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# Time Warner: The Cost of Equity

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In the previous part of the SLP you considered the market value of the company's long and short term debt and the market value of your company's equity.

In this section of the Session Long Project you'll estimate the cost of equity or the rate of return that TIME WARNER'S shareholders 'require'. This is an important piece of information that every top manager must be able to estimate because it will be an important input in any effort to determine whether any particular course of action by the company will or will not add value to the shareholders.

We are going to use the Capital Asset Pricing Model (CAPM) in order to estimate the rate of return that our shareholders require on their investment. This is the minimum rate of return that these shareholders require. As stated above - we call this rate 'the cost of equity' and it is expressed in percentages or in a decimal format.

The CAPM states the following equilibrium relationship between the (excess) rate of return that shareholders of a particular company "j" require (or actually in some sense 'deserve' if they fully diversify their investments) and the (excess) expected rate of return on the market portfolio:
Rj - RF =j [RM - RF]

It follows that the rate of return that shareholders require or expect to earn on their investment in the shares of the company, or 'the cost of equity' is:
Rj = RF + j [RM - RF]

In order to estimate the cost of equity for TIME WARNER you need to obtain an estimate of the company's 'beta' or systematic risk coefficient, on the annual rate of return on a risk-free investment, and on the expected rate of return on the 'market portfolio'. You can easily find that information by going to the following web site: http://finance.yahoo.com and insert the name of your company. The beta of the company is reported on that web site.

1. Find out what is the present Yield to Maturity (YTM) on a US Government bond that matures in one year. That rate is the 'risk-free rate'.

2. It is customary to assume that the difference between the expected rate of return on the 'market portfolio' and the risk-free rate rate of return is about 7.0%. This is the expression [RM - RF] . So if for example the risk-free rate of interest is, say, 3% per year, than the expected rate of return on the 'market portfolio', RM, is 10%. So, multiply the 'beta' of your SLP Company by 7.0%. That will be the equivalent of your company's &#946;j [RM - RF] . Then add to that number the current yield to maturity on a US Government bond [see step (1) above].

3. The above procedure provides you with an estimate of the rate of return that the shareholders of TIME WARNER require on their investment. This rate is called the cost of equity of your company.
You'll be using this estimate in your SLP4.

4. The systematic risk coefficient or the beta of TIME WARNER is affected by the nature of the business, that is, by the extent to which the operating performance of the company is or is not closely related to the performance of the economy as a whole, and by the debt to equity ratio of the company, or the financial leverage. The relationship between the so-called 'equity beta' and the 'operating, or 'asset beta' of a company is expressed in the following equation:
A [1 + (1 - T) (D*/E*)] ,

Where is the equity beta, or the beta that you actually obtained by browsing for information on your company, A is the 'asset beta' or the systematic risk coefficient of the operating performance of the company, T is the tax rate (assume that the tax rate is 34%) and D* and E* are the market value of debt and of equity of your company (information you reported on in your Module 2 SLP report.)

You now have all the information to compute and to report on your company's 'asset beta'. The asset beta reflects the extent to which the company's business performance is related to the overall performance of the economy. Are you surprised by the 'asset beta' of your company? Explain.

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