Fundamentals of Finance - Math Problem Example

Qs1 (a). (Option 1) effective rate (ie) = [(in + 1)1/n ]- 1 (Grinols, 2001). ie = [(0.105+1)1/365]-1 ie = (1.105)0.00274-1 ie = 0.027% (Option 2) effective rate = [(0.1055+1)1/4] – 1 Effective rate = (1.1055)0.25 – 1 Effective rate = 0.0254 or 2.5% (Option 3) effective rate = [(0.095+1)1/2] – 1 Effective rate = (1.095)0.5 – 1 Effective rate = 4.64% The best source of finance from the effective rates calculated is ABC Friendly Finance Company. (b) Total payment at the end of fifth year will be; Interest payment = (1000000*0.0475*10) Interest payment = 475000 Total payment =1000000+475000+1000 Total payment = 1476000 Nominal rate = [476000/ (1000000*5)]*100 Nominal rate = 9.52% Effective rate = [(0.0952+1)1/2)]-1 Effective rate = (1.09520.5) - 1 Effective rate = 4.65% (c) Nominal rate = real rate + rate of inflation Real rate = nominal rate - rate of inflation (Grinols, 2001). Real rate = 10.5% – 3% Real rate = 7.5% Next year nominal rate of return = 7.5% + 3%+ 3.5% Nominal rate will be = 14% Qs 2. (a) Principal = $10 millions, rate = 0.12, t = 10 years and n = 12 A = p (1 + r/n)t*n A = 10000000(1 + 0.12/12)10*12 A = 10000000(1.01)120 A = $33003868.945 Monthly payments = 33003868.945/ (12*10) Monthly payments = $275032.241 (b) At the 40th payment, the balance will be; 33003868.945 – (275032.241* 40) = 33003868.945 – 11001289.64 Balance payment = $22002579.305 (c) Total payment periods are 120. Thus, 40th payment represents (40/120 * 100) = 33.33% of the principal and interest payment. Remaining principal amount not yet covered amounts to; (10000000* 0.6667) = 6667000 Remaining payment periods = 120- 40 = 80 A = 6667000(1 + 0.15/12)80 A = 6667000(1.0125)80 A = 48066188.63 Monthly payments = 48066188.63/ 80 Monthly installment payment = $48066188.63 Qs 3. (a) Future value = $600,000 and real rate of interest is = 5% (i) At 19 years old; t = 60 – 19 = 41 600000 = p.v (1 + 0.05/1)1*41 600000 = p.v (1.05)41 600000 = p.v*7.391 p.v = 600000/ 7.391 p.v = $81179.8133 (ii) At 23 years old; t = 60 – 23 = 37 600000 = p.v (1 + 0.05/1)1*37 600000 = p.v (1.05)37 600000 = p.v* 6.0814 p.v = 600000/ 6.0814 p.v = $98661.4924 (b) Annuity payment; w = [p.r (1+ r)n-1]/ (1+r)n-1 (i) At 19 years; w = [600000* 0.05(1+ 0.05)41-1]/ (1+0.05)41 -1 W = [30000* (1.05)40 ]/ (1.05)41 – 1 W = (30000* 7.039988)/ (7.3919881 – 1) W = 211199.64/ 6.3919881 W = $33041.31 (ii) At 23 years; W = [(600000* 0.05(1+ 0.05)37-1]/ (1+0.05)37 -1 W = [30000 (1.05)36]/ (1.05)37 – 1 W = [30000* 5.791816]/ (6.081406943 – 1 W = 173754.48/5.081406943 W = $34194.167 (c) (i) At 19 years; w = [600000* 0.045(1+ 0.045)41-1]/ (1+0.045)41 -1 W = [27000* (1.045)40]/ (1.045)41 – 1 W = (27000* 5.8163645)/ (6.0781 – 1) W = 157041.842 / 5.0781 W = $30925.315 c. (ii) At 23 years; W = [(600000* 0.045(1+ 0.045)37-1]/ (1+0.045)37 -1 w = [27000* (1.045)36]/ (1.045)37 – 1 w = (27000* 4.877)/ (5.09686 – 1) w = 131679/ 4.09686 w = $32141.445 (d) At 19 years; w = $33041.31; 10% of 33041.31 = 3304.131 Total annuity = 33041.31 + 3304.131 = 36345.231 At 60 years old = 36345.231* 41 = $1490154.471 At 23 years W = $34194.167; 10% of 34194.167 = 3419.4167 Total annuity = 34194.167+ 3419.4167 = 37613.5837 At 60 years saving will be = 37613.5837* 37 = $1391702.60 Qs 4. DUP FUND MANAGEMENT MEMORANDUM To: Dup#2 fund clients. From: Nigel Tan, Manager. Date: 28 April 2012 Subject: Australia ordinary stock return in the year 2008 in relation to foreign investment. 1. Introduction At the end of annual meeting on 28 December 2011, members requested to be informed the reasons why the fund investment firm trades in the international stock market. This was as a result of the some of the members opinion that the returns in Australian stock market is highly correlated to stock market of other developed market. 2. Background In 2008, fund investment across international stock market generated a loss of 25% in return. The firm has not recovered the loss since then and this has prompted members to be dissatisfied as to why they should continue having their funds diversified across the international stock market. The stock market investment average return at the Australia stock market from our finding showed that the market also registered a loss of 4.46% in the year 2008. 