Question 1

A project has an expected risky cash flow of $500 in year 3. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 3, CEQ₃.

Accepted Answer

The certainty equivalent cash flow can be calculated using the formula: CEQ = Expected Cash Flow / (1 + Risk Premium)^n, where the Risk Premium = Expected Market Return - Risk-Free Rate, and n is the number of periods (in this case, 3 years). Given the project's beta is 1.20, the project's required return can be calculated using the CAPM formula: Required Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate) = 4% + 1.20 * (14% - 4%) = 16%. The certainty equivalent cash flow is then calculated as $500 / (1 + 0.16)^3 = $360.33.

Question 2

Which of the following informational updates would prompt a financial manager to use a higher cost of capital to analyze a project?

Accepted Answer

A higher percentage of fixed costs increases the business risk of a project. This increased risk necessitates a higher cost of capital to account for the higher risk of not covering those fixed costs, especially in scenarios of fluctuating sales or economic downturns.

Question 3

The historical returns for the past three years for Stock B and the stock market portfolio were Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the observed variance of the market portfolio returns. (Ignore the correction for the loss of a degree of freedom set out in the text.)

Accepted Answer

The answer of The historical returns for the past three...

Question 4

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the average return for Stock B and the market portfolio.

Accepted Answer

To calculate the average return, we add up the returns for each year and divide by the total number of years (in this case, three years). 
Average return for Stock B: (24% + 0% + 24%) / 3 = 16%
Average return for market portfolio: (10% + 12% + 20%) / 3 = 14%

Therefore, the best choice is A because it correctly calculates the average returns for both Stock B and the market portfolio.

Question 5

The historical returns for the past three years for Stock B and the stock market portfolio were Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the observed covariance of returns between Stock B and the market portfolio. (Ignore the correction for the loss of a degree of freedom set out in the text.)

Accepted Answer

The covariance is calculated as the average of the products of deviations of each pair of returns from their respective means. The mean return for Stock B is 16% and for the market is 14%. The deviations are (8, -16, 8) for Stock B and (-4, -2, 6) for the market. The products of these deviations are (-32, 32, 48). The average of these products is 16.

Question 6

Company A's historical returns for the past three years are 6 percent, 15 percent, and 15 percent. Similarly, the market portfolio's returns were 10 percent, 10 percent, and 16 percent. Suppose the risk-free rate of return is 4 percent and that investors expect the market to return 10 percent. What is the cost of equity capital (required rate of return of company A's common stock), computed with the CAPM?

Accepted Answer

The correct answer is A because the cost of equity capital using CAPM is 8.5 percent. The formula for CAPM is:Cost of equity = Risk-free rate + Beta * (Expected market return - Risk-free rate)In this case, the risk-free rate is 4 percent, the expected market return is 10 percent, and the beta of Company A is 1.5 (calculated as the covariance of Company A's returns with the market returns divided by the variance of the market returns). Plugging these values into the formula, we get:Cost of equity = 4% + 1.5 * (10% - 4%) = 8.5%

Question 7

The market portfolio's historical returns for the past three years were 10 percent, 10 percent, and 16 percent. Suppose the risk-free rate of return is 4 percent. Estimate the market risk premium.

Accepted Answer

The market risk premium is calculated as the average return of the market portfolio minus the risk-free rate. The average return of the market portfolio is (10% + 10% + 16%) / 3 = 12%. Subtracting the risk-free rate of 4% from this gives a market risk premium of 8%.

Question 8

Financial slang referring to the reduction of cash flows from a project's forecasted value to its certainty equivalent is a(n)

Accepted Answer

A "haircut for risk" refers to the reduction in cash flows from a project's forecasted value to its certainty equivalent, taking into account the level of risk involved. It is a common financial slang used to describe this concept. The other options (A, C, and D) do not accurately describe this phrase.

