Finance Chapter: Risk and Return Calculations
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The stock in Bowie Enterprises has a beta of 1.17. The expected return on the market is 11.90 percent and the risk-free rate is 3.10 percent. What is the required return on the company's stock?

13.40%

Mojo Mining has a bond outstanding that sells for $2,156 and matures in 16 years. The bond pays semiannual coupons and has a coupon rate of 5.98 percent. The face value is $2,000. If the company's tax rate is 35 percent, what is the aftertax cost of debt?

3.41%

Take It All Away has a cost of equity of 11.05 percent, a pretax cost of debt of 5.40 percent, and a tax rate of 35 percent. The company's capital structure consists of 69 percent debt on a book value basis, but debt is 55 percent of the company's value on a market value basis. What is the company's WACC?

6.90%

Total risk is measured by _____, and systematic risk is measured by ______?

<p>Standard deviation; beta</p> Signup and view all the answers

A stock has a beta of .85 and a reward-to-risk ratio of 6.51 percent. If the risk-free rate is 2.1 percent, what is the stock's expected return?

<p>7.63%</p> Signup and view all the answers

Unsystematic risk:

<p>Can be effectively eliminated by portfolio diversification.</p> Signup and view all the answers

The risk-free rate is 2.4 percent and the market expected return is 12.1 percent. What is the expected return of a stock that has a beta of .88?

<p>10.94%</p> Signup and view all the answers

Which of the following statements are correct concerning diversifiable risks? 1. Idiosyncratic risks can be reduced by investing in unrelated securities. 2. There is no reward for accepting diversifiable risks. 3. Diversifiable risks are generally associated with an individual firm or industry. 4. Beta measures diversifiable risk.

<p>1, 2, and 3 only (B)</p> Signup and view all the answers

You have a portfolio that is invested 16 percent in Stock R, 36 percent in Stock S, and the remainder in Stock T. The beta of Stock R is .61, and the beta of Stock S is 1.16. The beta of your portfolio is 1.27. What is the beta of Stock T?

<p>1.57</p> Signup and view all the answers

Kountry Kitchen has a cost of equity of 10.6 percent, a pretax cost of debt of 5.2 percent, and the tax rate is 39 percent. If the company's WACC is 7.59 percent, what is its debt-equity ratio (i.e., ratio of market value of debt over market value of equity)?

<p>0.68</p> Signup and view all the answers

ABC Inc. just paid an annual dividend of $3.49 on its common stock. The firm increases its dividend by 3.60 percent annually. What is the company's cost of equity if the current stock price is $43.00 per share?

<p>12.01%</p> Signup and view all the answers

Dyrdek Enterprises has equity with a market value of $10.3 million and the market value of debt is $3.40 million. The company is evaluating a new project that has more risk than the firm. As a result, the company will apply a risk adjustment factor of 1.1 percent (that is, adding 1.1% to the firm WACC to get the project discount rate). The new project will cost $2.10 million today and provide annual cash flows of $551,000 for the next 6 years. The company's cost of equity is 10.87 percent and the pretax cost of debt is 6.83 percent. The tax rate is 35 percent. What is the project's NPV?

<p>$273,667</p> Signup and view all the answers

Here I Sit Sofas has 7,400 shares of common stock outstanding at a price of $97 per share. There are 720 bonds that mature in 33 years with a coupon rate of 7.1 percent paid semiannually. The bonds have a face value of $2,000 each and sell at 150 percent of face value. The company also has 6,300 shares of preferred stock outstanding at a price of $50 per share. What is the capital structure weight of the debt?

<p>0.6765</p> Signup and view all the answers

What is the beta of a portfolio comprised of the following securities? Stock Amount Invested Security Beta A $3,900 1.42 B $4,900 1.53 C $7,400 1.00

<p>1.261</p> Signup and view all the answers

The expected return on ABD stock is 14.50 percent while the expected return on the market is 13.2 percent. The beta of ABD is 1.15. What is the risk-free rate of return?

<p>4.53%</p> Signup and view all the answers

Suppose the risk-free rate is 4%. The expected return of the market portfolio is 12%, while the standard deviation of the market portfolio return is 15%. The return of stock A has a standard deviation of 20% and correlation coefficient with the market portfolio return of 0.06. What is stock A's beta? What is stock A's expected return?

<p>Beta: 0.08, Expected Return: 4.64%</p> Signup and view all the answers

Flashcards

Required Return

The rate of return an investor expects to receive on a given investment, considering its risk level.

Beta

A measure of a security's volatility relative to the overall market. A beta of 1 indicates the security moves in sync with the market. A beta greater than 1 means the security is more volatile than the market, and a beta less than 1 means it's less volatile.

