weaverbirdllm/famma · Datasets at Hugging Face

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Statistics for three stocks, A, B, and C, are shown in the following tables.<image_1>

Only on the basis of the information provided in the tables, and given a choice between a port- folio made up of equal amounts of stocks A and B or a portfolio made up of equal amounts of stocks B and C, which portfolio would you recommend? Justify your choice.

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A portfolio comprised of Stocks B and C will have lower total risk than a portfolio comprised of Stocks A and B.

Since we do not have any information about expected returns, we focus exclusively on reducing variability. Stocks A and C have equal standard deviations, but the correlation of Stock B with Stock C (0.10) is less than that of Stock A with Stock B (0.90). Therefore, a portfolio comprised of Stocks B and C will have lower total risk than a portfolio comprised of Stocks A and B.

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George Stephenson’s current portfolio of $2 million is invested as follows:<image_1> Stephenson soon expects to receive an additional $2 million and plans to invest the entire amount in an index fund that best complements the current portfolio. Stephanie Coppa is evaluating the four index funds shown in the following table for their ability to produce a portfolio that will meet two criteria relative to the current portfolio: (1) maintain or enhance expected return and (2) maintain or reduce volatility. Each fund is invested in an asset class that is not substantially represented in the current portfolio.<image_2>

State which fund Coppa should recommend to Stephenson. Justify your choice by describ- ing how your chosen fund best meets both of Stephenson’s criteria. No calculations are required.

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Fund D

Fund D represents the single best addition to complement Stephenson's current portfolio, given his selection criteria. Fund D’s expected return (14.0 percent) has the potential to increase the portfolio’s return somewhat. Fund D’s relatively low correlation with his current portfolio (+0.65) indicates that Fund D will provide greater diversification benefits than any of the other alternatives except Fund B. The result of adding Fund D should be a portfolio with approximately the same expected return and somewhat lower volatility compared to the original portfolio. The other three funds have shortcomings in terms of expected return enhancement or volatility reduction through diversification. Fund A offers the potential for increasing the portfolio’s return, but is too highly correlated to provide substantial volatility reduction benefits through diversification. Fund B provides substantial volatility reduction through diversification benefits, but is expected to generate a return well below the current portfolio’s return. Fund C has the greatest potential to increase the portfolio’s return, but is too highly correlated with the current portfolio to provide substantial volatility reduction benefits through diversification.

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Abigail Grace has a $900,000 fully diversified portfolio. She subsequently inherits ABC Com- pany common stock worth $100,000. Her financial adviser provided her with the following forecast information:<image_1>.The correlation coefficient of ABC stock returns with the original portfolio returns is .40.

The inheritance changes Grace’s overall portfolio and she is deciding whether to keep the ABC stock. Assuming Grace keeps the ABC stock, calculate the: Expected return of her new portfolio which includes the ABC stock.

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0.73%

E(rNP) = wOP E(rOP ) + wABC E(rABC ) = (0.9 × 0.67) + (0.1 × 1.25) = 0.728%

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The inheritance changes Grace’s overall portfolio and she is deciding whether to keep the ABC stock. Assuming Grace keeps the ABC stock, calculate the: Covariance of ABC stock returns with the original portfolio returns.

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2.7966 ≅ 2.80

Cov = \rho × \deltaOP × \deltaABC = 0.40 × 2.37 × 2.95 = 2.7966 ≅ 2.80

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The inheritance changes Grace’s overall portfolio and she is deciding whether to keep the ABC stock. Assuming Grace keeps the ABC stock, calculate the: Standard deviation of her new portfolio, which includes the ABC stock.

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2.2673% ≅ 2.27%

\deltaNP = [wOP2 \deltaOP2 + wABC2 \deltaABC2 + 2 wOP wABC (CovOP , ABC)]1/2 =[(0.92 ×2.372)+(0.12 ×2.952)+(2×0.9×0.1×2.80)]1/2 = 2.2673% ≅ 2.27%

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If Grace sells the ABC stock, she will invest the proceeds in risk-free government securities yielding .42% monthly. Assuming Grace sells the ABC stock and replaces it with the gov- ernment securities, calculate the Expected return of her new portfolio, which includes the government securities.

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0.65%

E(rNP)=wOP E(rOP)+wGS E(rGS)=(0.9×0.67)+(0.1×0.42)=0.645%

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If Grace sells the ABC stock, she will invest the proceeds in risk-free government securities yielding .42% monthly. Assuming Grace sells the ABC stock and replaces it with the gov- ernment securities, calculate the Covariance of the government security returns with the original portfolio returns.

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Cov=\rho ×\deltaOP ×\deltaGS =0×2.37×0=0

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If Grace sells the ABC stock, she will invest the proceeds in risk-free government securities yielding .42% monthly. Assuming Grace sells the ABC stock and replaces it with the gov- ernment securities, calculate the Standard deviation of her new portfolio, which includes the government securities.

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2.133% ≅ 2.13%

\deltaNP = [wOP2 \deltaOP2 + wGS2 \deltaGS2 + 2 wOP wGS (CovOP , GS)]1/2 =[(0.92 ×2.372)+(0.12 ×0)+(2×0.9×0.1×0)]1/2 = 2.133% ≅ 2.13%

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Determine whether the systematic risk of her new portfolio, which includes the government securities, will be higher or lower than that of her original portfolio.

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Adding the risk-free government securities would result in a lower beta for the new portfolio.

Adding the risk-free government securities would result in a lower beta for the new portfolio. The new portfolio beta will be a weighted average of the individual security betas in the portfolio; the presence of the risk-free securities would lower that weighted average.

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The following are estimates for two stocks.<image_1> The market index has a standard deviations of 22% and the risk-free rate is 8%.

What are the standard deviations of stocks A and B?

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σA = 34.78% σB = 47.93%

The standard deviation of each individual stock is given by: \deltai =[\beta_{i}^2\delta^2_{M} +\delta&2(ei)]1/2 Since\betaA =0.8,\betaB =1.2,\delta(eA)=30%,\delta(eB)=40%,and\deltaM =22%,weget: \deltaA = (0.82 × 222 + 302 )1/2 = 34.78% \deltaB = (1.22 × 222 + 402 )1/2 = 47.93%

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Suppose that we were to construct a portfolio with proportions:<image_2> Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio.

