FNCE 4

Which one of the following statements related to capital gains is correct?

An increase in an unrealized capital gain will increase the capital gains yield.

The risk-free rate of return is 2.7 percent, the inflation rate is 3.1 percent, and the market risk premium is 6.9 percent. What is the expected rate of return on a stock with a beta of 1.08?

E(r) = .027 + 1.08(.069) E(r) = .1015, or 10.15%

Assume all stock prices fairly reflect all of the available information on those stocks. Which one of the following terms best defines the stock market under these conditions?

Efficient capital market

The expected return on a portfolio: I. can never exceed the expected return of the best performing security in the portfolio. II. must be equal to or greater than the expected return of the worst performing security in the portfolio. III. is independent of the unsystematic risks of the individual securities held in the portfolio. IV. is independent of the allocation of the portfolio amongst individual securities.

I, II, and III only

hich one of the following is an example of systematic risk?

Investors panic causing security prices around the globe to fall precipitously

Which one of the following statements related to market efficiency tends to be supported by current evidence?

Markets tend to respond quickly to new information.

Which one of the following statements is correct?

Over time, the average unexpected return will be zero.

Which one of the following statements related to WACC is correct for a company that uses debt in its capital structure?

The WACC would most likely decrease if the firm replaced its preferred stock with debt.

A company's current cost of capital is based on:

both the returns currently required by its debtholders and stockholders.

The cost of capital for a new project:

depends upon how the funds raised for that project are going to be spent.

A company's overall cost of equity is:

directly related to the risk level of the firm.

The primary purpose of portfolio diversification is to:

eliminate asset-specific risk.

If a company uses its WACC as the discount rate for all of the projects it undertakes then the company will tend to:

increase the average risk level of the company over time.

Assume Russo's has a debt-equity ratio of .4 and uses the capital asset pricing model to determine its cost of equity. As a result, the company's cost of equity:

is dependent upon a reliable estimate of the market risk premium.

The expected rate of return on a stock portfolio is a weighted average where the weights are based on the:

market value of the investment in each stock.

Simple Foods has a zero coupon bond issue outstanding that matures in 14 years. The bonds are selling at 56 percent of par value. What is the company's aftertax cost of debt if the combined tax rate is 23 percent? (Use semiannual compounding.)

.56($1,000) = $1,000/[1 + (r/2)]14(2) r = .04185, or 4.185% Aftertax cost of debt = 4.185%(1 − .23) Aftertax cost of debt = 3.22%

Which one of the following is the best example of a diversifiable risk?

A firm's sales decrease

Which one of the following statements is correct concerning a portfolio beta?

A portfolio beta is a weighted average of the betas of the individual securities contained in the portfolio.

A group of individuals got together and purchased all of the outstanding shares of common stock of DL Smith Inc. What is the return that these individuals require on this investment called?

Cost of equity

The expected return on JK stock is 16.28 percent while the expected return on the market is 11.97 percent. The stock's beta is 1.63. What is the risk-free rate of return?

E(r) = .1628 = rf + 1.63(.1197 − rf) rf = .0513, or 5.13%

ATTEMPT TWO

QUESTIONS

Which one of the following is a positively sloped linear function that is created when expected returns are graphed against security betas?

Security market line

The cost of preferred stock:

is equal to the dividend yield.

You want your portfolio beta to be .95. Currently, your portfolio consists of $4,000 invested in Stock A with a beta of 1.26 and $7,000 in Stock B with a beta of .94. You have another $8,000 to invest and want to divide it between an asset with a beta of 1.74 and a risk-free asset. How much should you invest in the risk-free asset?

βPortfolio = .95 = ($4,000/$19,000)(1.26) + ($7,000/$19,000)(.94) + [($8,000 − x)/$19,000](1.74) + (x/$19,000)(0) x = $4,305

Which one of the following is represented by the slope of the security market line?

Market risk premium

Steve has invested in twelve different stocks that have a combined value today of $121,300. Fifteen percent of that total is invested in Wise Man Foods. The 15 percent is a measure of which one of the following?

Portfolio weight

Which one of the following statements related to risk is correct?

The systematic risk of a portfolio can be effectively lowered by adding T-bills to the portfolio

A news flash just appeared that caused about a dozen stocks to suddenly increase in value by 12 percent. What type of risk does this news flash best represent?

Unsystematic

Textile Mills borrows money at a rate of 8.7 percent. This interest rate is referred to as the:

cost of debt.

Assigning discount rates to individual projects based on the risk level of each project:

may cause the company's overall weighted average cost of capital to either increase or decrease over time.

