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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.

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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. ...

#### Solution Summary

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

\$2.19

## Choose the best method for estimating cost of equity

The cost of equity capital and the CAPM

Part I

The cost of equity capital for a company is the rate of return on investment required by the company's shareholders. The rate of return consists of both the dividends and capital gains (e.g., an increase in the share price). The rates of return are expected future returns, not historical returns. Therefore, the returns on equity can be expressed as the anticipated dividends on the shares every year in perpetuity. Thus, the cost of equity is the cost of capital which will equate the current market price of the share with the discounted value of all future dividends in perpetuity.

To complete Part I, please review the background material on the capital asset pricing model, the material on the dividend growth model, and arbitrage pricing theory. These models provide some insights and tools to estimate the rate of return that investors in our company â??requireâ? in the sense that if they don't see the possibility that they will earn that rate of return they will sell the shares and that of course will lower the market price per share.

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

You are asked by your board of directors to explain the challenge of estimating or coming with a good â??feelâ? 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.

A report for the board of directors on 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 JetBlue Airlines? Based on your analysis and findings, what would you recommend to the board of directors of JetBlue Airlines?

Discussion of the following issues:

1. Ease of use of these three models

2. Accuracy of each of these three models

3. How realistic the assumptions of each model are

Part II

The cost of equity (discount rate) can also be determined by using the Capital Asset Pricing Model (CAPM). Calculating the cost of equity using CAPM model is often more difficult than using the dividend discount model. The companiesâ?? financial statements do not show the cost of equity.

The following table shows necessary (hypothetical) information to calculate the cost of equity by using CAPM model:

Company
Listing
RRF
RM
Ã?j

Nike Inc.
NYSE: NKE
1%
4.49%
0.91

Sony Corporation
NYSE: SNE
1%
6.83%
1.48

McDonaldâ??s Corporation
NYSE: MCD
1%
2.94%
0.36

E(rj )= RRF + b(RM - RRF)

E(rj ) - The cost of equity

RRF - Risk free rate of return)

Ã?j - Beta of the security

RM - Return on market portfolio)

Based on the above information, which company has higher cost of equity? Why?

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