Mark Washington, CFA, is an analyst with BIC. One year ago, BIC analysts predicted that the U.S. equity market would most likely experience a slight downturn and suggested delta-hedging the BIC portfolio. As predicted, the U.S. equity markets did indeed experience a downturn of approximately 4% over a 12-month period. However, portfolio performance for BIC was disappointing, lagging its peer group by nearly 10%. Washington has been told to review the options strategy to determine why the hedged portfolio did not perform as expected. Washington considers a put option that has a delta of −.65. If the price of the underlying asset decreases by $6, then what is the best estimate of the change in option price?

Norris Company implemented a quality improvement program and tracked the following for the 5 years:

$$\begin{array}{lccc} & \text { Quality Costs } & \text { Actual Sales } & \text { Costs as a Percentage of Sales } \\ \hline 20 \times 1 & \$ 880,000 & \$ 4,000,000 & 22.00 \% \\ 20 \times 2 & 840,000 & 4,200,000 & 20.00 \\ 20 \times 3 & 765,000 & 4,500,000 & 17.00 \\ 20 \times 4 & 700,000 & 5,000,000 & 14.00 \\ 20 \times 5 & 594,000 & 5,400,000 & 11.00 \end{array}$$

By cost category as a percentage of sales for the same period of time:

$$\begin{array}{lcccc} & \text { Prevention } & \text { Appraisal } & \text { Internal Failure } & \text { External Failure } \\ \hline 20 \mathrm{X} 1 & 1.50 \% & 2.50 \% & 6.50 \% & 11.50 \% \\ 20 \mathrm{X} 2 & 2.75 & 3.25 & 4.00 & 10.00 \\ 20 \mathrm{X} 3 & 3.00 & 5.00 & 2.75 & 6.25 \\ 20 \mathrm{X} 4 & 3.50 & 3.50 & 2.00 & 5.00 \\ 20 \mathrm{X} 5 & 3.75 & 2.25 & 1.50 & 3.50 \end{array}$$

1. Prepare a bar graph that reveals the trend in quality cost as a percentage of sales (time on the horizontal axis and percentages on the vertical). Comment on the message of the graph.

2. Prepare a bar graph for each cost category as a percentage of sales. What does this graph tell you?

A square cross-section duct $(0.5 \mathrm{~m} \times 0.5 \mathrm{~m} \times 30 \mathrm{~m})$ is used to convey air $\left(\rho=1.1 \mathrm{~kg} / \mathrm{m}^{3}\right)$ into a clean room in an electronics manufacturing facility. The air is supplied by a fan and passes through a filter installed in the duct. The duct friction factor is $f=0.03$, the filter has a loss coefficient of $K=12$, and the clean room is kept at a positive gage pressure of $50 \mathrm{~Pa}$. The fan performance is given by $\Delta p=1020-25 Q-30 Q^{2}$, where $\Delta p$ $\mathrm{(Pa)}$ is the pressure generated by the fan at flow rate $Q\left(\mathrm{~m}^{3} / \mathrm{s}\right)$. Find the flow rate delivered to the room.

Is the number of years of competitive running experience related to a runner's distance running performance? The data on nine runners, obtained from the study by Scott Powers and colleagues, are shown in the table:

Runner: 1, 2, 3, 4, 5, 6, 7, 8, 9 Years of Competitive Running: 9, 13, 5, 7, 12, 6, 4, 5, 3 10-Kilometer Finish Time (minutes): 33.15, 33.33, 33.50, 33.55, 33.73, 33.86, 33.90, 34.15, 34.90

a. Calculate the rank correlation coefficient between years of competitive running x and a runner's finish time in the 10-kilometer race. b. Do the data provide evidence to indicate a significant rank correlation between y and x? Test using $\alpha$=.05.

In order to study the relationship between the amount of sleep a student gets and his or her school performance, a researcher collected data from 120 students. The two-way frequency table shows the number of students who passed and failed an exam and the number of students who got more or less than 6 hours of sleep the night before.

To the nearest percent, give the probability that a student who failed the exam got less than 6 hours of sleep.

Plot the magnitude of the resultant R of the three forces as a function of $\theta$ for $0 \leq \theta \leq 360^{\circ}$ and determine the value of $\theta$ which makes the magnitude R of the resultant of the three loads (a) a maximum and (b) a minimum. Record the magnitude of the resultant in each case. Use values of $\phi=75^{\circ} \text { and } \psi=20^{\circ}$.

