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?

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Answer:

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

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