What is the beta of the stock market?
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One.
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What is the beta of the stock market?
One.
What is the par value of ABC Company's preferred stock?
$120.
What is the standard deviation for firm BFI?
21.2%.
Is the use of the firm's WACC appropriate for estimating the cost of capital for a division within a firm?
Yes, if the division has the same risk profile as the firm's overall operations.
What is the formula for the Treynor Ratio?
Treynor Ratio = (Expected Return - Risk-Free Rate) / Beta.
What is the conversion value of the bond?
$1,050.
How is D_1 calculated?
D_1 = D_0 (1 + g)
What do most models of expected return agree on?
Expected return = Risk-free rate + Risk premium.
How does interest expense affect the cost of debt?
It reduces tax liability, effectively lowering the after-tax cost of debt.
What is the market value of equity?
$1,040 million.
What is the expected return for Stock B based on its beta of 1.1?
Expected return = Risk-free rate + (Beta × Market risk premium) = 3% + (1.1 × 10%) = 14%.
What is the market value of debt?
$201.68 million.
What is the average percent change in dividends over the given years?
5.1%.
What is the current price per share of ABC Co.?
$10.40.
What is the market risk premium?
9%.
What relationship is explored in the outline?
The relation between Return and Risk.
How many years are left to maturity for the bond?
25 years.
What is the calculated cost of equity?
11.1%.
What is the selling price of ABC Company's perpetual preferred stock?
$100 per share.
What is the return for Year 7?
50%.
What type of stocks should be added to reduce portfolio volatility?
Lowly correlated stocks.
What is the empirical distribution of annual returns?
It is a statistical representation of the actual returns observed over a specific period.
How often are returns roughly within one standard deviation from the mean?
About 2/3 of the time.
Why is the empirical distribution of annual returns important?
It helps investors understand the historical performance and volatility of an asset or portfolio.
What does the cost of debt represent?
The effective rate that a company pays on its borrowed funds.
How is the beta of a portfolio calculated?
Using the formula 𝛽ₚ = σᵢ × 𝑥ᵢ × 𝛽ᵢ.
What is the key insight of the Capital Asset Pricing Model (CAPM)?
Higher expected returns are associated with greater risk of doing badly in bad times.
What is variance in the context of measuring risk for a single asset?
The expected squared deviation from the mean.
What is the formula for calculating the Treynor Ratio?
(Portfolio Return - Risk-Free Rate) / Beta.
What factors influence the expected return of a portfolio?
The expected returns of the individual assets and their respective weights in the portfolio.
What is the current price of the stock?
$25.
What does WACC stand for?
Weighted Average Cost of Capital.
What is the coupon rate of the bond in the example?
9%.
What is a probability distribution of returns?
It describes the likelihood of different outcomes for investment returns.
What is a limitation of the Dividend Growth Method regarding the relationship between r and g?
It can only be used if r (required return) is greater than g (growth rate).
What is the Treynor Ratio for a fixed income portfolio with a return of 5% and a risk-free rate of 2%?
4.3.
What is the face value of the convertible bond?
$1,000.
What is the simplest way to estimate the discount rate?
Using the average return estimate based on realized returns.
Why is the Cost of Capital important for a company?
It helps in making investment decisions and evaluating projects.
What can the empirical distribution of annual returns indicate?
It can indicate the likelihood of various return outcomes based on historical data.
What is the significance of the Security Market Line in finance?
It helps investors assess whether an asset is fairly valued based on its risk and expected return.
What are the main components of the Cost of Capital?
Debt and equity.
What is the mean return for the given years?
10%.
What does R_t represent in the average return formula?
The realized return of a security in year t.
How does CAPM differ from the Dividend Growth Method?
CAPM does not have to deal with the difficulty of predicting the growth rate 'g'.
What is the formula for the conversion ratio of a bond?
Conversion ratio = Bond face value / Conversion price.
What happens to the volatility of a portfolio when lowly correlated stocks are added?
The volatility of the portfolio declines.
What is a characteristic of preference share dividends?
Preference share dividends are fixed.
Do investors need to be compensated for bearing unsystematic risk?
No, because it can be eliminated relatively costlessly by holding a portfolio.
What is a requirement for a company to use the Dividend Growth Method?
The company must pay a meaningful dividend.
What is the risk-return relation?
It is the relationship between systematic risk and expected return.
