# Gremlins are investing in stock

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.

• It accidently got edited weird, sorry. It supposed to state that the stock will grow by 4% each year. Also, that the current price is 22.40 per share Mar 31, 2014 at 1:29
• On this site, \$...\$ is used to enter nicely typeset mathematics, not to represent the dollar sign symbol. To represent dollar signs, type \\$. Mar 31, 2014 at 1:32
• This question is about finance and finance-specific formulae, not mathematics, so this is not quite the right place to ask.
– Newb
Mar 31, 2014 at 1:32

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)