One of the starkest contrasts in finance is found in comparing the elegance of capital-asset pricing theory with the coarseness of its application. Although the capital-asset pricing model (CAPM) is well understood, the theory says nothing about which risk-free rates, market premia, and betas to use in the model. Possibilities abound, and any sampling of academicians and practitioners will summon up many combinations and permutations of methods. Rather than use all approaches, these notes cling to two:

Short-term risk-free rate and arithmetic market premium: The argument for this approach is that short-term rates are the best proxy for riskless rates: as obligations of the U.S. (or other) government, short-term rates are the closest to being default-risk free. As short-term rates, they suffer little risk of illiquidity or capital loss because of sudden rises in market yields. For the purposes of these notes, “short term” is defined as 90 to 360 days. The corresponding market premium used is the arithmetic average premium estimated over the long term (e.g., 1926 to the date of the case). For the period through 1992, this average was estimated to be 8.6 percent.2 If there is a bias in academia and in practice, it is toward the arithmetic premium, because, when compounded over many periods, an arithmetic mean return is the one that gives the expected value (i.e., mean) of the probability distribution of expected ending values.

Long-term risk-free rate and geometric-mean market premium: Partisans of the long-term risk-free rate argue that most corporate investments are for the long term and that the long rate better matches the term of the asset being valued. According to this view, investors want to earn a market-risk premium equal to the compound rate of return (over time) that the stock market has earned over and above returns on long-term bonds. For the purposes of these notes, “long term” is...

...Pricing Model (CAPM) and Arbitrage Pricing Theory (APT).
The board of directors for Apple Computer Corporation will receive this report, and based on the findings and analysis included, Apple will be given a recommendation as to the costequity model they should implement to estimate their future rate of returns.
This report will discuss the accuracy and ease of use of these three models. The main consideration will be determined by how realistic each model is at developing the assumed rate of return.
Part 2 of this paper will discuss the cost of equity or discount rate based on hypothetical data to be calculated using the CAPM model. Considering the information presented, the cost of equity for each company will be explained and what factors influence company beta.
I will explain how to apply dividend growth when estimating the cost of equity of stable companies. I will show my understanding of APT and how it relates to CAPM and dividend growth, while also applying CAPM to estimate the rate of return that a company’s investors require.
In conclusion I will reiterate what I perceive to have learnt as well as give my evaluation of the module 3 case assignment.
Part I
Report to Apple Board of Directors
Apple stock has been extremely stable with a beta of .74 and that number has...

...
Equity
In accounting and finance, equity is the residual value or interest of the most junior class of investors in assets, after all liabilities are paid; if liability exceeds assets, negative equity exists. In an accounting context, shareholders' equity (or stockholders' equity, shareholders' funds, shareholders' capital or similar terms) represents the remaining interest in the assets of a company, spread among individual shareholders of common or preferred stock; a negative shareholders' equity is often referred to as a positive shareholders' deficit. At the very start of a business, owners put some funding into the business to finance operations. This creates a liability on the business in the shape of capital as the business is a separate entity from its owners. Businesses can be considered, for accounting purposes, sums of liabilities and assets; this is the accounting equation. After liabilities have been accounted for, the positive remainder is deemed the owners' interest in the business. This definition is helpful in understanding the liquidation process in case of bankruptcy. At first, all the secured creditors are paid against proceeds from assets. Afterwards, a series of creditors, ranked in priority sequence, have the next claim/right on the residual proceeds. Ownership equity is the last or residual claim against assets, paid only after all...

...Cost of equity refers to a shareholder's required rate of return on an equity investment. It is the rate of return that could have been earned by putting the same money into a different investment with equal risk.
How It Works/Example:
The cost of equity is the rate of return required to persuade an investor to make a given equity investment.
In general, there are two ways to determinecost of equity.
First is the dividend growth model:
Cost of Equity = (Next Year's Annual Dividend / Current Stock Price) + Dividend Growth Rate
Second is the Capital Asset Pricing Model (CAPM):
ra = rf + Ba (rm-rf)
where:
rf = the rate of return on risk-free securities (typically Treasuries)
Ba = the beta of the investment in question
rm = the market's overall expected rate of return
Let's assume the following for Company XYZ:
Next year's dividend: $1
Current stock price: $10
Dividend growth rate: 3%
rf: 3%
Ba: 1.0
rm: 12%
Using the dividend growth model, we can calculate that Company XYZ's cost of capital is ($1 / $10 ) + 3% = 13%
UsingCAPM, we can calculate that Company XYZ's cost of capital is 3% + 1.0*(12% - 3%) = 12%
Why It Matters:
Cost of equity is a key component of stock valuation. Because an...

