FIN 325 Exam 3 - Chapter 11, Chapter 12, Chapter 13

Sue purchased a stock for $25 a share, held it for one year, received a $1.34 dividend, and sold the stock for $26.45. What nominal rate of return did she earn?

11.16%

What is the expected yield on the market portfolio at a time when Treasury bills yield 6% and a stock with a beta of 1.4 is expected to yield 18%?

14.57%

From a historical perspective (1900-2013), what would you expect to be the approximate return on a diversified portfolio of common stocks in a year that Treasury bills offered 7.5%?

15.1%

What is the pretax cost of debt for a firm in the 35% tax bracket that has a 10% aftertax cost of debt?

15.38%

What is the yield to maturity on Dotte Inc.'s bonds if its after-tax cost of debt is 10% and its tax rate is 35%?

15.38%

Which one of the following guarantees is offered to common stock investors?

No guarantees of any form

Should a project be accepted if it offers an annual after-tax cash flow of $1,250,000 indefinitely, costs $10 million, is riskier than the firm's average projects, and the firm's WACC is 12.5%?

No, since the project's NPV is negative

How is it possible for real rates of return to increase during times when the rate of inflation increases?

Nominal returns increased more than inflation

Which one of the following statements seems most appropriate when the Dow Jones Industrial Average increases by 2%?

One market indicator was up by 2%

Which one of the following statements is more likely to be correct concerning the comment, "Stock A has a higher expected return than Stock B"?

Stock A has a higher beta

Which one of the following statements is correct when Treasury bills yield 7.5% and the market risk premium is 9.5%?

The S&P 500 would be expected to yield about 17.00%

Which one of the following portfolios might be expected to exhibit less unique risk?

Twelve random stocks; portfolio beta unknown

1). Use the data in the tables below to answer the following questions: Average rates of return on Treasury bills, government bonds, and common stocks, 1900-2013. Portfolio Average Annual Rate of Return Average Premium (Extra return versus Treasury bills) Treasury bills 3.9 Treasury bonds 5.2 1.3 Common stocks 11.5 7.6 Standard deviation of returns, 1900-2013. Portfolio Standard Deviation, % Treasury bills 2.8 Long-term government bonds 8.9 Common stocks 19.9 a. What was the average rate of return on large U.S. common stocks from 1900 to 2013? b. What was the average risk premium on common stocks? c. What was the standard deviation of returns on common stocks?

a. Average rate of return 11.5% b. Average risk premium 7.6% c. Standard deviation of returns 19.9%

Investment projects that plot above the security market line would be considered to have:

a positive NPV.

15). Suppose that the S&P 500, with a beta of 1.0, has an expected return of 12% and T-bills provide a risk-free return of 3%. a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) .25; (iii) .50; (iv) .75; (v) 1.0? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places.) b. How does expected return vary with beta? (Do not round intermediate calculations.)

a. Expected return Beta 3.00% 0 5.25% .25 7.50% .50 9.75% .75 12.00% 1.00 b. increases 9%

15). Suppose that the S&P 500, with a beta of 1.0, has an expected return of 13% and T-bills provide a risk-free return of 6%. a. What would be the expected return and beta of portfolios constructed from these two assets with weights in the S&P 500 of (i) 0; (ii) .25; (iii) .50; (iv) .75; (v) 1.0? (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places.) b. How does expected return vary with beta? (Do not round intermediate calculations.)

a. Expected return Beta 6.00% 0 7.75% .25 9.50% .50 11.25% .75 13.00% 1.00 b. increases 7%

8). You purchase 100 shares of stock for $40 a share. The stock pays a $2 per share dividend at year-end. a. What is the rate of return on your investment if the end-of-year stock price is (i) $23; (ii) $25; (iii) $28? b. What is your real (inflation-adjusted) rate of return if the inflation rate is 5%?

a. Stock price Rate of return $23 0% $25 8% $28 20% b. Stock price Real rate of return $23 -4.76% $25 2.86% $28 14.29%

8). You purchase 100 shares of stock for $40 a share. The stock pays a $2 per share dividend at year-end. a. What is the rate of return on your investment if the end-of-year stock price is (i) $38; (ii) $40; (iii) $42? b. What is your real (inflation-adjusted) rate of return if the inflation rate is 4%?

a. Stock price Rate of return $38 0% $40 5% $42 10% b. Stock price Real rate of return $38 -3.85% $40 .96% $42 5.77%

6). Assume these are the stock market and Treasury bill returns for a 5-year period: Year Stock Market Return T-Bill Return Year 1 − 35.23 3.60 Year 2 30.70 1.90 Year 3 15.16 .23 Year 4 2.68 .08 Year 5 18.96 .10 a. What was the risk premium on common stock in each year? b. What was the average risk premium? c. What was the standard deviation of the risk premium?

a. Year Risk premium Year 1 -38.83% Year 2 28.80% Year 3 14.93% Year 4 2.60% Year 5 18.86% b. Average risk premium 5.27% c. Standard deviation 23.59%

12). Nodebt Inc. is a firm with all-equity financing. Its equity beta is .80. The Treasury bill rate is 2%, and the market risk premium is expected to be 8%. a. What is Nodebt's asset beta? (Round your answer to 2 decimal places.) b. What is Nodebt's WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

a. Asset beta: .80 b. WACC: 8.40%

Assume last month a stock with a beta of 1.0 lost 2% while the S&P 500 had a 1% gain. Given this it is most likely that the:

firm released some negative information about itself

WACC can be used to determine the value of a firm by discounting the firm's:

free cash flows

Treasury bonds have provided a higher historical return than Treasury bills, which can be attributed to their:

greater exposer to interest rate risk

If the market portfolio is expected to return 16%, then a portfolio that is expected to return 13%:

has a beta that is less than 1.0

If the slope of the line measuring a stock's historic returns against the market's historic returns is positive, then the stock:

has a positive beta

If a company's cost of capital is less than the required return on equity, then the firm:

