FIN 315 Final

The Shoe Outlet has paid annual dividends of $.58, $.66, $.72, and $.75 per share over the last four years, respectively. The stock is currently selling for $10.08 a share. What is the cost of equity?

($.66 − .58)/$.58 = .13793 ($.72 − .66)/$.66 = .09091 ($.75 − $.72)/$.72 = .04167 g = (.13793 + .09091 + .04167)/3 g = .09017 RE = [$.75(1.09017)]/$10.08 + .09017 RE = .1713, or 17.13%

Consider the following information: Probability of State of Economy Recession: .04 Normal: .72 Boom: .24 Rate of Return if State Occurs Stock A Recession: .097 Normal: .114 Boom: .156 Stock B Recession: .102 Normal: .133 Boom: .148 The market risk premium is 7.4 percent, and the risk-free rate is 3.1 percent. The beta of Stock A is ________ and the beta of Stock B is ________.

1.25; 1.41 E(RA) = .04(.097) + .72(.114) + .24(.156) E(RA) = .1234 .1234 = .031 + βA(.074) βA = 1.25 E(RB) = .04(.102) + .72(.133) + .24(.148) E(RB) = .1354 .1354 = .031 + βB(.074) βB = 1.41

Suppose you observe the following situation: Security Beta Expected Return A 1.16 .1137 B .92 .0984 Assume these securities are correctly priced. Based on the CAPM, what is the return on the market?

10.35% Market risk premium = (.1137-.0984)/(1.16-.92) =6.38% Risk free rate = .1137-(1.16*6.38%) =3.98% Expected return on market = 6.38%+3.98% = 10.35%

Fashion Wear has bonds outstanding that mature in 11 years, pay interest annually, and have a coupon rate of 6.45 percent. These bonds have a face value of $1,000 and a current market price of $994. What is the company's aftertax cost of debt if its tax rate is 21 percent?

11 N 64.50 PMT -994 PV 1000 FV CPT I/Y = 6.528 6.528(1-.21) = 5.16%

All else constant, which one of the following will increase a company's cost of equity if the company computes that cost using the security market line approach? Assume the firm currently pays an annual dividend of $1 a share and has a beta of 1.2.

A reduction in the risk-free rate

You have a $15,000 portfolio which is invested in Stocks A and B, and a risk-free asset. $6,000 is invested in Stock A. Stock A has a beta of 1.63 and Stock B has a beta of .95. How much needs to be invested in Stock B if you want a portfolio beta of 1.10?

BetaPortfolio = 1.10 = ($6,000/$15,000)(1.63) + (x/$15,000)(.95) + [($15,000 − 6,000 − x)/$15,000](0) x = $7,073.68

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

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%

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 40 PMT 26 N -960 PV 1000 FV CPT I/Y = 4.25733 x 2 = .0851 or 8.51% RE = .036 + 1.54(.075) = .1515 RP = [.07($100)]/$83 = .0843 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%

Consider the following information on three stocks: Probability of State of Economy Boom: .25 Normal: .65 Bust: .10 Rate of Return if State Occurs Stock A: Boom: .27 Normal: .14 Bust: -.19 Stock B: Boom: .15 Normal: .11 Bust: -.04 Stock C: Boom: .11 Normal: .09 Bust: .05 A portfolio is invested 45 percent each in Stock A and Stock B and 10 percent in Stock C. What is the expected risk premium on the portfolio if the expected T-bill rate is 3.2 percent?

E(RP)Boom=.45(.27) + .45(.15) + .10(.11)=.2000 E(RP)Normal=.45(.14) + .45(.11) + .10(.09)=.1215 E(RP)Bust=.45(-.19) + .45(-.04) + .10(.05)=-.0985 E(RP) = .25(.2000) + .65(.1215) + .10(−.0985) E(RP) = .1191, or 11.91% RPP= .1191 − .032 RPP= .0871, or 8.71%

A stock has an expected return of 13.24 percent, the risk-free rate is 4.4 percent, and the market risk premium is 8.98 percent. What is the stock's beta?

E(Ri) = .1324 = .044 + βi(.0898) βi = .98

Your portfolio is invested 25 percent each in Stocks A and C, and 50 percent in Stock B. What is the standard deviation of your portfolio given the following information? Probability of State of Economy Boom: .07 Good: .55 Poor: .36 Bust: .02 Rate of Return if State Occurs Stock A: Boom: .28 Good: .19 Poor: -.21 Bust: -.65 Stock B: Boom: .14 Good: .12 Poor: .07 Bust: .03 Stock C: Boom: .11 Good: .09 Poor: .06 Bust: -.03

E(Rp)Boom=.25(.28) + .5(.14) + .25(.11)= .1675 E(Rp)Good=.25(.19) + .5(.12) + .25(.09)= .1300 E(Rp)Poor=.25(−.21) + .5(.07) + .25(.06)= −.0025 E(Rp)Bust=.25(−.65) + .5(.03) +.25(−.03)= −.155 E(Rp) = .07(.1675) + .55(.13) + .36(−.0025) + .02(−.155) E(Rp) = .0792 σp= [.07(.1675 − .0792)^2+ .55(.13 − .0792)^2+ .36(−.0025 − .0792)^2+ .02(−.155 − .0792)^2]^.5 σp= .0739, or 7.39%

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%

The common stock of Manchester & Moore is expected to earn 14 percent in a recession, 7 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 15 percent while the probability of a recession is 5 percent. What is the expected rate of return on this stock?