...CAPMCAPM provides a framework for measuring the systematic risk of an individual security and relate it to the systematic risk of a well-diversified portfolio. The risk of individual securities is measured by β (beta). Thus, the equation for security market line (SML) is:
E(Rj) = Rf + [E(Rm) – Rf] βj
(Equation 1)
Where E(Rj) is the expected return on security j, Rf the risk-free rate of interest, Rm the expected return on the market portfolio and βj the undiversifiable risk of security j. βj can be measured as follows:
βj = Cov (Rj, Rm)
Var (Rm)
= σj σm Cor jm
σ2 m
= σj Cor jm
σm
(Equation 2)
In terms of Equation 2, the undiversifiable (systematic) risk (βj) of a security is the product of its standard deviation (σj) and its correlation with the market portfolio divided by the market portfolio’s standard deviation. It can be noted that if a security is perfectly positively correlated with the market portfolio, then CML totally coincides with SML.
Equation 1 shows that the expected rate of return on a security is equal to a risk-free rate plus the risk-premium. The risk-premium equals to the difference between the expected market return and the risk-free rate multiplied by the security’s beta. The risk premium varies directly with systematic risk measured by beta.
The figure above illustrates the security market line. For a given amount of systematic risk (β), SML shows the...

...Model commonly known as CAPM defines the relationship between risk and the return for individual securities. CAPM was first published by William Sharpe in 1964. CAPM extended “Harry Markowitz’s portfolio theory” to include the notions of specific and systematic risk. CAPM is a very useful tool that has enabled financial analysts or the independent investors to evaluate the risk of a specific investment while at the same time setting a specific rate of return with respect to the amount of the risk of a portfolio or an individual investment. The CAPM method takes into consideration the factor of time and does not get wrapped up over by the systematic risk factors, which are rarely controlled. In this research paper, I will look at the implications of CAPM in the light of the recent development. I will start by attempting to explain and discuss the various assumptions of the CAPM. Secondly, I will discuss the main theories and moreover, the whole debate that is surrounding this area more specifically through the various critics of the CAPM assumptions.
When Sharpe (1964) and Lintner (1965) proposed CAPM, it was majorly seen as the leading tool in measuring and determining whether an investment will yield negative or positive return. The model attempts to expound the relationship between expected reward/return and the investment risk of very risky...

...pricing model (CAPM)
Using the Capital Asset Pricing Model, we need to keep three things in mind. 1 there is a basic reward for waiting, the risk free rate. 2 the greater the risk, the greater the expected reward. 3 there is a consisted trade off between risk and reward.
In finance, It is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. The security market line plots the results of the CAPM for all different risks (betas - a model that calculates the expected return of an asset based on its beta and expected market returns.)
Using the CAPM model and the following assumptions, we can compute the expected return of a stock in this CAPM example: if the risk-free rate is 3%, the beta (risk measure) of the stock is 2 and the expected market return over the period is 10%, the stock is expected to return 17%=(3%+2(10%-3%)).
Risk of a Portfolio
We all know that investments have risk, so it’s safe to assume that all stocks have risk as well? But did you know that there are different types of...

...|
Table of Contents
Cost of Capital 2
Value of Equity 2
Cost of Equity 2
CAPM Model 2
Dividend Growth Model 3
Value of Debt 3
Cost of Debt 4
WACC (Weighted Average Cost of Capital) 4
Comparison to Joanna Cohen’s Analysis 4
Financial Statement Analysis 5
Nike Inc. 5
Financial Ratios 6
Leverage Ratios 6
Efficiency Ratios 6
Liquidity Ratios 7
Profitability Ratios 7
Valuation Ratios 7
Conclusion 8
Appendix A – Ratio Calculation 9
Leverage Ratios 9
Efficiency Ratios 9
Liquidity Ratios 9
Profitability Ratios 10
Valuation Ratios 10
Cost of Capital
Value of Equity
Cohen's calculation considered the book values to calculate the proportion of equity for calculating the value of WACC which should only be done if the target or market values are not available. In order to determine a more realistic cost of equity, it is recommended to use the market value. The current market share price of Nike as of 2001 is $42.09 and there are 271.5 total shares outstanding.
Therefore the market value of equity is:
Current share price * Average shares outstanding: (42.09 * 271.5) = $11,427.44 million
This figure is much higher than the book value of $3,494.5 million that Cohen used to calculate the value of equity.
Cost of...

...CAPM
1 Calculate the expected return for A Industries which has a beta of 1.75 when the risk free rate is 0.03 and you expect the market return to be 0.11.
2 Calculate the expected return for B Services which has a beta of 0.83 when the risk free rate is 0.05 and you expect the market return to be 0.12.
3 Calculate the expected return for C Inc. which has a beta of 0.8 when the risk free rate is 0.04 and you expect the market return to be 0.12.
4 Calculate the expected return for D Industries which has a beta of 1.0 when the risk free rate is 0.03 and you expect the market return to be 0.13.
5 Calculate the expected return for E Services which has a beta of 1.5 when the risk free rate is 0.05 and you expect the market return to be 0.11.
6 Calculate the expected return for F Inc. which has a beta of 1.3 when the risk free rate is 0.06 and you expect the market return to be 0.125.
USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS
Rates of Return
Year RA Computer Market Index
1 13 17
2 9 15
3 -11 6
4 10 8
5 11 10
6 6 12
7 Compute the beta for RA Computer using the historic returns presented above.
8 Compute the correlation coefficient between RA Computer and the Market Index.
9 Compute the intercept of the characteristic line for RA Computer.
10 The equation of the characteristic line for RA is
11 If you expected return on the Market Index to be 12%, what would you expect the return on RA Computer to be?...

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