Question 9

Generally, for CAPM calculations, the value to use for the risk-free interest rate is the

Accepted Answer

The risk-free interest rate used in CAPM calculations should reflect a rate that is virtually free of credit risk and therefore the short-term U.S. Treasury bill rate is generally the best choice.

Question 10

An analyst computes the beta of the computer company WinDoze as 1.7 and the standard error of the estimate as 0.3. What is the 95 percent confidence interval for the calculated beta?

Accepted Answer

To calculate the 95% confidence interval for the beta, we use the formula: beta ± (1.96 * standard error). Here, beta = 1.7 and standard error = 0.3. Thus, the confidence interval is 1.7 ± (1.96 * 0.3) = 1.7 ± 0.588. This gives us a range of 1.112 to 2.288, which rounds to 1.1 to 2.3.

Question 11

The historical returns for the past four years for Stock C and the stock market portfolio are Stock C: 10 percent, 30 percent, 20 percent, 20 percent; market portfolio: 5 percent, 15 percent, 25 percent, 15 percent. Calculate the beta of Stock C.

Accepted Answer

The answer of The historical returns for the past four...

Question 12

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the beta for Stock B.

Accepted Answer

The beta for Stock B is 0.86. This is calculated by dividing the covariance of Stock B and the market portfolio by the variance of the market portfolio. The covariance is 16.8, and the variance is 36.

Question 13

Company A's historical returns for the past three years were 6 percent, 15 percent, and 15 percent. Similarly, the market portfolio's returns were 10 percent, 10 percent, and 16 percent. According to the security market line (SML), Stock A was

Accepted Answer

The Security Market Line (SML) is a graphical representation of the Capital Asset Pricing Model (CAPM), which describes the relationship between the expected return of an investment and its risk as measured by beta. To determine if Stock A was overpriced, underpriced, or correctly priced according to the SML, we need information about the risk-free rate and the beta of Stock A relative to the market portfolio. Without this information, we cannot accurately assess the stock's pricing relative to the SML.

Question 14

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. The expected market return is 12 percent. Calculate the required rate of return (cost of equity)for Stock B using the CAPM. (The risk-free rate of return = 4%.)

Accepted Answer

The answer of The historical returns for the past three...

Question 15

On a graph with common stock returns on the y-axis and market returns on the x-axis, the slope of the regression line represents

Accepted Answer

The slope of the regression line represents beta, which measures the sensitivity of the stock's returns to changes in the market returns. Alpha represents the intercept of the regression line, R-squared measures the goodness of fit of the regression line, and standard error measures the degree of variability in the regression line. None of these are represented by the slope of the regression line.

Question 16

A project has an expected risky cash flow of $200 in year 1. The risk-free rate is 6 percent, the expected market rate of return is 16 percent, and the project's beta is 1.50. Calculate the certainty equivalent cash flow for year 1, CEQ₁.

Accepted Answer

The formula for calculating the certainty equivalent cash flow is:

CEQ = RF + (EMRP x Beta x Risk Premium)

Where RF is the risk-free rate, EMRP is the expected market return premium (i.e., the difference between the expected market rate of return and the risk-free rate), and Beta is the project's beta. The Risk Premium is the difference between the expected risky cash flow and the risk-free cash flow.

Using the given values, we get:

RF = 6%
EMRP = 16% - 6% = 10%
Beta = 1.50
Risk Premium = $200 - ($200 / (1 + 6%)) = $188.68

So, CEQ = 6% + (10% x 1.50 x $188.68) = $175.21

Therefore, the best choice is A as it correctly calculates the certainty equivalent cash flow for year 1.

Question 17

A project has an expected risky cash flow of $500 in year 2. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 2, CEQ₂.

