4. (30%) Consider a firm whose current marker value is $150 at the beginning of the first period. The firm lasts for two periods. The rate of return on the firm's assets over each period is equally likely to be either 20% or -20%. The risk-free rate is 5% in each period. If any cash payout, coupon and/or dividend, is made at the end of the first period, then the ex-payout firm value will change by either 20% or -20% over the second period. There are no taxes and bankruptcy costs. (a) At the beginning of the first period, the firm issues a coupon bond and pays out the proceeds as dividends to shareholders. The bond has a face value of $100 and a per-period coupon rate of 6% to be matured at the end of the second period. The firm pays no dividends at the end of the first period. What is the market value of the bond at the beginning of the first period? (b) Consider now that the firm can choose between two sets of assets with the same initial value of $150. The first set of assets is as described above, which has the rate of return over each period equally likely to be either 20% or -20%. The second set of assets, on the other hand, has the rate of return over each period equally likely to be either 35% or -35%. The choice of the set of assets by the firm is unobservable to outsiders, and thereby non-contractable. The firm chooses the set of assets to maximize the value of equity. This objective is known to outsiders, Redo part (a). 4. (30%) Consider a firm whose current marker value is $150 at the beginning of the first period. The firm lasts for two periods. The rate of return on the firm's assets over each period is equally likely to be either 20% or -20%. The risk-free rate is 5% in each period. If any cash payout, coupon and/or dividend, is made at the end of the first period, then the ex-payout firm value will change by either 20% or -20% over the second period. There are no taxes and bankruptcy costs. (a) At the beginning of the first period, the firm issues a coupon bond and pays out the proceeds as dividends to shareholders. The bond has a face value of $100 and a per-period coupon rate of 6% to be matured at the end of the second period. The firm pays no dividends at the end of the first period. What is the market value of the bond at the beginning of the first period? (b) Consider now that the firm can choose between two sets of assets with the same initial value of $150. The first set of assets is as described above, which has the rate of return over each period equally likely to be either 20% or -20%. The second set of assets, on the other hand, has the rate of return over each period equally likely to be either 35% or -35%. The choice of the set of assets by the firm is unobservable to outsiders, and thereby non-contractable. The firm chooses the set of assets to maximize the value of equity. This objective is known to outsiders, Redo part (a)