Risk-Free Rate

The return on a risk-free investment, typically considered a U.S. Treasury bond.

Market Expected Return

The expected return on the overall market, often represented by a broad market index like the S&P 500.

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After-Tax Cost of Debt

The cost of debt after considering the tax savings from interest expense deductions. Formula: After-tax cost of debt = Pretax cost of debt * (1 - Tax rate)

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WACC (Weighted Average Cost of Capital)

The weighted average cost of capital (WACC) represents the average cost of financing for a company, considering both debt and equity. Formula: WACC = (Weight of Debt * After-Tax Cost of Debt) + (Weight of Equity * Cost of Equity)

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Cost of Equity

The cost of raising capital through equity financing, representing the return required by investors for holding the company's stock. This can be calculated using various models like the Capital Asset Pricing Model (CAPM).

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Total Risk

A measure of the overall risk of an investment, encompassing both systematic (market) and unsystematic (firm-specific) risks. It's calculated as the standard deviation of an investment's returns.

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Systematic Risk

Risk that is inherent in the overall market, affecting all investments to some extent. Also known as market risk or non-diversifiable risk.

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Unsystematic Risk

Company-specific risk that can be reduced or eliminated through portfolio diversification. Also known as diversifiable risk.

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Portfolio Beta

A portfolio's beta is a weighted average of the betas of the individual assets in the portfolio. Formula: Portfolio Beta = Weight of Asset 1 * Beta 1 + Weight of Asset 2 * Beta 2 + ...

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Expected Return

The rate of return expected from an investment, considering its risk level. Formula: Expected Return = Risk-Free Rate + Beta * (Market Expected Return - Risk-Free Rate)

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Debt-Equity Ratio

The ratio of a company's debt to its equity, indicating the proportion of financing that comes from debt and equity. Formulas: Market Value Debt-Equity Ratio = Market Value of Debt / Market Value of Equity, Book Value Debt-Equity Ratio = Book Value of Debt / Book Value of Equity

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Cost of Preferred Stock

The rate of return required by investors for holding preferred stock, typically fixed and paid out as dividends.

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Net Present Value (NPV)

The value that a project is expected to add to the company's worth, calculated by discounting future cash flows at the project's discount rate (adjusted WACC) and subtracting the initial investment. Formula: NPV = Sum of Present Value of Future Cash Flows - Initial Investment.

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Capital Structure Weight of Debt

The value of a company's total assets that are financed by debt. It's represented as a percentage of the company's total capital structure. Formula: Capital Structure Weight of Debt = Market Value of Debt / (Market Value of Debt + Market Value of Equity + Market Value of Preferred Stock).

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Diversification

The practice of spreading investments across different asset classes, industries, and securities to reduce risk. By diversifying, investors can reduce the impact of unsystematic risk.

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Risk Adjustment

The process of determining the appropriate discount rate to use for evaluating a project, taking into account its specific risk profile and the company's overall cost of capital.

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Capital Asset Pricing Model (CAPM)

A model used to calculate the required rate of return for an investment based on its risk level, the risk-free rate of return, and the market risk premium. Formula: CAPM = Risk-Free Rate + Beta * (Market Expected Return - Risk-Free Rate)

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Market Risk Premium

The difference in expected return between a risky asset and a risk-free asset, representing the extra return that investors demand for taking on risk. Formula: Market Risk Premium = Market Expected Return -Risk-Free Rate.

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Cost of Capital

The rate of return that a company's investors expect to earn on their investments, considering the mix of debt and equity financing. Formula: Cost of Capital = (Weight of Debt * After-Tax Cost of Debt)+ (Weight of Equity * Cost of Equity) + (Weight of Preferred Stock * Cost of Preferred Stock).

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Dividend Yield

The annual dividend paid on a stock, expressed as a percentage of the stock's current price. Formula: Dividend Yield = Annual Dividend / Stock Price.

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Dividend Growth Rate

The rate at which a company's dividend is expected to grow over time. Formula: Dividend Growth Rate = (Dividend in Year 2 - Dividend in Year 1) / Dividend in Year 1.

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Cost of Equity (Dividend Discount Model)

The return that a company's shareholders expect to earn on their investment, considering the company's dividend growth rate and the current stock price. Formula: Cost of Equity = (Dividend in Year 1 / Stock Price) + Dividend Growth Rate.

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Beta Coefficient

A measure of the correlation between the return of a stock and the return of the overall market. A beta of 1 indicates perfect correlation, a beta of 0 indicates no correlation, and a beta less than 0 indicates negative correlation.

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Standard Deviation

A measure of an investment's risk relative to the overall market. A higher standard deviation indicates a more volatile investment.

