issuance of share options to the managers is one way of ensuring that managers maximize the shareholders goals. This might not be the case especially where the managers are given a large portion of the company shares. This can bring a conflict of interest, for example, when making a decision on the amount of divided to issue. A manager might increases the level of dividends because he will make a lot of money from that. The best form of compensation is the use of bonuses after meeting certain set objectives. References Ross, S. A., Westerfield, R., & Jordan, B. D. (2006). Fundamentals of corporate finance. Boston, Mass: McGraw-Hill/Irwin. Buchanan, J. R. (2006). An undergraduate introduction to financial mathematics. New Jersey: World Scientific Publishing. Cartledge, P. C. (2000). The handbook of financial mathematics. London: Euromoney Books. Giroux, G. A. (2003). Financial analysis: A user approach. Hoboken, N.J: Wiley. Kimmel, P. D. (2007). Fiancial accounting: Tools for business decision making. S.l.: John Wiley. Read More