3. Average stock return in Australia stock market The average returns findings for the year 2008 on monthly basis is as shown below (Yahoo! Finance: more on ^AORD. Historical cost 2008). Date Open Close Return 12/1/2008 3669.8 3659.3 -0.00286 11/3/2008 4003 3672.7 -0.08251 10/1/2008 4662.4 3982.7 -0.14578 9/1/2008 5209.2 4631.3 -0.11094 8/1/2008 5047.4 5215.5 0.033304 7/1/2008 5345.8 5052.6 -0.05485 6/2/2008 5774 5332.9 -0.07639 5/1/2008 5654.2 5773.9 0.02117 4/1/2008 5416.1 5657 0.044478 3/3/2008 5639.3 5409.7 -0.04071 2/1/2008 5717.2 5674.7 -0.00743 1/2/2008 6418.6 5697 -0.11242 Average -0.04458 The average returns for the year 2008 shows that, if the fund investors had invested only in the Australia stock exchange, they would as well have incurred a loss. The loss nevertheless, would not have being as high as the one the fund investors incurred that same year. 4. Benefits of investing in two highly positively correlated assets. The firm has invested in two highly correlated stock assets A and B portfolios. Their returns and standard deviation are as follows. Asset A Asset B Return 15% 24% Standard Deviation 12% 19% The two assets have combined standard deviation of; Sp = (w1*0.12+ w2*0.19+ 2(w1w2)0.8* 0.12* 0.19 Sp = w1*0.12+ w2*0.19+ 2(w1w2)* 0.01824 w1+ w2 = 1 w1 = 1-w2 Substituting the sp to be in w2, the sp will be as follows; Sp = [(1- w2)* 0.12+ w2*(0.19- 0.12)] + [2* (1-w2+ w2)* 0.01824] = 0.12- w2* (0.12) + w2* (0.7) + 2* 0.01824 Sp = 0.12- w2* (0.12) + w2* (0.7) + 0.03648 Sp = 0.12 – w2 (0.5) + 0.03648 Sp = 0.15648 - w2* (0.5) The two assets earning proportion is as follows; Ep = (w1*0.15+ w2*0.24) Substituting the sp to be w2, the sp will be as follows; Ep = 0.15+ w2* (0.24- 0.15) = 0.15 + w2 (0.9) Thus, both risk and return are in proportion of w2. Sp = 0.15648 - w2* (0.5) Ep = 0.15 + w2 (0.9) For the proportion to be of benefit, sp must be equal to zero. The value of w2 will be as follows. Sp = 0.15648 - w2* (0.05) = 0 W2* (0.05) = 0.15648 W2 = 0.15648/ 0.05 W2 = 3.1296 W1 = 1- 3.1296 = -2.1296 From the above portfolio investment evaluation, investing in the two assets can be accomplished by taking a higher position in asset B and a short position in asset A. This means the investment will take a formation of offsetting positions in the two assets which will be the same as investing in two negatively correlated assets (Reilly, 2011). Thus, there is no added advantage in investing in the two positively correlated assets. 5. Investing in two negatively correlated assets (correlation coefficient -1) Sp = (w1*0.12+ w2*0.19+ 2(w1w2) -1* 0.12* 0.19 Sp = (w1* 0.12 + w2* 0.19 + 2* (w1w2)* -0.0228 Substituting sp to in w2; W1 + w2 = 1 W1 = 1 – w2 Sp = [(1- w2)* 0.12+ w2*(0.19- 0.12)] + [2* (1-w2+ w2)* - 0.0228 Sp = 0.12- w2* (0.12) + w2* (0.07) – 0.0456 For the portfolio investment of the two assets to be of benefit, sp will be zero. Thus, the value of w2 will be; 0.0744 – 0.05w2 = 0 0.0744 = 0.05w2 W2 = 0.0744/ 0.05 W2 = 1.48 W1 = 1- 1.48 W1 = -0.48 Thus, the weight of asset B will offset that of asset A by 48%. 6. Global risk exposures to investment funds By investing at international stock markets, investment funds firms undertakes some special risks. These international risks include; 1. Change in currency; this is the risk involved in the change of exchange rates between foreign currencies in an international investment. When the exchange rate changes between foreign currency of an international currency and that of Australian dollar, investment funds are likely to increase or decrease their investment returns (Grinols, 2001). This is because foreign companies trade and pay dividends in their local currency. When investment funds companies receive their dividends from an international investment, they convert the cash they receive into Australian dollar. Thus, during the periods when the foreign currency is stronger than that of Australian dollar, investment firms in international investments will increase their returns as the dividends received results into more Australian dollars. Also, when the foreign currency is weaker compared to that of Australian dollar, investment funds under international market will reduce their returns when the dividends are converted into Australian dollars. Also, in some countries foreign currency are under state controls that restricts the movement of currency from their country. This may delay or limit the amount of foreign currency a fund investment company can move from that country. 