# Essays on Financial Mathematics And Managerial Shareholding And Incentive Structure For 2 Selected Companies Coursework

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Financial Mathematics and Managerial ShareholdingQuestion 1 Amount to be invested (present value) = \$1590Number of years 20Interest rate = 5%For Interest compounding annually, FV = PV x (1 + r/100) nWhere: FV is the future value (or final balance) PV is the present value or capital (the amount originally invested) r is the interest rate per yearn is the number of yearsAt the end of the twentieth year, the accumulated amount is For a rate of 5%FV = 1590 x (1 + 5/100) 20FV = 1590 x (1 + 0.05) 20FV = 1590 x 1.0520FV = 1590 x 2.653FV = 4218.27After 20 years, the savings would amount to \$4218For a rate of 6%FV = 1590 x (1 + 6/100) 20FV = 1590 x (1 + 0.06) 20FV = 1590 x 1.0620 FV = 1590 x 3.207FV = 5099.13FV ≈ 5099 (i) For a rate of 8%Savings would amount to FV = 1590 x (1 + 8/100) 20FV = 1590 x (1 + 0.08) 20FV = 1590 x 1.0820 FV = 1590 x 4.661FV = 7410.99FV ≈ \$7411(ii) For a rate of 10%Savings would amount to FV = 1590 x (1 + 10/100) 20FV = 1590 x (1 + 0.1) 20FV = 1590 x 1.120 FV = 1590 x 6.727FV = 10695.93FV ≈ \$10696 (iii) For a rate of 4%Savings would amount to FV = 1590 x (1 + 4/100) 20FV = 1590 x (1 + 0.04) 20FV = 1590 x 1.0420 FV = 1590 x 2.191FV = 3483.

69FV ≈ 3484 Table 1: Summary of Savings Rate %Amount434845421865099874111010696Table 2: Relation of Interest Rates and Future Value Graphically An increase in interest rate would result to a similar increase in future value Question 2 Age = 30 years oldExpected retirement age 65 years (35 years from today)Expected life span 100 years (35 years in retirement) Cost of moving to Coast 10 = \$250,000Expected living expenses per year = \$35,000Expected interest rates 6% for the next 35 years and 8% thereafter Calculations FV = PV x (1 + r/100) nAnnuities = 35 years before retirement and 35 years after retirement Retirement plan cost = Cost of Moving to Coast 10 + (Expenses per year for 35 years)= \$250,000 + (35,000 x 35)= \$250,000 + 1,225,000= \$1,475,000She needs to have saved \$1, 475,000 for her to take this course of action If she has \$50,000 in savings, FV = PV x (1 + r/100) nThe future value with savings of \$50,000 will be equal to FV = 50,000 x (1.08)35FV = 50,000 x 14.785FV = 739,250From the retirement plan, the deficiency will be equal to\$1, 475,000 - \$739, 250= \$735,750 \$1, 475,000 = PV x (1 + 8/100)35 PV = \$1, 475,000/ (1.08)35PV = 99,761PV – Savings\$99,761 – 50,000= \$49,761If she starts to save after 5 years, the annuity would change to 30 years Using the formula FV = PV x (1 + r/100) n\$1, 475,000 = PV x (1 + 6/100)30PV = \$1, 475,000/ (1 + 6/100)30PV = \$1, 475,000/5.743PV = \$256834.41Amount to be saved per year256834.41/30 = \$8561.15Question 3Managerial Shareholding and Incentive StructureTwo companies listed on Australian Stock/Securities Exchange (ASX).

The companies of choice are Emmerson Resources Limited and the National Australia Bank. Emmerson Resources LimitedEmmerson Resources is an Australian company listed on ASX and based in Tennant Creek, Northern Territory, Australia.

The company was incorporated as a private company in November 2005, by T. Kestell, who is currently a non-executive director. The company acquired a suite of exploration and mining tenements in July, 2006 covering a large area near Tenant Creek Mineral Field. The company owns the Warrego gold plant. The company completed an Initial Public Offering (IPO) of its shares in December, 2007 making it a public company. The shares of the company were listed on the Australian Securities Exchange (ASX) on 17 December, 2007.

Board of Directors of Emmerson Resources LimitedThe information below on board of directors of the company was sourced directly from the company’s website (http: //www. emmersonresources. com. au/Board-of-Directors-Emmerson-Resources. htm)

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