Finance Midterm 3 chap 7,10,11

If shareholders are granted a preemptive right they will:

have priority in the purchase of any newly issued shares.

Stock

-Stock represents the ownership shares in a publicly-held company. -Different types of stocks Preferred stocks Common stocks

The Nature of Equity Capital: Voice in Management

-Unlike bondholders and other credit holders, holders of equity capital are owners of the firm. -Common equity holders have voting rights that permit them to elect the firm's board of directors and to vote on special issues. -Bondholders and preferred stockholders receive no such privileges.

Wesen Corp. will pay a dividend of $3.30 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? If you want a return of 12 percent, how much will you pay for the stock?

Here, we need to value a stock with two different required returns. Using the constant growth model and a required return of 18 percent, the stock price today is: P0 = D1 / (R - g) P0 = $3.30 / (.18 - .0525) P0 = $25.88 And the stock price today with a required return of 12 percent will be: P0 = D1 / (R - g) P0 = $3.30 / (.12 - .0525) P0 = $48.89

What is the beta of the following portfolio? stock value beta M 18,400 .97 N 6,320 1.04 O 32,900 1.23 P 11,850 .88

Portfolio value = $18,400 + 6,320 + 32,900 + 11,850 = $69,470 βP = ($18,400/$69,470)(.97) + ($6,320/$69,470)(1.04) + ($32,900/$69,470)(1.23) + ($11,850/$69,470)(.88) = 1.08

Which type of stock pays a fixed dividend, receives first priority in dividend payment, and maintains the right to a dividend payment, even if that payment is deferred?

Cumulative preferred

A stock has a beta of 1.32, the expected return on the market is 12.72, and the risk-free rate is 4.05. What must the expected return on this stock be?

E(R) = .0405 + 1.32(.1272 -.0405) = .1549, or 15.49 percent

The dividend yield is defined as:

next year's expected dividend divided by the current market price per share.

Ben & Terry's has an expected return of 13.2 percent and a beta of 1.08. The expected return on the market is 12.4 percent. What is the risk-free rate?

E(R)=.132=Rf+1.08(.124-Rf) Rf=.0240, or 2.40percent

Computing the present value of a growing perpetuity is most similar to computing the current value of which one of the following?

Stock with a constant-growth dividend

Equity = Ownership

-Equity: Ownership interest in a corporation in the form of common stock or preferred stock. -It also refers to total assets minus total liabilities, in which case it is also referred to as shareholder's equity or net worth or book value. -Debt: An amount owed to a person or organization for funds borrowed

Equity: Preferred vs Common Stock

-Preferred stock is equity that usually pays a fixed dividend and has a prior claim on the firm's earnings and assets in case of liquidation. -Common stock is equity that may pay no dividend or a discretionary dividend. -Common stock receives a residual claim on the firm's earnings and assets. Common stock receives voting rights.

The Nature of Equity Capital: Maturity

-Unlike debt, equity capital is a permanent form of financing. -Equity has no maturity date and never has to be repaid by the firm.

The Nature of Equity Capital: Tax Treatment

-While interest paid to bondholders is tax-deductible to the issuing firm, dividends paid to preferred and common stockholders of the corporation is not. -In effect, this further lowers the cost of debt relative to the cost of equity as a source of financing to the firm.

You purchased 400 shares of KNO stock five years ago and have earned annual returns of 8.3 percent, 9.6 percent, 18.25 percent, -7.7 percent, and 1.8 percent, respectively. What is your arithmetic average return?

Arithmetic average = (.083 + .096 + .1825 -.077 + .018)/5 = .0605, or 6.05 percent

Over the past five years, a stock returned 6.2 percent, -10.4 percent, -2.2 percent, 16.9 percent, and 5.8 percent, respectively. What is the variance of these returns?

Average return = (.062-.104-.022 + .169 + .058)/5 = .0326 σ2 = [(.062 -.0326)^2 + (-.104-.0326)^2 + (-.022 -.0326)^2 + (.169 -.0326)^2 + (.058 -.0326)^2]/(5 - 1) =.010439

A stock has returns for five years of 14 percent, -16 percent, 12 percent, 23 percent, and 4 percent, respectively. The stock has an average return of ______ percent and a standard deviation of _____ percent.

