A firm just paid a dividend of $3.34. The dividend is expected to grow at a constant rate of 3.30% forever and the required rate of return is 12.24%. What is the value of the stock?

Answer 1

To find the value of a stock that pays dividends growing at a constant rate, you can use the Gordon Growth Model (also known as the Dividend Discount Model). The formula is:

$$P=\frac{D_1}{r-g}$$

Where:

• $P$ = Price of the stock
• $D_1$ = Dividend in the next period
• $r$ = Required rate of return
• $g$ = Growth rate of the dividend

Given that the firm just paid a dividend ($D_0$) of $3.34 and that it is expected to grow at a constant rate of 3.30% forever, we first need to find $D_1$:

$$D_1=D_0\times (1+g)=3.34\times (1+0.033)=3.34\times 1.033=3.45$$

Now we can use the required rate of return ($r=12.24$) and the growth rate ($g=3.30$) to find the stock price ($P$):

$$P=\frac{D_1}{r-g}=\frac{3.45}{0.1224-0.033}=\frac{3.45}{0.0894}$$

Calculating the denominator:

$$0.1224-0.033=0.0894$$

Now calculating the final stock price:

$$P\approx \frac{3.45}{0.0894}\approx 38.63$$

So, the value of the stock is approximately $38.63.