A bicycle shop plans to offer 2 specially priced children’s models at a sidewalk sale. The basic model will return a profit of $120 and the deluxe model $150. Past experience indicates that sales of the basic model will have a mean of 5.4 bikes with a standard deviation of 1.2, and sales of the deluxe model will have a mean of 3.2 bikes with a standard deviation of 0.8 bikes. The cost of setting up for the sidewalk sale is $200.
Define the random variables and use them to express the bicycle shop’s net profit.
What’s the mean of the net profit?
What’s the standard deviation of the net profit?
Do you need to make any assumptions in calculating the mean? How about the standard deviation?
In: Statistics and Probability
In 2007, baseball players made on average $1.8 million. Using these randomly sample 12 players (All in Millions of Dollars) from 2011 , Is there evidence that salaries are now different? Assume a 5% significance level
$2.7, 2.9, 1.5, 2.2, 2.5, 2.0, 1.7, 2.9, 2.8, 2.6, 0.8, 2.7
Provide the following in your final analyses: the distribution to be used and why; all assumptions required for this study and if each assumption is met or not (if an assumption is not met, explain what you would do to correct the assumption violation); null and alternate hypotheses; the test statistic (rounded to four decimal places); the p-value (rounded to 4 decimal places); the decision to reject the hypothesis or not; and a conclusion in context of the study.
In: Statistics and Probability
ABC and XYZ are two identical firms except for their capital structure. The share price for both of firms is $10. ABC is an all equity firm. XYZ has D/E of 0.8. Investor A bought 100 shares of XYZ with his own money since he believes the levered firm will provide better return. If you decide to use homemade leverage to show him that leverage doesn’t matter, what would be your trading strategy? Please be specific (i.e. how much money of your own will be used, how much money you will borrow, and which firm’s share you are going to buy, etc.) Assume all assumptions hold for homemade leverage.
In: Finance
In: Chemistry
In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In one hour the average cockroach running at 0.08km/hr consumed 0.8 mL of O2 at 1 atm pressure and 24 ?C per gram of insect weight.
a)
How many moles of O2 would be consumed in 1 hr by a 5.4?g cockroach moving at this speed?
b)
This same cockroach is caught by a child and placed in a 1-qt fruit jar with a tight lid. Assuming the same level of continuous activity as in the research, will the cockroach consume more than 20% of the available O2 in a 48-hr period? (Air is 21 mol percent O2)
In: Chemistry
Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 5%, and the market’s average return was 14%. Performance is measured using an index model regression on excess returns.
| Stock A | Stock B | ||||||||||
| Index model regression estimates | 1% + 1.2(rM − rf) | 2% + 0.8(rM − rf) | |||||||||
| R-square | 0.611 | 0.454 | |||||||||
| Residual standard deviation, σ(e) | 10.9% | 19.7% | |||||||||
| Standard deviation of excess returns | 22.2% | 26.1% | |||||||||
a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.)
Stock A & Stock B
i.Alpha
ii.Information ratio
iii.Sharpe ratio
iv.Treynor measure
In: Finance
Company Q’s current return on equity (ROE) is 14%. It pays out
one half of earnings as cash dividends (payout ratio = 0.5).
Current book value per share is $50. Book value per share will grow
as Q reinvests earnings.
Assume that the ROE and payout ratio stay constant for the next
four years. After that, competition forces ROE down to 11.5% and
the payout ratio increases to 0.8. The cost of capital is
11.5%.
a. What are Q’s EPS and dividends in years 1, 2,
3, 4, and 5? (Do not round intermediate calculations. Round
your answers to 2 decimal places.)
b. What is Q’s stock worth per share?
In: Finance
In: Finance
Given an ideal steam regenerative cycle in which steam enters the turbine at 3.0 MPa, 400 oC, and exhausts to the condenser at 10 kPa. Steam is extracted from the turbine at 0.8 MPa for an open feedwater heater. The feedwater leaves the heater as saturated liquid. The net power is 45 MW. Assume any missing data. Draw a neat sketch for the cycle flow diagram showing all states
. Draw the T-s diagram.
Calculate the thermal efficiency of the cycle.
Calculate the steam mass flow rate (in kg/s).
Calculate the total power to the two pumps.
Calculate the mass flow rate of the cooling water in the condenser if its temperature rise is 9 oC.
In: Mechanical Engineering
Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 8%, and the market’s average return was 12%. Performance is measured using an index model regression on excess returns.
| Stock A | Stock B | ||||||||||
| Index model regression estimates | 1% + 1.2(rM − rf) | 2% + 0.8(rM − rf) | |||||||||
| R-square | 0.653 | 0.475 | |||||||||
| Residual standard deviation, σ(e) | 11.6% | 20.4% | |||||||||
| Standard deviation of excess returns | 22.9% | 27.5% | |||||||||
a. Calculate the following statistics for each stock: (Round your answers to 4 decimal places.)
Sharpe ratio: Stock A = Stock B =
Treynor Measure: Stock A = Stock B =
In: Finance