Final answer:
To find the dividend amount X for Company A's stock, we must use the dividend discount model and consider the present value of the known future dividends and solve for X in the perpetuity formula. The stock price reflects the sum of discounted dividends, and by applying the 10% required rate of return, we can derive the unknown dividend X.
Step-by-step explanation:
The question revolves around valuing a stock from Company A based on its future dividend payments and the required rate of return by investors, using a dividend discount model. Since Company A's stock is trading at $30 and is set to pay dividends of $2 in year 1, $3 in year 2, and an unknown amount X thereafter, we need to find the present value of these future payments based on a 10% required rate of return. To find the value of X that would make the present value of these dividends equal to $30, we need to consider the price as the sum of the present value of dividends for year 1 and 2, plus the present value of the perpetual dividends from year 3 onwards (also known as a perpetuity).
The calculation involves first finding the present value of the first two dividends, and then solving for X using the formula for a perpetuity, which is the dividend amount divided by the required rate of return (X / 0.10). After discounting the future dividends back to their present value, we must set the sum equal to $30 and solve for X. The exact formulae and calculations would need to be provided to give a complete answer.