The excess return earned by an asset that has a beta of 1.34 over that earned by a risk-free asset is referred to as the:

risk premium.

Decline Inc. is trying to determine its cost of debt. The firm has a debt issue outstanding with 13 years to maturity that is quoted at 105.2 percent of face value. The issue makes semiannual payments and has an embedded cost of 6 percent annually. What is the aftertax cost of debt if the tax rate is 21 percent?

1.052($1,000) = [.06($1,000)/2][(1 − {1/[1 + (r/2)]13(2)})/(r/2)] + $1,000/[1 + (r/2)]13(2) Using trial-and-error, a financial calculator, or a computer: r = 5.437% RD Aftertax = 5.437%(1 − .21) RD Aftertax = 4.30%

A stock had annual returns of 5.1 percent, 12.2 percent, −3.8 percent, and 9.4 percent for the past four years. The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.

Arithmetic average = (.051 + .122 − .038 + .094)/4 Arithmetic average = .0573, or 5.73% Geometric return = [1.051 (1.122) (.962) (1.094)].25 − 1 Geometric return = .0555, or 5.55%

A stock had returns of 5 percent, 14 percent, 11 percent, −8 percent, and 6 percent over the past five years. What is the standard deviation of these returns?

Average return = (.05 + .14 + .11 − .08 + .06)/5 Average return = .056 σ = {[1/(5 − 1)] [(.05 − .056)2 + (.14 − .056)2 + (.11 − .056)2 + (−.08 − .056)2 + (.06 − .056)2]}.5 σ = .0844, or 8.44%

A stock had annual returns of 6 percent, 13 percent, 11 percent, −8 percent, and 3 percent for the past five years, respectively. What is the standard deviation of returns for this stock?

Average return = (.06 + .13 + .11 − .08 + .03)/5 Average return = .05, or 5% σ = {[1/(5 − 1)] [(.06 − .05)2 + (.13 − .05)2 +(.11 − .05)2 +(−.08 − .05)2 + (.03 − .05)2]}.5 σ = .0828, or 8.28%

Florida Groves has a $380,000 bond issue outstanding that is selling at 97.4 percent of face value. The firm also has 2,600 shares of preferred stock valued at $61 a share and 37,500 shares of common stock valued at $19 a share. What weight should be assigned to the common stock when computing the weighted average cost of capital?

D = .974($380,000) = $ 370,120 P = 2,600($61) = $ 158,600 E = 37,500($19) = $ 712,500 V = $370,120 + 158,600 + 712,500 V = $1,241,220 WE = $712,500/$1,241,220 WE = .5740, or 57.40%

Theresa's Flower Garden has 650 bonds outstanding that are selling for $1,007 each, 2,100 shares of preferred stock with a market price of $68 a share, and 42,000 shares of common stock valued at $44 a share. What weight should be assigned to the preferred stock when computing the weighted average cost of capital?

D = 650($1,007) = $ 654,550 P = 2,100($68) = $ 142,800 E = 42,000($44) = $ 1,848,000 V = $654,550 + 142,800 + 1,848,000 V = $2,645,350 WP = $142,800/$2,645,350 WP = .0540, or 5.40%

One year ago, you purchased a stock at a price of $38.22 a share. Today, you sold the stock and realized a total loss of 11.09 percent on your investment. Your capital gain was -$4.68 a share. What was your dividend yield?

Dividend yield = −.1109 − (−$4.68/$38.22) Dividend yield = .0115, or 1.15%

Wayco Industrial Supply has a pretax cost of debt of 8.3 percent, a cost of equity of 14.7 percent, and a cost of preferred stock of 8.9 percent. The firm has 165,000 shares of common stock outstanding at a market price of $33 a share. There are 15,000 shares of preferred stock outstanding at a market price of $43 a share. The bond issue has a face value of $750,000 and a market quote of 101. The company's tax rate is 21 percent. What is the weighted average cost of capital?

E = 165,000($33) = $ 5,445,000 P = 15,000($43) = $ 645,000 D = 1.01($750,000) = $ 757,500 V = $5,445,000 + 645,000 + 757,500 V = $6,847,500 WACC = ($5,445,000/$6,847,500)(.147) + ($645,000/$6,847,500)(.089) + ($757,500/$6,847,500)(.083)(1 − .21) WACC = .1325, or 13.25%

Deep Mines has 43,800 shares of common stock outstanding with a beta of 1.54 and a market price of $51 a share. There are 10,000 shares of 7 percent preferred stock outstanding with a stated value of $100 per share and a market value of $83 a share. The 8 percent semiannual bonds have a face value of $1,000 and are selling at 96 percent of par. There are 5,000 bonds outstanding that mature in 13 years. The market risk premium is 7.5 percent, T-bills are yielding 3.6 percent, and the tax rate is 21 percent. What discount rate should the firm apply to a new project's cash flows if the project has the same risk as the company's typical project?

