And the firms cost of capital remains unchanged the

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and the firm’s cost of capital remains unchanged. The required return on common stock is now . 30 . 0 ) 10 . 0 20 . 0 ( 1 20 . 0 D A L L A E r r E D r r Thus, the stockholders perceive higher financial risk and demand compensation for bearing that risk. (c) (i) The value of the unlevered firm will change when we introduce corporate taxes. The after-tax cash flows generated by the assets of the firm will now be . 800 , 1 000 , 3 ) 4 . 0 1 ( ) 1 ( X t c Thus, the value of the unlevered firm is . 000 , 9 20 . 0 800 , 1 ) 1 ( E c U r X t V The value of the levered firm is then . 000 , 12 ) 500 , 7 ( 4 . 0 000 , 9 L c U L D t V V (ii) The value of debt remains at . 500 , 7 L D (iii) The value of the equity is now . 500 , 4 500 , 7 000 , 12 L L L D V E (iv) We have 500 , 4 ) 000 , 1 ( L E P n and 500 , 7 L D nP . We can then
solve for n = 625 and P = 12. (v) The required rate of return on equity is again . 30 . 0 500 , 4 ) 750 000 , 3 )( 4 . 0 1 ( ) )( 1 ( L L D c E E D r X t r (vi) However, the weighted average cost of capital for the firm is now . 15 . 0 000 , 12 000 , 3 ) 4 . 0 1 ( ) 1 ( L c L V X t WACC Notice that alternatively L L E L L D c L V E r V D r t WACC ) 1 ( . 15 . 0 000 , 12 500 , 4 ) 3 . 0 ( 000 , 12 500 , 7 ) 10 . 0 )( 4 . 0 1 ( Bankru ptcy risks would reduce the amount by which the firm’s value would increase due to leverage and would increase the average cost of capital.
Problem Set #8 1. The net income of Novis Corporation, which has 10,000 outstanding shares and a 100% payout policy, is $32,000 today. The expected value of the firm one year hence is $1,545,600. The appropriate discount rate for Novis is 12%. (a) What is the current value of the firm? (b) What is the ex- dividend price of Novis’ stock if the board follows its current dividend policy? (c) At the dividend declaration meeting, several board members claimed that the dividend is too meager and is probably depressing Novis’ stock price. They propose that Novis sell enough new shares to finance a $4.25 dividend. (i) Comment on the claim that the low dividend is depressing the stock price. Support your argument with calculations. (ii) If the proposal is adopted, at what price will the new shares sell and how many will be sold? Answer: (a) The value of the firm is the present value of its dividends and future value: . 000 , 412 , 1 12 . 1 600 , 545 , 1 000 , 32 0 V (b) Before the dividend is paid, each share is worth . 20 . 141 000 , 10 000 , 412 , 1 0 P After the dividend is paid, the shares will be worth . 00 . 138 000 , 10 12 . 1 / 600 , 545 , 1 ' 0 P Notice that the difference between 0 P and 0 P is the dividend per share, 32 , 000 / 10 , 000 = 3 . 20. (c) (i) According to Modigliani and Miller, it cannot be true that the low dividend is depressing the price. In fact, since the dividend policy is irrelevant, the level of the dividend should not matter: any funds not distributed as dividends add to the value of the firm through the stock price (capital gains). These directors merely want to change the timing of the dividends (more now, less in the future). As shown below, the current shareholders’ wealth is unaffected by this dividend increase, i.e. the shareholders are not made better off. To pay the $4.25 dividend per share (for a total dividend of $42,500), new shares must be sold. These new shares must have a value of $10,500 ($42 , 500 - $32 , '

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