ABC Inc., will pay no dividends over the next 13 years because the firm needs to retain its earnings for growth purposes. The company will pay a $6 per share dividend in 14 years and will increase the dividend by 4 percent per year thereafter.
If the required return on this stock is 9 percent, what is the current (t=0) share price?
No dividends will be paid on the stock over the next 13 years.Once the stock begins paying dividends, it will have a constant growth rate of dividends.
The general constant dividend growth formula is:
Pt = [Dt × (1 + g)] / (R − g)
We will use the dividend in Year 14 to find the stock price in Year 13.
P13 = D14 / (R − g) = $6 / (0.09 - 0.04) = $120
The price of the stock today is simply the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be:
P0 = $120 / 1.09^13 = $39.14
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