E = 43,800($51) = $2,233,800 P = 10,000($83) = $830,000 D = 5,000($1,000)(.96) = $4,800,000 V = $2,233,800 + 830,000 + 4,800,000 V = $7,863,800 RE = .036 + 1.54(.075) RE = .1515 RP = [.07($100)]/$83 RP = .0843 RD = .96($1,000) = [.08($1,000)/2][(1 − {1/[1 + (r/2)]13(2)/(r/2)] + $1,000/[1 + (r/2)]13(2) RD = .0851 WACC = ($2,233,800/$7,863,800)(.1515) + ($830,000/$7,863,800)(.0843) + ($4,800,000/$7,863,800)(.0851)(1 − .21) WACC = .0930, or 9.30%

A stock had returns of 12.4 percent, 16.6 percent, 10.2 percent, 19.0 percent, −15.7 percent, and 6.3 percent over the last six years. What is the geometric average return on the stock for this period?

Geometric average = (1.124) (1.166) (1.102) (1.190) (.843) (1.063)1/6 − 1 Geometric average = .0746, or 7.46%

Which one of the following statements is correct concerning a portfolio of 20 securities with multiple states of the economy when both the securities and the economic states have unequal weights?

Given both the unequal weights of the securities and the economic states, an investor might be able to create a portfolio that has an expected standard deviation of zero.

Leo purchased a stock for $63.80 a share, received a dividend of $2.68 a share and sold the shares for $59.74 each. During the time he owned the stock, inflation averaged 2.8 percent. What is his approximate real rate of return on this investment?

Nominal return = ($59.74 − 63.80 + 2.68)/$63.80 Nominal return = −.0216, or −2.16% Approximate real return = −.0216 − .028 Approximate real return = −.0496, or −4.96%

Chelsea Fashions is expected to pay an annual dividend of $1.26 a share next year. The market price of the stock is $24.09 and the growth rate is 2.6 percent. What is the cost of equity?

RE = ($1.26/$24.09) + .026 RE = .0783, or 7.83%

Street Corporation's common stock has a beta of 1.33. The risk-free rate is 3.4 percent and the expected return on the market is 10.97 percent. What is the cost of equity?

RE = .034 + 1.33(.1097 − .034) RE = .1347, or 13.47

Estimates of the rate of return on a security based on the historical arithmetic average will probably tend to _____ the expected return for the long-term and estimates using the historical geometric average will probably tend to _____ the expected return for the short-term.

overestimate; underestimate

Jenner's is a multi-division firm that uses its overall WACC as the discount rate for all proposed projects. Each division is in a separate line of business and each presents risks unique to those lines. Given this, a division within the firm will tend to:

prefer higher risk projects over lower risk projects.

When a manager develops a cost of capital for a specific project based on the cost of capital for another firm that has a similar line of business as the project, the manager is utilizing the _____ approach.

pure play

The cost of preferred stock is computed the same as the:

rate of return on a perpetuity.

The _____ of a security divided by the beta of that security is equal to the slope of the security market line if the security is priced fairly.

risk premium

You are aware that your neighbor trades stocks based on confidential information he overhears at his workplace. This information is not available to the general public. This neighbor continually brags to you about the profits he earns on these trades. Given this, you would tend to argue that the financial markets are at best _____ form efficient.

semi strong

Jiminy's Cricket Farm issued a 20-year, 7 percent, semiannual bond four years ago. The bond currently sells for 108 percent of its face value. What is the aftertax cost of debt if the company's combined tax rate is 23 percent?

1.08($1,000) = [.07($1,000)/2][(1 − {1/[1 + (r/2)]16(2)})/(r/2)] + $1,000/[1 + (r/2)]16(2) Using trial-and-error, a financial calculator, or a computer: r = 6.204 percent RD Aftertax = 6.204%(1 − .23) RD Aftertax = 4.78%

What is the expected return of an equally weighted portfolio comprised of the following three stocks? Probability Rate of Return Stock A Stock B Stock C Boom .25 .19 .13 .07 Normal .72 .15 .05 .13 Bust .03 -.29 - .14 .22

E(RP)Boom = (.19 + .13 + .07)/3 E(RP)Boom = .13, or 13% E(RP)Normal = (.15 + .05 + .13)/3 E(RP)Normal = .11, or 11% E(RP)Bust = (−.29 − .14 + .22)/3 E(RP)Bust = −.07, or -7% E(RP)Boom = .25(.13) + .72(.11) + .03(−.07) E(RP)Boom = .1096 or 10.96%

You have $21,600 to invest in a stock portfolio. Your choices are Stock X with an expected return of 14.3 percent and Stock Y with an expected return of 8.1 percent. Your goal is to create a portfolio with an expected return of 12.5 percent. All money must be invested. How much will you invest in Stock X?