What is the Treynor Ratio used for?
To measure the risk-adjusted return of a portfolio.
What is the Weighted Average Cost of Capital (WACC)?
The average rate of return a company is expected to pay its security holders to finance its assets.
What is the reward for bearing risk in asset i?
The asset’s risk premium, E(Ri) – rf.
How does the cost of capital affect capital budgeting projects?
It determines the required return for those projects.
What does the value of a bond represent?
The present value (PV) of future cash flows.
What is the formula for calculating the pre-tax cost of debt?
Interest expense for the year / Interest-bearing debt.
What axis represents systematic risk (beta) on the Security Market Line?
The horizontal axis.
When is the firm's WACC an appropriate discount rate for an investment decision?
When evaluating projects that have the same risk as the firm's current operations.
What is the total outstanding debt?
$1 billion.
What is risk in the context of finance?
Risk refers to the potential for loss or the uncertainty regarding the return on an investment.
What does historical volatility measure in individual stocks?
The degree of variation in stock prices over a specific period.
What is the CAPM method used for?
Calculating the cost of equity.
What is the Treynor Ratio formula?
(r e – r f) / β.
What is volatility in the context of investments?
A measure of the price fluctuations of an investment over time.
What is the formula for the expected return on asset i in the CAPM?
E(Ri) = Rf + βi(E(RM) - Rf)
What is return uncertainty?
The unpredictability of investment returns over time.
Why is historical average return important for investors?
It helps in assessing the potential future performance of an investment.
Is the predicted return range for the S&P 500 considered promising?
Yes, it suggests a potentially favorable return.
What types of debt can complicate the cost of debt calculation?
Convertible bonds and multiple types of debt.
What is the current stock price?
$75.
How can undiversified investors reduce risk without sacrificing return?
By diversifying their portfolio.
Why are convertible bonds issued?
To lower yields on bonds.
Why is the expected return important for investors?
It helps investors assess the potential profitability of their investment choices.
What are the components of cash flows for a bond?
Coupon payments and principal payment.
What is the typical expiration of a convertible bond?
Long-dated expiration.
How is the standard deviation of BFJ’s returns calculated?
Using the formula √[0.25(0 - 0.10)² + 0.50(0.10 - 0.10)² + 0.25(0.20 - 0.10)²].
Why is the year 1925 significant in investment history?
It marks a period before significant market events like the Great Depression.
What is the range of the true return required by S&P 500 investors?
From 7.7% to 16.9%.
What is the Cost of Capital?
The return a company needs to generate to cover the cost of financing its operations.
What time period does the historical volatility data for individual stocks cover?
1926 to 2004.
How many shares are outstanding for the equity information?
50 million shares.
What formula is used in the Dividend Growth Method?
The growing perpetuity formula: V₀ = D(1+g)/(1+r) + D/(1+g)²/(1+r)² + ... + D/(1+g)ᵀ/(1+r)ᵀ.
What does the Treynor Ratio measure?
The reward-to-risk ratio.
What must be true about the growth of dividends in the Dividend Growth Method?
Dividends must grow at a constant rate.
What do investors typically hold to manage risk?
Investors would hold the market portfolio, which includes all assets.
How does pooling of risks work in a large portfolio?
Unsystematic risks for each stock will average out and be diversified.
How does the estimated growth rate affect the cost of equity in the Dividend Growth Method?
The cost of equity calculated is highly sensitive to the estimated growth rate.
What is the standard deviation of BFI’s returns?
21.2%
Can systematic risk be diversified?
No, systematic risk will affect all firms and cannot be diversified.
What is the relationship between historical average return and volatility?
Typically, higher historical average returns are associated with higher volatility.
According to William Sharpe, why is there no reason to expect reward just for bearing risk?
Because there must be some economic rationale behind the risk-reward relationship.
What happens when you rearrange the terms of the Treynor Ratio?
You can derive the CAPM formula.
What is the CAPM approach used for?
To calculate the cost of equity.
What is the formula for Portfolio Return?
𝑅𝑃 = 𝑥1𝑅1 + 𝑥2𝑅2 + ... + 𝑥𝑛𝑅𝑛.
What is the value of $100 invested at the end of 1925?
The value would depend on the specific investment vehicle and its performance over the years.
What benefits does diversification provide in a portfolio?
