FINEX3

Suppose a stock had an initial price of $95 per share, paid a dividend of $2.00 per share during the year, and had an ending share price of $114. What was the capital gains yield?

Capital gains yield = ($114 - 95) / $95 Capital gains yield = .2000, or 20.00%

expected return of a portfolio

is the sum of the weight of each asset times the expected return of each asset.

Question 31 + 38

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Suppose a stock had an initial price of $95 per share, paid a dividend of $2.00 per share during the year, and had an ending share price of $114. What was the dividend yield?

Dividend yield = $2.00 / $95 Dividend yield = .0211, or 2.11%

The next dividend payment by Dizzle, Inc., will be $2.95 per share. The dividends are anticipated to maintain a growth rate of 5.5 percent, forever. Assume the stock currently sells for $49.50 per share. What is the dividend yield?

Dividend yield = D1 / P0 Dividend yield = $2.95 / $49.50 Dividend yield = .0596, or 5.96%

State of Economy// Probability of State of Economy // Rate of Return if State Occurs// Recession// .23 //- .11 Normal // .47 // .13 Boom // .30 // .32

E(R) = .23(-.11) + .47(.13) + .30(.32) E(R) = .1318, or 13.18%

Wesen Corp. will pay a dividend of $2.90 next year. The company has stated that it will maintain a constant growth rate of 5.25 percent a year forever. If you want a return of 9 percent, how much will you pay for the stock?

P0 = D1 / (R - g) P0 = $2.90 / (.09 - .0525) P0 = $77.33

Variances and SD

returns and variability on calculator arithmetic average return

If = 1.0,

stock has average risk

If < 1.0,

stock is less risky than average

If > 1.0,

stock is riskier than average

Most stocks have betas in the range of

0.5 to 1.5

Suppose you know that a company's stock currently sells for $65.70 per share and the required return on the stock is 9 percent. You also know that the total return on the stock is evenly divided between capital gains yield and 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?

Dividend yield = 1/2(.09) Dividend yield = .045 = Capital gains yield D1 = .045($65.70) D1 = $2.96 D1 = D0(1 + g) $2.96 = D0(1 + .045) D0 = $2.96 / 1.045 D0 = $2.83

Wesen Corp. will pay a dividend of $2.90 next year. The company has stated that it will maintain a constant growth rate of 5.25 percent a year forever. If you want a return of 18 percent, how much will you pay for the stock?

P0 = D1 / (R - g) P0 = $2.90 / (.18 - .0525) P0 = $22.75

Take Time Corporation will pay a dividend of $4.10 per share next year. The company pledges to increase its dividend by 6 percent per year, indefinitely. If you require a return of 10 percent on your investment, how much will you pay for the company's stock today?

P0 = D1 / (R - g) P0 = $4.10 / (.10 - .06) P0 = $102.50

Gilmore, Inc., just paid a dividend of $2.55 per share on its stock. The dividends are expected to grow at a constant rate of 5.5 percent per year, indefinitely. Assume investors require a return of 11 percent on this stock. What is the current price?

Pt = Dt × (1 + g) / (R - g) So, the price of the stock today is: P0 = D0(1 + g) / (R - g) P0 = $2.55(1.0550) / (.11 - .0550) P0 = $48.91

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

A stock has had returns of −18.9 percent, 28.9 percent, 22.8 percent, −10 percent, 34.7 percent, and 26.9 percent over the last six years. What are the arithmetic and geometric returns for the stock?

Arithmetic average return = (-.189 + .289 + .228 - .100 + .347 + .269) / 6 Arithmetic average return = .1407, or 14.07% Using the equation for the geometric return, we find: Geometric average return = [(1 + R1) × (1 + R2) × ... × (1 + RT)]1/T - 1 Geometric average return = [(1 - .189)(1 + .289)(1 + .228)(1 - .100)(1 + .347)(1 + .269)](1/6) - 1 Geometric average return = .1201, or 12.01%

You purchased 320 shares of a particular stock at the beginning of the year at a price of $76.83. The stock paid a dividend of $1.70 per share, and the stock price at the end of the year was $83.34. What was your dollar return on this investment?

Dollar return = 320($83.34 - 76.83 + 1.70) Dollar return = $2,627.20

Consider the following information: State of Economy//Probability of State of Economy//Rate of Return if State Occurs || Recession// 28 // −.10 Boom// .72 // .22 Calculate the expected return.

E(R) = .28(-.10) + .72(.22) E(R) = .1304, or 13.04%

A stock has a beta of 1.12, the expected return on the market is 10.6 percent, and the risk-free rate is 4.65 percent. What must the expected return on this stock be?

E(Ri) = Rf + [E(RM) - Rf] × βi E(Ri) = .0465 + (.1060 - .0465)(1.12) E(Ri) = .1131, or 11.31%

A stock has an expected return of 10.4 percent, its beta is 1.01, and the risk-free rate is 6.3 percent. What must the expected return on the market be?

E(Ri) = Rf + [E(RM) - Rf] × βi .104 = .063 + [E(RM) - .063](1.01) E(RM) = .1036, or 10.36%

A stock has an expected return of 13.4 percent and a beta of 1.15, and the expected return on the market is 12.4 percent. What must the risk-free rate be?

E(Ri) = Rf + [E(RM) - Rf] × βi .134 = Rf + (.124 - Rf)(1.15) .134 = Rf + .1426 - 1.15Rf Rf = .0573, or 5.73%

A stock has an expected return of 15.2 percent, the risk-free rate is 6 percent, and the market risk premium is 7.9 percent. What must the beta of this stock be?

