Question 1
Mr Adams borrowed $1 million from the bank at a rate of 8% per annum at the start of a year. He decides on a repayment schedule of $100,000 at the end of each year.
(a) By using present values or future values, calculate the number of years Mr Adams would take to completely pay off his loan. In the last year, how much would he pay?
(b) Suppose that at the end of the second year, the bank informs him that the interest rate would be raised by 0.5% henceforth. Assuming that he continues to pay $100,000 every year after the interest rate increase. Calculate the total number of years Mr Adams would take to completely pay off his loan in this new scenario. In the last year, how much would he pay?
(c) Explain the reason for the difference between your answers in (a) and (b).
Question 2
Mr Neo works in Jules Burns Bank as an asset manager and he manages an equity fund. His fund implements a focussed strategy and comprises 4 stocks. The expected returns of the 4 stocks in various scenarios are shown here:
Scenario Stock 1 Stock 2 Stock 3 Stock 4
1 14.3% 8.0% 2.0% 8.0%
2 18.2% 8.4% 7.5% 4.0%
3 16.7% 9.5% 9.4% 2.0%
4 15.0% 10.1% 12.4% -1.0%
5 15.1% 9.1% 12.5% -2.0%
6 11.0% 8.9% 11.4% 3.0%
7 6.5% 6.0% 8.5% 6.0%
8 9.6% 8.5% 8.2% 4.0%
9 9.8% 7.8% 7.8% 5.0%
10 11.3% 7.5% 6.9% 3.0%
Assuming that the probabilities of the scenarios occurring are all equal, answer the following questions:
(a) Calculate the expected return, variance and standard deviation for each stock.
(b) Suppose Mr Neo's portfolio has weights of 50%, 25%, 15% and 10% respectively for Stock 1, Stock 2, Stock 3 and Stock 4. Calculate the expected return, variance and expected return per unit risk for the portfolio.
Question 3
R2D-Star is a technology startup firm that is confident about its prospects. The company plans to pay a dividend of $5 per share at the end of the first year. It then promises its investors that its dividends will grow at a rate of 7% for the next 10 years after the end of the first year and at 5% after that. Suppose that you are given the additional information: risk-free rate = 1.25%, beta of stock = 0.8, expected market return = 12%.
(a) Apply the Capital Asset Pricing Model to compute a suitable discount rate for the stock of R2D-Star.
(b) Compute the value of the stock of R2D-Star.
(c) If the investor thinks that the growth projection is too optimistic and the growth rates need to be reduced to 5% for the next 10 years after the first year and 0% after that, how would she value the stock now?
Question 4
The following question requires you to analyse a mortgage loan that is offered by a bank. Consider a $500,000 mortgage at 4% per annum that is compounded quarterly and amortized over 30 years. Analyse this mortgage loan by answering the following questions:
(a) Calculate the required quarterly payment for this mortgage.
(b) Answer the following questions:
(i) What is the principal amount outstanding at the end of the first year?
(ii) What is the amount of interest paid in the final quarter?
(iii) What is the principal repaid in the final quarter?
Now suppose that the bank allows you to quicken your repayment by giving you the choice to double your payment amount in the second and last quarters of each year and you decide to do so.
(c) Calculate the number of years that is required to pay off the mortgage assuming that
the loan is initiated at the start of the year and the instalment payments are at the end of each quarter.
Question 5
K&L Construction is studying its finances for an island resort development project. The project is planned to initiate on 1 Jan 2016 and is able to produce revenue cash flows startingfrom $20 million on 1 Jan 2017 and this is expected to grow at 13% per year until Jan 2025. All revenue cash flows are assumed to occur on the 1 Jan of each year. The initial cost of the project is $100 million.Assume that the beta of K&L Construction is 1.1, the risk-free rate is 1.7% and the market risk premium is 9.5%.
(a) Compute the cost of capital for the project. Explain the assumption that is made.
(b) Calculate the net present value for the project (regarding the present to be 1 Jan 2016).
(c) Calculate the internal rate of return for the project.