has debt in its capital structure

The primary difference between U.S. Treasury bills and U.S. Treasury bonds is that the bills:

have a shorter maturity at time of issue

Perhaps the best way to reduce macro risk in a stock portfolio is to invest in stocks that:

have low exposure to business cycles

The standard deviations of individual stocks are generally higher than the standard deviation of the market portfolio because individual stocks:

have no diversification of risk

If you were willing to bet that the overall stock market was heading up on a sustained basis, it would be logical to invest in:

high beta stocks

The wider the dispersion of returns on a stock, the:

higher the standard deviation

The CAPM provides a model of determining expected security returns that is:

imprecise, but generally an acceptable guideline

Investing borrowed funds in a stock portfolio will generally:

increase the beta of the portfolio

When viewing the long-term trend of the price volatility of U.S. stocks, it is readily apparent that volatility has:

increased and decreased but has no specific pattern

Real rates of return are typically less than nominal rates of return due to:

inflation

An investor prefers to invest in companies that have high fixed costs. How can this be accomplished if the investor also requires a portfolio beta of 1.0?

invest a portion of the portfolio in the US treasury securities

A firm's WACC:

is a benchmark discount rate that is adjusted for the riskiness of each project

Assume market interest rates have risen substantially in the 5 years since an investor purchased Treasury bonds that were offering a 6% return over their 15-year life. If the investor sells now he or she is likely to realize a total return that is:

less than 6%

If a stock's beta is 0.8 during a period when the market portfolio was down by 10%, then, a priori, we could expect this individual stock to:

lose, but less than 10%

When the overall market experiences a decline of 8%, investors with portfolios of aggressive stocks will probably experience portfolio:

losses greater than 8%

A project will generate a $1 million net cash flow annually in perpetuity. If the project costs $7 million, what is the break-even WACC?

14.29%

Suppose an analyst estimates that free cash flow will be $2.43 million in year 5. What is the present value of this free cash flow if the company cost of capital is 12%, the WACC is 10%, and the equity cost of capital is 15%?

$1,508,839

How much will a firm need in cash flow before tax and interest to satisfy debtholders and equityholders if the tax rate is 35%, there is $13 million in common stock requiring a 10% return, and $6 million in bonds requiring a 6% return?

$2,360,000

How much will a firm need in cash flow before tax and interest to satisfy debtholders and equityholders if the tax rate is 40%, there is $10 million in common stock requiring a 12% return, and $6 million in bonds requiring an 8% return?

$2,480,000

Al's Market plans to close after 3 more years. The firm expects to have free cash flows of $148,000 next year, $128,000 in Year 2, and $65,000 in Year 3 after incurring the costs of closing. The firm's cost of equity is 15.5% and its cost of debt is 6.2%. What is the present value of the firm if its debt to value ratio is 30%?

$277,467

An investor receives a 15% total return by purchasing a stock for $40 and selling it after one year with a 5% capital gain. How much was received in dividend income during the year?

$4.00

What dividend is paid on preferred stock if investors require a 9% rate of return and the stock has a market value of $54 per share and a book value of $50 per share?

$4.86

A firm is considering a project that will generate perpetual cash flows of $50,000 per year beginning next year. The project has the same risk as the firm's overall operations. If the firm's WACC is 12%, and its debt-to-equity ratio is 1.33, what is the most it could pay for the project and still earn its required rate of return?

$416,667

Assume when a coin is tossed the observance of a head rewards you with a dollar and the observance of a tail costs you fifty cents. How much would you expect to gain after 20 tosses?

$5.00

If equity investors require a 20% rate of return, what is the maximum acceptable amount of equity financing for a project with $2 million annual cash flows before tax and interest, $3 million in debt with a 10% coupon, and a 35% tax rate?

$5.53 million

A share of stock currently sells for $60, pays an annual dividend of $4.00, and earned a rate of return of 20% over the past year. What did this stock sell for one year ago?

$53.33

A firm sells a product that it realizes is short-lived and thus the firm plans to close after 2 more years. The firm expects to have free cash flows of $398,000 next year and $211,000 in Year 2 after incurring the costs of closing. The firm's cost of equity is 14% and its cost of debt is 5.5%. What is the present value of the firm if its debt to value ratio is 40%?

$532,349

Over a 20-year period an investment of $1,000 in common stocks returned an average of 11% in nominal terms and 4% in real terms. At the end of the 20 years, the portfolio value was:

$8,062.31 in nominal terms

How much cash flow before tax and interest is necessary to support a project that requires $4 million annually for equity investors and $2 million annually in interest payments if the firm's tax rate is 35%?

$8.15 million

A common stock was held for 2 years during which time total dividends of $20 were paid. The stock was sold for $100. What was the purchase price of the stock if the total rate of return for the period was 32%?

$90.91

What is the percentage return on a stock that was purchased for $48.40, paid a $1.67 dividend, and was then sold after one year for $46.20?

-1.10%

What real rate of return is earned by a one-year investor in a bond that was purchased for $1,000, has a coupon rate of 8%, and was sold for $960 when the inflation rate was 6%?

-1.89%

What was the percentage return on a non-dividend-paying stock that was purchased for $40.00 and then sold after one year for $39.00?

-2.50%

What is the beta of a U.S. Treasury bill?

0

What is the beta of a US Treasury bill?

0

What percentage return is achieved by an investor who purchases a stock for $30, receives a $1.50 dividend, and sells the share one year later for $28.50?

0%

Assume the market rate of return is 12.5% and the risk-free rate is 3.1%. What will be the change in a stock's rate of return if its beta increases from 1.12 to 1.14?

0.19%

What is the beta of a security with an expected return of 12% if Treasury bills yield 6% and the market risk premium is 8%?

0.75

An investor divides her portfolio into thirds, with one part in Treasury bills, one part in a market index, and one part in a diversified portfolio with beta of 1.50. What is the beta of the investor's overall portfolio?

