MFS HW4

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Risk and Return: Introduction

Risk is an important concept affecting security prices and rates of return. Risk is the chance that some unfavorable event will occur, and there is a trade-off between risk and return. The higher an investment’s risk, the -__________-lowerhigherequivalentItem 1 the return required to induce investors to purchase the asset. This relationship between risk and return indicates that investors are risk -____________ ambivalentaverseItem 2 ; investors dislike risk and require ________lowerhigherequivalentItem 3 rates of return as an inducement to buy riskier securities. A -________-risk premiumpar valuecorrelation coefficientItem 4 represents the additional compensation investors require for bearing risk; it is the difference between the expected rate of return on a given risky asset and that on a less risky asset. An asset’s risk can be considered in two ways: On a stand-alone basis and in a portfolio context.

Risk and Return: Stand-Alone Risk

Stand-alone risk is the risk an investor would face if he or she held only ________-one portfolioone assetmultiple assetsCorrect 1 of Item 1. No investment should be undertaken unless its expected rate of return is high enough to compensate for its perceived ________ riskcostreturnCorrect 2 of Item 1. The expected rate of return is the return expected to be realized from an investment; it is calculated as the __________ -combined sumstandard deviationweighted averageCorrect 3 of Item 1 of the probability distribution of possible results as shown below:

The ________tighterbroaderCorrect 4 of Item 1 an asset’s probability distribution, the lower its risk. Two useful measures of stand-alone risk are standard deviation and coefficient of variation. Standard deviation is a statistical measure of the variability of a set of observations as shown below:

If you have a sample of actual historical data, then the standard deviation calculation would be changed as follows:

The coefficient of variation is a better measure of stand-alone risk than standard deviation because it is a standardized measure of risk per unit; it is calculated as the____________ correlation coefficientrisk premiumstandard deviationCorrect 5 of Item 1 divided by the expected return. The coefficient of variation shows the risk per unit of return, so it provides a more meaningful risk measure when the expected returns on two alternatives are not _________ -identicaldifferentcorrelatedCorrect 6 of Item 1.

Quantitative Problem: You are given the following probability distribution for CHC Enterprises:

State of Economy

Probability Rate of Return

Strong 0.25 19%

Normal 0.5 9

Weak 0.25 -4

What is the stock’s expected return? Round your answer to 2 decimal places. Do not round intermediate calculations.
% ________

What is the stock’s standard deviation? Round your answer to two decimal places. Do not round intermediate calculations.
% _______

What is the stock’s coefficient of variation? Round your answer to two decimal places. Do not round intermediate calculations. _______

Risk and Return: Risk in Portfolio Context

The capital asset pricing model (CAPM) explains how risk should be considered when stocks and other assets are held________ -by themselvesin portfoliosCorrect 1 of Item 1. The CAPM states that any stock’s required rate of return is________ less thangreater thanequal toCorrect 2 of Item 1 the risk-free rate of return plus a risk premium that reflects only the risk remaining ________ afterbeforeCorrect 3 of Item 1 diversification. Most individuals hold stocks in portfolios. The risk of a stock held in a portfolio is typically _________ equal tolower thanhigher thanCorrect 4 of Item 1 the stock’s risk when it is held alone. Therefore, the risk and return of an individual stock should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held.

The expected rate of return on a portfolio equals the weighted average of the expected returns on the assets held in the portfolio. A portfolio’s risk ________ sisn’tCorrect 5 of Item 1 calculated as the weighted average of the individual stock’s standard deviations; the portfolio’s risk is generally ________ largersmallerCorrect 6 of Item 1 because diversification _______ raiseslowersCorrect 7 of Item 1 the portfolio’s risk.

