# Business -- Corporate Finance A-Level Coursework

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for $19.77 Business -- Corporate Finance -- the Cost of Equity Capital and the CAPM

Estimating Required Rate of Return

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

a) Dividend Growth Model

The Dividend Growth Model is used to determine whether stock is a good or bad buy by calculating what the stock's value should be through a formula using the stock's dividend. The generic formula uses: the stock's current dividend payout per share per year; the dividend's growth per year, usually based on 5 years of growth; the required rate of return on investment to make the stock a good buy. Those 3 factors are used in a formula of: (current dividend x (1+ dividend growth))/(required return -- dividend growth). One well-known Dividend Growth Model is the Gordon Growth Model:

(Investopedia U.S., 2013)

In this formula: D = Anticipated dividend per share one year from now; k = Required rate of return for equity investor; G = Growth rate in dividends (in perpetuity). The formula is relatively easy to use, requiring a prospective investor to plug 3 numbers into a simple formula. Unfortunately, the accuracy of this model is questionable: it unrealistically assumes constant, eternal dividend growth; however, dividend growth is not constant and dividends can be cut. In addition, its reliance on constant growth means it should be used for mature companies with low -- to -- moderate growth rates; however, Facebook is a relatively young company with fluctuating growth rates. Consequently, the Dividend Growth Model is not the optimal model for estimating Facebook stock's required rate of return.

b) CAPM

The Capital Asset Pricing Model (CAPM) was developed by William Sharpe to calculate investment risk and return on investment so potential investors can determine whether an investment is worth the risk. Sharpe argued that there are two types of risk: unsystematic risk, which is risk specifically posed by a particular stock, is not governed by the general market and can be efficiently countered by diversifying one's stock portfolio; systematic risk, which is dependent on such market factors as interest rates, wars, recessions and depressions, and cannot be effectively countered through diversification. CAPM measures systematic risk. Believing that return on stock should equal the stock's cost of capital, Sharpe developed a theory based on the association between risk and anticipated return. The formula is: Here:

(Sharpe, 2013).

The "risk free rate is usually the yield on a 10-year government bond; then a premium demanded by investors to make the risk worthwhile is added; then the equity market premium is calculated by determining the anticipated whole market return minus the risk-free rate of return; then the equity risk premium is multiplied by "beta." "Beta" is a measure of a stock's volatility relative to other market stock: the subject stock's rise and fall in the market is compared to the rise and fall of other stock in the market over a period of time; if the subject stock's rise and fall is the same as the market, its beta is 1; if the subject stock's rise and fall would be 15% higher or lower than the market, its beta is 1.5 (Wikipedia, 2013). Using Sharpe's formula, if the stock's beta is 3.0, the risk-free rate is 5% and the market rate of return is 10%, the market's excess return is 5% (10% - 5%) and the stock's excess return is 15% (3 X 5%, market return x beta), and the stock's total required return is 20% (15% + 5%, excess return + risk-free rate) (Sharpe, 2013). This shows the return investors would demand for taking on the additional risk of the more volatile stock; the riskier the stock, the greater the return should be.

The CAPM is relatively easy, using only the market risk factor to create a simple formula for a simple result that says an investor should earn more by investing in a riskier stock (Boehme, n.d., p. 1). Unfortunately, beta has proved to be somewhat unrealistic because experts have found: that the different betas for different stocks do not explain their performance over a long period of time; a stock's beta and the stock's performance do not necessarily coincide. Consequently, CAPM may be mistaken when applying one beta to one stock's performance. CAPM assumes that: investors will hold the market portfolio; investors have uniform expectations about securities and their relationships; returns on assets are distributed normally according to multiple variations; beta (market risk) is the only relevant risk; there is a linear relationship between beta and the anticipated return; risk that can be eliminated by diversification is not relevant (Boehme, n.d., p. 1). Nevertheless, CAPM remains a dominant model in the market because investors with large, diversified portfolios can still generally rely on high beta stock to move more than the market and low beta stock to be consistent with the market (Sharpe, 2013).