E(Rp) = .125 = .143x + .081(1 − X) x = .70968, or 70.968 percent Investment in Stock X = .70968($21,600) Investment in Stock X = $15,329

You own a portfolio that has $2,800 invested in Stock A and $3,250 invested in Stock B. The expected returns on these stocks are 14.7 percent and 9.3 percent, respectively. What is the expected return on the portfolio?

E(Rp) = [$2,800/($2,800 + 3,250)](.147) + [$3,250/($2,800 + 3,250)](.093) E(Rp) = .1180, or 11.80%

The rate of return on the common stock of Lancaster Woolens is expected to be 18 percent in a boom economy, 8 percent in a normal economy, and only 2 percent in a recessionary economy. The probabilities of these economic states are 12 percent for a boom and 10 percent for a recession. What is the variance of the returns on this common stock?

E(r) = .12(.18) + .78(.08) + .10(.02) E(r) = .086 σ2 = .12(.18 − .086)2 + .78(.08 − .086)2 + .10(.02 − .086)2 σ2 = .001524

What is the standard deviation of the returns on a stock given the following information? State of Economy. Probability of State of Economy Rate of Return if State Occurs Boom .28 .175 Normal .67 .128 Recession .05 .026

E(r) = .28(.175) + .67(.128) + .05(.026) E(r) = .13606 σ = [.28(.175 − .13606)2+ .67(.128 − .13606)2 + .05(.026 − .13606)2]^.5 σ = .0328, or 3.28%

What is the standard deviation of the returns on a $30,000 portfolio that consists of Stocks S and T? Stock S is valued at $18,000. Probability Rate of Return Stock S Stock T Boom .05 .11 .09 Normal .85 .08 .07 Bust. .10. − .05 .04

E(r)Boom = [$18,000/$30,000](.11) + [($30,000 − 18,000)/$30,000](.09) = .102 E(r)Normal = [$18,000/$30,000](.08) + [($30,000 − 18,000)/$30,000](.07) = .076 E(r)Bust = [$18,000/$30,000](−.05) + [($30,000 − 18,000)/$30,000](.04) = -.014 E(r)Portfolio = .05(.102) + .85(.076) + .10(−.014) E(r)Portfolio = .0683 σPortfolio = [.05(.102 − .0683)2 + .85(.076 − .0683)2 + .10(−.014 − .0683)2].5 σPortfolio = .0280, or 2.80%

What is the expected return on a portfolio comprised of $9,750 of Stock X and $4,520 of Stock Y if the economy enjoys a boom period? State of Economy Probability Rate of Return Stock X Stock Y Boom .25 .108 .156 Normal .65 .087 .097 Recession .10 .024 − .069

E(r)Boom = [$9,750/($9,750 + 4,520)](.108) + [$4,520/($9,750 + 4,520)](.156) E(r)Boom = .1232, or 12.32%

Christina purchased 500 shares of stock at a price of $62.30 a share and sold the shares for $64.25 each. She also received $738 in dividends. If the inflation rate was 3.9 percent, what was her exact real rate of return on this investment?

Nominal return = [$64.25 − 62.30 + ($738/500)]/$62.30 Nominal return = .0550, or 5.50% Exact real return = 1.0550/1.039 − 1 Exact real return = .0154, or 1.54%

You bought one of Shark Repellant's 6 percent coupon bonds one year ago for $867. These bonds pay annual payments, have a face value of $1,000, and mature 12 years from now. Suppose you decide to sell your bonds today when the required return on the bonds is 7.4 percent. The inflation rate over the past year was 2.9 percent. What was your total real return on this investment?