Two important terms when discussing ________ symmetrydiscountingdiversificationCorrect 8 of Item 1 are correlation and correlation coefficient. Correlation is the tendency of two variables to move together, while correlation coefficient is a measure of the degree of relationship between two variables. If a portfolio consists of two stocks that are perfectly ________ positivelynegativelyCorrect 9 of Item 1 correlated then the portfolio is riskless because the stocks’ returns move counter cyclically to each other. If the returns of the stocks are perfectly -________ positivelynegativelyCorrect 10 of Item 1 correlated then the stocks’ returns would move up and down together and the portfolio would be exactly as risky as the individual stocks. In this situation, diversification would be completely ________ usefuluselessCorrect 11 of Item 1 for reducing risk. In reality, most stocks are __________ positivelynegativelyCorrect 12 of Item 1 correlated but not perfectly. So, combining stocks into portfolios reduces risk but does not completely eliminate it. This illustrates that ________ symmetrydiscountingdiversificationCorrect 13 of Item 1 can reduce risk, but not completely eliminate risk.

Portfolios risk can be broken down into two types. ________ SystematicDiversifiableMarketCorrect 14 of Item 1 risk is that part of a security’s risk associated with random events. It can be eliminated by proper diversification and is also known as company-specific risk. On the other hand, _________ unystematicdiversifiablemarketCorrect 15 of Item 1 risk is the risk that remains in a portfolio after diversification has eliminated all company-specific risk. Standard deviation is not a good measure of risk when a stock is held in a portfolio. A stock’s relevant risk is the risk that remains once a stock is in a diversified portfolio. Its contribution to the portfolio’s market risk is measured by a stock’s ______ correlation coefficientrisk premiumbeta coefficientCorrect 16 of Item 1, which shows the extent to which a given stock’s returns move up and down with the stock market. An average stock’s beta is -________ less thanequal togreater thanCorrect 17 of Item 1 1 because an average-risk stock is one that tends to move up and down in step with the general market. A stock with a beta _________ less thanequal togreater thanCorrect 18 of Item 1 1 is considered to have high risk, while a stock with beta _______ less thanequal togreater thanCorrect 19 of Item 1 1 is considered to have low risk.

Quantitative Problem: You are holding a portfolio with the following investments and betas:

StockDollar

investment Beta

A $250,000 1.2

B 100,000 1.5

C 500,000 0.75

D 150,000 – 0.25

Total investment1,000,000

The market’s required return is 9% and the risk-free rate is 5%. What is the portfolio’s required return? Round your answer to 3 decimal places. Do not round intermediate calculations.
% ______

Risk and Return: Security Market Line

The security market line (SML) is an equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities. The SML equation is given below:

If a stock’s expected return plots on or above the SML, then the stock’s return is _________ insufficientsufficientCorrect 1 of Item 1 to compensate the investor for risk. If a stock’s expected return plots below the SML, the stock’s return is _________ insufficientsufficientCorrect 2 of Item 1 to compensate the investor for risk.

The SML line can change due to expected inflation and risk aversion. If inflation changes, then the SML plotted on a graph will shift up or down parallel to the old SML. If risk aversion changes, then the SML plotted on a graph will rotate up or down becoming more or less steep if investors become more or less risk averse. A firm can influence market risk (hence its beta coefficient) through changes in the composition of its assets and through changes in the amount of debt it uses.

Quantitative Problem: You are given the following information for Wine and Cork Enterprises (WCE):

rRF = 3%; rM = 8%; RPM = 5%, and beta = 1

What is WCE’s required rate of return? Round your answer to 2 decimal places. Do not round intermediate calculations.
% _________

If inflation increases by 2% but there is no change in investors’ market risk premium, what is WCE’s required rate of return now? Round your answer to two decimal places. Do not round intermediate calculations.
% ________

Assume now that there is no change in inflation, but market risk premium increases by 2%. What is WCE’s required rate of return now? Round your answer to two decimal places. Do not round intermediate calculations.
% ________

If inflation increases by 2% and market risk premium increases by 2%, what is WCE’s required rate of return now? Round your answer to two decimal places. Do not round intermediate calculations.
% _______

Problem 6-02
Required Rate of Return

AA Corporation’s stock has a beta of 0.9. The risk-free rate is 3% and the expected return on the market is 12%. What is the required rate of return on AA’s stock? Round your answer to two decimal places.

