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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.

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  • $\begingroup$ 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 $\endgroup$
    – Jake Nagel
    Commented Mar 31, 2014 at 1:29
  • $\begingroup$ On this site, \$...\$ is used to enter nicely typeset mathematics, not to represent the dollar sign symbol. To represent dollar signs, type \$. $\endgroup$ Commented Mar 31, 2014 at 1:32
  • $\begingroup$ This question is about finance and finance-specific formulae, not mathematics, so this is not quite the right place to ask. $\endgroup$
    – Newb
    Commented Mar 31, 2014 at 1:32

1 Answer 1

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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)

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