FIN 3

You have a portfolio that is equally invested in Stock F with a beta of 1.16, Stock G with a beta of 1.53, and the risk-free asset. What is the beta of your portfolio? 1.03 .96 1.37 .90 1.23

.90 βPortfolio = 1/3(1.16) + 1/3(1.53) + 1/3(0)βPortfolio = .90

Gugenheim, Inc., has a bond outstanding with a coupon rate of 6.2 percent and annual payments. The yield to maturity is 7.4 percent and the bond matures in 18 years. What is the market price if the bond has a par value of $2,000? $1,763.36 $1,765.40 $1,768.11 $1,770.44 $1,800.71

$1,765.40 PV = $124{[1 − (1/1.07418)]/.074} + $2,000/1.07418PV = $1,765.40

The Bell Weather Co. is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 21 percent a year for the next 4 years and then decreasing the growth rate to 5 percent per year. The company just paid its annual dividend in the amount of $2.80 per share. What is the current value of one share of this stock if the required rate of return is 8.30 percent? $138.82 $153.71 $193.77 $190.97 $156.51

$153.71 P4 = ($2.80 × 1.214 × 1.05)/(0.083 - 0.05) = $190.97 P0 = ($2.80 × 1.21)/1.083 + ($2.80 × 1.212)/1.0832 + ($2.80 × 1.213)/1.0833 + ($2.80 × 1.214)/1.0834 + $190.97/1.0834 = $153.71

Burnett Corp. pays a constant $20 dividend on its stock. The company will maintain this dividend for the next 13 years and will then cease paying dividends forever. If the required return on this stock is 8 percent, what is the current share price? $170.72 $260.00 $154.91 $158.08 $165.98

$158.08 P0 = $20(PVIFA 8%,13) P0 = $158.08

Mannix Corporation stock currently sells for $35 per share. The market requires a return of 15 percent on the firm's stock. If the company maintains a constant 7 percent growth rate in dividends, what was the most recent dividend per share paid on the stock? $2.62 $2.51 $7.77 $4.72 $2.80

$2.62 We are given the stock price, the dividend growth rate, and the required return, and are asked to find the dividend. Using the constant dividend growth model, we get: P0 = $35 = D0(1 + g)/(R - g) Solving this equation for the dividend gives us: D0 = $35(0.15 - 0.07)/(1.07)D0 = $2.62

Navarro, Inc., plans to issue new zero coupon bonds with a par value of $1,000 to fund a new project. The bonds will have a YTM of 6.33 percent and mature in 20 years. If we assume semiannual compounding, at what price will the bonds sell? $280.36 $287.54 $277.96 $276.04 $293.01

$287.54 PV = $1,000/(1 + .0633/2)40PV = $287.54

Lohn Corporation is expected to pay the following dividends over the next four years: $10, $8, $5, and $4. Afterward, the company pledges to maintain a constant 4 percent growth rate in dividends forever. If the required return on the stock is 13 percent, what is the current share price? $56.12 $47.43 $46.91 $50.86 $49.38

$49.38 With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4, at the beginning of the constant dividend growth, as: P4 = D4 (1 + g)/(R - g) P4 = $4(1.04)/(.13 - .04) P4 = $46.22 The price of the stock today is the PV of the first four dividends, plus the PV of the Year 4 stock price. So, the price of the stock today will be: P0 = $10/1.13 + $8/1.132 + $5/1.133 + $4/1.134 + $46.22/1.134 P0 = $49.38

Suppose you know a company's stock currently sells for $100 per share and the required return on the stock is 12 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share? $11.32 $5.38 $6.06 $5.66 $6.00

$5.66 We know the stock has a required return of 12 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.12) Dividend yield = .060 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is the stock price times the dividend yield, so: D1 = .060($100) D1 = $6.00 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year: D1 = D0(1 + g) We can solve for the dividend that was just paid:$6.00 = D0(1 + .060)D0 = $6.00/1.060 D0 = $5.66

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next 7 years because the firm needs to plow back its earnings to fuel growth. The company will pay a dividend of $10 per share 8 years from today and will increase the dividend by 6 percent per year thereafter. If the required return on this stock is 12 percent, what is the current share price? $75.39 $77.65 $67.31 $79.16 $71.62

$75.39 Pt = [Dt × (1 + g)]/(R - g) P7 = D8/(R - g)P7 = $10/(.12 - .06)P7 = $166.67 The price of the stock today is the PV of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: P0 = $166.67/1.127 P0 = $75.39

