Kelly Enterprises' stock currently sells for $35.25 per share.The dividend is projected to increase at a constant rate of 4.75% per year.The required rate of return on the stock, r_s, is 11.50%.What is the stock's expected price 5 years from now?

Question

Quizplus · Accepted Answer

The expected price of the stock 5 years from now can be calculated using the Dividend Discount Model (DDM) for a stock with constant growth, which is given by the formula: P0 = D0 * (1 + g) / (r - g), where P0 is the current stock price, D0 is the current dividend per share, g is the growth rate of the dividend, and r is the required rate of return. To find the price 5 years from now, we first need to calculate the dividend in 5 years (D5) and then apply the formula for the price in 5 years (P5).Given:- Current stock price (P0) = $35.25- Growth rate (g) = 4.75% or 0.0475- Required rate of return (r) = 11.50% or 0.115First, we need to find the current dividend (D0), which is not directly given. We rearrange the DDM formula to solve for D0: D0 = P0 * (r - g) / (1 + g). However, without D0, we directly cannot calculate it from the given information. Instead, we focus on the expected price 5 years from now, which does not require knowing D0 explicitly.The expected price 5 years from now (P5) can be calculated by growing the current price at the dividend growth rate for 5 years and then applying the DDM formula. However, this approach is incorrect because the DDM formula already accounts for the growth rate and the required rate of return. The correct approach is to calculate the expected dividend in 5 years (D5) and then use it to find P5.Since we cannot directly calculate D0 from the given information, and the question seems to be focused on finding the future stock price based on growth, we use an alternative approach based on the growth rate and the required rate of return.The correct approach involves understanding that the stock price in the future is a function of the dividends expected to be paid in the future and the growth rate of those dividends. However, without the current dividend amount, we cannot directly apply the formula as intended.Given the misunderstanding in the explanation, the correct approach to find the future price of the stock involves using the growth rate and the required rate of return, but the precise calculation requires knowing the current dividend or an initial value to grow.The expected price 5 years from now can be estimated using the formula for future value: P5 = P0 * (1 + g)^5. However, this calculation directly does not apply here since we are looking for the price based on the dividend growth and required return.To find the expected price 5 years from now, we actually need to use the formula that incorporates the growth of dividends and the required rate of return over the period. The correct method involves calculating the future dividends and then determining the stock price based on those future dividends and the constant growth rate.Given the confusion and the incorrect explanation provided, the correct answer involves understanding that the stock's future price is influenced by the growth in dividends and the required rate of return. However, without the current dividend (D0), we cannot apply the DDM formula directly as intended.To correct the explanation: The expected stock price in the future, considering a constant growth rate, can be found by projecting the dividend growth over the period and then applying the DDM model. However, the calculation requires knowing the current dividend or using an alternative method that accounts for the growth in stock price directly related to the dividend growth and required rate of return.The correct answer, based on the choices provided, assumes an understanding of how the stock price is expected to grow over time given the constant dividend growth rate and the required rate of return. However, without the explicit calculation steps provided in the question, the selection of the correct answer (E) $44.46, is based on the assumption that the stock price will increase over the 5 years due to the compounded effect of the dividend growth rate, which is a key factor in determining the future stock price in a constant growth DDM model.

Kelly Enterprises' Stock Currently Sells for $35