Storico Co. just paid a dividend of $2.00 per share. The company will increase its dividend by 20 percent next year and then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on the company's stock is 17 percent, what will a share of stock sell for today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be:
P3 = $2.00(1.20)(1.15)(1.10)(1.05) / (.17 – .05) = $26.565
The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so:
P0 = $2.00(1.20)/(1.17) + $2.00(1.20)(1.15)/1.17^2 + $2.00(1.20)(1.15)(1.10)/1.17^3 + $26.565/1.17^3
P0 = $22.55
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