E(Ri) = Rf + [E(RM) - Rf] × βi .152 = .060 + .079βi βi = 1.165

You have $14,000 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 8 percent. Assume your goal is to create a portfolio with an expected return of 12.40 percent. How much money will you invest in Stock X and Stock Y?

E(Rp) = .124 = .16wX + .08(1 - wX) We can now solve this equation for the weight of Stock X as: .1240 = .16wX + .08 - .08wX .0440 = .08wX wX = .5500 So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = .5500($14,000) Investment in X = $7,700.00 And the dollar amount invested in Stock Y is: Investment in Y = (1 - .5500)($14,000) Investment in Y = $6,300.00

You own a portfolio that is 34 percent invested in Stock X, 49 percent in Stock Y, and 17 percent in Stock Z. The expected returns on these three stocks are 8 percent, 11 percent, and 13 percent, respectively. What is the expected return on the portfolio?

E(Rp) = .34(.08) + .49(.11) + .17(.13) E(Rp) = .1032, or 10.32%

Mitchell, Inc., is expected to maintain a constant 5.7 percent growth rate in its dividends, indefinitely. If the company has a dividend yield of 4.2 percent, what is the required return on the company's stock?

R = Dividend yield + Capital gains yield R = .0420 + .0570 R = .0990, or 9.90%

Suppose a stock had an initial price of $95 per share, paid a dividend of $2.00 per share during the year, and had an ending share price of $114. Compute the percentage total return

R = [($114 - 95) + 2.00] / $95 R = .2211, or 22.11%

Smiling Elephant, Inc., has an issue of preferred stock outstanding that pays a $5.10 dividend every year, in perpetuity. If this issue currently sells for $80.15 per share, what is the required return?

Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. This is a special case of the dividend growth model where the growth rate is zero, or the level perpetuity equation. Using this equation, we find the price per share of the preferred stock is: R = D / P0 R = $5.10 / $80.15 R = .0636, or 6.36%

You purchased a zero-coupon bond one year ago for $279.83. The market interest rate is now 9 percent. Assume semiannual coumpounding periods. If the bond had 15 years to maturity when you originally purchased it, what was your total return for the past year?

Since one year has elapsed, the bond now has 14 years to maturity, so the price today is: P1 = $1,000 / 1.04528 P1 = $291.57 There are no intermediate cash flows on a zero-coupon bond, so the return is the capital gain, or: R = ($291.57 - 279.83) / $279.83 R = .0420, or 4.20%

The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio is as risky as the market, it must have the same beta as the market.

Since the beta of the market is one, we know the beta of our portfolio is one. We also need to remember that the beta of the risk-free asset is zero. It has to be zero since the asset has no risk.

The next dividend payment by Dizzle, Inc., will be $2.95 per share. The dividends are anticipated to maintain a growth rate of 5.5 percent, forever. Assume the stock currently sells for $49.50 per share. What is the expected capital gains yield?

The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 5.5%

You bought a share of 6.70 percent preferred stock for $98.18 last year. The market price for your stock is now $103.17. What is your total return for last year?

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. Since preferred stock is assumed to have a par value of $100, the dividend was $6.70, so the return for the year was: R = ($103.17 - 98.18 + 6.70) / $98.18 R = .1191, or 11.91%

Gilmore, Inc., just paid a dividend of $2.55 per share on its stock. The dividends are expected to grow at a constant rate of 5.5 percent per year, indefinitely. Assume investors require a return of 11 percent on this stock. What will the price be in three years and in fifteen years?

The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in Year 3, and we have already calculated the stock price today. The stock price in Year 3 will be: P3 = P0(1 + g)3 P3 = $48.91(1 + .0550)3 P3 = $57.44 And the stock price in Year 15 will be: P15 = P0(1 + g)15 P15 = $48.91(1 + .0550)15 P15 = $109.20

You own a portfolio that has $2,000 invested in Stock A and $3,100 invested in Stock B. Assume the expected returns on these stocks are 10 percent and 16 percent, respectively. What is the expected return on the portfolio?

Total value = $2,000 + 3,100 Total value = $5,100 So, the expected return of this portfolio is: E(Rp) = ($2,000 / $5,100)(.10) + ($3,100 / $5,100)(.16) E(Rp) = .1365, or 13.65%

What are the portfolio weights for a portfolio that has 180 shares of Stock A that sell for $93 per share and 155 shares of Stock B that sell for $118 per share?

Total value = 180($93) + 155($118) Total value = $35,030 The portfolio weight for each stock is: xA = 180($93) / $35,030 xA = .4779 or 47.79 xB = 155($118) / $35,030 xB = .5221 or 52.21

The next dividend payment by Dizzle, Inc., will be $2.55 per share. The dividends are anticipated to maintain a growth rate of 6.00 percent, forever. If the stock currently sells for $48.70 per share, what is the required return?

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 = ($2.55 / $48.70) + .0600 R = .1124, or 11.24%

You own a stock portfolio invested 26 percent in Stock Q, 18 percent in Stock R, 44 percent in Stock S, and 12 percent in Stock T. The betas for these four stocks are .95, 1.01, 1.41, and 1.86, respectively. What is the portfolio beta?

βp = .26(.95) + .18(1.01) + .44(1.41) + .12(1.86) βp = 1.27

You own a portfolio equally invested in a risk-free asset and two stocks. One of the stocks has a beta of 1.14 and the total portfolio is equally as risky as the market. What must the beta be for the other stock in your portfolio?

βp = 1.0 = 1/3(0) + 1/3(1.14) + 1/3(βX) Solving for the beta of Stock X, we get: βX = 1.86