a) Assume that a swap contract just had an interest payment calculated on a 20 million principal The three-months Libor rate observed 1.5 months ago was 4.8% (quarterly compounded) and todays 1.5 months Libor and 4.5 months Libor are 4.9% and 5.1% respectively continuous compounded). If the swap contract matures in 4.5 months, calculate the value of the swap to the receiver of the swap rate (fixed term receiver). Assume that the swap pays Libor exchange for a 4.4% fixed rate quarterly compounded. What would happen to foxed term payer position (value of the swap) if interest rates increase? (10 marks) b) What is the CAPM beta of a combination of the stock portfolio and a short position in the stock Index futures contract that minimises the variance of the portfolio? Motivate your answer. (Full marks will be awarded for an analytical demonstration of the result.) (10 mark) c) Assume that the LUMS plc stock price follows the log-normal distribution. The stock pays no dividends and currently it sells at 75 per share. Calculate the values of a call and a put option, both with an exercise price of 76 and maturity of 6-months. Assume that the annualized volatility of stock returns (a) is 0.16 and the continuously compounded interest rate for all maturities is 5% (10 mark) d) Using information from part (c), calculate how many put options with the exercise price of 76 you need to buy or sell to hedge the price risk of 500 shares of LUMS. Would the calculated hedge still be optimal for a different stock price? (10 mark) e) Assume the following for LUMS plc. Common Equity: 100,000 shares selling for 75 per share, The beta of the common shares is 1.3. Preferred stock; 10,000 shares selling for 68 per share, The preferred stock pays a dividend of 2 per year. Debt: 25,000 bonds with 2 years to maturity a face value of 100 and a coupon of 4% payed annually. The bonds sell at par value. The market risk premium is 7%, Treasury bills are yielding 3% and the corporate tax is 27%. Calculate the cost of common equity using the security market line (SML) method. What is the weighted average cost of capital (WACC) of LUMS plc (10 mark) (TOTAL 50 MARKS) a) Assume that a swap contract just had an interest payment calculated on a 20 million principal The three-months Libor rate observed 1.5 months ago was 4.8% (quarterly compounded) and todays 1.5 months Libor and 4.5 months Libor are 4.9% and 5.1% respectively continuous compounded). If the swap contract matures in 4.5 months, calculate the value of the swap to the receiver of the swap rate (fixed term receiver). Assume that the swap pays Libor exchange for a 4.4% fixed rate quarterly compounded. What would happen to foxed term payer position (value of the swap) if interest rates increase? (10 marks) b) What is the CAPM beta of a combination of the stock portfolio and a short position in the stock Index futures contract that minimises the variance of the portfolio? Motivate your answer. (Full marks will be awarded for an analytical demonstration of the result.) (10 mark) c) Assume that the LUMS plc stock price follows the log-normal distribution. The stock pays no dividends and currently it sells at 75 per share. Calculate the values of a call and a put option, both with an exercise price of 76 and maturity of 6-months. Assume that the annualized volatility of stock returns (a) is 0.16 and the continuously compounded interest rate for all maturities is 5% (10 mark) d) Using information from part (c), calculate how many put options with the exercise price of 76 you need to buy or sell to hedge the price risk of 500 shares of LUMS. Would the calculated hedge still be optimal for a different stock price? (10 mark) e) Assume the following for LUMS plc. Common Equity: 100,000 shares selling for 75 per share, The beta of the common shares is 1.3. Preferred stock; 10,000 shares selling for 68 per share, The preferred stock pays a dividend of 2 per year. Debt: 25,000 bonds with 2 years to maturity a face value of 100 and a coupon of 4% payed annually. The bonds sell at par value. The market risk premium is 7%, Treasury bills are yielding 3% and the corporate tax is 27%. Calculate the cost of common equity using the security market line (SML) method. What is the weighted average cost of capital (WACC) of LUMS plc (10 mark) (TOTAL 50 MARKS)