Ragan, Inc., was formed nine years ago by brother and sister Carrington and Genevieve Ragan. The company manufactures and installs commercial heating, ventilation, and cooling (HVAC) units. Ragan, Inc., has experienced rapid growth because of a proprietary technology that increases the energy efficiency of its units. The company is equally owned by Carrington and Genevieve. The original partnership agreement between the siblings gave each 50,000 shares of stock. In the event either wished to sell stock, the shares first had to be offered to the other at a discounted price.

 Although neither sibling wants to sell, they have decided they should value their holdings in the company. To get started, they have combined the information about their main competitors in the table below.

 Expert HVAC Corporation’s negative earnings per share were the result of an accounting write-off last year. Without the write-off, earnings per share for the company would have been $1.10. The ROE for Expert HVAC is based on net income excluding the writeoff.

 In the previous year, Ragan, Inc., had an EPS of$3.15 and paid a dividend to Carrington and Genevieve of $45,000 each. The company also had a return on equity of 17%. The siblings believe that 14% is an appropriate required return for the company.

Ragan, Inc., Competitors
	EPS	DPS	Stock Price	ROE	R
Arctic Cooling, Inc.	$1.30	$.16	$25.34	8.50%	10.00%
National Heating & Cooling	1.95	.23	29.85	10.50	13.00
Expert HVAC Corp.	-.37	.14	22.13	9.78	12.00
Industry Average	$.96	$.18	$25.77	9.59%	11.67%

QUESTION

After discussing the stock value with Josh, Carrington and Genevieve agree that they would like to increase the value of the company stock. Similar to many small business owners, they want to retain control of the company, so they do not want to sell stock to outside investors. They also feel that the company’s debt is at a manageable level and do not want to borrow more money. How can they increase the price of the stock? Are there any conditions under which this strategy would not increase the stock price?

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

$$\begin{array}{|c c c c c c c c c c c|} \hline \small\textbf{(Total Daily Cost}& + & \small\textbf{Total Mileage Cost} & +& \small\textbf{Gasoline Cost} & = & \small\textbf{Total Cost)} & \div & \small\textbf{Miles} & = & \small\textbf{Cost per}\\ & & & & & & & &\small\textbf{Driven} & & \small\textbf{Mile}\\ \hline (\$160.00 & + & \$94.00 & + & \$23.89 & = & ?) & \div & 500 & = & ? \\ \hline \end{array}$$

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.

The Grandmother Calendar Company clearly had a cash flow problem. In the context of the cash flow analysis we developed in Chapter 2, what was the impact of customers not paying until orders were shipped?

The change in the size of businesses in a certain Canadian city from one year to the next can be described by a Markov chain. The businesses are classified into three categories based on size: small (2-10 employees), medium (11-43 employees), and large (44 or more employees). The transition matrix for a 1-year period is given below.

$$\begin{array}{l} \\ Small \\ Medium \\ Large \end{array} \left[\begin{array}{ccc} \text { Small } & \text { Medium } & \text { Large } \\ 0.9216 & 0.0780 & 0.0004 \\ 0.0460 & 0.8959 & 0.0581 \\ 0.0003 & 0.0301 & 0.9696 \end{array}\right]$$

Suppose that in 2015, there were 2094 small, 2363 medium, and 2378 large businesses. Based on this model, find the number of businesses of each type that would be expected in each of the following years. (a) 2016 (b) 2017 (c) Write the transition matrix for a 2-year period. Based on your answer to part (c), what percent of medium businesses are in each of the following categories after 2 years? (d) Small businesses (e) Large businesses.

Mark Denton cosigned a $101,250 loan issued by the First Interstate Bank (FIB) in Missoula, Montana, to Denton’s friend Eric Anderson. Denton’s business assets—a mini-warehouse operation—secured the loan. On his own, Anderson obtained a$260,000 U.S. Small Business Administration (SBA) loan from FIB at the same time. The purpose of both loans was to buy logging equipment so that Anderson could start a business. Two years after the loan was made, the business failed. As a consequence, FIB repossessed and sold the equipment and applied the proceeds to the SBA loan. FIB then asked Denton to pay the other loan’s outstanding balance ($98,460), plus interest. When Denton refused, FIB initiated proceedings to obtain his business assets. Denton filed a suit in a Montana state court against FIB. He claimed, in part, that Anderson’s equipment was the collateral for the loan that FIB was attempting to collect from Denton.

(a) Denton’s assets served as the security for Anderson’s loan because Anderson had nothing to offer. When the loan was obtained, Dean Gillmore, FIB’s loan officer, explained to them that if Anderson defaulted, the proceeds from the sale of the logging equipment would be applied to the SBA loan first. Under these circumstances, is it fair to hold Denton liable for the unpaid balance of Anderson’s loan? Why or why not?

A physics instructor wants to produce a double-slit interference pattern large enough for her class to see. For the size of the room, she decides that the distance between successive bright fringes on the screen should be at least $2.50 \mathrm{~cm}$. If the slits have a separation $d=0.0220 \mathrm{~mm}$, what is the minimum distance from the slits to the screen when $632.8 \mathrm{~nm}$ light from a $\mathrm{He}-\mathrm{Ne}$ laser is used?

In a small printing business, $P=2 N^{0.6} V^{0.4}$, where $N$ is the number of workers, $V$ is the value of the equipment, and $P$ is production, in thousands of pages per day. This company has a labor force of $300$ workers and $200$ units worth of equipment. If the labor force is doubled (to $600$ workers), how does production change?

Complete the problem.

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

How does Einstein's explanation account for each of these characteristics of the photoelectric effect? a. The photoelectric current is zero for frequencies below some threshold. b. The photoelectric current increases with increasing light intensity. c. The photoelectric current is independent of $\Delta V$ for $\Delta V \geq 1 \mathrm{V}$. d. The photoelectric current decreases slowly as $\Delta V$ becomes more negative. e. The stopping potential is independent of the light intensity. Which of these cannot be explained by classical physics? Explain.

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 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 three years later.

Product Pricing The firm actually priced its product to be about $20$ percent less than that of competitors, even though the Grandmother calendar was more detailed. In retrospect, was this a wise choice?

After a great deal of experimentation, two Atlantic Institute of Technology senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked, its cork travels according to

$$s(t)=-16 t^2+40 t+3,$$

where s is its height (in feet) above the ground t seconds after being released. (a) How high will it go? (b) How long is it in the air?

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?

Presented below are five independent situations.

(e) Jack Yaeger has developed a low-cost GPS device that can be implanted into pets so that they can be easily located when lost. He would like to build a small manufacturing facility to make the devices and then sell them to veterinarians across the country. Jack has no savings or personal assets. He wants to maintain control over the business.

Instructions

In each case, explain what form of organization the business is likely to take—sole proprietorship, partnership, or corporation. Give reasons for your choice.