why does the dividend discount formula outcome differ from the current common stock price?

The Dividend Discount Model is just one of many approaches to evaluating a stock.  It is not fact.  You should not expect it to exactly explain the prices you observe in the market.

The model is a useful tool, but has many limitations:

- Many stocks do not pay a dividend.
- Companies pay dividends at very different percentages of earnings.
- Some companies buy back stock in lieu of paying dividends.
- The model works poorly on fast growing companies.
- Growth rates in the model are only estimates.
- Discount rates in the model are only estimates.
- Taxes matter.

Did you actually do a dividend discount valuation?  Usually people don't ask why is the DDM different from the stock price, they ask what is the discount rate I am supposed to use and what is the growth rate I am supposed to use.

The DDM is a metaphor and a teaching tool.  Ultimately the value of any investment is the discounted cash flows that come from that investment.  That means that the DDM is tautologically true - the only cash flows that come from a stock are dividends or a terminal value when you sell it so the value of the stock must be that given by the DDM.

However, when you actually try to apply the DDM you run into this problem - it's impossible to forecast growth of dividends accurately even for next year to say nothing of 3 or 5 years down the road and it is unclear what discount rate you should use (btw - if you blindly use CAPM and beta you get off Yahoo, you should know that CAPM isn't true and nobody thinks it's true, the beta from Yahoo is a poor predictor of beta over the next year to say nothing of 5 years from now, the risk-free rate is unknown and using the 10-yr Treasury as a proxy in the midst of massive Fed manipulation of interest rates is wrong, etc).  If you value a stock using DDM you should step back and look at what you did and see if any of it makes sense to you.  

The message then is that DDM is tautologically true but not very useful.  However, it does say that the keys to equity valuation are growth (for the dividend growth rate) and risk (for the discount rate).  Real equity analysis is then about deciding how much risk there is in future cash flows (and it's probably something like free cash flow to equity rather than dividends) and how much growth there is going to be in the company.