Focal length and angular velocity A cylindrical container, partially filled with mercury, is rotated about its axis so that the angular speed of each cross section is $\omega$ radians/second. From physics, the function $f$, whose graph generates the inside surface of the mercury (see the figure), is given by

$$f(x)=\frac{1}{64} \omega^2 x^2+k,$$

where $k$ is a constant. Determine the angular speed $\omega$ that will result in a focal length of $2$ feet.

The simplest cost function is the linear cost function, C(x) = mx + b, where the y-intercept b represents the fixed costs of operating a business and the slope m represents the cost of each item produced. Suppose that a small bicycle manufacturer has daily fixed costs of $1800 and each bicycle costs$90 to manufacture. Graph the model.

What are the benefits of a free enterprise economy?

We often think of the American free enterprise economy as having several distinct "players" that ensure its success. These players include entrepreneurs, consumers, and the government. How do you fit in? How does the system benefit you? As a student, you may find that you need extra spending money to cover your school and your living expenses. You may begin thinking about becoming an entrepreneur by creating a small business that will earn you money. You may also decide to look into getting a job. Or you may visit your school's financial aid office to see if there is some form of government student aid, such as a loan, grant, or work-study program.

Answer the following questions:

2. What type of part-time job might I like that is available near my school?

Solve. Find the cost per mile to the nearest cent.

$$\begin{array}{|c c c c c c c c c c c|} \hline \small\textbf{(Total Daily Cost}& + & \small\textbf{Total Mileage Cost} & +& \small\textbf{Gasoline Cost} & = & \small\textbf{Total Cost)} & \div & \small\textbf{Miles} & = & \small\textbf{Cost per}\\ & & & & & & & &\small\textbf{Driven} & & \small\textbf{Mile}\\ \hline (\$60.00 & + & \$45.00 & + & \$11.88 & = & \$116.88) & \div & 300 & = & ? \\ \hline \end{array}$$

Heisey Company is a very profitable small business. It has not, however, given much consideration to internal control. For example, in an attempt to keep clerical and office expenses to a minimum, the company has combined the jobs of cashier and bookkeeper. As a result, Terry Baden handles all cash receipts, keeps the accounting records, and prepares the monthly bank reconciliations.

The balance per the bank statement on October 31, 2014, was $18,380. Outstanding checks were: No. 62 for$140.75, No. 183 for $180, No. 284 for$253.25, No. 862 for $190.71, No. 863 for$226.80, and No. 864 for $165.28. Included with the statement was a credit memorandum of$185 indicating the collection of a note receivable for Heisey Company by the bank on October 25. This memorandum has not been recorded by Heisey.

The company’s ledger showed one Cash account with a balance of $21,877.72. The balance included undeposited cash on hand. Because of the lack of internal controls, Terry took for personal use all of the undeposited receipts in excess of$3,795.51. He then prepared the following bank reconciliation in an effort to conceal his theft of cash.

$$\begin{array}{lrr} \text{Cash balance per books, October 31}&&\text{\$\hspace{1pt}21,877.72}\\ \text{Add: Outstanding checks}\\ \qquad\text{No. 862}&\text{\$\hspace{1pt}190.71}\\ \qquad\text{No. 863}&\text{226.80}\\ \qquad\text{No. 864}&\underline{\text{\hspace{5pt}165.28}}&\underline{\text{\hspace{18pt}482.79}}\\ &&\text{22,360.51}\\ \text{Less: Undeposited receipts}&&\underline{\text{\hspace{11pt}3,795.51}}\\ \text{Unadjusted balance per bank, October 31}&&\text{18,565.00}\\ \text{Less: Bank credit memorandum}&&\underline{\text{\hspace{19pt}185.00}}\\ \text{Cash balance per bank statement, October 31}&&\underline{\underline{\text{\$\hspace{1pt}18,380.00}}}\\ \end{array}$$

Instructions

(b) Indicate the three ways that Terry attempted to conceal the theft and the dollar amount involved in each method.

Mibanco in Peru plays an important role in the Latin American microfinance sector. The bank issues working capital and loans to micro-entrepreneurs and small and mediumsized businesses. Besides this, it offers current accounts, savings, deposit accounts and insurance products to private individuals - many of whom find it difficult to gain support from traditional commercial banks. In $2014$ Mibanco's profit margin fell to under $1 \%$ and $12 \%$ of its loans to small businesses had not been repaid within one month of the required date; and $61 \%$ of its customers had also taken out loans with other banks.

KEY INDICATORS Mibanco at year-end $2013$:

• number of loan clients: over 400000

• percentage female clients: $55 \%$

• percentage rural clients: $23 \%$

• average loan amount: $\$ 2800$

Describe two features of the microfinance loans provided by Mibanco.