% ______

Portfolio Beta

Your retirement fund consists of a $7,500 investment in each of 20 different common stocks. The portfolio’s beta is 1.85. Suppose you sell one of the stocks with a beta of 1.0 for $7,500 and use the proceeds to buy another stock whose beta is 2.25. Calculate your portfolio’s new beta. Do not round intermediate calculations. Round your answer to two decimal places. _______

Problem 6-12
Required Rate of Return

Stock R has a beta of 1.4, Stock S has a beta of 0.30, the expected rate of return on an average stock is 9%, and the risk-free rate is 6%. By how much does the required return on the riskier stock exceed that on the less risky stock? Round your answer to two decimal places.

% ______

Problem 6-13
Historical Realized Rates of Return

Stocks A and B have the following historical returns:

Year

A B

2012-17.00% -12.60%

2013 27.25 27.80

2014 16.75 31.30

2015 -3.50 -8.00

2016 30.25 15.25

Calculate the average rate of return for each stock during the 5-year period. Round your answers to two decimal places.
Stock A % _______
Stock B % ________
Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Round your answers to two decimal places.
YearPortfolio
2012 _______ %
2013 ________%
2014 _________%
2015 _________%
2016 _________%
Average return ______%
1. Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places.
  rA rB Portfolio
Std. Dev. _______% _______% _______%
If you are a risk-averse investor then, assuming these are your only choices, would you prefer to hold Stock A, Stock B, or the portfolio?
____________ Stock AStock BPortfolio

Problem 6-14
Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time:

Year Stock X Stock Y Market

2012 13% 13% 13%

2013 18 8 12

2014 -16 -3 -11

2015 5 3 3

2016 22 12 13

Assume that the risk-free rate is 4% and the market risk premium is 7%. Do not round intermediate calculations.

What is the beta of Stock X? Round your answer to two decimal places.
What is the beta of Stock Y? Round your answer to two decimal places.
What is the required rate of return on Stock X? Round your answer to one decimal place.
%
What is the required rate of return on Stock Y? Round your answer to one decimal place.
%
What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? Round your answer to one decimal place.
%

10.

Determining the Cost of Capital: Introduction

Companies issue bonds, preferred stock, and common equity to raise capital to invest in capital budgeting projects. Capital is a necessary factor of production, and like any other factor, it has a cost. This cost is equal to the _________ security analyst’smarginal investor’scompany vendor’sItem 1 required return on the applicable security. The rates of return that investors require on bonds, preferred stocks, and common equity represent the costs of those securities to the firm. Companies estimate the required returns on their securities, calculate a weighted average of the costs of their different types of capital, and use this average cost for capital budgeting purposes.

The firm’s primary financial objective is to _________ -minimizemaintain the initial level ofmaximizeItem 2 shareholder value. To do this, companies invest in projects that earn _______-more thanless thanequal toItem 3 their cost of capital. So, the cost of capital is often referred to as the _________crossoverhurdleindifferenceItem 4 rate: When calculating the weighted average cost of capital (WACC), our concern is with capital that must be provided by -_________managersvendorsinvestorsItem 5 —interest-bearing debt, preferred stock, and common equity. _________-Notes payableAccounts payableLong-term debtItem 6 and accruals, which arise spontaneously from operations when capital budgeting projects are undertaken, are not included as part of total invested capital because they do not come directly from investors.

Which of the following would be included in the calculation of the book value of total invested capital? Choose the response that is most correct.

Notes payable.
Taxes payable.
Retained earnings.
Responses a and c would be included in the calculation of total invested capital.
None of the above would be included in the calculation of total invested capital.

The correct response is _________Statement aStatement bStatement cStatement dStatement eItem

11.

