Question

You expect a stock to pay annual dividends of $1.78,$1.66, and $1.48 in each of the next three years, with the first dividend payment occurring one year from today. You also expect a stock price of $46.92 immediately after the stock pays the third annual dividend (i.e. exactly three years from today). If the stock's required rate of return is 14%. what is a fair price for the stock today? Round your answer to the nearest penny.

Answer 1

The fair price of the stock today, based on the expected future dividends and the stock price after the third dividend, discounted at a rate of return of 14%, is $37.16.

Step-by-step explanation:

To find a fair price for the stock today, we need to calculate the present value of the expected future cash flows from the dividends and the sale of the stock after the third dividend payment. This process involves discounting the future cash flows back to their value today using the given required rate of return of 14%.

The present value of each dividend is calculated as:

• Dividend 1: $1.78 / (1 + 0.14)1 = $1.56
• Dividend 2: $1.66 / (1 + 0.14)2 = $1.28
• Dividend 3: $1.48 / (1 + 0.14)3 = $1.05

The present value of the stock price immediately after the third dividend payment is:

$46.92 / (1 + 0.14)3 = $33.27

The fair price for the stock today is the sum of these present values:

$1.56 + $1.28 + $1.05 + $33.27 = $37.16
Therefore, rounded to the nearest penny, a fair price for the stock today is $37.16.