It reduces the overall risk, leading to a portfolio standard deviation that is less than the weighted average of individual stock standard deviations.
What are the two main types of risk?
Systematic risk and unsystematic risk.
How are preference share dividends expressed?
As a percentage of the par value of the share.
What does the Security Market Line (SML) represent?
It is a graphical representation of the relationship between expected return and systematic risk (beta) of assets.
What is systematic risk?
Systematic risk is the risk inherent to the entire market or market segment.
Why is historical volatility important for investors?
It helps assess the risk associated with individual stocks.
What does the cost of capital indicate?
How the market views the risk of the firm's assets.
How is the empirical distribution of annual returns typically constructed?
By collecting historical return data and plotting the frequency of different return levels.
What does the standard deviation represent in a probability distribution of returns?
It measures the volatility or risk of the investment returns.
What is compared in the outline regarding assets?
Single vs. Multiple Assets.
What is the variance calculated from the returns?
4.28%.
What is the standard deviation of BFJ’s returns?
7.07%
What can WACC be calculated for?
For the firm or project.
What is the conversion value of the bond?
75).
Is the use of the firm's WACC appropriate when evaluating the expansion of an existing plant?
Yes, if the expansion has the same risk as current operations.
What is the variance for firm BFI?
0.045.
What is the formula for calculating portfolio returns?
Weighted average of individual stock’s return.
How is the Expected Return calculated in the example provided?
E(R) = 25%(-0.20) + 50%(0.10) + 25%(0.40) = 10%
How many shares can the convertible bond be converted into?
14 shares.
What is the confidence level for the average return of the S&P 500 based on data from 1926 to 2004?
95%.
What is the cost of capital from the firm's perspective?
It is the return to an investor, which equals the cost to the firm.
Why is it necessary for a firm to earn at least the required return?
To compensate investors for the financing provided.
What is a method to approximate the pre-tax cost of debt?
Interest expense for the year divided by interest-bearing debt.
What is the price per share of the equity?
$80 per share.
What is a major drawback of the Dividend Growth Method?
Future dividends are highly uncertain and depend on estimating the growth rate.
What does the Treynor Ratio indicate?
Excess return earned per unit of risk taken.
How is variance mathematically represented?
Var(R) = E(R) - E(R)^2 = σ_sp × R - E(R)^2.
What is the risk premium in the CAPM?
E(RM) - Rf, which is the excess return of the market portfolio over the risk-free rate.
What is the primary use of the Treynor Ratio?
To compare different investment alternatives.
What is the standard deviation in relation to variance?
The square root of the variance.
What does βi represent in the CAPM?
The systematic risk of asset i.
Why is understanding return uncertainty important for investors?
It helps in making informed investment decisions and managing risk.
What does Sharpe imply about securities that perform poorly in bad times?
They are undesirable unless they have some redeeming virtue.
What does the expected return represent?
The weighted average of the possible returns, where the weights correspond to the state probabilities.
What does the capital asset pricing model (CAPM) help determine?
The cost of equity.
What is a major limitation of the DGM approach?
It can only be used if the company pays meaningful dividends.
What is the semiannual payment (PMT) for the bond?
$45.
Can the CAPM approach be applied to non-dividend paying companies?
Yes, as long as we can estimate beta.
What type of debt is typically focused on when discussing the cost of debt?
Long-term debt.
Which type of risk is rewarded in the market?
Only systematic risks.
What is the expected return for Stock A based on the Security Market Line (SML)?
10%.
What is the relationship between stock standard deviation and portfolio standard deviation?
The portfolio standard deviation is less than the weighted average due to diversification benefits.
What does historical average return refer to?
The average return of an investment over a specified period based on past performance.
What is the beta of a portfolio?
The weighted average beta of the securities in the portfolio.
What is the expected return of a portfolio?
The weighted average of the expected returns of the individual assets within the portfolio.
What are the common types of probability distributions used in finance?
Normal distribution, log-normal distribution, and binomial distribution.
What does the number of standard deviations from the mean indicate?
It indicates the range of returns relative to the mean.
What is the growth rate of preference share dividends?
The growth of preference share dividend is zero.
What is the steady growth rate of dividends?
5.1% per year.
What does Rf represent in the CAPM formula?
The return on a risk-free asset.
What is a convertible bond?
A bond that can be converted into a specified number of shares of stock.
How can volatility impact investment decisions?
