Crosby Inc. has an 11% required rate of return. It does not expect to initiate dividends for 20 years, at which it will pay $4.00 per share of dividends. At that time, Crosby expects its dividends will grow at 6% forever. What is an estimate of Crosby's price in 20 years (P20) if its dividend at the end of year 20 is $4.00?
84.80
To estimate Crosby Inc.'s price in 20 years (P20) based on its expected dividends, we can use the dividend discount model (DDM). The DDM calculates the present value of future dividends to determine the stock price.
In this case, we know that Crosby's dividend at the end of year 20 is expected to be $4.00. We also know that the required rate of return is 11% and the dividend growth rate is 6%.
To calculate P20 using the DDM formula, we need to determine the present value of the dividends. The formula is as follows:
P0 = D1 / (r - g)
Where:
P0 = Stock price today (present value)
D1 = Dividend at the end of year 20
r = Required rate of return
g = Dividend growth rate
Let's substitute the given values into the formula:
P0 = $4.00 / (0.11 - 0.06)
P0 = $4.00 / 0.05
P0 = $80.00
Therefore, an estimate of Crosby's price in 20 years (P20) if its dividend at the end of year 20 is $4.00 would be $80.00.