Flex Co. just paid total dividends of $850,000 and reported additions to retained earnings of $2,550,000. The company has 625,000 shares of stock outstanding and a benchmark PE of 16.4 times. What stock price would you consider appropriate? $22.30 $66.91 $89.22 $80.29 $84.76

$89.22 EPS = ($850,000 + 2,550,000)/625,000 = $5.44 P = $5.44(16.40) = $89.22

You own a portfolio that has a total value of $185,000 and a beta of 1.39. You have another $82,000 to invest and you would like the beta of your portfolio to decrease to 1.32. What does the beta of the new investment have to be in order to accomplish this? 1.219 1.017 1.355 1.276 1.162

1.162 βPortfolio = 1.32 = 1.39[$185,000/($82,000 + 185,000)] + βX[$82,000/($82,000 + 185,000)]βX = 1.162

You own a stock portfolio invested 20 percent in Stock Q, 15 percent in Stock R, 15 percent in Stock S, and 50 percent in Stock T. The betas for these four stocks are 1.43, 1.81, 0.75, and 1.44, respectively. What is the portfolio beta? 1.42 1.36 1.46 1.32 1.39

1.39 βp = 0.2(1.43) + 0.15(1.81) + 0.15(0.75) + 0.5(1.44)βp = 1.39

The Lo Sun Corporation offers a 5.1 percent bond with a current market price of $746.50. The yield to maturity is 8.58 percent. The face value is $1,000. Interest is paid semiannually. How many years until this bond matures? 23.35 years 5.84 years 22.39 years 11.68 years 29.27 years

11.68 years Semi-annual interest rate = 0.0858/2 = 0.04290 PV=$746.50=[(0.051×$1,000)/2]×1−[1/(1+0.04290)t]0.04290+$1,000/(1+0.04290)tPV=$746.50=[(0.051×$1,000)/2]×1−[1/(1+0.04290)t]0.04290+$1,000/(1+0.04290)t (Note: t is the number of semi-annual periods)$746.50=$25.50×1−[1/(1.04290)t]0.04290+$1,000/(1.04290)t$746.50=$25.50×1−[1/(1.04290)t]0.04290+$1,000/(1.04290)tDividing by $25.50, you get:29.2745 = {[1 - 1/1.0429t]/0.0429} + 39.2157/1.0429tMultiplying by 0.0429, you get:1.2559 = 1 - 1/1.0429t + 1.6824/1.0429t0.2559 = 0.6824/1.0429t1.0429t = 2.6667t = ln2.6667/ln1.0429 = 0.9809/0.0420 = 23.35 semi-annual periods = 11.68 years

Suppose the real rate is 9 percent and the inflation rate is 2.6 percent. What rate would you expect to see on a Treasury bill? 11.83% 10.65% 13.61% 10.06% 13.02%

11.83% The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is: (1 + R) = (1 + r)(1 + h)R = (1 + 0.026)(1 + 0.09) - 1R = 0.1183, or 11.83%

A stock has a beta of 1.55, the expected return on the market is 10 percent, and the risk-free rate is 4 percent. What must the expected return on this stock be? 13.96% 13.3% 12.64% 13.83% 19.5%

13.3% E(Ri) = Rf + [E(RM) - Rf] × βi Substituting the values we are given, we find:E(Ri) = 0.04 + (0.1 - 0.04)(1.55) E(Ri) = 0.133, or 13.3%

A stock has an expected return of 9 percent, its beta is 0.5, and the risk-free rate is 3.6 percent. What must the expected return on the market be? 13.68% 15.12% 14.98% 14.40% 10.80%

14.40% E(Ri) = 0.09 = 0.036 + [E(RM) - 0.036](0.5)E(RM) = 0.144, or 14.4%

You own a portfolio that has $1,800 invested in Stock A and $3,650 invested in Stock B. If the expected returns on these stocks are 13 percent and 17 percent, respectively, what is the expected return on the portfolio? 14.32% 15.00% 15.68% 15.99% 16.46%

15.68% 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 = $1,800 + 3,650 Total value = $5,450 So, the expected return of this portfolio is:E(Rp) = ($1,800/$5,450)(0.13) + ($3,650/$5,450)(0.17) E(Rp) = 0.1568, or 15.68%

Voltanis Corp. has preferred stock outstanding that will pay an annual dividend of $3.51 every year in perpetuity. If the stock currently sells for $96.61 per share, what is the required return? 2.75% 3.27% 3.40% 3.63% 4.15%

