Question

Apex Co. stock just paid $1.00 dividend per share. The market expects that the dividend will grow at 2% annually forever. Assuming a required return of 8% p.a., how much is the value of the stock in two years? (round to 4 decimals)

Answer 1

The value of Apex Co. stock in two years, calculated using the Gordon Growth Model with a $1.00 dividend, 2% growth rate, and 8% required return, is $17.3400.

Step-by-step explanation:

The student is asking how to calculate the value of a stock in two years given its current dividend, growth rate of the dividend, and required return. To find the stock value in two years, we need to use the Gordon Growth Model (also known as the Dividend Discount Model), which calculates the present value of the expected future dividends that will grow at a constant rate.

The formula for the Gordon Growth Model is:

Value of Stock = D1 / (r - g)

Where D1 is the dividend in the next period (D0*(1+g)), 'r' is the required rate of return, and 'g' is the growth rate of the dividends.

First, we calculate the dividend that will be paid in two years:

D2 = D1 * (1+g)^2 = $1.00 * (1+0.02)^2

Next, we substitute this into the dividend discount model:

Value of Stock in two years = D2 / (r - g) = ($1.00*(1+0.02)^2) / (0.08 - 0.02)

Performing the calculation gives us:
Value of Stock in two years = ($1.00*(1.0404)) / (0.06) = $1.0404 / 0.06

The value of the stock in two years is:

Value of Stock in two years = $17.3400 (rounded to four decimals)