# CAPM vs. DDM vs. APT

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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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INTRODUCTION

The Capital Asset Pricing Model (CAPM) best serves the function of determining the cost of equity Nike Inc, Sony Corporation, or McDonalds. Using CAPM calculations, at $6.58 per share, JetBlue's target security price for October 2011 is $7.46. If this security price becomes unrealistic within the year, then options to boost investor return through a dividend should be explored. (What better time than the New Year to revise expectations for the coming year?) 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 JetBlue's enterprise.

SPECFIC COMPANY COST OF EQUITY (Using Hypothetical Return Rates)

CAPM would calculate Nike's current cost of equity at 4.176%:

RE= RF + Beta(RM - RF)

RE= 1.00% + 0.91(4.49%-1.00%)

RE= 4.176%

This calculation is based on a variable market rate of return given as 4.49% and a risk free rate of 1.0%. Using a variable market rate of return may be appropriate in comparing companies assuming the market rate is risk-adjusted.

CAPM would calculate Sony's current cost of equity at 9.628%:

RE= RF + Beta(RM - RF)

RE= 1.00% + 1.48(6.83%-1.00%)

RE= 9.628%

CAPM would calculate McDonald Corporation current cost of equity at 1.698%:

RE= RF + Beta(RM - RF)

RE= 1.00% + 0.36(2.94%-1.00%)

RE= 1.698%

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, 2010). 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). 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, 2010).

Next, and more contentious than RF, is Beta. Beta represents a "statistical analysis of past price movments of an individual stock (against) the market as a whole," (Arman, J. & Biger, N. , (2008). In this calculation, 1.5 was used (NASDAQ, 2010). While Beta is purported to be a mathematical truth, the assumptions underpinning the concept are extremely fluid. Inevitable variation between Beta values exists due to how each defined the "market as a whole." Just to ...

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