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The expected rate of return on a portfolio is the weighted average of the expected returns of the individual securities: E(r_{P} ) = 14% The beta of a portfolio is similarly a weighted average of the betas of the individual securities: \beta_{P} = 0.78 The residual standard deviation of the portfolio is thus: \delta(e_{P} ) = 20.12% The total variance of the portfolio is then: \delta_{P}^2 = 699.47 The total standard deviation is 26.45%.

The expected rate of return on a portfolio is the weighted average of the expected returns of the individual securities: E(rP)=wA ×E(rA)+wB ×E(rB)+wf × rf E(rP ) = (0.30 × 13%) + (0.45 × 18%) + (0.25 × 8%) = 14% The beta of a portfolio is similarly a weighted average of the betas of the individual securities: \betaP =wA ×\betaA +wB ×\betaB +wf ×\betaf \betaP =(0.30×0.8)+(0.45×1.2)+(0.25×0.0)=0.78 The residual standard deviation of the portfolio is thus: \delta(eP ) = (405)1/2 = 20.12% The total variance of the portfolio is then: \delta^2P =(0.782 ×222)+405=699.47 The total standard deviation is 26.45%.

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Consider the following two regression lines for stocks A and B in the following figure.<image_1> <image_2>

Which stock has higher firm-specific risk?

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Stock A has higher firm-specific risk.

The two figures depict the stocks’ security characteristic lines (SCL). Stock A has higher firm-specific risk because the deviations of the observations from the SCL are larger for Stock A than for Stock B. Deviations are measured by the vertical distance of each observation from the SCL.

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Which stock has greater systematic (market) risk?

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Stock B’s systematic risk is greater.

Beta is the slope of the SCL, which is the measure of systematic risk. The SCL for Stock B is steeper; hence Stock B’s systematic risk is greater.

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Which stock has higher R^2?

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Stock B's R2 is higher than Stock A’s.

The R2 (or squared correlation coefficient) of the SCL is the ratio of the explained variance of the stock’s return to total variance, and the total variance is the sum of the explained variance plus the unexplained variance (the stock’s residual variance). <ans_image_1> Since the explained variance for Stock B is greater than for Stock A (the explained variance is\beta_{B}^2\delta_{M}^2 , which is greater since its beta is higher), and its residual variance \delta^2_{eB} is smaller, its R2 is higher than Stock A’s.

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Which stock has higher alpha?

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Stock A’s alpha is larger.

Alpha is the intercept of the SCL with the expected return axis. Stock A has a small positive alpha whereas Stock B has a negative alpha; hence, Stock A’s alpha is larger.

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Which stock has higher correlation with the market?

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Stock B’s correlation with the market is higher.

The correlation coefficient is simply the square root of R^2, so Stock B’s correlation with the market is higher.

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A portfolio manager summarizes the input from the macro and micro forecasters in the follow- ing table:<image_1>

Calculate expected excess returns, alpha values, and residual variances for these stocks.

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\delta^2(eA ) = 58^2 = 3,364 \delta^2(eB) = 71^2 = 5,041 \delta^2(eC) = 60^2 = 3,600 \delta^2(eD) = 55^2 = 3,025

<ans_image_1> Stocks A and C have positive alphas, whereas stocks B and D have negative alphas. The residual variances are: \delta^2(eA ) = 58^2 = 3,364 \delta^2(eB) = 71^2 = 5,041 \delta^2(eC) = 60^2 = 3,600 \delta^2(eD) = 55^2 = 3,025

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Here are data on two companies <image_1>. The T-bill rate is 4% and the market risk premium is 6%.

What would be the fair return for each company, according to the capital asset pricing model (CAPM)?

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E(r_{$1 Discount})=13% E(r_{Everything $5}=10%

The expected return is the return predicted by the CAPM for a given level of systematic risk. <ans_image_2>

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You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows (in millions of dollars):<image_1>

The project’s beta is 1.8. Assuming that rf=8% and E(rM) =16%, what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative?

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The appropriate discount rate for the project is 22.4% NPV = $18.09 The highest value that beta can take before the hurdle rate exceeds the IRR is determined by: 3.47

The appropriate discount rate for the project is: r_{f} + \beta × [E(r_{M} ) – r_{f} ] = .08 + [1.8 × (.16 – .08)] = .224 = 22.4% NPV = $18.09 The highest value that beta can take before the hurdle rate exceeds the IRR is determined by: .3573 = .08 + \beta × (.16 – .08) ⇒ \beta = .2773/.08 = 3.47

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Consider the following table, which gives a security analyst’s expected return on two stocks for two particular market returns:<image_1>

What are the betas of the two stocks?

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\beta_{A} = 2.00 \beta_{D} = 0.30

Call the aggressive stock A and the defensive stock D. Beta is the sensitivity of the stock’s return to the market return, i.e., the change in the stock return per unit change in the market return. Therefore, we compute each stock’s beta by calculating the difference in its return across the two scenarios divided by the difference in the market return: \beta_{A} = 2.00 \beta_{D} = 0.30

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What is the expected rate of return on each stock if the market return is equally likely to be 5% or 25%?

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E(r_{A} ) = 18% E(r_{D} ) = 9%

With the two scenarios equally likely, the expected return is an average of the two possible outcomes: E(rA ) = 0.5 × (–.02 + .38) = .18 = 18% E(rD ) = 0.5 × (.06 + .12) = .09 = 9%

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What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm’s stock?

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The hurdle rate is determined by the project beta (0.3), not the firm’s beta. The correct discount rate is 8.7%, the fair rate of return for stock D.

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If the simple CAPM is valid, each figure represents a situation. Please indicate whether it is possible or not, considering each situation independently.

If the situation is possible in <image_1>?

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Not possible.

Not possible. Portfolio A has a higher beta than Portfolio B, but the expected return for Portfolio A is lower than the expected return for Portfolio B. Thus, these two portfolios cannot exist in equilibrium.

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If the situation is possible in <image_2>?

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Possible.

