Prock Petroleum's stock has a required return of 13%,and the stock sells for $50 per share.The firm just paid a dividend of $1.00,and the dividend is expected to grow by 30% per year for the next 4 years,so D₄ = $1.00(1.30) ⁴ = $2.8561.After t = 4,the dividend is expected to grow at a constant rate of X% per year forever.What is the stock's expected constant growth rate after t = 4,i.e.,what is X?

A) 7.46%
B) 7.85%
C) 8.26%
D) 8.70%

The stock's price can be calculated using the dividend discount model for a stock that has a period of non-constant growth followed by perpetual constant growth. The formula for the price of the stock today (P0) is the present value of dividends during the non-constant growth period plus the present value of the stock price at the time when constant growth begins (P4), calculated as the dividend in year 5 (D5) divided by the required return minus the constant growth rate (r - g), all discounted back to the present.Given:- P0 = $50- D0 = $1.00- Growth for the first 4 years = 30%- Required return (r) = 13%First, calculate the dividends for the first 4 years and their present values:- D1 = D0 * 1.30 = $1.30- D2 = D1 * 1.30 = $1.69- D3 = D2 * 1.30 = $2.20- D4 = D3 * 1.30 = $2.86The present value of these dividends is calculated using the required return to discount them back to the present.Next, calculate the price of the stock at the end of year 4 (P4), which is based on the dividend in year 5 (D5). D5 is D4 grown by the constant rate (X%), but since we're solving for X, we express D5 in terms of D4 and X.The formula for P0 incorporates the present value of dividends for the first 4 years and the present value of P4. Rearrange this formula to solve for X, the constant growth rate after year 4.Given the complexity of the calculation and the need for numerical methods or trial and error to solve for X directly from the information provided, the correct answer is determined by applying financial formulas or a financial calculator to find the growth rate that matches the given stock price and dividend growth conditions. The correct constant growth rate after year 4, given the stock price and the required return, is 8.70%.