P = $60 [(1 − 1/1.07412)/.074] + $1,000/1.07412 P = $891.13 Nominal return = ($891.13 − 867 + 60)/$867 Nominal return = .097, or 9.7% Real return = 1.097/1.029 − 1 Real return = .0661, or 6.61%

What is the expected return on this portfolio? Expected Return Number of Shares Price per Share A .11 200 $. 18.60 B .06 400 $ 12.85 C .17 300 $ 43.90

Portfolio value = 200($18.60) + 400($12.85) + 300($43.90) Portfolio value = $3,720 + 5,140 + 13,170 Portfolio value = $22,030 E(r) = ($3,720/$22,030)(.11) + ($5,140/$22,030)(.06) + ($13,170/$22,030)(.17) E(r)= .1342, or 13.42%

Stock in Country Road Industries has a beta of 1.62. The market risk premium is 8.2 percent while T-bills are currently yielding 2.9 percent. Country Road's last paid annual dividend was $1.87 per share and dividends are expected to grow at an annual rate of 3.8 percent indefinitely. The stock sells for $25 a share. What is the estimated cost of equity using the average return of the CAPM and the dividend discount model?

RE = .029 + 1.62(.082) = .16184 RE = [$1.87(1.038)/$25] + .038 = .11564 RE Average = (.16184 + .11564)/2 RE Average = .1387, or 13.87%

Granite Works maintains a debt-equity ratio of .58 and has a tax rate of 21 percent. The pretax cost of debt is 8.9 percent. There are 18,000 shares of stock outstanding with a beta of 1.42 and a market price of $23 a share. The current market risk premium is 7.8 percent and the current risk-free rate is 3.1 percent. This year, the firm paid an annual dividend of $1.68 a share and expects to increase that amount by 2 percent each year. Using an average expected cost of equity, what is the weighted average cost of capital?

RE = .031+ 1.42(.078) RE = .14176 RE = [$1.68(1.02)/$23] + .02 RE = .09450 REAvg = (.14176+ .09450)/2 REAvg = .11813 WACC = (1/1.58)(.11813) + (.58/1.58)(.089)(1 − .21) WACC = .1006, or 10.06%

A stock has a beta of 1.18 and an expected return of 11.24 percent. If the risk-free rate is 3.3 percent, what is the stock's reward-to-risk ratio?

Reward-to-risk ratio = (.1124 − .033)/1.18 Reward-to-risk ratio = .0673, or 6.73%

A stock has a beta of .89 and an expected return of 9.2 percent. If the stock's reward-to-risk ratio is 6.17 percent, what is the risk-free rate?

Reward-to-risk ratio = .0617 = (.0920 − Rf)/.89 Rf = .0371, or 3.71%

Why does the tax amount need to be adjusted when valuing a firm using the cash flow from assets approach?

The tax effect of the interest expense must be removed.

Which one of the following events would be included in the expected return on Sussex stock?

This morning, Sussex confirmed that its CEO is retiring at the end of the year as was anticipated.

One year ago, you purchased 200 shares of SL Industries stock at a price of $18.97 a share. The stock pays an annual dividend of $1.42 per share. Today, you sold all of your shares for $17.86 per share. What is your total dollar return on this investment?

Total dollar return = ($17.86 − 18.97 + 1.42) (200) Total dollar return = $62

Which one of the following risks is irrelevant to a well-diversified investor?

Unsystematic risk

Which one of the following is the primary determinant of a firm's cost of capital?

Use of the funds raised

Rosa's has a weighted average cost of capital of 11.73 percent. The cost of equity is 15.8 percent and the pretax cost of debt is 7.6 percent. The tax rate is 21 percent. What is the target debt-equity ratio?

WACC = .1173 = (E/V)(.158) + (D/V)(.076)(1 − .21) .1173(V/E) = .158 + .06004(D/E) .1173(1 + D/E) = .158 + .06004 (D/E) D/E = .71

Mullineaux Corporation has a target capital structure of 46 percent common stock, 5 percent preferred stock, and the balance in debt. Its cost of equity is 15.8 percent, the cost of preferred stock is 8.3 percent, and the aftertax cost of debt is 6.8 percent. What is the WACC given a tax rate of 23 percent?

WACC = .46(.158) + .05(.083) + .49(.068) WACC = .1102, or 11.02%

Which one of the following is most indicative of a totally efficient stock market?

Zero net present values for all stock investments

The capital structure weights used in computing a company's weighted average cost of capital:

are based on the market values of the outstanding securities

The standard deviation of a portfolio:

can be less than the standard deviation of the least risky security in the portfolio.

Treynor Industries is investing in a new project. The minimum rate of return the firm requires on this project is referred to as the:

cost of capital.

The principle of diversification tells us that:

spreading an investment across many diverse assets will eliminate some of the total risk.

The _____ tells us that the expected return on a risky asset depends only on that asset's nondiversifiable risk.

systematic risk principle

Efficient financial markets fluctuate continuously because:

the markets are continually reacting to new information.

The discount rate assigned to an individual project should be based on:

the risks associated with the use of the funds required by the project.