Possible. If the CAPM is valid, the expected rate of return compensates only for systematic (market) risk, represented by beta, rather than for the standard deviation, which includes nonsystematic risk. Thus, Portfolio A’s lower rate of return can be paired with a higher standard deviation, as long as A’s beta is less than B’s.

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If the situation is possible in <image_3>?

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Not possible.

Not possible. The reward-to-variability ratio for Portfolio A is better than that of the market. This scenario is impossible according to the CAPM because the CAPM predicts that the market is the most efficient portfolio. Using the numbers supplied: SA = 0.5 SM = 0.33 Portfolio A provides a better risk-reward tradeoff than the market portfolio.

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If the situation is possible in <image_4>?

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Not possible.

Not possible. Portfolio A clearly dominates the market portfolio. Portfolio A has both a lower standard deviation and a higher expected return.

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If the situation is possible in <image_5>?

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Not possible.

Not possible. The SML for this scenario is: E(r) = 10 + \beta × (18 – 10) Portfolios with beta equal to 1.5 have an expected return equal to: E(r) = 10 + [1.5 × (18 – 10)] = 22% The expected return for Portfolio A is 16%; that is, Portfolio A plots below the SML (\alpha_{A} = –6%), and hence, is an overpriced portfolio. This is inconsistent with the CAPM.

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If the situation is possible in <image_6>?

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Not possible.

Not possible. Here, Portfolio A’s required return is: .10 + (0.9 × .08) = 17.2% This is greater than 16%. Portfolio A is overpriced with a negative alpha: αA =–1.2%

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If the situation is possible in <image_7>?

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Possible.

Possible. Portfolio A plots below the CML, as any asset is expected to. This scenario is not inconsistent with the CAPM.

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The following table shows risk and return measures for two portfolios.<image_1>

When plotting portfolio R on the preceding table relative to the SML, portfolio R lies:

[ "A. On the SML.", "B. Below the SML.", "C. Above the SML.", "D. Insufficientdatagiven." ]

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When plotting portfolio R relative to the capital market line, portfolio R lies:

[ "A. On the CML.", "B. Below the CML.", "C. Above the CML.", "D. Insufficientdatagiven." ]

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Briefly explain whether investors should expect a higher return from holding portfolio A versus portfolio B under capital asset pricing theory (CAPM). Assume that both portfolios are fully diversified.<image_1>

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Under the CAPM, the only risk that investors are compensated for bearing is the risk that cannot be diversified away (systematic risk).

Under the CAPM, the only risk that investors are compensated for bearing is the risk that cannot be diversified away (systematic risk). Because systematic risk (measured by beta) is equal to 1.0 for both portfolios, an investor would expect the same rate of return from both portfolios A and B. Moreover, since both portfolios are well diversified, it doesn’t matter if the specific risk of the individual securities is high or low. The firm-specific risk has been diversified away for both portfolios.

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Identify and justify which stock would be more appropriate for an investor who wants to add this stock to a well-diversified equity portfolio.

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Kay should recommend Stock X.

Kay should recommend Stock X because of its positive alpha, compared to Stock Y, which has a negative alpha. In graphical terms, the expected return/risk profile for Stock X plots above the security market line (SML), while the profile for Stock Y plots below the SML. Also, depending on the individual risk preferences of Kay’s clients, the lower beta for Stock X may have a beneficial effect on overall portfolio risk.

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Identify and justify which stock would be more appropriate for an investor who wants to hold this stock as a single-stock portfolio.

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Kay should recommend Stock Y.

Kay should recommend Stock Y because it has higher forecasted return and lower standard deviation than Stock X. The respective Sharpe ratios for Stocks X and Y and the market index are: Stock X: Stock Y: Market index: (14% − 5%)/36% = 0.25 (17% − 5%)/25% = 0.48 (14% − 5%)/15% = 0.60 The market index has an even more attractive Sharpe ratio than either of the individual stocks, but, given the choice between Stock X and Stock Y, Stock Y is the superior alternative.

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Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 45%. The following are well-diversified portfolios:<image_1>

What is the expected return–beta relationship in this economy?

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E(r_{P})=6%+(\betaP1 ×10%)+(\betaP2 ×5%)

<ans_image_1>

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Consider the following data for a one-factor economy. <image_1>. All portfolios are well diversified.

Suppose that another portfolio, portfolio E, is well diversified with a beta of .6 and expected return of 8%. Would an arbitrage opportunity exist? If so, what would be the arbitrage strategy?

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An arbitrage opportunity exists by buying Portfolio G and selling an equal amount of Portfolio E. The profit for this arbitrage will be: r_{G} –r_{E} =[9%+(0.6×F)]−[8%+(0.6×F)]=1% That is, 1% of the funds (long or short) in each portfolio.

The expected return for Portfolio F equals the risk-free rate since its beta equals 0. For Portfolio A, the ratio of risk premium to beta is: (12 − 6)/1.2 = 5 For Portfolio E, the ratio is lower at: (8 – 6)/0.6 = 3.33 This implies that an arbitrage opportunity exists. For instance, you can create a Portfolio G with beta equal to 0.6 (the same as E’s) by combining Portfolio A and Portfolio F in equal weights. The expected return and beta for Portfolio G are then: E(rG ) = (0.5 × 12%) + (0.5 × 6%) = 9% βG =(0.5×1.2)+(0.5×0%)=0.6 Comparing Portfolio G to Portfolio E, G has the same beta and higher return. Therefore, an arbitrage opportunity exists by buying Portfolio G and selling an equal amount of Portfolio E. The profit for this arbitrage will be: rG –rE =[9%+(0.6×F)]−[8%+(0.6×F)]=1% That is, 1% of the funds (long or short) in each portfolio.

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Assume that security returns are generated by the single-index model, <image_1> where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the follow- ing data: <image_2>

If σM = 20%, calculate the variance of returns of securities A, B, and C.

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\delta^2 =\beta^2\delta^2_{M} +\delta^2(e) \delta^2_{A} = 881 \delta^2_{B} = 500 \delta_{C}^{2} = 976

\delta^2 =\beta^2\delta^2_{M} +\delta^2_{e} \delta^2_{A} =(0.82 ×202)+252 =881 \delta^2_{B} =(1.02 ×202)+102 =500 \delta_{C}^2 =(1.22×202)+202 =976

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Is there an arbitrage opportunity in this market? What is it ?Analyze the opportunity graphically.