c) APT

Arbitrage Pricing Theory (APT) is also based on the existence of 2 types of risk: systematic and unsystematic. However, APT moves beyond CAPM by maintaining that a stock's beta(s) can consist of many more variables than simply market risk, and those risks can change over time and according to differing economies (Boehme, n.d., p. 2). Risks are significant according to: their impact on the stock's price, which is shown in surprise rising or falling of the stock; the fact that they cannot be effectively countered through diversification; their timing and accuracy; their economic relationship with the stock (Boehme, n.d., p. 2). Some of these risk factors are macro-economic in that they reflect surprises in: inflation; gross national product; investor confidence; yield curve shifts.

While APT is based on the same risks as CAPM, APT is more difficult to apply due to the sheer number of possible risks considered, the changing nature and number of those risks and the careful attention that must be paid to a number of variables in order to determine and chart those risks. Simultaneously, APT is not rigidly tied to the single risk factor of market risk, assumes very little about the consistency of factors affecting risk, and is necessarily more flexible and more cognizant of numerous factors and their linear relationships in calculating risk investment and return. Consequently, APT would tend to be more accurate than the Dividend Growth Model or the CAPM and should be used to calculate risk and return on investment.

b. Cost of Equity Using CAPM Model

Company

Listing

RRF

RM

ssj

Nike Inc.

NYSE: NKE

0.65%

7.50%

1.10

Sony Corporation

NYSE: SNE

0.65%

10.50%

1.40

McDonald's Corporation

NYSE: MCD

0.65%

9.50%

0.70

E (rj)= RRF + ?j (RM - RRF)

E (rj) - The cost of equity

RRF - Risk-free rate of return ssj - Beta of the security

RM - Return on market portfolio

1) Based on the above information, which company has higher cost of equity? Why? Briefly explain your reasoning.

Applying the above formula:

Nike, Inc.: Cost of equity = 0.65% + 1.10 (7.50% - 0.65%)

0.65% + 1.10 (6.85%)

0.65% + 7.535%

8.185%

Sony: Cost of equity = 0.65% + 1.40 (10.50% - 0.65%)

0.65% + 1.40 (9.85%)

0.65% + 13.79%

14.44%

McDonald's: Cost of equity = 0.65% + 0.70 (9.50% - 0.65%)

0.65% + 0.70 (8.85%)

0.65% + 6.195%

6.845%

Therefore, Sony has the highest cost of equity (14.44%), Nike has the next highest cost of equity (8.185%) and McDonald's has the lowest cost of equity (6.845%). The brief explanations are in the calculations by plugging each company's given numbers into the formula.

2) What type of factors influence company beta? Briefly describe the factors that influence company beta. For example, higher financial leverage (total liabilities to total assets ratio) can lead to higher company beta

Company beta consists of risk; higher company beta equals higher risk; therefore, factors that make a company riskier lead to higher company beta. Those factors can include: financial variables, such as financial leverage measures, operating leverage, company size and dividend yield; and macroeconomics variables, such as inflation, market capitalization and government deficit (Al-Qaisi, 2011, p. 9). "Financial leverage" is a company's use of fixed-income securities like debt and preferred equity; the greater the use of those securities, the higher the company's financial leverage, the higher the interest payments, and the greater the risk (Investopedia U.S., 2013). "Operating leverage" is the measurement of a company's acquisition of fixed and variable costs: a company with relatively few sales in which each sale provides a high gross margin (such as a car dealership) is highly leveraged, whereas a company with many relative sales in which each sale provides a small margin (such as Wal-Mart) is less leveraged (Investopedia U.S., 2013). Company size tends to influence company beta with smaller organizations tending to be severely-based downward (Al-Qaisi, 2011, p. 7). "Dividend Yield" is the amount a company pays out yearly in dividends relative to its stock price and is a way to measure cash flow relative to investment. The… [END OF PREVIEW] . . . READ MORE

for $19.77 Business -- Corporate Finance -- the Cost of Equity Capital and the CAPM

