Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 31.6 and 4.9 mpg, respectively.

a. What is the probability that a randomly selected passenger car gets more than 35 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that the average mpg of two randomly selected passenger cars is more than 35 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If two passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 35 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 35.9 and 2.5 mpg, respectively. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected passenger car gets more than 37 mpg?

b. What is the probability that the average mpg of three randomly selected passenger cars is more than 37 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If three passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 37 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

____ 4. Stephanie is self-employed. In 2019 she drove 1,000 miles for business out of a total 10,000 miles for the year. Her auto expenses for the year were: gasoline - $500; insurance - $1,000; repairs - $200; business parking - $400. How much is her automobile deduction if she uses the standard mileage method?

            a.         $580

            b.         $980

            c.         $2,680

            d.         $2,100

            e.         $210

            f.          $0.

____ 5. An aggressive young attorney is an employee of a small law firm that provides him with an adequate office. He uses the den in his home to prepare legal briefs and review legal documents related to his employment. Assuming the attorney lives near the firm's office and he always has easy access to the office, which of the following statements most accurately describes the deductibility of the home office expenses incurred by the attorney?

            a.         If the den is used exclusively for business purposes, the expenses are deductible.

            b.         If the den is used exclusively for business purposes on a regular basis, the expenses are deductible.

            c.         If the den is used exclusively for business purposes on a regular basis to work for and see clients, the expenses are deductible.

            d.         In this situation, the expenses are not deductible.

            e.         The home office deduction was completely eliminated as a result of the Tax Cuts and Jobs Act of 2017.

____ 6. T's employer provides an office for her in its downtown headquarters. Which of the following statements is true?

            a.         T maintains an office in her home that she uses to conduct work related to her rental property. Even though the rental activities may be considered a business, no deduction can be allowed because T's principal business is that of being an employee and its primary location is downtown.

            b.         T regularly meets with clients of her employer's business in her home office, which is exclusively used for such purpose. T is entitled to the home office deduction without further inquiry.

            c.         T maintains a home office that is exclusively used on a regular basis to conduct work regarding her investment portfolio. No deduction is allowed.

            d.         None of the statements above are true.

The research director at the Nie Pójdzie Motor Club was interested whether the annual miles driven by residents of Arkansas was greater than the 2019 average of 13,452 annual miles for a driver in the South Central region. A random sample of licensed Arkansan drivers was drawn, and a hypothesis test was performed using the .05 significance level. Some parts of the output are shown below. Please answer the following questions (a to g) using the output below. (3.5 pts.)

a) What are the degrees of freedom?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc)

f) What is the p value?

g) Do you reject or not reject H₀? Explain your decision using the output

The research director at the Nie Pójdzie Motor Club was interested whether the annual miles driven by residents of Arkansas was greater than the 2019 average of 13,452 annual miles for a driver in the South Central region. A random sample of licensed Arkansan drivers was drawn, and a hypothesis test was performed using the .05 significance level. Some parts of the output are shown below. Please answer the following questions (a to g) using the output below. (3.5 pts.)

a) What are the degrees of freedom?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc).

f) What is the p value?

g) Do you reject or not reject H₀? Explain your decision using the output.

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon.

16.2 20.3 31.5 30.5 21.5 31.9 37.3 27.5 27.2 34.1 35.1 29.5 31.8 22.0 17.0 21.6

Find the mean, standard deviation, five - number summary, IQR, and identify any outliers. Use the five - number summary to sketch a boxplot. What does the boxplot tell you about the distribution of the data? (20 points)

The table below contains the overall miles per gallon​ (MPG) of a type of vehicle.

Construct a 95​% confidence interval estimate for the population mean MPG for this type of​ vehicle, assuming a normal distribution.The 95​% confidence interval estimate is from ____ MPG to ____ MPG.

​(Round to one decimal place as​ needed.)

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 30.9 and 2.7 mpg, respectively. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected passenger car gets more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that the average mpg of four randomly selected passenger cars is more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Gas Mileage. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 MPG and a standard deviation of 3.5 MPG.

a) What is the probability that a randomly selected Cobalt gets more than 34 MPG?

b) Suppose that 10 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

c) Suppose 20 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

Harvey’s REIT is a company that invests in income generating land and buildings. Since Harvey’s is organized as a REIT it must pay out most if not all of its income to shareholders as a dividend. Since the firm is a “pass through” vehicle (passes income straight threw to investors), the REIT pays no taxes (its investors get taxed at the personal level with all income treated as ordinary income). With little retained earnings, new real estate acquisitions are debt or equity financed.

Harvey has two categories of investment. One category is hotels and the second is land for special events parking. The land business is very interesting because you can simply buy the land and there is little or no working capital or capital expenditure needs since the land is often just fields near ballparks, state fairs, concert facilities, etc…

For most of Harvey’s businesses, the cash flow grows at roughly the inflation rate. Hotel fares and parking rates trend up with inflation. Acquisitions rarely add much value, since they are bought in competitive real estate markets. What you pay is pretty close to the discounted cash flow value of what you buy. No acquisitions are currently on the radar and most believe that there should be little “value from future acquisitions” in Harvey’s REIT share prices.

Harvey has entertained breaking up the two units perhaps by divesting one and keeping the other. He wonders what each unit is worth. Here are the cash flows of each business

Hotels: FCF = 90m upcoming year

Parking land FCF = 30m upcoming year

Both business are expected to grow their FCF at 2.4% in perpetuity (due to inflation)

Recall from your prior classes a growing perpetuity is worth:  

Value now = FCF(upcoming year) / (discount rate on FCF – growth rate in perpetuity)

For the most part, given the absence of taxes, it is believed that the firm’s situation approximates perfect market conditions (assuming debt is not 75% plus of total financing which could raise bankruptcy concerns).

Similar (non-taxed) REITS have the following data:

Pure plays (MV stands for market Value and all figures in millions):

The land parking business is unique in the world of publicly traded equities. There are no pure plays out there. All the above firms with D/E below 1.1 are able to borrow at approximately 4.5%. The market risk premium is 5% and the risk free rate is 4.5%. The same is true for Harvey.

Harvey currently has market value of debt = 1000m

Harvey has a market value of equity = 1500m

Harvey has an equity beta of 0.9.

Harvey does not “allocate debt” between divisions. He views the debt ratio of each to be the same.

Assume that Harvey views the market valuation of his firm as likely accurate – he believes that markets are “efficient.” He also views the valuation of competitors as reasonably accurate. He thinks the listed hotel competitors have properties with fairly similar risk, but realizes there may be slight errors in beta estimates (up or down) and averages of beta will have less errors.

How can Harvey figure out the value of his hotel business (not equity or debt pieces, the whole value) and what is the estimate for it? Show the steps for doing so for partial credit

What is the value of the Land business, its’ WACC, and its’ unlevered beta?

Assume that no divestiture takes place. If the Land business got an unexpected opportunity to acquire a piece of land that would generate FCF = 2m growing at 2.4% in perpetuity, and it had an asking price of 48m, should it do the deal? Why or why not?

Some at the firm say that 2/48 = 4.1667%. They note that the accounting return is not even sufficient to cover the cost of borrowing (if the project is financed with all debt) and therefore the project should not be taken. Does this logic make sense? Explain why or why not? (An explanation of what is right or wrong with argument would be useful.