Proof The company has 5,000 shares outstanding and the stock price is $140.The company is expected to pay a dividend of $20 per share next year and thereafter the dividend is expected to grow indefinitely by 5%a year.The president now makes a surprise announcement:the company will henceforth distribute half the cash in the form of dividends and remainder will be used to repurchase stock.What is the expected stream of dividends per share for an investor who plans to retain his shares rather than sell them back?Is there any change in its present value? slide 15
slide 15 Proof The company has 5,000 shares outstanding and the stock price is $140. The company is expected to pay a dividend of $20 per share next year and thereafter the dividend is expected to grow indefinitely by 5% a year. The president now makes a surprise announcement: the company will henceforth distribute half the cash in the form of dividends and remainder will be used to repurchase stock. What is the expected stream of dividends per share for an investor who plans to retain his shares rather than sell them back? Is there any change in its present value?
Answer r=DiV1/Po+g=20/140+0.05=19.29% P1=140*(1+19.29%)=167 Shares that will be repurchased =5000*10/167=299(6%) Div1=5000*10/(5000-299)=10.64 P2=P1*(1+r1)=P1*(1+DiV2/P1+g) =167*(1+(10.64*1.05)/167+0.05)=186.5 Shares that will be repurchased 281.5(6%) Div2=50000*(1+5%)/(5000-299-281)=11.88 slide 16
slide 16 Answer r = Div1/P0 + g = 20/140 + 0.05 =19.29% P1 = 140 *(1+19.29%) = 167 Shares that will be repurchased = 5000*10/167=299 (6%) Div1 = 5000*10/ (5000-299)=10.64 P2 = P1*(1+r1)=P1*(1+Div2/P1+g) =167*(1+ (10.64*1.05)/167+0.05) =186.5 Shares that will be repurchased = 281.5 (6%) Div2 = 50000*(1+5%)/(5000-299-281)=11.88
Answer -The earning will increase =5%per year. The number of share will decrease =I/[PO*(1+g)+Div1]6%per year ■The g will be(1+5%)/(1-6%)=11.7% ■PV=10.64/(19.3%-11.7%)=140 Conclusion:there is no difference between two alternatives. slide 17
slide 17 Answer The earning will increase =5% per year. The number of share will decrease =I/[P0*(1+g)+Div1] = 6% per year The g will be (1+5%)/(1-6%) =11.7% PV = 10.64/ (19.3% - 11.7%) = 140 Conclusion: there is no difference between two alternatives
Price Behavior around the Ex-Dividend Date In a perfect world,the stock price will fall by the amount of the dividend on the ex-dividend date. -t ·-2 +1 +2 SP 十十 The price drops Ex-dividend by the amount of Date the cash Taxes complicate things a bit.Empirically, dividend the price drop is less than the dividend and occurs within the first few minutes of the ex-date. slide 18
slide 18 Price Behavior around the Ex Price Behavior around the Ex -Dividend Date Dividend Date In a perfect world, the stock price will fall by the amount of the dividend on the ex-dividend date. $ P $P - div Ex-dividend Date The price drops by the amount of the cash dividend - t … -2 -1 0 +1 +2 … Taxes complicate things a bit. Empirically, the price drop is less than the dividend and occurs within the first few minutes of the ex-date