Cost of Equity Capital & the CAPM

I need assistance with the following assignment:

Review the background material on the capital asset pricing model and the material on the dividend growth model (of Module 2). Both models provide some insights and tools to estimate the rate of return that investors in our company 'require' in the sense that if they don't see the possibility that they'll earn that rate of return they'll sell the shares and that of course will lower the market price per share.

Both models use a set of assumptions that are not necessarily tenable.

You are asked by your board of directors to write a report explaining the challenge of estimating or coming with a good 'feel' for the "cost of equity capital" or the rate of return that you feel your company investors require as the minimum rate of return that that expect of require your company to earn on their investment in the shares of the company. Note that the investment is not the amount shareholders spent buying the share of the company in the past. The true investment is in terms of today's share prices because shareholders COULD have sold their shares today, and if they decided to hang on to these shares instead of selling these shares off this is their true investment in the shares of the company as of today. (This is the correct concept of the opportunity cost to the investors or the shareholders.)

Write a report to the board of directors of KMART regarding the following issues:

(1) In estimating the rate of return required by the shareholders on their investments in the company's equity one approach is to use the dividend growth model. Explain the assumptions that are necessary for using the dividend growth model, how you would estimate the cost of equity or the required rate of return by the shareholders of a company using that model, and then briefly state and defend your position as to whether the model is appropriate for your SLP Company's use.

(2) An alternative, more sophisticated approach is to use the CAPM. Explain and state the assumptions used in the CAPM and how you would estimate the cost of equity of the required rate of return by the shareholders of a company using that CAPM.

(3) How the CAPM is related to the so-called 'modern portfolio theory'.

And here's a challenge: suppose you try to estimate the cost of equity of a company that is not traded on any stock exchange. How would you go about estimating its cost of equity or the required rate of return by the shareholders of that company. (Hint: Read question (4) - the 'optional question' of the Session Long Project of this Module before you answer this question).

The report should be three to four pages in length. Be sure to include a reference list.

References:
http://www.investopedia.com/terms/g/gordongrowthmodel.asp

http://www.investopedia.com/university/concepts/concepts8.asp

Thanks in advance for your time and assistance!!