Professors note: Ragan Inc. minicase $($pp$.276-77$ of the text$)$ is this week$$s assignment. Note that g $($the constant growth rate of the dividends$)$ could be calculated using the following formula: g$=$ ROE $(1-$payout Ratio$)=$ ROE x b $($retention Ratio$).$ Secondly, since industry$$s average EPS was calculated ignoring the write off by Expert HVAC, you need to recalculate the industry$$s average EPS by substituting $1\mathrm{.}06$ as Expert HVAC$$s EPS. $[$note also that R in the book stands for required return by equity holders, k$.]$

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$-$ff$,$

earnings per share for the company would have been $$1\mathrm{.}06.$ The ROE for Expert HVAC is based on net income excluding the writeoff.

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 io

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 pricecarnings ratio? What is the price$-$carnings 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$-$carnings ratio:

$\frac{P_0}{E_1}=\frac{1-b}{R-(\text{R}\text{O}\text{E}b)}$

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 cquity does this imply, assuming a

What is the industry aRagan, 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 of them $50,000$ 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 that they should value their holdings in the company. To get started, they have gathered the following information about their main competitors:

Expert HVAC Corporation$$s negative earnings per share were the result of an accounting write$-$off last year. Without the write$-$off, earnings per share $($EPS$)$ for the company would have been $$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.

assuming

Questions $1-6$ are on the pitcutre attached