Gremlin Industries will pay a dividend of \$1.80 per share this year. It is expected that this dividend will grow by 4% each year in the future. The current price of gremlins stock is \$22.40 per share. What is Gremlin's equity cost of capital?
The answer is 12% percent but I cannot figure out why. The problem is missing certain pieces of information that I need for each formula I use.
Suppose $i$ is Gremlin's equity cost of capital. Then, based on the Dividend Discount Model, the price of the stock can be constructed as follows: $$22.40 = 1.80(1+i)^{-1}+1.80(1.04)(1+i)^{-2}+...$$
This is an infinite geometric series with first term $1.80(1+i)^{-1}$ and common ratio $(1.04)(1+i)^{-1}$ and can be represented by: $$22.40 = 1.80(1+i)^{-1}\frac{1}{1-(1.04)(1+i)^{-1}}$$ or $$22.40=1.80\frac{1}{1+i-1.04}$$
Solving, $i=0.12$ (rounded)