Financial Calculations - Math Problem Example

Group Assignment by Course: Tutor: University: Department: Date due Question 1 Deposit $10,000 Withdraw $7,500 after 5 years Interest 5% p.a Future value of money after 5 years: Less drawings: Value of 5,262.82 after 3 years Money in the account 8 years from now: Question 2 Annuity: $1,000 at the end of year 1 to 10 Discount rate: 8% per annum Present value: Annuity: $2,000 at the end of years 21-30 Discount rate: 8% per annum Total present value of the cash flow: Question 3 a) The expected return of the investment Returns (x) Probability, p(x) 2% 0.1 0.002 5% 0.3 0.015 9% 0.45 0.0405 14% 0.15 0.021 b) Standard deviation of returns for this investment Possible Return 2% 0.1 0.002 0.0004 0.00004 5% 0.3 0.015 0.0025 0.00075 9% 0.45 0.0405 0.0081 0.003645 14% 0.15 0.021 0.0196 0.00294 0.0785 c) Standard deviation measures the spread of returns about the mean hence it gives the variability. A decreasing standard deviation implies that most returns fall within a narrow band. The calculated standard deviation of 0.0348 implies that the returns spread narrowly from the mean of 0.0785. The risk of the investment is low because of low standard deviation. Question 4 a) Finding the monthly returns for Hogo Construction Ltd's shares Month Price Monthly Returns Dec-01 $ 8.29 January $ 8.46 $ 0.17 February $ 8.63 $ 0.17 March $ 8.51 $ (0.12) April $ 8.74 $ 0.23 May $ 8.95 $ 0.21 June $ 9.06 $ 0.11 July $ 8.88 $ (0.18) August $ 9.26 $ 0.38 September $ 9.47 $ 0.21 October $ 9.75 $ 0.28 November $ 9.53 $ (0.22) December $ 9.78 $ 0.25 b) Average monthly returns Hogo Construction Ltd's shares Is obtained by adding monthly returns and dividing by the 12 months c) Standard deviation of returns Month Price Monthly Returns (x) (x-xbar (x-xbar)^2 Dec-01 $ 8.29 January $ 8.46 $ 0.17 $ 0.05 $0.0021 February $ 8.63 $ 0.17 $ 0.05 $0.0021 March $ 8.51 $ (0.12) $ (0.24) $0.0596 April $ 8.74 $ 0.23 $ 0.11 $0.0112 May $ 8.95 $ 0.21 $ 0.09 $0.0074 June $ 9.06 $ 0.11 $ (0.01) $0.0002 July $ 8.88 $ (0.18) $ (0.30) $0.0925 August $ 9.26 $ 0.38 $ 0.26 $0.0655 September $ 9.47 $ 0.21 $ 0.09 $0.0074 October $ 9.75 $ 0.28 $ 0.16 $0.0243 November $ 9.53 $ (0.22) $ (0.34) $0.1185 December $ 9.78 $ 0.25 $ 0.13 $0.0158 $ 0.12 $0.4065 x bar = $0.12 Question 5 a) Finding the value of the bond Mature in 15 years Face value of $1,000 Interest coupon rate of 7% RRR of 11% Interest paid annually b) Finding the price of Square bond Par value = $1,000 Interest of $70 every six months Mature in 8 years YTM = 12 % Question 6 Current price of ordinary shares: $35 Expected divided is $1.38 Current dividend is $1.08 Rate of return implicit in the current share price Applying Gordon growth mode (Bhat, 2008): Question 7 Cost of new machine: $1,000,000 Estimated useful life: 5 years Salvage value: $350,000 Finding the NPV The NPV is positive hence continue with the purchase of the new machine. Question 8 New Machine: $28,000, life of 5 years, salvage of 7,000 a) Payback period Year Net Cash Flows 0 $ (21,000.00) $ (21,000.00) 1 $ 6,000.00 $ (15,000.00) 2 $ 6,200.00 $ (8,800.00) 3 $ 6,600.00 $ (2,200.00) 4 $ 5,900.00 $ 3,700.00 5 $ 5,500.00 $ 9,200.00 b) Accounting rate of return Year Net cash flows 1 $ 6,000.00 2 $ 6,200.00 3 $ 6,600.00 4 $ 5,900.00 5 $ 12,500.00 Total $ 37,200.00 Average $ 7,440.00 Part 2 a) Beta and standard deviation According to Cheng-Few and John (2010), risk is the possibility of success or failure. Both standard deviation and beta are used in measurement of risk. The quantitative measure of risk is developed using standard deviation or variance of possible outcomes. Standard deviation measures the spread of distribution about the mean hence it gives the variability. A decreasing standard deviation implies that most returns fall within a narrow band resulting in low risk. However, a number of problems are associated with standard deviation as a measure of risk. First, the measure lacks intuition given that it is not relative and lacks a benchmark. Secondly, two investments with the same standard