Higher volatility may indicate higher risk, influencing an investor's choice.
What does Beta measure in the context of CAPM?
Beta measures the risk of a security in relation to market movements.
What factors contribute to return uncertainty?
Market volatility, economic conditions, and company performance.
How is variance estimated using realized returns?
Var(R) = (1/(T-1))Σ(Rt - R̄)².
What is the relationship between risk and Cost of Capital?
Higher risk typically leads to a higher Cost of Capital.
How is standard deviation mathematically represented?
SD(R) = Var(R).
What are diversifiable risks also known as?
Unsystematic risks.
What role does diversification play in managing return uncertainty?
Diversification can reduce risk by spreading investments across various assets.
What are examples of systematic risks?
Major war, global recession, etc.
What is the Treynor ratio used for?
To measure the reward-to-risk ratio of an asset.
What factors affect beta?
Business risk and financial risk.
Under what condition is the DGM approach not applicable?
If dividends aren't growing at a reasonably constant rate.
What is the formula used to find the cost of debt?
RATE(NPER, PMT, PV, FV).
What are financial risks related to?
Capital structure, exchange rate, interest rates, credit risks, and liquidity.
What is the market risk premium identified by the investor?
10%.
What factors influence the value of an investment over time?
Market performance, interest rates, inflation, and the type of investment.
What is the Treynor Ratio for an equity portfolio with a return of 7% and a risk-free rate of 2%?
What does CAPM stand for?
Capital Asset Pricing Model.
What is systematic risk?
Risk that affects all securities due to market-wide news.
What time period does the data used to predict the S&P 500 returns cover?
1926 to 2004.
What is unsystematic risk?
Risk that affects a particular security due to firm-specific news.
How many shares can the convertible bond be converted into?
14 shares.
What is unsystematic risk?
Unsystematic risk is specific to a particular company or industry.
How does risk relate to investment returns?
Higher risk typically correlates with the potential for higher returns.
What axis represents expected return on the Security Market Line?
The vertical axis.
What is the cost of equity?
The return required by equity investors given the risk of the cash flows from the firm.
What are portfolio weights?
The fraction of the total investment in the portfolio held in each individual investment.
What is the conversion price of the bond?
1,000 / 14 shares).
What is the trade-off when seeking lower risk in investments?
You must be prepared to sacrifice returns.
What is the standard deviation of the returns?
20.68%.
What is the present value of a constant annuity?
The present value of a series of equal cash flows received at regular intervals.
What is the exercise price of a convertible bond?
It is above the current stock price.
What analogy does Sharpe use to illustrate the irrationality of expecting rewards for risk without economic justification?
He compares it to making money in Las Vegas.
What is the valuation status of Stock A?
Under-valued.
What are the probabilities and returns for BFI and BFJ?
BFI: 0.25 (0.40), 0.50 (0.10), 0.25 (-0.20); BFJ: 0.00 (0.00), 0.10 (0.10), 0.20 (0.20).
Which model is included in the outline?
Capital Asset Pricing Model.
What is the formula for conversion value?
Conversion value = Conversion ratio x Stock price.
What is the cost of debt?
The effective rate that a company pays on its borrowed funds.
What is the expected return for the Equity Portfolio?
7%.
Why is understanding the cost of capital important for businesses?
It helps in making investment decisions and evaluating projects.
What is the return for Year 4?
0%.
What is the tax rate (T C) used in the after-tax cost of debt calculation?
0.4 (or 40%).
What is the weighted return for Stock B with a return of 6%?
4.5%.
How is the conversion value calculated?
By multiplying the number of shares by the stock price (14 x 75).
What is the historical tradeoff between risk and return for large portfolios from 1926 to 2004?
There is a positive relationship between volatility and average returns.
What is the probability that returns will be lower than the mean minus one standard deviation?
12%.
What is the cost of equity?
The return required by equity investors for their investment in a company.
What makes finding the cost of debt for a company difficult?
Having many types of debt, convertible bonds, or unknown bond values.
What is the expected dividend per share next year?
$1.50.
What is the focus of the current discussion?
Finding a method to accurately estimate the discount rate.
How does a normal distribution relate to investment returns?
It assumes that returns are symmetrically distributed around the mean.
What type of work is being introduced?
A Nobel-prize winning work.
How is the Treynor Ratio related to the Capital Asset Pricing Model (CAPM)?
