A 7X Corp. just paid a dividend of $2.30 per share. The dividend are expected to grow at 23 percent for the next eight years and then level off to a growth rate of 7 percent indefinitely. If the required return is 15 percent, what is the price of the stock today?

 Price of stock=$ 77.88

Explanation:

The Dividend Valuation Model is a technique used to value the worth of an asset. According to this model, the worth of an asset is the sum of the present values of its future cash flows discounted at the required rate of return.  

The price of the stock will the sum of the present value of the growing annuity and the growing perpetuity

Present value of dividend from year 1 to 8

The PV of the growing annuity = A/r-g) ( 1- (1+g)/(1+r)^n )  

A- dividend payable now , r- required of return, g-growth rate, number of years

PV =  (2.30×1.23)/(0.15-0.23)×   (1- (1.23/1.15)^8) = 25.199

PV of Dividend from year 9 and beyond:

P = D× g/(r-g)  

This will be done in two steps:

Step 1: PV(in year 8)of dividend = 2.30× 1.23^8×1.07/(0.15-0.07) = 161.16

Step 2 : PV in year 0 = 161.16× 1.15^(-8)= 52.684

PV of Dividend from year 9 and beyond =  52.684                                  

Price of stock = 25.19  + 52.68= 77.88

 Price of stock=$ 77.88

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