0.83

The weighted-average cost of capital for a firm with a 40/60 debt/equity split, 8% cost of debt, 15% cost of equity, and a 34% tax rate would be:

11.11%

If a two-stock portfolio is equally invested in stocks with betas of 1.4 and 0.7, then the portfolio beta is:

1.05

What is the beta of a 3-stock portfolio including 25% of stock A with a beta of 0.90, 40% of stock B with a beta of 1.05, and 35% of stock C with a beta of 1.73?

1.25

If a stock consistently goes down (up) by 1.6% when the market portfolio goes down (up) by 1.2%, then its beta equals:

1.33

What should be the beta of a replacement stock if an investor wishes to achieve a portfolio beta of 1.2 by replacing stock C in the following equally weighted portfolio: stock A = 0.9 beta; stock B = 1.1 beta; stock C = 1.35 beta?

1.6

You want to develop a portfolio containing U.S. Treasury bills and two stocks that is equally as risky as the market. The securities will be equally weighted. If the beta of the first stock is 1.23, what does the beta of the second stock have to be?

1.77

A stock is expected to return 11% in a normal economy, 19% if the economy booms, and lose 8% if the economy moves into a recessionary period. The economists predict a 65% chance of a normal economy, a 25% chance of a boom, and a 10% chance of a recession. What is the expected return on the stock?

11.10%

Calculate the risk premium on stock C given the following information: risk-free rate = 5%, market return = 13%, stock C beta = 1.3.

10.4%

A project has an assigned beta of 1.24, the risk-free rate is 3.8%, and the market rate of return is 9.2%. What is the project's expected rate of return?

10.50%

What is the approximate standard deviation of returns for a one-year project that is equally likely to return 100% as it is to provide a 100% loss?

100%

In a year in which common stocks offered an average return of 18%, Treasury bonds offered 10%, and Treasury bills offered 7%. The risk premium for common stocks was:

11%

What is the WACC for a firm using 55% equity with a required return of 15%, 35% debt with a required return of 8%, 10% preferred stock with a required return of 10%, and a tax rate of 35%?

11.07%

The yield-to-maturity of a firm's bond is 8.5%. The firm has a beta of 1.3 and a tax rate of 34%. The market risk premium is 8.4% and the risk-free rate is 3.8%. What is the firm's WACC if the firm has a capital structure that is 40% debt financed?

11.08%

XYZ Company issues common stock at a price of $25 a share. The firm expects to pay a dividend of $2.20 a share next year. If the dividend is expected to grow at 2.5% annually, what is XYZ's cost of common equity?

11.3%

What return on equity do investors seem to expect for a firm with a $55 share price, an expected dividend of $4.60, a beta of 0.9, and a constant growth rate of 3.5%?

11.86%

A project has an assigned beta of 0.97, the risk-free rate is 4.1%, and the market risk premium is 8.1%. What is the project's expected rate of return?

11.96%

What is the after-tax cost of preferred stock that pays a 12% dividend and sells at par if the firm's tax rate is 35%?

12.0%

What is the WACC for a firm with 40% debt, 20% preferred stock, and 40% equity if the respective costs for these components are 6% after tax, 12% after tax, and 18% before tax? The firm's tax rate is 35%.

12.00%

What is the WACC for a firm with 40% debt, 20% preferred stock, and 40% equity if the respective costs for these components are 9.23% before tax, 12% after tax, and 18% before tax? The firm's tax rate is 35%.

12.00%

What is the after-tax cost of preferred stock that sells for $10 per share and offers a $1.20 dividend when the tax rate is 35%?

12.00%

What rate of return should an investor expect for a stock that has a beta of 0.8 when the market is expected to yield 14% and Treasury bills offer 6%?

12.4%

What is the variance of returns of a 3-stock portfolio (with unequal weights 25%, 50%, and 25%) that produced returns of 20%, 25%, and 30%, respectively?

12.50

The capital structure for the CR Corporation includes bonds valued at $5,500 and common stock valued at $11,000. If CR has an after-tax cost of debt of 6%, and a cost of common stock of 16%, what is its WACC?

12.67%

A firm with a beta of 1.22 just paid its annual dividend of $5.64 a share. The dividends increase at a rate of 2% annually. The risk-free rate is 3.5%, the market rate of return is 12.4%, and the dividend discount rate is 11.6%. What is the best estimate of the firm's cost of equity if the firm's stock currently sells for $60 a share using an average of methods?

12.97%

Calculate a firm's WACC given that the total value of the firm is $2 million, $600,000 of which is debt, the pre-tax cost of debt is 10%, and the cost of equity is 15%. The firm pays no taxes.

13.5%

What is the standard deviation of a portfolio's returns if the mean return is 15%, the variance of returns is 184, and there are three stocks in the portfolio?

13.56%

An investor was expecting a return of 14.7% on her portfolio with a beta of 1.13 before the market risk premium decreased from 8 to 7%. Based on this change, what return should she now expect on the portfolio?

13.57%

What is the WACC for a firm with 50% debt and 50% equity that pays 12% on its debt, 20% on its equity, and has a 40% tax rate?

13.6%

A firm has 12,000 shares of common stock outstanding with a book value of $20 per share and a market value of $39. There are 5,000 shares of preferred stock with a book value of $10 and a market value of $26. There is a $400,000 face value bond issue outstanding that is selling at 87% of par. What weight should be placed on the preferred stock when computing the firm's WACC?

13.74%

What is the approximate variance of returns if over the past 3 years an investment returned 8%, -12%, and 15%?

131

What is the WACC for a firm financed with 30% debt if the debt requires an after-tax return of 10% and equity requires a 16% return?

14.2%

What would you estimate as the cost of equity if a stock sells for $40, pays a $4.25 dividend, and is expected to grow at a constant rate of 5%?

15.63%

What is the standard deviation of the market portfolio if the standard deviation of a fully diversified portfolio with a beta of 1.25 equals 20%?

16.00%

Find the required rate of return for equity investors of a firm with a beta of 1.3 when the risk free rate is 5% and the return on the market is 13.6%.