The Treynor Ratio can be derived from the CAPM formula when considering a market portfolio.
What is the beta of the equity?
1.15.
How does debt affect the Cost of Capital?
Debt can lower the overall Cost of Capital due to tax benefits.
What is the formula for CAPM?
Expected return = Risk-free rate + Beta * (Market return - Risk-free rate).
What are the two major methods for determining the cost of equity?
Constant dividend growth model (DGM) and Capital asset pricing model (CAPM).
What must the reward-to-risk ratio of asset i equal for investors to hold it?
It must equal that of the market.
What is the risk-free rate?
5%.
What historical aspect is included in the outline?
Capital Market History.
What does the straight bond value represent?
The value of the bond if conversion does not take place, valued using cash flows of the bond.
What is an advantage of the CAPM approach?
It explicitly adjusts for systematic risk.
What does the Expected Portfolio Return represent?
The weighted average of the expected return of the investments within the portfolio.
What is the cost of debt (R D) calculated in the example?
R D = 3.927(2) = 7.854%
What is the constant dividend rate of the preferred stock?
5.0%.
When should you use the firm's WACC for a project?
If systematic risks are the same, the project is in the same line of business, and the project is not exceptionally large compared to the firm.
What condition must be met for the DGM approach to be valid?
The required return (r) must be greater than the growth rate (g).
How many years are left to maturity for the debt?
15 years.
Why is standard deviation not used to predict expected return?
Because it measures total risk.
What is the Yield to Maturity (YTM) for the bond?
10%.
What must be estimated in the CAPM approach that varies over time?
Both the expected market risk premium and beta.
What is the return for Year 10?
-5%.
How is risk typically measured?
Risk is often measured using statistical metrics such as standard deviation or beta.
Why is understanding probability distributions important in finance?
It helps investors assess risk and make informed decisions.
What is required for the valuation of stocks and bonds?
An estimate of the corresponding discount rates.
Which portfolio has a higher reward-to-risk ratio?
The Fixed Income Portfolio.
How do you calculate the expected return of a portfolio?
By multiplying the expected return of each asset by its weight in the portfolio and summing the results.
What formula represents the average return estimate?
R̄ = (1/T)(R1 + R2 + ... + RT) = (1/T)ΣRt.
What do the symbols in the formula 𝛽ₚ = σᵢ × 𝑥ᵢ × 𝛽ᵢ represent?
σᵢ is the standard deviation of the security, 𝑥ᵢ is the weight of the security in the portfolio, and 𝛽ᵢ is the beta of the security.
How can historical volatility impact expected returns?
Higher volatility often indicates higher potential returns and risks.
What are some pitfalls of WACC?
Assuming constant capital structure, ignoring market conditions, and not accounting for risk differences.
How is the relative systematic risk measure for asset i represented?
βi = Systematic risk of asset i / Systematic risk of market portfolio.
What is the relationship between historical volatility and stock performance?
Stocks with higher historical volatility may offer higher returns but also come with greater risk.
How is the cost of equity calculated in this example?
R E = (1.50/25) + 0.051.
How is the portfolio weight for an investment calculated?
𝑥𝑖 = Value of investment i / Total value of portfolio.
What does the constant dividend growth model (DGM) help determine?
The cost of equity.
What are the sources of financing included in WACC?
Ordinary shares (E), preference shares (P), and debt (D).
What is the standard deviation of a portfolio that comprises 50% BFI and 50% BFJ?
The calculation is not provided in the text.
What concept related to investment strategy is mentioned?
Diversification and Types of Risk.
What is the cost of debt?
The required return on a firm's debt.
What does the weight of a stock in a portfolio represent?
The proportion of money invested in each stock.
What is the formula for Expected Portfolio Return?
𝐸𝑅𝑃 = σ𝑖𝑥𝑖𝐸𝑅𝑖.
What are the parameters used to find the cost of debt?
NPER = 30; PV = -1,100; PMT = 45; FV = 1,000.
What is the expected return in the given example?
10%.
What formula is used to calculate the standard deviation of BFI’s returns?
=((0.25*(0.4 - 0.1)^2)+(0.5*(0.1 - 0.1)^2)+(0.25*(-0.2 - 0.1)^2))^0.5*100
What is the current price of the bond?
$100.84.
What is the current stock price?
$75.