deviation mean that they are equally risky. An investor therefore remains indifferent as to which investment is better. There is also a possibility of owning an investment with low standard deviation but still lose money. Bhat asserts that beta measures volatility of an investment relative to the market as a whole. According to the researcher, beta is usually used in capital asset pricing model to find the expected return of an asset. The equation below shows that expected return is a function of beta measured against market portfolio. . In the equation, expected return depends on value of beta. Beta is affected by the type of business as well as level of operating and financial leverage of a firm. Beta is the best estimator of risk because it clearly specifies how returns respond to market turbulence. Loth (2007, par. 8) proposes that investors focusing on preserving capital ought to focus on assets whose betas are low. In the same line, investors looking for high returns should concentrate on investments with high beta values. Moreover, beta is advantageous in the sense that it can help an investor to separate systematic risk from non-systematic risk. b) In a study by Khan (2004) risk is a probability that returns from an investment is different from the expected. It is the chance of losing some or all of the original investment. Standard deviation or beta is used to measure risk. Low levels of uncertainties imply that the risks are low. The low risks are associated with low returns. Conversely, high risks give high potential returns. Khan elaborates that the trade-off between risk and return indicates the balance between the desire for lowest possible risk and the highest possible return. A high standard deviation is comparable to high risk effectively giving higher possible returns. The trade-off is illustrated using the following graph. Figure 1: Risk/ Return Trade Off a) b) c) d) e) f) g) h) i) j) According to the graph, higher risk is associated with the probability of higher returns. It therefore means that there is no guarantee that higher risks yield higher returns or lower risks yield lower returns. c. In a research by Shim and Siegel (2007), payback is the number of years taken to recover the initial investment. Investment whose payback period is short indicates that the investment faces less risk compared with investment whose risk is long. Furthermore, payback further implies that the project has an improved liquidity and a faster rate of return. One of the benefits associated with payback is that companies that face cash flow issues are able to evaluate turnover of scarce resources with a view of recovering funds. d. Profit maximization vs wealth maximization In the past, businesses were focused on meeting their expenses. Some companies have however moved to wealth maximization, which entails improving value of the business. While wealth maximization looks at long-term, profit maximization concentrates at the short-term goal (Shim and Siegel, 2008). This new approach is superior since it is sensitive to time value of money. In line with this approach, investment choices are made after subjecting future earnings to discount rates. The present values obtained from the operation gives a wider perspective of an investment because risks have been factored into the equation. A company can then proceed to raise capital bearing in mind that the projects have gone through a good appraisal. References Bhat, S. (2008). Financial Management. New Delhi: Excel Books India. Cheng-Few, L., & John, L. (2010). Handbook of Quantitative Finance and Risk Management. New York: Springer. Khan, M.Y. (2004). Financial Management: Text, Problems and Cases. New Delhi: Tata McGraw-Hill Education. Loth, R 2007, ‘Measuring Risk with Apha, Beta, and Sharpe’, forbes, 5 November, viewed 11 April 2014, http://www.forbes.com/2007/11/05/risk-alpha-beta-pf-education- in_rl_11050investopedia_inl.html. Shim, J. K., & Siegel, J. G. (2007). Handbook of financial analysis, forecasting, and modeling. Chicago, IL: Wolters Kluwer/CCH. Read More