2. Dramatic change in market value. If a fund investment company engages in timing the foreign market on when to invest, they face the risk of not knowing when to move out of the stock market when prices are going down and when to get into the market before the prices start to rise (Grinols, 2001). If an investment fund company fails to make the right timing, it risks losing the value of the stock assets it has invested in due to falling prices or investing when the stock prices are already at the peak. 3. Political, economic and social environment. When an investment fund company decides to invest in an international stock market, it faces the difficulty of establishing all the political, economic and social factors of that particular country. This poses as a risk to the firm as it risks losing its investment incase the political, economic and social environment turns chaotic for any economic growth to prosper (Grinols, 2001). 4. Lack of liquidity. An investment fund may trade in an international market that has low trading volumes and a few listed companies (Grinols, 2001). The markets may be trading for a few hours in day before they close and restrictions on the amount or type of stocks that a foreign investor is allowed to purchase. Also, the market may require foreign investors to pay premium prices for them to be able to buy foreign securities and when they buy, because of low trading volume, they face a lot of difficulty locating for a buyer when they want to sell. 5. Inadequate information. An investment fund may invest in international companies that do not provide adequate information about their financial position(Grinols, 2001). This may lead to the fund company investing in a company that is on verge of collapsing. Thus, the fund company risks losing all the investment it has invested in such company. 6. Different market operations. An investment fund may find the operations of the foreign market differing from that of Australian trading market. The clearance periods and settlement of securities transactions differs in the international markets. Rules covering the safety of shares held by the custodian banks or depositories may not be well developed which puts the shares invested by fund investment firms at such markets at risk if the custodian is facing credit problems(Grinols, 2001). 7. Reliance on foreign legal assistance. If an investment fund company comes into problems with its investment, the firm has no capacity to sue the company it has invested in, at Australian court. Once again, thank you for your support. Qs 5. In finance, systematic stability can be defined as the capacity of a financial structure to aid and enhance economic processes, manage risks and absorb shocks (Schinasi, 2006). Financial stability is dynamic process because it changes with time as it adjusts to remain consistent with other financial elements. Financial institutions are said to be in systematic stability when they are sound in term of having enough capital to absorb normal times and abnormal times losses and adequate liquidity to manage operations and volatility in regular periods of time (Schinasi, 2006). Thus, financial systematic stability involves avoidance of financial crises which means managing systematic financial risk. Systematic financial risk is managed by market participants by undertaking private risk management and the responsible authorities by undertaking banking supervision, market inspections and systematic risk management (Green, Pentecost, and Weyman-Jones, 