New Gadgets, Inc., currently pays no dividend but is expected to pay its first annual dividend of $5.30 per share exactly 9 years from today. After that, the dividends are expected to grow at 3.9 percent forever. If the required return is 12.1 percent, what is the price of the stock today?

The multiple choices are:

$64.63 '

$23.12

$30.24

$47.59

$25.92

The correct option is $25.92

Explanation:

The price of the stock today is the present of dividend of $5.30 payable in nine years' time and present value of the dividend terminal value:

present of dividend=dividend/discount factor

where discount factor=(1+r)^n

r is the required rate of return of 12.1%

n is the number of years which is 9

present value of dividend=$5.30/(1+12.1%)^9=$ 1.90  

Terminal value=dividend*(1+g)/(r-g)

g is the dividend growth rate of 3.9%

r is the required return of 12.1%

terminal value=$5.3*(1+3.9%)/(12.1%-3.9%)=$ 67.15  

Present value of terminal value=$ 67.15/(1+12.1%)^9=$ 24.02  

Sum of both present values=$ 24.02 +$1.90=$25.92