What is the before-tax coupon rate of the bond?
9%.
What is the formula for calculating WACC?
WACC = wE * RE + wD * RD * (1 - TC).
What is the maturity period of the bond?
12 years.
What is the current risk-free rate in the example?
6.1%.
What is the tax rate applied in the calculation?
30%.
How is WACC calculated in this example?
WACC = 0.7843 (15.35%) + 0.2157 (4.712%).
What is the relationship between systematic risk and reward in stocks?
The greater the systematic risk, the higher the reward.
What is the formula for calculating the Expected Return for a single asset?
Expected Return = Σ (Probability × Return)
What does the term T represent in the formulas?
The total number of years for which returns are realized.
What is a key advantage of the Dividend Growth Model (DGM) approach for calculating the cost of equity?
It is easy to understand and use.
What is the selling price of the bond?
1,000 bond.
What is the cost of equity?
The return required by equity investors given the risk of the investment.
What is the conversion price?
The price at which the bond can be converted to stock.
What is the face value of the convertible bond in the example?
$5,000.
What is the valuation status of Stocks B and C?
Over-valued.
What is the conversion price of the bond?
$71.43.
What values should be used in WACC calculations?
Market values, not book values.
What is the lower bound for convertible bond (CB) value?
Lower bound for CB value = Max (straight bond value, conversion value).
What is the combined market value of a company represented as?
V = E + P + D.
What is true about CB value before the maturity of the conversion option?
CB value > lower bound.
What does beta measure?
Systematic risk only.
What is the risk-free rate given in the scenario?
2%.
What does D_1 represent in the Dividend Growth Model?
Next year's dividend.
What was the latest historical dividend per share for ABC Co.?
$1 per share.
What is the calculated WACC in the example?
13.06%.
What is the relationship between the portfolio's standard deviation and the weighted average of component stocks' standard deviations?
Portfolio SD < Weighted average of component stocks’ SDs due to diversification benefit.
Which portfolio has a better reward-to-risk ratio?
The Fixed Income Portfolio with a Treynor Ratio of approximately 4.29%.
If a bond can be converted into 10 shares worth $200 each in 3 years, what is the conversion value?
$2000.
How does beta affect expected return in the context of the SML?
Higher beta indicates higher expected return due to increased risk.
What is the IRR for the cash flows of the convertible bond described?
7.3%.
What percentage of the company is equity?
83.8%.
How is the conversion premium calculated?
Conversion premium = (Conversion price – Stock price) / Stock price.
How is the systematic risk of a stock measured?
By 'beta'.
What is the equation that represents the relationship between asset i and the market?
E(Ri) - rf / βi = E(RM) - rf / 1.
What is the face value of the convertible bond?
$1,000.
What is the present value of a single cash flow?
The current worth of a future sum of money or stream of cash flows given a specified rate of return.
When will conversion not take place?
If Conversion Price > Stock Price throughout the conversion period.
How is the cost of equity typically calculated?
Using the Capital Asset Pricing Model (CAPM).
What is the return minus mean for Year 5?
15%.
What is the conversion price of the bond?
$80.
In a portfolio context, what does it mean if a stock is under-valued?
It suggests that the stock may have potential for higher returns compared to its current price.
What should you do if the systematic risk of a project is different?
Find the appropriate beta for the project.
What implication does over-valued status have for Stocks B and C?
They may be priced higher than their intrinsic value, indicating potential risk.
What is the formula to calculate the cost of equity capital using CAPM?
R_E = Risk-free rate + Beta * Market risk premium.
What aspect does the DGM approach not explicitly consider?
Risk.
What is the pre-tax cost of debt?
8.7%.
What is the formula for the expected return on asset i in the Capital Asset Pricing Model (CAPM)?
E(Ri) = rf + βi(E(RM) - rf)
Calculate the Treynor Ratio for the Fixed Income Portfolio.
Treynor Ratio = (5% - 2%) / 0.70 ≈ 4.29%.
What is the after-tax cost of debt?
6.1%.
What does the formula V_0 = D_1 / (R_E - g) represent?
The value of a stock using the growing perpetuity formula.
What is the expected return for a portfolio combining BFI and BFJ?
10%, regardless of the portfolio weights.
What was the percent change in dividend from 2004 to 2005?
5.1%.
What does V represent in the WACC formula?
The market value of the firm, which is D + E.
