To find the value of a stock that pays dividends growing at a constant rate, we can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula for the value of the stock \( P_0 \) is given by:
\[ P_0 = \frac{D_0 \times (1 + g)}{r - g} \]
where:
- \( D_0 \) = the most recent dividend paid ($1.26)
- \( g \) = the growth rate of the dividend (4.64% or 0.0464)
- \( r \) = the required rate of return (13.75% or 0.1375)
First, we calculate the expected dividend next year \( D_1 \):
\[ D_1 = D_0 \times (1 + g) = 1.26 \times (1 + 0.0464) \] \[ D_1 = 1.26 \times 1.0464 \approx 1.320384 \]
Now we can plug \( D_1 \), \( r \), and \( g \) into the Gordon Growth Model formula:
\[ P_0 = \frac{D_1}{r - g} = \frac{1.320384}{0.1375 - 0.0464} \] \[ P_0 = \frac{1.320384}{0.0911} \approx 14.482 \]
Thus, the estimated value of the stock is approximately $14.48.