Ragan, Inc., was founded 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 gathered 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\mathrm{.}06.$ The ROE for Expert HVAC is based on net

income excluding the write$-$off.

Last year, Ragan, Inc., had an EPS of $$4\mathrm{.}54$ and paid a dividend to Carrington and

Genevieve of $$60,000$ each. The company also had a return on equity of $18$

percent. The siblings believe that $15$ percent is an appropriate required return for

the company.

QUESTIONS

Assuming the company continues its current growth rate, what is the value per

share of the company's stock?

To verify their calculations, Carrington and Genevieve have hired Josh

Schlessman as a consultant. Josh was previously an equity analyst and covered

the HVAC industry. Josh has examined the company's financial statements, as

well as its competitors' financials. Although Ragan, Inc., currently has a

technological advantage, his research indicates that other companies are

investigating methods to improve efficiency. Given this, Josh believes that the

company's technological advantage will last only for the next five years. After

that period, the company's growth will likely slow to the industry growth

average. Additionally, Josh believes that the required return used by the company

is too high. He believes the industry average required return is more appropriate.

Under this growth rate assumption, what is your estimate of the stock price?

What is the industry average price$-$earnings ratio? What is the price$-$earnings

ratio for Ragan, Inc.? Is this the relationship you would expect between the two

ratios? Why?

Carrington and Genevieve are unsure how to interpret the price$-$earnings ratio.

After some head scratching, they've come up with the following expression for

the price$-$earnings ratio:

$\frac{P_0}{E_1}=\frac{1-b}{R-(ROEb)}$

Beginning with the constant dividend growth model, verify this result. What

does this expression imply about the relationship between the dividend payout

ratio, the required return on the stock, and the company's ROE?

Assume the company's growth rate slows to the industry average in five years.

What future return on equity does this imply, assuming a constant payout ratio?

After discussing the stock value with Josh, Carrington and Genevieve agree that

they would like to increase the value of the company stock. Like 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?Expert solved pleased and all six parts