What is the formula to calculate the cost of equity (R E)?
R E = 5 + 1.15(9) = 15.35%
How is WACC determined?
It is the weighted average of all financing sources.
What is the current quote of the debt?
What is the formula to calculate the weight of equity (wE) in the capital structure?
wE = E/V, where E is equity and V is total value.
What is the coupon rate of the debt?
9%, semiannual coupons.
What is a disadvantage of the CAPM approach?
It requires estimating the expected market risk premium, which varies over time.
Is the cost of debt the same as the coupon rate?
No, the cost of debt is not necessarily the coupon rate.
What is the weighted return for Stock A with a return of 10%?
2.5%.
What does WACC stand for?
Weighted Average Cost of Capital.
What is the formula for the Cost of Equity using the Dividend Growth Model (DGM)?
R_E = D_1 / (P_0 + g)
What is the expected growth rate of dividends for ABC Co.?
4%.
What formula is used to calculate the standard deviation of BFJ’s returns?
=((0.25*(0 - 0.1)^2)+(0.5*(0.1 - 0.1)^2)+(0.25*(0.2 - 0.1)^2))^0.5*100
What is the market risk premium for all stocks listed?
10%.
What is the yield of similar bonds?
7.5 percent.
What is the expected market risk premium in the example?
8.6%.
What factors should be considered if conversion of convertible debt is expected?
Number of years to conversion and conversion value (not par value).
What is the conversion ratio of the bond?
62.5.
What was the percent change in dividend from 2003 to 2004?
4.6%.
What are the probabilities and returns for BFI?
0.25 probability for 0.40 return, 0.50 probability for 0.10 return, and 0.25 probability for 0.00 return.
How long until the bonds issued by ABC Co. mature?
Three years.
Is the use of the firm's WACC appropriate when evaluating the introduction of a new product?
Yes, if the new product has the same risk as current operations.
What is the squared difference for Year 2?
6.25%.
Are unsystematic risks rewarded in the market?
No, unsystematic risk is not rewarded.
What are the weights used in the expected return calculation?
The weights correspond to the state probabilities.
What is the standard deviation of BFI’s returns?
21.2%
How much is the dividend paid by the preferred stock?
120).
How is the conversion price calculated?
By dividing the bond face value by the conversion ratio (1000 / 14).
How sensitive is the DGM approach to the estimated growth rate?
An increase in g of 1% increases the cost of equity by at least 1%.
How is the cost of debt frequently estimated?
By computing the Yield to Maturity (YTM) on existing debt.
What is the weight of Stock B in the portfolio?
75%.
What does wE represent in the WACC formula?
The percent financed with equity (E/V).
What is the risk-free rate determined by the investor?
3%.
What is the current price of the stock?
$41.20 per share.
What is the calculated cost of equity capital in the example?
11.1%.
What is the corporate tax rate for ABC Co.?
30%.
What is the par value of debt?
$200 million.
What is the par value of ordinary shares at ABC Co.?
$1 par.
What is the basis for the weight in WACC calculations?
The dollar amount of each source.
What are business risks related to?
Product/service offering and variability in profits due to operating leverage.
What is the value of equity (E) in the example?
4 billion.
What is the calculated semiannual rate (RATE) for the bond?
5%.
What is the value of debt (D) in the example?
1.1 billion.
What is the tax rate applied?
40%.
What is the total value (V) in the capital structure?
5.1 billion.
Calculate the Treynor Ratio for the Equity Portfolio.
Treynor Ratio = (7% - 2%) / 1.25 = 4%.
What is the total portfolio return?
7.0%.
What was the dividend in 2002?
1.23.
What is the market value of the bonds per $100 nominal?
$100.84.
What is the expected return for Stock B based on the SML?
14%.
What are the cash flows for a convertible bond with a coupon of -1750 in Year 0 and 50 in Years 1 and 2, and 2050 in Year 3?
Year 0: -1750, Year 1: 50, Year 2: 50, Year 3: 2050.
What factors does WACC ultimately depend on?
The market’s perception of the risk of the firm’s assets.
What is the formula to calculate the weighted average cost of capital (WACC)?
WACC = (E/V * Re) + (D/V * Rd * (1 - Tc))
If $25,000 is invested in Stock A, what is its weight in the portfolio?
25%.
What is the sum of the differences for all years?
38.50%.
