a. In a study of monthly salary distribution of residents in Paris conducted in year 2015, it was found that the salaries had an average of €2200 (EURO) and a standard deviation of €550. Assume that the salaries were normally distributed.

(i): Consider sampling with sample size 64 on the above population. Compute the mean of the sampling distribution of the mean (X).

(ii): Compute the standard deviation of the sampling distribution of the mean in Question 1 above.

(iii): A random sample of 64 salaries (sample 1) was selected from the above population. What is the probability that the average of the selected salaries is above €2330?

(iv): Would the calculation you performed in Question 3 still be valid if the monthly salaries were NOT normally distributed? Why?

(b) In another study conducted in the same year (2015), the average monthly salary of residents in Bordeaux was found to be about €2353. And the standard deviation of the monthly salaries was €420. A random sample of 81 salaries (sample 2) was selected from this population.

Set 1 = Paris (2015); 2 = Bordeaux (2015)

(i): Compute the mean of X1 − X2.

(ii): Compute the standard deviation of X1 − X2.

(iii): What is the probability that the average of the salaries in the sample 1 is less than the average of the salaries in sample 2?

(c) In 2017, a study on the salary distribution of Paris residents was conducted. Assume that the salaries were normally distributed. A random sample of 10 salaries was selected and the data are listed below: 3200 3500 3000 2100 2950 2050 2440 3100 3500 2500

(i): Assume that the standard deviation of the salaries was still the same as in 2015. Estimate the average salary (in 2017) with 95% confidence. Question 9: The assumption made in Question 8 was certainly unrealistic. Estimate the average salary (in 2017) with 95% confidence again assuming that the standard deviation had changed from 2015.

(ii): Estimate the variance of monthly salaries of Paris residents (in 2015) based on the sample provided above at a 95% confidence level.

(iii): How would you interpret the result in Question 10 above?

(d) A similar study was conducted on salary distribution of Paris residents in 2019. The research team aimed to estimate the average salary. They chose the 98% confidence and assumed that the population standard deviation was the same as in 2015. Assume again that those salaries were normally distributed.

(i) If they would like the (margin of) error to be no more than €60, how large a sample would they need to select?

A.

B.

A project with an initial cost of $22,350 is expected to generate cash flows of $5,200, $7,300, $8,400, $7,300, and $6,000 over each of the next five years, respectively. What is the project's payback period?

C.

A new project has an initial cost of $133,000. The equipment will be depreciated on a straight-line basis to a book value of $39,000 at the end of the four-year life of the project. The projected net income each year is $14,000, $17,450, $22,100, and $13,900, respectively. What is the average accounting return?

At the end of the current year, the accounts receivable account has a debit balance of $777,000 and sales for the year total $8,810,000. The allowance account before adjustment has a debit balance of $10,500. Bad debt expense is estimated at 3/4 of 1% of sales. The allowance account before adjustment has a debit balance of $10,500. An aging of the accounts in the customer ledger indicates estimated doubtful accounts of $33,600. The allowance account before adjustment has a credit balance of $9,300. Bad debt expense is estimated at 1/4 of 1% of sales. The allowance account before adjustment has a credit balance of $9,300. An aging of the accounts in the customer ledger indicates estimated doubtful accounts of $77,200.

Determine the amount of the adjusting entry to provide for doubtful accounts under each of the assumptions (a through d) listed above.

Suppose there are three stocks with the same expected returns of 10% per year and the same risk (standard deviation) of 100%. The correlation between any two of them is 50%.

a. What is the risk of the equal-weighted portfolio of two stocks?

b. What is the risk of the equal-weighted portfolio of three stocks?

c. What is the minimum possible risk of the portfolio of the three stocks?
  
d. If the third stock has a correlation of -50% instead of 50% with the rest, what is the risk of the equal-weighted portfolio of three stocks, and what is the minimum possible risk?

On July 24 of the current year, Sam Smith was involved in an accident with his business use automobile. Sam had purchased the car for $30,000. The automobile had a fair market value of $20,000 before the accident and $8,000 immediately after the accident. Sam has taken $20,000 of depreciation on the car. The car is insured for the fair market value of any loss. Because of Sam's history, he is afraid that if he submits a claim, his policy will be canceled. Therefore, he is considering not filing a claim. Sam believes that the tax loss deduction will help mitigate the loss of the insurance reimbursement. Sam's current marginal tax rate is 35%.

a. Complete the letter to Sam that contains your advice with respect to the tax and cash-flow consequences of filing versus not filing a claim for the insurance reimbursement for the damage to his car.

Hoffman, Young, Raabe, Maloney, & Nellen, CPAs
5191 Natorp Boulevard
Mason, OH 45040

January 26, 2018

Mr. Sam Smith
450 Colonel's Way
Warrensburg, MO 64093

Dear Mr. Smith:

This letter is to inform you of the tax and cash-flow consequences of filing a claim versus not filing a claim with your insurance company for reimbursement for damages to your business-use car.

If an insurance claim is filed, you will have a of $.

This is determine by computing the difference between the and the of the adjusted basis or . The result will produce a net cash flow of $.

If no insurance claim is filed, you will have a of $, which will your tax liability by $.

The net cash resulting from filing an insurance reimbursement claim would be $.

Should you need more information or need to clarify anything, please contact me.

Sincerely,

John J. Jones, CPA
Partner

b. Complete a memo for the tax files.

TAX FILE MEMORANDUM

DATE: January 26, 2018

FROM: John J. Jones
SUBJECT: Tax consequences for Sam Smith if he does not file an insurance claim for reimbursement for damages to his business use car.

If an insurance claim is filed, Sam will have a   of $. This will produce a net cash flow of $.

If no insurance claim is filed, Sam will have a   of $, which will   his tax liability by $.

In my correspondence with Sam, I pointed out that the net cash   from filing an insurance reimbursement claim would be $.

deposit $10,000 per year into an account at the end of each of the next 4 years, and $15,000 into the account each year for the following 6 years. How much money will you have in the account at the end of the 10th year? Assume that we earn 10 percent nominal interest compounded annually on our investments.

• A. $76,319.18
• B. $197,972.30
• C. $130,000.00
• D. $89,174.29
• E. Something Else

A) A certain area is hit by 6 Heat Waves a year on average. Find the probability that in a given year that area will be hit by fewer than 5 Heat Waves (5 is not included).

a) 0.2851

b) 0.4457

c) 0.1339

d) 0.1606

B) The probability of a successful rocket launch is 0.9. Test launches are conducted until three successful launches are achieved. Let X be the total number of launches needed. What kind of distribution does X follow?

C) What are the properties of a Bernoulli process?

The price of a stock is $40. The price of a one-year put with strike price $30 is $0.70 and a call with the same time to maturity and a strike of $50 costs $0.50. Both options are European.

(a) An investor buys one share, shorts one call and buys one put. Draw and comment upon the payoff of this portfolio at maturity as a function of the underlying price.

(b) How would your answer to (a) change if the investor buys one share, shorts two calls and buys two puts instead.