Average return = (.14 -.16 + .12 + .23 + .04)/5 = .074, or 7.40 percent σ2 = [(.14-.074)^2 + (-.16-.074)^2 + (.12-.074)^2 + (.23-.074)^2 + (.04-.074)^2]/(5 - 1) = .021680 σ = .021680.5 = .1472, or 14.72 percent

A stock has produced returns of 19 percent, 6 percent, -21 percent, -2 percent, and 14 percent for the past five years, respectively. What is the standard deviation of these returns?

Average return = (.19 + .06 -.21 -.02 + .14)/5 = .032 σ2 = [(.19 -.032)^2 + (.06 -.032)^2 + (-.21 -.032)^2 + (-.02 -.032)^2 + (.14 -.032)^2]/(5 - 1) = .02467 σ = .02467.5 = .1571, or 15.71 percent

A stock produced returns of 14 percent, 17percent, and -1 percent over three of the past four years, respectively. The arithmetic average for the past four years is 6 percent. What is the standard deviation of the stock's returns for the four-year period?

Average return = .06 = (.14 + .17 -.01 + x)/4 x = -.06 σ2 = [(.14 -.06)^2 + (.17 -.06)^2 + (-.01-.06)^2 + (-.06-.06)^2]/(4 - 1) = .01260 σ = .01260.5= .1123, or 11.23 percent

You own a portfolio that has $2,200 invested in Stock A and $1,300 invested in Stock B. If the expected returns on these stocks are 11 percent and 17 percent, respectively, what is the expected return on the portfolio?

E(R) = [$2,200 / ($2,200 + 1,300)]×.11 + [$1,300/($2,200 + 1,300)]×.17 = .1323, or 13.23 percent

Given the following information, what is the variance of the returns on a portfolio that is invested 40 percent in both Stocks A and B, and 20 percent in Stock C? state of probability of return of rate if state occurs economy state occurring a b c boom .08 15.8 9.4 21.2 normal .09 10.6 6.8 10.4

E(RNormal) = (.40 ×.158) + (.40 ×.094) + (.20 ×.212) = .1432 E(RRecession) = (.40 ×.106) + (.40 ×.068) + (.20 ×.104) = .0904 E(RPortfolio) = (.08 ×.1432) + (.92 ×.0904) = .0946 Variance = .08(.1432 -.0946)2 + .92(.0904-.0946)2 = .000205

The common stock of The DownTowne should return 23 percent in a boom, 16 percent in a normal economy, and lose 32 percent in a recession. The probabilities of a boom, normal economy, and recession are 5 percent, 90 percent, and 5 percent, respectively. What is the variance of the returns on this stock?

Expected return = (.05 ×.23) + (.90 ×.16) + [.05 ×(-.32)] =.1395 Variance = .05(.23-.1395)^2 + .90(.16-.1395)^2 + .05(-.32 -.1395)^2 = .011345

Blue Bell stock is expected to return 8.4 percent in a boom, 8.9 percent in a normal economy, and 9.2 percent in a recession. The probabilities of a boom, normal economy, and a recession are 6 percent, 92 percent, and 2 percent, respectively. What is the standard deviation of the returns on this stock?

Expected return = (.06 ×.084) + (.92 ×.089) + (.02 ×.092) = .0888 Variance = .06(.084-.0888)^2 + .92(.089 -.0888)^2 + .02(.092-.0888)^2 = .000002 Standard deviation = .000002.5 = .0013, or .13 percent

E-Eyes.com has a new issue of preferred stock it calls 20/20 preferred. The stock will pay a $20 dividend per year, but the first dividend will not be paid until 20 years from today. If you require a return of 10.75 percent on this stock, how much should you pay today?

Here, we have a stock that pays no dividends for 20 years. Once the stock begins paying dividends, it will have the same dividends forever, a preferred stock. We value the stock at that point, using the preferred stock equation. It is important to remember that the price we find will be the price one year before the first dividend, so: P19 = D20 / R P19 = $20 / .1075 P19 = $186.05 The price of the stock today is simply the present value 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 = $186.05 / 1.1075^19 P0 = $26.74

E-Eyes.com has a new issue of preferred stock it calls 20/20 preferred. The stock will pay a $20 dividend per year, but the first dividend will not be paid until 20 years from today. The required return on the stock is 7.25 percent. What is the price of the stock 19 years from today? What is the price of the stock today?