What is the coupon rate of the bond?
6 percent.
What is the beta value for Stock B?
1.1.
What is the standard deviation of BFJ’s returns?
7.07%
What is the risk-free rate used in the portfolio?
3%.
Why is the Capital Asset Pricing Model (CAPM) not used to estimate the cost of debt?
Because it is more appropriate for equity rather than debt.
What is the weight of debt (wD) in the capital structure?
0.2157.
What should be done if a firm does not have existing debt?
Alternative methods such as using industry averages or estimating based on similar firms can be used.
What is the cost of convertible debt if conversion is not expected?
It is the same as non-convertible debt.
What assumption is made about dividends in the DGM approach?
Dividends grow at a constant rate.
What does the diversification benefit imply about the portfolio's risk?
It reduces the overall risk compared to individual stocks.
Would you expect the DGM and CAPM approaches to yield similar estimates?
Yes, but they may not always do so.
What is the par value of the 9% bond issued by ABC Co.?
$200.
Is Stock A under or over-valued based on its expected return?
Over-valued (expected return 10% vs actual 15%).
What percentage of the company is debt?
16.2%.
What is the after-tax cost of debt?
R D (1 - T C ) = 7.854(1 - .4) = 4.712%
What is the formula to calculate the cost of preferred stock?
Cost of preferred stock = Dividend / Price.
How can you determine the beta for a project?
By using the beta of a listed company in that business.
What is the cost of preferred stock for ABC Company?
6% (calculated as 100).
What is the equity beta of the company in the example?
0.58.
What is the standard deviation of the portfolio’s returns?
7.07%
What is the expected return for Stock C based on the SML?
17%.
What is the expected return on BFI?
10%.
What was the percent change in dividend from 2002 to 2003?
5.7%.
What is the functional form of the relation between asset expected return and systematic risk?
It is linear, as represented by the CAPM formula.
What should be considered if DGM and CAPM do not result in similar estimates?
Evaluate the assumptions and inputs used in both models.
What was the percent change in dividend from 2005 to 2006?
4.9%.
What is the WACC of the company?
12.7%.
Why is the cost of equity sensitive in the CAPM approach?
It is highly sensitive to the choice of market risk premium and beta.
What is the beta for the Fixed Income Portfolio?
0.70.
How often does the bond pay interest?
Semi-annually.
What is necessary when using the beta of a comparable company?
The capital structure must be the same; otherwise, it needs to be adjusted for capital structure.
What is the firm's marginal tax rate?
40%.
What is one method for estimating the dividend growth rate?
Using the historical average of percent changes in dividends.
What does wD represent in the WACC formula?
The percent financed with debt (D/V).
What is the beta value for Stock A?
0.7.
What is the expected return for Stock A based on its beta of 0.7?
Expected return = Risk-free rate + (Beta × Market risk premium) = 3% + (0.7 × 10%) = 10%.
What is the conversion value of the bond?
$2,575.
What is the expected return for Stock C based on its beta of 1.4?
Expected return = Risk-free rate + (Beta × Market risk premium) = 3% + (1.4 × 10%) = 17%.
Is Stock B under or over-valued based on its expected return?
Under-valued (expected return 14% vs actual 10%).
Which term on the right-hand side of the CAPM formula is related to the asset?
βi (beta).
What is the after-tax cost of debt formula?
After-tax cost of debt = RD * (1 - TC).
Why are dividends not tax deductible?
Because there is no tax impact on the cost of equity.
What are the probabilities and returns for BFJ?
0.25 probability for 0.20 return, 0.50 probability for 0.10 return, and 0.25 probability for -0.20 return.
Is Stock C under or over-valued based on its expected return?
Under-valued (expected return 17% vs actual 12%).
How is the expected return on BFJ calculated?
Expected return on BFJ = 0.25(0) + 0.50(0.10) + 0.25(0.20) = 10%.
What is the relationship between V_0 and P_0 in the context of fair valuation?
If fairly valued, V_0 = P_0.
What is the interpretation of beta in the context of CAPM?
Beta measures the sensitivity of the asset's returns to the returns of the market.
What is the total value of the company?
$1,242 million.
What is the focus of the outline provided?
Measuring Return and Risk.
What are the two time perspectives discussed in the outline?
Past vs. Future.
What is the primary focus of Lecture 2?
Risk and Return.
