Predictable Corp has increased its annual dividend each year of its life by 2% (and will continue to do so indefinitely). If Predictable paidits annual dividend yesterday of $8 and the required return is currently 4%, then by what amount will the stock price decrease by if the required return increases to 5%.
To calculate the decrease in stock price, we can use the Gordon Growth Model, which states that the stock price is equal to the dividend divided by the difference between the required return and the dividend growth rate.
Let's first calculate the initial stock price using the current required return of 4% and the annual dividend of $8. According to the Gordon Growth Model:
Stock Price = Dividend / (Required Return - Dividend Growth Rate)
Stock Price = $8 / (0.04 - 0.02) = $8 / 0.02 = $400
Therefore, the initial stock price is $400.
Now, let's calculate the decrease in stock price if the required return increases to 5%:
Stock Price (new) = Dividend / (Required Return (new) - Dividend Growth Rate)
Stock Price (new) = $8 / (0.05 - 0.02) = $8 / 0.03 = $266.67
Therefore, if the required return increases to 5%, the stock price will decrease by $400 - $266.67 = $133.33.