16.18%

What is the variance of returns of a 3-stock portfolio (each stock being equally weighted) that produced returns of 20%, 25%, and 30%?

16.67

According to CAPM estimates, what is the cost of equity for a firm with a beta of 1.5 when the risk-free interest rate is 6% and the expected return on the market portfolio is 15%?

19.5%

If Treasury bills yield 6% and the market risk premium is 9%, then a stock with a beta of 1.5 would be expected to yield:

19.5%

How much is added to a firm's weighted-average cost of capital for 45% debt financing with a required rate of return of 10% and a tax rate of 35%?

2.93%

Most of the beneficial effects of diversification will have been received by the time a portfolio of common stocks contains approximately _____ stocks.

20

An investor was expecting a return of 18% on his portfolio with a beta of 1.25 before the market risk premium increased from 8 to 10%. Based on this change, what return should he now expect on the portfolio?

20.5%

A company's CFO wants to maintain a target debt-to-equity ratio of 1/4. If the WACC is 18.6%, and the pretax cost of debt is 9.4%, what is the cost of common equity assuming a tax rate of 34%?

21.70%

Company X has 2 million shares of common stock outstanding at a book value of $2 per share. The stock trades for $3 per share. It also has $2 million in face value of debt that trades at 90% of par. What is the weight of debt for WACC purposes?

23.08%

If a firm has three times as much equity as debt in its capital structure, then the firm is financed with:

25.0%

A stock has a beta of 1.4 and an expected return of 13.53%. What is the risk-free rate if the market rate of return is 10.6%?

3.275%

What appears to be the targeted debt ratio of a firm that issues $15 million in bonds and $35 million in equity to finance its new capital projects?

30%

What return should be expected from investing in the market portfolio that is expected to yield 18% if the investment includes all of the investor's funds plus 100% of additional funds borrowed at the risk-free rate of 6%?

30.0%

A project's expected return is 15%, which represents a 35% return in a booming economy and a 5% return in a stagnant economy. What is the probability of a booming economy occurring if these are the only two economic states?

33.33%

What is the standard deviation of returns of a 4-stock portfolio (each stock being equally weighted) that produced returns of 20%, 20%, 25%, and 30%?

4.15%

Assume a firm's debt is selling at face value. What is the firm's cost of debt if the debt has a coupon rate of 7.5% and the tax rate is 35%?

4.88%

What nominal return was received by an investor when inflation averaged 3.46% and the real rate of return was 2.5%?

6.05%

What percentage of value should be allocated to equity in WACC computations for a firm with $50 million in debt selling at 85% of par, $50 million in book value of equity, and $65 million in market value of equity?

60.47%

What proportion of a firm is equity financed if the WACC is 14%, the after-tax cost of debt is 7%, the tax rate is 35%, and the required return on equity is 18%?

63.64%

If a firm has twice as much equity as debt in its capital structure, then the firm is financed with:

66.7% equity

A firm has 12,500 shares of stock outstanding that sell for $42 each. The book value of equity is $400,000. The firm has also issued $250,000 face value of debt that is currently quoted at 101.2. What value should be used as the weight of equity when computing WACC?

67.48%

If a share of stock provided a 14.84% nominal rate of return over the previous year while the real rate of return was 6.65%, then the inflation rate was:

7.68%

A portfolio is comprised of 60% of Stock A and 40% of Stock B. What is the expected return of the portfolio?

7.7%

A portfolio consists of an index mutual fund which represents the overall market and Treasury bills. The fund has a portfolio weight of 60%. The risk-free rate is 3.2% and the market risk premium is 7.6%. What is your best estimate of the portfolio expected rate of return?

7.76%

What is the expected growth rate in dividends for a firm in which shareholders require an 18% rate of return and the dividend yield is 10%?

8.0%

The weighted-average cost of capital for a firm with a 65/35 debt/equity split, 8% pre-tax cost of debt, 15% cost of equity, and a 35% tax rate would be:

8.63%

What is the expected return on a portfolio that will decline in value by 13% in a recession, will increase by 16% in normal times, and will increase by 23% during boom times if each scenario has an equal likelihood of occurrence?

8.67%

When Treasury bills yield 7% and the expected return on the market is 16%, then the risk premium on an asset is equal to:

9% times the asset's beta.

Plasti-tech Inc. is financed 60% with equity and 40% with debt. Currently, its debt has a pretax interest rate of 12%. Plasti-tech's common stock trades at $15.00 per share and its most recent dividend was $1.00. Future dividends are expected grow by 4%. If the tax rate is 34%, what is Plasti-tech's WACC?

9.73%

If the standard deviation of a portfolio's returns is known to be 30%, then its variance is:

900.00% squared.

Stock A has 10 million shares outstanding and stock B has 5 million shares outstanding. Both stocks sell for $10 a share. What is their relative weighting if both stocks are represented in the S&P 500?

A has twice the weighting, to account for having more shares

Which one of the following companies is most apt to be exposed to the least amount of macro risk?

A large producer of flour.

A stock investor owns a diversified portfolio of 15 stocks. What will be the most likely effect on the portfolio's standard deviation if one more stock is added?

A slight decrease will occur.

18). if the expected rate of return on the market portfolio is 16% and T-bills yield 7%, what must be the beta of a stock that investors expect to return 15%? (Round your answer to 4 decimal places.)

Beta of a stock: 0.8889

10). The inflation rate in the United States has averaged 3.1% a year since 1900. Use the data in the table below to answer the following question: Average rates of return on Treasury bills, government bonds, and common stocks, 1900-2013. Portfolio Average Annual Rate of Return Average Premium (Extra return versus Treasury bills) Treasury bills 3.9 Treasury bonds 5.2 1.3 Common stocks 11.5 7.6 What was the average real rate of return on Treasury bills, Treasury bonds, and common stocks in that period? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Asset class Real rate of return Treasury bills: .78% Treasury bonds: 2.04% Common stocks: 8.15%

18). if the expected rate of return on the market portfolio is 12% and T-bills yield 6%, what must be the beta of a stock that investors expect to return 10%? (Round your answer to 4 decimal places.)

