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.

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$$ Although neither sibling wants to sell, they have decided they should value their holdings in the company.$$ To get started, they have gathered the following information about their main competitors:

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Ragan, Inc. $$ Competitors

$$ EPS $$ Dividend $$ Stock Price $$ ROE $$ R

Arctic Cooling, Inc.

$$0\mathrm{.}84$

$$0\mathrm{.}39$

$$17\mathrm{.}83$

$16\mathrm{.}00\%$

$10\mathrm{.}00\%$

National Heating & Cooling

$$1\mathrm{.}34$

$$0\mathrm{.}65$

$$19\mathrm{.}23$

$14\mathrm{.}00\%$

$13\mathrm{.}00\%$

Expert HVAC Corp.

$$$$0\mathrm{.}55$

$$0\mathrm{.}43$

$$18\mathrm{.}14$

$15\mathrm{.}00\%$

$12\mathrm{.}00\%$

Industry Average

$$0\mathrm{.}54$

$$0\mathrm{.}49$

$$18\mathrm{.}40$

$15\mathrm{.}00\%$

$11\mathrm{.}67\%$

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$$ Expert HVAC Corporation$$s negative earnings per share $($EPS$)$ were the result of an accounting write$-$off last year.$$ Without the write$-$off, EPS for the company would have been $$0\mathrm{.}54.$

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$$ Last year, Ragan, Inc., had an EPS of $$4\mathrm{.}85$ and paid a dividend to Carrington and Genevieve of $$75,000$ each.$$ The company also had a return on equity $($ROE$)$ of $17\%.$ The siblings believe that $14\%$ is an appropriate required return $($R$)$ for the company.$$

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Questions:

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$1.$ Assuming the company continues its current growth rate, what is the value per share of the company$$s stock?$($Hint: growth rate $($g$)=$ retention ratio $$ ROE;

$1$

retention ratio was discussed in Chapter $3$ of textbook.$$ Use $4$ decimals when calculating the growth rate $($g$).)$

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$2.$ 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$$s financial statements, as well as those of its competitors.$$ 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?

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$($Use $4$ decimals when calculating the industry growth average and the industry average required return.$)$