Nonconstant Dividends – Bucksnort, Inc., has an odd dividend policy. The company has just paid a dividend of $10 per share and has announced that it will increase the dividend by $3 per share for each of the next five years, and then never pay another dividend. If you require an 11 percent return on the company’s stock, how much will you pay for a share today?
P0 = $13 /1.11 + $16/1.112 + $19/1.113 + $22/1.114 +$25/1.115 = $67.92
Differential Growth – Hughes Co. is growing quickly. Dividends are expected to grow at a 25% rate for the next three years, with the growth rate falling off to a constant 7% thereafter. If the required return is 12% and the company just paid a $2.40 dividend, what is the current share price?
With differential dividends, we find the price of the stock when the dividend level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the differential growth period.
The stock begin constant growth in year 4, so we can find the price of the stock in year 3, one year before the constant dividend growth begins as:
P3 = D3 (1+g) (R – g) = D0 (1+g1)3 (1+g2)/ (R – g2) = $2.40 (1.25)3(1.07) / (0.12 – 0.07) = $100.31
The price of the stock today is the PV of the first three dividends, plus the PV of the year 3 stock price. The price of stock today will be:
P0 = $2.40 (1.25)/1.12 + $2.40 (1.25)2/1.122 +$2.40(1.25)3/1.123 +$100.31/1.123
P0 = $80.40
Reference: Chapter 9, Corporate Finance Book, Stephen A.Ross, Randolph W.Westerfield and Jeffrey Jaffe, Ninth Edition.
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