Stock Valuation at Ragan, Inc.

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 $16$ percent. The siblings believe that $14$ percent is an appropriate required

return for the company.

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?