1. Bankers trust has bonds maturing in 27 yrs. the total principal that must be repaid by the bank at that time is $950 million. The relevant discount rate is 7.5% per yr. what is the present value of this liability assuming quarterly compounding?

2. Comparing two annuities which offer monthly payments of $1,750 for 10 yrs and pay interest at an annual rate of 4.5%. Annuity A will pay you on the 1st day of each month while B will pay on the last day of each month. Which one of the following statements is correct?

A. Annuity b is an annuity due

b. Annuity b has smaller future value than A

c. Both have different present values as of today and equal future values at the end of year 10.

D. Both have equal present values but unequal futures values at the end of yr 10

Problem 27-01 Lease or Buy [LO3] You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a very common practice with expensive, high-tech equipment). The scanner costs $5,300,000, and it would be depreciated straight-line to zero over four years. Because of radiation contamination, it actually will be completely valueless in four years. You can lease it for $1,550,000 per year for four years. Assume that the tax rate is 23 percent. You can borrow at 7 percent before taxes. What is the NAL of the lease? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Should you lease or buy?

(HW5-27)

The amount of energy released by burning a fuel source, measured in energy per mass, is called the fuel value. If all the energy obtained from burning 1.27 pounds of butane (fuel value is 10.85 kcal/g) is used to heat 127.5 kg of water at an initial temperature of 18.7 °C, what is the final temperature?

2. Mrs. D who 27 years old plans to retire at the age of 55. Mrs. D would like to be able to withdraw $132,000 per year from her retirement account for 45 years after retirement beginning the year after her retirement. She is also expecting an inheritance of $54,000 to be transferred to her on her 35th birthday. a How much does she need to have in her retirement account by retirement date if the interest rate is 6% per year during the post-retirement years? b Suppose she already has $12,000 in her retirement investment account that earns 9% per year. What will be the value of this amount by her retirement date? c Given her goal, her expected inheritance, and the investment she already has in 1b, how much does she need to invest per year from now till retirement (at 9% annual rate of return) in order to reach her retirement goal?

27. Determine a venture’s sustainable growth rate based on the following information: sales = $1,000,000; net income = $150,000; common equity at the end of last year = $520,000; and the dividend payout percentage = 20%.

                        a.   10%

                        b.   16%

                        c.   20%

                        d. 24%

                        e.   30%

On this worksheet, make an XY scatter plot linked to the following data:

20)

Use R to do each of the following. Use R code instructions that are as general as possible, and also as efficient as possible. Use the Quick-R website for help on finding commands. 1. The following is a random sample of CT scores selected from 32 Miami students. 28, 27, 29, 27, 29, 31, 32, 30, 34, 30, 27, 25, 30, 32, 35, 32 23, 26, 27, 33, 33, 33, 31, 25, 28, 34, 30, 33, 28, 26, 30, 28 (a) Find the mean and standard deviation of this sample. Give the interpretation of the mean in the context. (b) Find the five numbers summary and provide the interpretation of the sample median in the context. (c) Draw the histogram of the data. What can you say about the distribution of the data. (d) Draw the Boxplot of the data. Is there any potential outlier? 2. The weekly amount spent for maintenance and repairs in a certain company has an approximately normal distribution, with a mean of $600 and a standard deviation of $40. If $700 is budgeted to cover repairs for next week, (a) what is the probability that the actual costs will exceed the budgeted amount? (b) how much should be budgeted weekly for maintenance and repairs to ensure that the probability that the budgeted amount will be exceeded in any given week is only 0.1?