Here, we have a stock that pays no dividends for 20 years. Once the stock begins paying dividends, it will have the same dividends forever, a preferred stock. We value the stock at that point, using the preferred stock equation. It is important to remember that the price we find will be the price one year before the first dividend, so: P19 = D20 / R P19 = $20 / .0725 P19 = $275.86 The price of the stock today is the present value of the stock price in the future. We discount the future stock price at the required return. So, the price of the stock today will be: P0 = $275.86 / 1.0725^19 P0 = $72.97

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next 11 years, because the firm needs to plow back its earnings to fuel growth. The company will then pay a dividend of $13.75 per share 12 years from today and will increase the dividend by 5.5 percent per year thereafter. The required return on the stock is 13.5 percent. What is the price of the stock 11 years from today? What is the current share price?

Here, we have a stock that pays no dividends for eleven years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember the general constant dividend growth formula is: Pt = [Dt × (1 + g)] / (R - g) This means that since we will use the dividend in Year 12, we will be finding the stock price in Year 11. The dividend growth model is similar to the present value of an annuity and the present value of a perpetuity: The equation gives you the present value one period before the first payment. So, the price of the stock in Year 11 will be: P11 = D12 / (R - g) P11 = $13.75 / (.135 - .055) P11 = $171.88 The price of the stock today is the PV of the stock price in the future. We discount the future stock price at the required return. The price of the stock today will be: P0 = $171.88 / 1.135^11 P0 = $42.68

Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years, because the firm needs to plow back its earnings to fuel growth. The company will then pay a dividend of $15.75 per share 10 years from today and will increase the dividend by 5 percent per year thereafter. If the required return on this stock is 13 percent, what is the current share price?

Here, we have a stock that pays no dividends for nine years. Once the stock begins paying dividends, it will have a constant growth rate of dividends. We can use the constant growth model at that point. It is important to remember the general constant dividend growth formula is: Pt = [Dt × (1 + g)] / (R - g) This means that since we will use the dividend in Year 10, we will be finding the stock price in Year 9. The dividend growth model is similar to the present value of an annuity and the present value of a perpetuity: The equation gives you the present value one period before the first payment. So, the price of the stock in Year 9 will be: P9 = D10 / (R - g) P9 = $15.75 / (.13 - .05) P9 = $196.88 The price of the stock today is the PV of the stock price in the future. We discount the future stock price at the required return. The price of the stock today will be: P0 = $196.88 / 1.13^9 P0 = $65.54

You find a certain stock that had returns of 13.4 percent, -21.7 percent, 27.7 percent, and 18.7 percent for four of the last five years. Assume the average return of the stock over this period was 11.4 percent. What was the stock's return for the missing year? What is the standard deviation of the stock's returns?

Here, we know the average stock return, and four of the five returns used to compute the average return. We can work the average return equation backward to find the missing return. The average return is calculated as: .1140 = (.134 - .217 + .277 + .187 + R) / 5 .57 = .134 - .217 + .277 + .187 + R R = .1890, or 18.90% The missing return has to be 18.90 percent. Now we can use the equation for the variance to find: Variance = 1/4[(.134 - .114)^2 + (-.217 - .114)^2 + (.277 - .114)^2 + (.187 - .114)^2 + (.189 - .114)^2] Variance = .036871 And the standard deviation is: Standard deviation = .036871^1/2 Standard deviation = .1920, or 19.20%

A stock has an expected return of 11.8 percent, its beta is .93, and the risk-free rate is 5.9 percent. What must the expected return on the market be?

Here, we need to find the expected return of the market, using the CAPM. Substituting the values given, and solving for the expected return of the market, we find: E(Ri) = Rf + [E(RM) - Rf] × βi .118 = .059 + [E(RM) - .059](.93) E(RM) = .1224, or 12.24%

A stock has an expected return of 12.2 percent and a beta of 1.18, and the expected return on the market is 11.2 percent. What must the risk-free rate be?