Estimating Required Rate of Return

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

a) Dividend Growth Model

The Dividend Growth Model is used to determine whether stock is a good or bad buy by calculating what the stock's value should be through a formula using the stock's dividend. The generic formula uses: the stock's current dividend payout per share per year; the dividend's growth per year, usually based on 5 years of growth; the required rate of return on investment to make the stock a good buy. Those 3 factors are used in a formula of: (current dividend x (1+ dividend growth))/(required return -- dividend growth). One well-known Dividend Growth Model is the Gordon Growth Model:

(Investopedia U.S., 2013)

In this formula: D = Anticipated dividend per share one year from now; k = Required rate of return for equity investor; G = Growth rate in dividends (in perpetuity). The formula is relatively easy to use, requiring a prospective investor to plug 3 numbers into a simple formula. Unfortunately, the accuracy of this model is questionable: it unrealistically assumes constant, eternal dividend growth; however, dividend growth is not constant and dividends can be cut. In addition, its reliance on constant growth means it should be used for mature companies with low -- to -- moderate growth rates; however, Facebook is a relatively young company with fluctuating growth rates. Consequently, the Dividend Growth Model is not the optimal model for estimating Facebook stock's required rate of return.

b) CAPM

The Capital Asset Pricing Model (CAPM) was developed by William Sharpe to calculate investment risk and return on investment so potential investors can determine whether an investment is worth the risk. Sharpe argued that there are two types of risk: unsystematic risk, which is risk specifically posed by a particular stock, is not governed by the general market and can be efficiently countered by diversifying one's stock portfolio; systematic risk, which is dependent on such market factors as interest rates, wars, recessions and depressions, and cannot be effectively countered through diversification. CAPM measures systematic risk. Believing that return on stock should equal the stock's cost of capital, Sharpe developed a theory based on the association between risk and anticipated return. The formula is: Here:

(Sharpe, 2013).

The "risk free rate is usually the yield on a 10-year government bond; then a premium demanded by investors to make the risk worthwhile is added; then the equity market premium is calculated by determining the anticipated whole market return minus the risk-free rate of return; then the equity risk premium is multiplied by "beta." "Beta" is a measure of a stock's volatility relative to other market stock: the subject stock's rise and fall in the market is compared to the rise and fall of other stock in the market over a period of time; if the subject stock's rise and fall is the same as the market, its beta is 1; if the subject stock's rise and fall would be 15% higher or lower than the market, its beta is 1.5 (Wikipedia, 2013). Using Sharpe's formula, if the stock's beta is 3.0, the risk-free rate is 5% and the market rate of return is 10%, the market's excess return is 5% (10% - 5%) and the stock's excess return is 15% (3 X 5%, market return x beta), and the stock's total required return is 20% (15% + 5%, excess return + risk-free rate) (Sharpe, 2013). This shows the return investors would demand for taking on the additional risk of the more volatile stock; the riskier the stock, the greater the return should be.

The CAPM is relatively easy, using only the market risk factor to create a simple formula for a simple result that says an investor should earn more by investing in a riskier stock (Boehme, n.d., p. 1). Unfortunately, beta has proved to be somewhat unrealistic because experts have found: that the different betas for different stocks do not explain their performance over a long period of time; a stock's beta and the stock's performance do not necessarily coincide. Consequently, CAPM may be mistaken when applying one beta to one stock's performance. CAPM assumes that: investors will hold the market portfolio; investors have uniform expectations about securities and their relationships; returns on assets are distributed normally according to multiple variations; beta (market risk) is the only relevant risk; there is a linear relationship between beta and the anticipated return; risk that can be eliminated by diversification is not relevant (Boehme, n.d., p. 1). Nevertheless, CAPM remains a dominant model in the market because investors with large, diversified portfolios can still generally rely on high beta stock to move more than the market and low beta stock to be consistent with the market (Sharpe, 2013).