Beta of a stock .6667

Which one of these statements is correct?

CAPM is widely used as a means of valuing stock

Which one of the following security classes has the highest standard deviation of returns?

Common stocks

14). The following table shows betas for several companies. Calculate each stock's expected rate of return using the CAPM. Assume the risk-free rate of interest is 8%. Use a 10% risk premium for the market portfolio. Company Beta Cost of capital Cisco 1.16 Apple 1.38 Hershey 33 Coca-Cola .47

Company Cost of capital Cisco: 10.96% Apple: 12.28% Hershey: 5.98% Coca-Cola: 6.82%

14). The following table shows betas for several companies. Calculate each stock's expected rate of return using the CAPM. Assume the risk-free rate of interest is 8%. Use a 10% risk premium for the market portfolio. Company Beta Cost of capital Cisco 1.18 Apple 1.40 Hershey 35 Coca-Cola .49

Company Cost of capital Cisco: 19.80% Apple: 22.00% Hershey: 11.50% Coca-Cola: 12.90%

Which one of the following concerns is likely to be most important to portfolio investors seeking diversification?

Correlation of returns between securities

Which one of these is a specific risk?

Retirement of a company executive

What decision should be made on a project of above-average risk if the project's IRR exceeds the WACC?

Decide after discounting at an appropriate rate

5). Top hedge fund manager Diana Sauros believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $41. The stock will pay a dividend at year-end of $2.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.6%. Average rates of return on Treasury bills, government bonds, and common stocks, 1900-2013 (figures in percent per year) are as follows. Portfolio Average Annual Rate of Return Average Premium (Extra return versus Treasury bills) Treasury bills 3.9 Treasury bonds 5.2 1.3 Common stocks 11.5 7.6 What is the discount rate on the stock? (Enter your answer as a percent rounded to 2 decimal places.) What price should she be willing to pay for the stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Discount rate 9.20% Stock price $39.38

Which one of the following firms is likely to exhibit the least macro risk exposure?

Dog food processor

What would you recommend to an investor who is considering an investment that, according to its beta, plots below the security market line?

Don't invest; the risk is high relative to the return

20). A mutual fund manager expects her portfolio to earn a rate of return of 14% this year. The beta of her portfolio is .6. The rate of return available on risk-free assets is 6% and you expect the rate of return on the market portfolio to be 16%. What expected rate of return would you demand before you would be willing to invest in this mutual fund? (Do not round intermediate calculations. Enter your answer as a whole percent.)

Expected rate of return 12% Is this fund attractive to you? Yes

20). A mutual fund manager expects her portfolio to earn a rate of return of 7% this year. The beta of her portfolio is .6. The rate of return available on risk-free assets is 5% and you expect the rate of return on the market portfolio to be 16%. What expected rate of return would you demand before you would be willing to invest in this mutual fund? (Do not round intermediate calculations. Enter your answer as a whole percent.)

Expected rate of return 8% Is this fund attractive to you? No

What is the most logical explanation for a +2.0% return on a stock with a beta of 1.0 in a month where the market returned +1.0%?

Favorable firm-specific news was reported.

Estimate a stock's beta based on the following information: Month 1 = Stock +1.5%, Market +1.1%; Month 2 = Stock +2.0%, Market +1.4%; Month 3 = Stock -2.5%, Market -2.0%.

Greater than 1.0

Which statement is correct concerning macro risk exposure?

Macro risk exposure affects the cost of capital

What type of risk is properly reflected in a project's discount rate?

Market risk

Which one of the following risks is most important to a well-diversified investor in common stocks?

Market risk

17). Stock A has a beta of .5, and investors expect it to return 3%. Stock B has a beta of 1.5, and investors expect it to return 5%. Use the CAPM to calculate the market risk premium and the expected rate of return on the market. (Do not round intermediate calculations. Enter your answers as a whole percent.)

Market risk premium: 2% Expected market rate of return: 4%

17). Stock A has a beta of .8, and investors expect it to return 14%. Stock B has a beta of 1.2, and investors expect it to return 18%. Use the CAPM to calculate the market risk premium and the expected rate of return on the market. (Do not round intermediate calculations. Enter your answers as a whole percent.)

Market risk premium: 6% Expected market rate of return: 16%

Which one of the following statements is incorrect concerning stock indexes?

Most indexes include all of the publicly-traded common stocks

A project with higher than average risk offers an expected return of 14%. Which statement is correct if the company's opportunity cost of capital is 12% and the project's opportunity cost of capital is 15%?

Project NPV is negative; it should be rejected

9). The Costaguanan stock market provided a rate of return of 95%. The inflation rate in Costaguana during the year was 83%. In the United States, in contrast, the stock market return was only 14%, but the inflation rate was only 3%. Calculate the real rate of return for both the Costaguana and the United States stock markets. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Which country's stock market provided the higher real rate of return?

Real rate of return Costaguana 6.56% United States 10.68% United States

9). The Costaguanan stock market provided a rate of return of 95%. The inflation rate in Costaguana during the year was 80%. In the United States, in contrast, the stock market return was only 12%, but the inflation rate was only 2%. Calculate the real rate of return for both the Costaguana and the United States stock markets. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Which country's stock market provided the higher real rate of return?

Real rate of return Costaguana 8.33% United States 9.80% United States

Which one of the following changes offers the greatest chance of changing a project's NPV from negative to positive?

Reducing the risk level of the project

Which one of the following risks would be classified as a unique risk for an auto manufacturer?