Here, we need to find the risk-free rate, using the CAPM. Substituting the values given, and solving for the risk-free rate, we find: E(Ri) = Rf + [E(RM) - Rf] × βi .122 = Rf + (.112 - Rf)(1.18) .122 = Rf + .13216 - 1.18Rf Rf = .0564, or 5.64%

Assume that large-company stocks had an average rate of return of 12.1 percent over the past 88 years while T-bills returned an average of 3.5 percent and inflation averaged 3.0 percent. Given this, the real return on large-company stocks was:

Real return = (1.121 / 1.030) - 1 = .0883, or 8.83 percent

A stock has a beta of 1.22, the expected return on the market is 12 percent, and the risk-free rate is 4.65 percent. What must the expected return on this stock be?

The CAPM states the relationship between the risk of an asset and its expected return. The CAPM is: E(Ri) = Rf + [E(RM) - Rf] × βi Substituting the values we are given, we find: E(Ri) = .0465 + (.1200 - .0465)(1.22) E(Ri) = .1362, or 13.62%

Calculate the average returns for X and Y Calculate the variances for X and Y Calculate the standard deviations for X and Y

The average return is the sum of the returns, divided by the number of returns. The average return for each stock was: 1formula37.mml 1formula38.mml We calculate the variance of each stock as: 1formula39.mml 1formula40.mml 1formula41.mml The standard deviation is the square root of the variance, so the standard deviation of each stock is: σX = .0253911/2 σX = .1593, or 15.93% σY = .0513111/2 σY = .2265, or 22.65%

Gilmore, Inc., just paid a dividend of $3.30 per share on its stock. The dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely. Assume investors require a return of 9 percent on this stock. What is the current price? What will the price be in six years and in thirteen years?

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 = $3.30(1.0450) / (.09 - .0450) P0 = $76.63 There is another feature of the constant dividend growth model: 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 6, and we have already calculated the stock price today. The stock price in Year 6 will be: P6 = P0(1 + g)^6 P6 = $76.63(1 + .0450)^6 P6 = $99.80 And the stock price in Year 13 will be: P13 = P0(1 + g)^13 P13 = $76.63(1 + .0450)^13 P13 = $135.81

he next dividend payment by Dizzle, Inc., will be $2.55 per share. The dividends are anticipated to maintain a growth rate of 6 percent, forever. Assume the stock currently sells for $48.70 per share. What is the dividend yield? What is the expected capital gains yield?

The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = D1 / P0 Dividend yield = $2.55 / $48.70 Dividend yield = .0524, or 5.24% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 6%

What are the portfolio weights for a portfolio that has 150 shares of Stock A that sell for $87 per share and 125 shares of Stock B that sell for $94 per share?

The portfolio weight of an asset is the total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 150($87) + 125($94) Total value = $24,800 The portfolio weight for each stock is: xA = 150($87) / $24,800 xA = .5262 or 52.62 xB = 125($94) / $24,800 xB = .4738 or 47.38

Smiling Elephant, Inc., has an issue of preferred stock outstanding that pays a $5.00 dividend every year, in perpetuity. If this issue currently sells for $80.10 per share, what is the required return?

The price of a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. 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 = $5.00 / $80.10 R = .0624, or 6.24%

Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of $10.75 per share and has announced that it will increase the dividend by $8.75 per share for each of the next four years, and then never pay another dividend. If you require a return of 15 percent on the company's stock, how much will you pay for a share today?

The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends discounted at the required return. So, the price of the stock is: P0 = $19.50 / 1.15 + $28.25 / 1.15^2 + $37.00 / 1.15^3 + $45.75 / 1.15^4 P0 = $88.80

Burkhardt Corp. pays a constant $14.90 dividend on its stock. The company will maintain this dividend for the next six years and will then cease paying dividends forever. If the required return on this stock is 10 percent, what is the current share price? (

The price of any financial instrument is the present value of the future cash flows. The future dividends of this stock are an annuity for six years, so the price of the stock is the present value of an annuity, which will be: P0 = $14.90(PVIFA10%,6) P0 = $64.89

Mitchell, Inc., is expected to maintain a constant 6.2 percent growth rate in its dividends, indefinitely. If the company has a dividend yield of 4.7 percent, what is the required return on the company's stock?

