Joshua is planning for his retirement. He is in mid-thirties, has two children, and an annual income of $120,000 before taxes. He has estimated the following:

Years till retirement 30 years Estimated years in retirement (based on actuarial tables) 27 years Current level of household expenditures $84,000 % of household expenditures needed in retirement 80% Estimated annual end-of year income in retirement from CPF $53,000 CPF payments are based on current dollars and will increase with the expected inflation until retirement Expected annual inflation rate until retirement 5% Expected annual inflation rate during retirement 4% Expected annual rate of return on investments before retirement 8% Expected annual rate of return on investments during retirement 10%

Joshua is considering investment in the preferred stock of Big Oil. This preferred stock promises an annual dividend payment of $4. Joshua requires 8% return on investment. Unfortunately, Big Oil recently suffered losses and has decided to suspend its preferred dividends for the next two years. The company says it expects to begin paying preferred dividends again three years from now. To make up for the dividends that it skipped, Big Oil will pay a one-time dividend of $12 in three years, that is, $8 for the dividends it skipped for two years and $4 for the normal dividend in year 3. After that preferred shareholders will continue to receive the annual $4 dividend that they had come to expect.  

Alternatively, Joshua is thinking of allocating a certain portion of his investments in a safer asset class like bonds. You suggested for him to consider bonds issued by Bank Corp and the salient terms are detailed as follows:

? Issue date = January 1, 2016 ? Amount issued = $800 million ? Maturity date = December 31, 2025 ? Interest = 7% ? Payment = Semi-annually ? Par value = $100.00 ? Required rate of return = 8%

Joshua is also considering investing in common stock of Thunderbird. The company has paid a dividend of $2 recently. It is expected that the dividend will grow at 8% per annum for the next 3 years and will grow at 4% per annum from year 4 onwards into perpetuity. Joshua has ascertained that the beta of Thunderbird is 1.2; He has also estimated the risk free rate as 3% and the market risk premium as 6%.  

Joshua is considering forming a portfolio of stocks of three companies, A, B, and C. He has collected the following information regarding the three stocks:

Company Expected return Standard deviation A 10% 14% B 12% 18% C 9% 12%

Correlation coefficients:

A B C A 1.00 0.80 0.60 B 0.80 1.00 0.40 C 0.60 0.40 1.00

He would like to invest 30% in A, 50% in B and 20% in C.

Question 1  

Based on the information given, calculate the annual end-of-year savings required for investment during the period until retirement.   

Question 2  

Calculate the price of the preferred stock of Big Oil. If Joshua wants to invest $9,500 now in the preferred stock of Big Oil, how many preferred stocks can he purchase?

Question 3  

Calculate the price of the bonds of Bank Corp. If Joshua wants to invest $9,500 in the bonds of Bank Corp, how many bonds can he buy?

Question 4  

Calculate the price of the stock of Thunderbird. If Joshua wants to invest $9,500 in the stocks of Thunderbird, how many shares can he buy?

Question 5

If Joshua wants to invest in the portfolio of stocks of A, B, and C, calculate the expected return and the standard deviation of the portfolio.