Steel prices

12). A share of stock with a beta of .67 now sells for $42. Investors expect the stock to pay a year-end dividend of $3. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors' expectation of the price of the stock at the end of the year? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Stock price $ 42.650

12). A share of stock with a beta of .71 now sells for $46. Investors expect the stock to pay a year-end dividend of $3. The T-bill rate is 4%, and the market risk premium is 7%. If the stock is perceived to be fairly priced today, what must be investors' expectation of the price of the stock at the end of the year? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Stock price $47.130

In general, which stocks should be combined into a portfolio if the goal is the greatest reduction possible in overall portfolio risk?

Stocks with returns that are negatively correlated

Why is debt financing said to include a tax shield for the company?

Taxable income is reduced by the amount of the interest

What will be the effect of using the book value of debt in WACC decisions if interest rates have decreased substantially since a firm's long-term bonds were issued?

The debt-to-value ratio will be understated.

What is the typical relationship between the standard deviation of an individual common stock and the standard deviation of a diversified portfolio of common stocks?

The individual stock's standard deviation will be higher

Assuming positive returns on Treasury bills, what can you assume about an investor whose diversified portfolio of stocks yielded 25% when the market portfolio yielded 15%?

The portfolio beta is greater than 1.0

Which one of the following is most likely correct for a diversified stock portfolio that exhibits a higher standard deviation than the market index?

The portfolio contains fairly aggressive stocks

Based on your analysis, you believe that Alpha stock which has a beta of 1.32 is going to yield 14.05% this coming year. The market is expected to yield 11.4% and T-bills are yielding 3.8%. According to CAPM, which one of these statements is correct given this information?

The stock is currently underpriced.

Which one of the following statements is incorrect concerning the equity component of the WACC?

There is a tax shield on the dividends paid.

Which one of these is considered to be the safest investment?

U.S. Treasury bill

Which one of the following risk types can be most eliminated by adding stocks to a portfolio?

Unique risk

Why do stock market investors seem to ignore unique risks when calculating expected rates of return?

Unique risks are assumed to be diversified away.

8). Here is some information about Stokenchurch Inc.: Beta of common stock = 1.7 Treasury bill rate = 4% Market risk premium = 7.0% Yield to maturity on long-term debt = 7% Book value of equity = $390 million Market value of equity = $780 million Long-term debt outstanding = $780 million Corporate tax rate = 35% What is the company's WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

WACC: 10.23%

11). The total book value of WTC's equity is $8 million, and book value per share is $20. The stock has a market-to-book ratio of 1.5, and the cost of equity is 13%. The firm's bonds have a face value of $5 million and sell at a price of 110% of face value. The yield to maturity on the bonds is 10%, and the firm's tax rate is 40%. What is the company's WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

WACC: 10.80%

11). The total book value of WTC's equity is $10 million, and book value per share is $20. The stock has a market-to-book ratio of 1.5, and the cost of equity is 15%. The firm's bonds have a face value of $5 million and sell at a price of 110% of face value. The yield to maturity on the bonds is 9%, and the firm's tax rate is 40%. What is the company's WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

WACC: 12.42%

9). Reactive Industries has the following capital structure. Its corporate tax rate is 40%. Security Market Value Required Rate of Return Debt $20 million 4% Preferred stock 10 million 6 Common stock 50 million 10 What is its WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

WACC: 7.60%

8). Here is some information about Stokenchurch Inc.: Beta of common stock = 1.2 Treasury bill rate = 4% Market risk premium = 7.5% Yield to maturity on long-term debt = 6% Book value of equity = $440 million Market value of equity = $880 million Long-term debt outstanding = $880 million Corporate tax rate = 35% What is the company's WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

WACC: 8.45%

9). Reactive Industries has the following capital structure. Its corporate tax rate is 35%. Security Market Value Required Rate of Return Debt $20 million 6% Preferred stock 10 million 8 Common stock 50 million 12 What is its WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

WACC: 9.475%

The project cost of capital is:

not necessarily related to the company cost of capital

Which one of the following would you expect to represent the broadest-based index of U.S. stocks?

Wilshire 5000

A proposed project has a positive NPV when evaluated at the company cost of capital. If the firm employs debt in its capital structure, will the project remain acceptable after evaluation with the WACC?

Yes, using the WACC will increase the NPV

In practice, the market portfolio is often represented by:

a diversified stock market index.

11). Consider the following two scenarios for the economy and the returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D. Rate of Return Scenario Market Aggressive Stock A Defensive Stock D Bust −7% −10% −5% Boom 19 25 15 a. Find the beta of each stock. (Round your answers to 2 decimal places.) b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock. c. If the T-bill rate is 4%, what does the CAPM say about the fair expected rate of return on the two stocks? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)?

a. Beta: Stock A: 1.35 Stock D: .77 b. Expected return: Market portfolio: 6.00 Stock A: 7.50 Stock D: 5.00 c. Expected rate of return: Stock A: 6.69% Stock D: 5.54% d. better buy: "Stock A"

10). The common stock of Buildwell Conservation & Construction Inc. (BCCI) has a beta of .9. The Treasury bill rate is 4%, and the market risk premium is estimated at 8%. BCCI's capital structure is 30% debt, paying an interest rate of 5%, and 70% equity. The debt sells at par. Buildwell pays tax at 40%. a. What is BCCI's cost of equity capital? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) b. What is its WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) c. If BCCI is presented with a project with an internal rate of return of 12%, should it accept the project if it has the same level of risk as the current firm?

a. Cost of equity capital: 11.2% b. WACC: 8.74% c. Yes

10). The common stock of Buildwell Conservation & Construction Inc. (BCCI) has a beta of .9. The Treasury bill rate is 4%, and the market risk premium is estimated at 8%. BCCI's capital structure is 22% debt, paying an interest rate of 5%, and 78% equity. The debt sells at par. Buildwell pays tax at 40%. a. What is BCCI's cost of equity capital? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.) b. What is its WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) c. If BCCI is presented with a project with an internal rate of return of 12%, should it accept the project if it has the same level of risk as the current firm?