The required return of a stock is made up of two parts: The dividend yield and the capital gains yield. So, the required return of this stock is: R = Dividend yield + Capital gains yield R = .0470 + .0620 R = .1090, or 10.90%

You've observed the following returns on Barnett Corporation's stock over the past five years: -25.5 percent, 14 percent, 31 percent, 2.5 percent, and 21.5 percent. What was the arithmetic average return on the stock over this five-year period? What was the variance of the returns over this period? What was the standard deviation of the returns over this period?

To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (-.255 + .140 + .310 + .025 + .215) / 5 Arithmetic average return = .0870, or 8.70% Using the equation to calculate variance, we find: Variance = 1/4[(-.255 - .0870)^2 + (.140 - .0870)^2 + (.310 - .0870)^2 + (.025 - .0870)^2 + (.215 - .0870)^2] Variance = .047433 So, the standard deviation is: Standard deviation = .047433^1/2 Standard deviation = .2178, or 21.78%

One year ago, you purchased 600 shares of stock for $14 a share. The stock pays $.41 a share in dividends each year. Today, you sold your shares for $15.30 a share. What is your total dollar return on this investment?

Total dollar return = 600 ×($15.30 -14 + .41) = $1,026

You bought a share of 7.5 percent preferred stock for $91.60 last year. The market price for your stock is now $89.10. What is your total return to date on this investment?

Total return = ($89.10 -91.60 + 7.50)/$91.60 = .0546, or 5.46 percent

Take Time Corporation will pay a dividend of $4.50 per share next year. The company pledges to increase its dividend by 6.25 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?

Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R - g) P0 = $4.50 / (.10 - .0625) P0 = $120.00

Take Time Corporation will pay a dividend of $4.80 per share next year. The company pledges to increase its dividend by 7.75 percent per year, indefinitely. If you require a return of 11 percent on your investment, how much will you pay for the company's stock today?

Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R - g) P0 = $4.80 / (.11 - .0775) P0 = $147.69

Gontier Corporation stock currently sells for $64.58 per share. The market requires a return of 10 percent on the firm's stock. If the company maintains a constant 5.75 percent growth rate in dividends, what was the most recent dividend per share paid on the stock?

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 = D0(1 + g) / (R - g) Solving this equation for the dividend gives us: D0 = P0(R - g) / (1 + g) D0 = $64.58(.10 - .0575) / (1 + .0575) D0 = $2.60

A stock has an expected return of 16.1 percent, the risk-free rate is 6.45 percent, and the market risk premium is 7.2 percent. What must the beta of this stock be?

We are given the values for the CAPM except for the β of the stock. We need to substitute these values into the CAPM, and solve for the β of the stock. One important thing we need to realize is that we are given the market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. We must be careful not to use this value as the expected return of the market. Using the CAPM, we find: E(Ri) = Rf + [E(RM) - Rf] × βi .161 = .0645 + .072βi βi = 1.340

Suppose you know that a company's stock currently sells for $65.80 per share and the required return on the stock is 11 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?

We know the stock has a required return of 11 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.11) Dividend yield = .055 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so: D1 = .055($65.80) D1 = $3.62 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: $3.62 = D0(1 + .055) D0 = $3.62 / 1.055 D0 = $3.43

The stock price of Baskett Co. is $53.10. Investors require a return of 13 percent on similar stocks. If the company plans to pay a dividend of $3.20 next year, what growth rate is expected for the company's stock price?

We need to find the growth rate of dividends. Using the constant growth model, we can solve the equation for g. Doing so, we find: g = R - (D1 / P0) g = .13 - ($3.20 / $53.10) g = .0697, or 6.97%

The next dividend payment by Dizzle, Inc., will be $3.00 per share. The dividends are anticipated to maintain a growth rate of 4.25 percent, forever.

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 = ($3.00 / $49.60) + .0425 R = .1030, or 10.30%

Burton Corp. is growing quickly. Dividends are expected to grow at a rate of 29 percent for the next three years, with the growth rate falling off to a constant 6.3 percent thereafter. If the required return is 15 percent and the company just paid a dividend of $2.90, what is the current share price?

