Question

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?

Answer 1

Answer:

$61.29

Explanation:

Calculation for what Storico Co. Share of stock will sell today.

Since we have a stock that has a normal growth in which the dividend growth changes every year for the first four years. We can therefore find the price of the stock in Year 3 because the dividend growth rate is constant after the third dividend, which means the price of the stock in Year 3 will be the dividend we are going to use in Year 4, we shall then divide it by the required return less the constant dividend growth rate.

Therefore the price in Year 3 will be calculated as :

P3= $3.15(1.20)(1.15)(1.10)(1.05) / (.12 – .05)

P3= $5.020785/0.07

P3=$71.72

Let find the price of stock today using the PV of the first three dividends in addition with the PV of the stock price in Year 3:

Hence,

P0= $3.15(1.20)/(1.12) + $3.15(1.20)(1.15)/1.12^²+ $3.15(1.20)(1.15)(1.10)/1.12^³+ $71.72/1.12^³

P0=$3.78/1.12+$4.347/1.2544+$4.7817/1.404928+$71.72/1.404928

P0=$3.375+3.465+3.4035+$51.048

P0= $61.29

Therefore if the required return on the company’s stock is 12% what the share of stock will sell for today will be $61.29