Accepted Answer

The certainty equivalent cash flow (CEQ) can be calculated using the formula: CEQ = Expected Cash Flow / (1 + Risk Premium), where the Risk Premium = Beta * (Market Rate of Return - Risk-Free Rate). Here, the Risk Premium = 1.20 * (14% - 4%) = 12%. Thus, the CEQ for the $500 expected cash flow is $500 / (1 + 12%) = $500 / 1.12 = $446.43. However, none of the options match this calculation directly, suggesting a potential misunderstanding in the question's setup or a mistake in the calculation. Given the options, the closest approach to the correct methodology was intended, but it appears there's a discrepancy in the final values provided. Re-evaluating with the correct approach: The correct formula for adjusting for risk in this context should actually involve the CAPM to find the appropriate discount rate, then discount the cash flow at that rate. However, the provided answer choices and the calculation method initially described don't align with standard financial calculations for certainty equivalents or the use of CAPM directly for this purpose.

Question 18

The historical returns for the past four years for Stock C and the stock market portfolio are Stock C: 10 percent, 30 percent, 20 percent, 20 percent; market portfolio: 5 percent, 15 percent, 25 percent, 15 percent. If the risk-free rate of return is 5 percent and the expected market return is 12 percent, calculate the required rate of return on Stock C using the CAPM.

Accepted Answer

The required rate of return on Stock C using the CAPM is 8.5 percent. The CAPM formula is: Required rate of return = Risk-free rate + Beta * (Expected market return - Risk-free rate). The beta of Stock C can be calculated using the historical returns of Stock C and the market portfolio: Beta = Covariance(Stock C, market portfolio) / Variance(market portfolio). The covariance and variance can be calculated using the following formulas: Covariance(Stock C, market portfolio) = (1/n) * Sum((Stock C return - Average Stock C return) * (Market portfolio return - Average market portfolio return)) and Variance(market portfolio) = (1/n) * Sum((Market portfolio return - Average market portfolio return)^2). The historical returns for Stock C and the market portfolio are given in the question. The risk-free rate is 5 percent and the expected market return is 12 percent. Plugging these values into the CAPM formula, we get: Required rate of return = 5% + 1.5 * (12% - 5%) = 8.5%.

Question 19

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. If the risk-free rate is 4 percent, calculate the market risk premium.

Accepted Answer

The market risk premium is calculated by subtracting the risk-free rate from the average return of the market portfolio. The average return of the market portfolio is (10% + 12% + 20%) / 3 = 14%. Subtracting the risk-free rate of 4% from this gives a market risk premium of 10%.

Question 20

A project has an expected cash flow of $300 in year 3. The risk-free rate is 5 percent, the market risk premium is 8 percent, and the project's beta is 1.25. Calculate the certainty equivalent cash flow for year 3, CEQ₃.

Accepted Answer

The certainty equivalent cash flow (CECF) can be calculated using the formula:
CECF = Expected Cash Flow / (1 + Risk Premium)

Risk Premium = Beta * Market Risk Premium = 1.25 * 8% = 10%
CECF = 300 / (1 + 10%) = 273.07

Therefore, the closest choice to the calculated value is A) $228.35.

Quiz 9: Risk and the Cost of Capital

A project has an expected risky cash flow of $500 in year 3. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 3, CEQ₃.

Which of the following informational updates would prompt a financial manager to use a higher cost of capital to analyze a project?

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the average return for Stock B and the market portfolio.

The market portfolio's historical returns for the past three years were 10 percent, 10 percent, and 16 percent. Suppose the risk-free rate of return is 4 percent. Estimate the market risk premium.

Financial slang referring to the reduction of cash flows from a project's forecasted value to its certainty equivalent is a(n)

Generally, for CAPM calculations, the value to use for the risk-free interest rate is the

An analyst computes the beta of the computer company WinDoze as 1.7 and the standard error of the estimate as 0.3. What is the 95 percent confidence interval for the calculated beta?

The historical returns for the past four years for Stock C and the stock market portfolio are Stock C: 10 percent, 30 percent, 20 percent, 20 percent; market portfolio: 5 percent, 15 percent, 25 percent, 15 percent. Calculate the beta of Stock C.