a. Cost of equity capital: 11.2% b. WACC: 9.40% c. Yes

20). A stock will provide a rate of return of either −31% or 34%. a. If both possibilities are equally likely, calculate the stock's expected return and standard deviation. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.) b. If Treasury bills yield 1.5% and investors believe that the stock offers a satisfactory expected return, what must the market risk of the stock be? (Enter your answer as a whole percent.)

a. Expected return 1.5% Standard deviation 32.5% b. Market risk 0%

20). A stock will provide a rate of return of either −18% or 26%. a. If both possibilities are equally likely, calculate the stock's expected return and standard deviation. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.) b. If Treasury bills yield 4% and investors believe that the stock offers a satisfactory expected return, what must the market risk of the stock be? (Enter your answer as a whole percent.)

a. Expected return 4% Standard deviation 22% b. Market risk 0%

23). We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, −.4. a. If the interest rate on Treasury bills is 6% and the expected return on the market portfolio is 16%, what is the expected return on the shares of the law firm according to the CAPM? (Enter your answer as a whole percent.) b. Suppose you invested 60% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio? (Round your answer to 2 decimal places.)

a. Expected return: 2% b. Portfolio beta: 0.44

23). We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, −.2. a. If the interest rate on Treasury bills is 5% and the expected return on the market portfolio is 20%, what is the expected return on the shares of the law firm according to the CAPM? (Enter your answer as a whole percent.) b. Suppose you invested 70% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio? (Round your answer to 2 decimal places.)

a. Expected return: 2% b. Portfolio beta: 0.64

Which firms of each pair below would you expect to have greater market risk?

a. General Steel b. Club Med

7). A stock is selling today for $40 per share. At the end of the year, it pays a dividend of $2 per share and sells for $44. a. What is the total rate of return on the stock? (Enter your answer as a whole percent.) b. What are the dividend yield and percentage capital gain? (Enter your answers as a whole percent.) c. Now suppose the year-end stock price after the dividend is paid is $36. What are the dividend yield and percentage capital gain in this case? (Negative amounts should be indicated by a minus sign. Enter your answers as a whole percent.) d. Is there any change in the dividend yield calculated in parts (b) and (c)? The dividend yield is __________ correct; it is based on the _____________.

a. Rate of return 15% b. Dividend yield 5% Capital gains yield 10% c. Dividend yield 5% Capital gains yield -10% d. "unaffected; initial price"

10). The risk-free rate is 7% and the expected rate of return on the market portfolio is 12%. a. Calculate the required rate of return on a security with a beta of 1.96. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) b. If the security is expected to return 15%, is it overpriced or underpriced?

a. Required return 16.80% b. Overpriced

13). A share of stock with a beta of .78 now sells for $58. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 5%, and the market risk premium is 8%. a. Suppose investors believe the stock will sell for $60 at year-end. Is the stock a good or bad buy? What will investors do? b. At what price will the stock reach an "equilibrium" at which it is perceived as fairly priced today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

a. The stock is a "bad" buy and the investors "will not invest" b. Stock price $ 55.74

13). A share of stock with a beta of .71 now sells for $61. Investors expect the stock to pay a year-end dividend of $3. The T-bill rate is 4%, and the market risk premium is 7%. a. Suppose investors believe the stock will sell for $63 at year-end. Is the stock a good or bad buy? What will investors do? b. At what price will the stock reach an "equilibrium" at which it is perceived as fairly priced today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

a. The stock is a "bad" buy and the investors "will not invest" b. Stock price $ 60.41

9). You are considering acquiring a firm that you believe can generate expected cash flows of $14,000 a year forever. However, you recognize that those cash flows are uncertain. a. Suppose you believe that the beta of the firm is .8. How much is the firm worth if the risk-free rate is 4% and the expected rate of return on the market portfolio is 9%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. By how much will you overvalue the firm if its beta is actually 1.1? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

a. Value of the firm $ $ 175,000.00 b. Overvaluation $ 27,631.58

Consider the following scenario analysis: Rate of Return Scenario Probability Stocks Bonds Recession .30 −8 % 21 % Normal economy .50 22 9 Boom .20 32 9 a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?

a. Yes b. Expected Rate Standard of Return Deviation Stocks: 15.0% 15.5% Bonds: 12.6% 5.5 %

14). Consider the following scenario analysis: Rate of Return Scenario Probability Stocks Bonds Recession .20 −5 % 14 % Normal economy .60 15 8 Boom .20 25 4 a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms? b. Calculate the expected rate of return and standard deviation for each investment. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.)

a. Yes b. Expected Rate Standard of Return Deviation Stocks: 13.0% 9.8% Bonds: 8.4% 3.2 %

Which one of the following adjustment techniques would be preferred to account for additional project risk?

adjust expected cash flows downward

If a firm earns the WACC as an average return on its average-risk assets, then:

all investors will earn their minimum required rate of return

In theory, the "market portfolio" should contain:

all risky assets

A stock with a beta greater than 1.0 would be termed:

an aggressive stock, expected to increase more than the market increases

The Dow Jones Industrial Average is:

an index of 30 major industrial stocks

If the plotting of a portfolio's returns against returns on the market index produces a tight pattern, then the portfolio:

appears to be well diversified

Although Standard and Poor's Composite Index contains a limited number of U.S. publicly traded stocks, the Index represents:

approximately 75% of US stocks traded in market value

When the annual rate of return on U.S. Treasury bills is historically high, investors expect the risk premium on the stock market to be:

approximately normal

The benefits of portfolio diversification are highest when the individual securities within the portfolio have returns that:

are less than perfectly correlated with the rest of the portfolio

One common reason for reporting standard deviations rather than variances is that standard deviations:

are stated in understandable units

By reviewing the historical performance of the stock market, we can:

ascertain that losses will occur but cannot predict when or how large

If the company cost of capital is 20% and a proposed project's cost of capital is 15%, then discounting the projects' cash flows at 20% would:

be incorrect and could cause the projects to be erroneously rejected

The variance of a stock's returns can be calculated as the:

average value of squared deviations from the mean.