Determining the Cost of Capital: Cost of Debt

A firm’s before-tax cost of debt, rd, is the interest rate that the firm must pay on _________outstandingsecurednewItem 1 debt. Because interest is tax deductible, the relevant cost of -Select-outstandingsecurednewItem 2 debt used to calculate a firm’s WACC is the _______-after-taxbefore-taxItem 3 cost of debt, rd(1 – T). The ________after-taxbefore-taxItem 4 cost of debt is used in calculating the WACC because we are interested in maximizing the value of the firm’s stock, and the stock price depends on ________ after-taxbefore-taxItem 5 cash flows. It is important to emphasize that the cost of debt is the interest rate on ________outstandingnewItem 6 debt, not _______outstandingnewItem 7 debt because our primary concern with the cost of capital is its use in capital budgeting decisions. The rate at which the firm has borrowed in the past is _________relevantirrelevantItem 8 because we need to know the cost of _______ outstandingsecurednewItem 9 capital. For these reasons, the ________ current yield rateyield to maturitycoupon interest rateItem 10 on outstanding debt (which reflects current market conditions) is a better measure of the cost of debt than the _________ current yield rateyield to maturitycoupon interest rateItem 11 . The ______current yield rateyield to maturitycoupon interest rateItem 12 on the company’s _______longshortItem 13 -term debt is generally used to calculate the cost of debt because more often than not, the capital is being raised to fund _______ -longshortItem 14 -term projects.

Quantitative Problem: 5 years ago, Barton Industries issued 25-year noncallable, semiannual bonds with a $1,700 face value and a 7% coupon, semiannual payment ($59.5 payment every 6 months). The bonds currently sell for $845.87. If the firm’s marginal tax rate is 40%, what is the firm’s after-tax cost of debt? Round your answer to 2 decimal places. Do not round intermediate calculations.
_________%

Determining the Cost of Capital: Cost of Preferred Stock

The cost of preferred stock, rps, used in the weighted average cost of capital equation is calculated as the preferred dividend, Dps, divided by the current price of the preferred stock, Pps. _______ANoItem 1 tax adjustment is made when calculating rps because preferred dividends _______aren’tareItem 2 tax deductible; so _________thenoItem 3 tax savings are associated with preferred stock.

Quantitative Problem: Barton Industries can issue perpetual preferred stock at a price of $51 per share. The stock would pay a constant annual dividend of $4.30 per share. If the firm’s marginal tax rate is 40%, what is the company’s cost of preferred stock? Round your answer to 2 decimal places.
_________ %

13.

Determining the Cost of Capital: Cost of Retained Earnings

The cost of common equity is based on the rate of return that investors require on the company’s common stock. New common equity is raised in two ways: (1) by retaining some of the current year’s earnings and (2) by issuing new common stock. Equity raised by issuing stock has a(n) __________loweridenticalhigherItem 1 cost, re, than equity raised from retained earnings, rs, due to flotation costs required to sell new common stock. Some argue that retained earnings should be “free” because they represent money that is left over after dividends are paid. While it is true that no direct costs are associated with retained earnings, this capital still has a cost, a(n) __________externalityopportunityconfiscatoryItem 2 cost. The firm’s after-tax earnings belong to its stockholders, and these earnings serve to compensate them for the use of their capital. The earnings can either be paid out in the form of dividends to stockholders who could have invested this money in alternative investments or retained for reinvestment in the firm. Therefore, the firm needs to earn at least as much on any earnings retained as the stockholders could earn on alternative investments of comparable risk. If the firm cannot invest retained earnings to earn at least rs, it should pay those funds to its stockholders and let them invest directly in stocks or other assets that will provide that return. There are three procedures that can be used to estimate the cost of retained earnings: the Capital Asset Pricing Model (CAPM), the Bond-Yield-Plus-Risk-Premium approach, and the Discounted Cash Flow (DCF) approach.

CAPM

The firm’s cost of retained earnings can be estimated using the CAPM equation as follows:

rs = rRF + (RPM)bi = rRF + (rM – rRF)bi

The CAPM estimate of rs is equal to the risk-free rate, rRF, plus a risk premium that is equal to the risk premium on an average stock, (rM – rRF), scaled up or down to reflect the particular stock’s risk as measured by its beta coefficient, bi. This model assumes that a firm’s stockholders are ________wellsomewhatnot wellItem 3 diversified, but if they are ________wellsomewhatnot wellItem 4 diversified, then the firm’s true investment risk would not be measured by -Select-growthbetayieldItem 5 and the CAPM estimate would -________understateoverstateapproximateItem 6 the correct value of rs.

