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Question 1 (10 marks) Assume the expected rate of return on the market is 11% and the risk-free rate is 4%. a. NTF stock is now selling for $60 per share. It will pay a dividend of $2 per share at the end of the year. The expected price for NTF at the end of the year is $65.44. What is its beta? (3 marks) b. Jacky is buying a firm with an expected perpetual cash flow of $4,000 but is unsure of its risk. If Jacky thinks the beta of the firm is 0.9, when the beta is really 1.2, how much more will he offer for the firm than it is truly worth? [Hint: Value of perpetual cash flow = CF/r] (7 marks) Question 2 (17 marks) a. Peter buys a 3% annual coupon bond with five years to maturity. The bond has a yield-to-maturity of 8%. The par value is $1,000. i. Calculate the duration and modified duration of the bond. (5 marks) ii. If the yield decreases to 7.5%, what is the new bond price using the duration concept? (3 marks) b. At the end of next 2 years, you need to pay $100,000 and $150,000 respectively. i. If the market interest rate is 6% per annum., what will be the duration of your payment obligation? (4 marks) ii. Suppose you plan to fully fund the obligation using both 6-month zero coupon bonds and perpetuities. Determine how much of each of these bonds (in market value) you will hold in the portfolio. (5 marks) Question 3 (13 marks) a. The maturity of a futures contract on a stock market index is 1 year. The multiplier for the futures contract $50. The current level of the index is 30,000. The risk-free rate is 0.5% per month and dividend yield on the stock market index is 0.3% per month. The initial margin requirement is 10%. i. What is the parity value of the futures price now? (3 marks) ii. Assume the futures contract is fairly priced. How much initial margin you need to deposit if you long 1 contract? (2 marks) iii. Calculate the two-month holding-period return for your long position in the futures contract if the stock market index increases to 31,000 two months later. Assume the futures contract keeps being priced fairly. (5 marks) b. William sells six July futures contracts on coffee. Each contract is for the delivery of 37,500 pounds. The current futures price is $2.2565 per pound. The initial margin is $9,900 per contract and the maintenance margin is $9,000 per contract. What is the futures price per pound that would lead to a m gin call