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There is no arbitrage opportunity and there is no arbitrage.

There is no arbitrage opportunity because the well-diversified portfolios all plot on the security market line (SML). Because they are fairly priced, there is no arbitrage.

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The SML relationship states that the expected risk premium on a security in a one-factor model must be directly proportional to the security’s beta. Suppose that this were not the case. For example, suppose that expected return rises more than proportionately with beta as in the figure below: <image_1>

How could you construct an arbitrage portfolio? (Hint: Consider combinations of portfolios A and B, and compare the resultant portfolio to C.)

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chart

We can choose weights such that \beta_{P} = \beta_{C} but with expected return higher than that of Portfolio C. Hence, combining P with a short position in C will create an arbitrage portfolio with zero investment, zero beta, and positive rate of return.

A long position in a portfolio (P) comprised of Portfolios A and B will offer an expected return-beta tradeoff lying on a straight line between points A and B. Therefore, we can choose weights such that βP = βC but with expected return higher than that of Portfolio C. Hence, combining P with a short position in C will create an arbitrage portfolio with zero investment, zero beta, and positive rate of return.

hard

open question

portfolio management

english

290

1

0

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739

english_290_2_r1

nan

Some researchers have examined the relationship between average returns on diversified portfolios and 2 of those portfolios. What should they have discovered about the effect of 2 on portfolio return?

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chart

The argument in part (a) leads to the proposition that the coefficient of \beta^2 must be zero in order to preclude arbitrage opportunities.

nan

easy

open question

portfolio management

english

290

2

0

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740

english_291_1_r1

Consider the following multifactor (APT) model of security returns for a particular stock.<image_1>

If T-bills currently offer a 6% yield, find the expected rate of return on this stock if the mar- ket views the stock as fairly priced.

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E(r) = 18.1%

E(r) = 6% + (1.2 × 6%) + (0.5 × 8%) + (0.3 × 3%) = 18.1%

easy

open question

portfolio management

english

291

1

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741

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nan

Suppose that the market expected the values for the three macro factors given in column 1 below, but that the actual values turn out as given in column 2. Calculate the revised expecta- tions for the rate of return on the stock once the “surprises” become known.<image_2>

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17.80%

Surprises in the macroeconomic factors will result in surprises in the return of the stock: Unexpected return from macro factors = [1.2 × (4% – 5%)] + [0.5 × (6% – 3%)] + [0.3 × (0% – 2%)] = –0.3% E (r) =18.1% − 0.3% = 17.8%

easy

open question

portfolio management

english

291

2

1

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742

english_292_1_r1

Suppose that the market can be described by the following three sources of systematic risk with associated risk premiums.<image_1> The return on a particular stock is generated according to the following equation: r = 15% + 1.0I + .5R + .75C + e

Find the equilibrium rate of return on this stock using the APT. The T-bill rate is 6%. Is the stock over- or underpriced? Explain.

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The actually expected return on the stock is 15%. The stock is overpriced.

The APT required (i.e., equilibrium) rate of return on the stock based on rf and the factor betas is: required E(r) = 6% + (1 × 6%) + (0.5 × 2%) + (0.75 × 4%) = 16% According to the equation for the return on the stock, the actually expected return on the stock is 15% (because the expected surprises on all factors are zero by definition). Because the actually expected return based on risk is less than the equilibrium return, we conclude that the stock is overpriced.

medium

open question

portfolio management

english

292

1

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743

english_293_1_r1

Assume that both X and Y are well-diversified portfolios and the risk-free rate is 8%.<image_1>

In this situation you would conclude that portfolios X and Y:

[ "A. Are in equilibrium.", "B. Offer an arbitrage opportunity.", "C. Are both underpriced.", "D. Are both fairly priced." ]

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b.

Since Portfolio X has β = 1.0, then X is the market portfolio and E(RM) =16%. Using E(RM) = 16% and rf = 8%, the expected return for portfolio Y is not consistent.

medium

multiple-choice

portfolio management

english

293

1

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744

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nan

Match each example to one of the following behavioral characteristics.<image_1>

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a. – iv b. – iii c. – v d. – i e. – ii

nan

easy

open question

portfolio management

english

294

1

0

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745

english_295_1_r1

nan

Given the following data, is the confidence index rising or falling? What might explain the pattern of yield changes?<image_1>

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table

The confidence index is decreasing.

This year: Confidence Index = (8%/10.5%) = 0.762 Last year: Confidence Index = (8.5%/10%) = 0.850 Thus, the confidence index is decreasing.

easy

open question

portfolio management

english

295

1

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746

english_296_1_r1

The following annual excess rates of return were obtained for nine individual stocks and a market index:<image_1>

Perform the first-pass regressions and tabulate the summary statistics.

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Using the regression feature of Excel with the data presented in the text, the first- pass (SCL) estimation results are:<ans_image_1>

nan

medium

open question

portfolio management

english

296

1

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747

english_297_1_r1

A large corporation issued both fixed and floating-rate notes 5 years ago, with terms given in the following table:<image_1>

Why is the price range greater for the 9% coupon bond than the floating-rate note?

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table

The floating rate note pays a coupon that adjusts to market levels.

The floating rate note pays a coupon that adjusts to market levels. Therefore, it will not experience dramatic price changes as market yields fluctuate. The fixed rate note will therefore have a greater price range.

easy

open question

fixed income

english

297

1

0

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748

english_297_2_r1

nan

Why is the call price for the floating-rate note not of great importance to investors?

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table

The risk of call is low.

The risk of call is low. Because the bond will almost surely not sell for much above par value (given its adjustable coupon rate), it is unlikely that the bond will ever be called.

easy

open question

fixed income

english

297

2

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749

english_297_3_r1

nan

Is the probability of a call for the fixed-rate note high or low?

null

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table

The fixed-rate note to maturity is greater than the coupon rate.