c) APT

Arbitrage Pricing Theory (APT) is also based on the existence of 2 types of risk: systematic and unsystematic. However, APT moves beyond CAPM by maintaining that a stock's beta(s) can consist of many more variables than simply market risk, and those risks can change over time and according to differing economies (Boehme, n.d., p. 2). Risks are significant according to: their impact on the stock's price, which is shown in surprise rising or falling of the stock; the fact that they cannot be effectively countered through diversification; their timing and accuracy; their economic relationship with the stock (Boehme, n.d., p. 2). Some of these risk factors are macro-economic in that they reflect surprises in: inflation; gross national product; investor confidence; yield curve shifts.

While APT is based on the same risks as CAPM, APT is more difficult to apply due to the sheer number of possible risks considered, the changing nature and number of those risks and the careful attention that must be paid to a number of variables in order to determine and chart those risks. Simultaneously, APT is not rigidly tied to the single risk factor of market risk, assumes very little about the consistency of factors affecting risk, and is necessarily more flexible and more cognizant of numerous factors and their linear relationships in calculating risk investment and return. Consequently, APT would tend to be more accurate than the Dividend Growth Model or the CAPM and should be used to calculate risk and return on investment.

b. Cost of Equity Using CAPM Model

Company

Listing

RRF

RM

ssj

Nike Inc.

NYSE: NKE

0.65%

7.50%

1.10

Sony Corporation

NYSE: SNE

0.65%

10.50%

1.40

McDonald's Corporation

NYSE: MCD

0.65%

9.50%

0.70

E (rj)= RRF + ?j (RM - RRF)

E (rj) - The cost of equity

RRF - Risk-free rate of return ssj - Beta of the security

RM - Return on market portfolio

1) Based on the above information, which company has higher cost of equity? Why? Briefly explain your reasoning.

Applying the above formula:

Nike, Inc.: Cost of equity = 0.65% + 1.10 (7.50% - 0.65%)

0.65% + 1.10 (6.85%)

0.65% + 7.535%

8.185%

Sony: Cost of equity = 0.65% + 1.40 (10.50% - 0.65%)

0.65% + 1.40 (9.85%)

0.65% + 13.79%

14.44%

McDonald's: Cost of equity = 0.65% + 0.70 (9.50% - 0.65%)

0.65% + 0.70 (8.85%)

0.65% + 6.195%

6.845%

Therefore, Sony has the highest cost of equity (14.44%), Nike has the next highest cost of equity (8.185%) and McDonald's has the lowest cost of equity (6.845%). The brief explanations are in the calculations by plugging each company's given numbers into the formula.

2) What type of factors influence company beta? Briefly describe the factors that influence company beta. For example, higher financial leverage (total liabilities to total assets ratio) can lead to higher company beta

Company beta consists of risk; higher company beta equals higher risk; therefore, factors that make a company riskier lead to higher company beta. Those factors can include: financial variables, such as financial leverage measures, operating leverage, company size and dividend yield; and macroeconomics variables, such as inflation, market capitalization and government deficit (Al-Qaisi, 2011, p. 9). "Financial leverage" is a company's use of fixed-income securities like debt and preferred equity; the greater the use of those securities, the higher the company's financial leverage, the higher the interest payments, and the greater the risk (Investopedia U.S., 2013). "Operating leverage" is the measurement of a company's acquisition of fixed and variable costs: a company with relatively few sales in which each sale provides a high gross margin (such as a car dealership) is highly leveraged, whereas a company with many relative sales in which each sale provides a small margin (such as Wal-Mart) is less leveraged (Investopedia U.S., 2013). Company size tends to influence company beta with smaller organizations tending to be severely-based downward (Al-Qaisi, 2011, p. 7). "Dividend Yield" is the amount a company pays out yearly in dividends relative to its stock price and is a way to measure cash flow relative to investment. The… [END OF PREVIEW] . . . READ MORE

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