In physics, it is established that the acceleration due to gravity, g (in $meters/sec^2$), at a height h meters above sea level is given by $g(h)=\frac{3.99 \times 10^{14}}{\left(6.374 \times 10^{6}+h\right)^{2}}$ where $6.374 \times 10^{6}$ is the radius of Earth in meters. The Willis Tower in Chicago, Illinois, is 443 meters tall. What is the acceleration due to gravity at the top of the Willis Tower?

A key factor that an auditor provides is independence. The AICPA Code of Professional Conduct states that “a member in public practice should be independent in fact and appearance when providing auditing and other attestation services.”

Required:

Do you consider the following circumstances to suggest a lack of independence? Justify your position. (Use your imagination. Specific answers are not provided in the chapter.)

1. Jack Jones is a partner with a large audit firm and is assigned to the Ford audit. Jack owns 10 shares of Ford.

2. Melissa Chee has invested in a mutual fund company that owns 500,000 shares of Sears stock. She is the auditor of Sears.

3. Bob Franklin is a clerk/typist who works on the audit of AT&T. He has just inherited 50,000 shares of AT&T stock. (Bob enjoys his work and plans to continue despite his new wealth.)

4. Nancy Sodoma worked on weekends as the controller for a small business that a friend started. Nancy quit the job in midyear and now has no association with the company. She works full-time for a large CPA firm and has been assigned to do the audit of her friend’s business.

5. Mark Jacobs borrowed $100,000 for a home mortgage from First City National Bank. The mortgage was granted on normal credit terms. Mark is the partner in charge of the First City audit.

After completing his Certified Financial Planner designation (CFP), Andre was excited about the prospects of working with small business owners and their employees regarding retirement planning. Andre wanted to show the value of an annuity program as one of the viable investment options in a salary reduction retirement plan. In addition, he wanted to demonstrate the substantial tax benefits that annuities can provide. For instance, qualified annuities (by definition) not only reduce your current taxable salary, they also accumulate earnings on a tax-deferred basis-meaning you don't pay taxes on the earnings until they are withdrawn. Andre was developing a spreadsheet to show the way that annuities could grow using various rates of return.

Using the same information from Exercise earlier and assuming a $25 \%$ tax bracket, what would be the net effect of investing at $8 \%$ for $20$ years if taxes on the earnings were paid from the investment fund each year? How would this compare if no taxes had to be paid, such as in a tax-deferred annuity at $8 \%$ for $20$ years?

You work for the Plains State Bank as an analyst specializing in the financial statements of small businesses seeking loans from the bank. Digit Retail Enterprises Inc. provides you with its balance sheet for December 31, 2012 and 2013 (Exhibit 6.21), and its income statement for 2013 (Exhibit 6.22). Digit Retail Enterprises, Inc., acquired no new property, plant, and equipment during the year.

$$\begin{array}{lcc} &\textbf{Digit Retail Enterprises, Inc.}\\ &\textbf{Balance Sheet}\\ &\textbf{(Problem 33)}\\ &&\textbf{December}&\textbf{December}\\ &&\textbf{31, 2013}&\textbf{31, 2012}\\ \text{ASSETS}\\ \textbf{Current Assets}\\ \text{Cash}&&\$ 50,000&\$ 36,000\\ \text{Accounts Receivable}&&38,000&23,000\\ \text{Notes Receivable}&&—&7,500\\ \text{Interest Receivable}&&—&100\\ \text{Merchandise Inventory}&&65,000&48,000\\ \text{Prepaid Insurance}&&12,000&9,000\\ \text{Prepaid Rent}&&—&\underline{2,000}\\ \quad\text{Total Current Assets}&&\underline{\$165,000}&\underline{\$125,600}\\ \textbf{Property, Plant, and Equipment}&&&\\ \text{At Cost}&&\$ 90,000&\$100,000\\ \text{Less Accumulated Depreciation}&&\underline{(35,000)}&\underline{(20,000)}\\ \text{Net}&&\underline{\$ 55,000}&\underline{\$ 80,000}\\ \quad\text{Total Assets}&&\underline{\underline{\$220,000}}&\underline{\underline{\$205,600}}\\ \\ \text{LIABILITIES AND SHAREHOLDER’S EQUITY}\\ \textbf{Current Liabilities}\\ \text{Accounts Payable—Merchandise Suppliers}&&\$ 20,000&\$ 18,000\\ \text{Salaries Payable}&&2,800&2,100\\ \text{Rent Payable}&&3,000&—\\ \text{Advances from Customers}&&6,100&8,500\\ \text{Note Payable}&&5,500&—\\ \text{Dividends Payable}&&2,600&4,200\\ \text{Other Current Liabilities}&&\underline{3,700}&\underline{1,300}\\ \quad\text{Total Current Liabilities}&&\underline{\$ 43,700}&\underline{\$ 34,100}\\ \textbf{Shareholders’ Equity}&&&\\ \text{Common Stock}&&\$164,500&\$160,000\\ \text{Retained Earnings}&&11,800&11,500\\ \text{Total Shareholders’ Equity}&&\underline{\$176,300}&\underline{\$171,500}\\ \text{Total Liabilities and Shareholders' Equity}&&\underline{\underline{\$220,000}}&\underline{\underline{\$205,600}}\\ \end{array}$$

