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they also accumulate earnings on a tax-deferred basis-meaning you don't pay taxes on the earnings until they are withdrawn.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?

The Large Hadron Collider. In 2012, the Large Hadron Collider confirmed the existence of the Higgs boson with a mass of 125 GeV. Research this particle and its discovery: Why is the Higgs boson so interesting to physicists? What is its role in the standard model of particle physics? Why are some physicists a little disappointed that the Higgs particle appears to be almost exactly what they expected? An upgraded Large Hadron Collider was turned on in 2015. Has it made any further discoveries?

CarryALL, Inc., makes and sells small cargo trailers to individuals and small businesses. Since its opening in 1990, it has allocated indirect costs (IDC) to its three manufacturing plants based on direct materials cost per unit. Each plant builds different models and sizes. Because of advances in automation and materials, Judy, the CFO, plans to use build-time per unit as the new basis. Build-time is the average number of work-hours to complete a trailer. However, she initially wants to determine what the allocation would have been this year had the build-time basis been used prior to the incorporation of new technology and materials. The data shown below represents average costs and times. Use this data and the bases indicated to determine the allocation rates and IDC allocation of $1,000,000 for this year for the three bases.$

$$\begin{array}{lcccc} \text { Plant } & \text { New York } & \text { Virginia } & \text { Tennessee } & \text { Total } \\ \hline \text { Direct material cost, } & 20,000 & 12,700 & 18,600 & 51,300 \\ \text { \$ per unit } & & & & \\ \text { Previous build-time } & 400 & 415 & 580 & 1395 \\ \text { per unit, work-hours } & & & & \\ \text { New build-time per } & 425 & 355 & 480 & 1260\\ \text { unit, work-hours } & & & & \\ \hline \end{array}$$

$

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) The $^{210} \mathrm{Po}$ source used in a physics laboratory is labeled as having an activity of $1.0\ \mu \mathrm{Ci}$ on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the source was prepared 120 days before her lab. What fraction of the decays is she observing with her apparatus? (b) Identify some of the reasons that only a fraction of the $\alpha$ s emitted are observed by the detector.

Your small remodeling business has two work vehicles. One is a small passenger car used for job site visits and for other general business purposes. The other is a heavy truck used to haul equipment. The car gets 25 miles per gallon (mpg). The truck gets 10 mpg. You want to improve gas mileage to save money, and you have enough money to upgrade one vehicle. The upgrade cost will be the same for both vehicles. An upgraded car will get $40 \mathrm{mpg}$; an upgraded truck will get 12.5 mpg. The cost of gasoline is 2.65 per gallon. Assuming an upgrade is a good idea in the first place, which one should you upgrade to? Both vehicles are driven by 12,000 miles per year.

The simplest cost function is the linear cost function, $C(x)=m x+b,$ 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. How many bicycles could be manufactured for $3780?

A small business called The Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit, and sales soon sharply exceeded forecasts. The rush of orders created a huge backlog, so the company leased more space and expanded capacity; but it still could not keep up with demand. Equipment failed from overuse and quality suffered. Working capital was drained to expand production, and, at the same time, payments from customers were often delayed until the product was shipped. Unable to deliver on orders, the company became so strapped for cash that employee paychecks began to bounce. Finally, out of cash, the company ceased operations entirely 3 years later.

What are some of the actions that a small company like The Grandmother Calendar Company can take if it finds itself in a situation in which growth in sales outstrips production capacity and available financial resources? What other options (besides expansion of capacity) are available to a company when orders exceed capacity?

Hansus Enterprises is a start-up small business specializing in software systems for machine based high-school student tutoring in science and math. Sheryl Hansus, the owner, has spoken with lenders to obtain a loan of $50,000 now (year 0), and the same amount in years 3 and 6. Two different repayment schedules are available. They are: Schedule A: Pay a uniform amount of$19,500 in years 3 through 12. Schedule B: Pay a uniform amount of $20,000 in years 1 through 6, with “balloon” payments of an additional$20,000 in year 2 and a final amount of $40,000 in year 7. To assist in the decision of which schedule to select, determine the following: (a) Total amount repaid for each schedule. Which is smaller? (b) The equivalent annual worth of the loan amounts and of the repayments at i = 5% per year over a 12-year evaluation period. Which schedule has the smaller loss per year? Why is this the case?

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.

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.)

Complete the problem.

$$\begin{array}{|c| c c c c c c c |c|}\hline \small \textbf{Total} &\small \textbf{(Selling Price per Share} & \times & \small\textbf{Number of Shares} & - & \small\textbf{Commission)}& =& \small\textbf{Net Sale} &\small \textbf{Amount of}\\ \small\textbf{Paid} & & & & & & & &\small\textbf{Profit or Loss}\\ \hline \$5925 & (\small \$52 \frac{1}{4} & \times & 100) & - & \$59.60 &=& ? & ?\\ \hline \end{array}$$

Ortel Telecom sells telecommunication products and services to a variety of small businesses. Two of Ortel’s key clients are Square and Cloudburst, both fast-growing technology start-ups located in New York City. Ortel has compiled information regarding its transactions with Square and Cloudburst for 2017, as well as its expectations regarding their interactions over the next 3 years: Ortel’s transactions with Square and Cloudburst are in cash. Assume that they occur at year-end. Ortel is headquartered in the Cayman Islands and pays no income taxes. The owners of Ortel insist on a required rate of return of 12%. Required: 1. What is the expected net cash flow from Square and Cloudburst for the next 3 years? 2. Based on the net present value from cash flows over the next 3 years, is Cloudburst or Square a more valuable customer for Ortel? 3. Cloudburst threatens to switch to another supplier unless Ortel gives a 10% price reduction on all sales starting in 2018. Calculate the 3-year NPV of Cloudburst after incorporating the 10% discount. Should Ortel continue to transact with Cloudburst? What other factors should it consider before making its final decision?

$$\begin{matrix} \text{ } & \text{Expected Annual Percentage Increase} & \text{2017}\\ \text{ } & \text{Square } & \text{Cloudburst} & \text{Square} & \text{Cloudburst}\\ \text{Sales Revenues} & \text{6 \\\%} & \text{5.5 \\\%} & \text{\$ 567.000} & \text{\$ 3.510.000}\\ \text{Cost of Sales} & \text{5 \\\%} & \text{4.5 \\\%} & \text{\$ 364.800} & \text{\$ 3.060.000}\\ \text{Net cash flow} & \text{ } & \text{ } & \text{\$ 202.200} & \text{\$ 450.000}\\ \end{matrix}$$

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.