Total salary for Mathew for 25 years if he earns $10000 per month is (12*25) $10000 which is $3000000
If he withdraws $6000 for five years, the total withdrawal will be (12*5) $ 6000 which is $ 360000
Total money remained after Mathew death is $ (3000000-360000) which will be $ 2640000
Mathew’s son Sean inherits the savings and he receives equal payment for every month for 20 years with a fixed interest rate of 9% per annum.
Total amount for 20 years will be $ 2640000= S/5.6044 where S is the sum total
The sum total will be $147956160
If Sean receives equal pay for each month for 20 years that is 240 months, he will be receiving $147956160/240 which is $616484 per month.
The value of the bond after 10th interest if its face value is $1000 at 8% for five years can be calculated as follows: $1000=?/1.46933
Multiplying both sides by 1.46933 to get the total sum value which is $1000*1.46933=1469.33, this will be the value of the bond after 10th interest
If the bond were redeemable at $ 1100at end of year 4, the market price of the bond after the 6th interest payment will be:
Face value is $ 1000 and the interest rate will be 3% for three years.
It will be $1000=S/1.093 multiply both sides by 1.093 we get $1000*1.093=$1093 which is the market price after 6th interest payment.
The table below shows Les’s selected company’s total return and standard deviation. Table I
|Total share return||Standard deviation of daily returns||Beta coefficient|
|National Australia Bank||10.97%||1.62%||0.906|
|James Hardie Industries||9.28%||2.07%||0.626|
|Lend Lease Corporation||2.69%||1.75%||0.683|
|Sons of Gwalia||27.77%||2.45%||0.349|
|All Ordinaries Index||12.28%||0.92%||1.000|
The return and the standard deviation have to be positively related. In the table above, National Australia Bank has a positive relationship though of low value as the return is 10.97%. Coca-Cola Amantil return is negative while the standard deviation is positive. This is not consistent with the expected positive relationship; the risks cannot be covered by the returns.
James Hardie Industries has a return of 9.28% this is low when related to the risk of the investment, and its standard deviation is at 2.07%. Lend Lease Corporation has return of 2.69% and standard deviation of 1.75%, though positively related the return is low. News Corporation has a return of 57.90% and standard deviation of 3.42%.There is positive relationship and the return value is good as it is on average meaning the risks are fully covered by the returns though the risk is very high. Sons of Gwalia have positive relationship though the return is low (27.77%). Westfield Trust has positive relation but the return is low. Woodside Petroleum has return of 23.96%and standard deviation of 2.08%.
The companies with low return imply that the risks of the investment will not be well offset as high returns are desirable on the grounds that it will cover the risks associated with the investment, though an investor who expects high returns should accept more risks.
A company can be rejected on the basis that its return is low or its deviation from risk is low. In relation with Mr. Les selection of companies for investment some companies are not worthy for investment and hence should be rejected. These are Coca-Cola Amanti which has a return of -62.78% and standard deviation of 2.73%, this means that the risk associated with the investment cannot be covered hence it is unworthy for investment.
Also Lend Lease Corporation should be rejected on the basis that its return (2.69%) will not offset the risk as presented by the Beta coefficients (0.683). finally; James Hardie Industries may also be rejected as its return is only 9.28% while the standard deviation is 2.07%. The return is low for the risk.
Concept of Portfolio Theory
Markowitz (1958) contends that rational investors use diversification to optimize their portfolios. Markowitz assumes investors are risk averse. Investors will prefer the less risky investment and will only take risky investment if compensated by higher expected returns.
The concept of Portfolio theory holds when the portfolio risk is minimized by holding a well diversified portfolio of shares. In the case of Mr. Les selected companies for investment, the concept of Portfolio theory holds as the Beta coefficients are all positive which imply that the returns and the risks are positively correlated. The company with high risk is associated with high Beta coefficient, for instance, the News Corporation has a return of 57.90% standard deviation of 3.42% and Beta coefficient of 2.625.
The three companies that can be recommended for Mr. Les for investment are; Sons of Gwalia which has Beta value of 0.349. The value is low meaning that the risk associated with the investment is less. Also Westfield Trust which has the Beta coefficient of 0.381 and James Hardie Industries. Less risky investment can be recognized basing on the Beta coefficient. Large Beta coefficient means high risks associated while small coefficient means low risks associated.
The portfolio for the above companies chosen can be derived as follows:
Square the returns multiply by the square of its standard deviation of 3 companies then add after which we add the multiplication of the returns and the multiplication of the standard deviation of 3 selected companies. This will be 0.000052 which is the portfolio. The results outperforms the All Ordinaries Index
Using the Capital Asset Pricing Model (CAPM) for the Mr. Les data of 2001 financial year we can use the following CAPM formula in sequence with Markowitz (1952):
E (R¡) =Rƒ+ßί [E (Rm)-Rƒ]
Where; E (Rі) is the expected returns for share
Rƒ is the risk-free rate of return
ßί is the assets Beta and [E (Rm)-Rƒ] is the market premium or risk premium
Black, Fisher, Michael, Jancen and Scholes (1972) outline that the CAPM was introduced by Jack Treynor, William Shape, John Lintner and Jan Mossin independently building on the earlier work of Harry Markowitz on diversification and modern portfolio theory
The market premium can be obtained by getting the difference between the arithmetic average of the expected market return and the arithmetic average of the rate of free risk. This will be 9.45-2.145=7.305. Using the above CAPM formula, the expected returns for the shares is shown in the table below:
|Company name||Share return||Risk||Beta coefficient||Expected share return|
|National Australia Bank||10.97%||0.906%||0.906||17.588%|
|James Hardie Industries||9.28%||2.07%||0.626||13.853%|
|Lend Lease Corporation||2.69%||1.75%||0.683||7.679%|
|Sons of Gwalia||27.77%||2.45%||0.349||30.319%|
Comparing the share returns results, the CAPM results have increased a little bit as to the raw results. In-line with Markowitz (1952), this indicates that CAPM takes into account the sensitivity to no-diversifiable risk often represented by Beta in the financial industry, and though CAPM may be impressive it assumes that the assets returns are normally distributed, but in the some markets returns are not normally distributed. The model also does not appear to explain the variation in stock returns thus it is not that 100% accurate.
Black, Fisher, Micheal, Jancen, and Scholes. (1972). The capital Asset Pricing Model.
New York. Praeger publishers.
Markowitz H. (1952). Portfolio selection. Journal of finance, 7 (1), 77-91.