Quantitative Fund Management - Assignment Example

PROBLEM SOLVING By Student Name Course code + name Professor name University name City, State Date of submission Problem Solving Question 1 Savings after 3 years Current savings = $ 15,000 The first 3 years will earn a simple interest at the rate of 13 %. This means that at the end of the year the total savings will be; $ 15,000 + [(13 / 100 x $ 15,000) x 3] = $ 20,850. Savings for the next 12 years In this case the $ 20,850 will earn interest at the rate of 10 % compounded monthly. Compound interest means that the bank will pays interest on the principal amount and the interest that has already been earned by the account. The formula for compound interest is given by; A = P (1 + r / n) n t (Dempster, Mitra, & Pflug 2009). Where A is the amount, P is the principal, r is the rate of interest, n t is the time in years and n is the number of times interest is compounded in a year. A = $ 20,850 (1 + 10 % /12) 12 = $ 23,033.27 Savings for the next 8 years The money will be compounded quarterly at the rate of 9 % for the next 8 years. The formula for compound interest is given by A = P (1 + r / n) n t (Dempster, Mitra, & Pflug 2009). Where A is the amount, P is the principal, r is the rate of interest, n t is the time in years and n is the number of times interest is compounded in a year. A = $ 23,033.27 (1 + 9 % / 4) 8 = $ 29,177.86 Savings for the last 2 years In this case, the savings will earn interest at the rate of 15 % per annum compounded daily for a period of 2 years. A = P (1 + r / n) n t (Dempster, Mitra, & Pflug 2009). A = $ 29,177.86 (1 +15 % /360) 2 = $ 29,202.18 Bonus amount A bonus of $ 320 will be received for each of the last 12 years. Therefore the total bonus amount = 12 x $ 320 = $ 3,840 The first bonus of $ 320 will be invested and earn interest at the rate of 12 % per annum for the next 11 years. A = 320 (1 + 12 % / 1) 11 = $ 1,113 Total interest = $ 1,113 - $ 320 = $ 793 Total accumulated savings after 25 years = $ 29,202.18 + $ 793 + $ 1,113 = $ 31,108.18 b) Calculating the present value of the future amount Formula = A / (1 + r) n (Dempster, Mitra, & Pflug 2009). = $ 200,000 / (1 + 3.045) + $ 130,000 / (1 + 3.045) 3 +$ 96,000 / (1 + 3.045) 5 +$ 312,000 / (1 + 3.045) 8 +$ 1,250,000 / (1 + 3.045) 10 = $ 2,954,858 Question 2 a) Face value of the bond = $ 100,000, coupon rate = 8.25 % per annum, payment is made twice in a year, market interest rate = 11.5 % Since payment is made twice in a year, then the interest rate = 8.25 % / 2 = 4.125 %, market interest rate = 11.25 % / 2 = 5.625 %. The number of time periods = 6 x 2 = 12 4.125 % x $ 100,000 x [1 – (1 + 5.625 %) – 12] / 5.625 % + $ 100,000 / (1 + 5.625 %) 12 = $ 87,162 b) If the market interest rate on January 1, 2014 is 6% per annum, then 4.125 % x $ 100,000 x [1 – (1 + 3 %) – 12] / 3 % + $ 100,000 / (1 + 3 %) 12 = $ 70,142.09 would be paid for the bond. c) Reasons why the bond value is less than the face value A bond is said to be a debt instrument. The periodic interest payments that it pays are based on the coupon rate that is stated and the principal is returned on the maturity date (Dempster, Mitra, & Pflug 2009). The amount of cash flows on the bond that has got no embedded options are certain and the bond price is equal to the present value of the interest payments that will be made in future plus the present value of the bond’s face value (Dempster, Mitra, & Pflug 2009). It is important to note that the formula used to calculate the present value of the interest paid is that of the present value of annuity. That is the present value of a sum that is single occurring in the future. Therefore the entire concept is based on the time value of money which suggests that the money at the present carries more value as compared to the same amount in a future time period. That is why the value of the bond is less than its face value (Dempster, Mitra, & Pflug 2009). d) Hargrave Ltd Dividend per share paid $ 2.00, growth rate = 9 % indefinitely, required return 14 % per annum P = D [1] / (r - g) (Dempster, Mitra, & Pflug 2009). D [1] = next dividend = $ 2 + ($ 2 x 9 %) = $ 2.18 = $ 2.18 / (0.14 – 0.09) = $ 2.18 / 0.05 = $ 43.6 Question 3 Face book Inc. After the historical initial public offer, the shares of Menlo Park for instance fell down 13 % in Face book Inc based in California. Being one of the largest in the US IPOs, the technology company’s early performance of shares has been worse. This is despite the fact that the company had raised over $ 16 billion during the IPO. The company’s shares were being sold at $ 38 each. There has been a wide criticism on Morgan Stanley, the company’s lead underwriter who boosts the company’s number of shares sold in the IPO to $ 421.2 million. Besides the 25 $ boost, the asking price was also boosted from $ 28 to $ 35 from $ 34 to $ 38. It was a big mistake by the company and its underwriter to raise the price and the number of shares. That is why the shares have been performing worse through since the IPO up to July 2013 when they improved (Dempster, Mitra, & Pflug 2009). Question 4 Big Capital managed Fund 1 b) Risk and return Every investment has a risk, it is however important to note that some investments carry more risk than others. Risk and return have a positive relationship and correlation. The higher the risk the higher the potential returns and the lower the risk, the lower the potential returns. Like it has been noted, the bonds and stocks have a high risk with a high return (Dempster, Mitra, & Pflug 2009). 2 b) reasons for the fall in prices in 2008 The earnings reports indicated that in the year 2008, the profit margins were going down and the debts were going high. This was an indication of a declining net income. This induced investors to sell their shares. As a result, the prices of stocks went down. It is worth to note that the company earnings show the financial health of an organization. As shown in the income statements together with the profit and loss, when an organization does poor investors will sell their shares and invest in a better performing company which can promise them a return on their investment (Dempster, Mitra, & Pflug 2009). Question 5 a) Diversification Diversification is a strategy in business development that allows an organization to spread its risk by entering into other lines of trading other than its current line. Given the dynamics of the current market competition, it is critical that the businesses avoid having focus on a single product. When diversification is wisely implemented, it keeps a company stable especially in times of economic downturn. That is the reason why Big Capital Managed Fund offers three portfolios (Dempster, Mitra, & Pflug 2009). b) Investing in a managed fund If the group was to invest $ 50,000 in a managed fund, then the most appropriate portfolio would the balanced fund whereby 50 % will be in shares, 20 % bonds and 30 % property. This would be so given that the portfolio is relatively balanced between shares, bonds and property. This gives a stable form of investment in the changing and unstable economic environment. This is also informed by the financial objectives of the group to have a balanced portfolio that would be relatively stable (Dempster, Mitra, & Pflug 2009). References List Dempster, M. A. H., Mitra, G & Pflug, G. C. 2009. Quantitative fund management. Boca Raton, CRC Press. Read More