R-Studio (R Programming Language)

4. Let the data x be given by
`x <- c(1, 8, 2, 6, 3, 8, 5, 5, 5, 5)`
Use R to compute the following functions. Note, we use X1 to denote the first element of x (which is 1) etc.   
1. `(X1 + X2 + . . .+ X10)/10` (use sum)   
2. Find log10(Xi) for each i. (Use the log function which by default is base e)
3. Find `(Xi - 4.4)/2.875` for each i. (Do it all at once)   
4. Find the difference between the largest and smallest values of x. (This is the range. You can use `max` and
`min` or guess a built in command.)

```{r}
#insert your code
```

Write a small section of Python code that defines a function called check_even(value) - the function takes a numerical value as input and returns True or False based on whether the provided argument is divisible by 2 (i.e. is it odd or is it even). If the argument provided is not a number (as determined by built-in the isdigit() function - which only works on string data) then rather than crashing, the function should raise an exception which is caught outside the function (i.e. in the block of code calling the function). Provide three calls to the function: - One with an even value where the function should return True, - Another with an odd value where the function should return False, and - One with non-numerical data which should raise an exception that will be caught and displayed in the block of code that calls the function.

In the decimal system (base 10), a natural number is represented as a sequence dndn−1 . . . d0 of (decimal) digits, each of which is in the range 0..9. The value of the number is d0 ×100 +d1 ×101 +···+ dn ×10n. Similarly, in the binary system (base 2), a natural number is represented as a sequence bnbn−1 · · · b0 of (binary) digits, each of which is 0 or 1. The value of the number is b0 ×20 +b1 ×21 +···+bn ×2n. For example, the value of the number whose binary representation is 101is: 1×20+0×21+1×22 =1+0+4=5.

Without using any built-in functions for converting numbers, write a function that takes as input the binary representation of a positive integer n and returns its decimal representation.

Douglas and Pamela Frank are a married couple. They both worked for a railroad company for 30 years. At age 57, Douglas and age 52, Pamela retired and moved to the small town of Ovilla, TX, which has a population of approximately 3,500 residents. When the Franks moved to the town, they decided to start a child care business in their home called Nanna’s House.

Nanna’s House is licensed by the state. The state charges an annual fee of $225 to maintain the license. Insurance is required at a cost of $3,840 annually. The facility is licensed to care for a maximum of six children. The Franks charge a fee of $800 per month for each child. The monthly fee is based on a full day of care, from 8:00 a.m. to 4:00 p.m. If additional time is required beyond 4:00 p.m., parents must pay an additional charge of $15 per hour for each child. The couple provides two meals and a snack for the children. The cost of the meals and snack is $3.20 per child per day. There are six children currently enrolled.

The facility is very nice. It is an 820 square foot addition to their home that was built in 1964. The Franks purchased the home and completed the renovations for $79,500 and they believe the addition has a useful life of 25 years. The facility has a large open space for play, reading, and other activities. There is a section for sleeping which contains small cots. The facility is equipped with a small kitchen, two bathrooms and a small laundry area. The daycare increased the Franks’ utility cost by $50 each month.

During the first week of operations, the washer and dryer stopped working. Both appliances were old and had been used by the couple for many years. The old appliances cost a total of $440. While a laundry room was not initially a necessity, it became increasingly important for laundering the soiled clothes of the children, blankets, and sheets. A company nearby, Red Oak Laundry and Dry Cleaning, can launder clothing for the Franks, including pick-up and delivery, for $52 per month. Alternatively, the Franks can take clothes to the laundromat once a week, which is three miles away (one way). The applicable mileage rate is $0.56/mile. They can launder the clothes themselves at a cost of $8 per week. The self-service alternative does not include detergent or fabric sheets. The couple would need to purchase these items in order to use the laundromat. Purchasing laundry supplies in bulk from MegaMart would cost $35 every quarter. The final alternative is for the Franks to purchase a washer and dryer. The cost of the appliances is: washer $420 and dryer $380. The additional accessories for both appliances, needed for installation, cost $43.72. The store will deliver the appliances at a total cost of $35. The cost of installing the appliances is free. Both appliances are expected to last 8 years. According to the manufacturer the washer will increase energy costs by $120 per year. The dryer will increase energy costs by $145 per year. The Franks need some assistance in decision making and evaluation. They have contacted Emily Smith, their accountant, to provide some advice.

Requirements

Respond to the following Case Discussion Questions to help Douglas and Pamela make their decisions.

Case Discussion Questions

(If necessary, the Franks will use straight line depreciation. For monthly calculations, use 4.33 weeks

per month.)

1. Consider the different types of costs discussed in this course. List the costs discussed in the case and provide one specific example of each.

2. Based on the information provided, what information is relevant to the decision to purchase the appliances? What information is irrelevant to the decision to purchase the appliances? Why?

3. What could it cost the couple to launder clothes? Show your detailed calculations for each.

4. The couple has made a significant investment in this business. How long will it take for the couple to recoup their investment? Is the time required to recoup the investment a good measure of the success of the company? If not, how would you measure the success of the company? Explain.

5. As Emily Smith, prepare a letter to the Franks advising them on their laundry needs. What is your recommendation and why?

6. The Franks have a wait list for their daycare. They can hire an employee for $9 per hour for 40 hours each week. With the additional employee, the Franks can accept three additional children. Should the Franks hire the additional employee? Show your detailed calculations.

7. The Franks home can accommodate a maximum of nine children. They can move the daycare from their home to rented space in town, which can accommodate up to 14 children. The space will cost $650 per month and the utilities will cost $125 per month. Additionally, insurance will now cost the Franks $5,000 per year. Per state regulations, each adult can supervise no more than three children. As Emily Smith, prepare a letter to the Franks advising them on their space options. Should they continue to operate the facility at home or should they rent space in town? How many children should they accept? How many employees will they need to hire? Show your detailed calculations for each scenario.

3. The market portfolio expected return is 8% and its standard deviation is 16%. The risk-free rate is 1%. Assume that the CAPM holds. What is the standard deviation of the portfolio that invests 40% in the risk-free asset and 60% in the market? A. 8.1%. B. 9.6%. C. 10.5%. D. 11.1%. (use financial calculator)

4. The beta of company XYZ’s stock is 2. The annual risk-free rate is 2% and the market portfolio’s expected return is 9%. What is the expected return of the company’s stock? (use financial calculator) A 16% B.20% C.14 D.17%

5. The stock ABC has a beta of 1.6 and its standard deviation is 30%. Its correlation coefficient with the market return is 0.8. What is the standard deviation of the market return?(use financial calculator)

1. 18%.
2. 15%.
3. 20%.
4. None of the answers is correct