Question

# Storico Co. just paid a dividend of \$3.15 per share. The company will increase its dividend...

Storico Co. just paid a dividend of \$3.15 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 12 percent, what will a share of stock sell for today?

Here we have a stock with supernormal growth, but the dividend growth changes every year for the first four years. 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 = \$3.15(1.20)(1.15)(1.10)(1.05) / (.12 – .05) = \$71.73

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 = \$3.15(1.20)/(1.12) + \$3.15(1.20)(1.15)/1.122 + \$3.15(1.20)(1.15)(1.10)/1.123 + \$71.73/1.123

P0 = \$61.30