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# Under Armour Cost of Equity- CAPM, DDM, APT

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Which of the three models (dividend growth, CAPM, or APT) is the best one for estimating the required rate of return (or discount rate) of Under Armour?

Explain the challenge of estimating or coming with a good feel for the "cost of equity capital" or the rate of return that you feel Under Armour investors require as the minimum rate of return that they expect of require Under Armour to earn on their investment in the shares of the company.

##### Solution Summary

The solution calculates the cost of equity for Under Armour using CAPM, DDM, Gordon Growth model, and APT.

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INTRODUCTION
The Capital Asset Pricing Model (CAPM) best serves the function of determining the cost of equity for Under Armour, Inc. Using CAPM calculations, at \$84.30 per share, Under Armour's target security price for December 2012 is \$89.32, (Reuters, 2011). If this security price becomes unrealistic within the year, then options to boost investor return through a dividend should be explored. While less accurate than arbitrage pricing theory (APT) and dividend growth models, CAPM's ease of use, and the isolation of Beta assumptions into a single variable best fit the current state of Under Armour's enterprise.
UNDER ARMOUR'S COST OF EQUITY
CAPM would calculate the current cost of equity at 5.96%:
RE= RF + Beta(RM - RF)
RE= 3.25% +1.53(5%-3.25%)
RE= 5.96%

CAPM VARIABLES AND ASSUMPTIONS
Expanding the above calculation from left to right, each variable introduces new assumptions, and becomes progressively more contentious. RF comprises the risk-free rate. In this case, the US Prime Rate is used (Wall Street Journal, 2011). While traditionally, RF would use a "zero coupon government bond matching the time horizon of the cash flow being analyzed," the time horizon for our consideration is flexible, (Damodaran, nd). Instead, the Prime Rate captures current aggregate market conditions and while admittedly it is an "index, not a law," it closely matches various government treasury bonds, considers current inflation risk, and is a function of the Federal Open Market Committee's target rate for federal funds (Wall Street Journal, 2011).
Next, and more contentious than RF, is Beta. Beta represents a "statistical analysis of past price movements of an individual stock (against) the market as a whole," (Investopedia, nd). In this calculation, 1.53 was used (Reuters, 2011). While Beta is purported to be a mathematical truth, the assumptions underpinning the concept are extremely fluid. For example, four separate sources were consulted for Under Armour Beta value-these returned four distinct values ranging from .99 to 1.53 (Google Finance, Fidelity, Yahoo Finance, Reuters). The Reuters value was settled on based solely on the reputation of the source. The variance between these Beta values could be due to how each defined the "market as a whole." Just to scratch the surface, they could use: S&P 500 index, Wilshire 5000 index, Dow Jones Total Market Index, or any other infinite number of attempts to capture "the market." This, of course, also assumes that "the market" is comprised solely of the stock market- which further assumes that such stock market is limited to domestic securities of similar risk-adjusted expectations as the target security. In any case, Beta is a powerful variable used in CAPM, with results highly dependent on its selection. ...

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