$$\begin{array}{lr} &\textbf{Digit Retail Enterprises, Inc.}\\ &\textbf{Balance Sheet}\\ &\textbf{(Problem 33)}\\ &&\textbf{December}&\textbf{December}\\ \text{Sales Revenue}&\$270,000\\ \text{Gain on Sale of Property, Plant, and Equipment}&3,200\\ \text{Interest Revenue}&\underline{200}\\ \quad\text{Total Revenues}&\underline{\$273,400}\\ \textbf{Less Expenses:}&\\ \text{Cost of Goods Sold}&\$145,000\\ \text{Salaries Expense}&68,000\\ \text{Rent Expense}&12,000\\ \text{Insurance Expense}&5,000\\ \text{Depreciation Expense}&20,000\\ \text{Other Expenses}&\underline{13,800}\\ \quad\text{Total Expenses}&\underline{\$263,800}\\ \text{Net Income}&\underline{\underline{\$ 9,600}}\\ \end{array}$$

g. Calculate the amount of dividends paid during 2013.

Elite Service Company is a very profitable small business. It has not, however, given much consideration to internal control. For example, in an attempt to keep clerical and office expenses to a minimum, the company has combined the jobs of cashier and bookkeeper. As a result, Steve Evans handles all cash receipts, keeps the accounting records, and prepares the monthly bank reconciliations.

The balance per the bank statement on March 31, 2014, was $5,931.51. Outstanding checks were: No. 206 for$358.53, No. 441 for $292, No. 590 for$283.00, No. 781 for $286.00, No. 782 for$319.47, and No. 783 for $303.14. Included with the statement was a credit memorandum of$175 indicating the collection of a note receivable for Elite Service Company by the bank on March 21. This memorandum has not been recorded by Elite Service.

The company’s ledger showed one cash account with a balance of $6,889.53. The balance included undeposited cash on hand. Because of the lack of internal controls, Steve took for personal use all of the undeposited receipts in excess of$1,591.63. He then prepared the following bank reconciliation in an effort to conceal his theft of cash.

$$\begin{array}{lrr} \text{Cash balance per books, March 31}&&\text{\$\hspace{1pt}6,889.53}\\ \text{Add: Outstanding checks}\\ \qquad\text{No. 781}&\text{\$\hspace{1pt}286.00}\\ \qquad\text{No. 782}&\text{319.47}\\ \qquad\text{No. 783}&\underline{\text{\hspace{5pt}303.14}}&\underline{\text{\hspace{16pt}808.61}}\\ &&\text{7,698.14}\\ \text{Less: Undeposited receipts}&&\underline{\text{\hspace{8pt}1,591.63}}\\ \text{Unadjusted balance per bank, March 31}&&\text{6,106.51}\\ \text{Less: Bank credit memorandum}&&\underline{\text{\hspace{16pt}175.00}}\\ \text{Cash balance per bank statement, March 31}&&\underline{\underline{\text{\$\hspace{1pt}5,931.51 }}}\\ \end{array}$$

Instructions

(a) Prepare a correct bank reconciliation. (Hint: Deduct the amount of the theft from the adjusted balance per books.)

Which of the following is most likely to happen under hypnosis? a. A person, will remember a traumatic event from their past that they had forgotten. b. An adult, will regress to acting exactly like they did as a child. c. A person may be unable to report their grandmother's name if asked to forget it. d. An eyewitness to a crime will give a vivid and accurate description of events that they had forgotten. e. A person, will become less open to suggestions.

Describe a number of business ventures. For each exercise, Determine the break-even point. Describe what this means. A company that manufactures small canoes has a fixed cost of $18,000. It costs$20 to produce each canoe. The selling price is $80 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.)

You start a small bee-keeping business, spending $\$ 500$ for equipment and bees. You figure it will cost $\$ 1.25$ per pound to collect, clean, bottle, and label the honey. How many pounds of honey must you produce before your average cost per pound is $\$ 1.79$?