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Correlation Coefficient

A statistical measure of the degree to which two variables move together. A correlation coefficient of 1 indicates perfect positive correlation, a correlation coefficient of -1 indicates perfect negative correlation, and a correlation coefficient of 0 indicates no correlation.

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Discounting

The process of calculating the present value of future cash flows, taking into account the time value of money. Formula: Present Value = Future Value / (1 + Discount Rate) ^ Number of Periods.

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Discount Rate

The rate of return used to discount future cash flows to their present value. Formula: Cost of Capital = (Weight of Debt * After-Tax Cost of Debt) + (Weight of Equity * Cost of Equity).

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Beta (in terms of Covariance and Variance)

A measure of the relative volatility of an investment's returns, compared to the volatility of the market. Formula: Beta = Covariance of Investment Returns with Market Returns / Variance of Market Returns.

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Study Notes

Question 1: Required Return on Stock

  • Beta of Bowie Enterprises stock: 1.17
  • Expected market return: 11.90%
  • Risk-free rate: 3.10%
  • Required return on the company's stock: 13.40%

Question 2: Aftertax Cost of Debt

  • Bond price: $2,156
  • Maturity: 16 years
  • Coupon rate: 5.98%
  • Face value: $2,000
  • Company's tax rate: 35%
  • Aftertax cost of debt: 3.41%

Question 3: Weighted Average Cost of Capital (WACC)

  • Cost of equity: 11.05%
  • Pretax cost of debt: 5.40%
  • Tax rate: 35%
  • Book value debt percentage: 69%
  • Market value debt percentage: 55%
  • WACC: 6.90%

Question 4: Risk Measurement

  • Total risk is measured by standard deviation.
  • Systematic risk is measured by beta.

Question 5: Expected Return

  • Stock beta: 0.85
  • Reward-to-risk ratio: 6.51%
  • Risk-free rate: 2.1%
  • Stock's expected return: 7.63%

Question 6: Unsystematic Risk

  • Definition: Can be eliminated by portfolio diversification.

Question 7: Expected Return of Stock

  • Risk-free rate: 2.4%
  • Market expected return: 12.1%
  • Stock beta: 0.88
  • Expected return of the stock: 10.94%

Question 8: Diversifiable Risks

  • Idiosyncratic risks can be reduced by investing in unrelated securities.
  • There's no reward for accepting diversifiable risks.
  • Diversifiable risks are associated with individual firms or industries.
  • Beta doesn't measure diversifiable risk.

Question 9: Portfolio Beta

  • Portfolio invested in Stock R: 16%
  • Portfolio invested in Stock S: 36%
  • Stock R beta: 0.61
  • Stock S beta: 1.16
  • Portfolio beta: 1.27
  • Stock T beta: unknown

Question 10: Debt-Equity Ratio

  • Cost of equity: 10.6%
  • Pretax cost of debt: 5.2%
  • Tax rate: 39%
  • WACC: 7.59%
  • Debt-equity ratio (market value): 0.68

Question 11: Cost of Equity

  • Annual dividend: $3.49
  • Dividend growth rate: 3.60%
  • Current stock price: $43.00
  • Cost of equity: 12.01%

Question 12: Project Net Present Value (NPV)

  • Market value of equity: $10.3 million
  • Market value of debt: $3.40 million
  • Risk adjustment factor: 1.1%
  • Project cost: $2.10 million
  • Annual cash flows: $551,000 for 6 years
  • Cost of equity: 10.87%
  • Pretax cost of debt: 6.83%
  • Tax rate: 35%
  • Project's NPV: $273,667

Question 13: Common stock outstanding

  • Shares outstanding: 7,400
  • Price per share: $97

Question 14: Portfolio Beta Calculation

  • Stock A Amount Invested and beta: $3,900, 1.42
  • Stock B Amount Invested and beta: $4,900, 1.53
  • Stock C Amount Invested and beta: $7,400, 1.00
  • Portfolio beta: 1.261

Question 15: Risk-Free Rate

  • Expected return on ABD stock: 14.50%
  • Expected market return: 13.2%
  • ABD stock beta: 1.15
  • Risk-free rate: 4.53%

Question 16: Stock A Expected Return

  • Risk-free rate: 4%
  • Market portfolio expected return: 12%
  • Market portfolio standard deviation: 15%
  • Stock A standard deviation: 20%
  • Correlation coefficient: 0.06
  • Stock A beta: 0.08
  • Stock A expected return: 4.64%

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Description

This quiz covers key concepts in finance related to risk and return, including calculations for required return on stock, aftertax cost of debt, and weighted average cost of capital (WACC). It also explores the definitions of total, systematic, and unsystematic risk, along with expected returns. Perfect for students looking to test their understanding of financial principles.

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