A7X Corp. just paid a dividend of $1.25 per share. The dividends are expected to grow at 40 percent for the next 9 years and then level off to a growth rate of 6 percent indefinitely. If the required return is 13 percent, what is the price of the stock today

Price of stock =$159.48

Explanation:

The value of a stock, using the dividend valuation model, is the Present value of its future cash flows discounted at the required rate of return.

We can apply this model as follows:

Step 1: PV of a growing annuity of 1.27 at a growing rate of 40%

PV = A/(r-g) × (1- (1+g/1+r)^n)

I will break out the formula into two parts to make the workings very clear to follow. So applying this formula, we can work out the present value of the growing annuity (winnings) as follows.  

PV = 1.27/(0.13-0.4)× (1- (1.4/1.13)^(9)= 27.211

Step 2 : Present value of growing perpetuity at a growing rate of 6%

PV = D×(1+r)/(r-g)

PV in year 9 terms = 1.27× 1.4^9× 1.06/(0.13-0.06)= 397.341

PV in year 0 terms =97.341× 1.13^(-9)= 132.26

Price of stock = 132.26 + 27.211 =159.48

Price of stock =$159.48