With nonconstant dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the nonconstant growth period. The stock begins constant growth after the third dividend is paid, so we can find the price of the stock in Year 3, when the constant dividend growth begins as: P3 = D3(1 + g2) / (R - g2) P3 = D0(1 + g1)^3(1 + g2) / (R - g2) P3 = $2.90(1.29)^3(1.063) / (.15 - .063) P3 = $76.06 The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be: P0 = $2.90(1.29) / 1.15 + $2.90(1.29)^2 / 1.15^2 + $2.90(1.29)^3 / 1.15^3 + $76.06 / 1.15^3 P0 = $61.01

Burton Corp. is growing quickly. Dividends are expected to grow at a rate of 28 percent for the next three years, with the growth rate falling off to a constant 7.9 percent thereafter. The required return is 16 percent and the company just paid a dividend of $3.70. What are the dividends each year for the next four years? What is the share price in three years? What is the current share price?

With nonconstant dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the nonconstant growth period. The stock begins constant growth after the third dividend is paid, so we can find the price of the stock in Year 3, when the constant dividend growth begins as: P3 = D3(1 + g2) / (R - g2) P3 = D0(1 + g1)^3(1 + g2) / (R - g2) P3 = $3.70(1.28)^3(1.079) / (.16 - .079) P3 = $103.36 The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be: P0 = $3.70(1.28) / 1.16 + $3.70(1.28)^2 / 1.16^2 + $3.70(1.28)^3 / 1.16^3 + $103.36 / 1.16^3 P0 = $79.78

State of Probability of State Rate of Return if State Economy of Economy Occurs Stock A Stock B Stock C Boom .71 .09 .03 .29 Bust .29 .18 .24 -.09 a. What is the expected return on an equally weighted portfolio of these three stocks? b. What is the variance of a portfolio invested 26 percent each in A and B and 48 percent in C?

a. To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the return of the portfolio in each state of the economy is: Boom: Rp = (.09 + .03 + .29) / 3 Rp = .1367, or 13.67% Bust: Rp = (.18 + .24 - .09) / 3 Rp = .1100, or 11.00% This is equivalent to multiplying the weight of each asset (1/3 or .3333) times its expected return and summing the results, which gives: Boom: Rp = 1/3(.09) + 1/3(.03) + 1/3(.29) Rp = .1367, or 13.67% Bust: Rp = 1/3(.18) + 1/3(.24) + 1/3(-.09) Rp = .1100, or 11.00% To find the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum. Doing this, we find: E(Rp) = .71(.1367) + .29(.1100) E(Rp) = .1289, or 12.89% b. This portfolio does not have an equal weight in each asset. We still need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get: Boom: Rp = .26(.09) +.26(.03) + .48(.29) Rp = .1704, or 17.04% Bust: Rp = .26(.18) +.26(.24) + .48(-.09) Rp = .0660, or 6.60% And the expected return of the portfolio is: E(Rp) = .71(.1704) + .29(.0660) E(Rp) = .1401, or 14.01% 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 of the portfolio is: σp2 = .71(.1704 - .1401)^2 + .29(.0660 - .1401)^2 σp2 = .00224

Consider the following information: Probability of State Rate of Return if State of Economy Occurs Economy Stock A Stock B Recession .22 .020 -.37 Normal .57 .100 .27 Boom .21 .260 .50 a. Calculate the expected return for the two stocks. Calculate the standard deviation for the two stocks

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) = .22(.02) + .57(.10) + .21(.26) E(RA) = .1160, or 11.60% E(RB) = .22(-.37) + .57(.27) + .21(.50) E(RB) = .1775, or 17.75% 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 = .22(.02 - .1160)^2 + .57(.100 - .1160)^2 + .21(.26 - .1160)^2 σA2 = .00653 σA = .00653^1/2 σA = .0808, or 8.08% σB2 = .22(-.37 - .1775)^2 + .57(.27 - .1775)^2 + .21(.50 - .1775)^2 σB2 = .09266 σB = .09266^1/2 σB = .3044, or 30.44%

When valuing a stock using the constant-growth model, D1 represents the:

the next expected annual dividend.