E(r) = .05(.14) + .80(.07) + .15(−.04) E(r) = .057, or 5.7%

The common stock of Jensen Shipping has an expected return of 15.4 percent. The return on the market is 11.2 percent, the inflation rate is 3.1 percent, and the risk-free rate of return is 3.6 percent. What is the beta of this stock?

E(r) = .154 = .036 + β(.112 − .036) β = 1.55

You recently purchased a stock that is expected to earn 19 percent in a booming economy, 12 percent in a normal economy, and lose 8 percent in a recessionary economy. The probability of a boom economy is 16 percent while the probability of a normal economy is 78 percent. What is your expected rate of return on this stock?

E(r) = .16(.19) + .78(.12) + .06(−.08) E(r) = .1192, or 11.92%

What is the standard deviation of the returns on a stock given the following information? Probability of State of Economy Boom: .28 Normal: .67 Recession: .05 Rate of Return if State Occurs Boom: .175 Normal: .128 Recession: .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 portfolio that is invested 37 percent in Stock Q and 63 percent in Stock R? Probability of State of Economy Boom: .15 Normal: .85 Rate of Return if State Occurs Stock Q: Boom: .16 Normal: .09 Stock R: Boom: .15 Normal: .13

E(r)Boom = .37(.16) + .63(.15) = .1537 E(r)Normal = .37(.09) + .63(.13) = .1152 E(r)Portfolio = .15(.1537) + .85(.1152) E(r)Portfolio = .1210 σPortfolio = [.15(.1537 − .1210)^2 + .85(.1152 − .1210)^2]^.5 σPortfolio = .0137, or 1.37%

Which one of the following stocks is correctly priced according to CAPM if the risk-free rate of return is 3.4 percent and the market risk premium is 7.4 percent? Stock Beta Expected Return A: .87 .096 B: 1.09 .102 C: 1.62 .146 D: .98 .107 E: 1.16 .139

E(r)D=.034 + .98(.074)=.107, or 10.7% Stock D is correctly priced according to CAPM.

Which of the following statements concerning risk are correct? I. Non-diversifiable risk is measured by beta. II. The risk premium increases as diversifiable risk increases. III. Systematic risk is another name for non-diversifiable risk. IV. Diversifiable risks are market risks you cannot avoid.

I and III only

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

Tidewater Fishing has a current beta of 1.16. The market risk premium is 6.8 percent and the risk-free rate of return is 2.9 percent. By how much will the cost of equity increase if the company expands its operations such that the company beta rises to 1.18?

Increase = (1.18 − 1.16)(.068) Increase = .0014, or .14%

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

Market risk premium

Suzie owns five different bonds and twelve different stocks. Which one of the following terms most applies to her investments?

Portfolio

Dee's Fashions has a growth rate of 3.2 percent and is equally as risky as the market while its stock is currently selling for $32 a share. The overall stock market has a return of 10.9 percent and a risk premium of 6.8 percent. What is the expected rate of return on this stock?

RE = (.109 − .068) + 1(.068) RE = .109, or 10.9%

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%

Southern Bakeries just paid its annual dividend of $.48 a share. The stock has a market price of $17.23 and a beta of .93. The return on the U.S. Treasury bill is 3.1 percent and the market risk premium is 7.6 percent. What is the cost of equity?

RE = .031 + .93(.076) RE = .1017, or 10.17%

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%

Holdup Bank has an issue of preferred stock with a stated dividend of $7 that just sold for $87 per share. What is the bank's cost of preferred?

RP = $7/$87 RP = .0805, or 8.05%

Which one of the following is a risk that applies to most securities?

Systematic

Carson Electronics uses 58 percent common stock and 42 percent debt to finance its operations. The aftertax cost of debt is 5.4 percent and the cost of equity is 15.3 percent. Management is considering a project that will produce a cash inflow of $49,600 in the first year. The cash inflows will then grow at 2.5 percent per year forever. What is the maximum amount the firm can initially invest in this project to avoid a negative net present value for the project?

WACC = .58(.153) + .42(.054) WACC = .1114 PV = $49,600/(.1114 − .025) PV = $573,941

The expected return on a stock computed using economic probabilities is:

a mathematical expectation based on a weighted average and not an actual anticipated outcome.

Unsystematic risk:

can be effectively eliminated by portfolio diversification.

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

cost of debt.

A company's overall cost of equity is:

directly related to the risk level of the firm.

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.

A company's pretax cost of debt:

is based on the current yield to maturity of the company's outstanding bonds.

The dividend growth model:

is only as reliable as the estimated rate of growth.

Assume the market rate of return is 10.1 percent and the risk-free rate of return is 3.2 percent. Lexant stock has 2 percent less systematic risk than the market and has an actual return of 10.2 percent. This stock:

is underpriced.

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.

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

Standard deviation measures which type of risk?

total