The fixed-rate note currently sells at only 88% of the call price, so that yield to maturity is greater than the coupon rate. Call risk is currently low, since yields would need to fall substantially for the firm to use its option to call the bond

easy

open question

fixed income

english

297

3

0

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750

english_297_4_r1

nan

If the firm were to issue a fixed-rate note with a 15-year maturity, what coupon rate would it need to offer to issue the bond at par value?

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table

9.90%

The 9% coupon notes currently have a remaining maturity of fifteen years and sell at a yield to maturity of 9.9%. This is the coupon rate that would be needed for a newly-issued fifteen-year maturity bond to sell at par.

easy

open question

fixed income

english

297

4

1

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751

english_297_5_r1

nan

Why is an entry for yield to maturity for the floating-rate note not appropriate?

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table

Because the floating rate note pays a variable stream of interest payments to maturity, the effective maturity for comparative purposes with other debt securities is closer to the next coupon reset date than the final maturity date.

Because the floating rate note pays a variable stream of interest payments to maturity, the effective maturity for comparative purposes with other debt securities is closer to the next coupon reset date than the final maturity date. Therefore, yield-to-maturity is an indeterminable calculation for a floating rate note, with “yield-to-recoupon date” a more meaningful measure of return.

medium

open question

fixed income

english

297

5

0

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752

english_298_1_r1

On May 30, 2008, Janice Kerr is considering one of the newly issued 10-year AAA corporate bonds shown in the following exhibit.<image_1>

Suppose that market interest rates decline by 100 basis points (i.e., 1%). Contrast the effect of this decline on the price of each bond.

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The maturity of each bond is ten years, and we assume that coupons are paid semiannually. Since both bonds are selling at par value, the current yield for each bond is equal to its coupon rate. If the yield declines by 1% to 5% (2.5% semiannual yield), the Sentinal bond will increase in value to $107.79 [n=20; i = 2.5%; FV = 100; PMT = 3]. The price of the Colina bond will increase, but only to the call price of 102. The present value of scheduled payments is greater than 102, but the call price puts a ceiling on the actual bond price.

nan

medium

open question

fixed income

english

298

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753

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nan

Should Kerr prefer the Colina over the Sentinal bond when rates are expected to rise or to fall?

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table

If rates are expected to fall, the Sentinal bond is more attractive: since it is not subject to call, its potential capital gains are greater. If rates are expected to rise, Colina is a relatively better investment. Its higher coupon (which presumably is compensation to investors for the call feature of the bond) will provide a higher rate of return than the Sentinal bond.

nan

medium

open question

fixed income

english

298

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754

english_299_1_r1

A convertible bond has the following features:<image_1>

Calculate the conversion premium for this bond

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table

$191.76

Market conversion value = value if converted into stock = 20.83 × $28 = $583.24 14-11 Conversion premium = Bond price – market conversion value = $775.00 – $583.24 = $191.76

easy

open question

fixed income

english

299

1

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755

english_300_1_r1

The following is a list of prices for zero-coupon bonds of various maturities.<image_1>

Calculate the yields to maturity of each bond and the implied sequence of forward rates.

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Maturity 1's YTM is 6.00%, Maturity 2's YTM is 5.50%,Maturity 2's forward rate is 5.0%, Maturity 1's YTM is 5.67%,Maturity 3's forward rate is 6.0%, Maturity 1's YTM is 6.00%,Maturity 4's forward rate is 7.0%

<ans_image_1>

easy

open question

fixed income

english

300

1

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756

english_301_1_r1

Consider the following $1,000 par value zero-coupon bonds:<image_1>

According to the expectations hypothesis, what is the expected 1-year interest rate 3 years from now?

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table

If expectations theory holds, then the forward rate equals the short rate, and the one year interest rate three years from now would be 8.51%

nan

easy

open question

fixed income

english

301

1

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release_basic

757

english_302_1_r1

The term structure for zero-coupon bonds is currently:<image_1> Next year at this time, you expect it to be:<image_2>

What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond?

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6%.

A 3-year zero coupon bond with face value $100 will sell today at a yield of 6% and a price of: $100/1.063 =$83.96 Next year, the bond will have a two-year maturity, and therefore a yield of 6% (from next year’s forecasted yield curve). The price will be $89.00, resulting in a holding period return of 6%.

easy

open question

fixed income

english

302

1

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release_basic

758

english_303_1_r1

Below is a list of prices for zero-coupon bonds of various maturities.<image_1>

An 8.5% coupon $1,000 par bond pays an annual coupon and will mature in 3 years. What should the yield to maturity on the bond be?

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The current bond price is:$1,040.20 This price implies a yield to maturity of 6.97%, as shown by the following: $1,040.17

The current bond price is: ($85 × 0.94340) + ($85 × 0.87352) + ($1,085 × 0.81637) = $1,040.20 This price implies a yield to maturity of 6.97%, as shown by the following: [$85 × Annuity factor (6.97%, 3)] + [$1,000 × PV factor (6.97%, 3)] = $1,040.17

medium

open question

fixed income

english

303

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759

english_303_2_r1

nan

If at the end of the first year the yield curve flattens out at 8%, what will be the 1-year holding-period return on the coupon bond?

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table

If one year from now y = 8%, then the bond price will be: $1,008.92 The holding period rate of return is:5.16%

If one year from now y = 8%, then the bond price will be: [$85 × Annuity factor (8%, 2)] + [$1,000 × PV factor (8%, 2)] = $1,008.92 The holding period rate of return is: [$85 + ($1,008.92 – $1,040.20)]/$1,040.20 = 0.0516 = 5.16%

medium

open question

fixed income

english

303

2

1

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760

english_304_1_r1

Prices of zero-coupon bonds reveal the following pattern of forward rates:<image_1> In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $60 with par value $1,000.

What is the price of the coupon bond?

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Price = $984.10

Price = ($60 × 0.9524) + ($60 × 0.8901) + ($1,060 × 0.8241) = $984.10

easy

open question

fixed income

english

304

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761

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nan

What is the yield to maturity of the coupon bond?

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table

To find the yield to maturity, solve for y in the following equation: $984.10 = [$60 × Annuity factor (y, 3)] + [$1,000 × PV factor (y, 3)] This can be solved using a financial calculator to show that y = 6.60%

nan

medium

open question

fixed income

english

304

2

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762

english_304_3_r1

nan

Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond?

