Larissa has been talking with the company's directors about the future of East Coast Yachts. To this point, the company has used outside suppliers for various key components of the company's yachts, including engines. Larissa has decided that East Coast Yachts should consider the purchase of an engine manufacturer to allow East Coast Yachts to better integrate its supply chain and get more control over engine features. After investigating several possible companies, Larissa feels that the purchase of Ragan Engines, Inc., is a possibility. She has asked Dan Ervin to analyze Ragan's value.

Ragan Engines, Inc., was founded nine years ago by a brother and sister$$Carrington and Genevieve Ragan$$and has remained a privately owned company. The company manufactures marine engines for a variety of applications. Ragan has experienced rapid growth because of a proprietary technology that increases the fuel efficiency of its engines with very little sacrifice in performance. The company is equally owned by Carrington and Genevieve. The original agreement between the siblings gave each $125,000$ shares of stock.

Larissa has asked Dan to determine a value per share of Ragan stock. To accomplish this, Dan has gathered the following information about some of Ragan's competitors that are publicly traded:

Blue Ribbon Motors Corp :

EPS: $$1\mathrm{.}13$

DPS: $$\mathrm{.}35$

Stock Price: $$18\mathrm{.}25$

ROE: $11\mathrm{.}00\%$

R: $14\mathrm{.}00\%$

Bon Voyage Marine Inc. :

EPS: $$1\mathrm{.}41$

DPS: $$\mathrm{.}43$

Stock Price: $$15\mathrm{.}31$

ROE: $14\mathrm{.}00\%$

R: $17\mathrm{.}00\%$

Nautilus Marine Engines:

EPS: $$-\mathrm{.}23$

DPS: $$\mathrm{.}61$

Stock Price: $$28\mathrm{.}72$

ROE: N$/$A

R: $13\mathrm{.}00\%$

Industry Average:

EPS: $$\mathrm{.}77$

DPS: $$\mathrm{.}46$

Stock Price: $$20\mathrm{.}76$

ROE: $12\mathrm{.}59\%$

R: $14\mathrm{.}67\%$

Nautilus Marine Engines' negative earnings per share $($EPS$)$ was the result of an accounting write$-$off last year. Without the write$-$off, EPS for the company would have been $$1\mathrm{.}75.$ Last year, Ragan had an EPS of $$4\mathrm{.}10$ and paid a dividend to Carrington and Genevieve of $$215,000$ each. The company also had a return on equity of $18$ percent. Larissa tells Dan that a required return for Ragan of $13$ percent is appropriate.

$1.$ What is the industry average price$-$earnings ratio? What is Ragan's price$-$earnings ratio? Compare your estimates of the industry average PE ratio to Ragan$$s PE ratio estimates, calculated from information you used in Q$1($original assumption$),$ and Q$2($revised assumption$),$ respectively. Comment on any differences and explain why they may exist.