Question

JC Inc will pay dividends of $6.78 exactly one year from today and $6.86 exactly two years from today. After the second dividend, future dividends will grow at a constant rate of 7% per year indefinitely. Using a discount rate of 13.3%, estimate a fair price for JC's stock. Round your answer to the nearest penny.

Answer 1

To calculate JC Inc's stock price, the Gordon Growth Model was used with the first two dividends discounted individually and the perpetuity formula applied for subsequent dividends growing at 7%. The resulting fair stock price is $106.76.

Step-by-step explanation:

To estimate a fair price for JC's stock using the given dividend payments and growth rates, we need to use the Gordon Growth Model (also known as the Dividend Discount Model). The formula to calculate the price of a stock with constant dividend growth starting after a certain period is:

PV = D1 / (1 + r) + D2 / (1 + r)2 + D3 / (r - g) * (1 + r)-2

Where:

• PV is the present value of the stock.
• D1 and D2 are the dividends paid after one year and two years respectively.
• r is the discount rate.
• g is the constant growth rate of dividends after the second year.
• D3 is the dividend expected after the second year, calculated from D2.

Using the given information, we calculate the fair price as follows:

PV = $6.78 / (1 + 0.133) + $6.86 / (1 + 0.133)2 + ($6.86 * (1 + 0.07)) / (0.133 - 0.07) * (1 + 0.133)-2

Solving this, we find that the fair price of JC's stock is approximately $106.76, rounding to the nearest penny.