Description Question 2) Do the following exercises. Be sure to express your answers clearly in your own words, based on your own understanding, with Excel as an aid in your calculations and reasoning. What are the median, mode, arithmetic mean and geometric mean of the following numbers? 13, 7, 13, 4, 10, 15, 4, 12 Given a set of monthly returns with mean 1.2% and annual standard deviation 8%, assuming a normal probability distribution, what is the probability of a return worse than -5% over 1month (i.e. one twelfth of a year)? What is the volatility of the portfolio consisting of the following two assets? Current Value Volatility A 2 million 8.1% B 3 million 15.4% Correlation between A and B: +0.37 Question 3) Do the following exercises. Be sure to express your answers clearly in your own words, based on your own understanding, with Excel as an aid in your calculations and reasoning. (5 marks) Given the following data, what is the share value according to the Gordon Model, and what is the percentage fall in the share value if the dividend growth rate falls to 7%. Current Dividend per share: $1.03 Expected annual growth rate of the dividend 8% Investor’s required rate of return 10% Given the following data, what is the share’s yield according to the T-model and the Gordon model? Total earnings during a year $35,450,000 Book value at the start of the year $250 million Number of ordinary shares in issue 15 million Share price at the start of the year $19.06 Share price at the end of the year $21.93 Dividend per share during the year $1.03 Growth rate of book value 8% Expected growth rate of dividend 8% A company’s shares are trading at a price of 32.12. The company announces a “one-for-10” rights issue at 27.00 per share. What are the theoretical ex-rights price and the theoretical nil-paid rights price? Question 4 ) AxelRod Pte. Ltd. is a private company that has recently paid dividends of $3 per share. According to analysts, the dividend is expected to grow at a fixed rate of 3% for the next 10 years. Thereafter, the analysts expect it to grow at the lower rate of 1%. Assume that the risk-free rate is 1.2%, that the stock has a beta of 1.4 and the expected market return is 2.8%. (a) Calculate the value of AxelRod’s stock per share. (10 marks) (b) If instead, the dividend is expected to be constant after year 7 (i.e. the 8th, 9th, etc. years, see dividend amount unchanged and equal to that in the 7th year), re-calculate the value of AxelRod’s stock per share. (10 marks) Make the assumption that it is currently 1 Jan and dividends are paid out at the end of each year. Show your workings clearly with calculations performed on Excel. Question 5 ) Donald kept his savings in the bank for 10 years. In the first 3 years, he deposited $10,000, $15,000 and $ 17,000 respectively. In the 6th year, he used 20% of his savings to buy stocks. In the penultimate year, he took out $3000. In all other years, he did nothing to his savings. Suppose that the annual market interest rates that can be used for forward valuing over the 10 years are given by the formula: r(t) = 0.5% + t x 0.2% [i.e. the interest rate for the period between i and i + 1 is r(i)] Compute the holdings in his bank account at the end of the stated period, assuming that deposits and withdrawals are made at the END of the year and the 10-year period starts from time t=0 and ends at time t=10 (10 marks) (b) Give an assessment of how realistic the interest rate formula is. Show your workings clearly with calculations performed with Excel. (10 marks)
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