Fin 3200 Chapter 11-12

You have $16,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 16 percent and Stock Y with an expected return of 10 percent. Assume your goal is to create a portfolio with an expected return of 13.50 percent. How much money will you invest in Stock X and Stock Y?

E(Rp) = .135 = .16wX + .10(1 - wX) We can now solve this equation for the weight of Stock X as: .1350 = .16wX + .10 - .10wX .0350 = .06wX wX = .5833 So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = .5833($16,000) Investment in X = $9,333.33 And the dollar amount invested in Stock Y is: Investment in Y = (1 - .5833)($16,000) Investment in Y = $6,666.67

Sixth Fourth Bank has an issue of preferred stock with a $6.40 stated dividend that just sold for $126 per share. What is the bank's cost of preferred stock?

RP = $6.40 / $126 RP = .0508, or 5.08%

Information on Gerken Power Co., is shown below. Assume the company's tax rate is 38 percent. Debt: 10,300 8.9 percent coupon bonds outstanding, $1,000 par value, 22 years to maturity, selling for 95 percent of par; the bonds make semiannual payments. Common stock: 228,000 shares outstanding, selling for $84.80 per share; beta is 1.33. Preferred stock: 13,800 shares of 5.9 percent preferred stock outstanding, currently selling for $96.20 per share. Market: 7.15 percent market risk premium and 4.95 percent risk-free rate.

see question 5

A stock has a beta of 1.1, the expected return on the market is 10.4 percent, and the risk-free rate is 4.75 percent. What must the expected return on this stock be?

E(Ri) = .0475 + (.1040 - .0475)(1.10) E(Ri) = .1097, or 10.97%

Consider the following information:

Question 3 a. The expected return of an asset is the sum of the probability of each state occurring times the rate of return if that state occurs. So, the expected return of each asset is: E(RA) = .23(.05) + .63(.13) + .14(.32) E(RA) = .1382, or 13.82% E(RB) = .23(-.43) + .63(.33) + .14(.56) E(RB) = .1874, or 18.74% b. To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then sum. The result is the variance. So, the variance and standard deviation of each stock is: σA2 = .23(.05 - .1382)2 + .63(.130 - .1382)2 + .14(.32 - .1382)2 σA2 = .00646 σA = .006461/2 σA = .0804, or 8.04% σB2 = .23(-.43 - .1874)2 + .63(.33 - .1874)2 + .14(.56 - .1874)2 σB2 = .11992 σB = .119921/2 σB = .3463, or 34.63%

An all-equity firm is considering the following projects:

See question 6 a. Projects Y and Z have a higher expected return than the firm's cost of capital. b. Using the CAPM to consider the projects, we need to calculate the expected return of the project, given its level of risk. This expected return should then be compared to the expected return of the project. If the return calculated using the CAPM is lower than the project expected return, we should accept the project; if not, we reject the project. After considering risk via the CAPM: E(W) = .050 + .66(.120 - .050) = .0962 > .095, so reject W E(X) = .050 + .73(.120 - .050) = .1011 < .105, so accept X E(Y) = .050 + 1.35(.120 - .050) = .1445 > .140, so reject Y E(Z) = .050 + 1.46(.120 - .050) = .1522 < .170, so accept Z

You own a portfolio that has $2,300 invested in Stock A and $3,400 invested in Stock B. Assume the expected returns on these stocks are 9 percent and 15 percent, respectively. What is the expected return on the portfolio?

The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total value = $2,300 + 3,400 Total value = $5,700 So, the expected return of this portfolio is: E(Rp) = ($2,300 / $5,700)(.09) + ($3,400 / $5,700)(.15) E(Rp) = .1258, or 12.58% question 1

ICU Window, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with eight years to maturity that is quoted at 114.5 percent of face value. The issue makes semiannual payments and has an embedded cost of 10 percent annually. 1. What is the company's pretax cost of debt? 2. If the tax rate is 34 percent, what is the aftertax cost of debt?

The pretax cost of debt is the YTM of the company's bonds, so: P0 = $1,145 = $50(PVIFAR%,16) + $1,000(PVIFR%,16) R = 3.776% YTM = 2 × 3.776% YTM = 7.55% And the aftertax cost of debt is: RD = .0755(1 - .34) RD = .0498, or 4.98% see question 3

Stock in CDB Industries has a beta of 1.12. The market risk premium is 7.2 percent, and T-bills are currently yielding 4.2 percent. CDB's most recent dividend was $3.60 per share, and dividends are expected to grow at an annual rate of 5.2 percent indefinitely. If the stock sells for $58 per share, what is your best estimate of the company's cost of equity?

We have the information available to calculate the cost of equity, using the CAPM and the dividend growth model. Using the CAPM, we find: RE = .042 + 1.12(.072) RE = .1226, or 12.26% And using the dividend growth model, the cost of equity is: RE = [$3.60(1.052) / $58] + .052 RE = .1173, or 11.73% Both estimates of the cost of equity seem reasonable based on the historical return on large capitalization stocks. Given this, we will use the average of the two, so: RE = (.1226 + .1173) / 2 RE = .1200, or 12.00%

Bargeron Corporation has a target capital structure of 63 percent common stock, 8 percent preferred stock, and 29 percent debt. Its cost of equity is 12.8 percent, the cost of preferred stock is 5.8 percent, and the pretax cost of debt is 7.5 percent. The relevant tax rate is 38 percent. a. What is the company's WACC? b. What is the aftertax cost of debt?

a. Using the equation to calculate the WACC, we find: WACC = .63(.128) + .08(.058) + .29(.075)(1 - .38) WACC = .0988, or 9.88% b. Since interest is tax deductible, the aftertax cost of debt is: RD = .075(1 - .38) RD = .0465, or 4.65%

Consider the following information on a portfolio of three stocks:

see question 7

You own a stock portfolio invested 27 percent in Stock Q, 17 percent in Stock R, 43 percent in Stock S, and 13 percent in Stock T. The betas for these four stocks are .96, 1.02, 1.42, and 1.87, respectively. What is the portfolio beta?

βp = .27(.96) + .17(1.02) + .43(1.42) + .13(1.87) βp = 1.29

You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.29 and the total portfolio is equally as risky as the market.

βp = 1.0 = 1/3(0) + 1/3(1.29) + 1/3(βX) Solving for the beta of Stock X, we get: βX = 1.71