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table

6.66%

<ans_image_1>

medium

open question

fixed income

english

304

3

0

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763

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nan

If you forecast that the yield curve in 1 year will be flat at 7%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period?

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table

5.88%

<ans_image_2>

medium

open question

fixed income

english

304

4

1

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release_basic

764

english_305_1_r1

Fountain Corporation’s economists estimate that a good business environment and a bad business environment are equally likely for the coming year. The managers of the company must choose between two mutually exclusive projects. Assume that the project the company chooses will be the firm’s only activity and that the firm will close one year from today. The company is obligated to make a $3,500 payment to bondholders at the end of the year. The projects have the same systematic risk but different volatilities. Consider the following information pertaining to the two projects: <image_1>

What is the expected value of the company if the low-volatility project is undertaken?

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$3,600

The expected value of each project is the sum of the probability of each state of the economy times the value in that state of the economy. Low-volatility project value = .50($3,500) + .50($3,700) Low-volatility project value = $3,600

easy

open question

equity

english

305

1

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765

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nan

What is the expected value of the company if the high-volatility project is undertaken?

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table

$3,600

The expected value of each project is the sum of the probability of each state of the economy times the value in that state of the economy. High-volatility project value = .50($2,900) + .50($4,300) High-volatility project value = $3,600

easy

open question

equity

english

305

2

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766

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nan

Which of the two strategies maximizes the expected value of the firm?

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table

Same

Since this is the only project for the company, the company value will be the same as the project value

easy

open question

equity

english

305

3

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767

english_305_4_r1

nan

What is the expected value of the company’s equity if the low-volatility project is undertaken?

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table

$100

The value of the equity is the residual value of the company after the bondholders are paid off. If the low-volatility project is undertaken, the firm’s equity will be worth $0 if the economy is bad and $200 if the economy is good. Since each of these two scenarios is equally probable, the expected value of the firm’s equity is: Expected value of equity with low-volatility project = .50($0) + .50($200) Expected value of equity with low-volatility project = $100

easy

open question

equity

english

305

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768

english_305_5_r1

nan

What is the expected value of the company’s equity if the high-volatility project is undertaken?

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table

$400

And the value of the company if the high-volatility project is undertaken will be: Expected value of equity with high-volatility project = .50($0) + .50($800) Expected value of equity with high-volatility project = $400

easy

open question

equity

english

305

5

1

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769

english_305_6_r1

nan

Which project would the company’s stockholders prefer? Explain.

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table

High-volatility project

Risk-neutral investors prefer the strategy with the highest expected value. Thus, the company’s stockholders prefer the high-volatility project since it maximizes the expected value of the company’s equity.

easy

open question

equity

english

305

6

0

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770

english_305_7_r1

nan

Suppose bondholders are fully aware that stockholders might choose to maximize equity value rather than total firm value and opt for the high-volatility project. To minimize this agency cost, the firm’s bondholders decide to use a bond covenant to stipulate that the bondholders can demand a higher payment if the company chooses to take on the high-volatility project. What payment to bondholders would make stockholders indifferent between the two projects?

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$4,100

In order to make stockholders indifferent between the low-volatility project and the high- volatility project, the bondholders will need to raise their required debt payment so that the expected value of equity if the high-volatility project is undertaken is equal to the expected value of equity if the low-volatility project is undertaken. As shown in part b, the expected value of equity if the low-volatility project is undertaken is $100. If the high-volatility project is undertaken, the value of the firm will be $2,900 if the economy is bad and $4,300 if the economy is good. If the economy is bad, the entire $2,900 will go to the bondholders and stockholders will receive nothing. If the economy is good, stockholders will receive the difference between $4,300, the total value of the firm, and the required debt payment. Let X be the debt payment that bondholders will require if the high-volatility project is undertaken. In order for stockholders to be indifferent between the two projects, the expected value of equity if the high-volatility project is undertaken must be equal to $100, so: Expected value of equity = $100 = .50($0) + .50($4,300 – X) X = $4,100

hard

open question

equity

english

305

7

0

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release_basic

771

english_306_1_r1

North Pole Fishing Equipment Corporation and South Pole Fishing Equipment Corporation would have identical equity betas of 1.10 if both were all equity financed. The market value information for each company is shown here: <image_1> The expected return on the market portfolio is 10.9 percent, and the risk-free rate is 3.2 percent. Both companies are subject to a corporate tax rate of 35 percent. Assume the beta of debt is zero.

What is the equity beta of the company North Pole?

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1.6

The equity beta of a firm financed entirely by equity is equal to its unlevered beta. Since each firm has an unlevered beta of 1.10, we can find the equity beta for each. Doing so, we find $\beta_{Equity} = [1 + (1 – t_C)(B/S)]\beta_{Unlevered}$ $\beta_{Equity} = [1 + (1 – .35)(\$2,700,000 / \$3,900,000](1.10) $ $\beta_{Equity}= 1.60 $

easy

open question

equity

english

306

1

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772

english_306_2_r1

nan

What is the equity beta of the company South Pole?

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table

2.13

$\beta_{Equity} = [1 + (1 – t_C)(B/S)]\beta_{Unlevered}$ $\beta_{Equity} = [1 + (1 – .35)(\$3,900,000 / \$2,700,000](1.10) $ $\beta_{Equity}= 2.13 $

easy

open question

equity

english

306

2

1

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773

english_306_3_r1

nan

What is the required rate of return on the company North Pole’ equity?

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table

15.48%

We can use the Capital Asset Pricing Model to find the required return on each firm’s equity. Doing so, we find: $R_S = R_F + \beta_{Equity}(R_M – R_F)$ $R_S = 3.20\% + 1.60(10.90\% – 3.20\%)$ $R_S = 15.48\%$

easy

open question

equity

english

306

3

1

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774

english_306_4_r1

nan

What is the required rate of return on the company South Pole’ equity?

null

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table

19.62%

$R_S = R_F + \beta_{Equity}(R_M – R_F)$ $R_S = 3.20\% + 2.13(10.90\% – 3.20\%)$ $R_S = 19.62\%$

easy

open question

equity

english

306

4

1

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release_basic

775

english_307_1_r1

Bolero, Inc., has compiled the following information on its financing costs:<image_1> The company is in the 35 percent tax bracket and has a target debt–equity ratio of 60 percent. The target short-term debt/long-term debt ratio is 20 percent.