2011). The effects of systematic stability problems in a real economy include a rising disruption scenario in payment structure, and credit flows and also, asset values destruction (Green, Pentecost, and Weyman-Jones, 2011). In Australia, the responsibility on stability of the financial sector is vested in the Reserve Bank. The reserve bank of Australia in its mandate to advance financial stability has taken several measures to prevent against financial disturbances that have potential systematic costs and also, measures that respond to any eventuality of financial disturbance when it occurs. The measures that the reserve bank of Australia has taken include (Reserve bank of Australia: Financial stability. About financial stability 2012); 1. Laying down a foundation that promotes an environment that is favorable to financial stability by way of low and stable inflation and economic growth that is sustainable. The Reserve Bank undertakes this measure by way of assessing a range of collective financial and economic information that helps weighing the security of the financial system and likely vulnerabilities. The findings of the analysis are made public half yearly by publishing in the financial stability review booklet. 2. Ensuring a safe and vigorous payment system. The Reserve Bank Payment Board has precise authority over the payment system safety and stability. The authority of the board is made useful as it enjoys the support of strong regulatory powers. The board in undertaking its mandate of ensuring a safe and robust payment system, shares its recommendations with other related agencies. In the domestic market, the Bank shares its views to the Council of Financial Regulators forum. The council is chaired by the Reserve Bank Governor with other members being the Bank, Australian Prudential Regulatory Authority, the treasury and Australian Securities and investments Commission. Their mandate is to make contribution that can help in enhancing efficiency and effectiveness in the stability regulation of the financial system. Also, the Reserve Bank as a member of Financial Stability Board (FSB) and Basel Committee on Banking Supervision (BCBS) makes contributions towards systematic stability on international financial system at international debates. The roles of FSB is to evaluate the vulnerabilities that might affect the financial system, try to identify actions to address them and oversee implementations of the identified measures and enhance sharing of information among authorities that engage in financial stability. BCBS on the other hand, provides to the international debate an international framework that can enhance prudential regulation on banks that are active across internationally. 3. Management of solvency crisis in financial institutions. The Reserve Bank cooperates with other council members in solving solvency problems in the financial institutions. The Bank in this regard, engages in monitoring financial markets, payment and settlement structures and advising treasury or any relevant minister about dangers emerging in these markets and structures. Also, the Bank has the responsibility in evaluating and giving an opinion around the character and degree of systematic impact of any considerable financial anxiety and the implication on the financial market and payment system. The Bank also plays the role of evaluating response measures towards liquidity support or using the powers of payments systems and their implementation. References Green, C, Pentecost, E and Weyman-Jones, T, 2011. The financial crisis and the regulation of finance. London. Oxford press. Grinols, E, 2001. Uncertainty and the theory of international trade. New York. Oxford press. Reilly, F, 2011. investment analysis and portfolio management. London. Oxford press. Schinasi, J, 2006. Safeguarding financial stability. Theory and practice. California. Telso publication. Reserve bank of Australia: Financial stability. About financial stability 2012, viewed 28 April 2012, . Yahoo! Finance: more on ^AORD. Historical cost 2008, viewed 28 April 2012, . Read More