The correct opportunity cost for a project is determined to be 15% and the project is expected to generate $1 million in cash flows at the end of the next 4 years after an initial outlay of $3 million. Based on this information, the project would plot:

below the security market line

The line plotted to fit observations of a stock's returns versus the market's returns determines the:

beta of the stock

Stock returns can be explained by the stock's _________ and the stock's __________.

beta; unique risk

Capital structure decisions refer to the:

blend of equity and debt used by the firm

Historically, periods of market declines:

can e sudden and severe

If a stock's returns are volatile, then the stock:

can still be considered a negative risk asset

The fact that historical returns on Treasury bills are less volatile than common stock returns indicates that:

common stocks should offer a higher return than Treasury bills

As debt is added to the capital structure, the:

cost of debt can be expected to rise

Industries that generally perform well when other industries are performing well are referred to as:

cyclical industries

When high growth is expected in the economy, an investor should receive higher returns from:

cyclical investments

Changing the capital structure by adding debt will not:

decrease debt holder risk

Increasing debt financing will do all of the following except:

decrease the firm's cost of common equity

Which one of the following changes would tend to increase the WACC for a traditional firm?

decrease the proportion of debt financing

Assume a tax-paying firm is currently financed with 50% debt and 50% equity. The after-tax cost of debt is 6% and the cost of equity is 12%. If the firm issues some 8% preferred stock at par, then the firm's WACC will:

decreases

Investment risk can best be described as the:

dispersion of possible returns

Risk factors that are expected to affect only a specific firm are referred to as:

diversifiable risk

Averaging the deviations from the mean for a portfolio of securities will:

equal zero

The average of the beta values for all individual stocks is:

exactly 1.0; these stocks represent the market

The company cost of capital is the return that is expected on a portfolio of the company's:

existing securities

A firm is considering expanding its current operations and has determined the internal rate of return on that expansion is 12.2%. The firm's WACC is 11.8%. Given this, you know the:

expansion should be undertaken as it has a positive net present value

A stock's risk premium is equal to the:

expected market risk premium times beta

Although unique risk is present in differing amounts, individual stocks are:

exposed to differing amounts of market risk also

Although several stock indexes are available to inform investors of market changes, the Dow Jones Industrial Average:

is the best-known of the US market indexes

What happens to the expected portfolio return if the portfolio beta increases from 1.0 to 1.5, the risk-free rate decreases from 5 to 4%, and the market risk premium increases from 8 to 9%?

it increases from 13 to 17.5%

What will happen to a stock that offers a lower return than predicted by the CAPM?

its market price will decrease causing its yield to increase

The incremental risk to a portfolio from adding another stock:

may be either positive or negative

The company cost of capital:

measures that investors require from the company

The actual real rate of return on an investment will be positive as long as the:

nominal return exceeds the inflation rate

If a security plots below the security market line, it is:

offering too little return to justify its risk.

A firm is said to be countercyclical if its returns:

outperform when most stocks do poorly

When the overall market is up by 10%, investors with portfolios of defensive stocks will probably have:

positive portfolio returns less than 10%

The appropriate opportunity cost of capital is the return that investors give up on alternative investments that:

possess the same level of risk

A proposed investment must earn at least as much as the ______ if it is to be deemed acceptable.

project cost of capital

The minimum acceptable expected rate of return on a project of a specific risk is the:

project cost of capital

If changing discount rates from the company cost of capital to the project cost of capital changes NPV from negative to positive, then the project should use the:

project cost of capital and be accepted

The basic tenet of the CAPM is that a stock's expected risk premium should be:

proportionate to the stock's beta

Based on the period 1926-2013, value stocks have:

provided a higher long-run return than growth stocks

One of the easiest methods of diversifying away firm-specific risks is to:

purchase the shares of a mutual fund

The major benefit of diversification is the:

reduction in the portfolio's total risk

An implicit cost of increasing the proportion of debt in a firm's capital structure is that:

shareholders will demand a higher rate of return

If the line measuring a stock's historic returns against the market's historic returns has a slope greater than 1.0, then the:

stock has a beta exceeding 1.0.

The slope of the regression line that exhibits the past relationship between a stock's returns and the market's returns is the:

stock's beta

An increase in which one of the following is most apt to decrease the WACC of a firm that has both debt and equity in its capital structure?

tax rate

"Dow up 14. Story at 6:00." This means that:

the Dow index increased by 14 points in today's trading

For a company that pays no corporate taxes, its WACC will be equal to:

the expected return on it assets

A maturity premium is offered on long-term Treasury bonds due to:

the risk of changing interest rates

An estimation of the opportunity cost of capital for projects that have an "average" level of risk is the rate of return on:

the market portfolio

The slope of the security market line equals:

the market risk premium

For purposes of computing the WACC, if the book value of equity exceeds the market value of equity, then:

the market value of equity should be used

The company cost of capital may be an inappropriate discount rate for a capital budgeting proposal if:

the proposal has a different degree of risk

If an investor's portfolio is allocated 75% to the market portfolio and 25% to Treasury bills, then the investor should expect to receive:

the risk-free rate plus 75% of the expected market risk permium

Macro events only are reflected in the performance of the market portfolio because:

the unique risks have been diversified away.

Which one of the following statements best explains the fact that cyclical firms tend to have high betas?

their earnings are not stable

The idea that investors in a common stock may expect a lower total return if they purchase a stock with limited price volatility rather than one with high price volatility suggests that:

there is a relationship between risk and return

The return on a security includes premium for:

time and value of money and market risk

A considerable scattering in the plot of points representing the historic returns of a stock versus the returns on the market reflects the:

unique risk of the stock

A stock's beta measures the

variability in the stock's returns compared to that of the market portfolio.

The variance of an investment's returns is a measure of the:

volatility of the rates of return

To calculate the present value of a business, the firm's free cash flows should be discounted at the firm's:

weighted-average cost of capital

The higher the standard deviation of a stock's annual returns, the:

wider the dispersion of those returns over time