What is the company’s weighted average cost of capital using book value weights?

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0.0609

The company has a capital structure with three parts: long-term debt, short-term debt, and equity. Since interest payments on both long-term and short-term debt are tax-deductible, multiply the pretax costs by (1 – tC) to determine the aftertax costs to be used in the weighted average cost of capital calculation. The WACC using the book value weights is: $R_{WACC} = (X_{STD})(R_{STD})(1 – t_C) + (X_{LTD})(R_{LTD})(1 – t_C) + (X_{Equity})(R_{Equity})$ $R_{WACC} = (\$12 / \$41)(.041)(1 – .35) + (\$20 / \$41)(.072)(1 – .35) + (\$9 / \$41)(.138)$ $R_{WACC} = .0609 , or \, 6.09\%$

medium

open question

corporate finance

english

307

1

0

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776

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nan

What is the company’s weighted average cost of capital using market value weights?

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table

0.099

Using the market value weights, the company’s WACC is: $R_{WACC} = (X_{STD})(R_{STD})(1 – t_C) + (X_{LTD})(R_{LTD})(1 – t_C) + (X_{Equity})(R_{Equity})$ $R_{WACC} = (\$12.5 / \$89.5)(.041)(1 – .35) + (\$23 / \$89.5)(.072)(1 – .35) + (\$54 / \$89.5)(.138) $ $R_{WACC} = .0990, or \,9.90\%$

medium

open question

corporate finance

english

307

2

1

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777

english_307_3_r1

nan

What is the company’s weighted average cost of capital using target capital structure weights?

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table

0.1025

Using the target debt–equity ratio, the target debt–value ratio for the company is: B/S = .60 B = .6S Substituting this in the debt–value ratio, we get: B/V = .6S / (.6S + S) B/V = .6 / 1.6 B/V = .375 And the equity–value ratio is one minus the debt–value ratio, or: S/V = 1 – .375 S/V = .625 We can use the ratio of short-term debt to long-term debt in a similar manner to find the short- term debt to total debt and long-term debt to total debt. Using the short-term debt to long-term debt ratio, we get: STD/LTD = .20 STD = .2LTD Substituting this in the short-term debt to total debt ratio, we get: STD/B = .2LTD / (.2LTD + LTD) STD/B = .2 / 1.2 STD/B = .167 And the long-term debt to total debt ratio is one minus the short-term debt to total debt ratio, or: LTD/B = 1 – .167 LTD/B = .833 Now we can find the short-term debt to value ratio and long-term debt to value ratio by multiplying the respective ratio by the debt–value ratio. So: STD/V = (STD/B)(B/V) STD/V = .167(.375) STD/V = .063And the long-term debt to value ratio is: LTD/V = (LTD/B)(B/V) LTD/V = .833(.375) LTD/V = .313 So, using the target capital structure weights, the company’s WACC is: $R_{WACC} = (X_{STD})(R_{STD})(1 – t_C) + (X_{LTD})(R_{LTD})(1 – t_C) + (X_{Equity})(R_{Equity}) $ $R_{WACC} = (.063)(.041)(1 – .35) + (.313)(.072)(1 – .35) + (.625)(.138) $ $R_{WACC} = .1025, or\, 10.25\%$

hard

open question

corporate finance

english

307

3

1

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778

english_307_4_r1

nan

What is the difference between WACCs?

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table

The different weighting schemes

The differences in the WACCs are due to the different weighting schemes.

easy

open question

corporate finance

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Which is the correct WACC to use for project evaluation?

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WACC computed with target weights

The company’s WACC will most closely resemble the WACC calculated using target weights since future projects will be financed at the target ratio. Therefore, the WACC computed with target weights should be used for project evaluation.

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MVP, Inc., has produced rodeo supplies for over 20 years. The company currently has a debt–equity ratio of 50 percent and is in the 40 percent tax bracket. The required return on the firm’s levered equity is 16 percent. The company is planning to expand its production capacity. The equipment to be purchased is expected to generate the following unlevered cash flows: <image_1>The company has arranged a debt issue of $8.7 million to partially finance the expansion. Under the loan, the company would pay interest of 9 percent at the end of each year on the outstanding balance at the beginning of the year. The company would also make year- end principal payments of $2,900,000 per year, completely retiring the issue by the end of the third year.

Calculate the adjusted present value.

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$2,713,293.68

The adjusted present value of a project equals the net present value of the project under all-equity financing plus the net present value of any financing side effects. First, we need to calculate the unlevered cost of equity. According to Modigliani-Miller Proposition II with corporate taxes: $R_S = R_0 + (B/S)(R_0 – R_B)(1 – t_C) .16 = R_0 + (.50)(R_0 – .09)(1 – .40)$ $R_0 = .1438, or\, 14.38\%$ Now we can find the NPV of an all-equity project, which is: NPV = PV(Unlevered Cash Flows) $NPV = –\$15,100,000 + \$5,400,000 / 1.1438 + \$8,900,000 / 1.14382 + \$8,600,000 / 1.14383 NPV = \$2,169,595.50$ Next, we need to find the net present value of financing side effects. This is equal to the aftertax present value of cash flows resulting from the firm’s debt. So: NPV = Proceeds – Aftertax PV(Interest Payments) – PV(Principal Payments) Each year, an equal principal payment will be made, which will reduce the interest accrued during the year. Given a known level of debt, debt cash flows should be discounted at the pre-tax cost of debt, so the NPV of the financing effects is: $NPV = \$8,700,000 – (1 – .40)(.09)(\$8,700,000) / 1.09 – \$2,900,000 / 1.09 – (1 – .40)(.09)(\$5,800,000) / 1.092 – \$2,900,000 / 1.09^2 – (1 – .40)(.09)(\$2,900,000) / 1.093 – \$2,900,000 / 1.09^3$ $NPV = \$543,698.19$ So, the APV of project is: APV = NPV(All-equity) + NPV(Financing side effects) $APV = \$2,169,595.50 + 543,698.19$ $APV = \$2,713,293.68$

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The balance sheet for Levy Corp. is shown here in market value terms. There are 14,000 shares of stock outstanding. <image_1> The company has declared a dividend of $1.60 per share. The stock goes ex dividend tomorrow.

