HW 5

Unsystematic

A news flash just appeared that caused about a dozen stocks to suddenly increase in value by 12 percent. What type of risk does this news flash best represent?

0.815

A portfolio has average return of 13.2 percent and standard deviation of returns of 18.9 percent. Assuming that the portfolioi's returns are normally distributed, what is the probability that the portfolio's return in any given year is between -24.6 percent and 32.1 percent? (Assume that 68 percent, 95 percent, and 99 percent of the returns in any given year fall within one, two, and three standard deviations, respectively, of the mean.)

0.005

A portfolio has expected return of 13.2 percent and standard deviation of 18.9 percent. Assuming that the returns of the portfolio are normally distributed, what is the probability that, in any given year, the return of the portfolio will be less than -43.5 percent. (Assume that 68 percent, 95 percent, and 99 percent of the returns in any given year fall within one, two, and three standard deviations, respectively, of the mean.)

7.81 percent

A portfolio is invested 45 percent each in Stock A and Stock B and 10 percent in Stock C. What is the expected risk premium on the portfolio if the expected T-bill rate is 4.1 percent?

1.59 Find the present value of the project's cash flows: C01 = 500,000; F01 = 5; NPV. I = 12; CPT. $1,802,388.10 Since the NPV of the project is $672,000 and NPV = PV (Project's Cash Flows) - Initial Investment Initial Investment = 1,802,388.10 - 672000 = $1,130,388.10 Profitability Index = 1,802,388.10/1,130,388.10 = 1.59

A project has net present value of $672,000 and generates cash flows of $500,000 a year for the next five years. If the project's required return is 12 percent, calculate the project's profitability index.

$199,178

A project requires an initial investment of $2,640,000. The projects generates cash flows of $750,000 in year 1, $800,000 in year 2, $800,000 in year 3, $800,000 in year 4 and $800,000 in year 5. If the required rate of return for the project is 12 percent, calculate the net present value (NPV) of the project.

3.3 years; 4.2 years Payback Period = 3 + (973000 - 850000)/400000 = 3.3075 years Discounted Payback Period = 4 + (973000 - 930113.8)/226970.7 = 4.18895 years.

A project requires an initial investment of $973,000. The projects generates cash flows of $250,000 in year 1, $300,000 in year 2, $300,000 in year 3, $400,000 in year 4 and $400,000 in year 5. If the required rate of return for the project is 12 percent, the payback period is ____________ and the discounted payback period is _______________.

$71,245.65 NPV = 234500/1.1354 + 234500/1.1355 + 312000/1.1356 - 340500 = $71,245.65 Alternatively, use the cash flow keys: CF0 = -340,500; C01 = 0; F01 = 3; C02 = 234500; F02 = 2; C03 = 312000; F03 = 1; NPV. I = 13.5; CPT. $71,245.65

A project requires an investment of $3,874,900 today. The project is expected to generate cash flows of $1,000,000 in year 1, $1,500,000 in year 2, $1,500,000 in year 3, and $2,000,000 in year 4. Calculate the internal rate of return of the project.

17.93 percent

A project requires an investment of $3,874,900 today. The project is expected to generate cash flows of $1,000,000 in year 1, $1,500,000 in year 2, $1,500,000 in year 3, and $2,000,000 in year 4. Calculate the internal rate of return of the project.

−16.2 percent to 28.2 percent

A stock had returns of 14 percent, 13 percent, −10 percent, and 7 percent for the past four years. What is the 95 percent probability range of returns for this stock?

60%

A stock has a beta of 1.50 and an expected return of 15.4 percent. A risk-free asset currently earns 3.7 percent. The beta of a portfolio comprised of these two assets is .90. What percentage of the portfolio is invested in the stock?

less than 0.005

A stock has an expected rate of return of 9.8 percent and a standard deviation of 15.4 percent. Which one of the following best describes the probability that this stock will lose at least half of its value in any one given year? (Assume that 68 percent, 95 percent, and 99 percent of the returns in any given year fall within one, two, and three standard deviations, respectively, of the mean.)

a higher return than expected for the level of risk assumed.