The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions (“Experimental Measurement of the Stopping Performance of a Tractor-Semitrailer from Multiple Speeds,” NHTSA, DOT HS 811 488, June 2011):

$$\begin{matrix} \text{32.1} & \text{30.6} & \text{31.4} & \text{30.4} & \text{31.0} & \text{31.9}\\ \end{matrix}$$

The cited report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using $\alpha=.01$.

Refer to this chapter's opening feature about Apple. Assume that the owners decide to open a new company with an innovative mobile app devoted to microblogging for accountants and those learning accounting. This new company will be called AccountApp.

Required

1. AccountApp obtains a $500,000 loan and the two owners contribute$250,000 in total from their ownsavings in exchange for ownership of the new company.

a. What is the new company's total amount of liabilities plus equity?

b. What is the new company's total amount of assets?

2. If the new company earns $80,250 in net income in the first year of operation, compute its return on assets (assume average assets equal$750,000). Assess its performance if competitors average a 10% return.

Table of yearly discharge (cubic kilometers of water) of the Mississippi river gives the volume of water discharged by the Mississippi River into th Gulf of Mexico for each year from 1954 to 2001. The units are cubic kilometers of water-the Mississippi is a big river.

(a) Make a graph of the distribution of water volume. Describe the overall shape of the distribution and any outliers.

(b) Based on the shape of the distribution, do you expect the mean to be close to the median, clearly less than the median, or clearly greater than the median? Why? Find the mean and the median to check your answer.

$$\begin{array}{cc|cc|cc} \text { YEAR } & \text { DISCHARGE } & \text { YEAR } & \text { DISCHARGE } & \text { YEAR } & \text { DISCHARGE } \\ \hline 1954 & 290 & 1970 & 540 & 1986 & 600 \\ \hline 1955 & 420 & 1971 & 480 & 1987 & 450 \\ \hline 1956 & 390 & 1972 & 600 & 1988 & 420 \\ \hline 1957 & 610 & 1973 & 880 & 1989 & 630 \\ \hline 1958 & 550 & 1974 & 710 & 1990 & 680 \\ \hline 1959 & 440 & 1975 & 670 & 1991 & 700 \\ \hline 1960 & 470 & 1976 & 420 & 1992 & 510 \\ \hline 1961 & 600 & 1977 & 430 & 1993 & 900 \\ \hline 1962 & 550 & 1978 & 560 & 1994 & 640 \\ \hline 1963 & 360 & 1979 & 800 & 1995 & 590 \\ \hline 1964 & 390 & 1980 & 500 & 1996 & 670 \\ \hline 1965 & 500 & 1981 & 420 & 1997 & 680 \\ \hline 1966 & 410 & 1982 & 640 & 1998 & 690 \\ \hline 1967 & 460 & 1983 & 770 & 1999 & 580 \\ \hline 1968 & 510 & 1984 & 710 & 2000 & 390 \\ \hline 1969 & 560 & 1985 & 680 & 2001 & 580 \\ \hline \end{array}$$

(c) Based on the shape of the distribution, does it seem reasonable to use $\bar{x}$ and s to describe the center and variability of this distribution? Why? Find $\bar{x}$ and s if you think they are a good choice. Otherwise, find the five-number summary.

Assume the role of assistant buyer for a costume jewelry store. You are ordering a shipment of earrings in five styles from a supplier. The cost of the earrings is $\$ 1.50$ per pair. You know that if you set too low a selling price the earrings will not sell well. The buyer (judge) has asked you to prepare a pricing strategy for the earrings. Among the decisions you must make is whether to price all the styles at one price point or to price the different styles at separate price points.

Present your pricing strategy to your supervisor (judge).

You will be evaluated on how well you meet the following performance indicator:

Use psychological pricing to adjust base prices

$(a)$ What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? $(b)$ Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.

Your bank account has a balance of $-\$ 12$. You deposit $\$ 60$. What is your new balance?

Identify the four types of tissue membranes found in the body.

Polo Ralph Lauren Corporation designs, markets, and distributes a variety of apparel, home decor, accessory, and fragrance products. The company's products include such brands as Polo by Ralph Lauren, Ralph Lauren Purple Label, Ralph Lauren, Polo Jeans Co., and Chaps. Polo Ralph Lauren reported the following (in thousands) for two recent years:

$$\begin{array}{lrr} & \textbf{For the Period Ending} \\ & \textbf{ Year 2 } & \textbf{Year 1} \\ \hline \text{Sales} & \$ 6,859,500 & \$ 5,660,300 \\ \text{Accounts receivable} & 690,000 & 592,700 \end{array}$$

Assume that accounts receivable (in millions) were $\$ 486,200$ at the beginning of Year 1.

c. What conclusions can be drawn from these analyses regarding Ralph Lauren's efficiency in collecting receivables?