Question 4 (a) The table below lists some partial information about a firm. Assume that the number of shares outstanding stays constant forever. Year 1 3 4 0 100 2 132.25 Book equity per share Earnings per share (EPS) Return on equity (ROE) Payout ratio Dividends per share Dividend growth rate 0.20 0.25 5 0.20 0.25 0.15 0.50 21.325 0.15 0.50 0.075 i. Fill in the missing values in the table from years 1 to 4. (6 marks) ii. Assume that after year 4, the company maintains its ROE and payout ratio at year 4 levels. The cost of capital is 12.5%. What is the fair price of the company's stock today (i.e. at t = 0)? (3 marks) i. Suppose the company announces today that it expects any new investments made in or subsequent to year 4 to only earn the cost of capital. The values you calculated in part (i) will be unaffected by this announcement. By how much will the share price change today after the announcement? (4 marks) Question 4 (a) The table below lists some partial information about a firm. Assume that the number of shares outstanding stays constant forever. Year 0 1 2 3 4 Book equity per share 100 132.25 Earnings per share (EPS) 21.325 Return on equity (ROE) 0.20 0.20 0.15 0.15 Payout ratio 0.25 0.25 0.50 0.50 Dividends per share 5 Dividend growth rate 0.075 i. ii. Fill in the missing values in the table from years 1 to 4. (6 marks) Assume that after year 4, the company maintains its ROE and payout ratio at year 4 levels. The cost of capital is 12.5%. What is the fair price of the company's stock today (i.e. at t = 0)? (3 marks) ii. Suppose the company announces today that it expects any new investments made in or subsequent to year 4 to only earn the cost of capital. The values you calculated in part (i) will be unaffected by this announcement. By how much will the share price change today after the announcement? (4 marks) (b) Consider the following statement: "For markets to be informationally efficient, all investors must be rational". Is this statement true? Why/why not? (you will be marked on the justification(s) provided). (4 marks) (c) Companies sometimes try to match the duration of their assets and liabilities. Explain how you think this approach may be useful in protecting net worth from interest rate risk (net worth = A-L, the difference between the market value of assets and liabilities). When is this approach likely to prove less effective? Why? (5 marks) (d) Assume that the CAPM holds. Consider two firms X and Y, and the risk-free asset, with the following return characteristics: o? cov(r) E(r) x 225 200 7.5 Y 1600 600 0 IT 5 What is the expected return of stock Y? (5 marks) (e) Exactly one year ago, you entered into a forward agreement to purchase one unit of a commodity for $F in exactly T years from now. The current price of the commodity in the spot market is SS. The risk-free continuously compounded interest rate in the market is currently r per year. There are no convenience yields or storage costs associated with holding the commodity. Using a replicating portfolio approach, show that the current value of your forward agreement, f, is: f=s-Ferr (6 marks) Question 4 (a) The table below lists some partial information about a firm. Assume that the number of shares outstanding stays constant forever. Year 1 3 4 0 100 2 132.25 Book equity per share Earnings per share (EPS) Return on equity (ROE) Payout ratio Dividends per share Dividend growth rate 0.20 0.25 5 0.20 0.25 0.15 0.50 21.325 0.15 0.50 0.075 i. Fill in the missing values in the table from years 1 to 4. (6 marks) ii. Assume that after year 4, the company maintains its ROE and payout ratio at year 4 levels. The cost of capital is 12.5%. What is the fair price of the company's stock today (i.e. at t = 0)? (3 marks) i. Suppose the company announces today that it expects any new investments made in or subsequent to year 4 to only earn the cost of capital. The values you calculated in part (i) will be unaffected by this announcement. By how much will the share price change today after the announcement? (4 marks) Question 4 (a) The table below lists some partial information about a firm. Assume that the number of shares outstanding stays constant forever. Year 0 1 2 3 4 Book equity per share 100 132.25 Earnings per share (EPS) 21.325 Return on equity (ROE) 0.20 0.20 0.15 0.15 Payout ratio 0.25 0.25 0.50 0.50 Dividends per share 5 Dividend growth rate 0.075 i. ii. Fill in the missing values in the table from years 1 to 4. (6 marks) Assume that after year 4, the company maintains its ROE and payout ratio at year 4 levels. The cost of capital is 12.5%. What is the fair price of the company's stock today (i.e. at t = 0)? (3 marks) ii. Suppose the company announces today that it expects any new investments made in or subsequent to year 4 to only earn the cost of capital. The values you calculated in part (i) will be unaffected by this announcement. By how much will the share price change today after the announcement? (4 marks) (b) Consider the following statement: "For markets to be informationally efficient, all investors must be rational". Is this statement true? Why/why not? (you will be marked on the justification(s) provided). (4 marks) (c) Companies sometimes try to match the duration of their assets and liabilities. Explain how you think this approach may be useful in protecting net worth from interest rate risk (net worth = A-L, the difference between the market value of assets and liabilities). When is this approach likely to prove less effective? Why? (5 marks) (d) Assume that the CAPM holds. Consider two firms X and Y, and the risk-free asset, with the following return characteristics: o? cov(r) E(r) x 225 200 7.5 Y 1600 600 0 IT 5 What is the expected return of stock Y? (5 marks) (e) Exactly one year ago, you entered into a forward agreement to purchase one unit of a commodity for $F in exactly T years from now. The current price of the commodity in the spot market is SS. The risk-free continuously compounded interest rate in the market is currently r per year. There are no convenience yields or storage costs associated with holding the commodity. Using a replicating portfolio approach, show that the current value of your forward agreement, f, is: f=s-Ferr (6 marks)