A stock with an actual return that lies above the security market line has:

strong form efficient.

Inside information has the least value when financial markets are:

5.63% Geometric average return = {1.1 x 0.92 x 1.23 x 1}1/4 - 1 = 5.63%

Over the past four years a stock had returns of 10%, -8%, 23%, and 0%, respectively. What was the geometric average return on this stock?

Since both projects have negative NPV values, we reject both of them.

Project A requires an initial investment (today) of $560,000 and generates cash flows of $170,000 a year for each of the next four years. Project B requires an investment of $710,000 today and generates cash flows of $220,000 in year 1, $220,000 in year 2, $250,000 in year 3, and $250,000 in year 4. The two projects are mutually exclusive and the required return for each project is 13 percent.

10.96 percent Capital gains Yield = (81 - 73)/73 = 8/73 = 0.1096 = 10.96 percent.

Suppose a stock had an initial price of $73 per share, paid a dividend of $1.42 per share during the year, and had an ending share price of $81. What was the capital gains yield?

10.66% Average return = (.117 + .088 + .167 − .079)/4 Average return = .07325 or 7.325% σ = {[1/(4 − 1)] [(.117 − .07325)2 + (.088 − .07325)2 + (.167 − .07325)2 + (−.079 − .07325)2]}.5 σ = .1066, or 10.66%

The common stock of Air Express had annual returns of 11.7 percent, 8.8 percent, 16.7 percent, and −7.9 percent over the last four years, respectively. What is the standard deviation of these returns?

The actual expected stock return indicates the stock is currently overpriced. E(r)CAPM = .033 + 1.18(.1220 − .033) E(r)CAPM = .1380, or 13.80 Investors require an expected return of 13.80% on this stock given its beta. The stock is overpriced because its actual expected return is less than the CAPM required expected return.

The common stock of Alpha Manufacturers has a beta of 1.18 and an actual expected return of 13.33 percent. The risk-free rate of return is 3.3 percent and the market rate of return is 12.20 percent. Which one of the following statements is true given this information?

1.66 E(r) = .162 = .036 + β(.112 − .036). 0.126 = 0.076β β = 0.126/0.076 = 1.66

The common stock of Jensen Shipping has an expected return of 16.2 percent. The return on the market is 11.2 percent, the inflation rate is 3.1 percent, and the risk-free rate of return is 3.6 percent. What is the beta of this stock?

5.25% E(r) = .05(.17) + .80(.07) + .15(−.08) E(r) = .0525, or 5.25%

The common stock of Manchester & Moore is expected to earn 17 percent in a recession, 7 percent in a normal economy, and lose 8 percent in a booming economy. The probability of a boom is 15 percent while the probability of a recession is 5 percent. What is the expected rate of return on this stock?

discount rate applied to the project is decreased.

The discounted payback period of a project will decrease whenever the

will provide the same accept/reject decision as NPV when cash flows are conventional and projects are independent.

The internal rate of return

Treasury bills

The rate of return on which type of security is normally used as the risk-free rate of return?

5.40 Capital Gains Yield = 0.063 - 117/(540 x 24) = 0.063 - 0.0090 = 0.054 = 5.40 percent. Total Percentage Return = Dividend Yield + Capital Gains Yield

Today, you sold 540 shares of stock and realized a total return of 6.3 percent. You purchased the shares one year ago at a price of $24 a share and have received a total of $117 in dividends. What is your capital gains yield on this investment?

standard deviation; beta

Total risk is measured by ________ and systematic risk is measured by ________.

0 percent Treasury bills are risk free assets so the risk premium on a Treasury bill is zero.