Drive-through Service Time at McDonald’s When you are on the go and looking for a quick meal, where do you go? If you are like millions of people every day, you make a stop at McDonald’s. Known as “quick service restaurants” in the industry (not “fast food”), companies such as McDonald’s invest heavily to determine the most efficient and effective ways to provide fast, high quality service in all phases of their business. Drive-through operations play a vital role. It’s not surprising that attention is focused on the drive-through process. After all, over 60% of the individual restaurant revenues in the United States come from the drive-through operations. Yet understanding the process is more complex than just counting cars. Marla King, professor at the company’s international training center, Hamburger University, got her start 25 years ago working at a McDonald’s drive-through. She now coaches new restaurant owners and managers. “Our stated drive-through service time is 90 seconds or less. We train every manager and team member to understand that a quality customer experience at the drive-through depends on them,” says Marla. Some of the factors that affect a customers’ ability to complete their purchases with 90 seconds include restaurant staffing, equipment layout in the restaurant, training, and efficiency of the grill team, and frequency of customer arrivals to name a few. Customer order patterns also play a role. Some customers will just order drinks, while others seem to need enough food to feed an entire soccer team. And then there are the special orders. Obviously, there is plenty of room for variability here. Yet that doesn’t stop the company from using statistical techniques to better understand the drive-through action. In particular, McDonald’s utilizes numerical measures of the center (mean) and spread (variance) in the data and to help transform the data into useful information. In order for restaurant managers to achieve the goal in their own restaurants, they need training in proper restaurant and drive-through operations. Hamburger University, McDonald’s training center located near Chicago, Illinois, satisfies that need. In the mock-up restaurant service lab, managers go through a “before and after” training scenario. In the “before” scenario, they run the restaurant for thirty minutes as if they were back in their home restaurants. Managers in the training class are assigned to be crew, customers, drive-through cars, special needs guests (such as hearing impaired), or observers. Statistical data about the operations, revenues, and service times are collected and analyzed. Without the right training, the restaurant’s operation usually starts breaking down after 10-15 minutes. After debriefing and analyzing the data collected, the managers make suggestions for adjustments and head back to the service lab to try again. This time, the results usually come in well within standards. “When presented with the quantitative results, managers are pretty quick to make the connections between better operations, higher revenues, and happier customers,” Marla states. When managers return to their respective restaurants, the training results and techniques are shared with staff who are charged with implementing the ideas locally. The results of the training eventually are measured when McDonald’s conducts a restaurant operations improvement process study, or ROIP. The goal is simple: improved operations. When the ROIP review is completed, statistical analyses are performed and managers are given their results. Depending on the results, decisions might be made that require additional financial resources, building construction, staff training, or reconfiguring layouts. Yet one thing is clear: Statistics drive the decisions behind McDonald’s drive-through service operations.

Questions:

1. After returning from the training session at Hamburger University, a McDonald’s store owner
selected a random sample of 323 drive-through customers and carefully measured the time it took
from when a customer entered the McDonald’s property until the customer had received the order at
the drive-through window.
These data are provided, using Excel spreadsheet. Note that the owner
selected some customers during the breakfast period, others during lunch or dinner time. For the
overall sample, compute the key measures of the central tendency and variation.
Based on these measures, what conclusion might the owner reach with respect to how well his store is
doing in meeting the 90 second customer service goal? Support your argument with appropriate
hypothesis testing.

2. Compute the key measures of central tendency and variation for drive-through times broken down by
breakfast, lunch, and dinner time periods. Based on these calculations, does it appear that the store is
doing better at one of these time periods than the others in providing shorter drive-through waiting
times? Support your argument with appropriate hypothesis testing.

3. Determine if there are any outliers in the sample data. Discuss.

show the steps of doing it in excel when answering it please

James Bond, Q, and M have agreed to meet at a pub after work for drinks. Bond cannot remember if they agreed to meet at the “Fanny on the Hill” or at “My Father’s Moustache” - so he tosses a coin to decide which pub to go to. Q is also in the same predicament; he tosses a coin to decide between “My Father’s Moustache” and “The Quiet Woman”. M faced with same quandary flips a coin first to decide whether or not he needs to head to the “Fanny on the Hill”. If the answer is “no”, then he flips again to decide between “My Father’s Moustache” and “The Quiet Woman”. What is the probability that

(a) Bond and Q meet? (b) Q and M meet? (c) all three meet? (d) all three go to different places? (e) at least two meet?

At an auto parts place, the inspection time for a vehicle is approximately normally distributed with the mean 25 minutes and the standard deviation 3

minutes.

1. What is the probability that a randomly selected car's inspection time

is between 20 and 31 minutes? Round your answer to three decimal places.

2. The owner of this auto parts places will give a gift card to the customer if his

car takes more than the longest 5% of the inspection time. What is the required

inspection time to get a gift card? Round your answer to three decimal places.

3. This place also offers a free car wash and the relationship between the car's

inspection time and washing time can be written as

            inspection time = 1.5 x washing time + 2.5

What are the mean and variance of total {inspection and washing} time?