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the beta for Stock B.

Company A's historical returns for the past three years were 6 percent, 15 percent, and 15 percent. Similarly, the market portfolio's returns were 10 percent, 10 percent, and 16 percent. According to the security market line (SML) , Stock A was

On a graph with common stock returns on the y-axis and market returns on the x-axis, the slope of the regression line represents

A project has an expected risky cash flow of $200 in year 1. The risk-free rate is 6 percent, the expected market rate of return is 16 percent, and the project's beta is 1.50. Calculate the certainty equivalent cash flow for year 1, CEQ₁.

A project has an expected risky cash flow of $500 in year 2. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 2, CEQ₂.

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. If the risk-free rate is 4 percent, calculate the market risk premium.

A project has an expected cash flow of $300 in year 3. The risk-free rate is 5 percent, the market risk premium is 8 percent, and the project's beta is 1.25. Calculate the certainty equivalent cash flow for year 3, CEQ₃.

Quiz 9: Risk and the Cost of Capital

A project has an expected risky cash flow of $500 in year 3. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 3, CEQ3.

Which of the following informational updates would prompt a financial manager to use a higher cost of capital to analyze a project?

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the average return for Stock B and the market portfolio.

The market portfolio's historical returns for the past three years were 10 percent, 10 percent, and 16 percent. Suppose the risk-free rate of return is 4 percent. Estimate the market risk premium.

Financial slang referring to the reduction of cash flows from a project's forecasted value to its certainty equivalent is a(n)

Generally, for CAPM calculations, the value to use for the risk-free interest rate is the

An analyst computes the beta of the computer company WinDoze as 1.7 and the standard error of the estimate as 0.3. What is the 95 percent confidence interval for the calculated beta?

The historical returns for the past four years for Stock C and the stock market portfolio are Stock C: 10 percent, 30 percent, 20 percent, 20 percent; market portfolio: 5 percent, 15 percent, 25 percent, 15 percent. Calculate the beta of Stock C.

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. Calculate the beta for Stock B.

Company A's historical returns for the past three years were 6 percent, 15 percent, and 15 percent. Similarly, the market portfolio's returns were 10 percent, 10 percent, and 16 percent. According to the security market line (SML) , Stock A was

On a graph with common stock returns on the y-axis and market returns on the x-axis, the slope of the regression line represents

A project has an expected risky cash flow of $200 in year 1. The risk-free rate is 6 percent, the expected market rate of return is 16 percent, and the project's beta is 1.50. Calculate the certainty equivalent cash flow for year 1, CEQ1.

A project has an expected risky cash flow of $500 in year 2. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 2, CEQ2.

The historical returns for the past three years for Stock B and the stock market portfolio are Stock B: 24 percent, 0 percent, 24 percent; market portfolio: 10 percent, 12 percent, 20 percent. If the risk-free rate is 4 percent, calculate the market risk premium.

A project has an expected cash flow of $300 in year 3. The risk-free rate is 5 percent, the market risk premium is 8 percent, and the project's beta is 1.25. Calculate the certainty equivalent cash flow for year 3, CEQ3.

A project has an expected risky cash flow of $500 in year 3. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 3, CEQ₃.

A project has an expected risky cash flow of $200 in year 1. The risk-free rate is 6 percent, the expected market rate of return is 16 percent, and the project's beta is 1.50. Calculate the certainty equivalent cash flow for year 1, CEQ₁.

A project has an expected risky cash flow of $500 in year 2. The risk-free rate is 4 percent, the expected market rate of return is 14 percent, and the project's beta is 1.20. Calculate the certainty equivalent cash flow for year 2, CEQ₂.

A project has an expected cash flow of $300 in year 3. The risk-free rate is 5 percent, the market risk premium is 8 percent, and the project's beta is 1.25. Calculate the certainty equivalent cash flow for year 3, CEQ₃.