Bond-Yield-Plus-Risk-Premium

If reliable inputs for the CAPM are not available as would be true for a closely held company, analysts often use a subjective procedure to estimate the cost of equity. Empirical studies suggest that the risk premium on a firm’s stock over its own bonds generally ranges from 3 to 5 percentage points. The equation is shown as: rs = Bond yield + Risk premium. Note that this risk premium is _______identical todifferent fromItem 7 the risk premium given in the CAPM. This method doesn’t produce a precise cost of equity, but does provide a ballpark estimate.

DCF

The DCF approach for estimated the cost of retained earnings, rs, is given as follows:

s = D1/P0 + Expected gL

Investors expect to receive a dividend yield, , plus a capital gain, gL, for a total expected return. In -__________recessionsequilibriumupturnItem 8 , this expected return is also equal to the required return. It’s easy to calculate the dividend yield; but because stock prices fluctuate, the yield varies from day to day, which leads to fluctuations in the DCF cost of equity. Also, it is difficult to determine the proper growth especially if past growth rates are not expected to continue in the future. However, we can use growth rates as projected by security analysts, who regularly forecast growth rates of earnings and dividends.

Which method should be used to estimate rs? If management has confidence in one method, it would probably use that method’s estimate. Otherwise, it might use some weighted average of the three methods. Judgment is important and comes into play here, as is true for most decisions in finance.

Quantitative Problem: Barton Industries estimates its cost of common equity by using three approaches: the CAPM, the bond-yield-plus-risk-premium approach, and the DCF model. Barton expects next year’s annual dividend, D1, to be $2.10 and it expects dividends to grow at a constant rate gL = 4.5%. The firm’s current common stock price, P0, is $26.00. The current risk-free rate, rRF, = 4.3%; the market risk premium, RPM, = 5.6%, and the firm’s stock has a current beta, b, = 1.3. Assume that the firm’s cost of debt, rd, is 8.48%. The firm uses a 3.6% risk premium when arriving at a ballpark estimate of its cost of equity using the bond-yield-plus-risk-premium approach. What is the firm’s cost of equity using each of these three approaches? Do not round intermediate calculations. Round your answers to 2 decimal places.

CAPM cost of equity:_______%

Bond-Yield-Plus-Risk-Premium: ________%DCF

cost of equity: _________%

If you are equally confident of all three methods, then what is the best estimate of the firm’s cost of equity?
_______The best estimate is the highest percentage of the three approaches.The best estimate is the average of the three approaches.The best estimate is the lowest percentage of the three approaches.Item 12

14.

Determining the Cost of Capital: Cost of New Common Stock

If a firm plans to issue new stock, flotation costs (investment bankers’ fees) should not be ignored. There are two approaches to use to account for flotation costs. The first approach is to add the sum of flotation costs for the debt, preferred, and common stock and add them to the initial investment cost. Because the investment cost is increased, the project’s expected return is reduced so it may not meet the firm’s hurdle rate for acceptance of the project. The second approach involves adjusting the cost of common equity as follows:

The difference between the flotation-adjusted cost of equity and the cost of equity calculated without the flotation adjustment represents the flotation cost adjustment.

Quantitative Problem: Barton Industries expects next year’s annual dividend, D1, to be $1.70 and it expects dividends to grow at a constant rate gL = 4.7%. The firm’s current common stock price, P0, is $24.40. If it needs to issue new common stock, the firm will encounter a 5.7% flotation cost, F. Assume that the cost of equity calculated without the flotation adjustment is 12% and the cost of old common equity is 11.5%. What is the flotation cost adjustment that must be added to its cost of retained earnings? Round your answer to 2 decimal places. Do not round intermediate calculations.
_________ %

What is the cost of new common equity? Round your answer to 2 decimal places. Do not round intermediate calculations.
________%

15.