Ignoring any tax effects, what is the stock selling for today?

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$36.21 per share

The stock price is the total market value of equity divided by the shares outstanding, so: $P_0 = \$507,000 equity / 14,000\, shares$ $P_0 = \$36.21 per \,share$

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nan

What will it sell for tomorrow?

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$34.61 per share

Ignoring tax effects, the stock price will drop by the amount of the dividend, so: $P_X = \$36.21 – 1.60 $ $P_X = \$34.61$

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english_310_1_r1

The market value balance sheet for Outbox Manufacturing is shown here. Outbox has declared a stock dividend of 25 percent. The stock goes ex dividend tomorrow (the chronology for a stock dividend is similar to that for a cash dividend). There are 22,000 shares of stock outstanding. <image_1>

What will the ex-dividend price be?

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$23.82 per share

The stock price is the total market value of equity divided by the shares outstanding, so: $P_0 =\$655,000 equity / 22,000 shares$ $P_0 = \$29.77 per share$ The shares outstanding will increase by 25 percent, so: New shares outstanding= 22,000(1.25) New shares outstanding = 27,500 The new stock price is the market value of equity divided by the new shares outstanding, so: $P_X = \$655,000 / 27,500 shares $ $P_X = \$23.82$

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The company with the common equity accounts shown here has declared a stock dividend of 15 percent when the market value of its stock is $57 per share. Find what effects on the equity accounts will the distribution of the stock dividend have.<image_1>

What is the value of new common stock?

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$500,250

With a stock dividend, the shares outstanding will increase by one plus the dividend amount, so: New shares outstanding = 435,000(1.15) New shares outstanding = 500,250

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What is the value of new capital surplus?

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$5,804,000

The capital surplus is the capital paid in excess of par value, which is $1, so: Capital surplus for new shares = 65,250($56) Capital surplus for new shares = $3,654,000 The new capital surplus will be the old capital surplus plus the additional capital surplus for the new shares, so: Capital surplus = $2,150,000 + 3,654,000 Capital surplus = $5,804,000

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The all-equity firm Metallica Heavy Metal Mining (MHMM) Corporation wants to diversify its operations. Some recent financial information for the company is shown here: <image_1> MHMM is considering an investment that has the same PE ratio as the firm. The cost of the investment is $1,500,000, and it will be financed with a new equity issue. The return on the investment will equal MHMM’s current ROE.

What is the current EPS?

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$15.08 per share

The current ROE of the company is: $ROE_0 = NI_0 / TE_0$ $ROE_0 = \$980,000 / (\$9,400,000 – 4,100,000)$ $ROE_0 = .1849, or 18.49\%$ The new net income will be the ROE times the new total equity, or: $NI_1 = (ROE_0)(TE_1)$ $NI_1 = .1849($5,300,000 + 1,500,000)$ $NI_1 = \$1,257,358$ The company’s current earnings per share are: $EPS_0 = NI_0 / Shares outstanding_0$ $EPS_0 = \$980,000 / 65,000 shares $ $EPS_0 = \$15.08$

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What is the value of EPS after the stock offer ?

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$14.79 per share

The number of shares the company will offer is the cost of the investment divided by the current share price, so: Number of new shares = $1,500,000 / $75 Number of new shares = 20,000 The earnings per share after the stock offer will be: $EPS_1 = \$1,257,358 / (65,000 + 20,000 shares) $ $EPS_1 = \$14.79$

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What is the current book value per share?

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$81.54 per share

The current PE ratio is: $(PE)_0 = \$75 / \$15.08 $ $(PE)_0 = 4.974$ Assuming the PE remains constant, the new stock price will be: $P_1 = 4.974(\$14.79) $ $P_1 = \$73.58$ The current book value per share and the new book value per share are: $BVPS_0 = TE_0 / shares_0$ $BVPS_0 = \$5,300,000 / 65,000 shares $ $BVPS_0 = \$81.54 per share$

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What is the new book value per share?

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$80.00 per share

$BVPS_1 = TE_1 / shares_1$ $BVPS_1 = (\$5,300,000 + 1,500,000) / 85,000 shares $ $BVPS_1 = \$80.00 per share$

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What is the current market value per share?

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0.9198

$Market-to-book_0 = \$75 / \$81.54 $ $Market-to-book_0 = .9198$

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What is the new market value per share?

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0.9198

$Market-to-book_1 = \$73.58 /\ $80.00 $ $Market-to-book_1 = .9198$

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What is the NPV of this investment?

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–$120,283

The NPV of the project is the new market value of the firm minus the current market value of the firm, or: NPV = –$1,500,000 + [$73.58(85,000) – $75(65,000)] NPV = –$120,283

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Does dilution take place?

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Yes.

Accounting dilution takes place here because the market-to-book ratio is less than one. Market value dilution has occurred since the firm is investing in a negative NPV project.

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Use the option quote information shown here to answer the questions that follow. The stock is currently selling for $83. <image_1>

Are the call options in the money?

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Yes.

The calls are in the money.

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313

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795

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nan

What is the intrinsic value of an RWJCorp.call option?

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$3

The intrinsic value of the calls is $3.

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796

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Are the put options in the money?

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No.

The puts are out of the money.

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nan

What is the intrinsic value of an RWJ Corp. put option?

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$0

The intrinsic value of the puts is $0.

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798

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Two of the options are clearly mispriced. Which ones?

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Mar call and the Oct put.

The call is mispriced because it is selling for less than its intrinsic value. The October put is mispriced because it sells for less than the July put.

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Use the option quote information shown here to answer the questions that follow. The stock is currently selling for $114.<image_1>

Suppose you buy 10 contracts of the February 110 call option. How much will you pay, ignoring commissions?

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$7,600

Each contract is for 100 shares, so the total cost is: Cost = 10(100 shares/contract)($7.60) Cost = $7,600

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