3.63% R = $3.51/$96.61 = .0363, or 3.63%

Gabriele Enterprises has bonds on the market making annual payments, with 6 years to maturity, a par value of $1,000, and selling for $810. At this price, the bonds yield 9.8 percent. What must the coupon rate be on the bonds? 10.93% 5.46% 9.80% 5.56% 6.74%

5.46% Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $810 = C(PVIFA9.8%,6) + $1,000(PVIF9.8%,6) Solving for the coupon payment, we get:C = $54.63 The coupon payment is the coupon rate times par value. Using this relationship, we get:Coupon rate = $54.63/$1,000Coupon rate = 0.0546, or 5.46%

A bond that pays interest semiannually has a price of $965.18 and a semiannual coupon payment of $29.00. If the par value is $1,000, what is the current yield? 5.71% 5.80% 6.01% 3.00% 2.90%

6.01% Current yield = ($29.00 × 2)/$965.18 = .0601, or 6.01%

A stock has a beta of 1.21 and an expected return of 11.33 percent. If the risk-free rate is 3.6 percent, what is the stock's reward-to-risk ratio? 6.39% 9.36% 5.90% 5.59% 7.88%

6.39% Reward-to-risk ratio = (.1133 − .036)/1.21Reward-to-risk ratio = .0639, or 6.39%

A 15-year, semiannual coupon bond sells for $985.72. The bond has a par value of $1,000 and a yield to maturity of 6.57 percent. What is the bond's coupon rate? 3.21% 6.10% 5.78% 4.81% 6.42%

6.42% $985.72 = C{[1 − 1/(1 + .0657/2)30]/(.0657/2)} + $1,000/(1 + .0657/2)30C = $32.09 Coupon rate = ($32.09 × 2)/ $1,000 = .0642, or 6.42%

Crossfade Corp. has a bond with a par value of $2,000 that sells for $2,040.74. The bond has a coupon rate of 6.66 percent and matures in 18 years. If the bond makes semiannual coupon payments, what is the YTM of the bond? 4.85% 6.14% 3.23% 6.47% 5.82%

6.47% $2,040.74 = $66.60{[1 − 1/(1 + r)36]/r} + $2,000/(1 + r)36r = .0323, or 3.23% YTM = 3.23% × 2 = 6.47%

The next dividend payment by Savitz, Inc., will be $3.85 per share. The dividends are anticipated to maintain a growth rate of 3 percent forever. If the stock currently sells for $60 per share, what is the required return? 9.42% 8.95% 6.42% 9.23% 3.00%

9.42% We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find:R = (D1/P0) + g R = ($3.85/$60) + .03 R = .0942, or 9.42%

West Corp. issued 17-year bonds 2 years ago at a coupon rate of 9.3 percent. The bonds make semiannual payments. If these bonds currently sell for 98 percent of par value, what is the YTM? 4.78% 11.46% 10.51% 9.55% 8.60%

9.55% Here we are finding the YTM of a semiannual coupon bond. The bond price equation is: P = 980 = $46(PVIFAR%,30) + $1,000(PVIFR%,30) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 4.7768% Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: YTM = 2 × 4.7768% YTM = 9.55%

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.48 per share on its stock. The dividends are expected to grow at a constant rate of 5 percent per year indefinitely. a. If investors require a return of 12 percent on the company's stock, what is the current price? b. What will the price be in 19 years?

a. $22.20 The constant dividend growth model is:Pt = Dt × (1 + g)/(R - g) So the price of the stock today is:P0 = D0 (1 + g)/(R - g) P0 = $1.48 (1.05)/(.12 - .05) P0 = $22.20 b. $56.10 We can do the same thing to find the dividend in Year 20, which gives us the price in Year 19, so:P19 = D19 (1 + g)/(R - g) P19 = D0 (1 + g)20/(R - g)P19 = $1.48 (1.05)20/(.12 - .05) P19 = $56.10

A portfolio has 90 shares of Stock A that sell for $32 per share and 105 shares of Stock B that sell for $21 per share. What is the portfolio weight of Stock A? What is the portfolio weight of Stock B?

a.The portfolio weight of an asset is total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 90($32) + 105($21) Total value = $5,085 The portfolio weight for stock A is: WeightA = 90($32)/$5,085 WeightA = .5664 b.The portfolio weight for stock B is: WeightB = 105($21)/$5,085 WeightB = .4336

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 5 years to maturity, and a coupon rate of 6 percent paid annuallly. If the yield to maturity is 10 percent, what is the current price of the bond? €890.79 €1,172.49 €848.37 €1,030.00 $805.95

€848.37 The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = €60({1 - [1/(1 + 0.10)]5 }/0.10) + €1,000[1/(1 + 0.10)5] P = €848.37