Determining the Cost of Capital: Weighted Average Cost of Capital

The firm’s target capital structure is the mix of debt, preferred stock, and common equity the firm plans to raise funds for its future projects. The target proportions of debt, preferred stock, and common equity, along with the cost of these components, are used to calculate the firm’s weighted average cost of capital (WACC). If the firm will not have to issue new common stock, then the cost of retained earnings is used in the firm’s WACC calculation. However, if the firm will have to issue new common stock, the cost of new common stock should be used in the firm’s WACC calculation.

Quantitative Problem: Barton Industries expects that its target capital structure for raising funds in the future for its capital budget will consist of 40% debt, 5% preferred stock, and 55% common equity. Note that the firm’s marginal tax rate is 40%. Assume that the firm’s cost of debt, rd, is 7.1%, the firm’s cost of preferred stock, rps, is 6.6% and the firm’s cost of equity is 11.1% for old equity, rs, and 11.98% for new equity, re. What is the firm’s weighted average cost of capital (WACC1) if it uses retained earnings as its source of common equity? Round your answer to 3 decimal places. Do not round intermediate calculations.
____%

What is the firm’s weighted average cost of capital (WACC2) if it has to issue new common stock? Round your answer to 3 decimal places. Do not round intermediate calculations.
________%

Problem 9-7
WACC

Shi Import-Export’s balance sheet shows $300 million in debt, $50 million in preferred stock, and $250 million in total common equity. Shi’s tax rate is 35%, rd = 7%, rps = 8.9%, and rs = 11%. If Shi has a target capital structure of 30% debt, 5% preferred stock, and 65% common stock, what is its WACC? Round your answer to two decimal places.

________%

Problem 9-10
Cost of Equity

The earnings, dividends, and stock price of Shelby Inc. are expected to grow at 8% per year in the future. Shelby’s common stock sells for $26.75 per share, its last dividend was $2.00, and the company will pay a dividend of $2.16 at the end of the current year.

Using the discounted cash flow approach, what is its cost of equity? Round your answer to two decimal places.
_______ %
If the firm’s beta is 1.5, the risk-free rate is 4%, and the expected return on the market is 12%, then what would be the firm’s cost of equity based on the CAPM approach? Round your answer to two decimal places.
________%
If the firm’s bonds earn a return of 12%, then what would be your estimate of rs using the over-own-bond-yield-plus-judgmental-risk-premium approach? Round your answer to two decimal places. (Hint: Use the midpoint of the risk premium range.)
________%
On the basis of the results of parts a through c, what would be your estimate of Shelby’s cost of equity? Assume Shelby values each approach equally. Round your answer to two decimal places.
__________ %

18.

Problem 9-15
WACC Estimation

On January 1, the total market value of the Tysseland Company was $60 million. During the year, the company plans to raise and invest $20 million in new projects. The firm’s present market value capital structure, here below, is considered to be optimal. There is no short-term debt.

Debt $30,000,000

Common equity 30,000,000

Total capital $60,000,000

New bonds will have an 6% coupon rate, and they will be sold at par. Common stock is currently selling at $30 a share. The stockholders’ required rate of return is estimated to be 12%, consisting of a dividend yield of 4% and an expected constant growth rate of 8%. (The next expected dividend is $1.20, so the dividend yield is $1.20/$30 = 4%.) The marginal tax rate is 40%.

In order to maintain the present capital structure, how much of the new investment must be financed by common equity? Enter your answer in dollars. For example, $1.2 million should be entered as $1200000.
$ _______
Assuming there is sufficient cash flow for Tysseland to maintain its target capital structure without issuing additional shares of equity, what is its WACC? Round your answer to two decimal places.
________ %
Suppose now that there is not enough internal cash flow and the firm must issue new shares of stock. Qualitatively speaking, what will happen to the WACC? No numbers are required to answer this question.
I. rs and the WACC will increase due to the flotation costs of new equity.
II. rs and the WACC will decrease due to the flotation costs of new equity.
III. rs will increase and the WACC will decrease due to the flotation costs of new equity.
IV. rs will decrease and the WACC will increase due to the flotation costs of new equity.
V. rs and the WACC will not be affected by flotation costs of new equity.
_________-IIIIIIIVVItem 3

MFS HW4

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