New Gadgets, Inc., currently pays no dividend but is expected to pay its first annual dividend of $4.90 per share exactly 7 years from today. After that, the dividends are expected to grow at 3.5 percent forever. If the required return is 11.3 percent, what is the price of the stock today

Price of stock today =$33.045

Explanation:

The price of a stock using the dividend valuation model is the present value of the the future dividend expected from the stock discounted at the required rate of return.  

This model would be applied as follows

PV  of the first dividend =

Dividend in year 7 ×  (1+r)^(-n)

r- 11.3%, n- 7

PV = 4.90× 1.113^(-7) = 2.315

Dividend in year 8 and beyond

PV (in year 7 terms) =4.90× 1.035/(0.113- 0.035)= 65.019

PV of dividend in year 0

=PV in year 7 × 1.113^(-7)

=65.019 × 1.113^(-7) = 30.73

Price of stock today =   2.315+ 30.73  = 33.045

Price of stock today =$33.045

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