What is the amount of the risk premium on a U.S. Treasury bill if the risk-free rate is 3.1 percent, the inflation rate is 2.6 percent, and the market rate of return is 7.4 percent?

1.20

What is the beta of the following portfolio?

8.42 percent; 5.69 percent E(R) = .06(−.06) + .74(.07) + .20(.18) E(R)= .0842, or 8.42% σ = [.06(−.06 − .0842)^2 + .74(.07 − .0842)^2 + .20(.18 − .0842)2]^.5 σ = .0569, or 5.69%

What is the expected return and standard deviation for the following stock?

10.96 percent E(RP)Boom = (.19 + .13 + .07)/3 E(RP)Boom = .13, or 13% E(RP)Normal = (.15 + .05 + .13)/3 E(RP)Normal = .11, or 11% E(RP)Bust = (−.29 − .14 + .22)/3 E(RP)Bust = −.07, or -7% E(RP)Boom = .25(.13) + .72(.11) + .03(−.07) E(RP)Boom = .1096 or 10.96%

What is the expected return of an equally weighted portfolio comprised of the following three stocks?

13.42% Portfolio value = 200($18.60) + 400($12.85) + 300($43.90) Portfolio value = $3,720 + 5,140 + 13,170 Portfolio value = $22,030 E(r) = ($3,720/$22,030)(.11) + ($5,140/$22,030)(.06) + ($13,170/$22,030)(.17) E(r)= .1342, or 13.42%

What is the expected return on this portfolio?

.00091 E(r)Boom = .40(.22) + .60(.18) = .196 E(r)Normal = .40(.15) + .60(.14) = .144 E(r)Bust = .40(-.26) +.60(.09) = -.05 E(r)Portfolio = .06(.196) + .92(.144) + .02(−.050) E(r)Portfolio =.14324 σ2Portfolio = .06(.196 − .14324)2 + .92(.144 - .14324)2 + .02(−.050 − .14324)2 σ2Portfolio = .00091

What is the variance of the returns on a portfolio that is invested 40 percent in Stock S and 60 percent in Stock T?

weak

Which form of market efficiency would most likely offer the greatest profit potential to an outstanding professional stock analyst?

I and IV only

Which of the following are examples of diversifiable risk? I. An earthquake damages an entire town II. The federal government imposes a $100 fee on all business entities III. Employment taxes increase nationally IV. All toymakers are required to improve their safety standards

I, II and III only

Which of the following statements are correct concerning diversifiable risks? I. Diversifiable risks can be essentially eliminated by investing in 30 unrelated securities. II. There is no reward for accepting diversifiable risks. III. Diversifiable risks are generally associated with an individual firm or industry. IV. Beta measures diversifiable risk.

Investors panic causing security prices around the globe to fall precipitously

Which one of the following is an example of systematic risk?

B

Which one of the following stocks is correctly priced if the risk-free rate of return is 2.84 percent and the market rate of return is 10.63 percent?

$375,000 E(Rp) = .13 = .18x + .10(1 − X) x = .375, or 37.5 percent Investment in Stock X = .375($1,000,000) Investment in Stock X = $375,000

You have $1,000,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 18 percent and Stock Y with an expected return of 10 percent. Your goal is to create a portfolio with an expected return of 13 percent. All money must be invested. How much will you invest in Stock X?

2.78% Dividend yield = ($1,256/850)/$53.15 or Dividend Yield = 1256/(850x53.15) = 0.0278 Dividend yield = .0278, or 2.78%

You own 850 shares of Western Feed Mills stock valued at $53.15 per share. What is the dividend yield if your total annual dividend income is $1,256?

7.5% Arithmetic average return = (10 + 13 + 19 + -4 + 15)/5 = 10.6 percent Risk premium = 10.6% - 3.1% = 7.5%

You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 10 percent, 13 percent, 19 percent, −4 percent, and 15 percent. Suppose the T-bill rate was 3.1 percent. Based on this information, what was the risk premium?